VESTA: a Three-Dimensional Visualization System
for Electronic and Structural Analysis
Koichi MOMMA1
National Museum of Nature and Science,
4-1-1 Amakubo, Tsukuba, Ibaraki 305-0005, Japan
Fujio IZUMI2
Graduate School of Engineering, Kyoto University
January 27, 20191
2

E-mail: vesta.dev@gmail.com
E-mail: fizumi3776@gmail.com

Contents
LICENSE AGREEMENT

xi

1 INTRODUCTION AND BACKGROUND
1.1 Understanding Crystal and Electronic Structures in Three Dimensions . . . . . .
1.2 Circumstances behind the Development of VESTA . . . . . . . . . . . . . . . . .
1.3 What’s New in VESTA 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.4 Notes on this Manual . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1
1
1
2
3

2 OVERVIEW OF THE PROGRAM
2.1 General Features . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2 Visualization of Structural Models . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.1 A variety of structural information derived on selection of objects . . . . .
2.3 Visualization of Volumetric Data . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.4 Visualization of Crystal Morphologies . . . . . . . . . . . . . . . . . . . . . . . .
2.5 Cooperation with External Programs . . . . . . . . . . . . . . . . . . . . . . . . .
2.6 Input and Output Files . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.7 Programming Concept . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.7.1 Graphical user interface . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.7.2 Core libraries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4
4
4
9
9
11
13
13
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14
14

3 GETTING STARTED
15
3.1 Minimum requirements of hardware . . . . . . . . . . . . . . . . . . . . . . . . . 15
3.2 Windows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
3.3 macOS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
3.4 Linux . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
3.4.1 32-bit version . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
3.4.2 64-bit version . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
3.5 Trouble Shooting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
3.6 Loading Files . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
4 MAIN WINDOW
19
4.1 Components of the Main Window . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
4.2 Menus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
4.2.1 File menu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
4.2.2 Edit menu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
4.2.3 View menu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
4.2.4 Objects menu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
4.2.5 Utilities menu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
ii

4.3

4.4
4.5

4.2.6 Help menu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Tools in the Horizontal Toolbar . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3.1 Alignment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3.2 Rotation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3.3 Translation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3.4 Scaling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Tools in the Vertical Toolbar . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Text Area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.5.1 Output tab . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.5.2 Summary tab . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.5.3 Comment tab . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

23
23
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24
24
24
25
25
25
26
26

5 DISPLAY STYLES
27
5.1 Structural Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
5.1.1 Objects to be displayed . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
5.1.2 Styles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
5.2 Volumetric Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
5.3 Crystal Shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
5.3.1 Styles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
6 GIVING PHASE DATA
32
6.1 Defining Phases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
6.2 Symmetry and Unit Cell . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
6.2.1 Crystal systems and space groups . . . . . . . . . . . . . . . . . . . . . . . 33
6.2.2 Behavior when changing a space-group setting . . . . . . . . . . . . . . . 36
6.2.3 Lattice parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
6.2.4 Customization of symmetry operations . . . . . . . . . . . . . . . . . . . . 36
6.2.5 Reducing symmetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
6.2.6 Transformation of the unit cell . . . . . . . . . . . . . . . . . . . . . . . . 37
6.2.7 Magnetic Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
6.3 Structure Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
6.3.1 Symbols and Labels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
6.3.2 Formal charge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
6.3.3 Fractional coordinates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
6.3.4 Occupancy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
6.3.5 Atomic displacement parameters . . . . . . . . . . . . . . . . . . . . . . . 46
6.3.6 Importing structure parameters . . . . . . . . . . . . . . . . . . . . . . . . 47
6.3.7 Removing duplicate atoms . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
6.4 Volumetric Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
6.4.1 Volumetric data to draw isosurfaces . . . . . . . . . . . . . . . . . . . . . 49
6.4.2 Volumetric data for surface coloring . . . . . . . . . . . . . . . . . . . . . 49
6.5 Crystal Shape . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
6.5.1 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
7 OVERLAYING MULTIPLE DATA
54
7.1 Positioning of Phases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
7.2 Relative Orientation of Phases . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
7.3 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
iii

8 CREATING BONDS AND POLYHEDRA
57
8.1 Specifications of Searching for Bonds . . . . . . . . . . . . . . . . . . . . . . . . . 58
8.1.1 Search mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
8.1.2 Boundary mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
8.1.3 Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
8.1.4 A pair of atoms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
8.2 Operating Instructions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
8.2.1 Creating coordination polyhedra . . . . . . . . . . . . . . . . . . . . . . . 59
8.2.2 Searching for molecules and clusters . . . . . . . . . . . . . . . . . . . . . 60
8.2.3 Applications of the “Search molecules” mode to inorganic crystals . . . . . 60
8.2.4 Searching for hydrogen bonds . . . . . . . . . . . . . . . . . . . . . . . . . 61
8.2.5 Visualizing cage-like structures . . . . . . . . . . . . . . . . . . . . . . . . 61
9 ADDITIONAL OBJECTS
63
9.1 Vectors on Atoms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
9.1.1 Creation and editing of a vector . . . . . . . . . . . . . . . . . . . . . . . 64
9.1.2 Attachment of vectors to crystallographic sites . . . . . . . . . . . . . . . 66
9.1.3 Attachment of vectors to individual atoms . . . . . . . . . . . . . . . . . . 66
9.2 Lattice Planes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
9.2.1 Appearance of lattice planes . . . . . . . . . . . . . . . . . . . . . . . . . . 67
9.2.2 Calculate the best plane for selected atoms . . . . . . . . . . . . . . . . . 68
10 DEFINING DRAWING BOUNDARIES AND VIEW DIRECTIONS
69
10.1 Drawing Boundaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
10.1.1 Ranges of fractional coordinates . . . . . . . . . . . . . . . . . . . . . . . 70
10.1.2 Cutoff planes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
10.2 View Direction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
10.2.1 Manner of specifying directions . . . . . . . . . . . . . . . . . . . . . . . . 71
10.2.2 Orientation matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
10.2.3 View direction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
10.2.4 Viewing along crystallographic axes . . . . . . . . . . . . . . . . . . . . . 72
11 INTERACTIVE MANIPULATIONS
73
11.1 Rotate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
11.1.1 Drag mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
11.1.2 Animation mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
11.2 Magnify . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
11.3 Translate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
11.4 Select . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
11.4.1 Atom . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
11.4.2 Bond . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
11.4.3 Coordination polyhedron . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
11.5 Distance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
11.6 Bond angle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
11.7 Dihedral angle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
11.8 Interfacial angle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
iv

12 PROPERTIES OF OBJECTS
82
12.1 Properties Dialog Box . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
12.1.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
12.1.2 Atoms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
12.1.3 Bonds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
12.1.4 Polyhedra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
12.1.5 Isosurfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
12.1.6 Sections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
12.2 Objects Tab in the Side Panel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
12.2.1 List of phases and objects . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
12.2.2 Atoms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
12.2.3 Bonds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
12.2.4 Polyhedra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
12.2.5 Slices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
12.2.6 Shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
13 OVERALL APPEARANCE
97
13.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
13.2 Lighting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
13.3 Projection Mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
13.4 Depth-Cueing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
14 UTILITIES
101
14.1 Equivalent Positions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
14.2 Geometrical Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
14.3 Standardization of Crystal Data . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
14.4 Niggli-Reduced Cell . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
14.5 Site Potentials and Madelung Energy . . . . . . . . . . . . . . . . . . . . . . . . . 106
14.6 Powder Diffraction Pattern . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
14.7 Structure Factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
14.8 Fourier Synthesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
14.9 Model Electron Densities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
14.10Model Nuclear Densities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
14.11Patterson Densities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
14.122D Data Display . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
14.13Line Profile . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
14.14Peak Search . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
14.15Conversion of Electron Densities . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
15 TWO-DIMENSIONAL DATA DISPLAY
117
15.1 Components of the 2D Data Display Window . . . . . . . . . . . . . . . . . . . . 117
15.2 Menus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
15.3 Tools in the Toolbar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
15.3.1 Rotation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
15.3.2 Translation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
15.3.3 Scaling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
15.4 Tools in the Vertical Toolbar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
15.5 Create and Edit a 2D Image . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119v

15.5.1 (hkl) plane in the bounding box . . . . . . . . . . . . . . . . . . . . . . . 120
15.5.2 (hkl) plane defined by two vectors . . . . . . . . . . . . . . . . . . . . . . 120
15.5.3 Project along [hkl] axis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
15.6 Controlling Properties of a 2D Image . . . . . . . . . . . . . . . . . . . . . . . . . 122
15.7 Exporting 2D data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
16 PREFERENCES
125
16.1 Settings for RIETAN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
16.2 Font for Text Area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
16.3 Open a New File in . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
16.4 Animation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
16.5 Start-up Search for Bonds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
16.6 A Setting for Raster Image Export . . . . . . . . . . . . . . . . . . . . . . . . . . 126
16.7 Default isosurface level . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
16.8 History level . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
17 INPUT AND OUTPUT FILES
128
17.1 File Formats of Volumetric Data . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
17.2 Directories for User Settings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
17.2.1 Windows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
17.2.2 macOS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
17.2.3 Linux . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
17.3 Files Used by VESTA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
17.4 Input Files . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
17.4.1 Structural data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
17.4.2 Volumetric data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
17.4.3 Structural and volumetric data . . . . . . . . . . . . . . . . . . . . . . . . 137
17.5 Output Files . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
17.5.1 Data files . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
17.5.2 Raster images . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142
17.5.3 Vector images . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
17.5.4 Output text . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
APPENDIX

145

A Keyboard Shortcuts

145

vi

List of Figures
2.1
2.2
2.3

Screenshots of VESTA running on three kinds of operating systems . . . . . . . .
Crystal structure of masutomilite represented as the ball-and-stick model . . . .
Crystal structure of a polymorph of vitamin B1 represented as the space-fillingmodel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.4 Crystal structure of beryl . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.5 Crystal structure of sodalite . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.6 Crystal structure of the tetragonal form of melanophlogite . . . . . . . . . . . . .
2.7 A displacement ellipsoid model of 17-(2H -indazol-2-yl)androsta-5,16-dien-3β-ol
having an indazole substituent at the C17 position . . . . . . . . . . . . . . . . .
2.8 Electron-density distribution in MgB2 . . . . . . . . . . . . . . . . . . . . . . . .
2.9 A (001) slice illustrating electron-density distribution in MgB2 . . . . . . . . . .
2.10 Nuclear-density distribution in the paraelectric phase of KH2 PO4 . . . . . . . . .
2.11 An external morphology of an Al2 O3 crystal composed of {001}, {110}, and {113}faces. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.12 A crystal morphology of anatase-type TiO2 superimposed on its structural model,
where blue and red balls represent Ti and O atoms, respectively. . . . . . . . . .
2.13 Crystal morphologies of adularia . . . . . . . . . . . . . . . . . . . . . . . . . . .

5
6
6
7
7
8
8
10
10
11
12
12
13

4.1

Main window of VESTA running on Windows 10 . . . . . . . . . . . . . . . . . .

19

5.1
5.2
5.3
5.4

The Structural model frame box in the Style tab of the Side Panel . . . . . . . . .
Crystal structure of quartz represented as stick model with dot surfaces . . . . .
The Volumetric data frame box in the Style tab of the Side Panel . . . . . . . . . .
The Crystal shapes frame box in the Style tab of the Side Panel . . . . . . . . . .

27
27
29
30

New Data dialog box . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Unit cell page in the Edit Data dialog box . . . . . . . . . . . . . . . . . . . . . .
Equivalent Positions dialog box with editing mode . . . . . . . . . . . . . . . . . .
Unit Cell Transformation dialog box. . . . . . . . . . . . . . . . . . . . . . . . . . .
A warning dialog box for conversion of structure handedness . . . . . . . . . . . .
An example of lattice transformation between primitive and face-centered-cubic
lattices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.7 A dialog box for confirmation of unit cell transformation . . . . . . . . . . . . . .
6.8 A dialog box showing options for how to create a larger unit cell . . . . . . . . .
6.9 The Unit cell page in the Edit Data dialog box, with the “Magnetic structure”
option checked. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.10 Structure parameter page in the Edit Data dialog box . . . . . . . . . . . . . . . .
6.11 Periodic Table dialog box . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.12 Crystal structure of Cs6 C60 , with C60 represented by translucent polyhedra . . .

32
33
37
37
38

6.1
6.2
6.3
6.4
6.5
6.6

vii

41
42
42
43
44
45
46

6.13 Volumetric data page in the Edit Data dialog box . . . . . . . . . . . . . . . . . . 48
6.14 A dialog box to choose operations for volumetric data . . . . . . . . . . . . . . . 49
6.15 Distributions of electron densities and effective spin densities in an O2 molecule . 50
6.16 Crystal shape page in the Edit Data dialog box . . . . . . . . . . . . . . . . . . . . 51
6.17 Crystal morphologies of anatase-type TiO2 crystals . . . . . . . . . . . . . . . . . 51
6.18 The Objects tab of the Side Panel showing a list of crystallographic faces . . . . . 52
6.19 Crystal morphologies of anatase having faces that do not follow symmetry operations 53
7.1
7.2
7.3
7.4

Phase page in the Edit Data dialog box . . . . . . . . . . . . . . . . . . . . . . . . 54
Molecules of L-aspartic acid and 2,4,6-trichlorobenzoic acid on the (101̄4) surfaceof calcite . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
A moire pattern of graphene on the (111) surface of Ir . . . . . . . . . . . . . . . 56
Crystal structures of Ca-olivine (Ca2 SiO4 ) and isostrucural monticellite (CaMgSiO4 )overlapped with each other. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

8.1
8.2
8.3
8.4
8.5

Bonds dialog . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
Crystal structure of δ-AlOOH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
“Search molecules” mode with and without “Beyond the boundary” option enabled 60
Crystal structure of tetrakis(di-4-pyridylsulfane)dinitratocopper(II) . . . . . . . . 61
Crystal structure of the tetragonal variant of chibaite . . . . . . . . . . . . . . . . 62

9.1
9.2
9.3

Vectors dialog box displaying a list of atoms in SrFeO2 . . . . . . . . . . . . . . . 63
A dialog box to create or edit a vector . . . . . . . . . . . . . . . . . . . . . . . . 64
Results of applying a mirror operation to magnetic moments µ and polarization
vectors p . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
Effects of two options for vector styles . . . . . . . . . . . . . . . . . . . . . . . . 66
Lattice Plane dialog box . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
A section of a difference Fourier map inserted in a ball-and-stick model of δ−AlOOH 67
The best plane calculated for an aromatic ring in anthraquinone . . . . . . . . . 68

9.4
9.5
9.6
9.7

10.1 Boundary dialog . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
10.2 Electron density distribution in D-sorbitol . . . . . . . . . . . . . . . . . . . . . .
10.3 Crystal structure of diamond drawn in ranges from (−8, −8, −8) to (8, 8, 8) withand without a cutoff plane 111 . . . . . . . . . . . . . . . . . . . . . . . . . . . .
10.4 Orientation dialog box . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

69
70

11.1 The Tools tab of the Side Panel . . . . . . . . . . . . . . . . . . . . . . . . . . . .
11.2 Calculation of a dihedral angle for four carbon atoms in an aromatic ring in
3-[4-(dimethylamino)phenyl]-1-(2-hydroxyphenyl)-prop-2-en-1-one . . . . . . . . .
11.3 Calculation of an interfacial angle between (100) and (511) faces in quartz. . . .

73

12.1 General page in the Properties dialog box . . . . . . . . . . . . . . . . . . . . . .
12.2 Atoms page in the Properties dialog box . . . . . . . . . . . . . . . . . . . . . . .
12.3 Displacement ellipsoids of an atom (A) with principal ellipses and (B) without
them . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
12.4 A displacement ellipsoid model of a structure with some atoms having negative
mean square displacements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
12.5 General-position diagrams of space group F d3̄m with (A) light disabled and (B)light enabled . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

83
84

viii

71
72

80
81

85
85
86

12.6 Bonds page in the Properties dialog . . . . . . . . . . . . . . . . . . . . . . . . . 87
12.7 Polyhedra page in the Properties dialog . . . . . . . . . . . . . . . . . . . . . . . 88
12.8 Isosurfaces page in the Properties dialog box . . . . . . . . . . . . . . . . . . . . . 89
12.9 Comparison between the two modes of rendering isosurfaces . . . . . . . . . . . . 90
12.10The 64a1g orbital for the {Cd(S4 Mo3 (Hnta)3 )2 }4− ion with a ball-and-stick model 91
12.11Composite images of isosurfaces and a ball-and-stick model for albatrossene . . . 91
12.12Relations between orientation of isosurface and the two parameters for opacity
setting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
12.13Sections page in the Properties dialog box . . . . . . . . . . . . . . . . . . . . . . 93
12.14Distribution of nuclear densities obtained for KOD at 580 K by MEM from singlecrystal neutron diffraction data . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
12.15Relations among saturation levels, data values, and colors of sections . . . . . . . 94
12.16The Objects tab of the Side Panel . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
12.17A list of bond specifications in the Objects tab of the Side Panel . . . . . . . . . . 95
12.18A list of polyhedra in the Objects tab of the Side Panel . . . . . . . . . . . . . . . 95
12.19A list of slices in the Objects tab of the Side Panel . . . . . . . . . . . . . . . . . . 96
12.20A list of forms and faces of crystal morphologies in the Objects tab of the Side Panel 96
13.1 Overall Appearance dialog box . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
13.2 Crystal structure of milarite drawn with light effects (A) enabled and (B) disableddialog box . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
13.3 Crystal structure of post-perovskite, MgSiO3 , rendered by parallel and perspective projections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
13.4 Crystal structure of mordenite rendered with and without depth-cueing . . . . . 100
14.1 Equivalent Positions dialog box . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
14.2 The Equivalent Positions dialog box showing magnetic data . . . . . . . . . . . . . 102
14.3 Geometrical Parameters dialog box . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
14.4 Simulation of an X-ray powder diffraction pattern of YBa2 Cu4 O8 . . . . . . . . . 109
14.5 Structure Factors dialog box . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
14.6 Fourier Synthesis dialog box . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
15.1 2D Data Display window . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
15.2 A dialog box for three different modes to draw a 2D image . . . . . . . . . . . . . 120
15.3 Three modes of creating a 2D image . . . . . . . . . . . . . . . . . . . . . . . . . 121
15.4 Schematic image of the relation between the center of the projection and thecenter of the slice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
15.5 Bird’s eye view of a (001) slice of rutile-type TiO2 . . . . . . . . . . . . . . . . . 123
15.6 Electron-density distribution on the (001) plane in rutile-type TiO2 with andwithout grid edges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
15.7 Contours page in the Side Panel . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
16.1 Preferences dialog box . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
17.1 Two types of the grids for volumetric data . . . . . . . . . . . . . . . . . . . . . . 128

ix

List of Tables
6.1
6.2
6.3

Non-standard settings in two triclinic space groups . . . . . . . . . . . . . . . . .
Setting numbers of monoclinic space groups . . . . . . . . . . . . . . . . . . . . .
Axis choices in the orthorhombic space groups . . . . . . . . . . . . . . . . . . . .

35
35
35

14.1 Units of converted volumetric data . . . . . . . . . . . . . . . . . . . . . . . . . . 116
17.1 Files used by VESTA. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130

A.1 Keyboard shortcuts. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145

x

LICENSE AGREEMENTVESTA LICENSE
Version 3
Copyright © 2006–2019, Koichi Momma and Fujio Izumi
VESTA is currently copyrighted with its source code not open to the public; we wish tocontrol the development and future of VESTA by ourselves. This software is distributed freeof charge for academic, scientific, educational, and non-commercial users. Users belonging tocommercial enterprises may also use this software at no cost until a license for business users isestablished.
Permission to use this software is hereby granted under the following conditions:
1. Drawings produced by VESTA may be used in any publications (original and review
articles) provided that its use is explicitly acknowledged. A suitable reference for VESTA
is:
K. Momma and F. Izumi, “VESTA 3 for three-dimensional visualization of crystal, volumetric and morphology data,” J. Appl. Crystallogr., 44, 1272–1276 (2011).
2. You should not redistribute any copy of the distributed files including MADEL and
STRUCTURE TIDY unless you have a written permission from us.
Part of these terms may be changed without any prior announcement. This software isprovided “as is” without any expressed or implied warranty.

xiChapter 1

INTRODUCTION ANDBACKGROUND
1.1

Understanding Crystal and Electronic Structures in Three
Dimensions

Progress in modern structure-refinement techniques of the maximum-entropy method (MEM)[1, 2, 3, 4] and MEM-based pattern fitting (MPF) [5, 6, 7, 8, 9], has made it easier and more
popular to determine three-dimensional (3D) distribution of electron densities from X-ray diffraction data and densities of coherent-scattering lengths (nuclear densities) [10], bc , from neutron
diffraction data. On the other hand, rapid developments of computer hardware and software
have accelerated and facilitated electronic-structure calculations affording physical quantities
including electron densities, wave functions, and electrostatic potentials.
Such technological advances in recent years bring demands for integrated 3D visualization
systems to deal with both structural models and volumetric data such as electron and nuclear
densities. The crystal structures and spatial distribution of various physical quantities obtained
experimentally and by computer simulations should be understood three-dimensionally. Despite
the availability of many structure-drawing programs, cross-platform free software capable ofvisualizing both crystal and electronic structures in three dimensions is very few; if any, they
are not very suitable for displaying those of inorganic and metallic compounds.
To improve such a situation, we have developed a new integrated system VESTA (Visualization
for Electronic and STructural Analysis) for 3D visualization of crystal structures and volumetricdata on personal computers.

1.2

Circumstances behind the Development of VESTAVESTA [11, 12, 13, 14] is a successor to two visualization programs, VICS and VEND, in the
VENUS (Visualiza-tion of Electron/NUclear and Structures) software package1 [15, 16], which
was developed by Dilanian, Izumi, and Kawamura with help from Ohki and Momma during
2001–2006. VENUS comprises the following six programs:
1. VICS (VIsualization of Crystal Structures) for displaying and manipulating crystal structures [15, 16],
2. VEND (Visualization of Electron/Nuclear Densities) for displaying and manipulating
volumetric data [15, 16],1

http://fujioizumi.verse.jp/visualization/VENUS.html

1

3. PRIMA (PRactice Iterative MEM Analyses) for MEM analysis from X-ray and neutron
diffraction data [5],4. Dysnomia [7, 8, 9] which is a successor to PRIMA,
5. ALBA (After Le Bail Analysis) for the maximum-entropy Patterson method [17],6. Alchemy: A file converter to make it possible to analyze observed structure factors andtheir estimated standard uncertainty, which result from Rietveld analysis using GSAS [18]and FullProf [19], by MEM with Dysnomia [7, 8, 9].
VICS and VEND are programs for 3D visualization of crystal and electronic structures,
respectively. They were written in the ANSI C language with the full use of the OpenGL2
technology. The graphical user interfaces (GUIs) of VICS and VEND were constructed by using
GLUT and GLUI libraries.
VICS and VEND saw the light of day at the end of 2002, and since then, continued their
growth to be used widely in a variety of studies. However, we never get full satisfaction from theirusability and performance. First, the combined use of VICS and VEND to visualize both crystal
and electronic structures via text files is rather troublesome; on-the-fly visualization of these twokinds of images is highly desired. Second, their GUIs are not very user-friendly because they
are based on the old-fashioned toolkits, GLUT and GLUI, which have been no longer upgraded.
Above all things, they lack scalability and require large system resources owing to unrefinedprogramming.
To overcome the faults described above, we at first upgraded VICS to VICS-II employing
a modern C++ GUI framework wxWidgets3 [20]. Later, we further integrated VICS-II and
VEND into VESTA.

1.3

What’s New in VESTA 3

Main new features implemented in VESTA 3, which is a successor to VESTA v2.1.X, are listed
below:• Visualization of crystal morphologies• Superimposition of multiple structural models, volumetric data, and crystal faces on thesame Graphic Area
• Visualization of isosurfaces with multiple levels• An extended bond-search algorithm to allow more sophisticated search in complex molecules,
cage-like structures, etc.
• Calculations of electron and nuclear densities from structure parameters• Calculations of Patterson-function densities from structure parameters or volumetric data
• Integration of electron and nuclear densities by Voronoi tessellation [21]• Significant performance improvements in rendering of isosurfaces and calculation of slices• Output information about principal axes and mean square displacements for anisotropic
atomic displacements
23

http://www.opengl.org/
http://www.wxwidgets.org/

2• Determination of the best plane for selected atoms• Displaying labels of atoms• Customization of styles per sites or bond types• Customization of symmetry operations• Improvements in inputting files with various formats• Support of undo and redo in GUI operations

1.4

Notes on this Manual

Throughout this document, the following symbols are used to show kinds of input data:[Button] :“Option” :{Text Box} :Tab :<Key> :

A button (dotted lines appear after clicking it).
A radio button and a check box (words following it may be clicked to selectit).
An input item (e.g., a value or a name) including spinners and list boxes.
A page in a multiple-page user interface (an underscore is drawn below thetab name).
A key in the keyboard.

The text box supports four types of basic arithmetic operations: +, −, ×, and /, whichmeans that you can input, for example, “1/3” instead of “0.333333.” Pressing the <Tab> or<Enter> key will focus a next control, i.e., text box, button, ratio button, or check box, in a
dialog box. Press <Shift> + <Tab> to focus the preceding control.

3Chapter 2

OVERVIEW OF THE PROGRAM
2.1

General Features

VESTA [11, 12, 13, 14] is a 3D visualization system for structural models, volumetric data(“voxel” data), and crystal morphologies. A variety of physical quantities such as electron
densities, densities of coherent-scattering lengths bc (nuclear densities) [10], wave functions, andelectrostatic potentials can be superimposed on atomistic structures and external morphology
of crystals. Objects (atoms, bonds, coordination polyhedra, isosurfaces, etc.) can be rotated,scaled, and translated fast in three dimensions, particularly in the presence of graphics cards
supporting the OpenGL instruction set. The scalability of VESTA is very high; it enables us
to deal with a practically unlimited numbers of objects such as atoms, bonds, polyhedra, andpolygons on isosurfaces so long as memory capacity is enough. Drawing boundaries are definedby ranges along x, y, and z axes as well as lattice planes.
As Fig. 2.1 illustrates, VESTA runs on Microsoft Windows (hereafter referred to as Windows), macOS, and Linux. With VESTA, we can deal with multiple data in the same window,
using a “tab” user interface. VESTA further supports multiple windows, each of which may
contain multiple tabs corresponding to files.

2.2

Visualization of Structural Models

Structural models are represented as ball-and-stick (Fig. 2.2), space-filling (Fig. 2.3), polyhedral (Fig. 2.4), wireframe (Fig. 2.5), stick (Fig. 2.6), and displacement ellipsoid (Fig. 2.7)
models. Ball-and-stick, wireframe, and stick models can be overlapped with dotted surfaces toaccentuate outer surfaces of atoms. Polyhedra may be made translucent so as to make insideatoms and bonds visible.
Lattice planes with variable opacity can be inserted into a structural model. Vectors (arrows)
can be attached to atoms to represent magnetic moments or directions of static and dynamic
displacements.
You can superimpose multiple structural models in the same Graphic area to deal with grainboundary structures, absorption of atoms, molecules, nanosheet on a surface of cyrstal, or absorbed molecules in porous materials and layered structures.
Bond-search algorithm in VESTA is highly sophisticated; a variant of the cell index methodby Quentrec and Brot [22, 23] was adopted. This approach is widely used in programs formolecular dynamics simulation that needs to deal with a large number of atoms.

4

A

B

C

Figure 2.1: Screenshots of VESTA running on the three different operating systems: (A) Windows, (B) Linux, and (C) macOS.

5

Figure 2.2: Crystal structure of a variant of mica group minerals, masutomilite K(Li,Al,Mn2+ )3 [(Si,Al)4 O10 ](F,OH)2 [24].

Figure 2.3: Crystal structure of a polymorph of vitamin B1 [25].

6Figure 2.4: Crystal structure of beryl, Be3 Al2 Si6 O18 [26].

Figure 2.5: Crystal structure of sodalite, Na4 Al3 (SiO4 )3 Cl [27].

7Figure 2.6: Crystal structure of the tetragonal form of melanophlogite,
46SiO2 ·6M14 ·2M12 (M14 = N2 , CO2 ; M12 = CH4 , N2 ) [28]. Bright-blueand pink spheres in cages of the SiO4 framework represent M14 and M12
sites for guest molecules, respectively.

Figure 2.7: A displacement ellipsoid model of 17-(2H -indazol-2-yl)androsta-5,16-dien-3β-ol having an indazole substituent at the C17 position [29]. C: brown, N: green, O: red, H: sky-blue.
The probability for atoms to be included in the ellipsoids was set at 50 % except for the smalland spherical H atoms.

8

2.2.1

A variety of structural information derived on selection of objects

Selection of objects (atoms, bonds, and coordination polyhedra) by clicking with a mouse provides us with a variety of structural information:• fractional coordinates,• symmetry operations and translation vectors,• site multiplicities and Wyckoff letters [30],• site symmetries,• principal axes and mean square displacements of anisotropic atomic displacements,• interatomic distances, bond angles, and dihedral angles,• information about coordination polyhedra including volumes [31], Baur’s distortion indices[32], quadratic elongations [33], bond angle variances [33, 34, 35, 36], effective coordination
number [34, 35, 36], charge distribution [35, 36, 37], bond valence sums of central metals[38, 39, 40], and bond lengths expected from bond valence parameters.1

2.3

Visualization of Volumetric Data

Electron and nuclear densities, wave functions, electrostatic potentials, Patterson functions, etc.
are visualized as isosurfaces, bird’s-eye views, and two-dimensional (2D) maps. Multiple levelsof translucent isosurfaces can be overlapped with a structural model. VESTA has a feature ofsurface coloring to illustrate another kind of a physical quantity at each point on isosurfaces; thisfeature has been thoroughly redesigned to improve the quality of images [11]. In VESTA, thevisibility of both outlines of isosurfaces and an internal structural model has been surprisingly
improved by introducing two opacity parameters. Further, we can add 2D slices of volumetricdata in their 3D image. The quality of rendering isosurfaces, boundary sections, and slices by
VESTA is very high even when the resolution of data is relatively low [11]. The calculationof isosurface geometry has been appreciably accelerated in VESTA by virtue of new algorithm
adopted in VESTA [11].
VESTA has a feature to calculate electron and nuclear density distributions from structure
parameters and atomic scattering factors. This feature is useful for comparison of the results of
MEM with model densities.
Figure 2.8 illustrates isosurfaces of electron densities calculated with WIEN2k [41] for a
superconductor MgB2 [42]. A network of highly covalent B–B bonds on the z = 1/2 plane andthe ionic nature of bonds between Mg2+ ions (z = 0) and B atoms are clearly visualized in thisfigure. A (001) slice of electron densities at the z = 1/2 level is depicted in Fig. 2.9. Sucha kind of 2D maps are very useful particularly when part of atoms form 2D sheets e.g., CuO2
conduction sheets in high-Tc superconducting oxides.

1

http://fujioizumi.verse.jp/rietan/book/book.html#BVP

9

B
Mg
b

a
0

Figure 2.8: Electron-density distribution in MgB2 . Four hexagonal unit cells areshown with an isosurface level of 0.11a−3
0 (a0 : Bohr radius).

0.5
0.45
0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0.0a0-3

Figure 2.9: A (001) slice illustrating electron-density distribution on thez = 1/2 plane in MgB2 . Contours are plotted up to 0.5a−30 with an intervalof 0.05a−3
(a
:
Bohr
radius).
0
0

10

b

O
H
0

O

a

c
Figure 2.10: Nuclear-density distribution in the paraelectricphase of KH2 PO4 .

Figure 2.10 shows isosurfaces of scattering-length densities determined from neutron powder diffraction data of KH2 PO4 (paraelectric phase, space group: I 4̄2d) at room temperature by
MEM-based pattern fitting [43]. In this way, two different colors are assigned to positive andnegative isosurfaces. Blue isosurfaces (density: −2.5 fm/Å3 ) for H atoms are elongated toward
yellow ones (density: 2.5 fm/Å3 ) for O atoms because of double minimum potential with an
H–H distance of about 0.36 Å.

2.4

Visualization of Crystal Morphologies

Crystal morphologies can be drawn by inputting Miller indices of faces (see section 6.5). Crystal
faces can be overlapped with structural models as well as isosurfaces of volumetric data, as
exemplified by Fig. 2.11. Thus, VESTA facilitates understanding of the relationship between
crystal morphologies and chemical bonds, for example, by application of the periodic bond chain(PBC) theory [44]. For example, Fig. 2.12 illustrates an external morphology of anatase-type
TiO2 superimposed on its ball-and-stick model. According to Hartman [44], the {101} face ofanatase is an F face, where two PBCs are parallel to the plane. All the other {h0l} faces are S
faces, where only one PBC is parallel to the plane. The PBC along [010] is intuitively recognized
by interactive rotation of the model in three dimensions.
Morphologies of twinned crystals or epitaxial intergrowths of two or more crystals are visualized by inputting multiple crystal data (Fig. 2.13). After morphological data have been
given, information about Miller indices, distances from the center of the crystal to faces, andthe surface area of each face are output to the text area.
11

Figure 2.11: An external morphology of an Al2 O3 crystal
composed of {001}, {110}, and {113} faces.

Figure 2.12: A crystal morphology of anatase-type TiO2 superimposed on its
structural model, where blue and red balls represent Ti and O atoms, respectively.

12

A

B

C

Figure 2.13: Crystal morphologies of adularia, a variant of orthoclase (KAlSi3 O8 ). (A) A single
crystal. (B) A Hypothetical morphology composed of four individual crystals twinned after the
Babeno law. (C) An idealized morphology of repeated twins, which were found from Kobushi
mine, Japan, composed of eight individual crystals twinned after the Babeno and Manebach
laws.

2.5

Cooperation with External Programs

VESTA collaborates closely with external programs such as ORFFE [45], STRUCTURE TIDY[46], RIETAN-FP [12], and MADEL (see section 14.5). On selection of a bond (2 atoms) or abond angle (3 atoms) in a dialog box relevant to geometrical parameters output by ORFFE, thecorresponding object in a ball-and-stick model is highlighted in a graphic window, and vice versa.
STRUCTURE TIDY allows us to standardize crystal-structure data and transform the current
unit cell to a Niggli-reduced cell. RIETAN-FP makes it possible to simulate powder diffraction
patterns from lattice and structure parameters. With MADEL, electrostatic site potentials anda Madelung energy can be calculated from occupancies, fractional coordinates, and oxidation
states of all the sites.

2.6

Input and Output Files

VESTA can read in files with 42 kinds of formats such as CIF, ICSD, and PDB and output files
with 15 kinds of formats such as CIF and PDB (see chapter 17). Users of RIETAN-FP [12] must
be pleased to learn that standard input files, *.ins, can be both input and output by VESTA.
In addition, program ELEN [47] was built into VESTA for conversion of 3D electron densities
into electronic-energy densities and Laplacians [48].
The entire crystal data and various settings can be saved in a small text file, *.vesta, without
incorporating huge volumetric data. File *.vesta with the VESTA format contains relative paths
to external data files of volumetric-data and optionally of structure-data that are automaticallyread in when *.vesta is reopened. VESTA also makes it possible to export graphic-data files
with 14 image formats including 4 vector-graphic ones (see section 17.5).

2.7

Programming Concept

The source code of VESTA comprises GUI and core parts. In this section, only the fundamental concept of programming is briefly described. For further details in algorithmic techniques
adopted in VESTA, please refer to Ref. [11].
132.7.1Graphical user interface

The GUI of VESTA is built on top of a cross-platform application framework (toolkit), wxWidgets, written in the C++ language. The wxWidgets libraries are one of the best toolkits forcross-platform GUI programming. It provides us with a consistent look-and-feel inherent ineach operating system. The license agreement of wxWidgets,2 an LGPL-like license with some
exceptions allowing binary distribution without source code and copyright, is flexible enough topermit us to develop any types of applications incorporating wxWidgets.

2.7.2

Core libraries

In contrast to the GUI framework, the core parts of VESTA are carefully separated from the GUI
parts to make it easier to reuse the former code. The core libraries are basically independentof the wxWidgets libraries. However, few classes and functions proviced by wxWidgets are
exceptionally used in some core parts. In such a case, the function is wrapped by anotherfunction in a separate file to make the core parts quite independent of GUI toolkits and to makeclear which functions depend on external libraries.

2

http://www.wxwidgets.org/about/newlicen.htm

14Chapter 3

GETTING STARTED
3.1

Minimum requirements of hardware

CPU: MMX Pentium 233 MHz or faster.
RAM: 64 MB or more.
Video RAM: 16 MB or more is desirable.
Video card: A graphics card capable of hardware acceleration of the OpenGL instruction set isrecommended.
Display: A minimum resolution of 1024 × 768 pixels with ca. 65,000 or ca. 16.7 million colors.
Because VESTA utilizes OpenGL technology, the use of an OpenGL-capable graphics processing
unit (GPU) is highly recommended but not always mandatory. All the versions of VESTA werebuilt with Intel C++ Composer XE 2011 and linked with the MKL library.1

3.2

Windows

Both 32- and 64-bit versions of VESTA are available for Windows. They were tested on Windows
10, 8, 7, Vista, and XP. VESTA does not run on Windows ME or older.
The Windows versions of VESTA are archived in the zip format. To get the 32-bit versionof VESTA for Windows, download
http://jp-minerals.org/vesta/archives/VESTA.zip
To get the 64-bit version of VESTA for Windows, download
http://jp-minerals.org/vesta/archives/VESTA-win64.zip
Note that the 32-bit version of VESTA can also be used on 64-bit Windows. Extract the wholecontents of the archive file in the same directory. VESTA can be launched in the following four
fashions:
1. Double click the icon of VESTA.exe.
2. Type a command in a command line:
VESTA file1 file2 ...

This command will start VESTA and open specified files, file1, file2, etc. Input files may
be omitted. When the current directory is different from the directory of VESTA, you1

http://software.intel.com/en-us/articles/intel-sdp-products/

15

must input the absolute path of the executable binary file of VESTA. To execute VESTA
by simply typing VESTA regardless of the current directory, set environment variable PATH
to include absolute path of the directory where VESTA is placed.
3. Drag & drop file icons of supported file types on the icon of VESTA.exe.
4. Double click files with extensions associated with VESTA.
To associate an extension with VESTA, right click a file with the extension and select “Properties.” Then change the “Program” section in the Properties dialog box.
Beware that VESTA cannot be executed unless the zip file is decompressed. By default,
double-clicking a zip file on Windows XP or later will open it with Explore, i.e., the standard
file manager of Windows. However, the contents of the archive file seen in the Explore window
are actually not extracted but just ‘previewed’. In such a case, copy the whole contents ofthe ‘previewed’ archive into an appropriate directory, typically in C:\Program Files. Then,VESTA.exe in the VESTA folder can be executed as described above.

3.3

macOS

The macOS version of VESTA runs on OS X 10.9 or later using Macs equipped with Intel CPUs
that support 64 bit instruction sets. For those using older machines, VESTA v3.4.4 or earlier
runs on OS X 10.6 or later and Intel 64 bit CPU. VESTA 2.1.6 or earlier runs on Macs (MacOS X 10.4) equipped with PowerPC or Intel 32 bit CPUs.
The macOS version is contained in VESTA.dmg with a disc image format. Download
http://jp-minerals.org/vesta/archives/VESTA.dmg
and mount its disc image by double-clicking the icon of VESTA.dmg. Copy the whole contentsof the disc image into an appropriate directory, typically /Applications/VESTA.
VESTA can be launched in the following four fashions:
1. Double click the icon of VESTA (or VESTA.app).
2. Type a command in a command line:
open -a VESTA file1 file2 ...

3. Drag and drop file icons of supported file types on the icon of VESTA.
4. Double click files with extensions associated with VESTA.

3.4

Linux

Both 32- and 64-bit versions are available for Linux platforms.

3.4.1

32-bit version

1. Dependency(a) Gkt+ > 2.10(b) Cairo > 1.0(c) libstdc++.so.6(d) Mesa OpenGL library16

2. Distributions where VESTA is known to work(a) Fedora 10, 11, 12, 13, 14(b) openSUSE 11.2, 11.3(c) Red Hat Enterprise Linux 5, 6(d) Ubuntu 9.10, 10.10

3.4.2

64-bit version

1. Dependency(a) Gkt+ > 2.10(b) Cairo > 1.0(c) libstdc++.so.6(d) Mesa OpenGL library
2. Distributions where VESTA is known to work(a) Fedora 10, 11, 12, 13, 14(b) openSUSE 11.2, 11.3(c) Red Hat Enterprise Linux 5, 6, 7(d) Ubuntu 9.10, 10.10, 12.04, 16.04
Linux versions of VESTA are archived in the tar.bz2 format. For 32-bit OSs running on PCs
equipped with Intel x86 CPUs, download
http://jp-minerals.org/vesta/archives/VESTA-i686.tar.bz2
For 64-bit OSs running on PCs equipped with AMD 64 CPUs, download
http://jp-minerals.org/vesta/archives/VESTA-x86_64.tar.bz2
Extract the whole contents of the archive file to a directory. Then, execute VESTA in that
directory by double-clicking the “VESTA” file on a file manager or by typing the following
command in a command line:
VESTA file1 file2 ...

This command will start VESTA to open the specified files, file1, file2, etc. Of course, the input
files may be omitted. When the current directory is different from that of VESTA, you must
input the absolute path of the executable binary file of VESTA. To launch VESTA by simply
typing VESTA regardless of the current directory, create a symbolic link of VESTA in a directory
where environment variable path is set. You can optionally add VESTA to a panel, dock, or
the application menu.
VESTA always uses “.” (period) as decimal points regardless of locale settings of OSs,even though some languages use “,” (comma) as decimal points. Such behavior is achievedby internally changing locale settings on execution of the VESTA program. This is necessary
because most of file formats, such as Crystallographic Information Framework (CIF), use period
as decimal points.
VESTA crashes on Ubuntu 6.06 with some locale settings. In this case, try the following
command:
GTK_IM_MODULE=xim VESTA

17

3.5

Trouble Shooting

VESTA may not function properly with part of graphics cards; most of such troubles seem toarise from bugs of their drivers. Updating drivers to latest ones may solve the problems. If sometroubles are encountered on the use of VESTA, please try to run it on another machine to check
whether or not the trouble is caused by a bug in it.
If you fail in executing VESTA on a Linux platform, try to execute it in a command line.
Then you will probably get some information about the cause of the problem. Most likely, thefailure is caused by missing libraries. In such a case, the names of missing libraries are output
to the terminal.

3.6

Loading Files

Files can be loaded in four different fashions. Files to be opened can be specified on executionof VESTA in a command line. Files can be specified in a file selection dialog box, which is
opened from the “Open” item in the “File” menu. In the file selection dialog box, only files
with supported formats can be selected. You can also drag and drop a file icon onto the main
window of VESTA from a file manager (Finder in macOS or Explorer in Windows). If VESTA
has been associated with some file extensions, files having these extensions can be opened witha file manager by double-clicking their icons.

18

Chapter 4

MAIN WINDOW
4.1

Components of the Main Window

Figure 4.1 shows the main window of VESTA running on Windows 7. The Main Window
consists of the following seven parts:

2. Horizontal Toolbar

1. Menu Bar

3. Vertical Toolbar

6. Graphics Area
7. Text Area

4. Side Panel

5. Status Bar

Figure 4.1: Main window of VESTA running on Windows 10.

19

1. Menu bar: “File”, “Edit”, “View”, “Objects”, “Utilities”, and “Help” menus are placed on
the menu bar. The menu bar is placed at the top of the Main Window in Windows andLinux while the menus are displayed at the top of the screen in macOS.
2. Horizontal Toolbar: Tools used frequently (see section 4.3).
3. Vertical Toolbar: Other tools used frequently (see section 4.4).
4. Side Panel: Composed of three tab pages. The Tools tab contains options for GUI tools inthe Vertical Toolbar (see chapter 11). The Style tab contains GUI tools for display styles(see chapter 5). The Objects tab shows a list of phases and objects in each phase (seechapter 12.2).
5. Status Bar: An area to show brief information in a line of text.
6. Graphics Area: An area where various objects are displayed in three dimensions.
7. Text Area: Two types of texts are displayed here (see section 4.5). A variety of information
related to users’ operations is displayed in the Output tab. In the Comment tab, comments
on data displayed currently can be input.

4.2

Menus

4.2.1

File menu• New Structure...: Open a Edit Data dialog box to input crystal data of a new structure.
• New Window...: Open a new Main Window.
• Open...: Open files with a file selection dialog box.
• Save...: Save current data to a file, *.vesta, with the VESTA format. If the current data
has been input from *.vesta or once saved as *.vesta, *.vesta is overwritten. Otherwise, afile selection dialog box will appear to prompt you to input a new file name.
• Save As...: Save current data to a new file, *.vesta, with the VESTA format. A fileselection dialog box will appear to prompt you to input a new file name.
• Export Data...: Export current data to a file with formats other than the VESTA format.
• Export Raster Image...: Export a graphic image to a file with a raster (pixel-based)
format.
• Export Vector Image...: Export a graphic image to a file with a vector format.
• Save Output Text...: Save text data in the Text Area as a text file.
• Close: Close the current page. When no data are displayed, this menu is practically thesame as the Exit menu.
• Exit: Exit VESTA.
20

4.2.2

Edit menu• Undo: Undo the last action.
• Redo: Redo an action that has just been undone.
• Edit Data:− Phase…: Open an Edit Data dialog box to select the Phase page.
− Unit Cell…: Open an Edit Data dialog box to select the Unit Cell page.
− Structure Parameters…: Open an Edit Data dialog box to select the Structure parameters
page.
− Volumetric Data…: Open an Edit Data dialog box to select the Volumetric data
page.
− Crystal Shape…: Open an Edit Data dialog box to select the Crystal shape page.
• Bonds...: Open a Bonds dialog box to create or edit data related to bonds.
• Vectors...: Open a Vectors dialog box.
• Lattice Planes...: Open a Lattice Planes dialog box.
• Preferences...1 : Open a Preferences dialog box.

4.2.3

View menu• Antialiasing: Enable or disable antialiasing in the Graphics Area.
• Parallel: Switch to parallel representation.
• Perspective: Switch to perspective representation.
• Zoom In: Zoom in objects.
• Zoom Out: Zoom out objects.
• Fit to Screen: Scale and center justify objects to fit to the Graphics Area.
• Overall Appearance...: Open an Overall Appearance dialog box.
• Clear Text Are: Clear all the text in the Text Area.

4.2.4

Objects menu

• Structural Model: items of this menu can be also selected in the Side Panel.
− Show Model: Show or hide a structural model.
− Show Dot Surface: Show or hide outer surfaces of atoms as dotted surfaces.
− Ball-and-Stick: Show a ball-and-stick model.
− Space-filling: Show a space-filling model.
− Polyhedral: Show a a polyhedral model.
− Wireframe: Show a wireframe model.
− Stick: Show a stick model.
1

In the macOS version, the Preferences item is placed under the VESTA menu.

21• Volumetric Data: items of this menu can be also selected in the Side Panel.
− Show Isosurfaces: Show or hide isosurfaces.
− Show Sections: Show or hide sections of isosurfaces.
− Surface Coloring: Enable or disable the surface coloring of isosurfaces.
− Smooth Shading: Show isosurfaces with a smooth-shading model.
− Wireframe: Show isosurfaces with a wireframe model.
− Dot Surface: Show isosurfaces as dotted surface.
• Properties− General...: Open a Properties dialog box to select the General page.
− Atoms...: Open a Properties dialog box to select the Atoms page.
− Bonds...: Open a Properties dialog box to select the Bonds page.
− Polyhedra...: Open a Properties dialog box to select the Polyhedra page.
− Isosurfaces...: Open a Properties dialog box to select the Isosurfaces page.
− Sections...: Open a Properties dialog box to select the Sections page.
• Boundary...: Open a Boundary dialog box.
• Orientation...: Open an Orientation dialog box.

4.2.5

Utilities menu

• Equivalent Positions...: Open an Equivalent Positions dialog box to list general equivalent
positions.
• Geometrical Parameters...: Open a Geometrical Parameters dialog box.
• Standardization of Crystal Data...: Standardize the space-group setting and fractional
coordinates.
• Niggli-Reduced Cell: Transform the current unit cell to a Niggli-reduced cell.
• Site Potentials and Madelung Energy...: Calculate site potentials and the Madelungenergy of the currently displayed crystal by an external program, MADEL.
• Powder Diffraction Pattern...: Simulate a powder diffraction pattern with RIETANFP [12] and display the result with an external graph-plotting program.
• Structure Factors...: Calculate structure factors.
• Fourier Synthesis...: Calculate electron/nuclear densities from structure factors.
• Model Electron Densities: Calculate electron densities from structure parameters.
• Model Nuclear Densities: Calculate nuclear densities from structure parameters.
• Patterson Densities:− From Model Electron Densities…: Calculate and display density distributions ofPatterson function from model electron densities.
− From Model Nuclear Densities…: Calculate and display density distributions ofPatterson function from model nuclear densities.
22

− From Volumetric Data…: Calculate and display density distributions of Patterson
function from the currently displayed volumetric data.
• 2D Data Display...: Open a 2D Data Display window.
• Line Profile...: Calculate a line profile of volumetric data between two positions andoutput them in a text file.
• Peak Search...: Search peaks in volumetric data.
• Conversion of Electron Densities...: Convert 3D electron densities into electronicenergy densities and Laplacians.

4.2.6

Help menu• Manual...: Open the user’s manual of VESTA in a PDF viewer.2• Check for Updates...: Open the web page of VESTA3 with a browser to check whether
or not a new version of VESTA has been released.
• About VESTA...4 : Show information about VESTA.

4.3

Tools in the Horizontal Toolbar

4.3.1

Alignment
View along the a axis
View along the b axis
View along the c axis
View along the a* axis
View along the b* axis
View along the c* axis

The above six buttons are used to align objects parallel to the a, b, or c axis, or parallel to thea∗ , b∗ , or c∗ axis, respectively.
2
The present PDF file, VESTA_Manual.pdf, need to share the same folder with a binary executable file of
VESTA.
3
http://jp-minerals.org/vesta/
4
In the macOS version, this item is placed under the VESTA menu.

234.3.2

Rotation
Rotate around the x axis
Rotate around the x axis
Rotate around the y axis
Rotate around the y axis
Rotate around the z axis
Rotate around the z axis

These six buttons are used to rotate objects around the x, y, or z axis. The step width ofrotation (in degrees) is specified in the text box next to the sixth button:

4.3.3

Translation
Translate upward
Translate downward
Translate leftward
Translate rightward

These four buttons are used to translate objects upward, downward, leftward, and rightward,
respectively. The step width of translation (in pixels) is specified in the text box next to thefourth button:

4.3.4

Scaling
Zoom in
Zoom out
Fit to the screen

These three buttons are used to change object sizes. The step width of zooming (in %) is
specified in a text box next to the third button:

24

4.4

Tools in the Vertical Toolbar
RotateSelectTranslateMagnify
Measure distance
Measure angle
Measure dihedral angle
Measure an interfacial angle

4.5

Text Area

4.5.1

Output tab

The Output area is a standard-output window corresponding to the Command Prompt window
on Windows and a Terminal window on macOS or Linux. Just after launching VESTA, theOutput area displays information about the PC you are using. OpenGL version denotes theversion of OpenGL implementation supported by the system. Video configuration provides
information about the GPU. For example, in a Windows PC equipped with Quadro FX 4600, a
message
Video configuration: Quadro FX 4600/PCI/SSE2

is displayed in the Text Area. SSE2 means that Streaming SIMD Extensions 2 is supported inthis graphics card. In the case of a Power Mac G5 (Dual 2.5 GHz) equipped with ATI Radeon
9600 XT, a message
Video configuration: ATI Radeon 9600 XT OpenGL Engine

is issued in the Text Area. If the GPU of your PC does not support any hardware acceleration of
OpenGL, Video configuration would be GDI Generic on Windows, and Software Rasterizer
or Mesa GLX Indirect on Linux.
When a new file is loaded, a summary of data appears in the Output area, including theabsolute path of the file and the title of the data. For crystal-structure data, lattice parameters,a unit-cell volume, and structure parameters (element names, site names, fractional coordinates,
occupancies, isotropic atomic displacement parameters, multiplicities plus Wyckoff letters, andsite symmetries) are output. In the case of volumetric data, lattice parameters, number ofgrids along each axis, and number of polygons and unique vertices on slices and isosurfaces are
displayed. For instance, a CIF of PbSO4 affords the following output:
Title

O4 Pb1 S1

Lattice typeSpace group nameP
P n m a25

Space group number
Setting number

62
1

Lattice parametersa8.51600b
5.39900c6.98900

alpha
90.0000

beta
90.0000

gamma
90.0000

Unit-cell volume = 321.339447
Structure parameters

1 Pb
2 S
3 O
4 O
5 O

Pb1
S1
O1
O2
O3

x
0.188200.43700
0.59500
0.31900
0.41500y0.25000
0.75000
0.75000
0.75000
0.97400z0.16700
0.18600
0.10000
0.04300
0.30600

g
1.000
1.000
1.000
1.000
1.000

Occ
1.200
0.700
1.600
1.600
1.600

Site
4c
4c
4c
4c
8d

Sym.
.m.
.m.
.m.
.m.
1

Such a type of a list is also output when pressing [OK] button in the Edit Data dialog box.

4.5.2

Summary tab

The Summary tab gives a brief summary of data including data name, space group, unit cellparameters, unit cell volume, and number of grids of volumetric data. An example output is asfollows.
NaV6O11
Space Group: P 63/m m c (#194-1)
a = 5.70918 Å
α = 90.0000°
b = 5.70918 Å
β = 90.0000°
c = 13.08744 Å
γ =120.0000°
V = 369.4305 Å^3

4.5.3

grid(x) = 120
grid(y) = 120
grid(z) = 240

Comment tab

You can input any comments relevant to data displayed currently. VESTA also reads in some
information on the data from files (*.amc) of the American Mineralogist Crystal Structure
Database format. For example, the following information is read in from *.amc for anatase-type
TiO2 and displayed in the Comment area.
Horn M, Schwerdtfeger C F, Meagher E P
Zeitschrift fur Kristallographie 136 (1972) 273-281
Refinement of the structure of anatase at several temperatures
Sample: T = 25 C
Locality: Legenbach quarry, Binnatal, Switzerland_database_code_amcsd 0010735

26

Chapter 5

DISPLAY STYLES
Display styles of structural models, volumetric data, and crystal shapes are controlled either
from the Style tab of the Side Panel or from the “Objects” menu. Both of the methods allow us
to use the same options.

5.1

Structural Models

The Structural model frame box in the Style tab of the Side Panel(Fig. 5.1) contains frequently used tools to control representation of structural models. The same options can also be used by
selecting the Model item under the “Objects” menu. This framebox is disabled for data containing no structural model.

5.1.1

Objects to be displayed

Show modelThis option controls the visibility of a structural model. When
this option is checked (default), a structural model is visible;
otherwise, no structural model is shown. Uncheck this option
when you want to see only isosurfaces and sections for datacontaining both structural and volumetric ones.

Figure 5.1: The Structuralmodel frame box in the
Style tab of the Side Panel.

Show dot surface
In ball-and-stick, wireframe, and stick models, dot-surface
spheres are added with radii corresponding to 100 % of user
specified ones in the same manner as with a space-filling model
if Show dot surface is checked (Fig. 5.2). This mode is designed to accentuate outer surfaces of atoms. Each sphere isrepresented as though it were a hollow shell with numerous dots
placed on the surface. The combination of dot surface with astick model is useful for understanding how atoms are combinedwith each other in a molecule. The density of dots is controlled
by two parameters, {Stacks} and {Slices} in the Atoms pageof the Properties dialog box as with the same manner as solid
spheres.
27

Figure 5.2: Crystal structure of quartz [49] represented by a stick modelwith dot surfaces. Si: blue,
O: red.

5.1.2

StylesAs described in 2.2, VESTA represents crystal structures by the five different styles: ball-andstick, space-filling, polyhedral, wireframe, and stick models. When atoms are drawn as spheres,
they are rendered with radii corresponding to 40 % of actual atomic radii in all but the spacefilling model, where atoms are rendered with the actual atomic radii. Default radii of atoms are
selected from three types: atomic, ionic, and van der Waals radii. The radius of each element
and a type of radii are specified at the Atoms page in the Properties dialog box (see section
12.1.2). Features in each structural model are described below with screenshots of the structurefor quartz [49] on the right side.

“Ball-and-stick”
In the “Ball-and-stick” model, all the atoms are expressed as solid
spheres or displacement ellipsoids. Bonds are expressed as either
cylinders or lines.

“Space-filling”
In the “Space-filling” model, atoms are drawn as interpenetrating
solid spheres, with radii specified at the Atoms tab in the Properties
dialog box (see section 12.1.2). This model is useful for understanding
how atoms are packed together in the structure.

“Polyhedral”
In the polyhedral model, crystal structures are represented by coordination polyhedra where central atoms, bonds, and apex atoms
may also be included. Bonds between central and apex atoms haveto be searched with the Bonds dialog box to display coordination
polyhedra comprising them. Atoms are expressed as solid spheres ordisplacement ellipsoids. Bonds are expressed as either cylinders orlines. Needless to say, the transparency of the coordination polyhedra must be high enough to make it possible to see the central atoms
and bonds. One of six different styles for representing polyhedra is
specified at the Polyhedra tab in the Properties dialog box (see section
12.1.4).
28

“Wireframe”
In the “Wireframe” model, atoms having no bonds are drawn as wireframe spheres whereas those bonded to other atoms are never drawn.
All the bonds are presented as lines with gradient colors. This modelis useful for seeing and manipulating complex and/or large structures
because this is usually the fastest model for rendering structures on
the screen.

“Stick”
In the “Stick” model, atoms with no bonds are drawn as solid spheres
while atoms bonded to other atoms are never drawn. All the bonds
are expressed as cylinders, whose properties can be changed at theBonds tab in the Properties dialog box (see section 12.1.3). This model
serves to see frameworks or molecular geometry.

Displacement ellipsoids
In the ball-and-stick and polyhedral models, atoms can be renderedas displacement ellipsoids. The probability for atoms to be includedin the ellipsoids is also specified in the Properties dialog box (seesection 12.1.2).

5.2

Volumetric Data

The Volumetric data frame box in the Style tab of the Side Panel(Fig. 5.3) contains frequently used tools to control representation of volumetric data. The same options can also be used by
selecting the “Volumetric Data” item under the “Objects” menu.
This frame box is disabled for data containing no volumetricones.
• Show sections
This option controls whether or not sections of isosurfaces
are visible. When this option is checked (default), sections
are visible, otherwise they are not shown.

Figure 5.3: The Volumetricdata frame box in the Styletab of the Side Panel.

• Show isosurfaces
This option controls whether or not isosurfaces of volumetric data are visible. When this option is checked (default), isosurfaces are visible,
otherwise they are not shown. To see only a structural model for data containing both29

structural and volumetric ones, uncheck this option in addition to the “Show sections”
option.
• Surface coloring“Surface coloring” means that colors of isosurfaces drawn from one data set are determinedby a secondary data set. A typical example is coloring of electron-density isosurfaces on
the basis of electrostatic potentials (see Fig. 12.9). This option is enabled only when thesecondary volumetric data for surface coloring has been loaded with the Volumetric datatab in the Edit Data dialog box (see 6.4.2).
Styles of isosurfaces are chosen from the following three representations:• Smooth shading• Wireframe• Dot surface
Isosurfaces are drawn as solid surfaces with variable opacity in the Smooth shading mode whereas
isosurfaces are represented by lines and points, respectively, in the Wireframe and Dot surface
modes.

5.3

Crystal Shapes

The Crystal Shapes frame box in the Style tab of the Side Panel(Fig. 5.4) provides us with tools to control representation of
crystal morphologies. The same options can also be used by
selecting the “Crystal Shapes” item under the “Objects” menu.
This frame box is disabled for data containing no morphology
data (faces).
• Show shapes
This option controls whether or not the external morphology of crystals are visible. When this option is checked(default), morphologies are visible, otherwise they are notshown.

5.3.1

Figure 5.4: The Crystal
shapes frame box in the
Style tab of the Side Panel.

Styles

VESTA represents crystal morphologies by the following threestyles:“Unicolor”
All the faces of a crystal are filled with a single color, as the rightfigure (quartz) illustrates.

30

“Custom color”
Each face is filled with a color assigned to symmetrically equivalent{hkl} faces specified in the Edit Data dialog box (see section 6.5) orin the Side Panel.

“Wireframe”
Only edges of a crystal shape are drawn with lines.

31

Chapter 6

GIVING PHASE DATA
To create a new structure, choose the “File” menu ⇒ “New Structure…”. To edit current data,choose “Edit” menu ⇒ “Edit Data” ⇒ “Phase…”. In both of the cases, the same dialog box
named New Data or Edit Data appears (Fig. 6.1). This dialog box consists of the following fivetab pages:• Phase• Unit cell
• Structure parameters• Volumetric data
• Crystal shape
At the top of the dialog box, a serial number and a title are displayed for the selected phase.

Figure 6.1: New Data dialog box.

32

6.1

Defining Phases

In the Phase tab (Fig. 6.1) of the Edit Data dialog box, you can add, delete, copy, or importphase data that are overlaid on the same Graphics Area. To edit the title of a phase, select a row
in the list and click on the Title column. When dealing with a single phase, you have nothing
to do with this tab except for editing the title. The Positioning and Orientation frame boxes areused when superimposing two or more phases. See chapter 7 for how to visualize multiple phasedata in the same Graphics Area.

6.2

Symmetry and Unit Cell

The Unit cell tab in the Edit Data dialog box is used to give lattice parameters and the symmetryof a structure (Fig. 6.2).

Figure 6.2: Unit cell page in the Edit Data dialog box.

6.2.1

Crystal systems and space groups

Selection of crystal systems
The System list box is used to filter a list of space-group symbols in the Space group list box.
When an item in this list box is selected, only space groups belonging to the selected crystal
system will be highlighted in the Space group list box. The following ten items are listed in the
System list box.
• Molecule• Custom33• Triclinic• Monoclinic• Orthorhombic• Tetragonal• Trigonal• Hexagonal• Cubic• Rhombohedral
On selection of Molecule, a Cartesian-coordinate system is used instead of fractional-coordinate
system, which leads to the absence of “unit cell”. Therefore, text boxes and list boxes forsettings of a space group and lattice parameters are disabled. When Custom is selected, spacegroup settings cannot be specified, but symmetry operations can be manually customized (seepage 36).
Selection of a space group
Space group numbers and standard symbols are listed in the Space Group list box. Only spacegroups of a selected crystal system is highlighted in the list but you can select any space group.
On selection of a space group, the list boxes of System and Setting will be updated.
Settings for a space group
The number of available settings for the selected space group is listed in list box Setting. Settings
available in the list box are basically those compiled in International Tables for Crystallography,
volume A [30].
In some space groups, additional settings are contained in list box {Setting}. In the triclinic
system, complex lattices, A, B, C, I, F , and R, may be selected with setting numbers of 2, 3,
4, 5, 6, and 7, respectively (Table 6.1). In the monoclinic system, settings with unique axes a,b, and c are all available as built-in settings (Table 6.2).
In the orthorhombic system, any of six settings, i.e., abc, bac, cab, cba, bca, and acb
listed in Table 4.3.2.1 in Ref. [30] may be selected with setting numbers of 1, 2, 3, 4, 5, and6, respectively. In orthorhombic space groups having two origin choices, odd and even setting
numbers adopts origin choices 1 and 2, respectively. Then, settings 1 and 2 are of axis choiceabc, settings 3 and 4 are of bac, and so on (Table 6.3).
On changes in crystal axes, e.g., rhombohedral or hexagonal axes in a trigonal crystal, lattice
parameters are automatically converted.
When changing a setting number, consider whether you need to keep structure parameters
or 3D geometries (see the following subsection).

34

Table 6.1: Non-standard settings in two triclinic space groups.
Setting number

Space group (P 1)Space group (P 1̄)

1
2
3
4
5
6
7

P1
A1
B1
C1
I1
F1
R1

P 1̄
A1̄
B 1̄
C 1̄
I 1̄
F 1̄
R1̄

Table 6.2: Setting numbers of monoclinic space groups.
Axis choice
Cell choice
P2
P 21
C2
Pm
Pc
Cm
Cc
P 2/m
P 21 /mC2/m
P 2/c
P 21 /c
C2/c

abc
cba
1 2 3 12
3Unique axis b
1
1
1 2 3
1
1 2 3
1 2 3
1 2 3 10 11 12
1
1
1 2 3
1 2 3
1 2 3
1 2 3 10 11 12abc
bac
1 2 3 12
3Unique axis c
2
2
4 5 6
2
4 5 6
4 5 6
4 5 6 13 14 15
2
2
4 5 6
4 5 6
4 5 6
4 5 6 13 14 15

abc
acb
1 2 3 12
3Unique axis a
3
3
7 8 9
3
7 8 9
7 8 9
7 8 9 16 17 18
3
3
7 8 9
7 8 9
7 8 9
7 8 9 16 17 18

Table 6.3: Axis choices in the orthorhombic space groups.

Axis choice
abc
bac
cab
cba
bca
acb

Space groups
No. 48, 50, 59, 68, and 70
Origin choice 1

Origin choice 2

1
3
5
7
9
11

2
4
6
8
10
12

35

Others12
3
4
56

6.2.2Behavior when changing a space-group setting

The list box below the Setting controls the behavior when changing a space-group setting. There
are two options:• Update structure parameters to keep 3D geometry• Keep structure parameters unchanged
On the use of the first option (default), lattice parameters and fractional coordinates are converted to keep the structural geometry of a crystal when the setting number of a space groupis changed or a transformation matrix is specified. When the second option is used, lattice
parameters and fractional coordinates remain unchanged instead of the geometry.
If a correct structure is displayed in the Graphic Area but another space-group setting ispreferred to the current one, choose Update structure parameters to keep 3D geometry and change
the space-group setting. The second option is typically used to change a setting number when
the correct setting number is not recognized by VESTA after reading in a file such as CIF.
In such a case, lattice parameters and fractional coordinates are correct whereas symmetry
operations are incorrect. Then, choose Keep structure parameters unchanged and select the correct
setting number. When a setting number cannot be uniquely determined from data recorded ina structural-data file, VESTA assumes setting number 2 (a setting with the inversion center atthe origin) in centrosymmetric space groups with two origin choices, and setting number 1 in all
the other space groups.
Note that even if structure parameters remain unchanged, some lattice parameters may bechanged in conformity with constraints imposed on them in the current space-group setting.

6.2.3

Lattice parameters

In the Lattice parameters frame box, lattice parameters are input in the unit of Å (a, b, and c)
and degrees (α, β, and γ). Lattice parameters input by the user are automatically constrainedon the basis of a crystal system. Standard uncertainties (s.u.’s) of lattice parameters are used to
calculate s.u.’s of geometrical parameters. For structural data based on the Cartesian coordinates(when Molecule is selected as the Crystal system), text boxes in this frame box are disabled.

6.2.4

Customization of symmetry operations

To customize symmetry operations, click the [Customize…] button. Then, the Equivalent Positions
dialog box appears with an editing mode (Fig. 6.3), and a list of general equivalent positions
is displayed in this dialog box. When one of the equivalent positions in the list is selected, thecorresponding symmetry operation is displayed in a matrix form at the upper left of the dialog
box. If you input a value in one of the text boxes, representation of the corresponding equivalent
position in the list is updated. To add a new symmetry operation, click the [New] button. To
remove a symmetry operation, select an item in the list and click the [Delete] button. Clicking
the [Clear] button removes all the symmetry operations other than the identity operation.

6.2.5

Reducing symmetry

Clicking the [Remove symmetry] button generates all the atoms
in the unit cell as virtual independent sites by reducing the symmetry of the crystal to P 1. When the space group is changed tothat with higher symmetry, or when the unit cell is transformed
to a smaller one (see 6.2.6), the same atomic position may result
from two or more sites. In such a case, the redundant sites can
36

Figure 6.3: Equivalent Positions dialog box with an editing mode.
be removed by clicking the [Remove duplicate atoms] button in the Structure parameters tab (seepage 48).

6.2.6

Transformation of the unit cell

Clicking the [Transform...] button opens the Unit Cell Transformation dialog box (Fig. 6.4).
This dialog box allow you to transform crystal axes by specifying 3 × 3 rotation matrix P and3 × 1 translation vector p. The [View general positions] button in the dialog box is used toopen the Equivalent Positions dialog box to check the general equivalent positions and symmetry
operations of the transformed unit cell (see 14.1). Clicking the [Initialize current matrix] button
resets the transformation matrix to the identity matrix. Currently, this operation cannot becanceled. When option “Normalize the fractional coordinates” is checked, new atomic coordinatesof the transformed unit cell will be normalized within a range of 0 to 1.
In what follows, a more detailed explanation and use cases of the Unit Cell Transformation
dialog box will be given.

Figure 6.4: Unit Cell Transformation dialog box.
37

Non-conventional space-group settings
To convert a structure from a conventional setting to a non-conventional one, you have to selecta mode Update structure parameters to keep 3D geometry in the Unit cell tab of the Edit Datadialog box before opening the Unit Cell Transformation dialog box. With this mode, both lattice
parameters and fractional coordinates are automatically transformed into new ones to keep thecurrent geometry of the crystal structure. When the mode Keep structure parameters unchanged
is selected, only symmetry operations are transformed to those of the new setting, whereas
lattice parameters and fractional coordinates remain unchanged.
The new origin of the transformed unit cell is specified as the origin shift p. For instance, if
you specify (0.25, 0.25, 0.25) as an origin shift, a coordinate of (0.25, 0.25, 0.25) of a conventionalsetting becomes (0, 0, 0) of the transformed non-conventional unit-cell.
Orientations of the transformed crystal axes a′ , b′ , and c′ are specified as column vectors in
the 3 × 3 rotation matrix P , i.e., the first, second, and third columns of P represent a′ , b′ , andc′ respectively. For example, the following transformation matrix is used to swap the a and b
axes.


0 1 0


(6.1)
P = 1 0 0  .
0 0 −1
Note that the orientation of the c axis is inverted in this case, or otherwise the transformed
structure becomes enantiomorphic with respect to the original structure in non-centrosymmetricspace groups. In general, when the determinant of P , det(P ), is negative, the crystal-coordinate
system is transformed from right-handed to left-handed, and vice versa. When such a matrix is
specified as P , a warning dialog box will appear to confirm whether or not you proceed to thenext step.

Figure 6.5: A warning dialog box for conversion of
structure handedness.
The unit-cell volume, V , is transformed to V ′ by
V ′ = det(P )V.

(6.2)

Therefore, the unit-cell volume changes on the transformation unless det(P ) is 1.
The entire transformation including both a rotation and an origin shift can be expressed bysingle 4 × 4 transformation matrix P, which consists of the 3 × 3 rotation matrix P , the 3 × 1
translation vector p, and the row vector o = (0, 0, 0) [50]:
(
P
P=
o

)
p
1



P11 P12 P13 p1

P21 P22 P23 p2 =.
P31 P32 P33 p3 
0
0
0
1
38

(6.3)

Then each of the following crystallographic variables, i.e., primitive translation vectors a, b,
c, reciprocal lattice vectors a∗ , b∗ , c∗ , metric tensor G, metric tensor of reciprocal lattice G∗ ,atomic coordinate X, symmetry operation W, and anisotropic atomic displacement parametersβ, are transformed as described below.
Primitive translation vectors a, b and c are transformed by P as(a′ , b′ , c′ ) = (a, b, c)P
P11 P12 P13= (a, b, c) P21 P22 P23 
P31 P32 P33(6.4)= (P11 a + P21 b + P31 c, P12 a + P22 b + P32 c, P13 a + P23 b + P33 c).
The shift of the origin, i.e., (0, 0, 0), is defined with a shift vector t as
t = (a, b, c)p
 
p1
 
= (a, b, c) p2 
p3

(6.5)

= p1 a + p2 b + p3 c.
Let A be the representation matrix of primitive translation vectors, a, b, and c, on the basisof a set of orthonormal vectors, x, y, and z:ax bx cx
A = (a, b, c) = ay by cy  .
(6.6)
az bz cz
Then the transformation by Eq. (6.4) can be rewritten as
A′ = AP .

(6.7)

Alternatively, the use of the metric tensor, G, is often preferable to the direct use of A
owing to the unique definition of G. On the other hand, the number of representations for A
is infinite because the orthonormal bases, x, y, and z, may be arbitrarily chosen. The metrictensor (matrix) of the direct lattice is defined as 
a·a a·b a·c
a2
ab cos γ ac cos β G = At A =  b · a b · b b · c  = ba cos γ(6.8)
b2
bc cos α  ,2c·a c·b c·c
ca cos β cb cos αcwhere t denotes transposition. Then, G is transformed into G′ by
G′ = (A′ )t A′ = (AP )t (AP ) = P t (At A)P = P t GP .

(6.9)

Similarly, the representation matrix of the reciprocal basis vectors a∗ , b∗ , and c∗ is defined asa∗x b∗x c∗xA∗ = (a∗ , b∗ , c∗ ) = a∗y b∗y c∗y  .
(6.10)∗∗∗
az bz cz
39

The direct and reciprocal basis vectors are related byA∗ = (A−1 )t = (At )−1(6.11)(A∗ )t A = A(A∗ )t = A∗ At = At A∗ = E,

(6.12)

andwhere E is the identity matrix:


1 0 0


E = 0 1 0  .
0 0 1
(6.13)The metric tensor of the reciprocal lattice is defined as
 


a∗2
a∗ b∗ cos γ ∗ a∗ c∗ cos β ∗a∗ · a∗ a∗ · b∗ a∗ · c∗ G∗ = (A∗ )t A∗ =  b∗ · a∗ b∗ · b∗ b∗ · c∗  = b∗ a∗ cos γ ∗b∗2b∗ c∗ cos α∗  .
c∗ · a∗ c∗ · b∗ c∗ · c∗c∗ a∗ cos β ∗ c∗ b∗ cos α∗c∗2(6.14)The transformation of G∗ into G∗ ′ is represented byG∗ ′ = (A∗ ′ )t A∗ ′ = (AP )−1 ((AP )t )−1 = P −1 ((A∗ )t A∗ )(P −1 )t = QG∗ Qt ,(6.15)

where Q = P −1 .
The coordinates x, y, and z in the direct space are transformed by the 4 × 4 transformation
matrix Q as
 
 
x′
x
 ′
 
y 
y 
(6.16)
 ′ = Q   ,
z 
z 
1
1
where
(
)
P −1 −P −1 p
Q=
o
1
(
)
Q q
=
o 1

Q11 Q12 Q13
Q22 Q23
Q=  21
Q31 Q32 Q33
0
0
0


q1

q2 

q3 
1

(6.17)= P−1 .
In short, Eq. (6.16) can be expressed as:
X ′ = QX.

(6.18)The 4 × 4 symmetry operation matrix W transforms the coordinates x, y, and z, of point X to40

f with the coordinates, x̃, ỹ, and z̃, bya symmetrically equivalent point X
  
 
x̃
W11 W12 W13 w1
x
  
 
ỹ  W21 W22 W23 w2  y 
 =
 
 z̃  W31 W32 W33 w3   z 
1
0
0
0
1
1


W11 x + W12 y + W13 z + w1
W x + W22 y + W23 z + w2 
=  21
,W31 x + W32 y + W33 z + w3 
1or in short notation,

f = WX.
X(6.19)(6.20)

f to X ′ and X
f′ , respectively:
The matrix Q transforms both X and X
f′ = W′ X ′ ,X′

QWX = W QX.

(6.21)(6.22)

Then, the symmetry operation W is transformed with the relation
W′ = QWP.

(6.23)Let Qt be the transposed matrix of Q defined in Eq. (6.17). Then, anisotropic atomic
displacement parameters, β, are transformed by


′
′
′
β11
β12
β13
 ′
′
′ 
β ′ = β12
β22
β23

′
′
′
β13 β23 β33




(6.24)Q11 Q12 Q13β11 β12 β13
Q11 Q21 Q31




= Q21 Q22 Q23  β12 β22 β23  Q12 Q22 Q32 
Q31 Q32 Q33
β13 β23 β33
Q13 Q23 Q33= QβQt .

Figure 6.6: An example of lattice transformation between primitiveand face-centered-cubic lattices.

41

Creation of superstructures and substructures
The transformation matrix is also used to convert (primitive lattice)⇄(complex lattice) (Fig.
6.6), and to create superstructures and averaged substructures. To convert a structure, youhave to select mode Update structure parameters to keep 3D geometry in the Unit cell tab of theEdit Data dialog box before opening the Unit Cell Transformation dialog box.
When the determinant of P , det(P ) is larger than 1, the transformed unit-cell becomes larger
than the original one, and when det(P ) is smaller than 1, the transformed unit-dell becomes
smaller than the original one. In such cases, a dialog box appears to confirm whether you intend
to change the unit cell volume (Fig. 6.7).

Figure 6.7: A dialog box for confirmation of unit celltransformation.
When a rotation matrix with det(P ) > 1 is specified, or the transformed unit cell contains
additional lattice points even when det(P ) = 1, a dialog box appears to ask you how to convert
the structure (Fig. 6.8). There are the following three options:• “Add new equivalent positions to a list of symmetry operations”• “Search atoms in the new unit cell and add them as new sites”• “Do nothing”

Figure 6.8: A dialog box showing options for how tocreate a larger unit cell.
In the first and second options, the structural geometry of the original data will remainunchanged. On the other hand, on selection of the third option, some atoms in the new unit cell
will be missing. On selection of the first option, a superstructure will be created by examining thefollowing equation to find additional symmetry operations W′ having a translational component
in between (0, 0, 0) and (1, 1, 1):




′
′
′
W11
W12
W13
w1′
W11 W12 W13 w1 + nx
 ′



′
′
W22
W23
w2′ 
W
W21 W22 W23 w2 + ny 
W′ =  21
=
Q
 P,


′
′
′
W31
W31 W32 W33 w3 + nz 
W32
W33
w3′ 
(6.25)
0
0
0
1
0
0
0
1
(nx , ny , nz = 0, ±1, ±2, . . . ).
42

On selection of the second option, a superstructure will be created by examining the following
equation to find additional sites lying in between (0, 0, 0) and (1, 1, 1):
 


x′
x + nx
 ′


y 
 y + ny 
(nx , ny , nz = 0, ±1, ±2, . . . )(6.26)
 ′ = Q .
z 
 z + nz 
1
1
Note that the transformed new unit-cell should be symmetrically consistent with the spacegroup currently in use. Otherwise, reduce symmetry to P 1 by clicking [Remove symmetry] before
creating a superstructure, and input a new space group after the superstructure has been created.
If det(P ) < 1, the same position may result from two or more sites. In such a case, the redundantsites can be removed by clicking [Remove duplicate atoms] button in the Structure parameters tab(see page 48).

6.2.7

Magnetic Structures

VESTA fully supports 1651 magnetic space groups. Check the “Magnetic structure” check box
to use magnetic space groups. Then, the title of the Setting list box changes to BNS Setting,which shows a list of magnetic space groups for a selected space group. There are two types ofnotations of magnetic space groups: the Belov–Neronova–Smirnova (BNS) notation [51] and the
Opechowski–Guccione (OG) notation [52]. VESTA uses the BNS notation because symmetry
operations of the BNS notation are described with respect to the magnetic unit-cell with translational parts never exceeding 1. Atomic coordinates, displacement parameters, and occupancies
of a magnetic structure are specified exactly the same way as conventional structure (see Section
6.3). Magnetic moments of atoms are specified in the Vectors dialog box (see Section 9.1).

Figure 6.9: The Unit cell page in the Edit Data dialog box, withthe “Magnetic structure” option checked.

43

6.3

Structure Parameters

The Structure parameters tab in the Edit Data dialog box (Fig. 6.10) is used to input and edit
parameters related to atomistic structures. The following structural information is input oredited by using text boxes at the upper half of the page:• [Symbol...]: Symbol of an element (up to two characters).
• {Label}: Site name (up to six characters).
• {Charge}: Formal charge (oxidation number; optional)• {x}, {y}, and {z}: Fractional coordinates, x, y, and z (dimensionless).
• {s.u.(x)}, {s.u.(y)}, and {s.u.(z)}: Standard uncertainties of the fractional coordinates(default values: zero).
• {Occ}: Occupancy (dimensionless; optional).
• {B} or {U}: Isotropic atomic displacement parameter, B or U (in Å2 ; optional).
• {U11}, {U22}, {U33}, {U12}, {U13}, and {U23}: Anisotropic atomic displacement parameters, Uij (in Å2 , optional).
• {beta11}, {beta22}, {beta33}, {beta12}, {beta13}, and {beta23}: Anisotropic atomic displacement parameters, βij (dimensionless; optional).

Figure 6.10: Structure parameter page in the Edit Data dialog box.
A list of sites in the asymmetric unit is shown at the lower half of the page. Text boxes
are disabled when no site is selected in the list. When an item in the list is selected, the text
boxes are updated to show data relevant to the selected site. In-place editing of a list item isalso supported, as Fig. 6.10 shows.
44To add a new site, click the [New] button at first, and edit texts in the text boxes. A
modification in a text box is applied to the selected site immediately after the focus (caret)
has moved to another text box or another GUI control. In the case of text boxes for numericalvalues, modifications will be discarded if an input text is not a valid numerical value, or if thetext box is empty. Therefore, if you have accidentally changed a value in a text box, the originalvalue can be restored by erasing the entire text in the text box before moving the focus toanother GUI control.
To delete a site, select an item in the list, and click the [Delete] button or press the <Delete>
key. Clicking the [Clear] button will delete all the sites in the list.

6.3.1

Symbols and Labels

Up to two characters are input as an element symbol while up to nine characters are input as alabel of a site. Click the [Symbol…] button to select an element symbol from the Periodic Table
dialog box (Fig. 6.11).

Figure 6.11: Periodic Table dialog box.

6.3.2

Formal charge

Strictly speaking, formal charges are not structure parameters. They are, however, used toestimate a bond length from a bond valence parameter [38, 39, 40] (see 11.4.3), evaluate charge
distribution from bond lengths [35, 36, 37] (see 11.4.3), and calculate electrostatic site potentials
and a Madelung energy by the Fourier method (see 14.5).

6.3.3

Fractional coordinates

For special positions, input fractional numbers, e.g., 1/4, 1/2, and 1/3, or a sufficient numberof digits should be given, e.g., 0.333333 and 0.666667.
When displacement ellipsoids are drawn from anisotropic atomic displacement parametersrefined with RIETAN-FP [12], fractional coordinates corresponding to the first equivalent position described in International Tables for Crystallography, volume A [30] for each Wyckoff
position have to be entered. For example, input not (1/2, 0, z) but (0, 1/2, z) for a 4i site inspace group P 4/mmm (No. 123).
45

Figure 6.12: Crystal structure of Cs6 C60 [53], with C60 represented by translucent polyhedra. A virtual site X with an
occupancy of g = 0 was added at the center of C60 . Polyhedraof C60 were created by specifying X–C bonds in the Bonds dialog box. C–C bonds are also searched by a “Search molecules”
mode to represent polyhedral edges by solid cylinders. See
chapter 8 for details in creating bonds and polyhedra.

6.3.4

Occupancy

The occupancy is unity for full occupation and zero for virtual sites. If the occupancy of a site isless than unity, atoms occupying there are displayed as circle graphs for occupancies. If unicolorballs are preferred to bicolor ones, change the occupancy to unity for convenience.
If the occupancy of a site is zero, the site is treated as a virtual site that is not occupied
by any atoms in the real structure. Neither the virtual sites nor bonds connecting them aredisplayed on the screen. Virtual sites are used to visualize, for example, cage structures ofporous crystals as solid polyhedra without creating a large number of unnecessary bonds (Fig.
6.12).

6.3.5

Atomic displacement parameters

The Debye–Waller factor, Tj (h), which is often referred to as the temperature factor, is included
in formulae for structure factors, F (h), to represent the effect of static and dynamic displacementof atom j (see Eqs. 14.8 and 14.11). The displacement of atom is formulated in two different
ways: anisotropic and isotropic atomic displacement.
Anisotropic models
The anisotropic Debye–Waller factor, T (h), is defined as[()]
T (h) = exp −2π 2 h2 a∗2 U11 + k 2 b∗2 U22 + l2 c∗2 U33 + 2hka∗ b∗ U12 + 2hla∗ c∗ U13 + 2klb∗ c∗ U23[ ()]= exp − h2 β11 + k 2 β22 + l2 β33 + 2hkβ12 + 2hlβ13 + 2klβ23 ,(6.27)
46

where a∗ , b∗ , c∗ , α∗ , β ∗ , and γ ∗ are reciprocal lattice parameters.
The type of anisotropic atomic displacement parameters must be specified in list box {Anisotropic}:‘None’ to omit anisotropic atomic displacement parameters, ‘U’ to input Uij (U11 , U22 , U33 , U12 ,U13 , and U23 ), and ‘beta’ to input βij (β11 , β22 , β33 , β12 , β13 , and β23 ). Using this list box, we
can convert Uij into βij and vice versa.
Anisotropic atomic displacement parameters defined in different ways must be converted into
Uij or βij defined above.
On refinement of βij ’s by the Rietveld method with RIETAN-FP [12], βij ’s for each site haveto satisfy linear constraints imposed on them [54, 55].
Isotropic models
The isotropic Debye–Waller factor, T (h), is given by[() ]sin θ 2T (h) = exp −Bλ()
B= exp − 24d()
2π 2 U= exp − 2,d(6.28)

where B and U are the isotropic atomic displacement parameters (U = B/8π 2 ), θ is the Bragg
angle, λ is the X-ray or neutron wavelength,⟨ ⟩ and d is the lattice-plane spacing. B and U are
related to the mean square displacement, u2 , along the direction perpendicular to the reflection
plane with⟨ ⟩B = 8π 2 U = 8π 2 u2 .
(6.29)For example, a B value of 3 Å2 corresponds to a displacement of about 0.2 Å.
The type of isotropic atomic displacement parameters must be specified in list box {Isotropic}.
Using this list box, we can convert U into B and vice versa.
Isotropic atomic displacement parameters defined in different ways must be converted into
B or U defined above.
In crystallographic sites for which anisotropic atomic displacement parameters, Uij or βij ,have been input, equivalent isotropic atomic displacement parameters, Beq or Ueq , are calculated
from Uij , a∗ , b∗ , c∗ , and the metric tensor G [56, 57]:
Beq = 8π 2 Ueq(6.30)with1∑ ∑Uij a∗i a∗j ai · aj
3 i j
1[
= U11 (aa∗ )2 + U22 (bb∗ )2 + U33 (cc∗ )23]+ 2U12 a∗ b∗ ab cos γ + 2U13 a∗ c∗ ac cos β + 2U23 b∗ c∗ bc cos α .

Ueq =(6.31)

Beq and Ueq are regarded as B and U in the Structure parameters tab of the Edit Data dialog
box after reopening it.

6.3.6

Importing structure parameters

Structure parameters can be imported from a file storing structure parameters by clicking the[Import…] button at the bottom right of the Structure parameters page. Then, select a file witha format supported by VESTA in the file selection dialog box.
47

Option “Link” specifies the manner of outputting current structure data in a file, *.vesta,
with the VESTA format. Structure data are usually recorded in *.vesta. On the other hand,for volumetric data, relative paths (including a file name) of data files are recorded in *.vesta
instead of recording the volumetric data directly in it. When option “Link” is checked, structural
data are also recorded as the relative path of the data file. Then, even if the structural-data fileis changed after saving *.vesta, the changes are reflected in VESTA when *.vesta is reopened.
This option is useful in preparing a file, *.vesta, with the VESTA format as a template file forsetting objects and overall appearances. This option disables text boxes and list boxes in the
Structure parameters tab to prohibit users from editing structure data because any modifications
to structure data will not be saved to a file when this option is enableld.

6.3.7

Removing duplicate atoms

When the space group is changed to that with higher symmetry, or
when the unit cell is transformed to a smaller one (see 6.2.6), thesame atomic position may result from two or more sites. In such acase, the redundant sites can be removed by clicking the [Remove
duplicate atoms] button. Then, a dialog box (right figure) opens,prompting you to input a threshold of distances between two atoms to be regarded as a single
site. The threshold value is input in the unit of Å. Increasing the threshold value enablesus, for example, to extract an average structure from a large cell calculated by computational
simulations.

6.4

Volumetric Data

To input volumetric data for drawing isosurfaces with or without surface coloring, click theVolumetric data tab in the Edit Data dialog box (Fig. 6.13):

Figure 6.13: Volumetric data page in the Edit Data dialog box.

48

6.4.1

Volumetric data to draw isosurfaces

VESTA enables us to deal with more than two volumetric data sets. Clock [Import...] to selecta file in the file selection dialog box. Only files with extensions of supported formats are visible
in the file selection dialog box. After selecting a volumetric data file, a Choose operations dialog
box appears (Fig. 6.14).

Figure 6.14: A dialog box to choose operations for volumetric data.

Operation
In the Operation radio box, one of the following five data operations can be selected in addition
to conversion of data units.
• “Add to current data”• “Subtract from current data”• “Replace current data”• “Multiply to current data”• “Divide current data by new data”“Multiply to current data” is convenient when squaring wave functions to obtain electron densities(existing probabilities for electrons). The last two options are not displayed when no volumetricdata are contained in the current data. In such a case, the first and third options have also thesame effect.
Convert the unit
In the Convert the unit radio box, the unit of data can be converted from Å−3 to bohr−3 , andvice versa. Select option “Other factor” to multiply the data by an arbitrary factor. Then, click[OK] to import data. Repeating the above procedures allows you to import multiple data, as
exemplified in Fig. 6.15.

6.4.2

Volumetric data for surface coloring

Volumetric data for surface coloring can be imported in the same manner as with data forisosurfaces. A typical application of surface coloring is to color isosurfaces of electron densities
according to electrostatic potentials.
49

A

B

C

Figure 6.15: Distributions of electron densities and effective spin densities in an O2 molecule.
(A) up-spin electron densities, ρ↑ , (B) down-spin electron densities, ρ↓ , and (C) effective spin
densities, ∆ρ = ρ↑ − ρ↑ , calculated with VESTA. Both ρ↑ and ρ↓ were calculated with DVSCAT−3[58]. Isosurface levels were set at 0.01a−3
0 in (A) and (B), and at 0.001a0 in (C). where a0 is
the Bohr radius.
Interpolation
The spacial resolution of volumetric data can be increased using the algorithm of cubic splineinterpolation. The interpolation level is specified in the {Interpolation} text box.

6.5

Crystal ShapeThe Crystal Shape tab in the Edit Data dialog box (Fig. 6.16) is used to input and edit theexternal morphology of crystals. To add a new crystal face, click the [New] button at first, input
Miller indices hkl, and the distance from the origin, (0, 0, 0). The distance may be specified
in the unit of either its lattice-plane spacing, d, or Å. The color and opacity of the face are
specified either as four integers ranging from 0 to 255, or using a color selection dialog box anda slider, which are opened after clicking the square buttons on the right side of the text boxes.
When option “Apply symmetry operations” is checked, all the symmetrically equivalent faces areautomatically generated.
To delete a face, select an item in the list, and click the [Delete] button or press the <Delete>
key. Clicking the [Clear] button will delete all the faces in the list.

50

Figure 6.16: Crystal shape page in the Edit Data dialog box.

A

B

Figure 6.17: Crystal morphologies of anatase-type TiO2 crystals. In the inner crystalin (B), distances from the origin are set at 3.5 Å for both {101} and {103}. In theouter crystal, distances from the origin are set at 3.8 Å for {101} and 5 Å for {103}.

51

6.5.1

ExamplesFigure 6.17 shows morphologies of anatase-type TiO2 crystals composed of {101} and {103} faces. To visualize crystal morphologies, make sure that specified faces compose aclosed polyhedron. For example, if only {100} is specified fora tetragonal crystal, it has to form a prismatic shape having
an infinite length along the c axis. In this case, no objects
are visible in the Graphics Area.
To adjust relative sizes of faces, edit the distance fromthe origin to the face. In general, the relative area of the facedecreases with increasing distance as Fig. 6.17B illustrates.
When the distance of {103} faces is set at a larger valueof 5 Å, these faces become smaller with respect to {101}faces. The origin of the crystal shape is just the same asthat of a structural model, i.e., a position with the fractional
coordinate of (0, 0, 0) is placed at the center of the crystal
shape.
When option “Apply symmetry operations” is unchecked,
faces that do not follow space-group symmetry may be inserted (Fig. 6.19A). If multiple faces with the same indices
are specified, the face with the smallest distance from theorigin is visible (Fig. 6.19B, C). These features make it
possbile to represent crystal habits of real crystals.
To display indices of faces as demonstrated in Fig. 6.17B,
select the Objects tab in the Side Panel (Fig. 6.18, a), choose“Shape” in the list of phases at the upper half of the page(Fig. 6.18, b), and then click check boxes labeled as “L”(Fig. 6.18, c). See also section 12.2 for the function of the
Objects tab.

52

a

b

c

Figure 6.18: The Objects tabof the Side Panel showing a listof crystallographic faces.

A

B

C

Figure 6.19: Crystal morphologies of anatase having faces that do not follow symmetry operations. (A) Option “Apply symmetry operations” is unchecked for a (1̄03) face. (B) The distancefrom the origin was set at 3.8 Å for {101} and 5 Å for {103}, and a (1̄03) lattice plane wasinserted by setting a distance from the origin at 3.8 Å. (C) A (1̄03) face, which overlaps withthe (1̄03) lattice plane in (B), was further added.

53

Chapter 7

OVERLAYING MULTIPLE DATA
To display multiple-phase data in a single Graphics Area, set positioning and orientation of eachphase after clicking the Phase tab in the Edit Data dialog box (Fig. 7.1). The positioning andorientation of a phase are specified relative to another phase or the Cartesian coordinate systemthat is commonly used as internal representation of all phases. By default, the origin, (0, 0, 0),of a phase is placed at that of the internal coordinate system. The orientation of a phase is set
such that the [1 0 0] axis of a phase is parallel to the x axis of the internal coordinate systemwith the [0 1 0] axis parallel to the x–y plane.
To avoid the circular reference of phases, positioning and orientation must be set in descending order of the phase list.

7.1

Positioning of Phases

At first, select a phase to edit in the phase list (Fig. 7.1, a). In the Positioning frame box, selectanother phase (layer) which is used as a reference of positioning (Fig. 7.1, b). Layer 0 denotes

a

b
c

e

d

f

g
h

Figure 7.1: Phase page in the Edit Data dialog box.
54

the internal Cartesian coordinate system. Then, input (x, y, z) coordinates of the selected andreference layers; they are exactly overlapped with each other (Fig. 7.1, c).

7.2

Relative Orientation of Phases

Select a phase to edit in the phase list, and select ID’s of another phase (layer) in the Orientation
frame box (Fig. 7.1, d). As described above, layer 0 represents the internal Cartesian coordinate
system. A set of a lattice vector and a reciprocal-lattice vector is specified for both of the current
and reference layers. When the first vector is specified by a vector, [u v w], in the direct space,the other one is specified by a reciprocal-lattice vector, [h k l]∗ , and vise versa. The direct- andreciprocal-lattice vectors must be perpendicular to each other; in other words, the lattice vector,[u v w], must be parallel to the lattice plane, (h k l). Thus, the following condition must be
satisfied:hu + kv + lw = 0.
(7.1)
The type of the first vector is set by a pull down menu (Fig. 7.1, d, g). If a vector of thecurrent layer is parallel to that of the reference layer, select ∥ in the pull down menu (Fig. 7.1,f). If the two vectors are perpendicular to each other, select ⊥ in the pull down menu. Theninput indices in text boxes (Fig. 7.1, h).

7.3

ExamplesFigure 7.2 shows two kinds of organic molecules approaching a surface of calcite-type CaCO3 .
Figure 7.3 illustrates graphene on a (111) surface of Ir [59]. An example of overlaying isosturactural crystals is displayed in Fig. 7.4.

Figure 7.2: Molecules of L-aspartic acid and 2,4,6-trichlorobenzoic acid near a (101̄4) surface of
calcite (CaCO3 ) having a [441̄] step.

55

Figure 7.3: A moire pattern of graphene on the (111) surface of Ir.

Figure 7.4: Crystal structures of Ca-olivine (Ca2 SiO4 ) and isostrucuralmonticellite (CaMgSiO4 ) overlapped with each other.

56

Chapter 8

CREATING BONDS AND
POLYHEDRA
To search for bonds and atoms connected by them, and to create coordination polyhedra, choose
the “Edit” menu ⇒ “Bonds…”. At the top of the Bonds dialog box (Fig. 8.1), select a phase toedit. A list of bond specifications is shown at the lower half of the dialog box. GUI controls in
the Search bonds and atoms frame box are used to edit a bond specification. They are disabled
when no bond specification is selected in the list.
To add a new bond specification, click the [New] button at first, select atoms relevant to thebond, and edit minimum and maximum lengths. Modifications in the GUI control are applied to
the list either immediately or after the focus (caret) has moved from a text box to another GUI
control. To delete a bond specification, select it in the list, and then click the [Delete] button
or press the <Delete> key. Clicking the [Clear] button deletes all the bond specifications in thelist. Press the [OK] or [Apply] button to reflect editing results in the Graphics Area.

Figure 8.1: Bonds dialog.

57

8.1

Specifications of Searching for Bonds

8.1.1

Search mode

Bonds and, in turn, atoms connected by them are searched in one of the following three searchmodes:• “Search A2 bonded to A1”A2 atoms bonded to A1 atoms are searched on the basis of user-specified minimum andmaximum interatomic distances: {Min. length} and {Max. length}.
• “Search atoms bonded to A1”
All the atoms bonded to A1 atoms are searched on the basis of user-specified {Min. length}and {Max. length} regardless of the species of the A2 atoms.
• “Search molecules”
All the pairs of atoms are searched on the basis of user-specified {Min. length} and {Max.
length}. Neither A1 nor A2 is specified in this option. This mode best meets searching foratoms and bonds in molecular crystals.

8.1.2

Boundary mode

The Boundary mode specifies the extent of searching for atoms. Basically, atoms and bonds aresearched within a drawing boundary defined by ranges along x, y, and z axes, and by optional
cutoff planes (see chapter 10.1). However, on selection of a proper Boundary mode, atoms andbonds outside the drawing boundary are also searched so that all the atoms in coordination
polyhedra or molecules are included.
• “Do not search atoms beyond the boundary”
Only atoms within the drawing boundary are searched.
• “Search additional atoms if A1 is included in the boundary”
All the A2 atoms bonded to A1 atoms are searched even if A2 atoms are placed outside thedrawing boundary. If the A2 and A1 atoms are, respectively, located inside and outside
the boundary, the A1 atom is not searched. This mode is the default for the “Search A2
bonded to A1” and “Search atoms bonded to A1” modes.
• “Search additional atoms recursively if either A1 or A2 is visible”
All the pairs of A1 and A2 atoms are searched if either A1 or A2 has already been found.
When using this mode in inorganic crystals, beware lest bonds are infinitely connected.
This mode is the default for the “Search molecules” mode.

8.1.3

Options• “Search by label”
On selection of this option, a pair of atoms is specified by labels of sites. When this option
is unchecked, a pair of atoms is specified by elemental symbols.
• “Show polyhedra”
This option specifies that A1 atoms are central atoms of coordination polyhedra. This
option has no effect on bond specifications in the “Search molecules” mode because no
coordination polyhedra are searched in that mode.
58

8.1.4

A pair of atoms

Atoms A1 and A2 may be specified by entering either elemental symbols or site names. The{A1} and {A2} list boxes list elemental symbols of atoms if option “Search by label” is unchecked(default). On the other hand, {A1} and {A2} list site labels if option “Search by label” is checked.
The minimum and maximum bond lengths, {Min. length} and {Max. length}, are input inthe unit of Å. Though {Min. length} is usually set at zero, it may be positive when dealing witha disordered structure whose split-atom model gives seemingly very short bonds.

8.2

Operating Instructions

8.2.1

Creating coordination polyhedra

To build up coordination polyhedra, either the “Search A2 bonded to A1” or “Search atoms
bonded to A1” mode should be selected. The central atoms of the coordination polyhedra mustbe specified as A1. In the “Search molecules” mode, no coordination polyhedra are createdbecause VESTA does not have any information about central atoms. In the first two bondsearch modes, the Boundary mode 2 (“Search additional atoms if A1 is included in the boundary”)
enables us to search for all the A2 atoms bonded to A1 atoms so that no coordination polyhedra
are truncated even if A2 atoms lie outside the boundary. A1 atoms lying outside the boundary
are never searched.
To search for additional atoms bonded to A2 atoms, use the Boundary mode 3 (“Search
additional atoms recursively if either A1 or A2 is visible”). For example, if hydrogen atoms arecoordinated to some A2 atoms, those hydrogen atoms can be searched even if A2 atoms lie
outside the boundary (Fig. 8.2).

A

B

Figure 8.2: Crystal structure of δ-AlOOH, a high-pressure modification of aluminum oxidehydroxide, with displacement ellipsoids at a 99 % probability level [60]. The structures weredrawn in a coordinate range from (0, 0, 0) to (1, 1.5, 1). O–H bonds were searched (A) in the“Search additional atoms if A1 is included in the boundary” mode and (B) in the “Search additional
atoms recursively if either A1 or A2 is visible” mode. In (A), some H atoms were omitted when O
atoms lay outside of the boundary specified in the Boundary dialog box. On the hand, all the Hatoms bonded to O atoms displayed in the screen were searched in (B).

59

A

B

Figure 8.3: Crystal structure of anthraquinone [61]. Bonds are searched in the “Search molecules” mode with the boundary modes (A) “Do not search atoms beyond the boundary” and (B)“Search additional atoms recursively if either A1 or A2 is visible”. In both cases, the bounding box
has a range of coordinates from (0, 0, 0) to (1, 1, 1).

8.2.2

Searching for molecules and clusters

The “Search molecules” mode is similar to 406 instruction in ORTEP-III1 [62], i.e., “reiterative
convoluting sphere of enclosure add.” This mode is generally used in combination with theBoundary mode 3 to avoid some atoms in molecules being “truncated” (omitted) even if theylie outside the boundary (Fig. 8.3). In this mode, neither A1 nor A2 is specified; only {Min.
length} and {Max. length} are input.
A maximum distance of 1.6 Å is appropriate in typical organic compounds containing H,
C, N, O, and F atoms having covalent radii of 0.32, 0.77, 0.74, 0.66, and 0.72 Å, respectively.
Inputting a larger value may generates unreal bonds. To search for atoms and bonds in moleculesand clusters containing larger atoms such as P, S, Cl, and Br having covalent radii of 1.10, 1.04,
0.99, and 1.14 Å, respectively, add bond specifications in the “Search A2 bonded to A1” mode in
combination with the Boundary mode 3 (Fig. 8.4).

8.2.3

Applications of the “Search molecules” mode to inorganic crystals

In general, combination of the “Search molecules” mode and the Boundary mode 3 is unsuitablefor inorganic compounds or metals because a network of bonds may continue infinitely in theirstructures. In practice, an infinite number of atoms must be searched in such a case. Nevertheless, VESTA actually searches and shows a huge number of atoms and bonds in a finite range
1

http://www.ornl.gov/sci/ortep/doc/i400.html

60Figure 8.4: Crystal structure of tetrakis(di-4-pyridylsulfane)dinitratocopper(II) [63]. Bonds aresearched in the “Search molecules” mode with a maximum distance of 1.6 Å in combination withthe “Search A2 bonded to A1” mode for Cu–N and S–C bonds. The Boundary mode 3 was used.
because searching within a certain area ensures that all the atoms contained in molecules in theboundary are searched in cases of periodic structures.
There are exceptions where the combination of such modes is well-suited to search for bonds
in inorganic crystals, e.g., searching for O−H bonds. Usually, no bonds are shorter than O−H
ones; thus, the use of this mode is safe with a small value of {Max. length}. The maximum bondlength of ca. 1.1 Å leads to a search for all the H atoms bonded to O atoms in the Graphics Area.

8.2.4

Searching for hydrogen bonds

To display X−H· · · Y hydrogen bonds, select the “Search A2 bonded to A1” mode in the Searchmode frame box, set A1 at H and A2 at Y, and input the minimum and maximum distancesof H· · · Y bonds in {Min. length} and {Max. length}. Styles of the H· · · Y bonds can be set at
Objects tab in the Side Panel.

8.2.5

Visualizing cage-like structures

To represent cage-like voids in porous crystals by a polyhedral model, put a virtual site at thecenter of a cage (see page 46) and add a bond specification between the virtual site and atoms
at corners of the cage. Then, to visualize framework structures with solid bonds, add a bondspecification between the corner atoms. If Y atoms are bonded to X atoms at the corners, add
X–Y bonds. All of these bond specifications should be given with the Boundary mode 2 so thatneither atoms nor bonds in cages displayed are omitted (Fig. 8.5).

61

Figure 8.5: Crystal structure of the tetragonal variant of chibaite represented by a polyhedral model [64].

62Chapter 9

ADDITIONAL OBJECTS
9.1

Vectors on Atoms

To attach vectors (arrows) to part of atoms, choose “Edit” menu ⇒ “Vectors…”. These arrows
serve to represent magnetic moments or directions of static and dynamic displacements of atoms.
At the top of the Vectors dialog box (Fig. 9.1), select a phase to edit. When option “Preview”
is checked (default), changes in the dialog box are reflected in the Graphics Area in real time.

Figure 9.1: Vectors dialog box showing a list of atoms in SrFeO2 [65], with the atom
list filtered by elements. Atoms selected in the dialog box are highlighted in theunderlying Graphics Area displaying the magnetic structure of SrFeO2 .
63

Vectors can be assigned to either crystallographic sites or individual atoms in the Graphic
Area. When a vector is attached to a crystallographic site, all of its symmetrically equivalentatoms will bear the same vector, which is properly rotated in accordance with symmetry operations applied to the atoms. When a vector is assigned to each atom, only that atom will have thevector whereas no other symmetrically equivalent atoms will bear the vector. Multiple numbersof vectors can be attached to atoms and sites, and a vector can be attached to more than two
atoms and sites. The length of arrows, which are vectors rendered in the Graphics Area, is scaledby moduli of the vectors multiplied by the input value of the {Scale factor for modulus}. For
more details about the scaling of vectors, see 9.1.1 and Fig. 9.4.

9.1.1

Creation and editing of a vector

At the right pane of the Vectors dialog box, all the vectors are listed with the following threebuttons placed above the list (Fig. 9.1):[New]: Add a new vector.
[Edit]: Edit the selected vector.
[Delete]: Delete the selected vector.
The [Edit] and [Delete] buttons cannot be clicked unless a vector in the list has been selected.
Click the [New] button to create a new vector. Select a vector in the list of vectors, and click
the [Edit] button to edit it. Then, a dialog box appears to edit properties of the selected vector(Fig. 9.2).

Figure 9.2: A dialog box to create or edit a vector.
Two types of vectors can be specified: {Axial vector} and {Polar vector}. Because these twodiffer from each other in the mode of applying symmetry operations, the vector type affects only
vectors attached to crystallographic sites. When a vector is attached to individual atoms, nosymmetry operation is applied to the vector, with no differences between the two types of thevectors.
Typical examples of axial and polar vectors are magnetic moment, µ, and electrostatic polarization vector, p, respectively. The magnetic moment is induced by tiny electrical currents
resulting from electrons moving around the nucleus of an atom. The direction of the moment vector is determined by that of the current. For example, counter-clockwise and clockwise currents
generate upward and downward moment vectors, respectively. A mirror plane perpendicular to
the moment vector does not change the current direction, while a mirror plane parallel to themoment vector inverses the current direction. As a result, magnetic moments are transformed
by a mirror plane as Fig. 9.3A illustrates. In the case of the electrostatic polarization vector,
64

A

B
μ

p
Mirror plane

Mirror plane

Figure 9.3: Results of applying a mirror operation to (A) magnetic moments µ and (B) polarization vectors pon the other hand, a mirror plane perpendicular to the moment vector inverses the polarization
vector, while a mirror plane parallel to the polarization vector does not change the polarization
vector (Fig. 9.3B). To be more specific, p is transformed to p′ by a 3 × 3 operator matrix, M ,asp′ = M p(9.1)µ′ = P M µ,(9.2)

while µ is transformed to µ′ aswhere P is the determinant of M and referred to as the “parity” of the operator M . Note thatthe term P M is a scalar-matrix multiplication.
Aside from conventional symmetry operations M , there is another important symmetry
element for vectors, i.e. time reversal. In view of time reversal, the current direction around an
atom is changed, with a result that the direction of µ is reversed. Let the time reversal be T(= 1 or −1), then the transformation of µ is represented byµ′ = T P M µ.

(9.3)

For the polarization vector, time reversal has no effect at all.
In the Edit a Vector dialog box, three different representations of vector components areshown: {Lattice vector notation (u, v, w)}, {Modulus along crystallographic axes}, and {Cartesian
vector notation (x, y, z)}. Editing one representation of the vector components updates the restof the representations as well as the {Modulus} of the vector. After the {Modulus} has beenedited, vector components are linearly scaled.
When the “Penetrate atoms” check box is on (default), the length of an arrow (vector drawn
in the Graphic Area) is doubled with its center placed at the center of an atom (Figs. 9.4A and
9.4B). When this option is off, one end of an arrow is placed at the center of an atom so that
it appears only one side above the atom sphere (Figs. 9.4C and 9.4D).
When option “Add atom radius to the vector modulus” is checked, the length of an arrowappearing above an atom sphere is linearly scaled by the vector modulus, regardless of theradius of the atom sphere (Figs. 9.4B and 9.4D). Even if a vector with a very small modulus is
attached to an atom having a very large sphere, the arrow will not be hidden by the atom sphere.
If this option is disabled (default behavior), the arrow length including the part hidden by anatom sphere is linearly correlated to the vector modulus (Figs. 9.4A and 9.4C); consequently,
a very short arrow may be completely hidden by the atom sphere.
65

A

C

s×μ

s×μ

B

s×μ

D

s×μ

Figure 9.4: Effects of two options for vector styles. Option “Penetrateatoms”: on (A, B) and off (C, D), and option “Add atom radius to the vector
modulus”: off (A, C) and on (B, D). When the latter option is on, thelength of an arrow appearing above an atom sphere is linearly scaled by µ
multiplied by the {Scale factor for modulus}, s.

9.1.2

Attachment of vectors to crystallographic sites

To attach a vector to crystallographic sites, select the Crystallographic sites tab at the left paneof the Vectors dialog box. Then, select sites in the left pane, select a vector in the right pane,and click the [<< Set] button. In a similar manner, select crystallographic sites in the left pane,and click the [>> Remove] button to detach a vector from the sites.

9.1.3

Attachment of vectors to individual atoms

To attach a vector to individual atoms in the Graphics Area, select the Individual atoms tab at
the left pane of the Vectors dialog box. Select atoms from a list in the left pane or by clicking
atoms in the Graphics Area. Then, select a vector in the right pane of the Vectors dialog box,
and click the [<< Set] button. In a similar manner, select atoms in the left pane, and click the[>> Remove] button to detach a vector from the atoms. When atoms in the list in the left pane
are selected, the corresponding ones are highlighted in the Graphics Area, and vice versa.

9.2

Lattice Planes

To insert lattice planes in structural models, or to add 2D slices of volumetric data in 3D images,
choose “Edit” menu ⇒ “Lattice Planes…”. At the top of the Lattice Planes dialog box (Fig. 9.5),
select a phase to edit. A list of lattice planes is shown at the lower half of the dialog box. Someof buttons and text boxes are disabled when no lattice plane is selected in the list. On selectionof an item in the list, the text boxes are updated to show data relevant to the selected latticeplane. When option “Preview” is checked (default), changes in the dialog box are reflected in
the Graphics Area in real time.
To add a new lattice plane, click the [New] button at first, input Miller indices hkl, andthe distance from the origin, (0, 0, 0). The distance may be specified in the unit of either its
lattice-plane spacing, d, or Å. The color and opacity of the lattice plane is specified either asfour integers ranging from 0 to 255 or from a color selection dialog box, which is opened after
clicking the square button on the right side of the text boxes.
To delete a lattice plane, select an item in the list, and then click the [Delete] button or press
the <Delete> key. Clicking the [Clear] button deletes all the lattice planes in the list.
66

Figure 9.5: Lattice Plane dialog box.

Figure 9.6: A section of a difference Fourier map inserted in a ball-and-stickmodel of δ−AlOOH [60]. The maximum in the section corresponds to a positionof an H atom, which is not included in the structural model.

9.2.1

Appearance of lattice planes

When volumetric data are included in the current data, lattice planes are colored according tovolumetric data on the lattice planes. Saturation levels of colors are specified at Sections pagein the Properties dialog box (Fig. 9.6; see 12.1.6). When only structural information is includedin the current data, lattice planes are drawn with colors specified in this dialog box. To draw
lattice planes with specified colors for data having both structural and volumetric information,
volumetric data should be deleted at the Edit Data dialog box (see 6.4).
Material settings of lattice planes, i.e. specular color and shininess are input in the Material
67

frame box. Drawing of edges for lattice planes can be controlled in the Edge frame box. Thesesettings are common to all the lattice planes.

9.2.2

Calculate the best plane for selected atoms

To calculate the best plane for a group of atoms (Fig. 9.7), add a new lattice plane at first,
select three or more atoms in the Graphics Area, and press [Calculate the best plane for the selected
atoms] button.

Figure 9.7: The best plane calculated for an aromatic ring in anthraquinone [61].

68Chapter 10

DEFINING DRAWINGBOUNDARIES AND VIEW
DIRECTIONS
10.1

Drawing Boundaries

To change the size of a drawing boundary (box), select the [Boundary] button in the Side Panel,or choose “Objects” menu ⇒ “Boundary…”. Then, the Boundary dialog box appears as Fig. 10.1
illustrates. This dialog box can also be opened with a keyboard shortcut of <Ctrl> + <Shift>+ <B>. At the top of the dialog box, select a phase to edit. Press the [OK] or [Apply] button
to reflect editing results in the Graphics Area.
Changing the boundary regenerates all the atoms in the Graphics Area and reset all theproperties of objects to default values. Selected or hidden states of atoms, bonds, and polyhedra
are reset to the default states.

Figure 10.1: Boundary dialog box.

69

Figure 10.2: Electron density distribution determined for D-sorbitol[66] by the maximum-entropy method from synchrotron X-ray powder
diffraction data. Drawn in ranges from (0, 0, 0) to (1, 1, 1) with acutoff plane (1 1 0).

10.1.1

Ranges of fractional coordinates

Drawing boundaries are fundamentally specified by inputting ranges of fractional coordinatesalong x, y, and z axes.

10.1.2

Cutoff planes

In addition to ranges of fractional coordinates, we can further specify “cutoff planes,” as exemplified in Fig. 10.2. After atoms, bonds, and isosurfaces within the x, y, and z ranges have been
generated, those lying outside of the cutoff planes are excluded. Even though atoms, bonds, andpolyhedra can be hidden by another procedure described in 11.4, this is the only way to remove
part of isosurfaces and sections. This feature is, therefore, particularly useful for visualizing 2D
distribution of volumetric data on lattice planes in addition to isosurfaces. Each cutoff plane is
specified as Miller indices hkl and a distance from the origin, (0, 0, 0). The distance of a cutoff
plane from the origin may be specified in the unit of either its lattice-plane spacing, d, or Å.
When option “Apply symmetry operations” is checked, all the symmetrically equivalent Miller
planes are used as cutoff planes (Fig. 10.3). To define a cutoff plane with selected atoms, selectthree or more atoms in the Graphics Area and press the [Calculate the best plane for the selected
atoms] button.
The Cutoff planes frame box lists cutoff planes. Some of buttons and text boxes are disabled
when no cutoff plane is selected in the list. On selection of an item in the list, the text boxes
are updated to show data relevant to the selected cutoff plane. To add a new cutoff plane, click
the [New] button at first, and input Miller indices, hkl, and the distance from the origin. To
delete a cutoff plane, select an item in the list, and then click the [Delete] button or press the<Delete> key. Clicking the [Clear] button deletes all the cutoff planes in the list.
70Figure 10.3: Crystal structure of diamond drawn in ranges from (−8, −8, −8) to (8, 8, 8) withand without a cutoff plane {111}. The drawing boundaries are displayed as transparent faces.

10.2

View Direction

To specify a direction of viewing objects, select the [Orientation] button in Side Panel, or choose“Objects” menu ⇒ “Orientation…”. Then, the Orientation dialog box appears as Fig. 10.4 shows.
This dialog box can also be opened with a keyboard shortcut of <Ctrl> + <Shift> + <O>. At
the top of the dialog box, specify a phase to which the viewing direction is applied. To change
relative orientation of each phase, use the Phase tab in the Edit Data dialog box (see chapter 7).

10.2.1Manner of specifying directions

Either a lattice vector, [uvw], or a reciprocal-lattice vector, [hkl]∗ , perpendicular to a latticeplane (hkl) is specified as the direction of projection.
• Project along [uvw]The direction of projection is a lattice vector ua + vb + wc.
• Project along the normal to (hkl)
The direction of projection is a reciprocal-lattice vector ha∗ + kb∗ + lc∗ .

10.2.2

Orientation matrix

A 3 × 3 rotation matrix of the current orientation is displayed.
71

Figure 10.4: Orientation dialog box.

10.2.3

View direction

Two directions, i.e., the direction of projection (direction from the viewpoint to the screen) andthe upward direction on the screen are specified by a set of a lattice vector and a reciprocal-lattice
vector. The two vectors are perpendicular to each other. When the lattice vector, ua + vb + wc,
lies on the (hkl) plane, u, v, w, h, k, and l must satisfy the condition:
hu + kv + lw = 0.

(10.1)

This condition must, therefore, be satisfied in order to specify the upward direction on thescreen, otherwise the upward direction on the screen is automatically determined by VESTA.
• Projection vector: Direction of projection.
In the “Project along [uvw]” mode, this vector is u, v, and w in ua + vb + wc.
In the “Project along the normal to (hkl) plane” mode, this vector is h, k, and l in ha∗ +kb∗ + lc∗ .
• Upward vector: Upward direction on the screen.
In the “Project along [uvw]” mode, this vector is h, k, and l in ha∗ + kb∗ + lc∗ .
In the “Project along the normal to (hkl) plane” mode, this vector is u, v, and w in ua +vb + wc.

10.2.4

Viewing along crystallographic axes

To view the contents of Graphics Area along basis vectors of a unit cell or a reciprocal cell,
simply press one of the above buttons in the Horizontal Toolbar. When two or more phases arevisualized in the same Graphics Area, the above buttons set the viewing direction relative tothe first phase. To set a viewing direction relative to a phase other than the first one, use the
Orientation dialog box.

72

Chapter 11

INTERACTIVE MANIPULATIONS
11.1

RotateIn the Rotation mode, mouse behavior can be changed after clicking the Tools tab in the Side
Panel (Fig. 11.1).

11.1.1Drag mode

In the “Drag” mode, drag the mouse while pressing the left
mouse button to rotate objects in the Graphics Area. The objects
are rotated while dragging with the mouse. They are neverrotated after releasing the mouse button. In the [Free rotation]mode, the rotation axis becomes normal to the direction along
which the mouse is moved. To restrict the rotation axis, select[Around X axis], [Around Y axis], or [Around Z axis] in thepull-down menu of the Rotation modes frame box.

11.1.2

Animation mode

Three types of animation modes can be used in VESTA: “Click”,“Push”, and “Random” modes. The step width of rotation (indegrees/frame) and intervals between frames (in ms) are specified in the Preferences dialog box (see chapter 16).

Figure 11.1: The Tools tabof the Side Panel.

“Click” mode
In the “Click” mode, click the left mouse button to rotate the objects. In the “Click” plus
[Free] rotation modes, the rotation axis is perpendicular to a line connecting the clicked position
and the central point. To restrict the rotation axis, select [Around X axis], [Around Y axis],
or [Around Z axis] in the pull down menu of the Rotation modes frame box. To stop rotating
the objects, select either the “Drag” or “Push” mode. The animation speed (intervals between
frames in ms) is specified in the Preferences dialog box.
“Push” mode
In the “Push” mode, press the left mouse button at point 1 and drag the mouse to point 2. In
the [Free rotation] mode, objects are rotated around an axis perpendicular to a line connecting
points 1 and 2. The rotation speed is proportional to the speed of moving the mouse. The
objects stop rotating immediately after releasing the left mouse button. To restrict the rotation
73

axis, select [Around X axis], [Around Y axis], or [Around Z axis] in the pull down menu of the
Rotation modes frame box.
“Random” mode
In the “Random” mode, the rotation axis is automatically set and it changes dynamically. To
stop the rotation of the objects, select either the “Drag” or “Push” mode.

11.2

Magnify

Objects are magnified in proportion to the distance of dragging the mouse upward. On the other
hand, they are shrunk in inverse proportion to the distance of dragging the mouse downward.

11.3

Translate

Drag the mouse in the Graphics Area to translate objects. When a lattice plane with a color
specified in the Lattice Planes dialog box is selected and dragged in this mode, it is interactively
moved. Otherwise the entire objects are translated with the mouse along the same direction.

11.4

SelectSeveral ways of selecting objects can be used. On the use of the select mode in the Vertical
Toolbar, left click on an object to select it. To select all the objects in a certain area, press theleft mouse button and drag the mouse to specify an area. On selection of new objects, objects
that have previously been selected are reset to the normal state. To select additional objects
while keeping the present objects alive, press <Shift> while clicking or dragging the Graphics
Area. Regardless of the current manipulation mode, two or more objects can be selected byclicking or dragging on them while pressing the <Shift> key. A single object is selectable bydouble-clicking on it. Objects other than atoms, bonds, and polyhedra cannot be selected. For
example, atoms behind isosurfaces can be selected.
After a single object has been selected, a variety of information about it is output in the Text
Area. The estimated standard uncertainty is also displayed for interatomic distance, bond angle,
and dihedral angle if those of lattice parameters and fractional coordinates have been supplied.
However, note that VESTA gives only rough estimates of standard uncertainties by neglecting
off-diagonal elements of the variance-covariance matrix because no off-diagonal elements areincluded in crystal-data files.
Objects can also be selected by using the Objects tab in the Side Panel (see section 12.2),
the Vectors dialog box (see section 11.4), and the Geometrical Parameters dialog box (see section
14.2).
Press the <Delete> key to hide selected objects. The hidden objects are not actually deleted
but just made invisible. To restore all the hidden objects, press the <Esc> key. By hiding partof coordination polyhedra, you can easily mix polyhedra with a ball-and-stick model.

11.4.1Atom

On selection of an atom, site number, site name, symbol of the element, fractional coordinates (x, y, z), translation vector, symmetry operations (coordinate triplet), occupancy, isotropic
atomic displacement parameter, site multiplicity plus Wyckoff symbol, and site symmetry aredisplayed for the atom. For example, selection of Al and O atoms connected with each other ina ball-and-stick model of α-Al2 O3 gives the following lines:
74

Atom:

1

Atom:

2

Al Al 0.00000
Occ. = 1.000
O O 0.33333
Occ. = 1.000

1.00000 -0.15000
Ueq = 0.17370
0.97667 -0.08333
Ueq = 0.19915( 0, 1,-1)+ -y, -x, z+1/2
12c
3.
( 0, 0,-1)+ -y+1/3, x-y+2/3, z+2/3
18e.2

When atoms are rendered as displacement ellipsoids, information about principal axes andmean square displacements are also output:
Atom:

2

O O 0.97667
Occ. = 1.000

0.64333 0.08333
Ueq = 0.19915( 0, 0, 0)+ x-y+2/3, x+1/3, -z+1/3
18e.2

Principal axes of the anisotropic atomic displacement parameters
MSD (Å^2)
x
y
z
u
v
w
1
0.003223-0.043986 0.027435 -0.023150-0.005924 0.006668 -0.001785
2
0.002471
0.027516 0.041255 -0.003390
0.010805 0.010027 -0.000261
30.001873-0.013219 0.012054 0.039403-0.001318 0.002930 0.003038

11.4.2

Bond

When a bond is selected, its length is displayed with its estimated standard uncertainty, if any,in the Text Area as well as the Status Bar. Site number, site name, symbol of the element,
fractional coordinates (x, y, z), translation vector, and symmetry operations are also displayed
for two atoms connected with the bond. For example, on selection of an Al−O bond in theball-and-stick model of α-Al2 O3 , the following three lines are output:
Bond: l(Al-O) =
1
Al Al
2
O O

11.4.3

1.96249(0) Angstrom
1.00000 0.00000 0.15000 ( 1, 0, 0)+ y, x, -z+1/2
1.00000 0.31000 0.25000 ( 1, 0, 0)+ -y, x-y, z

Coordination polyhedron

When a coordination polyhedron with a coordination number of n is selected, information on
the central atom and coordinating atoms (ligands), distances between the central atom andcoordinating atoms are listed in the Text Area. Further, geometric information described below isdisplayed in the Text Area; the polyhedral volume, D, <λ>, and σ 2 are useful when investigating
structural changes under high/low temperature and high pressure [67].
Polyhedral volume
The volume of the selected coordination polyhedron is calculated as a fundamentally important
physical quantity [31]. For example, distortion in perovskite-type compounds, ABO3 can bequantified with polyhedral volume ratios, VA /VB , rather than with tilting angles [68].
Distortion index
A distortion index, D, based on bond lengths was defined by Baur [32] as
1 ∑ |li − lav |
,
n
lav
n

D=

(11.1)

i=1

where li is the distance from the central atom to the ith coordinating atom, and lav is the averagebond length.
75

Quadratic elongation
The quadratic elongation, <λ> [33], is defined only for tetrahedra, octahedra, cubes, dodecahedra, and icosahedra:n ( )1 ∑ li 2<λ> =,(11.2)nl0
i=1

where l0 is the center-to-vertex distance of a regular polyhedron of the same volume. <λ> isdimensionless, giving a quantitative measure of polyhedral disortion which is independent of theeffective size of the polyhedron.
Bond angle variance
The bond angle variance, σ 2 [33], is calculated only for tetrahedra, octahedra, cubes, dodecahedra, and icosahedra:
m
1 ∑
σ2 =
(ϕi − ϕ0 )2 ,(11.3)m−1
i=1

where m is (number of faces in the polyhedron)×3/2 (i.e., number of bond angles), ϕi is theith bond angle, and ϕ0 is the ideal bond angle for a regular polyhedron (for example, 90◦ for anoctahedron or 109◦ 28′ for a tetrahedron).
Effective coordination number
The coordination number denotes the number of atoms coordinated to a central atom in acoordination polyhedron. However, stating the coordination of the central atom as a single
number is somewhat difficult in relatively distorted coordination polyhedra. Several proposals
are made for calculation of a mean or ‘effective’ coordination number (ECoN) by adding all
surrounding atoms with a weighting scheme, where the atoms are not counted as full atoms but
as fractional atoms with numbers between 0 and 1. This number gets closer to zero with anincrease in distance from the central atom to a surrounding atom.
VESTA adopts ECoN [33, 34, 35, 36] defined as∑
ECoN =
wi ,(11.4)iwhere the quantity[(

wi = exp 1 −

li
lav

)6 ]
(11.5)

is called the “bond weight” of the ith bond. In Eq. (11.5), lav represents a weighted averagebond length defined as[]∑li exp 1 − (li /lmin )6i[] ,(11.6)
lav = ∑
exp 1 − (li /lmin )6iwhere lmin is the smallest bond length in the coordination polyhedron.
Charge distribution
Let qX be the formal charge (oxidation number) of the central atom, X. Then, the fraction of
the charge received by an ion at a corner of a coordination polyhedron is calculated as
∆qi =

wi qX
.
ECoNX
76

(11.7)

The total charge, QA , received by an ion A is obtained by summing the relevant charge fractions,−∆qi ’s, over its n bonds. Similarly, the charge, QX , received by the ion at the center of acoordination polyhedron is calculated by
QX =

[
]
∑ wi (qA /QA )i
i

ECoNX

qX .

(11.8)

Calculation of the charge distribution [35, 36, 37] in the crystal structure depends on the current
bond specifications. In other words, the fraction of the charge is not given to or received byions that are not bonded to each other. Formal charges of ions are read in from data files when
ICSD files or CIFs (see 17.4.1) including oxidation states (oxidation numbers) are opened. For
other file formats, formal charges of ions have to be input in the Structure parameters tab of
the Edit Data dialog box to calculate the charge distribution. Note that charge distribution in
nonstoichiometric compounds can be calculated because occupancies are used in the calculation.
Bond valence sum
In addition to the above physical quantities, the bond valence sum, V , defined as
V =

n
∑
i=1

)
(
l0 − liexpb(11.9)is also obtainable from the bond valence parameter, l0 , of the central atom [38, 39, 40]. In
VESTA, the empirical constant, b, in Eq. (11.9) is fixed at a typical value of 0.37 Å.
The bond valence model, which is a development of Pauling’s rules, has been theoreticallydescribed in terms of classical electrostatic theory without resorting to quantum mechanics.
Nevertheless, V serves, in practice, to estimate the oxidation state of the central atom only frombond lengths determined by X-ray or neutron diffraction.
A CIF, bvparm2011.cif, storing bond valence parameters of most chemical species is available
for download fromhttp://www.iucr.org/resources/data/datasets/bond-valence-parameters
This CIF is also included in the folder where the executable binary file of VESTA is located so
as to refer to it when l0 values are required. In bvparm2009.cif, an l0 value for a pair of a cation
and an anion is obtained, e.g., l0 = 1.620 Å for Al3+ and O2− and l0 = 2.172 Å for La3+ andO2− (b = 0.37 Å). Never select an l0 value for which b ̸= 0.37 Å.
If a coordination polyhedron is clicked in the Graphic Area while pressing the <Ctrl> key inthe manipulation mode of Select, you are asked to input a bond valence parameter, l0 , for thecentral metal of the selected coordination polyhedron. After entering l0 , the bond valence sum[38, 39, 40] for the central atom is calculated and displayed in the Text Area from all the bondlengths, li , for the current polyhedron and l0 .
Expected bond length
Unless oxidation states of sites have been input in the Structure parameters tab of the Edit Datadialog box or from some kinds of structural files, VESTA prompts you to enter an oxidation
number corresponding to V in Eq. (11.9); pressing the <Enter> key skips the subsequent calculation. After entering the value, an bond length expected with Eq. (11.9) is calculated andgiven in the Text Area.
77

An example of getting information on a coordination polyhedronSuppose that a TiO6 octahedron is selected in a structural model of perovskite (CaTiO3 ) [69]while pressing the <Ctrl> key. You are asked to enter the bond valence parameter of Ti4+(l0 = 1.815 Å) and the oxidation state of Ti (= +4) unless it has already been input in the
Structure parameters tab of the Edit Data dialog box. Then, the following data including thephysical quantities described above are output to the Text Area:

POLYHEDRON:
1
Ti1 Ti 1.00000 0.50000 0.00000 ( 1, 0, 0)+ x, y, z---------------------------------------------------------------------------4
O2 O 0.71030 0.71120 -0.03730 ( 1, 1, 0)+ -x, -y, -z
4
O2 O 0.78970 0.21120 -0.03730 ( 0, 0, 0)+ x+1/2, -y+1/2, -z
3
O1 O 0.92890 0.48390 0.25000 ( 1, 0, 0)+ -x+1/2, y+1/2, z
3
O1 O 1.07110 0.51610 -0.25000 ( 0, 0, 0)+ x+1/2, -y+1/2, -z
4
O2 O 1.28970 0.28880 0.03730 ( 1, 0, 0)+ x, y, z
4
O2 O 1.21030 0.78880 0.03730 ( 1, 0, 0)+ -x+1/2, y+1/2, z---------------------------------------------------------------------------l(Ti1-O2) = 1.9571(11) Ål(Ti1-O2) = 1.9569(11) Ål(Ti1-O1) = 1.9497(4) Ål(Ti1-O1) = 1.9497(4) Ål(Ti1-O2) = 1.9571(11) Ål(Ti1-O2) = 1.9569(11) Å--------------------------------------Average bond length = 1.9546 ÅPolyhedral volume = 9.9546 Å^3Distortion index (bond length) = 0.00168
Quadratic elongation = 1.0001
Bond angle variance =0.3773 deg.^2
Effective coordination number = 5.9994
Charge distribution---------------------------------------------------------------------------delta_q: Fraction of the charge received by the ion
Q: Total charge received by the ion
q: Formal charge (oxidation number)---------------------------------------------------------------------------xyz
delta_qQq
4
O2 O 0.71030 0.71120 -0.03730
0.661 -1.994 -2.000
4O2 O 0.78970 0.21120 -0.03730
0.662 -1.994 -2.000
3O1 O 0.92890 0.48390 0.25000
0.677 -2.013 -2.000
3O1 O 1.07110 0.51610 -0.25000
0.677 -2.013 -2.000
4O2 O 1.28970 0.28880 0.03730
0.661 -1.994 -2.000
4O2 O 1.21030 0.78880 0.03730
0.662 -1.994 -2.000---------------------------------------------------------------------------1
Ti1 Ti 1.00000 0.50000 0.00000
4.000 4.000
Input a bond valence parameter: 1.815000
Bond valence sum = 4.115
Oxidation state of the cation: +4
Expected bond length = 1.965 Angstrom

All the fractional coordinates, translations, equivalent positions, bond lengths with their estimated standard uncertainties for the TiO6 octahedron are output before the polyhedral volume.
78

11.5

Distance

To calculate an interatomic distance, select the fifth button in the Vertical Toolbar. In this mode,
only atoms can be selected. Select a pair of atoms, A and B, to obtain the interatomic distance
between A and B. Then, the two atoms are highlighted, and a dashed line connecting themis plotted on the screen. The A–B distance is displayed on the Status Bar with its estimatedstandard uncertainty [70], if any, enclosed by a pair of parentheses. The estimated standard
uncertainty is calculated only when those of lattice parameters and fractional coordinates havebeen input.
To obtain a bond length in a ball-and-stick model, selecting the relevant bond (see 11.4.2) isfaster than clicking two atoms. More information on the interatomic distance is displayed in the
Text Area, where site number, site name, symbol of the element, fractional coordinates (x, y, z),symmetry operations, and translation vector are displayed for each of atoms A and B.
For example, an interatomic distance for A = C7 and B = O2 in 2′ -Hydroxyl-4′′ -dimethylaminochalcone [71] is output as follows:l(C7-O2) = 1.254(4) Angstrom
15
C7 C 0.75640 0.11620
4O2 O 0.80530 0.04440

11.6

0.34510 ( 1,-1, 0)+ -x, y+1/2, -z+1/2
0.43470 ( 1,-1, 0)+ -x, y+1/2, -z+1/2

Bond angle

To calculate a bond angle, select the sixth button in the Vertical Toolbar. Then select threeatoms A, B, and C to calculate the bond angle (in degrees) with atom B at the apex. The
angle is displayed on the Status Bar with its estimated standard deviation, if any, in a pair ofparentheses. The estimated standard uncertainty [70] is calculated only when those of lattice
parameters and fractional coordinates have been input.
More information on the bond angle is displayed in the Text Area, where site number, site
name, symbol of the element, fractional coordinates (x, y, z), translation vector, and symmetry
operations are displayed for each of atoms A, B, and C.
For example, a bond angle for A = O1, B = Al1, and C = O1 in Al2 O3 [72] is output asfollows:phi(O1-Al1-O1) = 86.37(3) deg.
1
O1 O 1.33333 -0.02698
2
Al1 Al 1.00000 0.00000
1O1 O 1.00000 -0.30635

11.7

0.41667 ( 1, 0, 0)+ y+1/3, -x+y+2/3, -z+2/3
0.35217 ( 1, 0, 0)+ x, y, z
0.25000 ( 1,-1, 0)+ -y, x-y, z

Dihedral angle

To calculate a dihedral angle defined by four atoms, select the seventh button in the Vertical
Toolbar. For a sequence of four atoms A, B, C, and D, the dihedral angle, ω, is defined as the
positive angle between ABC and BCD planes. Let α = ∠(B−C−D), β = ∠(B−A−D′ ), andγ = ∠(A−B−C), where D′ denotes the D atom when C−D is translated in such a way that
the C atom overlaps with the A atom. Then, cos ω is formulated as [73]cos ω =

cos α cos γ − cos β.
sin α sin γ(11.10)

Select four atoms, A, B, C, and D. The dihedral angle (in degrees) for atom D and aplane on which atoms A, B, and C lie is displayed on the Status Bar with its estimated standard
uncertainty, if any, in a pair of parentheses. The estimated standard uncertainty [70] is calculated
only when those of lattice parameters and fractional coordinates have been input.
79More information about the dihedral angle is output in the Text Area, where site number,site name, symbol of the element, fractional coordinates (x, y, z), symmetry operations, andtranslation vector are displayed for each of atoms A, B, C, and D. For examples, in the caseof C1 (= A), C2 (= B), C3 (= C), and C4 (= D) atoms contained in an aromatic ring of 3[4-(dimethylamino)phenyl]-1-(2-hydroxyphenyl)prop-2-en-1-one [71] (Fig. 11.2), the following
five lines are output in the text area:

Figure 11.2: Calculation of a dihedral angle for four carbon atoms in an aromatic ring in
3-[4-(dimethylamino)phenyl]-1-(2-hydroxyphenyl)-prop-2-en-1-one

80

omega(C1-C2-C3-C4) =2.36(8) deg.
5
C1 C 0.58190 0.79990 0.21900 ( 0, 0, 0)+ x, y, z
7
C2 C 0.52280 0.72240 0.11990 ( 0, 0, 0)+ x, y, z
9
C3 C 0.41240 0.66560 0.09830 ( 0, 0, 0)+ x, y, z
10
C4 C 0.36010 0.68130 0.17850 ( 0, 0, 0)+ x, y, z

Data in lines No. 2−5 (selected lines in the Text Area in Fig. 11.2) can be used when imposing
nonlinear restraints on the dihedral angle in Rietveld refinement with RIETAN-FP [12].

11.8Interfacial angle

To calculate an interfacial angle, i.e., an angle between two crystal faces, select the eighth buttonin the Vertical Toolbar. In this mode, only crystal faces can be selected. Selection of a pair offaces A and B gives an angle between their normal vectors (Fig. 11.3).

Figure 11.3: Calculation of an interfacial angle between (100) and (511) faces in quartz.

81Chapter 12

PROPERTIES OF OBJECTS
Properties of various objects are edited in the Properties dialog box and the Objects tab of theSide Panel.

12.1

Properties Dialog Box

To open the Properties dialog box, press the [Properties] button in the Style tab of the Side
Panel. The same dialog box can be open by choosing one of submenus in the “Objects” menu
⇒ “Properties”. When “Preview” is checked, changes in the Properties dialog box are reflectedon the Graphics Area in real time. Click [OK] to apply all the changes or [cancel] to discard
the changes. Current properties are saved as default values in VESTA by clicking the [Save as
default] button.

12.1.1

GeneralThe first page in the Properties dialog box is General (Fig. 12.1).
Unit cell
The display of Unit cell edges in the Graphics Area is controlled with the following three radio
buttons:• “Do not show”: Do not show unit cell edges.
• “Single unit cell”: Show edges of a single unit cell.
• “All unit cells”: Show all the edges of unit cells within the drawing boundary.
Line styles of the unit cell edges are selected from three styles: “Solid lines”, “Dotted lines”, and“Dashed lines”. The width of lines is input in text box {Line width}. The color of lines is specified
either (A) by entering R, G, and B values ranging from 0 to 255 or (B) by picking a color froma color selection dialog box opened after clicking the [Select] button.
Axes“Show Compass” is used to turn on or off a display of three arrows indicating a, b, and c axes
(or x, y, and z axes in the case of Cartesian coordinates). “Show Axis Labels” is used to turnon or off a display of axis labels, ‘a’, ‘b’, and ‘c’ (or ‘x’, ‘y’, and ‘z’ in the case of Cartesian
coordinates).
82

Figure 12.1: General page in the Properties dialog box.
ShapesThe visibility, line width, and color of edges of crystal morphologies are input in the Shapes
frame box.

12.1.2Atoms

The second page in the Properties dialog box is Atoms (Fig. 12.2).
Material• {Specular} is a color of reflected light that bounces sharply in a particular direction in themanner of a mirror. A highly specular light tends to cause a bright spot on the surface it
shines upon, which is called the specular highlight.
• {Shininess} is a property, which specifies how small and focused the specular highlight. A
value of 0 specifies an unfocused specular highlight.
Resolution{Stacks} and {Slices} are parameters common to all the atoms, allowing you to change the resolution (quality) of atoms displayed on the screen. {Stacks} denotes the numbers of subdivisions
along the Z axis (similar to lines of latitude) while {Slices} denotes the number of subdivisions
around the Z axis (similar to lines of longitude). {Stacks} and {Slices} should be equal to eachother in ball-and-stick and space-filling models where atoms are represented by perfect spheres.
In general, decreasing {Stacks} and {Slices} accelerates the rendering of objects in the Graphics
Area.
83

Figure 12.2: Atoms page in the Properties dialog box.
Atom style
Select either of the following two radio buttons for the mode of displaying atoms on the Graphics
Area: (1) “Show as balls” or (2) “Show as displacement ellipsoids”.
• “Show as balls”: Atoms are rendered as spheres. List box {Radii type} is used to select a
type of default atomic radii from the following three:– Atomic: Metallic or covalent radii, whose values were mostly taken from Refs. [74,75, 76].
– Ionic: Effective ionic radii compiled by Shannon [77] for representative oxidation
states and coordination numbers.
– van der Waals: van der Waals radii [78].
The user may modify default values of atomic, ionic, and van der Waals radii by editing atext file, elements.ini, in the program folder of VESTA.
• “Show as displacement ellipsoids”: Atoms are rendered as ellipsoids to represent anisotropic
displacement of atoms whose shapes are calculated from anisotropic atomic displacement
parameters, βij or Uij (see 6.3.5). The probability (in percentage) for atomic nuclei to be
included in the ellipsoids is input in text box {Probability}. It is common to all the atoms
when drawing displacement ellipsoids. If option “Show principal ellipses” is checked, threeprincipal ellipses corresponding to three principal planes are plotted on the surface of each
ellipsoid (Fig. 12.3). The line width of the principal ellipses is input in text box {Linewidth}.
84

A

B

Figure 12.3: Displacement ellipsoids of an atom (A) with principal ellipses and (B) without them.

Figure 12.4: A displacement ellipsoid model of a structurewith four atoms having negative mean square displacements.

If one or more of principal axes have negative mean square displacements, atoms are
represented by cuboids so that the unusual atomic displacement parameters can easily berecognized (Fig. 12.4). Each cuboid is oriented in accordance with principal axes withthe dimension of the cuboid scaled according to the absolute value of the mean-squaredisplacement.
• “Hide non-bonding atoms”: This option hides atoms that are connected by no bonds but
the crystallographic site for those atoms have a coordination number larger than 0. In
other words, atoms are made invisible if all the coordinated atoms are lying outside of thedrawing boundary.

Radius and color
Select a symbol of an element from list box {Symbol} and then specify its {Radius}. The colorof an atom (element) is specified either (a) by entering R, G, and B values ranging from 0 to
255 or (b) by picking a color from a color selection dialog box opened when clicking the [Select]button.
85

A

B

Figure 12.5: General-position diagrams of space group F d3̄m with (A) light disabled and (B)light enabled.
LabelsSelect either of the following two types for atom labels: (1) “Names of elements” or (2) “Names ofsites”. Labels are displayed near atoms with an offset along the z axis, which is specified in theunit of Å. When option “Mark enantiomorphic sites” is checked, atoms generated by symmetry
operations of inversion, rotoinversion, or mirror are marked with a ‘,’ symbol. These positions
are enantiomorphs with respect to non-marked positions. This option can be used to draw
general position diagrams (Fig. 12.5) similar to those illustrated in “International Tables for
Crystallography,” Vol. A [30]. When an atom position coincides with an a enantiomorphic symmetry element, the original and enantiomorphic positions coincide. Such an atom is represented
by a ‘,’ mark on the left half of the atom separated with ‘|’ at its center.

12.1.3Bonds

The third page in the Properties dialog box is Bonds (Fig. 12.6).
Material
It is the same as that in Atoms (see 12.1.2).
Resolution
It is the same as that in Atoms (see 12.1.2).
Bond style
One of the following six types of bonds are specified in this frame box:
• “Unicolor cylinder”: Each bond is drawn as a cylinder, whose color can be changed in the
Color panel.
86

Figure 12.6: Bonds page in the Properties dialog box.
• “Bicolor cylinder”: Each bond is drawn as a cylinder with colors of two atoms connectedwith each other. The two colors of the bond are just the same as those of atoms connectedby bonds.
• “Color line”: Each bond is drawn as a straight line, whose color is changed in the Color
panel.
• “Gradient line”: Each bond is drawn as a line connecting two atoms with gradient distribution of colors. Colors of each bond at the ends of the line are the same as those of theatoms.
• “Dotted line”• “Dashed line”
Radius and color
The radius of each cylindrical bond in the stick model is changed in text box {Radius (cylinder)}.
The actual radius of cylinders is 40 % of the input value. The line width of line-style bonds ischanged in text box, {Width (line)}. The color of bonds in the single color style is changed in
the Color tool below these two text boxes.

12.1.4

Polyhedra

The fourth page in the Properties dialog box is Polydedra (Fig. 12.7).
87Figure 12.7: Polyhedra page in the Properties dialog box.
Material{Specular} and {Shininess} are just the same as those in Atoms page (see 12.1.2). The {Opacity}of coordination polyhedra is input with 255 corresponding to opaque planes (the inside of eachcoordination polyhedron is invisible) and 0 corresponding to fully transparent planes (coordination polyhedra are invisible).
Polyhedral style
Styles of coordination polyhedra are selected from the following six types of expressions that are
schematically illustrated in the Polyhedral style frame box:
• Show atoms and bonds without any coordination polyhedra.
• Show atoms, bonds, and coordination polyhedra (default).
• Show atoms and coordination polyhedra.
• Show central atoms and coordination polyhedra.
• Show only coordination polyhedra.
• Show only bonds.
Planes
The surface color of each coordination polyhedron is specified here. Select an element from list
box {Central atom} to specify its color. Default colors of coordination polyhedra are the sameas those of the central atoms.
88EdgesThe visibility, line width, and color of edges of coordination polyhedra are input in the Edges
frame box.

12.1.5

Isosurfaces

The fifth page in the Properties dialog box is Isosurface (Fig. 12.8).
Material
It is the same as that in Atoms (see 12.1.2).

Figure 12.8: Isosurfaces page in the Properties dialog box.

Isosurfaces
At the top of the Isosurfaces frame box, the minimum and maximum data values are displayed in
the unit of the raw data. Data values such as electron and nuclear densities, and wave functions
on isosurfaces are equal to {Isosurface level}, d(iso). All the points with densities larger thand(iso) lie inside the isosurfaces whereas those with densities smaller than d(iso) are situatedoutside the isosurfaces.
At the lower half of the frame box, a list of isosurface levels is shown. To add a new isosurface
level, add the [New] button, and edit the isosurface level and color. To delete an isosurface level,
select an item in the list, and press the [Delete] button. Pressing the [Clear] button deletes all
the isosurfaces.
Order of rendering polygons The sequence of drawing polygons can be changed with option“Render from front to back.” By default, polygons are rendered from behind so that isosurfaces
89behind the nearest surface are visible through translucent isosurfaces. In some cases with complex isosurfaces, it may become difficult to understand the shape of isosurfaces because theyheavily overlap each other. When option “Render from front to back” is checked, only the nearest
surfaces are rendered. The use of this option may sometimes improve the visibility of complex
isosurfaces because neither back surfaces nor internal ones are drawn.
Figure 12.9 illustrates a difference between the two rendering modes in 3D visualization of
results of an electronic-state calculation for the [Cd{S4 Mo3 (Hnta)3 }2 ]4− ion (H3 nta: nitrilotriacetic acid) [79] by a discrete variational Xα method with DVSCAT [58].

A

B

Figure 12.9: Comparison between the two modes of rendering isosurfaces for a molybdenumcadmium cluster [Cd{S4 Mo3 (Hnta)3 }2 ]4− . (A) “Render from behind (default)” and (B) “Renderfrom front to back.” Composite images of electron-density isosurfaces colored according toelectrostatic potentials and a ball-and-stick model are shown with an isosurface level of 0.03a−30
and electrostatic potentials on the isosurface ranging from −0.814 Ry (blue) to 0.174 Ry (red).

Kinds of isosurfaces For volumetric data having both positive and negative values, you canselect which surfaces are visible:• {Positive and negative},• {Positive},• {Negative}.
Figure 12.10 exemplifies isosurfaces of wave functions calculated with DVSCAT [58] for acomplex ion with a ball-and-stick model superimposed on the isosurfaces. Yellow and blue
surfaces show positive and negative values, respectively.
Opacity of isosurfaces The opacity of isosurfaces is specified by two parameters, {Opacity1} (O1 ) and {Opacity 2} (O2 ), as exemplified in Fig. 12.11. O1 is the opacity for polygons
parallel to the screen, and O2 is that for polygons perpendicular to the screen (Fig. 12.12).
The opacity, O(p), for polygon p with a normal vector of (x, y, z) is calculated with a linear
combination of O1 and O2 :90

Figure 12.10: The 64a1g orbital for the {Cd[S4 Mo3 (Hnta)3 ]2 }4−ion [79] with a ball-and-stick model. The isosurface levels of
−3/2
−3/2
the wave function were set at 0.01a0(yellow) and −0.01a0(blue), where a0 is the Bohr radius.

A

B

Figure 12.11: Composite images of electron-density isosurfaces and a ball-and-stick model
drawn for albatrossene (C114 H76 ) [80] with two pairs of opacity parameters: (A) O1 = 153
and O2 = 255; (B) O1 = 26 and O2 = 179. The electron densities were calculated withDVSCAT [58] and visualized with an equi-density level of 0.01a−3
0 .
Surface coloring
After volumetric data for surface coloring have been loaded, isosurfaces can be colored according
to those data. The saturation level of colors is specified as (a) a value normalized between 0
and 100, and (b) a value corresponding to raw data. This is mostly equal to color settings forlattice planes and sections of isosurfaces (see 12.1.6), except that the normalized values of 0 and
100 corresponds to the minimum and maximum data values on the current isosurfaces, not the91

data set itself.

O2

Isosurface

O1
Z
ScreenFigure 12.12: Schematic representation of relations between orientationof an isosurface and the two opacity parameters, O1 and O2 .
The color index, T , to determine the color of a data point with a value of d is calculated fromthe unit of the raw data: the minimum saturation level, Smin , and the maximum one, Smax , inthe unit of the raw data:d − SminT =.
(12.1)
Smax − Smin
Data points with values larger than Smax and smaller than Smin are given the same colors as
those assigned to Smin and Smax , respectively.
Op = O1 z + O2 (1 − z).

12.1.6(12.2)

Sections

The seventh (final) page in the Properties dialog box is Sections (Fig. 12.13).
For volumetric data, both lattice planes and sections of isosurfaces are colored according
to numerical values on them (Fig. 12.14). The saturation level of colors is specified as (a) avalue normalized between 0 and 100 corresponding the minimum and maximum data values,
respectively, and (b) a value corresponding to raw data. The color index, T , for a data pointwith a value of d is calculated from the minimum saturation level, Smin , and the maximum one,
Smax , in the unit of the raw data:d − SminT =.
(12.3)
Smax − Smin
Data points with numerical values larger than Smax and smaller than Smin are given the samecolors as those assigned to Smin and Smax , respectively. The color of each point is determinedfrom T , depending on color modes. One of six color modes, that is, B-G-R, R-G-B, C-M-Y,
Y-M-C, gray scale (from black to white), and inverse gray scale, is selected from a list box. For
example, blue is assigned to 0, green to 0.5, and red to 1 in the B-G-R mode, as shown in Fig.
12.15.
When option “Absolute values” is checked, colors are assigned on the basis of absolute valuesof data.
92

Figure 12.13: Sections page in the Properties dialog box.
Option “Assign colors recursively” assigns rainbow colors recursively to data points with values
smaller or larger than the saturation levels, which affords an effect similar to contour lines withgradient colors in between them. The opacity of sections are specified in the {Opacity of drawn
sections} box, and that of lattice planes in the Lattice Planes dialog box (see 9.2). When {Cutoff
level of lattice plane} is larger than 0, some parts of lattice planes with data values smaller thanthe cutoff level are omitted.

93

D
O
D

D
K

Figure 12.14: Distribution of nuclear densities obtained for KOD
at 580 K by MEM from single-crystal neutron diffraction data [81].
Coordinate ranges from (0, 0, 0) to (1, 1, 1) were drawn with a cutoff
plane of (111). D atoms are highly disordered around O atoms.

Data range

0%

Saturation level

100 %
Min.

Max.

Figure 12.15: Relations among saturation levels, data values, and colors of sections.

94

12.2

Objects Tab in the Side Panel

12.2.1

List of phases and objects

At the upper half of the Objects page, an overview of objects
contained in each phase is listed (Fig. 12.16). Atoms, bonds,
polyhedra, slices, and shapes are shown for each phase if they
are contained in the phase data. Select one of them to see
more details in objects at the lower half of the page.

12.2.2Atoms

The first column (Site) lists crystallographic sites grouped byelements. The second column (r (Å)) gives radii for elements
and crystallographic sites. To edit these data, select a row
and click on the text. The third column (C) shows colors
of atoms, which can be edited by double-clicking square areas. The fourth to sixth columns (L, S, and V) control visualproperties of atoms, i.e., labels, selection states, and visibility. If properties of an element are edited, the modifications
are applied to all the sites of the element.

12.2.3Figure 12.16: The Objects tabin the Side Panel showing alist of crystallographic sites
for the first phase.

Bonds

When a list of bond specifications is displayed in the lower
half of the Objects page (Fig. 12.17), the first column (Bond)
gives pairs of atoms that are bonded to each other. The second column (S) shows styles of bonds, which can be changed
by double-clicking the second column of a bond. The thirdcolumn (r/w) gives radii or line widths of bonds. When bonds
Figure 12.17: A list of bondare rendered as cylinders (styles 1 and 2), they are specified in
specificationsin the Objects
the unit of Å, which are then rescaled by a factor of 0.4 on rentab of the Side Panel.
dering of bonds. When bonds are rendered as solid, dashed,or dotted lines (styles 3–6), they are specified in the unitof pixels. The fourth column (C) displays colors of bonds,
which are edited by double-clicking the colored square. The
fifth and sixth columns (S and V) control selection states and visibilities of bonds, respectively.

12.2.4

Polyhedra

When a list of polyhedra is displayed in the lower half of the
Objects page (Fig. 12.18), the first column (polyhedra) gives
crystallographic sites grouped by elements. The second column (C) shows colors and opacities of polyhedra. The thirdand fourth columns (S and V) control selection states andvisibilities of polyhedra, respectively. If polyhedral properties of an element are edited, the modifications are applied
to all the sites of the element.
95

Figure 12.18: A list of polyhedra in the Objects tab of theSide Panel.

12.2.5

SlicesWhen a list of slices is displayed in the lower half of the
Objects page (Fig. 12.19), the first column (Slice) gives
Miller indices of slices. The second column (d (Å)) is distances from the origin to the slices, and the third column (C)shows colors and opacities of slices.

12.2.6

Figure 12.19: A list of slices
in the Objects tab of the Side
Panel.

ShapesWhen a list of forms and faces of crystal morphologies isdisplayed in the lower half of the Objects page (Fig. 12.20),
the first row is assigned to a special item to control a colorof shape in the “Unicolor” style and the visibility of labels
all at once. The first column (Face) gives Miller indices offaces grouped by crystallographically equivalent forms. The
second column (d (Å)) is distances from the origin to faces,
and the third one (C) shows colors and opacities of faces. The
fourth column (L) controls the visibility of labels for faces. If
properties of a form are edited, the modifications are applied
to all the faces that are crystallographically equivalent.

96

Figure 12.20: A list of forms
and faces of crystal morphologies in the Objects tab of theSide Panel.

Chapter 13

OVERALL APPEARANCEThe Overall Appearance dialog box (Fig. 13.1) appears on selection of the “Overall appearance...”item under the “View” menu.

Figure 13.1: Overall Appearance dialog box.

13.1

BackgroundThe background color is specified with three values in between 0 to 255, or selected from a color
selection dialog box after clicking the button at the right of the text boxes.
97

A

B

Figure 13.2: Crystal structure of milarite drawn with light effects (A) enabled and (B) disabled.

13.2

Lighting

When option “Enable lighting” is checked, the following light properties are set. When lighting
is disabled, the resulting figure looks like a traditional 2D plot with no gradients (Fig. 13.2).
• Ambient: A light that comes from all directions equally and is scattered in all directions
equally by objects. Specified by a value in between 0 to 100.
• Diffuse: A light that comes from a particular direction and hits objects with an intensitythat depends on the orientation of their surfaces. However, once the light hits a surface, it
reflects evenly off a surface and radiates in all directions. Specified by a value in between
0 to 100.
• Lighting direction: This can be changed by dragging the “track ball” placed below the“Lighting” frame box.
Even though the ambient and diffuse lights are evenly reflected, some part of lights are reflected
more in the manner of a mirror where most of the light bounces off in a particular direction.
A light having such a reflection component is called “specular” light. In VESTA, the intensityof the specular light is fixed at 100 %, and a color of a reflected specular light, i.e., “specularcolor” is controlled by two properties of objects, {Specular} and {Shininess}. The final color ofa surface is the sum of all three components of lights. A object surface appears to be brighter
than the color of object if the specular light is reflected in the direction of viewpoint.

13.3

Projection Mode

• Parallel: Objects are rendered by parallel projection.
• Perspective:: Objects are rendered by perspective projection. Accentuation of the perspective view is controlled by the slider placed below the radio button.
Figure 13.3 shows the structure of post-perovskite, MgSiO3 [82], visualized in the paralleland perspective modes.
end − zf=.
(13.1)
end − start

98

A

B

Figure 13.3: Crystal structure of post-perovskite, a high-pressure form of MgSiO3 , rendered by(A) parallel and (B) perspective projections.

13.4

Depth-Cueing

Depth-cueing blends a “fog” color with the original color of each object using the blending factor
f . The factor f at depth z is computed by Both of the starting depth, start, and the ending
depth, end, are input by the user. VESTA automatically assigns the background color of theGraphics Area to the fog color Cf . Then, the color of a rendering object, Cr, is replaced by
Cr′ = f ∗ Cr + (1 − f ) ∗ Cf .

(13.2)

When VESTA renders objects in the Graphics Area, internal coordinates of the OpenGL scene
are normalized in such a way that a radius of the bounding sphere for the scene becomes 0.9 andthat the center of the scene is placed at 0. Objects at z < start are clearly rendered without
any fog whereas objects at z > end are completely invisible.
Depth-cueing can be enabled or disabled in check box Enable depth-cueing. The effect of
depth-cueing is schematically displayed below the two text boxes Starting depth and Ending
depth.
Figure 13.4 illustrates the effect of depth-cueing on images of mordenite [83] viewed along
the c axis in the perspective-projection mode.

99

A

B

Figure 13.4: Crystal structure of mordenite rendered with and without depth-cueing. (A)Depth-cueing enabled by setting start and end parameters at −1.2 and 1.0, respectively. (B)Depth-cueing disabled.

100

Chapter 14

UTILITIES
14.1

Equivalent Positions

The Equivalent Positions dialog box (Fig. 14.1) appears on selection of the “Equivalent Positions...” item under the “Utilities” menu.

Figure 14.1: Equivalent Positions dialog box.

A list of general equivalent positions is displayed in this dialog box. When one of the equivalent
positions in the list is selected, the corresponding symmetry operation is displayed in a matrix
form at the upper left of the dialog box. In the right side of this dialog box, symmetry operation
W and transformation of fractional coordinates (x, y, z) with it are explicitly described (see6.2.6).
In the case of magnetic space groups, the time reversal term t and the resultant magnetic
moments mx, my, and mz are also displayed in the list as well as the x, y, z notation of general
positions.
101

Figure 14.2: The Equivalent Positions dialog box showing magnetic data.

14.2

Geometrical Parameters

This dialog box lists interatomic distances and bond angles recorded in a file *.ffe output by
ORFFE [45]. ORFFE calculates geometrical parameters from crystal data in file *.xyz created
by RIETAN-FP [12], outputting them in file *.ffe. When reading in input and/or output files
of RIETAN-FP (*.ins, *.lst), VESTA also inputs *.ffe automatically provided that *.ffe shares
the same folder with *.lst and/or *.ins. Otherwise, *.ffe can be input by clicking the [Read *.ffe]
button in the Geometrical Parameters dialog box.
VESTA allows us to locate the bonds and bond angles displayed in the Geometrical Parameters
dialog box in the Graphic Area. On selection of a bond (2 atoms) or a bond angle (3 atoms) in this
dialog box, the corresponding objects in a ball-and-stick model is selected (highlighted), and viceversa. Thus, atom pairs and triplets associated with geometrical parameters on which restraints
are imposed in Rietveld analysis with RIETAN-FP are easily recognized in the ball-and-stickmodel.
Figure 14.3 exemplifies visualization of a bond in a ball-and-stick model of fluorapatite; aP−O3 bond (grey line) selected in the dialog box is highlighted in the structural model in thegraphic window. The upper part of the dialog box displays detailed information on the P−O3
bond.
Because ORFFE calculates standard uncertainties of geometrical parameters from both diagonal and off-diagonal terms in the variance-covariance matrix output by RIETAN-FP, theresulting standard uncertaities are more accurate than those evaluated by VESTA from only
the diagonal terms. Accordingly, the standard uncertaities output by ORFFE should be described in papers rather than those calculated by VESTA.
102

Figure 14.3: The Geometrical Parameters dialog box showing a list of bonds recorded for fluorapatite [84] in FapatiteJ.ffe.

14.3

Standardization of Crystal Data

On the use of RIETAN-FP [12], it is highly desirable for an axis setting and fractional coordinates
to be standardized in compliance with definite rules [85]. In RIETAN-FP, the following lattice
settings are inhibited:
1. monoclinic system: c-axis unique setting (γ ̸= 90°),
2. trigonal system: rhombohedral lattice (a = b = c and α = β = γ ̸= 90°),
3. cubic and tetragonal systems: an inversion center not at the origin.
Unless standard settings are adopted, standardization of crystal axes and fractional coordinates
is indispensable for Rietveld analysis using RIETAN-FP; otherwise LAZY PULVERIX [86] built
in RIETAN-FP fails in generating diffraction indices hkl and their multiplicities.
103

Standardized crystal data are generally suitable for structure refinement because atoms in
the asymmetric unit are confined in a relatively narrow region. VESTA is capable of launching
STRUCTURE TIDY [46] for this purpose.
This feature of standardization of crystal-structure data is particularly useful when searchingfor compounds with similar structures using the Inorganic Crystal Structure Database (ICSD)[87].
In both STRUCTURE TIDY and LAZY PULVERIX, the following three standard settings
are preferred to other settings:
1. monoclinic system: b-axis unique setting (β ̸= 90°),
2. trigonal system: hexagonal lattice (a = b ̸= c and γ = 120°),
3. centrosymmetric space groups: an inversion center at the origin.
Let n be the number of atoms in the asymmetric unit, and (xj , yj , zj ; j = 1, 2, · · · , n) theirfractional coordinates. Then, the standardization parameter, Γ , is defined as
Γ =

n (
∑

x2j + yj2 + zj2)1
2(14.1).

j=1

Note that this equation does not contain occupancies, gj . STRUCTURE TIDY selects a setof xj , yj and zj (j = 1, 2, · · · , n) minimizing the Γ value. For better distinction between
different structure-type branches, STRUCTURE TIDY further outputs another standardization
parameter, CG, depending also on lattice parameters:()2 ( n)2 ( n
)2
n
∑
∑
1  ∑
CG =
a
xj + byj + c
zj
nV
j=1
j=1
j=1
(14.2)
( n
)
( n
)
( n
)12
∑
∑
∑
+2ab cos γ
xj yj + 2ac cos β
xj zj + 2bc cos αyj zj  ,
j=1

j=1

j=1

where V denotes the unit-cell volume.
VESTA automatically normalize the fractional coordinates between 0 to 1 before standardization of crystal-structure data because the absolute value of each fractional coordinate to
be converted by STRUCTURE TIDY should be less than unity; otherwise, the corresponding
part of the output text becomes disordered. If lattice parameters and fractional coordinates ofatoms in the asymmetric unit are changed on the transformation of the crystal lattice, current
crystal data are replaced with the standardized ones. The resulting data are output in the
Text Area while standard input and output files of STRUCTURE TIDY are, respectively, saved
as data.stin and data.sto in directory tmp under a directory for user settings (see 17.2);
data.sto provides us with more detailed information on the standardization of the crystal
data.
For example, suppose that a structure data file for Si (space group: F d3̄m) is created on
the basis of the first setting where Si in the asymmetric unit occupies the 8a site at (0, 0, 0).
Subsequent standardization using STRUCTURE TIDY moves Si from (0, 0, 0) to (1/8, 1/8,
1/8) in such a way that a center of symmetry is present at the origin (second setting). When
lattice parameters (a and α) and fractional coordinates based on a rhombohedral lattice are
input in a trigonal compound, STRUCTURE TIDY converts them into lattice parameters (aand c) and fractional coordinates based on a hexagonal lattice.
An example of standardization of crystal data is given below. The structure of a high-Tc
superconductor YBa2 Cu4 O8 is usually represented with the c axis perpendicular to the CuO2
104

conduction sheet and space group Ammm (No. 65) [88]. However, the standard setting describedin International Tables for Crystallography, volume A [30] is Cmmm; Rietveld analysis withRIETAN-FP has to be carried out on the basis of Cmmm.
Running STRUCTURE TIDY by selecting the “Standardization of Crystal Data” item underthe “Utilities” menus in VESTA, we obtain optimum crystal data based on space group Ammm;
they are listed at the tail of data.sto:
Axes changed to : b,c,aSetting x,y,z

origin0.00000 0.00000 0.00000

gamma =

2.9785( 65) C m m m- j2 i5 c
oS30------------------------------------------------------------------------DATAYBa2Cu4O8
2.9785 0.7284
CELL
3.8708 27.2309 3.8402
*
ATOM
O1
4(j)
0
0.05253 1/2
O2
ATOM
Ba
4(j)
0
0.36498 1/2
Ba
ATOM
Cu1
4(i)
0
0.06138 0
Cu2
ATOM
O2
4(i)
0
0.14562 0
O1
ATOM
Cu2
4(i)
0
0.21296 0
Cu1
ATOM
O3
4(i)
0
0.28178 0
O4
ATOM
O4
4(i)
0
0.44786 0
O3
ATOM
Y
2(c)
1/2
0
1/2
Y
TRANS b,c,a
REMARK Transformed from setting A m m m.

STRUCTURE TIDY converted a, b, and c axes in Ammm into b, c, and a axes in Cmmm,
respectively. The value of 2.9785 is the standardization parameter ‘gamma’, the last data,
0.7284, in the ‘DATA’ line is CG, and the last data of each site is the site name input by the
user.

14.4

Niggli-Reduced Cell

Low-symmetry unit cells can be selected in a variety of ways regardless of the method of determining the unit cell suitable for indexing the whole diffraction pattern. To compare and analyze
different indexing solutions, the lattice has to be reduced to a certain unique, peferably standard
form, which is usually achieved in the following way [89]:• In the orthorhombic system, the lattice parameters should be a ≤ b ≤ c.
• In the monoclinic system, the lattice parameters should be a ≤ c with the b-axis uniquesetting.
• In the triclinic system, the reduction becomes more complicated owing to possible multiple
choices of basis vectors in the lattice.
Niggli’s approach to unit-cell reduction [89, 90] defines the reduced cell in terms of theshortest vectors:
ν1 + ν2 + ν3 = minimum.
(14.3)STRUCTURE TIDY [46] transforms the given unit cell to a Niggli-reduced cell to describe thestructure in space group P 1 or P 1̄ when ‘*’ precedes a space-group symbol in an input file. If
the Niggli-reduction is successful, the solution is output in the Text Area.
From the reduced form, we can obtain the metric symmetry of the lattice, which is thehighest symmetry possible for the lattice on the basis of only geometric considerations. A
105second application of the Niggli-reduced cell is that different deformation variants of a basis
type (arstotype), probably conventionally described with different space groups and probably
non-comparable unit cells, can be compared if they have been standardized in their corresponding
Niggli-reduced cells.
The output in the Text Area on transformation to a Niggli-reduced cell for a spinel-type oxide
CoAl2 O4 is given below:
Lattice typeSpace group nameSpace group number
Setting numberF
F d -3 m
227
1

Lattice parametersa8.09500b
8.09500c
8.09500

alpha
90.0000

beta
90.0000

gamma
90.0000

Unit-cell volume = 530.457520
Structure parameters
x
y
z
g
B
Site
Sym.
1 Co Co1
0.00000
0.00000
0.00000
1.000
1.000
8a
-43m
====================================================================================
18 atoms, 16 bonds, 0 polyhedra; CPU time = 0 ms
Transformation to a Niggli-reduced cell====================================================================================
Setting x,y,z
origin 0.00000 0.00000 0.00000
gamma =
0.2165
ratio volume Niggli-reduced cell/original cell : 0.25
( 2) P -1- i
aP2------------------------------------------------------------------------DATA
0.2165 0.3437
CELL
5.7240 5.7240 5.7240
60.00060.00060.000
*
ATOM
Co
2(i)
0.12500 0.12500 0.12500
Co1
TRANS 0.5a+0.5b,0.5b+0.5c,0.5a+0.5c
REMARK Niggli-reduced cell

14.5

Site Potentials and Madelung Energy

VESTA utilizes an external program, MADEL [91], to calculate electrostatic site potentials, ϕi ,and the Madelung energy, EM , of a crystal. Three methods are used to calculate Madelung energies: Ewald, Evjen, and Fourier methods; the Fourier method is adopted in MADEL. MADEL
was originally written by Katsuo Kato (old National Institute for Research in Inorganic Materials) and slightly modified later by one of the authors (F.I.). An advantage of using MADEL
in VESTA is that troublesome inputting of formatted data, particularly symmetry operations,is avoidable.
The electrostatic potential, ϕi , for site i is computed by
ϕi =

∑
j

Zj
,
4πϵ0 lij(14.4)

where Zj is the valence (oxidation state) of the jth ion in the unit of the elementary charge, e(= 1.602177×10−19 C), ϵ0 is the vacuum permittivity (= 8.854188×10−12 F m−1 ), and lij is the106distance between ions i and j; the summation is carried out over all the ions j (i ̸= j) in the
crystal. In case site j is partially occupied, Zj should be multiplied by its occupancy, gj . EM
per asymmetric unit is calculated by using the formula
1∑
EM =ϕi Zi Wi ,(14.5)
2
i

with
Wi =

(occupncy) × (number of equivalent positions).
(number of general equivalent positions)(14.6)The summation in Eq. (14.5) is carried out over all the sites in the asymmetric unit. To obtainthe Madelung energy for the unit cell, EM must be multiplied by the number of general equivalent
positions .
Prior to the execution of MADEL, the oxidation numbers of atoms in the asymmetric unit
must be input in the Structure parameters tab of the Edit Data dialog box. Just after launching
MADEL, you are prompted to input two parameters, RADIUS and REGION:RADIUS:REGION:

Radius of an ionic sphere, s, in Å. The charge-density distribution, r, is givenby[]ρ(r) = ρ0 1 − 6(r/s)2 + 8(r/s)3 − 3(r/s)4 ,(14.7)
where r is the distance from the center of the ionic sphere (r < s and ρ(r) = 0
for r ≥ s). When lines for interstitial sites are not given in the input file, set
RADIUS at a value that is large enough but less than the smallest interatomic
distance (not half of it!).
Reciprocal-space range (in Å−1 ) within which Fourier coefficients are summed
up. MADEL sums up the Fourier coefficients with respect to all hkl’s withina sphere having a radius equal to RADIUS. Choose an appropriate value
ranging from 2 Å−1 to 4 Å−1 according to the desired precision of calculation.
Also, check whether or not a curve for Madelung energy versus REGION isnearly flat around the selected value of REGION.

The standard output of MADEL is displayed in the Text Area. The unit of ϕi is e/Å (1e/Å= 14.39965 V). The accuracy of ϕi and EM obtained using MADEL is limited to 3 or 4
digits.
The following lines give part of an output file when this feature is applied to investigating
distribution of hole carriers in a high-Tc superconductor, YBa2 Cu4 O8 [88, 92]:
Potentials of sites in the asymmetric unit

Ba
Y
Cu1
Cu2
O1
O2
O3
O4

ChargeWxyz
2.000000 0.250000 0.500000 0.135000 0.500000
3.000000 0.125000 0.500000 0.000000 0.500000
2.000000 0.250000 0.000000 0.213000 0.000000
2.500000 0.250000 0.000000 0.061400 0.000000-2.000000 0.250000 0.000000 0.145600 0.000000-2.000000 0.250000 0.000000 0.052500 0.500000-2.000000 0.250000 0.500000 0.052100 0.000000-2.000000 0.250000 0.500000 0.218200 0.000000

phi-1.330304E+00-1.639974E+00-2.164424E+00-1.798502E+00
1.310975E+00
1.931017E+00
1.925720E+00
1.133873E+00

Electrostatic energy per asymmetric unit
-3.318605 e**2/\AA = -47.78676 eV = -4.610721 MJ/mol

The electrostatic energy per mole is calculated by multiplying a factor of the Avogadro constant(6.02214×1023 mol−1 ) and EM together. In the above calculation, all the holes are assumed107

to be doped into the Cu2 atoms on the CuO2 conduction sheet with the Cu1 atoms having anoxidation state of +2.
Standard input files, *.pme, (see p. 141) for MADEL can be output by selecting the Export
Data... item under the File menu. This file is helpful in appending fractional coordinatesof interstitial sites to obtain their site potentials using the RIETAN-FP–VENUS integrated
assistance environment.

14.6

Powder Diffraction Pattern

VESTA utilizes RIETAN-FP [12] to simulate X-ray and neutron powder diffraction patterns fromlattice and structure parameters. As described in 16.1, a binary executable file of RIETAN-FP,
a graph plotting program, and a template input file, *.ins, for RIETAN-FP are specified in the
Preferences dialog box. Setting a variable NMODE at 1 (simulation of a powder diffraction pattern)in the template file is recommended. In addition, change the following data in the template file
if necessary:• Radiation (neutron, characteristic X-ray, or synchrotron X-ray diffraction).
• Wavelength (neutron and synchrotron X-ray diffraction) or target (diffraction using characteristic X rays).
• Geometry (Bragg–Brentano, transmission, or Debye–Scherrer geometry).
• Profile functions and profile parameters.
• Range of diffraction angles: 2θmin and 2θmax .
• Profile cutoff.
Profile parameters refined from typical diffraction data measured on a powder diffractometer,
which is often used on a routine basis, are preferable to those in one of template files includedin the distribution files of the RIETAN-FP–VENUS system. Further, a variable, NPAT, must be
given in the template file to specify a graph plotting program:
1. NPAT = 1: a pair of files, *.plt including commands to plot a graph and *.gpd storing data
to be graphed, for gnuplot1 (default),
2. NPAT = 2: an Igor text file, *.itx, for Igor Pro2 or WinPLOTR,3
3. NPAT = 3: a text file, *.itx, for RietPlot.4
The use of gnuplot is highly recommended because it is free software supporting many features;commands may be modified and added in *.plt to change the appearance of a graph. For details
in the content of *.plt, refer to RIETAN-FP_manual.pdf. If NPAT = 1, no graph plotting
program need to be specified in the Preferences dialog box.
Stable versions of gnuplot are included in the distribution files of the RIETAN-FP–VENUS
system5 for Windows and macOS.
Gnuplot can output a PDF file, *.pdf, whose margins are automatically cut, which is very
convenient when exporting the resulting PDF file to an application such as TEX, Microsoft
PowerPoint and Word, and Adobe Illustrator. (Windows) or ps2pdf (macOS).
1

http://www.gnuplot.info/
http://www.wavemetrics.com/
3
http://www-llb.cea.fr/winplotr/winplotr.htm
4
http://www.nims.go.jp/denzai/publ_rietplot.html
5
http://fujioizumi.verse.jp/download/download_Eng.html
2108Figure 14.4: Simulation of an X-ray powder diffraction pattern of a high-Tc superconductor,
YBa2 Cu4 O8 [88], which was plotted with Igor Pro.
On selection of the “Powder Diffraction Pattern...” item under the “Utilities” menu, a series ofprocedures, i.e., (a) generation of an input file, *.ins, for RIETAN-FP, (b) execution of RIETANFP in the simulation mode (NMODE = 1), and (c) representation of the resulting text file(s) by agraphing program are executed by VESTA as if the two programs were implemented in VESTA(Fig. 14.4). Text files, *.ins, *.lst (standard output), and a pair of files (*.plt and *.gpd forgnuplot) or *.itx, output by RIETAN-FP are saved in folder tmp under the settings directory(see 17.2).
For those who have not any program to plot data in *.itx with the Igor text format, asmall Java program named PowderPlot,6 which was developed by one of the authors (K.M.), is
included in the archive file of VESTA.
VESTA automatically standardizes lattice settings when outputting *.ins to satisfy conditions required by LAZY PULVERIX [86], which is embedded in RIETAN-FP to generate6

http://jp-minerals.org/powderplot/109diffraction indices, hkl, and their multiplicities, m. Standard lattice settings adopted in LAZYPULVERIX are just the same as those in STRUCTURE TIDY (see 14.3) [85, 46]: second settingsin centrosymmetric space groups with more than one origin choice and first settings in the otherspace groups. Then, beware that diffraction indices displayed in PowderPlot are incompatible
with the coordinate system adopted in VESTA if the lattice setting in VESTA is other than astandard one.
A list of reflections output at the tail of *.lst if NPRINT > 0 provides us with a variety of
information about hkl reflections included in a 2θ range specified by the user. For instance,
simulation of an X-ray diffraction pattern for fluorapatite gives the following output where line
heads were deleted for convenience:
h
1
1
1
1
1
1
2
2
1
1

k
0
0
0
0
1
1
0
0
1
1
.....

l
0
0
1
1
0
0
0
0
1
1

Code
+1
+2
+1
+2
+1
+2
+1
+2
+1
+2

2-theta
10.89510.92316.877
16.91918.92918.97621.891
21.94622.94523.003d
8.11382
8.113825.249195.249194.684524.68452
4.05691
4.05691
3.87283
3.87283

Ical |F(crys)| |F(magn)|
12287
16.7800
6113
16.7800
4465
11.15452221
11.15452079
12.09311034
12.09319679
30.29534814
30.29538580
21.18554268
21.1855
-

POF
1.001
1.001
0.999
0.999
1.001
1.001
1.001
1.001
1.000
1.000

FWHM
0.074510.074510.074430.074430.074450.074450.074530.074530.07457
0.07458

m
6
6
12
12
6
6
6
6
12
12

Dd/d
0.013637
0.013602
0.008757
0.008734
0.007795
0.007775
0.006726
0.006709
0.006413
0.006397

where Code +1 and Code +2 are, respectively, Kα1 and Kα2 reflections (‘+’ means not h̄k̄¯lbut hkl reflection in Friedel pairs), 2-theta is the diffraction angle 2θ, d is the lattice-planespacing, Ical is the calculated integrated intensity adjusted in such a way that the strongest
reflection has an intensity of 105 , F(nucl) and F(magn) are, respectively, the crystal-structure
and magnetic-structure factors, POF is the preferred-orientation function, FWHM is the full-width
at the half-maximum intensity, m is the multiplicity, and Dd/d is the resolution, ∆d/d.

14.7

Structure Factors

Figure 14.5: Structure Factors dialog box.
Selection of “Utilities” menu ⇒ “Structure Factors...” pops up the Equivalent Positions dialog
box (Fig. 14.5), whose use makes it possible to calculate structure factors from structural models(structure parameters) or volumetric data (electron or coherent-scattering length densities, ρ).
110

If multiple phase data are included in the data set, select a phase, for which structure factors
are calculated, at the top of the dialog box. If the phase data contain both structural andvolumetric data, select {Structural model} or {Volumetric data} in the list box to specify thetype of data from which structure factors are calculated. In the Source list box, {X-ray} and{Neutron} beam sources can be switched, and some typical characteristic X-rays can be selected
at a list box next to the Source list box. For the neutron source and the X-ray source with
its target specified as {Custom}, the wavelength can be edited in the text box. The minimum
lattice-plane spacing, d, of reflections whose structure factors are calculated is also specified in
the text box.
In X-ray diffraction, structure factor F of reflection h with diffraction indices hkl is formulated as
n
∑
)]
[ (
(14.8)
F (h) =
gj fj (h)Tj (h) exp 2πi hxj + kyj + lzj ,j=1

where j is the atom number, n is the total number of atoms in the unit cell, gj is the occupancy,
fj (h) is the (X-ray) atomic form factor, Tj (h) is the Debye–Waller factor, and xj , yj , and zj
are the fractional coordinates. The atomic form factor f (h) is a complex number that can bedivided into four separate components as
f (h) = f0 (h) + f ′ + if ′′ + fNT ,(14.9)

where f0 (h) is the coherent scattering factor, f ′ and f ′′ are the real and imaginary componentsof the dispersion correction, and fNT is the nuclear Thomson scattering [93],. The coherent
atomic scattering factor f0 , which is a function of sin θ/λ, is usually analytically approximatedby a sum of exponentials plus a constant:f0 (sin θ/λ) =

N
∑
i=1

)
(
sin2 θ
+ c.
ai exp −bi 2
λ(14.10)VESTA utilizes a set of parameters (ai , bi , and c) with N = 5 tabulated in [94]. These parameters
can be used in the range of 0 < sin θ/λ < 6. The real and imaginary parts, f ′ and f ′′ , ofthe dispersion correction are calculated by linear interpolation of theoretically calculated form
factors in energy ranges of E = 1–10 eV and E = 0.4–1.0 MeV [95, 96]. The nuclear Thompson
scattering term fNT is small and negative in the phase relative to the electronic form factor,
with small (negligible) dependences on λ and sin θ/λ.
In the case of neutron diffraction, fj (h) has to be replaced by the coherent-scattering length[10], bc :
n
∑
[ (
)]
F (h) =
gj bcj Tj (h) exp 2πi hxj + kyj + lzj .
(14.11)j=1

The value of bc is constant regardless of h because scattering of neutrons by negligibly small
atomic nuclei does not depend on sin θ/λ (in the absence of magnetic atoms).
On calculation of structure factors from structural models, ai , bi , ci , bc , f ′ , f ′′ , fNT , and themass attenuation coefficient, µ/ρ (µ: linear attenuation coefficient, ρ: density), of each element
are output in the Text Area as follows:a1
b1
Cu: 14.014192
3.738280
Se: 17.354071
2.349787
O: 2.960427

a2
b2
4.784577
0.003744
4.653248
0.002550
2.508818

a3
b3
5.056806
13.034982
4.259489
15.579460
0.637853

a4
b4
1.457971
72.554793
4.136455
45.181201
0.722838

111

a5
b5
6.932996
0.265666
6.749163
0.177432
1.142756cbc-3.254477
7.718000-3.160982
7.970000
0.027014

14.182259

5.936858

0.112726

34.958481

X-ray dispersion coefficients for λ = 0.154059 nm
f'
f''
f_NT
Cu: -2.02777E+00,
5.83511E-01, -7.26020E-03,
Se: -7.87865E-01,
1.13462E+00, -8.03140E-03,
O: 4.77543E-02,
3.20501E-02, -2.19440E-03,

0.390240

5.803000μ/ρ (cm^2/g)
5.01091E+01
7.75653E+01
1.09804E+01

If all the parameters of some elements are 0, the element names are not recognized by the
program; consequently, such elements do not contribute to calculated structure factors at all.
The element names can be edited in the Structure parameters page of the Edit Data dialog box.
When an option of “Ignore the effect of X-ray (anomalous) dispersion” is enabled, f ′ , f ′′ , and fNT
are set at 0, and none of these values are output in the Text Area.
Structure factors, F (h), can be calculated by the Fourier transform of ρ(x, y, z):∫∫∫
F (h) =
ρ(x, y, z) exp[2πi(hx + ky + lz)]dxdydz.
(14.12)In the {Volumetric data} mode, Eq. (14.12) is approximated by numerical integration of discretedensities:
1 ∑
1
1 ∑
∑
F (h) =
ρ(x, y, z)dV exp[2πi(hx + ky + lz)].
(14.13)x=0 y=0 z=0In this mode, only the minimum d value can be specified, and no other options affect calculation
results.

14.8

Fourier Synthesis

On selection of “Utilities” menu ⇒ “Fourier Synthesis...”, structure factors can be imported froman external file to carry out Fourier synthesis from them to visualize one of observed, calculated,or difference densities. Prior to the use of this menu, lattice parameters and space-group symmetry have to be given. The Fourier Synthesis dialog box is used to import and edit structure
factors (Fig. 14.6). To import structure factors, click the [Import...] button. One of observed,
calculated, or difference structure factors (Fo , Fc , or Fo − Fc ) can be imported from *.fcf files
output by SHELX-97 [97] with a “LIST 3” command. Fo can also be imported from input files,*.mem and *.fos, for MEM analysis [7, 8, 9]. To import structure factors from files with formats
other than the above ones, create a text file where each line contains the following data in freeformat:
h

k

l

|Fo|

|Fc|

Fc(real)Fc(imag)sigma(F)

Only unique reflections should be given in the file because all the equivalent reflections areautomatically generated according to the current space group. If parts of reflections in the list
do not satisfy conditions limiting possible reflections in the space group, a warning message willappear, and their structure factors will be reset to 0. F (000) is separately input in the text box
placed above the list of structure factors. In addition, the spacial resolution in real space mustbe specified in the unit of Å. After all the data have been input, press the [Calculate] button tocarry out Fourier synthesis from them.

14.9

Model Electron Densities

On selection of the “Utilities” menu ⇒ “Model Electron Densities”, electron densities are calculatedby the Fourier transform of structure factors, F (h), that are calculated from structure parameters and atomic scattering factors of free atoms [94] with Eq. (14.8). The spacial resolution of112

Figure 14.6: Fourier Synthesis dialog box.
electron densities is specified in the unit of Å. The number of grids along each crystallographic
axis, Nx , is automatically set such that Nx gives a resolution close to the specified value and thatNx satisfies symmetrical constraints. Then, the electron density, ρ(x, y, z), at the coordinatesof (x, y, z) is calculated byNx1
ρ(x, y, z) =
V

2
∑

Ny

2
∑

Nz

2
∑

F (h) exp[−2πi(hx + ky + lz)].

(14.14)

−N
−N
x
h= −N
k= 2 y l= 2 z
2

If the resolution is not sufficiently high, spurious noises appear in the resulting densities becauseof the so-called termination effect in Fourier synthesis. On the other hand, atomic scatteringfactors compiled in Ref. [94] are reliable only in a range of sin θ/λ < 6 Å−1 , which corresponds toa spacial resolution of approximately 0.042 Å. VESTA simply extrapolates the atomic scatteringfactors given in Ref. [94] even when the specified resolution is smaller than 0.042 Å.

14.10 Model Nuclear Densities
On selection of the “Utilities” menu ⇒ “Model Nuclear Densities”, densities of coherent-scattering
lengths [10], bc , are calculated by the Fourier transform of structure factors, F (h), that arecalculated from structure parameters and bc ’s of atoms with Eq. 14.11. The spacial resolution
is set in the same manner as with the calculation of model electron densities (see section 14.9).

14.11 Patterson Densities
On selection of the “Utilities” menu ⇒ “Patterson Densities”, Patterson functions in the unit cell
are calculated in three different modes:
1. “From Model Electron Densities” submenu: from structure parameters and atomic scatteringfactors of free atoms [94].
113

2. “From Model Nuclear Densities” submenu: from structure parameters and coherent-scattering
lengths of atoms.
3. “From Volumetric Data” submenu: by convolution of volumetric data that are currently
displayed.
On selection of the first two submenu, structure factors are calculated with Eqs. 14.8 and 14.11,
respectively, with the spacial resolution of electron or coherent-scattering-length densities specified in the unit of Å. Then, the Patterson density, P (x, y, z), at the coordinates of (x, y, z) is
calculated by
Nx1
P (x, y, z) =
V

2
∑

Ny

2
∑

Nz

2
∑

|F (h)|2 exp[−2πi(hx + ky + lz)],(14.15)

−N
−N
x
h= −N
k= 2 y l= 2 z2where Nx , Ny , and Nz are the numbers of grids along the x, y, and z axes, respectively (seesection 14.9).
When Patterson functions are calculated from the current volumetric data, structure factors
are calculated by∑∑∑
F (h, k, l) =ρ(x, y, z) exp[2πi(hx + ky + lz)],(14.16)xyz

and then P (x, y, z) is computed by Eq. (14.15). Therefore, the spacial resolution of the Patterson
function is the same as that of the volumetric data.

14.12 2D Data Display
We sometimes wish to visualize 2D distribution of a physical quantity on a plane. In such acase, open the 2D Data Display window to display 2D images of volumetric data. Details in thefeature of 2D Data Display are described in chapter 15.

14.13 Line Profile
Numerical values on a line segment with an equal step arecalculated from volumetric data by linear interpolationof volumetric data and output in a text file to plot a line
profile by a graphing program such as Igor Pro, gnuplot,
and WinPLOTR. After this item has been selected, adialog box (right figure) is opened to input fractional
coordinates, (x, y, z), of both ends and the total numberof data points to be calculated. After clicking the [OK]button, a file selection dialog box appears and prompts
you to input the name of an output file.
The top part of an output file when dealing with electron densities in rutile-type TiO2 islisted below:
TiO2 (rutile)
Point 1: 0.00000 0.00000 0.00000
Point 2: 0.30530 0.30530 0.00000
50
0.000000E+000 2.899010E+002
4.047903E-002 2.582953E+002

114

8.095806E-002
1.214371E-001
1.619161E-001.....

2.272991E+002
1.836505E+002
1.328268E+002

The first line gives a title, followed by two lines for the fractional coordinates of both ends,
those of Ti and O atoms in this case. The fourth line is the total number of data points (= 50),
followed by 50 lines. In each of the 50 lines, the first and second columns give a distance from
“Point 1” in the unit of Å and an interpolated value, respectively.

14.14 Peak Search
To search for peak positions in volumetric data, choose “PeakSearch” under the “Utilities” menu. When this item is selected,
a dialog box (right figure) is opened to restrict the maximum
number of peaks listed in the Text Area. Enter 0 to list all
the peaks detected in the volumetric data. The following data
are listed in the Text Area: integrated value of volumetric data,
number of peaks, peak positions, peak values, integrated valueof volumetric data for each peak, and Voronoi volume [21] calculated for each peak.
Results of peak search for electron densities in the unit cell of rutile-type TiO2 are exemplified
below:
Integrated value of volumetric data over the unit cell: 75.999979, 0.000000
Number of peaks in the volumetric data = 10
Number of voxels at Voronoi boundaries = 60870/262144
xyz
Peak value
Integrated
1
0.00000
0.00000
0.00000
2.89901E+02
1.99855E+01
20.50000
0.50000
0.50000
2.89901E+02
1.99855E+01
30.296880.29688
0.00000
5.66020E+01
9.00724E+00
40.703120.703120.00000
5.66020E+01
9.00724E+00
50.796880.203120.50000
5.66020E+01
9.00724E+00
60.203120.796880.50000
5.66020E+01
9.00724E+00

Volume7.64201E+00
7.64201E+00
1.17901E+01
1.17901E+01
1.17901E+01
1.17901E+01

The integrated values represent numbers of electrons per each site, which is calculated by summation of numbers of electrons over the Voronoi volume of the site.

14.15 Conversion of Electron Densities
We can extract some important physical quantities from electron densities obtained experimentally from X-ray diffraction experiments. Let ρ(r) be the electron density at the position vectorr, and ∇ρ(r) the gradient vector field of ρ(r). With VESTA, we can calculate Laplacians ofelectron densities ∇2 ρ(r), electronic kinetic-energy densities g(r), electronic potential-energy
densities ν(r), and electronic energy densities he (r) from electron densities displayed in the current page according to Tsirelson’s procedures [48]. Consideration of these functions, particularly∇2 ρ(r) and he (r), is not restricted by the bond critical point, rb , where ∇ρ(r) = 0, providing
us with a comprehensive characterization of chemical bonding in molecules and crystals.
The electronic kinetic-energy density is expressed as{}[]]5/3 λ ∇ρ(r) 2 k∇2 ρ(r)
ℏ2 3 ( 2 )2/3 [,(14.17)g(r) =
3π
ρ(r)
+
+
m 10
ρ(r)
2
115

where ℏ2 is Dirac’s constant, and m is the electron mass; the gradient ℏ-expansion of the Greenfunction around the classical Thomas-Fermi approximation [98] yields λ = 1/72 and k = 1/6.
The electronic-energy density equals the sum of g(r) and ν(r):(14.18)he (r) = g(r) + ν(r)with
ν(r) =ℏ2 2∇ ρ(r) − 2g(r).
4m(14.19)The electronic-energy density at rb gives a straightforward criterion for the recognition of the atomic interaction
type. That is, he (r) < 0 is observed in shared-type atomic
interactions whereas he (r) > 0 is observed in closed-shellinteractions. In a similar manner, if the electrons are locally concentrated around rb [∇2 ρ(rb ) < 0], the electrons
are shared by both nuclei, which is typical for shared or
covalent atomic interactions. Otherwise the electrons areconcentrated in each of the atomic basins [∇2 ρ(rb ) > 0],
and the atomic interaction belongs to the closed-shell type.
On selection of the “Conversion of Electron Densities”
item in the “Utilities” menu, a dialog box appears (rightfigure) to specify files to be output. The user-selected files
are output in the general volumetric-data format (see p. 135) to either a directory where theelectron densities are recorded or a directory specified by the user if VESTA fails in writing thefiles under that directory. By default, files storing volumetric data of ∇2 ρ(r) and he (r) are,respectively, output to files *.led and *.ted with their contents visualized in two pages.
The unit of input data should also be specified: either angstrom (Å−3 ) or atomic unit (a−30 ).
Table 14.1 lists units of output data.
Table 14.1: Units of converted volumetric data.
Input data∇2 ρ(r)

g(r)

Å−3

Å−5

a−3
0

a−5
0

Eh a−30
Eh a−30

Output dataν(r)Eh a−30
Eh a−30

he (r)
Eh a−30
Eh a−30a0 = 0.529177211 Å (a0 : Bohr radius), and Eh = 4.3597443 ×10−18 J (Eh : hartree).

116Chapter 15

TWO-DIMENSIONAL DATADISPLAY
15.1

Components of the 2D Data Display Window

Figure 15.1 shows the 2D Data Display window of VESTA running on Windows 7.

Figure 15.1: 2D Data Display window.
This window comprises the following four components:• Menu bar: On Windows and Linux, the menu bar is placed at the top of the Main Window.
On macOS, menus are displayed at the top of the screen. “File” and “View” menus areavailable in this window.
• Toolbar: Tools used frequently.
117• Side Panel: Colors, contours, and other properties of a 2D image are controlled in the Side
Panel. The minimum and maximum values in the 2D slice/projection data are displayed
at the top of the panel.
• Graphics Area: Display an 2D image of volumetric data.
If a 2D image has been previously displayed, it is restored as soon as this window is opened.
The default preferences of colors and width of contour lines, and the background color can bechanged when no 2D image is displayed in this window. To change these default settings, edit
values in the Side Panel and then close the window to save the settings.

15.2

Menus

• File menu
– Export 2D Data...: Export 2D data as a text file.
– Export Raster Image...: Export a graphic image as a file with a raster (pixelbased) format.
– Close: Close the 2D Data Display window.
• View menu
– Zoom In: Zoom in an image.
– Zoom Out: Zoom out an image.

15.3

Tools in the Toolbar

15.3.1

Rotation
Rotate around the x axis
Rotate around the x axis
Rotate around the y axis
Rotate around the y axis
Rotate around the z axis
Rotate around the z axis

These six buttons are used to rotate objects around one of the x, y, and z axes. The step widthof rotation (in degrees) is specified in a text box next to the sixth button:118

15.3.2

Translation
Translate upward
Translate downward
Translate leftward
Translate rightward

These four buttons are used to translate objects toward up, down, left, and right, respectively.
The step width of translation (in pixels) is specified in a text box next to the fourth button:

15.3.3

Scaling
Zoom in
Zoom out
Fit to the screen

These three buttons is used to change object sizes. The step width of zooming (in %) is specified
in a text box next to the third button:

15.4

Tools in the Vertical Toolbar
RotateTranslateMagnify
Magnify by mouse wheel
Shift slice by mouse wheel

15.5

Create and Edit a 2D Image

Click the [Slice...] button in the Side Panel to create a new image. Then, a dialog box named
Create New Slice is opened (Fig. 15.2).
Three different methods of creating a slice or a projection image can be used:
1. (hkl) plane in the bounding box
2. (hkl) plane defined by two vectors
3. Project along [hkl] axis.
Figure 15.3 schematically illustrates how a 2D image is created in each mode.
119

Figure 15.2: A dialog box for three different modes to draw a 2D image

15.5.1(hkl) plane in the bounding box

In this mode, a slice that cuts a bounding box is created. The size of the bounding box is
specified by ranges along x, y, and z axes. The position of the slice is given as a distance fromthe origin of 3D data in the unit of either its lattice-plane spacing, d, or Å.

15.5.2(hkl) plane defined by two vectors

In this mode, the size of the slice is defined by two lattice vectors: [u1 v1 w1 ] and [u2 v2 w2 ].
h, k, and l: Three values in an equation to represent the lattice vector, R = ha + kb + lc,
where a, b, and c denote fundamental lattice vectors.
Distance from the center of procection: The Center of projection lies on the projection vector that passes through the center of the slice (Fig. 15.4). The distance between the centerof slice and the Center of projection is specified in the unit of either its lattice-plane spacing,d, or Å. For example, when this value is 0, the (x, y, z) position specified as the Center ofprojection corresponds to the center of the slice.
Vectors parallel to the (hkl) plane: A pair of vectors, V1 and V2 , is specified in the expression of the lattice vector, ua + vb + wc, on the (hkl) plane. The two lattice vectors shouldbe parallel to the (hkl) plane but should not be parallel to each other.
Center of projection: Projection of this point along the [hkl] direction intersects the slice at
the center of the slice.
In this mode, two-dimensional data on the slice are recalculated by linear interpolation.
When the numbers of data points along x, y, and z directions in the volumetric data are N [0],N [1], and N [2], respectively, the number of data points, Nx , along the [u1 v1 w1 ] direction iscomputed by
Nx = (int)(N [0] ∗ u1 + N [1] ∗ v1 + N [2] ∗ w1 ).
(15.1)The same procedure is applied to the number of data points along the [u2 v2 w2 ] direction.

15.5.3

Project along [hkl] axis

This mode draws cumulative data of a series of (hkl) slices summed up along the [hkl] direction
in a user-specified range. The number of data points is calculated in the same way as with the“(hkl) plane defined by two vectors” mode.
In the Slice Properties dialog box for this mode, four kinds of data have to be input:
120

A

B

[u2 v2 w2][u1 v1 w1]C

Figure 15.3: Electron-density distribution drawn with the three different modes for the (111)plane in rutile-type TiO2 . (A) “(hkl) plane in the bounding box” mode, (B) “(hkl) plane definedby two vectors” mode, and (C) “Project along [hkl] axis” mode. The electron densities were
determined by MEM from X-ray powder diffraction data.

121

Distance from the center of projection

Center of the slice

Center of projection

Projection vector []Figure 15.4: Schematic image of the relation between the center of the projection
and the center of the slice.
h, k, and l: Three values in an equation to represent the lattice vector, R = ha + kb + lc,
where a, b, and c denote fundamental lattice vectors. The [hkl] direction is defined withR.
Range of projection: A pair of values specified by distances from the Center of projection.
They are input in the unit of either its lattice-plane spacing, d, or Å.
Vectors parallel to the (hkl) plane: A pair of vectors, V1 and V2 , is specified in the expression of the lattice vector, ua + vb + wc, on the (hkl) plane. The two lattice vectors shouldbe parallel to the (hkl) plane but should not be parallel to each other.
Center of projection: Projection of this point along the [hkl] direction intersects the slice at
the center of the slice.

15.6

Controlling Properties of a 2D Image

In the General page in the Side Panel, colors of the background and plane are mainly controlled(see Fig. 15.1).
Press a button at the right side of Background color: to change the background color. Checkbox “Bird’s eye view” enables or disables Bird’s eye view (Fig. 15.5). If “Draw grid edges” ischecked, edges of grids are drawn with solid lines of a color and a width specified below thecheck box (Fig. 15.6).
When “Fill polygons” is checked, the surface of the plane is filled with colors corresponding todata values. Colors of the plane are controlled in the same manner as with sections of isosurfaces(see 12.1.6).
122

Figure 15.5: Bird’s eye view of a (001) slice of rutile-type TiO2 .

A

BFigure 15.6: Electron-density distribution on the (001) plane in rutile-type TiO2 . (A) without
grid edges and (B) with grid edges drawn with solid lines.
In the Contours page (Fig. 15.7), various properties of contour lines are specified. Check“Draw contour lines” to draw contour lines, which are plotted in two different modes: linear or
logarithmic.
Contours are plotted in linear and logarithmic modes as solid lines (style L1) and dashedones (style L2). The width and colors of these lines are specified in the text boxes and buttons
in the Style frame box.
In the linear mode, lines are drawn at every Interval in data ranging from Min. to Max. The
numerical value at the N th line, F (N ), is given by
F (N ) = Min. + N × Interval.

(15.2)In this mode, line style L1 (solid line) is applied to lines of positive values, and line style L2(dashed line) to lines of negative values.
123

A

B

Figure 15.7: Contours page in the Side Panel. (A) Linear mode and (B) logarithmic mode.
In the logarithmic mode, F (N ) is computed by
F (N ) = A × B N /Step ,(15.3)

where A and B are constants specified by user. Line style L1 is applied to every “step” lines
starting from the first one, and for other lines the L2 style is applied. For example, when Nminis set to an integer value, the L1 style is used for lines with integer values of N /Step, and theL2 style is used for lines with non-integer values of N /Step.

15.7

Exporting 2D data

To export 2D data of the specified slice as a text file, choose “File” menu ⇒ “Export 2D Data…”
in the 2D Data Display window. No 2D data files can be output on selection of style “(hkl) planein the bounding box” in the Slice Properties dialog box.

124

Chapter 16

PREFERENCES
Default settings for the behavior of VESTA are changed in the Preferences dialog box (Fig.
16.1).

Figure 16.1: Preferences dialog box.

16.1

Settings for RIETAN

Settings for simulation of X-ray and neutron powder diffraction patterns are specified in framebox Settings for RIETAN.
Specify the absolute path of the executable binary file of RIETAN-FP [12], which is used for
simulating powder diffraction patterns, after clicking the [Browse...] button at the right of text
box {RIETAN}.
Click the [Browse...] button at the right of text box {Viewer} to specify an application toplot the powder diffraction pattern output to file *.itx by RIETAN-FP. This text box may beleft vacant on the use of Igor Pro because the extension, itx, is associated with Igor Pro bydefault if it has been installed.
VESTA uses a template file to export a standard input file of RIETAN-FP. The template
file is specified in text box {Template (*.ins)} by clicking the [Browse...] button at the right of
the text box. In the exported file, data other than a space group, and lattice and structure125

parameters are copied from the template file. Beware that the format of the template file
must be compatible with the version of RIETAN-FP used by VESTA. The use of *.ins for anolder version of RIETAN-FP may cause an error on execution of its latest version. The default
template file distributed with VESTA is that for the latest version of RIETAN-FP.

16.2

Font for Text Area

In frame box Font for Text Area, a text font for the Text Area is specified. Specify the text fontafter clicking the [Select...] button at the right of text box {Font for Text Area}.

16.3

Open a New File in

When VESTA reads in new data, a new page may be assigned to them, or an existing page may
be reused. To input new data under a new page, select “New tab” in radio box Open a new filein. When “Current tab” is selected, data assigned to the current page are discarded, and new
data are input in the current page. Unless changes in old data have been saved, VESTA asks
you whether or not the changed data should be saved in a file.

16.4

Animation

Two settings for animation speed, i.e., the rotation angle per frame and the interval between
frames are specified in frame box Animation. The rotation angle per frame is specified in text
box {Step (deg./frame)}. The interval between frames is specified in milliseconds in text box{Interval (ms)}. The number of frames per second is
1/ (tdraw + tinterval ) ,(16.1)

where tdraw is the time required to draw a single frame of an image on the Graphics Area, andtinterval is the interval between frames.

16.5

Start-up Search for Bonds

When this option is turned on, bonds will be automatically generated for atom pairs closer thancertain distances when opening files. The list of element pairs to search for bonds, and bonddistances, and styles for each pair are recorded in the “style.ini” file.

16.6

A Setting for Raster Image Export

Resolutions of atoms and cylindrical bonds are scaled when exporting pixel-based images. The
numbers of stacks and slices for the graphics image, Rg , is scaled as
Rg = Rd × s × f,

(16.2)

where Rd is the number of stacks or slices for display on the screen, s is the scale of the image,and f is the factor to increase Rg specified in text box {Increasing factor for stacks/slices}.
126

16.7

Default isosurface level

The default isosurface level, d(iso), after opening a file storing volumetric data, ρ, is calculatedasd(iso) = ⟨|ρ|⟩ + n × σ(|ρ|),(16.3)
where ⟨|ρ|⟩ is the average of |ρ|’s, σ(|ρ|) is the standard deviation of |ρ|, and n is a parameterto adjust d(iso).

16.8

History level

VESTA supports for undoing and redoing user’s operations. The default value of the maximum
number of history level is 100.

127

Chapter 17

INPUT AND OUTPUT FILES
17.1

File Formats of Volumetric Data

Volumetric data are composed of regular grids in 3D space. A volume element, “voxel,” at eachgrid point represents a value on the grid point. Voxels are analogous to pixels, which represent
2D image data.
In general, two types of formats are used to record volumetric data in files: general andperiodic grids. Figure 17.1 schematically illustrates the general concepts of the two kinds ofthe formats.
The general grid is a uniform one spanned inside a bounding box for molecules and a unit
cell for crystals. For crystal structures, part of data in the general grid are redundant owing to
the periodicity of the data. For example, a numerical value at (1, 1, 1) are equal to that at theorigin, i.e, (0, 0, 0). Grids where these redundant points have been omitted are called periodic
ones.
VESTA distinguishes the grid types automatically from file extensions. For volumetric datawith the periodic grid format, VESTA internally generates the general grid by adding redundantdata points. On preparation of volumetric data using a self-made script or a program, the user
must pay attention to the grid type of a file by himself.

AB: irreducible data points: redundant points (periodic replicas)

Figure 17.1: Two types of the grids for volumetric data on a plane. (A) general gridand (B) periodic grid.

128

17.2

Directories for User Settings

VESTA loads and saves two files, VESTA.ini and style/default.ini in a directory for user settings
to store user settings for the program and for graphics, respectively. A directory, tmp, to store
temporary files is also created in the same directory. The location of the settings directory
depends on operating systems, and is determined in the following order of priority.

17.2.1

Windows• When environmental variable VESTA_PREF is defined, the specified directory is used.
• When a directory named VESTA exists in %HOMEPATH%\AppData\Roaming\, it is used.
(%HOMEPATH% represents the full path of the user’s home directory, and %HOMEPATH%\AppData\
is a hidden directory.)• When the user has permission to write in the program directory of VESTA, that directoryis used so as not to put the home directory in disorder.
• A directory %HOMEPATH%\AppData\Roaming\VESTA\ is created on the first execution of
VESTA to use it.

17.2.2macOS• When environmental variable VESTA_PREF is defined, the specified directory is used. To
define environmental variables for GUI applications, they must be described in a text file
named environment.plist under a hidden directory, ~/.MacOSX. To make it easier to define
VESTA_PREF, a utility called set_VESTA_PREF.app is included in the RIETAN-VENUS
package1 ; refer to Readme_mac.pdf for details in set_VESTA_PREF.app.
• A directory ~/Library/Application Support/VESTA/ is created on the first executionof VESTA, and it is used. Note that ~/Library is a hidden directory under the home
directory (~/).

17.2.3Linux• When environmental variable VESTA_PREF is defined, the specified directory is used.
• A hidden directory ~/.VESTA/ is created on the first execution of VESTA to use it.

1

http://fujioizumi.verse.jp/download/download_Eng.html

129

17.3

Files Used by VESTA
Table 17.1: Files used by VESTA.

asfdc

A file storing parameters related to atomic form factors.

element.ini

A file storing default colors and radii of atoms.

spgra.dat

wyckoff.dat

A file storing information on 230 space groups, e.g., coordinates of equivalent positions compiled in International Tables for Crystallography, volume A [30].
A file storing non-conventional symbols of orthorhombic
space groups.
A file storing information on wyckoff positions.

mspgr.dat

A file storing information on 1651 magnetic space groups.

style.ini

Default file for styles of the graphic scene.

template.ins

A template file for the standard input of RIETAN-FP [12].
It is used for exporting *.ins and simulating of powder
diffraction patterns.
Default file for various settings of VESTA.

spgro.dat

VESTA_def.ini$USER_DIR/VESTA.ini†$USER_DIR/style/default.ini†

A file for user settings of VESTA. This file is copied from
VESTA_def.ini when VESTA is executed for the first timeby the user.
User settings file for styles of the graphic scene. This file iscopied from style.ini when VESTA is executed for the firsttime by the user.

† $USER_DIR is a directory for user settings (see 17.2).

17.4

Input Files

17.4.1

Structural data

1. VESTA format (*.vesta)
Text files containing the entire structure data and graphic settings. File *.vesta saved by
VESTA may contain relative paths to volumetric data files and a crystal-data file that areautomatically read in when *.vesta is reopened. If any one of keywords, IMPORT_STRUCTURE,
IMPORT_ORFFE, IMPORT_DENSITY, and IMPORT_TEXTURE, is included in *.vesta and followed by lines specifying relative paths to data files, these data files are also input by
VESTA when *.vesta are opened.
After Rietveld analysis with RIETAN-FP [12], lattice and structure parameters in *.vesta
are automatically updated provided that *.vesta and *.ins share the same folder.
2. VICS format (*.vcs)
http://fujioizumi.verse.jp/visualization/VENUS.html
VICS, which is the predecessor of the structure-drawing part of VESTA, is now obsolete.
Nevertheless, this format is still supported in VESTA to maintain compatibility.
1303. American Mineralogist Crystal Structure Database [99] (*.amc)
http://rruff.geo.arizona.edu/AMS/amcsd.php
In part of AMCSD text files, extra characters are attached to space group names, and nonstandard space-group symbols are used. Some of such non-standard space-group settings
may not be read in correctly. In such a case, modify the space-group symbol appropriately
and then change the setting number in the Unit cell tab of the Edit Data dialog box ifnecessary. Sometimes, you have to convert fractional coordinates by yourself if a nonstandard setting that is not described in International Tables for Crystallography, volume
A [30] is adopted.
4. asse (*.asse)
http://www.nims.go.jp/cmsc/staff/arai/asse/
5. Chem3D (*.cc1)
http://openbabel.org/docs/2.3.1/FileFormats/3D_viewer_Formats.html
6. Crystallographic Information File (CIF; *.cif) [100]http://www.iucr.org/resources/cif/
CIF has a variety of formats for crystal data. You can get detailed information about CIF
from the above Web site. For example, CIF files may contain Cartesian coordinates, but
VESTA cannot input them. Note that VESTA does not support all the formats allowedin the CIF format. For example, Cartesian coordinates included in CIFs cannot be input
with VESTA; only fractional coordinates should be given in CIFs. For readable formats,refer to example files of *.cif in VENUS/examples/VICS/CIF.
In the case of *.cif containing multiphase data, all the data are input in the same tab andoverlapped with each other. To visualize only one phase in such a case, select “Edit” menu
⇒ “Edit Data” ⇒ “Phase…”. Select an unnecessary phase in the list, and press [Delete]button.
The CIF specification presents multiple ways of inputting entries for space-group symmetry. VESTA searches the entries in the following order:_symmetry_equiv_pos_as_xyz_symmetry_space_group_number_symmetry_space_group_name_H-M

If one of the above entries are given in *.cif, VESTA recognizes space-group symmetry.
For example, CIFs created by SHELX-97 [97] through WinGX [101] contain neither spacegroup number nor space-group symbol but have a list of symmetry operations.
If none of the above entries are correctly given, the space group is regarded as P 1. In thiscase, set the space group in the Unit cell tab of the Edit Data dialog box after opening sucha file, or modify a line relevant to the space group in the CIF in the following manner:_symmetry_space_group_number 12or_symmetry_space_group_name_H-M 'P 21/n'

7. CrystalMaker text file (*.cmt, *.cmtx)
http://www.crystalmaker.com
CrystalMaker is a commercial program for building, displaying, and manipulating all kindsof crystal and molecular structures.
1318. Crystal Structure Search and Retrieval (CSSR; *.cssr)
http://www.maciejharanczyk.info/Zeopp/input.html
In a file with the CSSR format, a setting numbers may be given after ‘OPT =’. Unfortunately, we have no information about setting numbers in this format. Then, please change
it in the Unit cell tab of the Edit Data dialog box if necessary.
9. Cambridge Structural Database [102] (CSD/FDAT; *.csd, *.fdt))
http://www.ccdc.cam.ac.uk/Solutions/CSDSystem/Pages/CSD.aspx
10. DL_POLY [103] format (CONFIG, REVCON, *.config)
https://www.scd.stfc.ac.uk/Pages/DL_POLY.aspx
11. FEFF input file (feff.inp)
http://www.feffproject.org/
FEFF [104, 105] is an automated program for ab initio multiple-scattering calculationsof X-ray Absorption Fine Structure (XAFS) and X-ray Absorption Near-Edge Structure(XANES) spectra for clusters of atoms. The names of input files for FEFF must be either
feff.inp or FEFF.INP.
12. FHI-aims input file (*.in)https://aimsclub.fhi-berlin.mpg.de/FHI-aims is an accurate all-electron, full-potential electronic structure code package forcomputational materials science.
13. Output file of the Elk FP-LAPW Code (GEOMETRY.OUT)
http://elk.sourceforge.net/
Elk is an all-electron full-potential linearised augmented-planewave (FP-LAPW) code fordetermining the properties of crystalline solids.
14. GSAS [18] format (*.EXP)
http://www.ncnr.nist.gov/xtal/software/gsas.html
15. Inorganic Crystal Structure Database [87] (ICSD; *.ics)
http://www2.fiz-karlsruhe.de/icsd_home.html
Two retrieval programs, RETRIEVE for MS-DOS and FindIt for Windows, of ICSD output
text files with quite different formats. VESTA is capable of reading in both types of thecrystal data files.
In these *.ics files, extra characters are sometimes attached to space group names, e.g.,’P 42/n m c S’, which should be ’P 42/n m c’ (P42 /nmc). In addition, full HermannMauguin space-group symbols are sometimes given in ICSD text files. In such a case,an error message appears in both the Text Area and a message box. Read it carefully
to proceed to a next operation. When you encounter this type of an error, it is strongly
recommended to output a CIF instead of *.ics.
16. ICSD-CRYSTIN: (*.cry)
17. MDL Molfile (*.mol)
http://en.wikipedia.org/wiki/Chemical_table_file
18. MINCRYST (Crystallographic Database for Minerals; *.min)
http://database.iem.ac.ru/mincryst/
132

In part of MINCRYST text files, extra characters are attached to space group names, andnon-standard space-group symbols are used. In such a case, an error message appears in
the Text Area. Such space group names need to be appropriately changed. Change thesetting number in the Unit cell tab of the Edit Data dialog box if necessary.
19. MOLDA [106] (*.mld)
http://www3.u-toyama.ac.jp/kihara/cc/mld/readme.html
The Web site of MOLDA has been closed because the author, Hiroshi Yoshida passed awayin 2005. Then, the MODRAST/MOLDA format for *.mld is briefly explaned here. This
format consists of the following lines:(a) Line No. 1: A comment about the compound, e.g., its name(b) Line No. 2: Number of atoms, na , in the compound(c) Lines No. 3 − (3 + na ): Cartesian coordinates (x, y, and z) and an atomic number(d) Line No. (4 + na ): Number of bonds, nb , in the compound(e) Lines No. (5 + na ) − (5 + na + nb ): A pair of atom numbers
For example, in the case of ethylene, where na = 6 and nb = 5, the following lines are
required:"Ethylene (CH2=CH2)"
6.66958, 0, 0, 6
1.23873, -.94397, 0, 1
1.23873, .94397, 0, 1-.66958, 0, 0, 6
-1.23873, -.94397, 0, 1
-1.23873, .94397, 0, 1
5
1, 4
1, 2
1, 3
4, 5
4, 6

20. Protein Data Bank (PDB; *.pdb) [107]http://www.wwpdb.org/
PDB has a variety of formats for crystal data. You can get detailed information on PDB
in a Web page http://www.wwpdb.org/docs.html. Note that VESTA does not support
all the formats allowed in these two formats. For readable formats, refer to *.pdb in
VENUS/examples/VICS/PDB.
21. Input file of RIETAN-FP/2000 [12, 108] (*.ins)
http://fujioizumi.verse.jp/download/download_Eng.html
VESTA cannot input *.ins for versions of RIETAN (e.g., RIETAN-94) earlier than RIETAN2000. In the case of *.ins containing multiphase data, only the crystal data of the firstphase are input.
In *.ins, the volume name of International Tables should be not ’I’ but ’A’ in accordancewith a specification in RIETAN-FP. For example, ’A-230-2’ is input for the second setting133

of space group Fd 3̄m. The input of ’I-230-2’ causes an error. Lattice parameters must be
given within one line in the following way:
CELLQ 9.36884 9.36884 6.88371 90.0

90.0

120.0

0.0

1010000

22. Output file of RIETAN-FP [12] (*.lst)
http://fujioizumi.verse.jp/download/download_Eng.html
Beware lest *.lst output by RIETAN-2000 [108] is input.
23. Input file of SHELXL [97] (*.ins)
24. Output file of STRUCTURE TIDY (*.sto)
25. Structure data files output by USPEX (gatheredPOSCARS, BESTgatheredPOSCARS)[109, 110]
http://han.ess.sunysb.edu/~USPEX/
26. WIEN2k [41] (*.struct)
http://www.wien2k.at/
27. XMol XYZ (*.xyz)
http://en.wikipedia.org/wiki/XYZ_file_format
http://openbabel.org/docs/2.3.1/FileFormats/XYZ_cartesian_coordinates_format.html
XMol developed at the Minnesota Supercomputer Center is a utility for creating andviewing graphic images of molecules.
28. F01 for SCAT [58, 111] and C04D for contrd
http://www.dvxa.org/
VESTA need to read in c04d, which is an input file of contrd, in addition to f01 if astructural model is to be overlap with volumetric data. For this purpose, the dimensionsof a boundary box (an area where volumetric data are output to text files) in c04d are
required. For details in contrd, refer to Readme_contrd.txt in the VENUS package[15, 16]. Of course, c04d and f01 should be placed in the same folder. If c04d has notbeen input by VESTA, atomic coordinates are treated in the Cartesian coordinate system,
as is the case for *.xyz files. In this case, volumetric data, *.scat and *.sca, cannot be
overlapped with the structural model.
All the atoms recorded in f01 must be included within the above boundary box. Otherwise,atomic coordinates are normalized within the boundary box by assuming periodicity, whichleads to the appearance of incorrect structures in the Graphics Area.
The assistance environment for the DV-Xα method2 using Hidemaru Editor is very convenient when carrying out a series of electronic-state calculations.
The Web site of Genta Sakane of Okayama University of Science:
http://www.chem.ous.ac.jp/~gsakane/
is very useful for those who like to visualize physical quantities calculated with contrd.
“Introduction to the assistance environment for the DV-Xα method3 ” distributed there
is a detailed Japanese document suitable for beginners in the DV-Xα method as well as
VESTA.
2
3

http://fujioizumi.verse.jp/visualization/VENUS.html#assistance_environment
http://www.chem.ous.ac.jp/~gsakane/dvxa_assistance_environment_1.html

13429. MXDORTO/MXDTRICL [112, 113] (FILE06.DAT, FILE07.DAT)
http://kats-labo.jimdo.com/mxdorto-mxdtricl/
MXDORTO and MXDTRICL are Fortran programs for molecular dynamics simulation.
30. XTL format (*.xtl)
Text files used in Cerius2 (Accelrys, Inc.4 ). GULP [114] and GSAS [18] are capable ofoutputting crystal data with this format.

17.4.2

Volumetric data

31. MEM densities in binary format (*.pri, *.prim)
http://fujioizumi.verse.jp/visualization/VENUS.html
http://jp-minerals.org/dysnomia/en/
Binary files of 3D electron and nuclear densities output by PRIMA [5] or Dysnomia [7, 8]
and those of Patterson functions output by ALBA [17]. The unit of electron densities(strictly speaking, number densities of electrons) recorded in these files is Å−3 , and thatof nuclear densities is fm Å−3 .
32. MEM densities in text format (*.den)
Text files of 3D electron and nuclear densities output by PRIMA, Dysnomia, MEED [115],
MEND [116], and ENIGMA [117]. The unit of electron densities recorded in these files is
Å−3 while that of nuclear densities is fm Å−3 .
33. Energy Band (*.eb)
Text files having practically the same format with *.rho. Files *.eb are used to visualize
Fermi surfaces from results obtained with programs for band-structure calculations, e.g.,
WIEN2k [41]. As a matter of convenience, a constant is added to all the energy eigenvalues
in *.eb so as to make them greater or equal to zero. Therefore, the isosurface level has tobe set with this padding in mind.
Masao Arai of NIMS provides us with detailed information about *.eb in his Web site:
http://www.nims.go.jp/cmsc/staff/arai/
34. General volumetric-data (text format) (*.?ed)
A file with the general volumetric-data format stores one of the following physical quantities
converted from electron densities according to procedures proposed by Tsirelson [48] (see14.15):∇2 ρ(r):
g(r):
ν(r):
he (r):

Laplacian of the electron density (*.led).
Electronic kinetic-energy density (*.ked).
Electronic potential-energy density (*.ped).
Electronic energy density (*.ted).

with the format (common to all the files with the extension of ?ed):
Title:a, b, c, α, β, γ:N1+1, N2+1, N3+1:
4

Title up to 80 characters.
Lattice parameters with at least one space between two parameters (free format).
Numbers of voxels along the a, b, and c axes, respectively,
with at least one space between two integers (free format).

http://accelrys.com/

135followed by elements of a three-dimensional array, D(((D(I1, I2, I3), I3 = 1, N3+1), I2 = 1, N2+1), I1 = 1, N1+1)

with any number of data in each line and at least one space between two real data (freeformat). Note that voxels at N1+1, N2+1, and N3+1 lie on x = 1, y = 1, and z = 1,
respectively. A top part of an example of *.ted is given below:
TiO2 (rutile)4.593934.593932.95886
90.00000
90.00000
90.0000065
65
65-3.700291E+004 -3.355551E+004 -2.515189E+004 -1.581991E+004 -8.551052E+003 -4.096268E+003-1.802126E+003 -7.564262E+002 -3.147750E+002 -1.347187E+002 -6.129182E+001 -3.045389E+001-1.683229E+001 -1.043066E+001 -7.226008E+000 -5.529954E+000 -4.588889E+000 -4.036150E+000-3.669965E+000 -3.365605E+000 -3.043458E+000 -2.664371E+000 -2.229370E+000 -1.771544E+000-1.337361E+000 -9.658093E-001 -6.762105E-001 -4.680259E-001 -3.280885E-001 -2.393913E-001.....

VESTA allows you to save a file, *.?ed, with the general volumetric-data format. Accordingly, VESTA serves as a converter from a binary file to a text one.
35. Periodic volumetric-data (text format) (*.grd)
http://www.ncnr.nist.gov/xtal/software/gsas.html
Text files for 3D Fourier maps output by GSAS [18]. A program, 3DBVSMAPPER [118],
for automatically generating bond-valence sum images is also capable of outputting files
with this format. To create *.grd files that can be input by VESTA, select option “C –Select section (X, Y, or Z) selection” in Fourier calculation setup and then enter “X” forprompt “Enter section desired (X,Y,Z - choose Z for DSN6 maps).”
The file format is essentially the same as the general volumetric-data format, except thatthe three-dimensional data array, D, are output in the following range:(((D(I1, I2, I3), I3 = 1, N3), I2 = 1, N2), I1 = 1, N1)

VESTA also allows you to export volumetric data in this format.
36. General volumetric-data format (binary) (*.ggrid)
37. Periodic volumetric-data format (binary) (*.pgrid)
38. Compressed volumetric-data format (*.m3d)
39. SCAT volumetric-data files (*.sca, *.scat)
http://www.dvxa.org/
Electron densities, electrostatic potentials, and wave functions calculated with contrd fromfiles F09 and F39 output by SCAT [58, 111]. Text files (CHG3D.SCA, POT3D.SCA,
WXXX-3D.SCA, WXXXU-3D.SCA, and WXXXU-3D.SCA) created with a batch file
named contrd.bat can directly be input by VESTA, where XXX denotes an integer assigned
to a wave function. To learn details in *.SCA, refer to Readme_contrd.txt distributed136

as a part of package [15, 16]. Three-dimensional numerical data recorded in *.SCA or*.SCAT are drawn without any conversion.
Units for electron densities, electrostatic potentials, and wave functions are, respectively,bohr−3 , Ry (rydberg), and bohr−3/2 , where bohr is the atomic unit for length, i.e., 1 bohr
= a0 = 5.29177211 ×10−11 m = 0.529177211 Å (a0 : Bohr radius), and 1 Ry = Eh /2 =2.179 871 9 ×10−18 J (Eh : hartree).
Refer to No. 23 in 17.4.1 for the assistance environment for the DV-Xα method and its
detailed document written in Japanese.
40. WIEN2k (*.rho)
http://www.wien2k.at/ (WIEN2k)
http://www.nims.go.jp/cmsc/staff/arai/wien/venus.html (wien2venus.py)
A script, wien2venus.py, coded in Python5 by Masao Arai of NIMS makes it possible toexport electron densities calculated with WIEN2k [41] to a text file, *.rho, which is in turnvisualized by VESTA. The unit of electron densities stored in this file is bohr−3 .
41. WinGX 3D Fourier map (*.fou)
http://www.chem.gla.ac.uk/~louis/software/wingx/
Text files of 3D Fourier Maps output by WinGX [101]. To create *.fou that can be
input with VESTA, open “FOURIER MAP Control Panel” of WinGX from Maps menu
→ FOURIER MAP → Slant plane. Select “3D Fouier (Beevers-Lipson)” and “Write
MarchingCubes File” options and set “Projection” at Z axis. The minimum and maximumof “Summation limits” should be set at 0 and 1 for all of X, Y, and Z axes. A resolution
for each axis should be carefully set in view of the following matter.
In this format, data points along each axis are not uniformly distributed but just placed
at intervals of given resolutions. When length of an axis is L and resolution is set at d, thenumber of data points, NPIX, is set at the integer part of L/d + 1. The output files have ageneral grid format with nearly correct periodicity only if L/d is close to an integer. It is
recommended that special positions lie exactly on data grid. For example, if mirror planes
lie at x = 1/4 and x = 3/4, L/d should be multiples of 4.
42. X-PLOR/CNX (*.xplor)
http://en.wikipedia.org/wiki/X-PLOR (CNX)
http://superflip.fzu.cz/ (Superflip)
Superflip [119] is a computer program for ab initio structure solution of crystal structuresby the charge-flipping method [120, 121, 122]. Superflip outputs electron densities in theunit cell in file *.x-plor with the X-PLOR format [123], which can be directly visualized
by VESTA.

17.4.3Structural and volumetric data

43. CASTEP [124, 125] (*.cell, *.charg_frm)
http://www.castep.org/
File *.cell contains crystal-structure data while file *.charg_frm stores electron densities
in the unit of Å−3 . Only a structural model is visualized when *.cell is opened by VESTA.
On the other hand, both a structural model and electron-density distribution are displayedwhen opening *.charg_frm. Because no unit-cell dimensions are recorded in *.charg_frm,
it must be accompanied by *.cell.
5

http://www.python.org/

13744. GAMESS [126] input and volumetric data files output by MacMolPlt [127]http://www.msg.ameslab.gov/GAMESS/GAMESS.html (GAMESS)
https://brettbode.github.io/wxmacmolplt/ (MacMolPlt)
A GAMESS input file, *.inp, can readily be obtained from a GAMESS log file, *.log,
with MacMolPlt. At first, examine the unit of final Cartesian coordinates of atoms afterconvergence in this file using a text editor. Then, run MacMolPlt to open *.log. In the
Windows menu, select ‘Coordinates’ through the name of *.log and check whether the unitof Cartesian coordinates is Å or bohr (au). The unit should be Å, as is usual with VESTA.
If the unit is Bohr, select ‘Convert to Angstroms’ under the Molecule menu. Then, select‘Input Builder’ through the name of *.log in the Windows menu and click [Write File] tocreate *.inp storing atomic symbols and Cartesian coordinates.
Next, a volumetric data file, *.mmp, in which the origin of the 3D grid is recorded, has to be
output. In the Windows menu, select ‘Surfaces’ through the name of *.log. Specify an itemfrom ‘3D Orbital’, ‘3D Total Electron Density’, and ‘3D Molecular Electrostatic Potential’.
In the dialog box that appears subsequently, change the number of grid points and gridsize appropriately, select an orbital (in the case of ‘3D Orbital’), and click [Update]. An
isosurface plus a ball-and-stick model appear in the *.log window. The number of grid
points, origin, and grid increment are displayed by clicking [Parameters...]. Then, click[Export...]. Specify the name and location of *.mmp with the same basename as *.inp.
Note that *.inp and *.mmp must share the same folder.
45. Gaussian Cube format (*.cube, *.cub)
http://www.gaussian.com/
Text files storing electron densities, spin densities, electrostatic potentials, wave functions,and so forth calculated with Gaussian [128, 129] with a keyword of ‘Cube’.6 .
Cube files can also be created by Firefly (previously known as PC GAMESS).7
46. VASP (*.vasp, CHG, CHGCAR, PARCHG, LOCPOT, ELFCAR, POSCAR, CONTCAR)
http://www.vasp.at/
http://www.materialsdesign.com/medea (commercial software MedeA including VASP as
its component)
All the above files are text files storing crystal-structure and volumetric data output by
VASP [130, 131].
CHG stores lattice vectors, atomic coordinates, and total charge densities multiplied by
the unit-cell volume, V . PAW one-center occupancies are added to them in CHGCAR.
Though both CHG and CHGCAR provide us with the same information on the valencecharges, the file size of CHG is smaller than that of CHGCAR owing to the lower accuracyof the numerical data. PARCHG has the same format as CHG has, storing partial charge
densities of a particular k-point and/or band. When these files are read in to visualize
isosurfaces and sections, data values are divided by V in the unit of bohr3 . The unit ofcharge densities input by VESTA is, therefore, bohr−3 .
LOCPOT contains lattice vectors, atomic coordinates, and Coulomb potentials (unit:eV), i.e., total potentials without exchange-correlation contributions (unless the line of
LEXCHG=−1 is commented out in main.F). ELFCAR, which has the same format as
CHG has, stores dimensionless electron localization functions (ELF). POSCAR and CONTCAR include lattice vectors, atomic coordinates, and optionally starting velocities and6
7

Units used in Gaussian 03 are described in http://www.gaussian.com/g_tech/g_ur/k_constants.htm
http://classic.chem.msu.su/gran/gamess/138

predictor-corrector coordinates for molecular-dynamics calculation. POSCAR and CONTCAR, respectively, correspond to the initial structure and the final one output by VASP
at the end of a job; CONTCAR can be used to continue the job.
Owing to the absence of symbols of elements or atomic numbers in these files, they must
accompany another file, OUTCAR, to display structural models. OUTCAR may be renamed *.out having the same basename as *.vasp has. Only lines following ‘POTCAR:’
at the top part of OUTCAR are required to obtain symbols of elements.
When files are read in for surface coloring, no data values are scaled unless the file nameis CHGCAR or PARCHG.
47. XCrySDen XSF format (*.xsf)
http://www.xcrysden.org/ (XCrySDen)
http://www.abinit.org/ (ABINIT)
http://www.abinit.org/documentation/helpfiles/for-v6.4/users/cut3d_help.html (Cut3D)
http://www.quantum-espresso.org/ (Quantum ESPRESSO)The ABINIT package [132] for the ab initio computation of material properties has afeature to output binary files storing electron densities, electrostatic potentials, and wave
functions. They can be converted into text files, *.xsf, having the XSF format of XCrySDen [133, 134] using a converter named Cut3D. The unit of electron densities is bohr−3 .
Cut3D supports data Type 13 (XCrySDen/VENUS wavefunction real data), whereby wave
functions can be directly output in *.xsf.
Quantum ESPRESSO [135] for quantum simulations of materials has also a feature to
output files with the XSF format.
Detailed information about the XSF format can be obtained fromhttp://www.xcrysden.org/doc/XSF.html
In general, *.xsf consists of some sections that begins with keywords. VESTA reads involumetric data from a BEGIN_BLOCK_DATAGRID section. To make it possible to overlap
isosurfaces with a structural model, *.xsf should also contain (1) PRIMEVEC and PRIMCOORD
sections or (2) CONVVEC and CONVCOORD sections. Furthermore, lattice vectors in the
PRIMVEC or CONVVEC section must agree with spanning vectors in the BEGIN_DATAGRID
section. The unit of primitive lattice vectors (PRIMVEC) and Cartesian coordinates is Å inthe XSF format.

17.5

Output Files

17.5.1

Data files

Structure data
1. Original format of VESTA (*.vesta)
The entire information about data displayed currently are saved in a text file, *.vesta, with
the VESTA format. Files with the VESTA format contains all the structural data andgraphic settings whereas volumetric data are not directly recorded in *.vesta but imported
from external files. Directories and names of files storing volumetric data are recorded in*.vesta as relative paths to the volumetric-data files from the directory of *.vesta, whichmakes it possible to save the entire information about the current data in a small file
without duplicating huge volumetric data.
139

Structural data can be optionally imported from an external file in the same manner. To
prevent the structural data from being recorded directly in *.vesta, import structural datausing the Import Data dialog box with option “Link” (see 6.3.6). A name of file *.ffe output
by ORFFE [45] is also recorded in *.vesta so that geometrical parameters recorded in *.ffe
are automatically listed in the Geometrical Parameters dialog box after reopening *.vesta(see 14.2). After Rietveld analysis with RIETAN-FP [12], lattice and structure parametersin *.vesta are automatically updated provided that *.vesta and a standard input file, *.ins,
share the same folder.
2. Chem3D (*.cc1)
http://openbabel.org/docs/2.3.1/FileFormats/3D_viewer_Formats.html
3. Crystallographic Information File (CIF; *.cif)
http://www.iucr.org/resources/cif/
4. DL_POLY input file (*.config)
https://www.scd.stfc.ac.uk/Pages/DL_POLY.aspx
5. Protein Data Bank (PDB; *.pdb)
http://www.wwpdb.org/
6. User input file of RIETAN-FP/2000 (*.ins)
http://fujioizumi.verse.jp/download/download_Eng.html
The feature of outputting *.ins enables us to read in crystal data files of various formats
with VESTA, simulate powder diffraction patterns, and carry out subsequent Rietveld
refinements with RIETAN-FP [12]. Note that standard input files of RIETAN-2000 [108]and RIETAN-FP are incompatible with each other. VESTA uses a template file to export input files of RIETAN-FP/2000, and the default template file, template.ins, has the
RIETAN-FP format. If a standard input file with the RIETAN-2000 format is desired,change the template file to a file with the RIETAN-2000 format in the Preferences dialog
box (see 16).
In Rietveld refinement or simulations of powder diffraction patterns with RIETAN-FP, thefollowing standard lattice settings of STRUCTURE TIDY [85, 46] embedded in RIETANFP should be selected:• Monoclinic system: b-axis unique setting (β ̸= 90°),• Trigonal system: hexagonal lattice (a = b ̸= c and γ = 120°),• Centrosymmetric space groups: an inversion center at the origin (origin choice 2 inRef. [30]).
Unless these three standard settings are adopted, LAZY PULVERIX [86], which is also
incorporated in RIETAN-FP, fails in generating correct diffraction indices hkl and theirmultiplicities. Accordingly, VESTA automatically transforms the lattice setting of a crystal
structure to the standard one when exporting *.ins with the RIETAN-FP/2000 [108, 12]format.
It should be pointed out that fractional coordinates in part of crystal data recorded indatabases have too small significant digits, e.g., 0.3333 instead of 0.333333. In such a case,please increase the significant digit to 6 or 7 before outputting *.ins.
7. VASP (POSCAR, *.vasp)
http://www.vasp.at/140

8. VRML (*.wrl)
http://www.web3d.org/x3d/specifications/vrml/
9. XMol XYZ (*.xyz)
http://en.wikipedia.org/wiki/XYZ_file_format
http://openbabel.org/docs/2.3.1/FileFormats/XYZ_cartesian_coordinates_format.html
10. P 1 structure (*.p1)
Simple text files storing lattice parameters and atomic positions of all the atoms in theunit cell. Atomic positions are written in fractional coordinates, and the space group of
the crystal is converted into P 1 (triclinic, No. 1). This format is useful when preparing
initial atomic configurations in computational simulations.
11. Fractional coordinates (*.xtl)
Simple text files with the xtl file format storing atomic positions of all the atoms currently
displayed in the Graphics Area. Atomic positions are written in fractional coordinates. The
space group of the crystal is treated as P 1 (triclinic, No. 1) for convenience.
12. MADEL input files (*.pme)
Although MADEL can be executed from VESTA (see 14.5), input files of MADEL, *.pme,
should be manually edited to calculate electrostatic site potentials of interstitial (vacant)sites, whose fractional coordinates have to be input in FORMAT(3F9.6) at the tail of*.pme. The use of the RIETAN-FP–VENUS integrated assistance environment includedin the distribution file of the RIETAN-FP system is highly recommended to edit *.pme
and run MADEL to input it on Hidemaru Editor.8 For details in the above assistanceenvironment, read Readme_macros.txt contained in the distribution file.
When exporting files with this format, you are prompted to input two parameters, RADIUS
and REGION (see 14.5). Refer to the user’s manual of MADEL for details in theseparameters to be input in *.pme.
13. Input files of STRUCTURE TIDY (*.sto)
Volumetric data
14. PRIMA binary format (*.pri)
15. General volumetric-data format (*.3ed)
16. Periodic volumetric-data format (*.grd)
17. General volumetric-data format (binary) (*.ggrid)
The general volumetric-data format is the most recommended file format when exporting
volumetric data. It is lossless, and yet files with this format have sizes much smaller thanthose for text formats or even some other binary formats. In the case of periodic volumetricdata, *.pgrid described below is preferred because of better compression efficiency.
18. Periodic volumetric data (binary format) (*.pgrid)This file format is similar to *.ggrid format but assumes the periodicity of grids to minimize data redundancies. When there are more than two symmetry operations, which are
generated from space-group information set or directly edited by the user, only grid datain the asymmetric unit are recorded in *.pgrid.
8

http://hide.maruo.co.jp/software/hidemaru.html

14119. Compressed volumetric-data format (*.m3d)

Two-dimensional data
Suppose that the 2D Data Display window has been opened to choose option “(hkl) plane definedby two vectors” or “project along [hkl] axis” in the Create New Slice dialog box (see 15.5). Then,
two-dimensional data shown in 2D Data Display window can be output by selecting the 2D Data
Display item from the File menu. Note that this function is disabled on selection of the first
option: “(hkl) plane in the bounding box.”
For example, electron densities on the (100) plane with a distance of 0.5d from the origin in
rutile-type TiO2 are output as follows:
TiO2
(hkl)
:
1
0
0
Vector 1:0
10
Vector 2:001
Distance from the origin: 2.29696 2.29696
65
650.000000
0.000000
1.771768E-02
0.000000
0.046232
1.777942E-02
0.000000
0.092464
1.796342E-02
0.000000
0.138697
1.826639E-02
0.000000
0.184929
1.868208E-02.....

The two integers (65 and 65) in the sixth line are numbers of divisions along the x and y axes.
Three data in each data line are X, Y , and density, where X and Y are, respectively, x and ycoordinates (unit: Å) from the origin in the two-dimensional plot.

17.5.2

Raster images

1. BMP
2. EPS
3. JPEG9
4. JPEG 200010
5. PNG11
6. PPM
7. RAW
8. RGB (SGI)
9. TGA
10. TIFF
9

http://www.jpeg.org/jpeg/index.html
http://www.jpeg.org/jpeg2000/index.html
11
http://www.libpng.org/pub/png/
10142Images of structural and volumetric data displayed in the Graphics Area and the 2D Data Display
window can be recorded in files with a variety of graphics formats. When saving files storing
bit-mapped images, select “Export Raster Image...” in the “File” menu. The image size of theexported graphics files is scaled up as a multiple of the size of the Graphics Area. The scale factor
is input after the file name has been entered in a file selection dialog box. VESTA can exporthuge images that exceed the maximum width and height of the viewport, which are displayedin the Text Area just after launching VESTA, e.g.,
Maximum supported width and height of the viewport: 4096 x 4096

The resolution of objects, i.e., the number of stacks and slices for atoms and bonds, are also
scaled by two factors {Scale} and {Increasing factor for stacks/slices} specified in the Preferences
dialog box (see 12.1.2, 12.1.3, and 16).

17.5.3Vector images

1. Encapsulated PostScript (EPS)
2. Portable Document Format (PDF)
3. PostScript (PS)
4. Scalable Vector Graphics (SVG)
Images of structural and volumetric data displayed in the Graphics Area of the Main Window
can be saved as vector images. When saving files storing vector images, select “Export Vector
Image...” under the “File” menu. There are some limitations on exporting vector images. Colors
of isosurfaces and sections colored according to volumetric data cannot be represented with
vector image formats. Translucent polygons of polyhedra, lattice planes, and isosurfaces become
opaque in all the formats except for PDF.

17.5.4

Output text

The content of the Text Area can be saved as a text file by selecting “Save Output Text...” in the“File” menu.

143

CLOSING REMARKS
Feedback and Suggestions
The development of VESTA has been led by user feedback. Its phenomenal success results fromthe response from around the country. We assume that things are working fine provided that no
feedback is received. If its users were so selfish as to behave like “black holes,” VESTA would not
be improved very much. Please feel free to inform us of any bugs and your thoughts. Sending
us files relevant to your troubles could facilitate the debug.
Encouraging responses would present us with driving forces for further development andrefinement of VESTA.

Acknowledgments
We wish to thank Ruben A. Dilanian of Melbourne University for his dedication to a great dealof programming for VICS and VEND, the two predecessors of VESTA. Akiji Yamamoto of
NIMS coded a highly efficient compressed volumetric-data format (*.m3d), and Takashi Ida of
Nagoya Institute of Technology wrote Voronoi integration code for volumetric data. Masao Arai
of NIMS and Masataka Mizuno of Osaka University kindly coded file converters, wien2venus.py
for WIEN2k and contrd for SCAT, respectively. Hiroshi Ohki of Shinshu University helped
us improve VICS, VEND and VICS-II significantly. Genta Sakane of Okayama University of
Science, Takuji Ikeda of AIST, and Kazuki Komatsu of the University of Tokyo gave us manysuggestions and helped us debug the program.
Finally, we thank for all who have helped us improve the program by reporting bugs andoffering valuable ideas.

144

Appendix A

Keyboard Shortcuts
Table A.1: Keyboard shortcuts.
Global (Menu)
Ctrl + N

File menu - New Structure…

Ctrl + O
Ctrl + S
Ctrl + Shift + S
Ctrl + W
Ctrl + Q
Ctrl + E
Ctrl + B
Ctrl + +Ctrl + –Ctrl + Shift + A
Ctrl + Shift + P
Ctrl + Shift + B
Ctrl + Shift + O

File menu - Open…
File menu - Save…
File menu - Save as
File menu - Close
File menu - Exit
Edit menu - Edit Data - Phase…
Edit menu - Bonds…
View menu - Zoom In
View menu - Zoom Out
View menu - Overall Appearance…
Objects menu - Properties…
Objects menu - Boundary…
Objects menu - Orientation…

When the Graphics Area has focus
Change Manipulation to the Rotate mode
r
m
t
s
d
a
Left
Right
Up
Down
Ctrl + Up
Ctrl + Down
Shift + Left
Shift + Right
Shift + Up

Change Manipulation to the Magnify mode
Change Manipulation to the Translate mode
Change Manipulation to the Select mode
Change Manipulation to the Distance mode
Change Manipulation to the Angle mode
Rotate along −yRotate along +yRotate along −x
Rotate along +x
Rotate along −z
Rotate along +z
Rotate along −y (1/10 step)
Rotate along +y (1/10 step)
Rotate along −x (1/10 step)145

Table A.1: Continued from the previous page.
Shift + Down
Ctrl + Shift + Up
Ctrl + Shift + Down
Alt + Left
Alt + Right
Alt + Up
Alt + Down

Rotate along +x (1/10 step)
Rotate along −z (1/10 step)
Rotate along +z (1/10 step)
Translate along −x
Translate along +x
Translate along +yTranslate along −y146Bibliography[1] W. I. F. David, J. Appl. Crystallogr., 20, 316 (1987).
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153Index
2D Data Display, 114

CrystalMaker, 131
CSD, 132
CSSR, 132
Cut3D, 139
cutoff plane, 70

ABINIT, 139
ALBA, 2, 135
Alchemy, 2
AMCSD, 131
American Mineralogist Crystal Structure Database,Debye–Waller factor, 111
131depth-cueing, 99
anisotropic atomic displacement, 2
diffraction index, 111
anisotropic atomic displacement parameter,dihedral angle, 9, 74, 79
47
dispersion correction, 111asse, 131
displacement ellipsoid, 4, 8, 28, 29, 45, 59, 75,
atomic form factor, 111
84, 85axial vector, 64
distortion index, 9, 75
axis setting, 103
DL_POLY, 132, 140
dot surface, 21, 22, 27, 30
ball-and-stick model, 4, 21, 27–29, 74, 79, 83,
DV-Xα, 134
102
DVSCAT, 50
best plane, 3
dynamic displacement, 63
BMP, 142
Dysnomia, 2, 135
Bohr radius, 10, 50, 91, 116, 137
bond angle, 9, 74, 79
effective coordination number, 9, 76
bond angle variance, 9, 76
electronic kinetic-energy density, 115, 135bond valence parameter, 9electronic potential-energy density, 115, 135bond valence sum, 9, 77
electronic-energy density, 115, 135
electrostatic site potential, 45
Cartesian coordinate, 134
electrostatic site potentials, 106
CASTEP, 137
ELFCAR, 138
centrosymmetric space group, 104
Elk FP-LAPW Code, 132
CG, 104
encapsulated PostScript, 143
charge distribution, 9, 76
Energy Band, 135
charge-flipping method, 137
ENIGMA, 135
Chem3D, 131, 140
EPS, 142, 143
CHG, 138
equivalent isotropic atomic displacement
CHGCAR, 138, 139
parameter, 47
CIF, 13, 77, 131, 140
CNX, 137
FDAT, 132
coherent-scattering length, 111
FEFF, 132
complex lattice, 34, 42
FHI-aims, 132
CONTCAR, 138
FindIt, 132
contour line, 93, 118, 123
formal charge, 45
coordination polyhedron, 75
Fourier map, 136, 137
Crystallographic Information File, 131
fractional coordinate, 9, 103, 104, 111
154

GAMESS, 138
gamma, 105
Gaussian, 138
general equivalent position, 22, 37, 101
general grid, 128
general position diagram, 86
general volumetric data, 141general volumetric-data format, 141
GLUI, 2
GLUT, 2
gnuplot, 108, 114
Graphic Area, 102
GSAS, 132, 135, 136
GULP, 135

MINCRYST, 132, 133
MOLDA, 133
MS-DOS, 132
MXDORTO, 135
MXDTRICL, 135
neutron diffraction, 111
Niggli-reduced cell, 105
nuclear Thomson scattering, 111
occupancy, 46, 74, 111
opacity, 4, 9, 30, 88, 90, 91, 93
OpenGL, 2, 15–17, 99
ORFFE, 102, 140
ORTEP-III, 60
OUTCAR, 139
oxidation state, 13, 77

hexagonal lattice, 104
ICSD, 13, 77, 104, 132
ICSD-CRYSTIN, 132
Igor Pro, 108, 114
interatomic distance, 9interfacial angle, 81
inversion center, 103, 104
isotropic atomic displacement parameter, 47

PARCHG, 138, 139
Patterson function, 9, 135
Patterson-function density, 2
PDB, 13, 133, 140
PDF, 143
peak search, 115
periodic grid, 128
periodic volumetric-data format, 141
PNG, 142
polar vector, 64
polyhedra, 74
polyhedral model, 4, 21, 28, 29, 61
polyhedral volume ratio, 75
portable document format, 143
POSCAR, 138, 140
POTCAR, 139
powder diffraction pattern, 22, 108, 125, 130
PowderPlot, 109
PPN, 142
PRIMA, 2, 135
primitive lattice, 42
primitive translation vector, 39
principal axis, 2protein data bank, 133
PS, 143

JPEG, 142
JPEG 2000, 142
Laplacian, 115
Laplacian of electron density, 115, 135
lattice parameter, 36, 104lattice plane, 66
lattice-plane spacing, 47
LAZY PULVERIX, 103, 104, 109
Line Profile, 114
Linux, 4, 16–18, 20, 117
LOCPOT, 138
MacMolPlt, 138
macOS, 4, 16, 21, 23
MADEL, 22, 106, 141
Madelung energy, 45, 106
magnetic moment, 4, 63
maximum-entropy method, 1
maximum-entropy Patterson method, 2
MDL Molfile, 132
mean square displacement, 2, 47
MEED, 135
MEM-based pattern fitting, 1
MEND, 135
metric tensor, 39, 40, 47

quadratic elongation, 9, 76
RAW, 142
reciprocal basis vector, 39
reciprocal-lattice, 47, 71, 72
redo, 3
RETRIEVE, 132
155

RGB (SGI), 142
rhombohedral lattice, 103
RIETAN-2000, 133, 140
RIETAN-FP, 13, 22, 81, 102, 108, 109, 125,
130, 133, 134, 140
RietPlot, 108
rotation matrix, 37, 38

wxWidgets, 2, 14
X-PLOR, 137
XAFS, 132
XANES, 132
XCrySDen, 139
XMol XYZ, 134, 141
XSF format, 139
XTL format, 135

SCAT, 134, 136, 144
SHELX-97, 112, 131
shift of the origin, 39
shininess, 67, 83, 88, 98
space-filling model, 4, 6, 21, 27, 28, 83
specular, 67, 83
standard setting, 104, 105
standardization of crystal data, 103
standardization parameter, 104
static displacement, 63
stick model, 4, 21, 27–29, 87
STRUCTURE TIDY, 104, 105, 110
substructure, 42Superflip, 137
superstructure, 42
surface coloring, 9, 22, 30, 49, 91, 139
SVG, 143
symmetry operation, 9, 37, 38, 40, 41, 74, 75,
79, 80, 101
temperature factor, 46
TGA, 142
TIFF, 142transformation matrix, 38, 40
translation vector, 74
undo, 3unit-cell volume, 38
VASP, 138, 140
VEND, 1, 2, 144
VENUS, 1, 134, 137, 139
VICS, 1, 2, 130, 144
VICS-II, 2, 144
Voronoi tessellation, 2
voxel, 4, 128
VRML, 141
WIEN2k, 9, 134, 135, 137
Windows, 4, 15, 16, 19, 20, 117, 132
WinGX, 131, 137
WinPLOTR, 108, 114
wireframe model, 4, 21, 22, 27–29
156

USER’S MANUAL FOR MADEL
1. WHAT IS MADEL?
MADEL is a FORTRAN 77 program to calculate electrostatic site potentials, φi, and Madelungenergies, EM , of ionic crystals by the Fourier method. It was programmed by Dr. Katsuo Kato,
National Institute for Research in Inorganic Materials (NIRIM), 1-1 Namiki, Tsukuba, Ibaraki
305, Japan.
This manual was translated from Japanese into English with some modifications and additions
by Dr. Fujio Izumi of NIRIM during his short stay at the Argonne National Laboratory inMarch, 1991.

2. HOW TO COMPILE MADEL
This program should be compiled using an automatic double-precision option of a FORTRAN
77 compiler. If the compiler of your computer, unfortunately, does not support such a
convenient feature, declare IMPLICIT DOUBLE PRECISION (A–H, O–Z) in the main programand all the subprograms of MADEL.

3. CREATING AN INPUT FILE FOR MADEL
Line 1. Title (A72)
Line 2. Radius of an ionic sphere and Fourier-summation range (2F6.2)
RADIUS: radius of an ionic sphere, s, in Å. The charge-density distribution, r, is given byρ (r) = ρ0 [1 – 6(r/s)2 + 8(r/s)3 – 3(r/s)4 ],where r is the distance from the center of the ionic sphere (r < s and ρ (r) = 0 for r≥ s). When Lines 7 are not given, set RADIUS at a value that is large enough but
less than the smallest interatomic distance (not half of it!).
REGION: reciprocal-space range (in Å–1) within which Fourier coefficients are summed up.
MADEL sums up the Fourier coefficients with respect to all hkl ’s within a sphere
having a radius equal to RADIUS. Choose an appropriate value within the range
2.0–4.0 Å–1 according to the desired precision of calculation. Also, check whether
or not a curve for Madelung energy versus REGION is nearly flat around theselected value of REGION.
1

Line 3. Three integers related with the crystal structure (3I3)
NS: number of symmetry operations. Inverted positions (–x, –y, –z) in a centrosymmetriccell are not required, whereas translated positions in a complex lattice must be input.
NA: number of atoms contained in the asymmetric unit.
IZ: = 0, non-centrosymmetric cell.
= 1, centrosymmetric cell.
Line 4. Lattice constants (3F9.4, 3F9.3)
A(1): a (Å) or a* (Å–1).
A(2): b (Å) or b* (Å–1).
A(3): c (Å) or c* (Å–1).
A(4): α (degree) or cosα .
A(5): β (degree) or cosβ .
A(6): γ (degree) or cosγ.
Lines 5. Symmetry operations (F11.6, 2I2, F11.6, 2I2, F11.6, 2I2)
Input NS lines (j = 1, NS).
Column1 - 11: translational part of xj or blank.
12 - 13: 1, 2, 3, –1, –2, –3, or blank for x, y, z, –x, –y, –z, or blank, respectively, as used in
the expression for the transformed xj.
14 - 15: 1, 2, 3, –1, –2, –3, or blank for x, y, z, –x, –y, –z, or blank, respectively, as used in
the expression for the transformed x j. Columns 12 and 13 are exactly equivalent toColumns 14 and 15. Also, note that an expression such as xj = 2x must be treated as
xj = x + x.
16 - 26: translational part of yj or blank.
27 - 30: integers representing plus or minus x, y, or z in the expression for transformed yj as
described above.
31 - 41: translational part of zj or blank.
42 - 45: integers representing plus or minus x, y, or z in the expression for transformed zj as
described above.
These lines have the same format as those in ORFLS (least-squares structure-refinement
program) and ORFFE (program to calculate interatomic distances, bond angles, etc.) developed
at the Oak Ridge National Laboratory. Therefore, they can be copied easily from input files
for these two programs.

2Lines 6. Sites in the asymmetric unit (A8, 1X, 5F9.4)
Input NA lines (I = 1, NA).
ATOM(I): name of an atom occupying the ith site.
Z(I): valence (oxidation state) of the atom. Input a positive value for a cation and anegative one for an anion. In case this site is partially occupied, Z(I) must be
multiplied by its occupation factor (occupation probability).
W(I): (occupation factor for the ith site) × (number of equivalent positions for the ithsite) / (number of general equivalent positions).
X(1,I): fractional coordinate, xi.
X(2,I): fractional coordinate, yi.
X(3,I): fractional coordinate, zi.
Lines 7. Fractional coordinates of vacant sites whose potentials are to be calculated (3F9.6)
Input lines as many as you like (I = NA+1, NA+2, .....). These lines are optional.
X(1,I): fractional coordinate, xi.
X(2,I): fractional coordinate, yi.
X(3,I): fractional coordinate, zi.
In addition to the occupied sites input in Lines 6, electrostatic potentials containing no contribution
from each site input in Lines 7 can be calculated automatically. In such a case, RADIUS
should be set in such a way as not to overlap with each other: less than half the smallest
interatomic distance in the whole structure.
4. OUTPUT
The output of MADEL is described in German in the present version. The unit of theelectrostatic site potential, φi , for the ith site is e/Å (1 e/Å = 14.399652 V), where e is theelementary charge (= 1.6021773×10 –19 C). The precision of results obtained using MADEL islimited to 3 or 4 digits.

When the site input in Lines 7 is located within an ionic sphere, MADEL prints out a potential(POBBA) excluding contribution of the sphere and, in addition, a potential (PMBBA) calculated
by substituting an original point charge for the sphere. If the site is not contained in any ionicsphere, a potential in which contribution of the nearest neighbor (either one if two or morenearest neighbors are present) is subtracted is output as POBBA.
The Madelung energy for the asymmetric unit, E M, is calculated by using the formula3

EM = 1 ∑ φi Zi W i
2 i
where Zi is the valence (oxidation state) of the ith site in the unit of e, and Wi is W(I). EM mustbe multiplied by the number of general equivalent positions to obtain the Madelung energy forthe unit cell.

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