User manual of computer programs “RITS”
for data analysis of Bragg-edge neutrontransmission spectrum

16th September 2015
30th April 2022 Revised

Hirotaka Sato
Faculty of Engineering, Hokkaido University

Introduction
RITS (Rietveld Imaging of Transmission Spectra) is computer program series which can quantitatively evaluatevarious crystalline microstructural information in the pulsed neutron Bragg-edge transmission imaging method.
Owing to this data analysis code, the pulsed neutron Bragg-edge transmission imaging can become a useful material
characterization tool. The aim of this user manual is progress of materials science using the pulsed neutron imaging by
providing the information on how to use the RITS code, note and troubleshooting for users. The principle and thealgorithm of the RITS code were discussed in:
H. Sato: “Quantitative Imaging of Crystalline Structure Information by using a Pulsed Neutron
Transmission Method” Ph.D. Thesis, Hokkaido University, 2011. (In Japanese)or
H. Sato, T. Kamiyama and Y. Kiyanagi: “A Rietveld-Type Analysis Code for Pulsed Neutron Bragg-Edge
Transmission Imaging and Quantitative Evaluation of Texture and Microstructure of a Welded α-Iron
Plate” Materials Transactions 52(6) (2011) 1294-1302. (In English)
Additionally, I also prepared a PPT file (RITS_overview.ppt) explaining the algorithm. Note that this user manual
does not have the explanation of the algorithm.
Note⚫ Program distribution by a user is forbidden without the permission by me. Please discuss with me.
⚫ Please refer the five papers (see the next references) when you present results obtained by the RITS code.
[1] H. Sato, T. Kamiyama and Y. Kiyanagi: “A Rietveld-Type Analysis Code for Pulsed
Neutron Bragg-Edge Transmission Imaging and Quantitative Evaluation of Texture andMicrostructure of a Welded α-Iron Plate” Materials Transactions 52(6) (2011) 1294-1302.
(Texture and Crystallite size)[2] H. Sato, T. Shinohara, R. Kiyanagi, K. Aizawa, M. Ooi, M. Harada, K. Oikawa, F. Maekawa,
K. Iwase, T. Kamiyama and Y. Kiyanagi: “Upgrade of Bragg edge analysis techniques of
the RITS code for crystalline structural information imaging” Physics Procedia 43 (2013)
186-195. (Crystal structure)[3] H. Sato, T. Sato, Y. Shiota, T. Kamiyama, A. S. Tremsin, M. Ohnuma and Y. Kiyanagi:“Relation between Vickers Hardness and Bragg-Edge Broadening in Quenched SteelRods Observed by Pulsed Neutron Transmission Imaging” Materials Transactions 56(8)(2015) 1147-1152. (Bragg-edge shift (Macrostrain) and Bragg-edge broadening)[4] H. Sato, K. Watanabe, K. Kiyokawa, R. Kiyanagi, K. Y. Hara, T. Kamiyama, M. Furusaka, T.
Shinohara and Y. Kiyanagi: “Further Improvement of the RITS Code for Pulsed Neutron
Bragg-edge Transmission Imaging” Physics Procedia 88 (2017) 322-330. (Corrected crystal
structure factor and crystallite size)[5] H. Sato, M. Sato, Y. H. Su, T. Shinohara and T. Kamiyama: “Improvement of Bragg-edge
neutron transmission imaging for evaluating the crystalline phase volume fraction insteel composed of ferrite and austenite” ISIJ International 61(5) (2021) 1584-1593.
(Crystalline phase volume fraction)⚫ Originally, the RITS code was developed for research and development of data analysis method of Bragg-edge
neutron transmission data. In other words, this code is not user-friendly, and does not have enough data analysis
speed. The GUI type high-speed RITS code is now developed by J-PARC MLF BL22 “RADEN” (theresponsible person for software: Dr. Kenichi Oikawa).
⚫ The RITS code adopted the non-linear least-squares analysis. Therefore, all the users, please confirm not only
just the output data but also the crystallographic/metallographic validity of the output data. The try& error
iterations are important. It is also important to check the fitting curve by your eyes.
1⚫

I would like to advice about your data analysis. Therefore, please send the neutron TOF transmission data andyour “initial.dat” to me when you have a trouble.

Special thanks for technical cooperation and testing
Prof. Takashi Kamiyama (Hokkaido University)
Dr. Ryoji Kiyanagi (J-PARC Center)
Dr. Yoshinori Shiota (Metal Technology Co. Ltd.)Mr. Tomoya Sato (The Japan Steel Works, Ltd.)
Prof. Kenichi Watanabe (Kyushu University)
Dr. Kenichi Oikawa (J-PARC Center)2

Contents
1. Singe Bragg-edge analysis program
1.1 edge1.f
1.2 edge2.f
2. Rietveld-type Bragg-edge analysis program
2.1 rits1.f
2.2 rits2.f

4
4
10
14
14
21

3

1. Single Bragg-edge analysis program
The single Bragg-edge analysis program is a program for extraction of information on crystal lattice plane spacing
and strain from single Bragg-edge. The 3 stage fitting method was adopted as well as ISIS (Santisteban et al.), but theedge profile function was changed to the Jorgensen-type function in the RITS code. The program consists of two
types; edge1.f and edge2.f.
⚫ edge1.f: analysis of single neutron TOF transmission data
⚫ edge2.f: analysis of multiple position-dependent neutron TOF transmission data obtained by the imaging
experiment
Hereafter, how to use these programs is presented in detail.

1.1 edge1.f
Please prepare:
edge1.f… source program (or its execute program “edge1.o”)
initial.dat… initial crystalline microstructural parameter file before the fitting
input.dat… neutron TOF transmission data
Hereafter, detail of these files is presented.
1.1.1 input.dat
Fig. 1.1 shows a UNIX format of “input.dat” containing the neutron TOF-dependent transmission data.
1st column: TOF (μs) (e.g.: bin width: 0 μs ~ 5 μs → 2.5 μs, bin width: 5 μs ~ 10 μs → 7.5 μs)
2nd column: neutron transmission (e.g.: 0% → 0.0, 100% → 1.0)
3rd column: statistics error (the standard deviation σ) of neutron transmission (0% → 0.0, 100% → 1.0)
“input.dat” can accept up to 16000 rows, which is limited by the RITS source program. However, 16000 is enoughvalue because the 5 μs TOF analysis up to 8 Å can be done at the 40 m neutron flight path length beam-line under
the condition of accelerator repetition of 25 Hz.
Various TOF value, linear/log setting and existence of skipped TOF bin are acceptable.
Recommended TOF bin width for strain analysis: 5 or 10 μs

Fig. 1.1: input.dat.
4

1.1.2 initial.dat
Fig. 1.2 shows a UNIX format of “initial.dat”.
1st row: a0 in 23 page of “RITS overview.ppt” (0.0 is recommended)
2nd row: b0 in 23 page of “RITS overview.ppt” (0.0 is recommended)
3rd row: ahkl in 24 page of “RITS overview.ppt” (0.0 is recommended)
4th row: bhkl in 24 page of “RITS overview.ppt” (0.0 is recommended)
5th row: dhkl (Å) in 25 page of “RITS overview.ppt” (not 2dhkl)
6th row: σhkl in 26 page or σ0,hkl in 30 page of “RITS overview.ppt” (2.0 ~ 10.0 are recommended)
7th row: σ1’,hkl in 30 page of “RITS overview.ppt” (2.0 ~ 10.0 are recommended)
8th row: αhkl in 26 page of “RITS overview.ppt” (2.0 ~ 10.0 are recommended)
9th row: βhkl in 26 page of “RITS overview.ppt” (2.0 ~ 10.0 are recommended)
10th row: starting point (rate for 2dhkl) of the 2nd stage fitting (shorter wavelength region)
11th row: end point (rate for 2dhkl) of the 2nd stage fitting (shorter wavelength region)
12th row: starting point (rate for 2dhkl) of the 3rd stage fitting (near-edge region)
13th row: end point (rate for 2dhkl) of the 3rd stage fitting (near-edge region)
14th row: starting point (rate for 2dhkl) of the 1st stage fitting (longer wavelength region)
15th row: end point (rate for 2dhkl) of the 1st stage fitting (longer wavelength region)
16th row: neutron flight path length from moderator to detector (m)17th row: facility setting parameter changing the order of σhkl, αhkl and βhkl (HUNS: 1, J-PARC MLF BL10
and BL22: 2, J-PARC MLF BL19: 3)
18th row: 0: σ0,hkl, σ1’,hkl, αhkl and βhkl are constant; 1: σ0,hkl, αhkl and βhkl are variable (σ1’,hkl is constant);
2: σ1’,hkl is variable (σ0,hkl, αhkl and βhkl are constant).
19th row: iteration trial number (3 or 2 is recommended)
Incidentally, comment at the end of each row indicates the unit and which the parameter is constant or refined orrefinable.
Comment for 5th row
dhkl should be set a value near the value which you would like to investigate the crystal lattice plane spacing {hkl}.
Note that is not the Bragg-edge wavelength (λhkl = 2dhkl) but is the crystal lattice plane spacing (dhkl). The RITS code
automatically scans a Bragg-edge which should analyze based on this initial value.
Comment for 6th ~ 9th rows
Data set of 1.0 should be avoided. The order of these parameters is changed by setting “facility setting parameter(17th row)”.
Comment for 10th ~ 15th rows
Fig. 1.3 shows scheme of these parameters. For example, if 14th row and 15th row are set;
1.005
#14#
Start_position_1stFit[]constant
1.01
#15#
End_position_1stFit[]constantthese represent a wavelength region of the 1st stage fitting of the 3 stage fitting. In this case, it means that the
wavelength region λλhkl (= 2dhkl)×1.005 < λ < λhkl (= 2dhkl)×1.01
will be analyzed. As the same way,
10th row & 11th row: set of wavelength region of the 2nd stage fitting
12th row & 13th row: set of wavelength region of the 3rd (final) stage fitting
Incidentally, suitable values which I found are as follows:5

Hokkaido University Neutron Source (HUNS): 0.9~0.95 / 0.95~1.2 / 1.2~1.4
J-PARC MLF BL10 (NOBORU) and BL22 (RADEN): 0.98~0.99 / 0.99~1.02 / 1.02~1.04
J-PARC MLF BL19 (TAKUMI): 0.994~0.999 / 0.9975~1.005 / 1.005~1.01
Here, note that before/after “~” means starting/end position value, and “/” separates 2nd / final / 1st stage, respectively.
Comment for 17th row
This parameter decides the order of σ0,hkl, σ1’,hkl, αhkl and βhkl of initial.dat (#6# ~ #9#).
Facility setting parameter “1” (HUNS): ×10.0 μs / ×0.01 μs-1 / ×0.001 μs-1
Facility setting parameter “2” (NOBORU/RADEN): ×10.0 μs / ×0.01 μs-1 / ×0.01 μs-1
Facility setting parameter “3” (TAKUMI): ×1.0 μs / ×0.01 μs-1 / ×0.01 μs-1
These mean the order of σ / α / β, respectively. If σ (width) is smaller, or α (rise) and β (decay) are larger,
Bragg-“edge” becomes sharp. The unit of σ, 1/α, 1/β is μs (microsecond).
Comment for 18th row and Point for macrostrain/microstrain imaging
This parameter can change refining/constant setting of σ0,hkl, σ1’,hkl, αhkl and βhkl of initial.dat (#6# ~ #9#).
0: σ0,hkl, σ1’,hkl, αhkl and βhkl are constant.
1: σ0,hkl, αhkl and βhkl are variable (σ1’,hkl is constant).
2: σ1’,hkl is variable (σ0,hkl, αhkl and βhkl are constant).
(1) If you do not know your instrument resolution: Firstly, you set the broadening setting parameter is “1”, andonly σ1’,hkl is zero. Then, analyze data of no Bragg-edge broadening (e.g. a μm-order grained material), anddetermine σ0,hkl, αhkl and βhkl (instrument resolution).
(2) If you know your instrument resolution, and hope macrostrain imaging without Bragg-edge broadening
correction: You set the broadening setting parameter is “0”, σ0,hkl, αhkl and βhkl are set in suitable values(instrument resolution), and σ1’,hkl is zero. As a result, you can get refined dhkl information without Bragg-edge
broadening correction. This method is the most stable analysis decreasing the analysis error of dhkl.
(3) If you know your instrument resolution, and hope macrostrain and microstrain imaging: You set thebroadening setting parameter is “2”, σ0,hkl, αhkl and βhkl are set in suitable values (instrument resolution), and σ1’,hkl
is set in 2.0~10.0. As a result, you can get refined dhkl (relating to macrostrain) and σ1’,hkl (relating to microstrain)
information with Bragg-edge broadening correction.

Fig. 1.2: initial.dat.
6

2d110

#10

#12

#11

#13 & #14

#15

Neutron transmission

80%
75%
70%
65%

Measurement
FittingDifference

60%
55%
50%
45%
40%
0.402

0.404

0.406

0.408

0.410

Neutron wavelength / nm
Fig. 1.3: Definition of #10#～#15# (analyzing region of 3 stage fitting).
1.1.3 edge1.f
Here, how to use the source program “edge1.f” is described. Firstly, input.dat, initial.dat and edge1.f are put at thesame directly (folder). Then, the compile and the execution are done. Fig. 1.4 shows these commands. The compile
command is
f77 edge1.f -o edge1.o(if you already have the execution file “edge1.o”, the above compile procedure can be skipped), and the executioncommand is./edge1.oAfter several seconds, ChiSq (χ2 value) is displayed. That is all.

7

Fig. 1.4: Commands for check of files, the compile and the execution, and displayed χ2 value.
Next, output data are explained. The output files are
fit_para.dat… Refined crystalline microstructural parameters
fit_func.dat… Fitting curve with experimental data
Fig. 1.5 shows “fit_para.dat”. Please read the sentences from the most bottom row of this file. 1st column
represents refined parameter, and 2nd column indicates its error (standard deviation). Each row represents as follows:Case 1: The broadening setting parameter (#18#): 0
Final row: “Refined” parameter of 5th row in initial.dat (dhkl)
1st row above final row: “Refined” parameter of 4th row in initial.dat (bhkl)
2nd row above final row: “Refined” parameter of 3rd row in initial.dat (ahkl)
3rd row above final row: “Refined” parameter of 2nd row in initial.dat (b0)
4th row above final row: “Refined” parameter of 1st row in initial.dat (a0)Case 2: The broadening setting parameter (#18#): 1
Final row: “Refined” parameter of 9th row in initial.dat (βhkl)
1st row above final row: “Refined” parameter of 8th row in initial.dat (αhkl)
2nd row above final row: “Refined” parameter of 6th row in initial.dat (σ0,hkl)
3rd row above final row: “Refined” parameter of 5th row in initial.dat (dhkl)
4th row above final row: “Refined” parameter of 4th row in initial.dat (bhkl)
5th row above final row: “Refined” parameter of 3rd row in initial.dat (ahkl)
6th row above final row: “Refined” parameter of 2nd row in initial.dat (b0)
7th row above final row: “Refined” parameter of 1st row in initial.dat (a0)8Case 3: The broadening setting parameter (#18#): 2
Final row: “Refined” parameter of 7th row in initial.dat (σ1’,hkl)
1st row above final row: “Refined” parameter of 5th row in initial.dat (dhkl)
2nd row above final row: “Refined” parameter of 4th row in initial.dat (bhkl)
3rd row above final row: “Refined” parameter of 3rd row in initial.dat (ahkl)
4th row above final row: “Refined” parameter of 2nd row in initial.dat (b0)
5th row above final row: “Refined” parameter of 1st row in initial.dat (a0)Fig. 1.5: fit_para.dat (case 2).
Fig. 1.6 shows “fit_func.dat”.
1st column: TOF (μs)
2nd column: Wavelength from TOF (unit: Å, depending on #16# described in initial.dat)
3rd column: Experimental data of neutron transmission (from input.dat)
4th column: Fitting curve
5th column: Difference between experimental data and fitting curve
Fig. 1.7 shows graph of “fit_func.dat”. Please confirm the validity of fitting analysis by your eyes.

9Fig. 1.6: fit_func.dat.

Fig. 1.7: Graph of fit_func.dat.

1.2 edge2.f
Please prepare:
edge2.f
initial.dat
data.dat
Input files like “input.dat”… source program… initial parameters file (the same one as edge1.f)… including all input files name like “input.dat”, which you want to analyze

1.2.1 data.dat
Fig. 1.8 shows contents of “data.dat”. Many files name are described in this file; 1-1.dat, 1-2.dat, 1-3.dat, …. These10

files (1-1.dat, 1-2.dat, 1-3.dat, …) are the same ones as “input.dat” for edge1.f. In other words, many “input.dat”-likefiles can be successively analyzed, one after another, by read this file (data.dat). Therefore, of course, files described in“data.dat” (1-1.dat, 1-2.dat, 1-3.dat, …) must be prepared. So-called full-path setting is capable, therefore readoutfrom a USB memory is also possible. 65536 (256 × 256) of input files are acceptable at once.

Fig. 1.8: data.dat.
1.2.2 initial.dat
This is the same file explained in Sec. 1.1.2. It is better to use the refined typical parameters obtained by edge1.f, as
initial parameters for edge2.f.
1.2.3 edge2.f
The compile and the execution should be done. Hereafter, I introduce a convenient technique for edge2.f. Fig. 1.9
shows a result after the “normal” execution (see Sec. 1.1.3). The refined parameters are displayed in the monitor.
However, in this case, we cannot preserve the refined parameters as a text file. On the other hand, please command./edge2.o > result.dat
where “result.dat” (your arbitrary name) is the file name preserving the output data which would be displayed in themonitor. Thus, we can preserve the output data as a text data (see Fig. 1.10).
The output result consists of as follows.
Case 1: The broadening setting parameter (#18#): 0
1st column: refined dhkl
2nd column: error/standard-deviation of dhkl
3rd column: χ2 value

Case 2: The broadening setting parameter (#18#): 1
1st column: refined dhkl
2nd column: error/standard-deviation of dhkl
3rd column: refined σ0,hkl
4th column: refined αhkl
11

5th column: refined βhkl
6th column: χ2 value

Case 3: The broadening setting parameter (#18#): 2
1st column: refined dhkl
2nd column: error/standard-deviation of dhkl
3rd column: refined σ1’,hkl
4th column: error/standard-deviation of σ1’,hkl
5th column: χ2 value

Incidentally, obtained results are the same ones as edge1.f.

Fig. 1.9: Normal execution of edge2.o.

12

Fig. 1.10: Execution of edge2.o which we set a certain output file name.

132. Rietveld-type Bragg-edge analysis program
The Rietveld-type Bragg-edge analysis program was developed for quantitative analysis of texture and crystallite
size from whole pattern of Bragg-edge transmission spectrum. The program series consist of rits1.f and rits2.f.
⚫ rits1.f: analysis of single neutron TOF transmission data
⚫ rits2.f: analysis of multiple position-dependent neutron TOF transmission data obtained by the imaging
experiment
Hereafter, how to use these programs is presented in detail.

2.1 rits1.f
rits1.f has two functions. One is fitting analysis of experimental data, and the other is simulation calculation of total
cross-section data. Please prepare:
rits1.f… source program
initial.dat… initial data file of crystalline microstructurespgra… Space group database
input.dat… Neutron TOF-dependent transmission spectrum data (in case of simulation of
total cross-section, this file is not needed.)
2.1.1 input.dat
This is the same file as one explained in Sec. 1.1.1 Incidentally, this file is not needed in case of simulation
calculation mode of total cross-section.
Recommended TOF bin width for texture and crystallite size analysis (almost proportional to the neutron
flight path length):
50 μs (at HUNS (6 m))
100 μs (at J-PARC MLF BL10 “NOBORU” (14 m))
200 μs (at J-PARC MLF BL19 “TAKUMI” (40 m))
This is because too much TOF bin number causes slow data analysis speed.
2.1.2 spgra
Please put this file at the same directory (folder).
2.1.3 initial.dat
Refinable parameter is arbitrary parameter indicated by described as “refinable” in initial.dat. If you refine a certain
parameter, please add “? ” mark in front of the value as follows.
? 2.8665 #13#
Crystal_lattice_constant_parameter_a[angstrom]refinable
Space after “?” is necessary. Parameters with “?” will be refined, but parameters without “?” will not be refined(constant).
【Whole structure of “initial.dat”】
Parameters for experimental/analysis condition
Parameters for crystalline phase No. 1
Parameters for characteristics of phase No. 1
Parameters for atom No. 1 in phase No. 1
Parameters for atom No. 2 in phase No. 1…
14

Parameters for crystalline phase No. 2
Parameters for characteristics of phase No. 2
Parameters for atom No. 1 in phase No. 2
Parameters for atom No. 2 in phase No. 2…
These parameters are identified by the number of row from the most upper side in initial.dat. Therefore, you candelete domains about “phase” and “atom” which you do not use in inititial.dat. But, you must not delete rows
which are needed for analysis (e.g., first 7 rows, and information on space group, density, lattice parameters,edge profile, March-Dollase function, extinction function, the number of atoms of the phase).
【1st row】
Facility setting parameters. These are the same parameters as ones of edge.f series. The edge profile function isaffected by these parameters.
【4th and 5th rows】
4th row: the first number of TOF channel which you would like to analyze.
5th row: the last number of TOF channel which you would like to analyze.
Note that unit of them is not μs or Å, but is channel number.
【6th row】
The same effect as the edge.f series. 2 or 3 are recommended.
【7th row】
The number of crystalline phase, up to “2”. If you set “1”, you can delete all parameters for 2nd crystalline phase.
【8th ~ 11th rows】
Parameters for readout from the space group data file “spgra”. As a result, the primitive unit lattice can be formed in
the RITS code.
8th row: Normally, 0.
9th row: For example, 229 (BCC), 225 (FCC) and 194 (HCP).
10th row: Normally, 1.
11th row: Coordination number; e.g., 2.0 (BCC and HCP) or 4.0 (FCC)
About the detail, please refer and the crystallographic data base. I recommend:
http://www.crystallography.net/【12th row】
Projection data of atomic number density (atomic number density × thickness or so-called atomic number area
density). Refine is recommended. Incidentally, the ideal value of alpha-iron of 5 mm thickness is 4.24553 (×1022
cm-2), but the actual value is smaller than the ideal value.
【13th ~ 18th rows】
Crystal lattice constant parameters. The fitting analysis under the below settings is worked. Note that this function
about length parameters (#13#, #14# and #15#) case is also applicable to angle parameters (#16#, #17# and #18#)
case.
15



Case 1: If you analyze a crystal structure of #13# = #14# = #15# (e.g., BCC or FCC):
Please set #13# = #14# = #15# and #13#, and only #13# is refined as follows:? 2.8665 #13#
Crystal_lattice_constant_parameter_a[angstrom]refinable
2.8665#14#
Crystal_lattice_constant_parameter_b[angstrom]refinable
2.8665#15#
Crystal_lattice_constant_parameter_c[angstrom]refinableAs a result, #13# and #14# and #15# are simultaneously refined under the condition that these have the same value.
Note that you should describe quite same value in this case.
Case 2: If you analyze a crystal structure of #13# = #14#, but #15# is different from others (e.g., HCP):
Please set #13# = #14#, but #15# is different value from others, and #13# and #15# are refined as follows:? 2.8665 #13#
Crystal_lattice_constant_parameter_a[angstrom]refinable
2.8665#14#
Crystal_lattice_constant_parameter_b[angstrom]refinable? 1.8665 #15#
Crystal_lattice_constant_parameter_c[angstrom]refinableAs a result, #13# and #14# are simultaneously refined under the condition that only #13# and #14# have the samevalue.
Case 3: If you analyze a crystal structure of different values of #13# and #14# and #15#.
Please set different parameters in all, and refine all the parameters by three “?”. Note that you should describe
different values in this case.
【19th row】
“1” means the edge profile function is the Jorgensen-type resolution function. “0” means the edge profile functionis the Heaviside’s step function (the edge broadening does not exist), and parameters described in this edge-profile
section do not work.
【20th row and 21st row】
Wavelength range of the edge profile function. These are the same parameters as edge.f, also correspond to thesetting of #10# and #15# of Fig. 1.3, respectively.
【22nd ~ 28th rows】
If you set the 19th row is “1”, please input suitable values here. I recommend that #22# and #25# and #27# are set
in the same values as instrument resolution refined by edge1.f (σ0,hkl and αhkl and βhkl), and these parameters areconstant during the RITS analysis. This is because refinement of these parameters is difficult for rits.f (affection fromwhole pattern (spectrum) is too strong), and accuracy and precision of determination of these parameters are higher inthe single edge analysis and the Pawley-type analysis than the Rietveld-type analysis.
【29th row】
In this program, three March-Dollase functions can be combined. Please set the number of functions (0~3) here.
However, “0” or “1” are recommended because the calculation speed is too slow in case of “2” and “3”. In case 0 isset, there is not texture, and the calculation speed is faster than the case of using the March-Dollase function. For the
texture analysis, we usually select “1” in this row.
【30th row and 31st row】
If you set “1” as the 29th row, the contribution of the first (single) March-Dollase function is automatically set as
1.0 (100%).
16

If you set “2” as the 29th row, you have to set a certain contribution of the first March-Dollase function in the 30throw (the contribution of the second March-Dollase function is automatically set as “1.0 - (the contribution of the first
March-Dollase function)”).
If you set “3” as the 29th row, you have to set the 30th row (the contribution of the first March-Dollase function)and the 31st row (the contribution of the second March-Dollase function). The contribution of the third
March-Dollase function is automatically calculated in the program.
【32nd ~ 34th rows】
March-Dollase coefficients. The setting of “1.0” is forbidden when you refine the March-Dollase coefficient. About
the effects, please see 37 page of “RITS overview.ppt”.
【35th ~ 43rd rows】
H, K and L of preferred orientation vector <HKL> are integer. In the condition that ratio among H, K and L is same,the same March-Dollase function will be calculated because HKL is the Miller index of direction.
From 35th row to 37th row are preferred orientation vector of 1st March-Dollase function, from 38th row to 40th
row are preferred orientation vector of 2nd March-Dollase function, and from 41st row to 43rd row are preferredorientation vector of 3rd March-Dollase function.
【44th row】
Only the coherent elastic scattering total cross-section having Bragg-edges appearing at longer wavelength region
than this wavelength (Å) (44th row) will be multiplied by the March-Dollase function. Note that if too wide
wavelength range was set, the calculation time becomes too long. Please set a reasonable wavelength region.
【45th row】
Crystallite size (μm). The recommended initial value for fitting is about 2.0.
【46th row】
Under the same principle as the 44th row, the wavelength region multiplied by the primary extinction effectfunction is set. However, about this function, if the wavelength region becomes wider, the calculation time does not
become too long.
【47th row】
The number of element in the crystalline phase No. 1 is set.
【48th row】
Site occupancy. The principle is same as the Rietveld analysis codes such as GSAS, FullProf, RIETAN and
Z-Rietveld.
【49th row ~ 51st row】
Fractional coordinates (x, y, z). The database for crystallography
http://www.crystallography.net/
should be referred. Incidentally,
BCC (No. 229): 0.0, 0.0, 0.0
FCC (No. 225): 0.0, 0.0, 0.0
HPC (No. 194): 0.3333333333, 0.6666666666, 0.25

17

【52nd row and 53rd row】
Isotropic atomic displacement parameters (see page 13 and page 14 of RITS overview.ppt). If you want to know
reasonable values of them, rits1.f is executed under the simulation mode, and you can watch the theoretical values inyour PC monitor (see Fig. 2.2). Please use these theoretical values as initial values for fitting.
If you set these rows are 0.0, these parameters cannot be refined. However, simulation calculation of total crosssection and profile fitting analysis can be performed by using the theoretical (constant) values automatically calculated
in RITS.
On the other hand, if you want to refine the isotropic atomic displacement parameters, the theoretical values
outputted in the PC monitor above the method (Fig. 2.2) are recommended as the initial values of initial.dat.
【54th row ~ 59th row】
Please input nuclear data and atom data. Please refer the NIST database
https://www.ncnr.nist.gov/resources/n-lengths/【Hereafter】
The above explanation is for 1st element of 1st crystalline phase. Please follow the structure of initial.dat as
explained at the first of Sec. 3.1.3, and set another element/phase information.
【Point for better fitting】
You should avoid that the number of refinement parameters increases as possible as you can. Projected atomic
number density, March-Dollase coefficient and crystallite size are recommended as refinement parameter. Crystal
lattice constant parameter is also recommended. This is because these parameters are sensitive to vertical position,
shape, intensity and horizontal position of the neutron transmission spectrum, respectively.
2.1.4 rits1.f
Fig. 2.1 shows a PC monitor after the compile/execution of rits1.f. Here, the RITS program ask you
Rietveld refinement ? ( y / n )Please reply “y” (Yes) or “n” (No) (input/enter). In case of “y”, RITS carries out profile fitting analysis toward
experimental data (input.dat). In case of “n”, RITS carries out simulation calculation of total cross-section.
Fig. 2.2 shows a PC monitor after the execution of the simulation calculation mode of total cross-section. Isotropic
atomic displacement parameter and φ1(Θ)×φ3(Θ) are displayed. These values can be used for initial values of 52nd
row and 53rd row of initial.dat.

18

Fig. 2.1: rits1.o executed.

Fig. 2.2: Isotropic atomic displacement parameter Biso (× 0.1 Å2) and φ1(Θ)×φ3(Θ) (× 0.1) displayed after the RITS
execution (simulation mode). This example is Fe of 293.6 K (Biso = 0.29 Å2 and φ1(Θ)×φ3(Θ) = 0.63).
If “n” is selected, “simulation.dat” will be outputted. Fig. 2.3 shows simulation.dat (single crystalline phase case).
Fig. 2.4 shows a graph of simulation.dat (single crystalline phase case)
1st column: Neutron wavelength (Å)
2nd column: Coherent elastic scattering cross section (barn)
3rd column: Incoherent elastic scattering cross section (barn)
4th column: Coherent inelastic scattering cross section (barn)
5th column: Incoherent inelastic scattering cross section (barn)
6th column: Absorption cross section (barn)
Note that total cross section is not outputted. Please sum these cross section components by yourself.
On the other hand, double crystalline phase case:
1st column: Neutron wavelength (Å)
2nd column: Total cross section of 1st crystalline phase (barn)
3rd column: Total cross section of 2nd crystalline phase (barn)
4th column: Sum of total cross sections of 1st and 2nd crystalline phases (barn)
19Fig. 2.3: simulation.dat.

Fig. 2.4: Graph of simulation.dat.
If you select “y”, the profile fitting analysis is run (see Fig. 2.5). The outputted values are current status of refinedparameters indicated by “?” in initial.dat. If these parameters are out of control, please do forced termination by thecommand “ctrl + c”, and improve your initial.dat. The output monitor shows sometimes“trial number” “converging number” “χ2 value” (2 2 80.4640427 in Fig. 2.5)
Then, finally, χ2 value is also displayed.
In case the fitting analysis that the trial number is equal to the converging number is done, fitting is too good or too
20

bad. In case of the latter case, please improve your initial.dat. In this case, the crystallographic/metallographic
validity of the initial data and the calculated transmission spectrum should be checked by your knowledge andeyes. It is also important to check a result of simulation calculation of total cross-section and its failure.
After the fitting analysis, fit_para.dat and fit_func.dat are outputted. fit_func.dat corresponds to that explained atSec. 1.1.3. fit_para.dat almost corresponds to that explained at Sec. 1.1.3, however, each row quite corresponds to
the row set in initial.dat.

Fig. 2.5: PC monitor after the execution of profile fitting analysis.

2.2 rits2.f
Please prepare:
rits2.f
initial.dat

spgra

data.dat
Input files like “input.dat”

…
…
…
…

source program
initial parameters filespace group databaseincluding all input files name like “input.dat”, which you want to analyze

How to use “rits2.f” will be understood if you know how to use “edge2.f” and “rits1.f”. Note that the outputted data
are only 1st, 2nd, 3rd, 4th, ... 10th column refined parameters, and χ2 value. If you also need 11th, 12th, … data,
please contact me. Incidentally, if you set 7 as the number of refinement parameter, 8th, 9th 10th column output data
should be ignored.
data.dat can accept up to 4096 input.dat-like data files.

21