National Institute of Standards & Technology

Certificate of Analysis
Standard Reference Material 1990
Single Crystal Diffractometer Alignment Standard - Ruby SphereStandard Reference Material (SRM) 1990 is intended primarily for use as an alignment standard for single crystal
diffractometry. One unit consists of three chromium-doped single crystal aluminum oxide (ruby) spheres. The spheres
are nominally 152 µm in diameter with 1.3 µm sphericity. The spherical geometry was chosen to facilitate alignment andto avoid corrections for absorption. These spheres produce reflections at high angles for copper and molybdenumradiation. The space group is R3c.
Certified Values and Uncertainties: The certified lattice parameters of SRM 1990 at 25 °C are:a: 0.476080 nm ± 0.000029 nm
c: 1.299568 nm ± 0.000087 nm
The certified values were obtained using λ (CuKα1 ) = 0.154059292 (45) nm, and λ (MoKα1 ) = 0.070931631 (84) nm [1,2].
The estimated total uncertainty is an expanded uncertainty with a coverage factor, k = 3.18 (the resulting interval is anapproximate 95 % confidence level), and accounts for (1) uncertainty due to a small variation in chromium content, (2)random errors of measurement, and (3) the small uncertainty in λ (CuKα1) and λ (MoKα1) [3]. Other systematic effects
such as absorption, extinction, and divergence were not found to be significant and are not included in the uncertainty
estimate.
Expiration of Certification: The certification of this SRM is valid indefinitely within the measurement uncertainties
specified, provided the SRM is used in accordance with the instructions in this certificate. However, the certification willbe nullified if the SRM is physically damaged, contaminated, or otherwise altered. If alteration is suspected, discontinue
use and purchase a new unit. This SRM is a physical artifact, the physical properties of which are inherently stable undernormal laboratory and usage conditions.
Reference Value: SRM 1990 may also be used as a reference for chromium content. The spheres contain 0.42 % ± 0.01 %chromium oxide (Cr2O3) expressed as a mole fraction, where the uncertainty represents an expanded uncertainty. The
chromium content was measured using a microprobe, while specimen-to-specimen variability was measured by scanningelectron microscope energy dispersive spectroscopy.
Technical coordination leading to certification of this SRM was provided by W. Wong-Ng of the NIST Ceramics Division
with significant contributions from T. Siegrist of Lucent Technologies, Murray Hill, NJ.
Statistical consultation was provided by M.S. Levenson of the NIST Statistical Engineering Division.
Measurements of the chromium content were provided by J.T. Armstrong of the NIST Microanalysis Science Divisionand L.P. Cook of the NIST Ceramics Division.
The support aspects concerning the preparation, certification, and issuance of this SRM were coordinated through theNIST Standard Reference Materials Program by R.J. Gettings and C.R. Beauchamp.
Stephen W. Freiman, Chief
Ceramics Division
Gaithersburg, MD 20899
Certificate Issue Date: 28 February 2001
SRM 1990

Nancy M. Trahey, Chief
Standard Reference Materials Program
Page 1 of 4

Organization of the round robin project and demonstration of the viability of the ruby spheres were provided by G.T.
DeTitta of Hauptman-Woodward Medical Research Institute, Buffalo, NY and L. Finger of the Geophysical Laboratory,Washington, DC.
Preparation and Certification Procedures: A boule of single crystal ruby, supplied by Arcanum Corporation, Ann
Arbor, MI, was prepared by using the Verneuil technique (flame fusion) then ground into small spheres [4]. Four sets ofspheres were measured, both at NIST and by cooperating laboratories, on three Enraf-Nonius CAD-4 diffractometers andon a Picker diffractometer using both molybdenum and copper radiation 1. A total of 39 spheres were measured to obtain
45 data sets. The diffractometer control program, DIFRAC, developed at the National Research Council of Canada (NRC),
was used for data collection and reduction for all data sets [5]. The CuKα1 and MoKα1 peak positions were determinedby fitting the profiles of high angle peaks. Lattice parameters were obtained using least squares methods. Corrections
for thermal expansion [6] and refraction [7] were applied to convert the data to 25 °C for each sample. The thermal
expansion coefficients used were αa = 5.0 x 10-6 deg -1 and αc = 6.66 x 10-6 deg -1 [6]. These lattice parameters were verified
by a powder diffraction study conducted at the U.S. Geological Survey on 60 crushed spheres using the Guinier-Häggtransmission technique [8].
Instructions for Use: Select one of the spheres, clean off adhesive using acetone or alcohol, and mount securely on thetip of a fiber (or capillary tube) about 0.1 mm in diameter using a minimum amount of adhesive material in the area ofcontact between the sphere and the fiber. Additional spheres are provided in the event of loss. This SRM is intended
for use at ambient conditions. With appropriate thermal expansion corrections, the SRM can be used under non-ambient
temperature conditions.
Table 1 lists information values for high-angle 2θ reflections to obtain both the initial sphere orientation and to accuratelyalign the diffractometer. The h, k, and l values are the Miller indices, M is the multiplicity, and Fc is the calculatedstructure amplitude. The 2θ values are derived from the certified lattice parameters of the ruby spheres by using the PC
version (MICRO-POWD) of computer software POWD10 [9]. The structure amplitudes are listed to serve as anapproximate guide of the relative intensity of these reflections. These reflections, and symmetrically equivalent ones,
should be selected such that the Miller indices h, k, and l are evenly distributed in reciprocal space. The same reflection
should be measured at some or all of the eight possible diffractometer settings. It is recommended that the alignment
routine incorporates the algorithm by King and Finger for calculating various alignment corrections [10].
Table 1. Information Values for High Angle 2θ Reflections(A) For initial orientation

h01
10
30k l
1 20 4
1 00 60 00 12

M
6662
62

Fc
47
83
61
1314157

2θCuKα1 (°)
25.56735.13937.76241.66568.18090.678

2θMoKα1 (°)
11.69415.97817.13718.84829.91038.232

1Certain commercial equipment, instruments, or materials are identified in this report to specify adequately the experimental procedure. Suchidentification does not imply recommendation or endorsement by NIST, nor does it imply that the materials or equipment identified are necessarily the best
available for the purpose.

SRM 1990

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(B) For accurate alignment

h k1 32 20 4
2 1
4 0
3 1
2 23 20 1
4 1
4 1
1 3
3 0
2 0
4 1
1 1
4 0
0 5
1 21 03 30 4
5 1
7 1
7 0
3 3
1 7
1 1
5 4
6 30 8
4 2
2 2
2 6
8 1
3 4
6 14 6
7 30 70 0
5 2
3 0
1 9SRM 1990

l4
62104894
140
3
1012
14615
104
14
160
20
160
1018
624
40
420
24
14
42020
10102030
2430
10M
1212
6
12
6
12
12
12
6
6
12
12
66
12
12
66
12
6
6612
6
6
12
12
12
12
6
6
12
12
12
12
1212
12
12
6212
612Fc
51
7438
64
38
3630
6452
47
2666
41
585629695652
32
79
42
28
26
50
36
2941
32
4232
2637
3432
38
30
3641
39
44
2940
26

2θCuKα1 (°)
91.14495.20398.342101.031103.262110.931114.010116.030
116.553
117.777
121.956
127.605129.802131.031135.971
142.225145.049
149.060
149.986150.300
152.239

2θMoKα1 (°)

80.36380.79880.99882.76783.23484.09784.39785.78986.12088.33690.58492.03893.52595.97898.243103.425105.883108.546108.721109.913115.794118.280
119.713

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Cooperating Round Robin Laboratories:
Geophysical Laboratory, Washington, DC; L. Finger
Hauptman-Woodward Medical Research Institute, Buffalo, NY; G.T. DeTitta
Lucent Technology, Murray Hill, NJ; T. Siegrist
National Research Council of Canada, Ottawa, Ont; G.D. Enright
National Research Council of Canada, Ottawa, Ont; E.J. Gabe
Oak Ridge National Laboratory, Oak Ridge, TN; C.R. Hubbard
U.S. Geological Survey, Reston, VA; H. Evans
REFERENCES[1]

Härtwig, J., Hölzer, G., Förster, E., Goetz, K., Wokulska, K., and Wolf, J., “Remeasurement of Characteristic X-ray
Emission Lines and Their Application to Line Profile Analysis and Lattice Parameter Determination,” Phys. Stat.
Sol. A 143, p. 23, (1994).
[2] Cohen, E.R. and Taylor, B.N., “The 1986 Adjustment of the Fundamental Physical Constants,” Rev. Mod. Phys. 59,
p. 1121, (1987).
[3] Taylor, B.N. and Kuyatt, C.E., “Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurements,”
NIST Tech. Note 1297, U.S. Government Printing Office, Washington DC, (1994); available at
http://physics.nist.gov/Pubs/.
[4] Hurle, D.T.J., “Melt Growth,” in Crystal Growth: An Introduction, edited by P. Hartman, North-Holland Publishing
Company, p. 215, (1973).
[5] DIFRAC, software suite for data collection and reduction of x-ray single crystal diffractometers, developed by E.
Gabe, et al. at the National Research Council (NRC) in Ottawa, Canada.
[6] Belyaev, L.M., “Ruby and Sapphire,” Nauka Publishers, Moscow, translated from Russian, National Bureau ofStandards, National Science Foundation, and Amerind Publishing Co. Pvt. Ltd., New Delhi, India, p. 7, (1980).
[7] Hubbard, C.R. and Mauer, F.A., “Precision and Accuracy of the Bond Method as Applied to Small Spherical
Crystals,” J. Appl. Cryst. 9, p. 1, (1976).
[8] Hägg, G. and Ersson, N.O., “An Easily Adjustable Guinier Camera of Highest Precision,” Acta Cryst. A25, Sppl. p.
S64, (1960).
[9] Smith, D.K., Nichols, M.C., and Zolensky, M.E., “A FORTRAN IV Program for Calculating X-ray Powder Diffraction
Patterns-Version 10,” The Pennsylvania State University, University Park, PA, p. 72, (1983).
[10] King, H.E. and Finger, L.W., “Diffracted Beam Crystal Centering and Its Application to High Pressure
Crystallography,” J. Appl. Crystallography, 12, p. 374, (1979).

Users of this SRM should ensure that the certificate in their possession is current. This can be accomplished bycontacting the SRM Program at: telephone (301) 975-6776, fax (301) 926-4751, e-mail srminfo@nist.gov, or via theInternet www.nist.gov/srm.

SRM 1990

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