National Institute of Standards & Technology

Certificate
Standard Reference Material 660c
Line Position and Line Shape Standard for Powder Diffraction(Lanthanum Hexaboride Powder)This Standard Reference Material (SRM) is intended for use in calibration of diffraction line positions and line shapes
determined through powder diffractometry. A unit of SRM 660c consists of approximately 6 g of lanthanum
hexaboride, LaB6, powder bottled under argon gas.
Material Description: The SRM was prepared in a dedicated processing run using the 11B isotope enriched to anominal 99 % concentration. This isotopic enrichment renders this SRM relevant to the neutron diffraction
community. The resulting powder was then annealed and bottled under argon. An analysis of X-ray powder
diffraction data indicated that the SRM material is homogeneous with respect to diffraction properties.
Certified Value: The certified lattice parameter for a temperature of 22.5 °C is0.415 682 6 nm ± 0.000 008 nm
The interval defined by this value and its expanded uncertainty (k = 2) is dominated by a Type B uncertainty estimatedfrom a technical understanding of the measurement data and its distribution. A NIST certified value is a value forwhich NIST has the highest confidence in its accuracy in that all known or suspected sources of bias have been
investigated or taken into account. The certified values and uncertainties were calculated according to the method
described in the ISO/JCGM Guide [1]. The measurand is the lattice parameter. Metrological traceability is to the SI
unit for length (expressed as nanometers).
Information Values:
The analyses of the certification data included refinement of the full-width
half-maximum (FWHM) of a Lorentzian profile to account for sample-induced broadening. The angular dependenceof the FWHM term varying as 1/cos θ is interpreted as size-induced broadening. The value obtained was consistent
with a mean volume-weighted domain size of approximately 0.8 µm. The term varying as tan θ, interpreted as
microstrain, refined to zero. The information values for computed peak positions are given in Table 1. The typicalparticle size distribution as determined by laser scattering is given in Figure 1. An information value is considered tobe a value that will be of interest to the SRM user, but insufficient information is available to assess the uncertainty
associated with the value. Information values cannot be used to establish metrological traceability.
Expiration of Certification: The certification of SRM 660c is valid indefinitely, within the uncertainty specified,provided the SRM is handled and stored in accordance with the instructions given in this certificate (see “Instructionsfor Storage”). Periodic recertification of this SRM is not required. The certification is nullified if the SRM is damaged,
contaminated or otherwise modified.
Maintenance of SRM Certification: NIST will monitor this SRM over the period of its certification. If substantive
technical changes occur that affect the certification, NIST will notify the purchaser. Registration (see attached sheetor register online) will facilitate notification.
Overall coordination and technical direction of the certification were performed by J.P. Cline of the NIST Materials
Measurement Science Division.
The preparation, measurements and data analyses were performed by J.P. Cline, M.H. Mendenhall, and D. Black of theNIST Materials Measurement Science Division and A. Henins of the NIST Quantum Measurement Division.
John A. Small, Chief
Materials Measurement Science Division
Gaithersburg, MD 20899
Certificate Issue Date: 29 October 2015

Robert L Watters, Jr., Director
Office of Reference Materials

Certificate Revision History on Last Page

SRM 660cPage 1 of 5Collection of the laser scattering particle size data for informational value was performed by M. Peltz of the NIST
Materials and Structural Systems Division.
Statistical analysis was by provided J.J. Filliben of the NIST Statistical Engineering Division.
Support aspects involved in the issuance of this SRM were coordinated through the NIST Office of Reference
Materials.
INSTRUCTIONS FOR STORAGE
SRM 660c was bottled under argon to protect against humidity. When not in use, store the unused portion of thispowder tightly capped in the original bottle in a dry atmosphere such as a desiccator to protect against humidity.
SOURCE, PREPARATION, AND ANALYSIS(1)Source of Material: The 11boron-enriched boron carbide precursor was obtained from Ceradyne Boron
Products LLC, Quapaw, OK, USA. The lanthanum hexaboride was synthesized by H.C Starck GmbH, Goslar,Germany. The annealing was performed by Cerac Inc., Milwaukee, WI, USA.
Certification Method: Certification was performed using data from a NIST built diffractometer [2], with analyses
via the fundamental parameters approach (FPA) [3] using the Rietveld method [4]. These analyses were used to verify
homogeneity and certify the lattice parameters. The linkage of the certified lattice parameter values to the fundamental
unit for length, as defined by the International System of Units (SI) [5], was established with use of the emission
spectrum of Cu Kα radiation as the basis for constructing the diffraction profiles. With the use of the FPA, diffraction
profiles are modeled as a convolution of functions that describe the wavelength spectrum, the contributions from thediffraction optics, and the sample contributions resulting from microstructural features. Analysis of data from adivergent-beam instrument requires knowledge of both the diffraction angle and the effective source-sample-detector
distance. Two additional models are therefore included in the FPA analyses to account for the effect of the sample
height and attenuation. Certification data were analyzed in the context of both Type A uncertainties, assigned bystatistical analysis, and Type B uncertainties, based on knowledge of the nature of errors in the measurements, to resultin the establishment of robust uncertainties for the certified values.
Certification Procedure: The data were collected with a 2.2 kW sealed copper tube of long fine-focus geometry
which was operated at a power of 1.8 kW, 45 kV and 40 mA. The source size was approximately 12 mm × 0.04 mm
and the variable divergence slit was set nominally to 0.8°. Axial divergence of the incident beam was limited by a2.2° Soller slit. The goniometer radius was 217.5 mm. A 2 mm anti-scatter slit was placed approximately 113 mm infront of the 0.2 mm (0.05°) receiving slit. Scattered X-rays were filtered with a graphite post-sample monochromator,and counted with a scintillation detector. Samples were spun at 0.5 Hz during data collection. The machine waslocated within a temperature-controlled laboratory space where the nominal short-range control of temperature
was ± 0.1 K. The temperature and humidity were recorded during data collection using Veriteq SP 2000 monitors
stated to be accurate to ± 0.15 K. The source was allowed to equilibrate at operating conditions for at least an hourprior to recording any certification data. The performance of the machine was qualified with the use of SRM 660b
Line Position and Line Shape Standard for Powder Diffraction [6] and SRM 676a Alumina Powder for Quantitative
Analysis by X-Ray Diffraction [7] using procedures discussed by Cline et al. [2].
Ten units of SRM 660c were selected in a stratified random manner from the population of units during the bottlingoperation. Certification data were recorded from 2 samples prepared from each of 10 bottles, for a total of 20 samples.
Data were collected from 24 selected regions of the diffraction pattern, each region including one of the reflections
accessible within the 2θ range of 20° to 150°. The angular widths of the scan ranges were 20 to 30 times the observed
FWHM values of the profiles and were chosen to provide at least 0.3° 2θ of apparent background straddling eachpeak. The step width was chosen to include at least eight data points above the FWHM. The count time spent oneach profile was inversely proportional to the observed diffraction intensity so as to realize constant counting statistics
amongst the profiles. The total collection time for each sample was about 24 h.

(1)Certain commercial equipment, instruments, or materials are identified in order to adequately specify the experimental
procedure. Such identification does not imply recommendation or endorsement by the National Institute of Standards andTechnology, nor does it imply that the materials or equipment identified are necessarily the best available for the purpose.

SRM 660cPage 2 of 5

Data Analysis: The certification data were analyzed using the FPA method as implemented in TOPAS [8] as well asa NIST Python-based code that replicates the FPA models [9]. While TOPAS allows for a Rietveld analysis using astructural model, within the Python code, peak positions are constrained by space group symmetry to permit
refinement of lattice parameters. The initial analysis was performed using the Python-based code in a global
refinement using the entire suite of the twenty data sets. This allowed for determination of the parameters specific to
the instrument profile function (IPF) with highly favorable Poisson counting statistics. The analysis used theCu Kα1/Kα2 emission spectrum, including a satellite component, as characterized by G. Hölzer et al. andMaskil & Deutsch [10,11]. The breadths of the four Lorentzian profiles used to describe the Cu Kα emission spectrum
were refined in order to assess the impact of the post-monochromator [2]. The FWHM ratios of the two pairs of profiles,
the Kα11 vs. the Kα12 and the Kα21 vs. the Kα22, were constrained to those reported by Hölzer. The intensities andpositions of the Cu Kα2 line, the satellite line and the “tube tails” [12] were refined. Again, constraints were applied
to positions and intensities of the Kα21 and Kα22 lines to preserve the overall shape as per Hölzer. A Soller slit value,
constrained to be identical for both the incident and diffracted beam, using the “full” axial divergence model [13], wasrefined. Lastly, the analysis included a term for Lorentzian size broadening. With the exception of the size broadening
term, the parameter values obtained from this analysis were specific to the IPF, and were fixed in subsequent analyses.
The informational value for crystallite size reported in this certificate was obtained from this analysis.
TOPAS was used to refine the data sets individually with an FPA Rietveld analysis. The refined parameters included
the scale factors, Chebyshev polynomial terms for modeling of the background, the lattice parameters, specimen
displacement and attenuation terms, a Lorentzian size broadening term and structural parameters. With the NIST
Python-based code, a second global refinement was set up to use the twenty data sets to obtain a single lattice
parameter; the profile positions were constrained by space group symmetry and the specimen displacement andtransparency terms were allowed to refine independently. The lattice parameter obtained with the NIST Python-based
code and the average of the twenty values obtained from the analyses with TOPAS agreed to within ± 2 fm.
The results from the analyses using TOPAS were used to obtain the certified lattice parameters. The thermal expansionof lanthanum hexaboride as reported by Sirota et al. [14] was used to adjust the lattice parameter values to 22.5 °C.
A statistical analysis of the data indicated that the mean of the measurements was 0.415 682 62 nm with a k = 2 Type A
expanded uncertainty of 0.000 000 37 nm. However, a Type B uncertainty due to systematic error must be
incorporated into the uncertainty bounds of the certified lattice parameter. Consideration of trends in the data used in
the certification leads to an assignment of a Type B uncertainty and value stated.

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Table 1. Information Values for Peak Positions Computed for SRM 660c Using Cu Kα Radiation,
λ = 0.154 059 29 nmhkl2θ, degrees

11122223332334433443455501101120112220133223201100
10010001201000
10122001

21.35830.38537.44243.50748.95853.99063.22067.54971.74775.84679.872
83.84787.79495.67399.645103.663
107.752111.936116.248120.726130.413135.805
141.780148.685

Figure 1. Typical Particle Size Distribution as Determined by Laser Scattering

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REFERENCES
[1]

[2]

[3]
[4]

[5]
[6]
[7]
[8][9]

[10]
[11]
[12]

[13]

[14]

JCGM 100:2008; Guide to the Expression of Uncertainty in Measurement; (GUM 1995 with MinorCorrections), Joint Committee for Guides in Metrology (JCGM) (2008); available at
http://www.bipm.org/utils/common/documents/jcgm/JCGM_100_2008_E.pdf (accessed Mar 2015); see also
Taylor, B.N.; Kuyatt, C.E.; Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement
Results; NIST Technical Note 1297; U.S. Government Printing Office: Washington, DC (1994); available at
http://www.nist.gov/pml/pubs/index.cfm (accessed Mar 2015).
Cline, J.P.; Mendenhall, M.H.; Black, D.; Windover, D.; Henins, A.; The Optics and Alignment of theDivergent Beam Laboratory X-ray Powder Diffractometer and its Calibration Using NIST Standard Reference
Materials; J. Res. Natl. Inst. Stand. Technol., Vol. 120, pp. 173–222 (2015).
Cheary, R.W.; Coelho, A.A.; A Fundamental Parameters Approach to X-ray Line-Profile Fitting; J. Appl.
Cryst., Vol. 25, pp. 109–121 (1992).
Rietveld, H.M.; Line Profiles of Neutron Powder Diffraction Peaks for Structure Refinement; Acta
Crystallogr., Vol. 22, pp. 151–152 (1967); see also Rietveld, H.M., A Profile Refinement Method for Nuclear
and Magnetic Structures; J. Appl. Cryst., Vol. 2, pp. 65–71 (1969)
BIPM; International System of Units (SI), Bureau International des Poids et Mesures; 8th ed., Sèvres, France(2006); available at http://www.bipm.org/utils/common/pdf/si_brochure_8_en.pdf (accessed Mar 2015)
SRM 660b; Powder Line Position and Line Shape Standard for Powder Diffraction; National Institute ofStandards and Technology; U.S. Department of Commerce: Gaithersburg, MD (29 April 2010).
SRM 676a; Alumina Internal Standard for Quantitative Analysis by X-ray Powder Diffraction; NationalInstitute of Standards and Technology; U.S. Department of Commerce: Gaithersburg, MD (23 April 2012).
TOPAS, General Profile and Structure Analysis Software for Powder Diffraction Data, version 4.2; Bruker
AXS GmbH, Karlsruhe, Germany.
Mendenhall, M. H.; Mullen, K.; Cline, J. P.; .An implementation of the Fundamental Parameters Approach forAnalysis of X-ray Powder Diffraction Line Profiles; J. Res. Natl. Inst. Stand. Technol., Vol. 120, pp. 223–251(2015).
Hölzer, G.; Fritsch, M.; Deutsch, M.; Härtwig, J.; Förster, E.; Kα1,2 and Kβ1,3 X-Ray Emission Lines of the 3dTransition Metals; Phys. Rev. A, Vol. 56, pp. 4554–4568 (1997).
Maskil, M.; Deutsch, M.; X-Ray Kα Satellites of Copper; Phys. Rev. A, Vol. 38, pp. 3467–3472 (1988).
Bergmann, J.; Kleeberg, R.; Haase, A.; Breidenstein, B.; Advanced Fundamental Parameters Model for
Improved Profile Analysis; In Proceedings of the 5th European Conference on Residual Stresses,
Delft-Noordwijkerhout, The Netherlands, September 29-30, 1999, A.J. Böttger, R. Delhez, andE.J. Mittemeijer, Eds. Trans Tech Publications, 347–349, pp. 303–308 (2000).
Cheary, R.W.; Coelho, A.A.; Axial Divergence in a Conventional X-Ray Powder Diffractometer I. TheoreticalFoundations, J. Appl. Cryst., Vol. 31, pp. 851–861 (1998); see also Cheary, R.W.; Coelho, A.A.; AxialDivergence in a Conventional X-Ray Powder Diffractometer II, Implementation and Comparison withExperiment; J. Appl. Cryst., Vol. 31, pp. 862–868 (1998).
Sirota, N.N.; Novikov, V.V.; Vinokrov, V.A.; Paderno, B.Yu.; Temperature Dependence of Heat Capacity andLattice Constant of Lanthanum and Samarium Hexaborides; Phys. Sold State, Vol. 40,pp. 1856–1858 (1998).

Certificate Revision History: 29 October 2015 (Editorial changes); 10 March 2015 (Update of certified and information values, editorialchanges); 20 October 2014 (Original certificate date).

Users of this SRM should ensure that the Certificate in their possession is current. This can be accomplished bycontacting the SRM Program: telephone (301) 975-2200; fax (301) 948-3730; e-mail srminfo@nist.gov; or via theInternet at http://www.nist.gov/srm.

SRM 660c

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