Hostname: page-component-7c8c6479df-5xszh Total loading time: 0 Render date: 2024-03-19T11:31:49.927Z Has data issue: false hasContentIssue false

Modeling of hP3 intermetallics in space group P-3m1: Calculated powder patterns from CRYSTMET® X-ray cell data and ab initio coordinates

Published online by Cambridge University Press:  05 March 2012

Y. Le Page*
Affiliation:
ICPET, National Research Council of Canada, Ottawa K1A 0R6, Canada
John R. Rodgers
Affiliation:
Toth Information Systems, Inc., 2045 Quincy Avenue, Ottawa K1J 6B2, Canada
Peter S. White
Affiliation:
CB 3290 Venable Hall, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27599-3290
*
a)Electronic mail: yvon.le_page@nrc.ca

Abstract

There are 39 CRYSTMET® entries in the hexagonal space group P-3m1 (164) reporting both distinct pure phase compounds and atomic coordinates. Having the same Wyckoff positions in the same space group as the C6 structure type, all are isopointal with it. The range of observed c/a values extends from about 0.65 to 1.83. Three types are distinguished: Layered materials with CdI2 type, the CeCd2 type which is a slight distortion of the hexagonal AlB2 type, and the intermediate EuGe2 type made of the materials AuTe2, BaSi2, EuGe2, and SrGe2. Ab initio modeling of the 26 entries with CdI2 and EuGe2 type and atomic coordinates reproduces convincingly both their c/a axial ratios and z coordinates. For CoO2 and SiTe2, both c/a and z deviate to a degree from the reported values, indicating that those materials should be reexamined for superstructures, stoichiometry, etc. Ab initio modeling of the 11 cell-and-type entries with CdI2 type and no coordinates in CRYSTMET reproduced convincingly their reported axial ratios. The X-ray cell data and the ab initioz coordinates were then used in the production of reliable calculated powder patterns for CoTe2, CrSe2, HfS2, HfSe2, HfTe2, NbTe2, SnSe2, VS2, VTe2, ZrS2, and ZrTe2. All 11 patterns have been inserted in the intense diffraction line search system of CRYSTMET operated under the Materials Toolkit. Comparison of calculated patterns for SnSe2 and ZrTe2 with experimental entries in the PDF exposes the complementarity of calculated and experimental powder patterns and suggests that JCPDS pattern #15-223 should be reinterpreted in terms of the CdI2 structure type. The CeCd2⇔AlB2 type transformation is modeled and discussed on YCd2 using both ab initio methods and a hard-sphere model. For z<0.45, the ab initio solution is identical with that from the hard-sphere model while a quantum regime is predicted in the small region 0.45<z<0.467 beyond which YCd2 abruptly transforms to the AlB2 type. In spite of the new understanding gained, this modeling fell slightly short of allowing calculation of z values and powder patterns for the materials CaHg2, DyHg2, ErCd2, GdHg2, HoCd2, HoHg2, LuCd2, NdCd2, SmHg2, TbCd2, and TbHg2 with no coordinates in CRYSTMET.

Type
Technical Articles
Copyright
Copyright © Cambridge University Press 2002

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Blöchl, P. E. (1994). “Projector augmented-wave method,” Phys. Rev. B PRBMDO 50, 1795317979. prb, PRBMDO CrossRefGoogle ScholarPubMed
Borzoth, R. M. (1922). “The crystal structure of cadmium iodide,” J. Am. Chem. Soc. JACSAT 44, 22322236. acs, JACSAT Google Scholar
Catlow, C. R. A., Bell, R. G., and Gale, J. D. (1994). “Computer modeling as a technique for materials chemistry,” J. Mater. Chem. JMACEP 4 (6), 781792. jtc, JMACEP CrossRefGoogle Scholar
Dommann, A.and Hulliger, F. (1988). “On the structure types of UAu2 and U14Au51,J. Less-Common Met. JCOMAH 141, 261273. jco, JCOMAH CrossRefGoogle Scholar
Elmendorf, R.and Ryba, E. (1968). “A note on the structure of YCd2,Acta Crystallogr., Sect. B: Struct. Crystallogr. Cryst. Chem. ACBCAR 24, 462463. acb, ACBCAR CrossRefGoogle Scholar
Gabe, E. J., Le Page, Y., Charland, J. P., Lee, F. L., and White, P. S. (1989). “NRCVAX-An interactive program system for structure analysis,” J. Appl. Crystallogr. JACGAR 22, 384387. acr, JACGAR CrossRefGoogle Scholar
Hoffmann, R. D.and Pöttgen, R. (2001). “AlB2-related intermetallic compounds—a comprehensive view based on group-subgroup relations,” Z. Kristallogr. ZEKRDZ 216, 124145. zek, ZEKRDZ Google Scholar
Iandelli, A.and Palenzona, A. (1968). “On the occurrence of the MX2 Phases of the rare earths with the IB, IIB and IIIB Group Elements and their crystal structures,” J. Less-Common Met. JCOMAH 15, 273284. jco, JCOMAH CrossRefGoogle Scholar
Kirchmayr, H. R. (1964). “Gitterkonstanten und Strukturen der Verbindungen DyHg, HoHg, ErHg; DyHg2 ErHg2; DyHg3, HoHg3 und ErHg3,Monatsch. Chem. MOCMB7 95, 16671670. mnc, MOCMB7 CrossRefGoogle Scholar
Kresse, G. (1993). Ph.D. Thesis, Technische Universität Wien.Google Scholar
Kresse, G.and Hafner, J. (1993). “Ab initio molecular dynamics for open-shell transition metals,” Phys. Rev. B PRBMDO 48, 1311513118. prb, PRBMDO CrossRefGoogle ScholarPubMed
Kresse, G.and Hafner, J. (1994). “Ab initio molecular-dynamics simulation of the liquid–metal–amorphous-semiconductor transition in germanium,” Phys. Rev. B PRBMDO 49, 1425114269. prb, PRBMDO CrossRefGoogle ScholarPubMed
Kresse, G.and Joubert, J. (1999). “From ultrasoft pseudopotentials to the projector augmented-wave method,” Phys. Rev. B PRBMDO 59, 17581775. prb, PRBMDO CrossRefGoogle Scholar
Larson, A. C. (1969). “Computer programs for symmetry operations in crystal structure calculations,” Acta Crystallogr., Sect. A: Cryst. Phys., Diffr., Theor. Gen. Crystallogr. ACACBN 25, S1. aca, ACACBN Google Scholar
Le Page, Y.and Gabe, E. J. (1979). “Application of a segment description of the unique set of reflections to data collection and data reduction,” J. Appl. Crystallogr. JACGAR 12, 464466. acr, JACGAR CrossRefGoogle Scholar
Le Page, Y., Ashino, T., Raymond, S., Gabe, E. J., White, P. S., and Rodgers, J. R. (1997). “Wyckoff positions in alternate settings of space groups,” American Crystallographic Association Annual Meeting, St. Louis, Program and Abstract Book, Abstract ThC04.Google Scholar
Le Page, Y.and Saxe, P. W. (2001a). “Symmetry-general least squares extraction of stiffness coefficients from ab initio calculations of total energy,” Phys. Rev. B PRBMDO 63, 174103. prb, PRBMDO CrossRefGoogle Scholar
Le Page, Y.and Saxe, P. W. (2001b). “Ab initio vs literature stiffness values for Ga: a caveat about crystal settings,” Phys. Rev. B PRBMDO 307, 191193. prb, PRBMDO Google Scholar
Le Page, Y.and Saxe, P. W. (2002). “Symmetry-general least squares extraction of elastic data from ab initio calculations of stress,” Phys. Rev. B PRBMDO 65, 104104. prb, PRBMDO CrossRefGoogle Scholar
Le Page, Y., Saxe, P. W., and Rodgers, J. R. (2002a). “Ab initio stiffness for quartz and calcite,” Phys. Status Solidi B PSSBBD 229, 11551161. psb, PSSBBD 3.0.CO;2-O>CrossRefGoogle Scholar
Le Page, Y., Saxe, P. W., and Rodgers, J. R.(2002b). “Symmetry-general computation of physical properties using quantum software integrated with crystal-structure databases: Results and perspectives,” Acta Cryst. B ASBSDK 58, 349357 (2002). acl, ASBSDK CrossRefGoogle Scholar
Monkhorst, H. J.and Pack, J. D. (1976). “Special points for Brillouin-zone integrations,” Phys. Rev. B PLRBAQ 13, 51885192. prq, PLRBAQ CrossRefGoogle Scholar
Palenzona, A.and Cirafici, S. (1988). “The Phase Diagram of the U-Au System,” J. Less-Common Met. JCOMAH 143, 167171. jco, JCOMAH CrossRefGoogle Scholar
Pearson’s Handbook of Crystallographic Data for Intermetallic Phases. Desk Ed. (1997). edited by Villars, P. (American Society for Materials, Materials Park, OH).Google Scholar
Powder Diffraction File search manual, Hanawalt method: inorganic (1981). (JCPDS, Swarthmore, PA).Google Scholar
Rodgers, J. R. and Wood, G. H. (1987). Crystallographic Databases, The International Union of Crystallography, pp. 96106. See also http://www.TothCanada.com.Google Scholar
Saxe, P. W. (1998). Unpublished. See http://MaterialsDesign.com/Google Scholar
Schön, J. C. and Jansen, M. (2001a,b). “Determination, prediction, and understanding of structures, using the energy landscapes of chemical systems—Part I,” Z. Kristallogr. ZEKRDZ 212, 307325; zek, ZEKRDZ 216, 361383. zek, ZEKRDZ CrossRefGoogle Scholar
Strukturbericht, Band 1: 1913–1928 (1931). P. P. Ewald and C. Hermann, eds. (Akademische Verlagsgesellschaft M.B.H., Leipzig).Google Scholar
White, P. S., Le Page, Y., and Rodgers, J. R. (2000). European Crystallography Meeting, Nancy, abstract No. #s8b.m4.p2.Google Scholar
Winkler, B. (1999). “An introduction to computational crystallography,” Z. Kristallogr. ZEKRDZ 212, 506527. zek, ZEKRDZ CrossRefGoogle Scholar