Abstract
Electron count is one of the key factors controlling the formation of complex intermetallic structures. The delocalized nature of bonding in metals, however, has made it difficult to connect these electron counts to the various structural features that make up complex intermetallics. In this article, we illustrate how structural progressions in transition metal-main group intermetallics can in fact be simply understood with the 18-n bonding scheme, using as an example series the four binary phases of the Os–Al system. Our analysis begins with the CsCl-type OsAl phase, whose 11 electrons/Os count is one electron short of that predicted by the 18-n rule. This electron deficiency provides a driving force for Al incorporation to make more Al-rich intermetallic phases. In the structures of Os2Al3 (own type) and OsAl2 (MoSi2 type), each additional Al atom contributes three electrons, two of which go towards cleaving Os–Os isolobal bonds, with the third alleviating the original electron deficiency of OsAl. Across the series, the framework of isolobal Os–Os bonds is reduced from a primitive cubic network (n=6, OsAl) to layers of cubes (n=5, Os2Al3) to individual square nets (n=4, OsAl2). Upon adding more Al to form Os4Al13, the Os–Os contacts are further reduced to dumbbells at the interfaces between fluorite-type columns. At this point, the added Al raises the electron count beyond that needed for filled octadecets on the Os atoms; the excess electrons are accommodated by Al–Al bonds. Throughout this work, we emphasize how the 18-n scheme can be applied from structural inspection alone, with theoretical calculations confirming or refining these conclusions.
Acknowledgements
We thank Anastasiya Vinokur, Katerina Hilleke, and Gordon Peterson for engaging conversations about the 18-n rule and complex intermetallics. We also gratefully acknowledge the financial support of the National Science Foundation through grant DMR-1508496.
References
[1] S. Samson, Crystal structure of NaCd2. Nature1962, 195, 259.10.1038/195259a0Search in Google Scholar
[2] H. Takakura, C. P. Gómez, A. Yamamoto, M. De Boissieu, A. P. Tsai, Atomic structure of the binary icosahedral Yb–Cd quasicrystal. Nature Mater.2007, 6, 58.10.1038/nmat1799Search in Google Scholar
[3] S. Samson, The crystal structure of the phase β-Mg2Al3. Acta Crystallogr.1965, 220, 401.10.1107/S0365110X65005133Search in Google Scholar
[4] M. Conrad, B. Harbrecht, T. Weber, D. Y. Jung, W. Steurer, Large, larger, largest–a family of cluster-based tantalum copper aluminides with giant unit cells. II. The cluster structure. Acta Crystallogr. B2009, 65, 318.10.1107/S0108768109014013Search in Google Scholar
[5] T. Weber, J. Dshemuchadse, M. Kobas, M. Conrad, B. Harbrecht, W. Steurer, Large, larger, largest–a family of cluster-based tantalum copper aluminides with giant unit cells. I. Structure solution and refinement. Acta Crystallogr. B2009, 65, 308.10.1107/S0108768109014001Search in Google Scholar
[6] A. V. Morozkin, Y. D. Seropegin, V. K. Portnoy, I. A. Sviridov, A. V. Leonov, New ternary compounds R117Fe52Ge112 (R=Gd, Dy, Ho, Er, Tm) and Sm117Cr52Ge112 of the Tb117Fe52Ge112-type structure. Mater. Res. Bull.1998, 33, 903.10.1016/S0025-5408(98)00051-8Search in Google Scholar
[7] W. Carrillo-Cabrera, S. Budnyk, Y. Prots, Y. Grin, Ba8Ge43 revisited: a 2a′×2a′×2a′ superstructure of the clathrate-I type with full vacancy ordering. Z. Anorg. Allg. Chem.2004, 630, 2267.10.1002/zaac.200400268Search in Google Scholar
[8] K. Kovnir, M. Shatruk, Magnetism in giant unit cells – crystal structure and magnetic properties of R117Co52+δSn112+γ (R=Sm, Tb, Dy). Eur. J. Inorg. Chem.2011, 2011, 3955.10.1002/ejic.201100200Search in Google Scholar
[9] D. C. Schmitt, N. Haldolaarachchige, Y. Xiong, D. P. Young, R. Jin, J. Y. Chan, Probing the lower limit of lattice thermal conductivity in an ordered extended solid: Gd117Co56Sn112, a phonon glass–electron crystal system. J. Am. Chem. Soc.2012, 134, 5965.10.1021/ja300240gSearch in Google Scholar PubMed
[10] B. Chabot, K. Cenzual, E. Parthé, Sc44Os7 and Sc44Ir7 with the Mg44Rh7 structure type. Acta Crystallogr. B1980, 36, 2202.10.1107/S0567740880008394Search in Google Scholar
[11] R. F. Berger, P. L. Walters, S. Lee, R. Hoffmann, Connecting the chemical and physical viewpoints of what determines structure: from 1-D chains to γ-brasses. Chem. Rev.2011, 111, 4522.10.1021/cr1001222Search in Google Scholar PubMed
[12] U. Mizutani, T. Takeuchi, H. Sato, Interpretation of the Hume-Rothery rule in quasicrystals and their approximants. J. Non-Cryst. Solids2004, 334, 331.10.1016/j.jnoncrysol.2003.11.071Search in Google Scholar
[13] G. Kreiner, Y. Moguilnikov, U. Burkhardt, M. Schäpers, Hume-Rothery controlled formation of structurally complex alloy phases in the ternary Ga–Mg–Pd system. J. Non-Cryst. Solids2004, 334–335, 17.10.1016/j.jnoncrysol.2003.11.070Search in Google Scholar
[14] S. Andersson, An alternative description of the structure of Cu4Cd3. Acta Crystallogr. B1980, 36, 2513.10.1107/S0567740880009326Search in Google Scholar
[15] Q.-B. Yang, S. Andersson, L. Stenberg, An alternative description of the structure of NaCd2. Acta Crystallogr. B1987, 43, 14.10.1107/S0108768187098379Search in Google Scholar
[16] K. Cenzual, E. Parthé, R. M. Waterstrat, Zr21Re25, a New rhombohedral structure type containing 12 Å-thick infinite MgZn2(Laves)-type columns. Acta Crystallogr. C1986, 42, 261.10.1107/S0108270186096555Search in Google Scholar
[17] D. C. Fredrickson, S. Lee, R. Hoffmann, J. Lin, The Nowotny chimney ladder phases: following the cpseudo clue toward an explanation of the 14 electron rule. Inorg. Chem.2004, 43, 6151.10.1021/ic049427nSearch in Google Scholar PubMed
[18] Y. Guo, D. Fredrickson, PRINCEPS: a computer-based approach to the structural description and recognition of trends within structural databases, and its application to the Ce–Ni–Si system. Crystals2016, 6, 35.10.3390/cryst6040035Search in Google Scholar
[19] D. C. Fredrickson, S. Lee, R. Hoffmann, Interpenetrating polar and nonpolar sublattices in intermetallics: the NaCd2 structure. Angew. Chem. Int. Ed.2007, 46, 1958.10.1002/anie.200601678Search in Google Scholar PubMed
[20] R. T. Fredrickson, D. C. Fredrickson, Fragmentation of the fluorite type in Fe8Al17.4Si7.6: structural complexity in intermetallics dictated by the 18 electron rule. Inorg. Chem.2012, 51, 10341.10.1021/ic3015089Search in Google Scholar PubMed
[21] R. T. Fredrickson, D. C. Fredrickson, The modulated structure of Co3Al4Si2: incommensurability and Co–Co interactions in search of filled octadecets. Inorg. Chem.2013, 52, 3178.10.1021/ic302650rSearch in Google Scholar PubMed
[22] R. T. Fredrickson, B. J. Kilduff, D. C. Fredrickson, Homoatomic clustering in T4Ga5 (T=Ta, Nb, Ta/Mo): a story of reluctant intermetallics crystallizing in a new binary structure type. Inorg. Chem.2014, 54, 821.10.1021/ic501966vSearch in Google Scholar PubMed
[23] A. B. Hadler, V. J. Yannello, W. Bi, E. E. Alp, D. C. Fredrickson, π-Conjugation in Gd13Fe10C13 and its oxycarbide: unexpected connections between complex carbides and simple organic molecules. J. Am. Chem. Soc.2014, 136, 12073.10.1021/ja505868wSearch in Google Scholar PubMed
[24] V. J. Yannello, D. C. Fredrickson, Orbital origins of helices and magic electron counts in the Nowotny chimney ladders: the 18 – n rule and a path to incommensurability. Inorg. Chem.2014, 53, 10627.10.1021/ic501723nSearch in Google Scholar PubMed
[25] V. J. Yannello, B. J. Kilduff, D. C. Fredrickson, Isolobal analogies in intermetallics: the reversed approximation MO approach and applications to CrGa4- and Ir3Ge7-type phases. Inorg. Chem.2014, 53, 2730.10.1021/ic4031624Search in Google Scholar PubMed
[26] B. J. Kilduff, V. J. Yannello, D. C. Fredrickson, Defusing complexity in intermetallics: how covalently shared electron pairs stabilize the FCC variant Mo2CuxGa6−x (x≈0.9). Inorg. Chem.2015, 54, 8103.10.1021/acs.inorgchem.5b01333Search in Google Scholar PubMed
[27] V. J. Yannello, D. C. Fredrickson, Generality of the 18-n rule: intermetallic structural chemistry explained through isolobal analogies to transition metal complexes. Inorg. Chem.2015, 54, 11385.10.1021/acs.inorgchem.5b02016Search in Google Scholar PubMed
[28] J. Engelkemier, L. M. Green, R. N. McDougald, G. T. McCandless, J. Y. Chan, D. C. Fredrickson, Putting ScTGa5 (T=Fe, Co, Ni) on the map: how electron counts and chemical pressure shape the stability range of the HoCoGa5 type. Cryst. Growth Des.2016, 16, 5349.10.1021/acs.cgd.6b00855Search in Google Scholar
[29] A. I. Vinokur, D. C. Fredrickson, 18-Electron resonance structures in the BCC transition metals and their CsCl-type derivatives. Inorg. Chem.2017, 56, 2834.10.1021/acs.inorgchem.6b02989Search in Google Scholar PubMed
[30] G. Bergerhoff, R. Hundt, R. Sievers, I. D. Brown, The inorganic crystal structure data base. J. Chem. Inf. Comput. Sci.1983, 23, 66.10.1021/ci00038a003Search in Google Scholar
[31] G. Bergerhoff, I. D. Brown, in Crystallographic Databases (Eds. F. H. Allen, G. Bergerhoff and R. Sievers) International Union of Crystallography, Chester, p. 77, 1987.Search in Google Scholar
[32] J. Klingbeil, R. Schmid-Fetzer, Interaction of metals with AlAs and InAs: estimation of ternary Al-As-M and in-As-M phase diagrams. Calphad1989, 13, 367.10.1016/0364-5916(89)90026-6Search in Google Scholar
[33] W. Obrowski, B2-Phasen von aluminium mit T-Metallen der VII. und VIII. Gruppe des periodischen systems. Naturwissenschaften1960, 47, 14.10.1007/BF00628450Search in Google Scholar
[34] L.-E. Edshammar, The crystal structures of Os2Al3 and OsAl2. Acta Chem. Scand.1965, 19, 871.10.3891/acta.chem.scand.19-0871Search in Google Scholar
[35] L.-E. Edshammar, The crystal structure of Os4Al13. Acta Chem. Scand.1964, 18, 2294.10.3891/acta.chem.scand.18-2294Search in Google Scholar
[36] H. Schäfer, B. Eisenmann, W. Müller, Zintl phases: transitions between metallic and ionic bonding. Angew. Chem. Int. Ed.1973, 12, 694.10.1002/anie.197306941Search in Google Scholar
[37] Chemistry, Structure, and Bonding of Zintl Phases and Ions, (Ed. S. M. Kauzlarich) VCH, New York, 1996.Search in Google Scholar
[38] G. Kresse, J. Furthmüller, Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys. Rev. B1996, 54, 11169.10.1103/PhysRevB.54.11169Search in Google Scholar
[39] G. Kresse, J. Furthmüller, Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set. Comput. Mater. Sci.1996, 6, 15.10.1016/0927-0256(96)00008-0Search in Google Scholar
[40] P. E. Blöchl, Projector augmented-wave method. Phys. Rev. B1994, 50, 17953.10.1103/PhysRevB.50.17953Search in Google Scholar PubMed
[41] G. Kresse, D. Joubert, From ultrasoft pseudopotentials to the projector augmented-wave method. Phys. Rev. B1999, 59, 1758.10.1103/PhysRevB.59.1758Search in Google Scholar
[42] T. E. Stacey, D. C. Fredrickson, Perceiving molecular themes in the structures and bonding of intermetallic phases: the role of Hückel theory in an ab initio Era. Dalton Trans.2012, 41, 7801.10.1039/c2dt30298eSearch in Google Scholar PubMed
[43] G. A. Landrum, W. V. Glassey, YAeHMOP: yet another extended Hückel molecular orbital program. YAeHMOP is freely available via the internet at URL: https://sourceforge.net/projects/yaehmop/. Accessed: 26 Dec 2016.Search in Google Scholar
[44] S. Michael, F. Rüdiger, Electronic structures of three semiconducting intermetallics: RuAl2, RuGa2, and OsAl2. J. Phys.: Condens. Matter1998, 10, 701.Search in Google Scholar
[45] M. Krajcí, J. Hafner, Covalent bonding and bandgap formation in transition-metal aluminides: di-aluminides of group VIII transition metals. J. Phys.: Condens. Matter2002, 14, 5755.10.1088/0953-8984/14/23/309Search in Google Scholar
[46] In practice, this is done by calculating the crystal orbitals for the Os sublattice, removing those orbitals based on the Os–Os σ* MOs, and using this set as the eigenfunctions for the raMO model Hamiltonian.Search in Google Scholar
[47] T. A. Albright, J. K. Burdett, M.-H. Whangbo, Orbital Interactions in Chemistry, 2nd edition, Wiley, Hoboken, New Jersey 2013.10.1002/9781118558409Search in Google Scholar
Supplemental Material:
The online version of this article (DOI: https://doi.org/10.1515/zkri-2017-2044) offers supplementary material, available to authorized users.
©2017 Walter de Gruyter GmbH, Berlin/Boston
