Startseite Ab initio calculations and crystal structure simulations for mixed layer compounds from the tetradymite series
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Ab initio calculations and crystal structure simulations for mixed layer compounds from the tetradymite series

  • Jie Yao ORCID logo EMAIL logo , Cristiana L. Ciobanu ORCID logo , Nigel J. Cook ORCID logo , Kathy Ehrig ORCID logo , Gabriel I. Dima und Gerd Steinle-Neumann
Veröffentlicht/Copyright: 31. Juli 2024
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Abstract

Density functional theory (DFT) is used to obtain structural information of seven members of the tetradymite homologous series: Bi2Te3 (tellurobismuthite), BiTe (tsumoite), Bi4Te3 (pilsenite), Bi5Te3, Bi2Te, Bi7Te3 (hedleyite), and Bi8Te3. We use the formula S(Bi2kTe3)·L[Bi2(k+1)Te3] as a working model (k = 1–4) where S and L are short and long modules in the structures. The relaxed structures show an increase in the a parameter and decrease in the interlayer distance (dsub) from Bi2Te3 (2.029 Å) to Bi8Te3 (1.975 Å). DFT-derived formation energy for each phase indicates that they are all thermodynamically stable. Scanning transmission electron microscopy (STEM) simulations for each of the relaxed structures show an excellent match with atom models. Simulated electron diffractions and reflection modulation along c* are concordant with published data, where they exist, and with the theory underpinning mixed-layer compounds. Two modulation vectors, q = γ· csub (γ = 1.800–1.640) and qF = γF· dsub F = 0.200–0.091), describe the distribution of reflections and their intensity variation along dsub = 1/dsub. The γF parameter reinforces the concept of Bi2kTe3 and Bi2(k+1)Te3 blocks in the double module structures, and γ relates to dsub variation. Our model describing the relationship between γ and dsub allows prediction of dsub beyond the compositional range considered in this study, showing that phases with k >5 have values dsub within the analytical range of interlayer distance in bismuth. This, in turn, allows us to constrain the tetradymite homologous series between γ values of 1.800 (Bi2Te3) and 1.588 (Bi14Te3). Phase compositions with higher Bi/Te should be considered as disordered alloys of bismuth. These results have implications for mineral systematics and classification as they underpin predictive models for all intermediate structures in the group and can be equally applied to other mixed-layer series. Our structural models will also assist in understanding variation in the thermoelectric and topological insulating properties of new compounds in the broader tetradymite group and can support experimental work targeting a refined phase diagram for the system Bi-Te.

Acknowledgments and funding

We appreciate the constructive comments of two anonymous reviewers and editorial handling by Jianwei Wang. This work was supported by the Australian Research Council through Linkage grant LP200100156 “Critical Minerals from Complex Ores,” co-supported by BHP Olympic Dam. We acknowledge access to the Phoenix high-performance computer (HPC) at the University of Adelaide and thank Fabien Voisin and Mark Innes for the assistance with VASP installation and HPC configuration.

References cited

Adenis, C., Langer, V., and Lindqvist, O. (1989) Reinvestigation of the structure of tellurium. Acta Crystallographica Section C, 45, 941–942, https://doi.org/10.1107/S0108270188014453.Suche in Google Scholar

Amelinckx, S., Van Tendeloo, G., Van Dyck, D., and Van Landuyt, J. (1989) The study of modulated structures, mixed layer polytypes and 1-D quasi-crystals by means of electron microscopy and electron diffraction. Phase Transitions, 16, 3–40, https://doi.org/10.1080/01411598908245677.Suche in Google Scholar

Atuchin, V.V., Gavrilova, T.A., Kokh, K.A., Kuratieva, N.V., Pervukhina, N.V., and Surovtsev, N.V. (2012) Structural and vibrational properties of PVT grown Bi2Te3 microcrystals. Solid State Communications, 152, 1119–1122, https://doi.org/10.1016/j.ssc.2012.04.007.Suche in Google Scholar

Birch, F. (1947) Finite elastic strain of cubic crystals. Physical Review, 71, 809–824, https://doi.org/10.1103/PhysRev.71.809.Suche in Google Scholar

Blöchl, P.E. (1994) Projector augmented-wave method. Physical Review B, 50, 17953–17979, https://doi.org/10.1103/PhysRevB.50.17953.Suche in Google Scholar

Bos, J.W.G., Zandbergen, H.W., Lee, M.H., Ong, N.P., and Cava, R.J. (2007) Structures and thermoelectric properties of the infinitely adaptive series (Bi2)m(Bi2Te3)n. Physical Review B, 75, 195203, https://doi.org/10.1103/PhysRevB.75.195203.Suche in Google Scholar

Bos, J.W.G., Faucheux, F., Downie, R.A., and Marcinkova, A. (2012) Phase stability, structures and properties of the (Bi2)m(Bi2Te3)n natural superlattices. Journal of Solid State Chemistry, 193, 13–18, https://doi.org/10.1016/j.jssc.2012.03.034.Suche in Google Scholar

Cheng, W. and Ren, S.F. (2011) Phonons of single quintuple Bi2Te3 and Bi2Se3 films and bulk materials. Physical Review B, 83, 094301, https://doi.org/10.1103/PhysRevB.83.094301.Suche in Google Scholar

Ciobanu, C.L., Pring, A., Cook, N.J., Self, P., Jefferson, D., Dima, G.I., and Melnikov, V. (2009) Chemical-structural modularity in the tetradymite group: A HRTEM study. American Mineralogist, 94, 517–534, https://doi.org/10.2138/am.2009.2906.Suche in Google Scholar

Ciobanu, C.L., Birch, W.D., Cook, N.J., Pring, A., and Grundler, P.V. (2010) Petrogenetic significance of Au-Bi-Te-S associations: The example of Maldon, Central Victorian gold province, Australia. Lithos, 116, 1–17, https://doi.org/10.1016/j.lithos.2009.12.004.Suche in Google Scholar

Ciobanu, C.L., Kontonikas-Charos, A., Slattery, A., Cook, N.J., Wade, B.P., and Ehrig, K. (2017) Short-range stacking disorder in mixed-layer compounds: A HAADF STEM study of bastnäsite-parisite intergrowths. Minerals, 7, 227, https://doi.org/10.3390/min7110227.Suche in Google Scholar

Ciobanu, C.L., Slattery, A.D., Cook, N.J., Wade, B.P., and Ehrig, K. (2021) Bi8Te3, the 11-atom layer member of the tetradymite homologous series. Minerals, 11, 980, https://doi.org/10.3390/min11090980.Suche in Google Scholar

Ciobanu, C.L., Cook, N.J., Slattery, A., Ehrig, K., and Liu, W.Y. (2022) Nanoscale intergrowths in the bastnasite-synchysite series record transition towards thermodynamic equilibrium. MRS Bulletin, 47, 250–257, https://doi.org/10.1557/s43577-022-00318-1.Suche in Google Scholar

Cook, N.J., Ciobanu, C.L., Wagner, T., and Stanley, C.J. (2007) Minerals of the system Bi-Te-Se-S related to the tetradymite archetype: Review of classification and compositional variation. Canadian Mineralogist, 45, 665–708, https://doi.org/10.2113/gscanmin.45.4.665.Suche in Google Scholar

Cook, N.J., Ciobanu, C.L., Spry, P.G., and Voudouris, P. (2009) Understanding gold-(silver)-telluride-(selenide) mineral deposits. Episodes, 32, 249–263, https://doi.org/10.18814/epiiugs/2009/v32i4/002.Suche in Google Scholar

Cook, N.J., Ciobanu, C.L., Liu, W., Slattery, A., Wade, B.P., Mills, S.J., and Stanley, C.J. (2019) Polytypism and polysomatism in mixed-layer chalcogenides: Characterization of PbBi4Te4S3 and inferences for ordered phases in the aleksite series. Minerals, 9, 628, https://doi.org/10.3390/min9100628.Suche in Google Scholar

Cook, N.J., Ciobanu, C.L., Slattery, A., Wade, B.P., and Ehrig, K. (2021) The mixed-layer structures of ikunolite, laitakarite, joséite-B and joséite-A. Minerals, 11, 920, https://doi.org/10.3390/min11090920.Suche in Google Scholar

Feutelais, Y., Legendre, B., Rodier, N., and Agafonov, V. (1993) A study of the phases in the bismuth–tellurium system. Materials Research Bulletin, 28, 591–596, https://doi.org/10.1016/0025-5408(93)90055-I.Suche in Google Scholar

Frangis, N., Kuypers, S., Manolikas, C., Van Tendeloo, G., Van Landuyt, J., and Amelinckx, S. (1990) Continuous series of one-dimensional structures in compounds based on M2X3 (M= Sb, Bi; X= Se, Te). Journal of Solid State Chemistry, 84, 314–334, https://doi.org/10.1016/0022-4596(90)90330-Z.Suche in Google Scholar

Gibbs, J.W. (1973) A method of geometrical representation of the thermodynamic properties of substances by means of surfaces. Transactions of the Connecticut Academy of Arts and Sciences, 2, 382–404.Suche in Google Scholar

Goldsmid, H.J. (2014) Bismuth telluride and its alloys as materials for thermoelectric generation. Materials, 7, 2577–2592, https://doi.org/10.3390/ma7042577.Suche in Google Scholar

Grimme, S., Antony, J., Ehrlich, S., and Krieg, H. (2010) A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H-Pu. The Journal of Chemical Physics, 132, 154104, https://doi.org/10.1063/1.3382344.Suche in Google Scholar

Hasanova, G.S., Aghazade, A.I., Imamaliyeva, S.Z., Yusibov, Y.A., and Babanly, M.B. (2021) Refinement of the phase diagram of the Bi-Te system and the thermodynamic properties of lower bismuth tellurides. Journal of the Minerals Metals & Materials Society, 73, 1511–1521, https://doi.org/10.1007/s11837-021-04621-1.Suche in Google Scholar

Hohenberg, P. and Kohn, W. (1964) Inhomogeneous electron gas. Physical Review, 136, B864–B871, https://doi.org/10.1103/PhysRev.136.B864.Suche in Google Scholar

Imamov, R.M. and Semiletov, S.A. (1971) Crystal structure of the phases in the systems Bi-Se, Bi-Te and Sb-Te. Soviet Physics, Crystallography, 15, 845–850.Suche in Google Scholar

Kohn, W. and Sham, L.J. (1965) Self-consistent equations including exchange and correlation effects. Physical Review, 140, A1133–A1138, https://doi.org/10.1103/PhysRev.140.A1133.Suche in Google Scholar

Kresse, G. and Furthmüller, J. (1996) Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Physical Review B, 54, 11169–11186, https://doi.org/10.1103/PhysRevB.54.11169.Suche in Google Scholar

Kresse, G. and Joubert, D. (1999) From ultrasoft pseudopotentials to the projector augmented-wave method. Physical Review B, 59, 1758–1775, https://doi.org/10.1103/PhysRevB.59.1758.Suche in Google Scholar

Lange, P.W. (1939) Ein vergleich zwischen Bi2Te3 und Bi2Te2S. Naturwissenschaften, 27, 133–134, https://doi.org/10.1007/BF01490284.Suche in Google Scholar

Lind, H. and Lidin, S. (2003) A general structure model for Bi–Se phases using a superspace formalism. Solid State Sciences, 5, 47–57, https://doi.org/10.1016/S1293-2558(02)00080-8.Suche in Google Scholar

Ma, J., Hegde, V.I., Munira, K., Xie, Y., Keshavarz, S., Mildebrath, D.T., Wolverton, C., Ghosh, A.W., and Butler, W.H. (2017) Computational investigation of half-Heusler compounds for spintronics applications. Physical Review B, 95, 024411, https://doi.org/10.1103/PhysRevB.95.024411.Suche in Google Scholar

Mao, C., Tan, M., Zhang, L., Wu, D., Bai, W., and Liu, L. (2018) Experimental reinvestigation and thermodynamic description of Bi-Te binary system. Calphad, 60, 81–89, https://doi.org/10.1016/j.calphad.2017.11.007.Suche in Google Scholar

Medlin, D., Erickson, K., Limmer, S., Yelton, W., and Siegal, M.P. (2014) Dissociated dislocations in Bi2Te3 and their relationship to seven-layer Bi3Te4 defects. Journal of Materials Science, 49, 3970–3979, https://doi.org/10.1007/s10853-014-8035-4.Suche in Google Scholar

Murnaghan, F.D. (1944) The compressibility of media under extreme pressures. Proceedings of the National Academy of Sciences of the United States of America, 30, 244–247, https://doi.org/10.1073/pnas.30.9.244.Suche in Google Scholar

Nabok, D., Tas, M., Kusaka, S., Durgun, E., Friedrich, C., Bihlmayer, G., Blügel, S., Hirahara, T., and Aguilera, I. (2022) Bulk and surface electronic structure of Bi4Te3 from GW calculations and photoemission experiments. Physical Review Materials, 6, 034204, https://doi.org/10.1103/PhysRevMaterials.6.034204.Suche in Google Scholar

Nakajima, S. (1963) The crystal structure of Bi2Te3–xSex. Journal of Physics and Chemistry of Solids, 24, 479–485, https://doi.org/10.1016/0022-3697(63)90207-5.Suche in Google Scholar

Nakayama, A., Einaga, M., Tanabe, Y., Nakano, S., Ishikawa, F., and Yamada, Y. (2009) Structural phase transition in Bi2Te3 under high pressure. High Pressure Research, 29, 245–249, https://doi.org/10.1080/08957950902951633.Suche in Google Scholar

Pack, J.D. and Monkhorst, H.J. (1977) “Special points for Brillouin-zone integrations”—A reply. Physical Review B, 16, 1748–1749, https://doi.org/10.1103/PhysRevB.16.1748.Suche in Google Scholar

Palmer, D.C. (2015) Visualization and analysis of crystal structures using Crystal-Maker software. Zeitschrift für Kristallographie—Crystalline Materials, 230, 559–572, https://doi.org/10.1515/zkri-2015-1869.Suche in Google Scholar

Park, S., Ryu, B., and Park, S. (2021) Structural analysis, phase stability, electronic band structures, and electric transport types of (Bi2)m(Bi2Te3)n by Density Functional Theory calculations. Applied Sciences, 11, 11341, https://doi.org/10.3390/app112311341.Suche in Google Scholar

Perdew, J.P., Burke, K., and Ernzerhof, M. (1996) Generalized gradient approximation made simple. Physical Review Letters, 77, 3865–3868, https://doi.org/10.1103/PhysRevLett.77.3865.Suche in Google Scholar

Perdew, J.P., Ruzsinszky, A., Csonka, G.I., Vydrov, O.A., Scuseria, G.E., Constantin, L.A., Zhou, X., and Burke, K. (2008) Restoring the density-gradient expansion for exchange in solids and surfaces. Physical Review Letters, 100, 136406, https://doi.org/10.1103/PhysRevLett.100.136406.Suche in Google Scholar

Schiferl, D. and Barrett, C.S. (1969) The crystal structure of arsenic at 4.2, 78 and 299 K. Journal of Applied Crystallography, 2, 30–36, https://doi.org/10.1107/S0021889869006443.Suche in Google Scholar

Shelimova, L.E., Karpinskii, O.G., Kosyakov, V.I., Shestakov, V.A., Zemskov, V.S., and Kuznetsov, F.A. (2000) Homologous series of layered tetradymite-like compounds in Bi-Te and GeTe-Bi2Te3 systems. Journal of Structural Chemistry, 41, 81–87, https://doi.org/10.1007/BF02684732.Suche in Google Scholar

Stokes, H.T. and Hatch, D.M. (2005) FINDSYM: Program for identifying the space-group symmetry of a crystal. Journal of Applied Crystallography, 38, 237–238, https://doi.org/10.1107/S0021889804031528.Suche in Google Scholar

Vilaplana, R., Gomis, O., Manjón, F.J., Segura, A., Pérez-González, E., Rodríguez-Hernández, P., Muñoz, A., González, J., Marín-Borrás, V., Muñoz-Sanjosé, V., and others. (2011) High-pressure vibrational and optical study of Bi2Te3. Physical Review B, 84, 104112, https://doi.org/10.1103/PhysRevB.84.104112.Suche in Google Scholar

Warren, H.V. and Peacock, M.A. (1945) Hedleyite, a new bismuth telluride from British Columbia, with notes on wehrlite and some bismuth-tellurium alloys. University of Toronto Studies, Geology Series, 49, 55–69.Suche in Google Scholar

Woodcox, M., Young, J., and Smeu, M. (2019) Ab initio investigation of the elastic properties of bismuth-based alloys. Physical Review B, 100, 104105, https://doi.org/10.1103/PhysRevB.100.104105.Suche in Google Scholar

Wyckoff, R.W.G. (1963) Crystal Structures, 2nd ed. Interscience Publishers.Suche in Google Scholar

Yamana, K., Kihara, K., and Matsumoto, T. (1979) Bismuth tellurides BiTe and Bi4Te3. Acta Crystallographica Section B, 35, 147–149, https://doi.org/10.1107/S0567740879002788.Suche in Google Scholar

Zav’ylov, E.N., Begizov, V.D., and Nechelyustov, G.N. (1976) New data on hedleyite. Doklady Akademii Nauk SSSR, 230, 1439–1441 (in Russian).Suche in Google Scholar

Zurhelle, A.F., Deringer, V.L., Stoffel, R.P., and Dronskowski, R. (2016) Ab initio lattice dynamics and thermochemistry of layered bismuth telluride (Bi2Te3). Journal of Physics: Condensed Matter, 28, 115401, https://doi.org/10.1088/0953-8984/28/11/115401.Suche in Google Scholar

Received: 2023-04-05
Accepted: 2023-10-24
Published Online: 2024-07-31
Published in Print: 2024-08-27

© 2024 by Mineralogical Society of America

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