Review: New simple material model versus Goldschmidt's tolerance factor formalism

References

• F. S. Galasso, Structure, properties, and preparation of perovskite-type compounds London: Pergamon Press Inc.; (1969).
   Google Scholar
• S. C. Tidrow, Mapping comparison of Goldschmidt's tolerance factor with Perovskite structural conditions. Ferroelectrics, 470(1), 13–27; DOI:10.1080/00150193.2014.922372 (2014).
   Google Scholar
• V.L. Miller, S.C. Tidrow, Perovskites: “Effective” Temperature and Coordination Dependence of 38 Ionic Radii. Integr. Ferroelectr. 166(1), 30–47, DOI: 10.1080/10584587.2015.1092196 (2015).
   Google Scholar
• V.L. Miller, S.C. Tidrow, Perovskites: Some Polarization Induced Structural Phase Transitions Using “Effective” Temperature and Coordination Dependent Radii and Polarizabilities of Ions. Integr. Ferroelectr. 166(1), 206–224, DOI: 10.1080/10584587.2015.1092650 (2015).
   Google Scholar
• V. L. Miller, S. C. Tidrow, Perovskites: Temperature and coordination dependent ionic radii, Integr Ferroelectr 148(1), 1–16; DOI: 10.1080/10584587.2013.851576 (2013).
   Web of Science ®Google Scholar
• S.C. Tidrow, Linking Curie constant and phase transition temperature with fundamental ion properties, Integrated Ferroelectrics (accepted for publication)
   Google Scholar
• R. D. Shannon, Dielectric polarizabilities of ions in oxides and fluorides. J Appl Phys, 73(1), 348–366; DOI: 10.1063/1.353856 (1993).
   Google Scholar
• O. F. Mossotti, Mem di mathem e fisica in Modena 24, 49 (1850).
   Google Scholar
• R. Clausius, Die mechanische U'grmetheorie 2, 62 (1879).
   Google Scholar
• V. M. Goldschmidt, Skr. Norske Vidensk Akad., Mat.-naturv. Kl. No. 2 (1926a).
   Google Scholar
• C. Kittel, Solid State Physics, 5th Ed, John Wiley and Sons, 608 pg, Ch. 13 to 15; ISBN: 0-471-49024-5 (1976).
   Google Scholar
• J. R. Hall, H. E. Hook, Solid state physics, 2nd Ed, Wiley 486 pg; ISBN: 978-0-471-92805-8 (1995).
   Google Scholar
• P. Curie, Propriétés magnétiques des corps à diverses températures, Thèse – Faculté des sciences de Paris Paris, Gauthier-Villars (1895).
   Google Scholar
• J.C. Maxwell, A dynamical theory of the electromagnetic field, Philosophical Transactions of the Royal Society of London 155, 459–512; DOI:10.1098/rstl.1865.0008 (1865).
   Google Scholar
• R. D. Shannon, Revised effective ionic radii and systematic studies of interatomic distances in halides and chalcogenides, Acta Crystallogr A32(5), 751–767; DOI:10.1107/S0567739476001551 (1976).
   Google Scholar
• M. H. Francombe, B. Lewis, Structural and electrical properties of silver niobate and silver tantalate. Acta Crystallogr 11(3), 175–178; DOI: 10.1107/S0365110X58000463 (1958).
   Google Scholar
• G. Shirane, R. Newnham, R. Pepinsky, Dielectric properties and phase transitions of NaNbO₃ and (Na,K)NbO₃, Phys Rev, 96(3), 581–588; DOI: 10.1103/PhysRev.96.581 (1954).
   Web of Science ®Google Scholar
• C. N. W. Darlington, K. S. Knight, High-temperature phases of NaNbO₃ and NaTaO₃. Acta Crystallogr B55(1), 24–30; DOI: 10.1107/S010876819800963X (1999).
   Google Scholar
• B. J. Kennedy, A. K. Prodjosantoso, J. Howard, Powder neutron diffraction study of the high temperature phase transitions in NaTaO₃. J Phys: Condens Matter 11(33), 6319–6327; DOI: 10.1088/0953-8984/11/33/302 (1999).
   Google Scholar
• P. Vousden, A study of the unit-cell dimensions and symmetry of certain ferroelectric compounds of niobium and tantalum at room temperature. Acta Crystallogr 4(4), 373–376; DOI:10.1107/S0365110X5100115X (1951).
   Google Scholar
• S. K. Sali, N. K. Kulkarni, K. D. Singh Mudher, Thermal and x-ray studies of mixed alkali urinates of Na–K–U–O system. J Alloy Compd 425, 28–33; DOI: 10.1016/j.jallcom.2006.01.059 (2006).
   Google Scholar
• A. Yoshiasa, D. Sakamoto, H. Okudera, M. Ohkawa, K. Ota, Phase relations of N_1-xK_xMgF₃ (0 ≤ x ≤ 1) perovskite-type solid solutions, Mater Res Bull 38(3), 421–427; DOI: 10.1016/S0025-5408(02)01059-0 (2003).
   Google Scholar
• H. F. Kay, Preparation and Properties of Crystals of Barium Titanate, BaTiO₃. Acta Crystallogr 1, 229–237; DOI: 10.1107/S0365110X4800065X (1948).
   Web of Science ®Google Scholar
• H. F. Kay, P. Vousden, Symmetry changes in barium titanate at low temperatures and their relation to its ferroelectric properties. Philos Mag 40(309), 1019–1040 (1949).
   Google Scholar
• X. R. Xing, J. X. Deng, Z. Q. Zhu, G. R. Liu, Solid solution Ba_1-xPb_xTiO₃ and its thermal expansion. J Alloy Compd 353(1–2), 1–4; DOI: 10.1016/S0925-8388(02)01178-7 (2003).
   Google Scholar
• B. J. Kennedy, C. J. Howard, B. C. Chakoumakos, Phase transitions in perovskite at elevated temperature – a powder neutron diffraction study. J Phys: Condens Matter 11(6), 1479–1488; DOI:10.1088/0953-8984/11/6/012 (1999).
   Google Scholar
• S. A. T. Redfern, High-temperature structural phase transitions in perovskite, CaTiO₃, J Phys: Condens Matter 8(43), 8267–8275; DOI:10.1088/0953-8984/8/43/019 (1996).
   Web of Science ®Google Scholar
• X. Xing, J. Chen, J. Deng, G. Liu, Solid solution Pb_1-xSr_xTiO₃ and its thermal expansion. J Alloy Compd 360(1-2), 286–289; DOI: 10.1016/S0925-8388(03)00345-1 (2003).
   Google Scholar
• D. de Ligny, P. Richet, High-temperature heat capacity and thermal expansion of SrTiO₃ and SrZrO₃ perovskites. Phys. Rev. B 53(6), 3013–3022; DOI: 10.1103/PhysRevB.53.3013 (1996).
   Google Scholar
• W. T. Fu, D. J. W. Ijdo, “Unusual” phase transitions in CeAlO₃. J Solid State Chem 179(8), 2732–2738; DOI: 10.1016/j.jssc.2006.05.002 (2006).
   Web of Science ®Google Scholar
• L. Vasylechko, A. Senyshyn, D Trots, R. Niewa, W. Schnelle, M. Knapp, CeAlO₃ and Ce_1-xR_xAlO₃ (R = La, Nd) solid solutions: Crystal structure, thermal expansion and phase transitions. J Solid State Chem 180(4), 1277–1290; DOI:10.1016/j.jssc.2007.01.020 (2007).
   Google Scholar
• John S. Seybold, Introduction to RF propagation, Wiley-Interscience, John Wiley & Sons, Inc. 330 pg (2005).
   Google Scholar
• P. Sciau, A. Kania, B. Dkhil, E. Suard, A. Ratuszna, Structural investigation of AgNbO₃ phases using x-ray and neutron diffraction. J. Phys.: Condens. Matter 16(16), 2795–2810; DOI: 10.1088/0953-8984/16/16/004 (2004).
   Google Scholar
• M. Wolcryz, M. Lukaszewski, The crystal structure of the room-temperature phase of AgTaO₃, Zeitschrift fuer Kristallographie 177(1-2), 53; DOI: 10.1524/zkri.1986.177.1-2.53 (1986).
   Web of Science ®Google Scholar
• G. Meyer, R. Hoppe, Über Oxoniobate(V): Die Kristallstruktur von CsNbO₃, Zeitschrift fuer Anorganische und Allgemeine Chemie 436, 75–86; DOI: 10.1002/zaac.19774360108 (1977).
   Web of Science ®Google Scholar
• E. A. Wood, Polymorphism in potassium niobate, sodium niobate, and other ABO₃ compounds, Acta Cryst 4, 353–362; DOI:10.1107/S0365110X51001112 (1951).
   Google Scholar
• G. Shirane, H. Danner, A. Pavlovic, R. Pepinsky, Phase Transitions in Ferroelectric KNbO₃. Phys. Rev. 93, 672; DOI: 10.1103/PhysRev.93.672 (1954).
   Web of Science ®Google Scholar
• B. T. Matthias, New Ferroelectric Crystals. Phys Rev 75, 1771; DOI: 10.1103/PhysRev.75.1771 (1949).
   Web of Science ®Google Scholar
• P. G. Dickens, A. V. Powell, Powder neutron diffraction study of potassium urinate(v), KUO₃. J Mater Chem 1(1), 137–138; DOI: 10.1039/JM9910100137 (1991).
   Web of Science ®Google Scholar
• Y. Hinatsu, Y. Shimojo, Y. Morri, Magnetic and neutron diffraction studies on potassium urinate KUO₃. J Alloy Compd 270(1-2), 127–131; DOI: 10.1016/S0925-8388(98)00467-8 (1998).
   Google Scholar
• M. H. Francombe, High-temperature structure transitions in sodium niobate. Acta Cryst 9, 256–259; DOI: 10.1107/S0365110X56000711 (1956).
   Web of Science ®Google Scholar
• M. Wells, H. D. Megaw, The structures of NaNbO₃ and Na_0.975K_0.025NbO₃. Proc Phys Soc 78(6), 1258–1259; DOI: 10.1088/0370-1328/78/6/124 (1961).
   Web of Science ®Google Scholar
• H. F. Kay, J. L. Miles, The structure of cadmium titanate and sodium tantalate. Acta Cryst 10, 213–218; DOI: 10.1107/S0365110X57000663 (1957).
   Google Scholar
• G. A. Smolenskii, Doklady AN SSSR 70, 405; (1950).
   Google Scholar
  Zhurnal Tekhnicheskoi Fiziki 20(1950), 137 ( in Russian)
   Google Scholar
• A. M. Chippindale, P. G. Dickens, W. TA. Harrison, A structural study of the soldium (V)urinate, NaUO₃, by time-of-flight powder neutron diffraction, J Solid State Chem 78(2), 256–261; DOI: 10.1016/0022-4596(89)90106-0 (1989).
   Google Scholar
• M. Serafin, R. Hoppe, Zur kenntnis von RbNbO₃ – ein metaniobat mit pyrgomstruktur, J Less Common Met 76(1-2), 299–316; DOI: 10.1016/0022-5088(80)90033-8 (1980).
   Google Scholar
• M. Serafin, R. Hoppe, Zur kenntnis von RbTaO₃ – ein neuer Typ einer Schichtstruktur, Zeitschrift fuer Anorganische und Allgemeine Chemie 464(1), 240–254; DOI: 10.1002/zaac.19804640123 (1980).
   Web of Science ®Google Scholar
• S. Kemmler-Sack, W. Rüdorff, Ternäre oxide. VII. Ternäre uran(V)-oxide mit 1- und 2-wertigen kationnen. Zeitschrift fuer Anorganische und Allgemeine Chemie 354(5-6), 255–272; DOI: 10.1002/zaac.19673540505 (1967).
   Google Scholar
• Y. Hinatsu, Magnetic studies of alkali metal urinates(V) MUO₃ with the perovskite structure. J Alloy Compd 203, 251–257; DOI: 10.1016/0925-8388(94)90743-9 (1994).
   Google Scholar
• L. Quill, Über die Gitterdimensionen des Niobs, des Tantals und einiger Niobate und Tantalate, Zeitschrift fuer Anorganische und Allgemeine Chemie 208(3), 257–272 (1932).
   Google Scholar
• T. Sakudo, H. Unoki, Dielectric properties of SrTiO₃ at low temperatures, Phys Rev Lett 26(14), 851–853; DOI: 10.1103/PhysRevLett.26.851 (1971).
   Web of Science ®Google Scholar