Hostname: page-component-586b7cd67f-rdxmf Total loading time: 0 Render date: 2024-11-26T09:32:52.396Z Has data issue: false hasContentIssue false

Functional twin boundaries and tweed microstructures: a comparison between minerals and device materials

Published online by Cambridge University Press:  05 July 2018

Oktay Aktas*
Affiliation:
Department of Earth Sciences, Cambridge University, Downing Street, Cambridge CB2 3EQ, UK
Ekhard K. H. Salje
Affiliation:
Department of Earth Sciences, Cambridge University, Downing Street, Cambridge CB2 3EQ, UK

Abstract

In ferroelastic materials, the existence of degenerate strain states leads to the formation of nanoscale microstructures, such as domain boundaries (twin walls) and tweed. As the symmetry properties of microstructures differ from those of the bulk, they may dramatically change the macroscopic properties of a crystal. In addition, they are likely to have functional properties (ferroelecricity, piezoelectricity, magnetism, conductivity and rapid chemical transport) that are absent in the bulk. The existence of functional properties of twin walls, along with the advances in nano-scale characterization, has opened the door to domain boundary engineering, which aims to use domain boundaries as active elements in device materials. Hence, this relatively new field puts ferroelastic twin walls and possibly tweed at the heart of future electronic devices. Ferroelasticity is very common among minerals. Similar to manmade materials, the same crystallographic principles apply, which means that there are many minerals that await discovery for their functional properties. Thus, this review aims to raise attention to the discovery of minerals with functional microstructures. The current development of functional twin boundaries and tweed structures in physics and materials sciences is compared with the traditional observation of such structures in minerals. With an emphasis on chemical transport and piezoelectric/ ferroelectric behaviour, examples of functional microstructures are given from both man-made materials and minerals in addition to a discussion of the origin of polar twin walls and the introduction of a recent experimental technique, resonant piezoelectric spectroscopy (RPS), for their discovery.

Type
Research Article
Copyright
Copyright © The Mineralogical Society of Great Britain and Ireland 2014

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.)

Footnotes

Present address: Department of Materials, ETH Zürich, Vladimir-Prelog-Weg 4, 8093 Zurich, Switzerland

References

Aird, A. and Salje, E.K.H. (1998) Sheet superconductivity in twin walls: experimental evidence of WO3–x. Journal of Physics: Condensed Matter, 10, 377380.Google Scholar
Aird, A. and Salje, E.K.H. (2000) Enhanced reactivity of domain walls in WO3 with sodium. The European Physical Journal, 15, 205210.Google Scholar
Aktas, O., Carpenter, M.A. and Salje, E.K.H. (2013a) Polar precursor ordering in BaTiO3 detected by resonant piezoelectric spectroscopy. Applied Physics Letters, 103, 142902142906.CrossRefGoogle Scholar
Aktas, O., Salje, E.K.H., Crossley, S., Lampronti, G.I., Whatmore, R.W., Mathur, N.D. and Carpenter, M.A. (2013b) Ferroelectric precursor behavior in PbSc0.5.Ta0.5O3 detected by field induced resonant piezoelectric spectroscopy, Physical Review B, 88, 174112174124.CrossRefGoogle Scholar
Bleser, T., Berge, B., Bismayer, U. and Salje, E.K.H. (1994) The possibility that the optical secondharmonic generation in lead phosphate, Pb3(PO4)2 , is related to structural imperfections. Journal of Physics: Condensed Matter, 6, 20932099.Google Scholar
Blinc, R., Zalar, B.C.V., Laguta, V.V. and Itoh, M. (2005) Order-disorder component in the phase transition mechanism of 18O enriched strontium t i tanate. Physical Review Letters, 94, 147601147605.CrossRefGoogle Scholar
Bokov, A.A. and Ye, Z.G. (2006) Recent progress in relaxor ferroelectrics with perovskite structure. Journal of Materials Science, 41, 3152.CrossRefGoogle Scholar
Bratkovsky, A.M., Marais, S.C. and Salje, E.K.H. (1994a) The theory of fluctuations and texture embryos in structural phase transitions mediated by strain. Journal of Physics: Condensed Matter, 6, 36793696.Google Scholar
Bratkovsky, A.M., Salje, E.K.H. and Heine, V. (1994b) Overview of the origin of tweed texture. Phase Transitions, 52, 7783.CrossRefGoogle Scholar
Bratkovsky, A.M., Salje, E.K.H., Marais, S.C and Heine, V. (1994c) Theory and computer simulation of tweed texture. Phase Transitions, 48, 113.CrossRefGoogle Scholar
Burkhard, M. (1993) Calcite twins, their geometry, appearance and significance as stress-strain markers and indicators of tectonic regime: a review. Journal of Structural Geology, 15, 351368.CrossRefGoogle Scholar
Burns, G. and Dacol, F.H. (1983) Crystalline ferroelectrics with glassy polarization behavior. Physical Review B, 28, 25272530.CrossRefGoogle Scholar
Burton, B.P., Cockayne, E. and Waghmare, U.V. (2005) Correlations between nanoscale chemical and polar order in relaxor ferroelectrics and the lengthscale for polar nanoregions. Physical Review B, 72, 064113064118.CrossRefGoogle Scholar
Busmann-Holder, A., Beige, H. and Volkel, G. (2009) Precursor effects, broken local symmetry, and coexistence of order-disorder and displacive dynamics in perovskite ferroelectrics. Physical Review B, 79, 184111184117.CrossRefGoogle Scholar
Cady, W. (1964) Piezoelectricity: an Introduction to the Theory and Applications of Electromechanical Phenomena in Crystals, 1. Dover Publications, New York, 806 pp.Google Scholar
Calleja, M., Dove, M.T. and Salje, E.K.H. (2001) Anisotropic ionic transport in quartz: the effect of twin boundaries. Journal of Physics: Condensed Matter, 13, 94459454.Google Scholar
Calleja, M. Dove, M.T. and Salje, E.K.H. (2003) Trapping of oxygen vacancies on twin walls of CaTiO3: a computer simulation study. Journal of Physics: Condensed Matter, 15, 23012307.Google Scholar
Cámara, F., Doukhan, J.C. and Salje, E.K.H. (2000) Twin walls in anorthoclase are enriched in alkali and depleted in Ca and Al. Phase Transitions, 71, 227242.CrossRefGoogle Scholar
Carpenter, M.A., Salje, E.K.H., Graeme-Barber, A., Wruck, B., Dove, M.T. and Knight, K.S. (1998) Calibration of excess thermodynamic properties and elastic constant variations associated with the a$b phase transition in quartz. American Mineralogist, 83, 222.CrossRefGoogle Scholar
Catalan, G., Seidel, J., Ramesh, R. and Scott, J.F. (2012) Domain wall nanoelectronics. Reviews of Modern Physics, 84, 119156.CrossRefGoogle Scholar
Chrosch, J. and Salje, E.K.H. (1994) Thin domain walls in YBa2Cu3O7–d and their rocking curves an x-ray diffraction study. Physica C, 225, 111116.CrossRefGoogle Scholar
Chrosch, J. and Salje, E.K.H. (1999) Temperature dependence of the domain wall width in LaAlO3 . Journal of Applied Physics, 85, 722727.CrossRefGoogle Scholar
Conti, S., Müller, S., Polikovsky, A and Salje, E.K.H. (2011) Coupling of order parameters, chirality, and interfacial structures in multiferroic materials. Journal of Physics: Condensed Matter, 23, 142203142211.Google ScholarPubMed
Cowley, R.A., Gvasaliya, S.N., Lushkinov, S.G., Roessli, B., Rotaru, G.M (2011) Relaxing with relaxors: a review of relaxor ferroelectrics. Advances in Physics, 60, 229327.CrossRefGoogle Scholar
Daraktchiev, M., Harrison, R., Mounstevens, E. and Redfern, S (2006) Effect of transformation twins on the anelastic behavior of polycrystalline Ca1–xSrx TiO3 and SrxBa1-xSnO3 perovskite in relation to the seismic properties of earth’s mantle perovskite. Material Science and Engineering: A, 442, 199203.CrossRefGoogle Scholar
David, F., Walker, F., Lee, M. and Parsons, I. (1995) Micropores and micropermeable texture in alkali feldspars-geochemical and geophysical implications. Mineralogical Magazine, 59, 505534.Google Scholar
Ding, X., Lookman, T., Saxena, A. and Salje, E.K.H. (2012) High junction and twin boundary densities in driven dynamical systems. Advanced Materials, 24, 53855389.CrossRefGoogle ScholarPubMed
Ding, X., Lookman, T., Salje, E.K.H. and Saxena, A. (2013) Twinning in strained ferroelastics: Microstructure and statistics. JOM, 65, 401407.CrossRefGoogle Scholar
Dkhil, B., Gemeiner, P., Al-Barakaty, A., Bellaiche, L., Dul’kin, E., Mojaev, E. and Roth, M. (2009) Intermediate temperature scale T* in lead-based relaxor systems, Physical Review B, 80, 064103064109.CrossRefGoogle Scholar
Dul’kin, E., Mihailova, B., Catalan, G., Gospodinov, M. and Roth, M. (2010) Phase transformation above Tm in PbSc0.5Ta0.5O3 relaxor as seen via acoustic emission. Physical Review B, 82, 180101180105.CrossRefGoogle Scholar
Fiebig, M., Pavlov, V.V. and Pisarev, R.V. (2005) Second-harmonic generation as a tool for studying electronic and magnetic structures of crystals: review. The Journal of the Optical Society of America B, 22, 96118.CrossRefGoogle Scholar
Fousek, J., Cross, L. and Litvin, D. (1999) Possible piezoelectric composites based on the flexoelectric effect. Materials Letters, 39, 287291.CrossRefGoogle Scholar
Frey, M.H. and Payne, D.A. (1996) Grain-size effect on structure and phase transformations for barium titanate. Physical Review B, 54, 31583168.CrossRefGoogle ScholarPubMed
Goncalves-Ferreira, L., Redfern, S.A.T., Artacho, E. and Salje, E.K.H. (2008) Ferrielectric twin walls in CaTiO3 . Physical Review Letters, 101, 097602097606.CrossRefGoogle ScholarPubMed
Goncalves-Ferreira, L., Redfern, S.A.T., Artacho, E. and Salje, E.K.H. (2009) The intrinsic elasticity of twin walls: Ferrielectric twin walls in ferroelastic CaTiO3 . Applied Physics Letters, 94, 081903081906.CrossRefGoogle Scholar
Goncalves-Ferreira, L., Redfern, S.A.T., Artacho, E. and Salje, E.K.H. (2010) Trapping of oxygen vacancies in the twin walls of perovskite. Physical Review B, 81, 024109024116.CrossRefGoogle Scholar
Hayward, S.A., Chrosch, J., Salje, E.K.H. and Carpenter, M.A. (1996) Thickness of pericline twin walls in anorthoclase; an x-ray diffraction study. European Journal of Mineralogy, 8, 13011310.CrossRefGoogle Scholar
Hong, J., Catalan, G., Scott, J.F. and Artacho, E. (2010) The flexoelectricity of barium and strontium titanates from first principles. Journal of Physics: Condensed Matter, 22, 112201112207.Google ScholarPubMed
Houchmandzadeh, B., Lajzerowicz, J. and Salje, E.K.H. (1991) Order parameter coupling and chirality of domain walls. Journal of Physics: Condensed Matter, 3, 51635169.Google Scholar
Houchmandzadeh, B., Lajzerowicz, J. and Salje, E.K.H. (1992) Interfaces and ripple states in ferroelastic crystals: a simple model. Phase Transitions, 38, 7787.CrossRefGoogle Scholar
Johnson, E.A. and Rossman, G.R. (2004) A survey of hydrous species and concentrations in igneous feldspars. American Mineralogist, 89, 586600.CrossRefGoogle Scholar
Kaercher, P., Speziale, S., Miyagi, L., Kanitpanyacharoen, W. and Wenk, H.R. (2012) Crystallographic preferred orientation in wüstite (FeO) through the cubic-to-rhombohedral phase transition. Physics and Chemistry of Minerals, 39, 613626.CrossRefGoogle Scholar
Khachaturian, A.G. (1983) Theory of Structural Transformations in Solids. Dover Books on Engineering Series , Dover Publications Incorporated, New York., 572 pp.Google Scholar
Kholkin, A., Kalinin, S., Roelofs, A. and Gruverman, A. (2007) Review of ferroelectric domain imaging by piezoresponse force microscopy. Pp. 173214. in: Scanning Probe Microscopy: Electrical and Electromechanical Phenomena at the Nanoscale, 2 Volumes (Kalinin, S. and Gruverman, A., editors). Springer Science + Business Media, New York.CrossRefGoogle Scholar
Locherer, K.R., Chrosch, J. and Salje, E.K.H. (1998) Diffuse x-ray scattering in WO3 . Phase Transitions, 67, 5163.CrossRefGoogle Scholar
Lottermoser, T., Meier, D., Pisarev, R.V. and Fiebig, M. (2009) Giant coupling of second-harmonic generation to a multiferroic polarization. Physical Review B, 80, 100101100105.CrossRefGoogle Scholar
Maier, J. (2005) Nanoionics: ion transport and electrochemical storage in confined systems. Nature Materials, 4, 805815.CrossRefGoogle ScholarPubMed
McLaren, A.C. and Fitz Gerald, J.D. (1987) CBED and ALCHEMI investigation of local symmetry and Al S. ordering in K-feldspars. Physics and Chemistry of Minerals, 14, 281292.CrossRefGoogle Scholar
Meier, D., Leo, N., Yuan, G., Lottermoser, Th., Fiebig, M., Becker, P. and Bohatý , L. (2010) Second harmonic generation on incommensurate structures: The case of multiferroic MnWO4 . Physical Review B, 82, 155112155117.CrossRefGoogle Scholar
Morozovska, A.N., Eliseev, E.A., Glinchuk, M.D., Chen, L.-Q. and Gopalan, V. (2012) Interfacial polarization and pyroelectricity in antiferrodistortive structures induced by a flexoelectric effect and rotostriction. Physical Review B, 85, 094107094116.CrossRefGoogle Scholar
Neder, R.B. (1999) Refinement of the kaolinite structure from single-crystal synchrotron data. Clay and Clay Minerals, 47, 487494.CrossRefGoogle Scholar
Nye, J. (1957) Physical Properties of Crystals: Their Representation by Tensors and Matrices. Clarendon Press, New York, 322 pp.Google Scholar
Ohno, I., Harada, K. and Yoshitomi, C. (2006) Temperature variation of elastic constants of quartz across the a-b transition. Physics and Chemistry of Minerals, 33, 19.CrossRefGoogle Scholar
Palmer, D., Putnis, A. and Salje, E.K.H. (1988) Twinning in tetragonal leucite. Physics and Chemistry of Minerals, 16, 298303.CrossRefGoogle Scholar
Palmer, D., Salje, E.K.H. and Schmahl, W. (1989) Phase transitions in leucite: X-ray diffraction studies. Physics and Chemistry of Minerals, 16, 714719.CrossRefGoogle Scholar
Parkin, S.S.P., Hayashi, M. and Thomas, L. (2008a) Magnetic domain-wall racetrack memory. Science, 320, 190194.CrossRefGoogle Scholar
Parkin, S. (2008b) Magnetic race-track – a novel storage class spintronic memory. International Journal of Modern Physics B, 22, 117118.CrossRefGoogle Scholar
Parlinski, K., Heine, V. and Salje, E.K.H. (1993a) Origin of tweed texture in the simulation of a cuprate superconductor. Journal of Physics: Condensed Matter, 5, 497518.Google Scholar
Parlinski, K., Salje, E.K.H. and Heine, V. (1993b) Annealing of tweed microstructure in high Tc superconductors studied by a computer simulation. Acta Materialia, 41, 839847.CrossRefGoogle Scholar
Pawley, A.R., Redfern, S.A.T. and Holland, T.J.B. (1996) Volume behavior of hydrous minerals at high pressure and temperature; I, thermal expansion of lawsonite, zoisite, clinozoisite, and diaspore. American Mineralogist, 81, 335340.CrossRefGoogle Scholar
Penn, R.L. and Banfield, J.F. (1998) Oriented attachment and growth, twinning, polytypism, and formation of metastable phases; insights from nanocrystalline TiO2 . American Mineralogist, 83, 10771082.CrossRefGoogle Scholar
Penn, R.L. and Banfield, J.F. (1999) Formation of rutile nuclei at anatase (112) twin interfaces and the phase transformation mechanism in nanocrystalline titania. American Mineralogist, 84, 871876.CrossRefGoogle Scholar
Petzelt, K., Ostapchuk, T., Gregora, I., Rychetský, I., Hoffmann-Eifert, S., Pronin, A.V., Yuzyuk, Y., Gorshunov, B.P., Kamba, S., Bovtun, V., Pokorn, J. Savinov, M., Porokjonskyy, V., Rafaja, D., Vaněk, P., Almeida, A., Chaves, M.R., Volkov, A.A., Dressel, M. and Waser, R. (2001) Dielectric, infrared, and Raman response of undoped SrTiO3 ceramics: Evidence of polar grain boundaries. Physical Review B, 64, 184111184121.CrossRefGoogle Scholar
Pugachev, A.M., Kovalevskii, V.I., Surovtsev, N.V., Kojima, S., Prosandeev, S.A., Raevski, I.P. and Raevskaya, S.I. (2012) Broken local symmetry in paraelectric BaTiO3 proved by second harmonic generation. Physical Review Letters, 108, 247601247606.CrossRefGoogle ScholarPubMed
Putnis, A. and Salje, E. (1994) Tweed microstructures: Experimental observations and some theoretical models. Phase Transitions, 48, 85105.CrossRefGoogle Scholar
Putnis, A., Salje, E. Redfern, S., Fyfe, C. and Strobl, H. (1987) Structural states of Mg-cordierite I: Order parameters from synchrotron X-ray and NMR data. Physics and Chemistry of Minerals, 14, 446454.CrossRefGoogle Scholar
Salje, E.K.H. (2010) Multiferroic domain boundaries as active memory devices: Trajectories towards domain boundary engineering. ChemPhysChem, 11, 940950.CrossRefGoogle ScholarPubMed
Salje, E.K.H. (2012) Ferroelastic materials. Annual Review of Materials Research, 42, 265283.CrossRefGoogle Scholar
Salje, E.K.H. and Bismayer, U. (1997) Hard mode spectroscopy: The concept and applications. Phase Transitions, 63, 175.CrossRefGoogle Scholar
Salje, E.K.H. and Carpenter, M.A. (2011) Linearquadratic order parameter coupling and multiferroic phase transitions. Journal of Physics: Condensed Matter, 23, 462202462207.Google Scholar
Salje, E.K.H. and Zhang, H.L. (2009) Domain boundary engineering. Phase Transitions: A Multinational Journal, 82, 452469.CrossRefGoogle Scholar
Salje, E.K.H. and Zhang, M. (2006) Hydrous species in ceramics for the encapsulation of nuclear waste: OH in zircon. Journal of Physics: Condensed Matter, 18, 277281.Google Scholar
Salje, E., Kuscholke, B., Wruck, B. and Kroll, H. (1985) Thermodynamics of sodium feldspar II: Experimental results and numerical calculations, Physics and Chemistry of Minerals, 12, 99107.CrossRefGoogle Scholar
Salje, E.K.H., Ding, X., Zhao, Z. and Lookman, T. (2011) Thermally activated avalanches: Jamming and the progression of needle domains. Physical Review B, 83, 104109104120.CrossRefGoogle Scholar
Salje, E.K.H., Ding., X., Zhao, Z. and Lookman, T. (2012) How to generate high twin densities in nanoferroics: Thermal quench and low temperature shear. Applied Physics Letters, 100, 222905222908.CrossRefGoogle Scholar
Salje, E.K.H., Aktas, O., Carpenter, M.A., Laguta, V.V. and Scott, J.F. (2013a) Domains within domains and walls within walls: Evidence for polar domains in cryogenic SrTiO3, Physical Reviews Letters, 111, 247603247608.CrossRefGoogle Scholar
Salje, E.K.H., Carpenter, M.A., Nataf, G.F., Picht, G., Webber, K., Weerasinghe, J. Lisenkov, S. and Bellaiche, L. (2013b) Elastic excitations in BaTiO3 single crystals and ceramics: Mobile domain boundaries and polar nanoregions observed by resonant ultrasonic spectroscopy. Physical Review B, 87, 014106014126.CrossRefGoogle Scholar
Schmahl, W.W., Outnis, A., Salje, E., Freeman, P., Graeme-Barber, A., Jones, R., Singh, K.K., Blunt, J., Edwards, P.P., Loram, J. and Mirza, K. (1989) Twin formation and structural modulations in orthorhombic and tetragonal YBa2(Cu1–xCox)3O7–d. Philosophical Magazine Letters, 60, 241248.CrossRefGoogle Scholar
Schmalzried, H. (editor) (1981) Solid State Reactions, 2nd Edition. Verlag Chemie, Weinheim, Germany, 254 pp.Google Scholar
Seidel, J., Martin, L.W., He, Q., Zhan, Q., Chu, Y.-H., Rother, A., Hawkridge, M.E., Maksymovych, P., Yu., P. Gajek, M., Balke, N., Kalinin, S.V., Gemming, S., Wanf, F., Catalan, G., Scott, J.F., Spaldin, N.A., Orensteinm, J. and Ramesh, R. (2009) Conduction at domain walls in oxide multiferroics. Nature Materials, 8, 229234.CrossRefGoogle Scholar
Seidel, J., Maksymovych, P., Batra, Y., Katan, A., Yantg, S.-Y., He, Q., Baddore, A.P., Kalinin, S.V., Yang, C.-H., Yang, J.-C., Chu, Y.-H., Salje, E.K.H., Wormeester, H., Salmeron, M. and Ramesh, R. (2010) Domain wall conductivity in La-doped BiFeO3 . Physical Review Letters, 105, 197603197606.CrossRefGoogle ScholarPubMed
Shapiro, S.M., Yanf, B.X., Noda, Y., Tanner, L.E. and Schryvers, D. (1991) Neutron-scattering and electron- microscopy studies of the premartensitic phenomena in NixAl100–x alloys. Physical Review B, 44, 93019313.CrossRefGoogle ScholarPubMed
Shilo, D., Ravichandran, G. and Bhattacharya, K. (2004) Investigation of twin-wall structure at the nanometre scale using atomic force microscopy. Nature Materials, 3, 453457.CrossRefGoogle ScholarPubMed
Smith, J.V. and Brown, W.L. (1988) Feldspar Minerals. Volume 1 Crystal Structures, Physical, Chemical, and Microtextural Properties. Springer-Verlag, Berlin, Heidelberg.CrossRefGoogle Scholar
Stengel, M., Vanderbilt, D. and Spaldin, N.A. (2009) Enhancement of ferroelectricity at metal-oxide interfaces. Nature Materials, 8, 392397.CrossRefGoogle ScholarPubMed
Tagantsev, A.K. and Yurkov, A.S. (2012) Flexoelectric effect in finite samples. Journal of Applied Physics, 112, 044103044110.CrossRefGoogle Scholar
Trepmann, C. and Stöckhert, B. (2001) Mechanical twinning of jadeite – an indication of synseismic loading beneath the brittle–plastic transition. International Journal of Earth Sciences, 90, 413.CrossRefGoogle Scholar
Tsatkis, I., Salje, E.K.H. and Heine, V. (1994) Pattern formation during phase transitions: kinetics of partially conserved order parameters and the role of gradient energies. Journal of Physics: Condensed Matter, 6, 1102711034.Google Scholar
Tullis, T.E. (1980) The use of mechanical twinning in minerals as a measure of shear stress magnitudes. Journal Geophysical Research, 85, 62636268.CrossRefGoogle Scholar
Uno, T., Tashiro, H. and Noge, S. (2012) Temperature characteristics of b-phase quartz resonators and their application to accurate temperature sensors in high temperature region. Electronics and Communications in Japan, 95, 918.CrossRefGoogle Scholar
Van Aert, S., Turner, S., Delville, R., Schryvers, D., Van Tendeloo, G. and Salje, E.K.H. (2012) Direct observation of ferrielectricity at ferroelastic domain boundaries in CaTiO3 by electron microscopy. Advanced Materials, 24, 523527.CrossRefGoogle ScholarPubMed
Vernon, R.H. (1999) Quartz and feldspar microstructures in metamorphic rocks. The Canadian Mineralogist, 37, 513524.Google Scholar
Vernon, R.H. and Paterson, S. (2008) How late are K-feldspar megacrysts in granites? Lithos, 104, 327336.Google Scholar
Wada, S., Yako, K. Yokoo, K., Kakemoto, H. and Tsurumi, T. (2006) Domain wall engineering in barium titanate single crystals for enhanced piezoelectric properties. Ferroelectrics, 334, 1727.CrossRefGoogle Scholar
Wang, Y.M., Hamza, A.V. and Ma, E. (2005) Activation volume and density of mobile dislocations in plastically deforming nanocrystalline Ni. Applied Physics Letters, 86, 241917241920.CrossRefGoogle Scholar
Wang, D., Salje, E.K.H., Mi, S.-B., Jia, C.-L. and Bellaiche, L. (2013) Multidomains made of different structural phases in multiferroic BiFeO3: A firstprinciples- based study. Physical Review B, 88, 134107134114.CrossRefGoogle Scholar
Wruck, B., Salje, E.K.H., Zhang, M., Abraham, T. and Bismayer, U. (1994) On the thickness of ferroelastic twin walls in lead phosphate Pb3(PO4)2 an x-ray diffraction study. Phase Transitions, 48, 135148.CrossRefGoogle Scholar
Yang, H. and Konzett, J. (2000) High-pressure synthesis of Na2Mg6Si6O18(OH)2 – a new hydrous silicate phase isostructural with aenigmatite. American Mineralogist, 85, 259262.CrossRefGoogle Scholar
Yokota, H., Usami, H., Haumont, R., Hicher, P., Kneshiro, J., Salje, E.K.H. and Uesu, Y. (2014) Direct evidence of polar nature of ferroelastic twin boundaries in CaTiO3 obtained by second harmonic generation microscope. Physical Review B, 89, 144109144118.CrossRefGoogle Scholar
Zhang, M., Wruck, B. Graeme-Barber, A., Salje, E.K.H. and Carpenter, M.A. (1996) Phonon spectra of alkali feldspars; phase transitions and solid solutions. American Mineralogist, 81, 92104.CrossRefGoogle Scholar
Zhang, M., Salje, E.K.H., Carpenter, M.A., Wang, J.Y., Groat, L.A. and Lager, G.A. (2007) Temperature dependence of IR absorption of hydrous/hydroxyl species in minerals and synthetic materials. American Mineralogist, 92, 15021517.CrossRefGoogle Scholar
Zubko, P., Catalan, G., Buckley, A., Welche, P.R.L. and Scott, J.F. (2007) Strain-gradient-induced polarization in SrTiO3 single crystals. Physical Review Letters, 99, 167601167605.CrossRefGoogle ScholarPubMed