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Phase diagram and thermodynamic properties of AIPO4 based on first-principles calculations and the quasiharmonic approximation

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Abstract

We calculated the phase diagram of \(\hbox {AlPO}_{4}\) up to 15 GPa and 2,000 K and investigated the thermodynamic properties of the high-pressure phases. The investigated phases include the berlinite, moganite-like, \(\hbox {AlVO}_{4},\, P2_1/c\), and \(\hbox {CrVO}_{4}\) phases . The computational methods used include density functional theory, density functional perturbation theory, and the quasiharmonic approximation. The investigated thermodynamic properties include the thermal equation of state, isothermal bulk modulus, thermal expansivity, and heat capacity. With increasing pressure, the ambient phase berlinite transforms to the moganite-like phase, and then to the \(\hbox {AlVO}_{4}\) and \(P2_1/c\) phases, and further to the \(\hbox {CrVO}_{4}\) phase. The stability fields of the \(\hbox {AlVO}_{4}\) and \(P2_1/c\) phases are similar in pressure but different in temperature, as the \(\hbox {AlVO}_{4}\) phase is stable at low temperatures, whereas the \(P2_1/c\) phase is stable at high temperatures. All of the phase relationships agree well with those obtained by quench experiments, and they support the stabilities of the moganite-like, \(\hbox {AlVO}_{4}\), and \(P2_1/c\) phases, which were not observed in room-temperature compression experiments.

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References

  • Agrawal GP (2001) Nonlinear fiber optics, 3rd edn. Academic Press, San Diego

    Google Scholar 

  • Baroni S, de Gironcoli S, Dal Corso A, Giannozzi P (2001) Phonons and related crystal properties from density-functional perturbation theory. Rev Mod Phys 73:515–562

    Article  Google Scholar 

  • Baroni S, Giannozzi P, Isaev E (2010) Density-functional perturbation theory for quasi-harmonic calculations. In: Chantilly VA (ed) Reviews in Mineralogy, vol 71. Mineralogical Society of America, Washington, pp 39–57

    Google Scholar 

  • Beck WR (1949) Crystallographic inversions of the aluminum orthophosphate polymorphs and their relation to those of silica. J Am Ceram Soc 32:147–151

    Article  Google Scholar 

  • Bethke J, Eckold G, Hahn T (1992) The phonon dispersion and lattice dynamics of \(\alpha{-}\text{AlPO}_{4}\): an inelastic neutron scattering study. J Phys Condens Matter 4:5537–5550

    Article  Google Scholar 

  • Birch F (1952) Elasticity and constitution of the Earth’s interior. J Geophys Res 57:227–286

    Article  Google Scholar 

  • Bradley CJ, Cracknell AP (1972) The mathematical theory of symmetry in solids: representation theory for point groups and space groups. Clarendon, Oxford

    Google Scholar 

  • Christie DM, Chelikowsky JR (1998) Structural properties of α-berlinite AIPO4. Phys Chem Miner 25:222–226

    Article  Google Scholar 

  • Cohen LH, Klement WJ (1973) Determination of the high-low inversion in berlinite (AIPO4) to 6 kbar. Am Miner 58:796–798

    Google Scholar 

  • Da Cunha M, Fagundes SA (1999) Investigation on recent quartz-like materials for SAW applications. IEEE Trans Ultrason Ferroelectr Freq Control 46:1583–1590

    Article  Google Scholar 

  • Delin A, Fast L, Eriksson O, Johansson B (1998) Effect of generalized gradient corrections on lanthanide cohesive properties. J Alloys Compd 275:472–475

    Article  Google Scholar 

  • Fischer TH, Almlof J (1992) General methods for geometry and wave function optimization. J Phys Chem 96:9768–9774

    Article  Google Scholar 

  • Giannozzi P, Baroni S, Bonini N, Calandra M, Car R, Cavazzoni C, Ceresoli D, Chiarotti GL, Cococcioni M, Dabo I, de Gironcoli S, Fabris S, Fratesi G, Gebauer R, Gerstmann U, Gougoussis C, Kokalj A, Lazzeri M, Martin-Samos L, Marzari N, Mauri F, Mazzarello R, Paolini S, Pasquarello A, Paulatto L, Sbraccia C, Scandolo S, Sclauzero G, Seitsonen AP, Smogunov A, Umari P, Wentzcovitch RM (2009) Quantum espresso: a modular and open-source software project for quantum simulations of materials. J Phys Condens Matter 21:395502–395521

    Article  Google Scholar 

  • Gillet P, Badro J, Varrel B, McMillan PF (1995) High-pressure behavior in α-AIPO4: amorphization and the memory-glass effect. Phys Rev B 51:11262–11269

    Article  Google Scholar 

  • Haines J, Cambon O (2004) The effects of pressure, temperature and composition on the crystal structures of \(\alpha \)-quartz homeotypes. Z Kristallogr 219:314–323

    Article  Google Scholar 

  • Heaney PJ, Post JE (2001) Evidence for an I2/a to Imab phase transition in the silica polymorph moganite at 570 K. Am Miner 86:1358–1366

    Google Scholar 

  • Hemley RJ, Prewitt CT, Kingma KJ (1994) High-pressure behavior of silica. Rev Mineral Geochem 29:41–81

    Google Scholar 

  • Jaffe JE, Snyder JA, Lin Z, Hess AC (2000) LDA and GGA calculations for high-pressure phase transitions in ZnO and MgO. Phys Rev B 62:1660

    Article  Google Scholar 

  • Kanzaki M, Xue X (2012) Structural characterization of moganite-type \(\text{ AlPO}_{4}\) by NMR and powder X-ray diffraction. Inorg Chem 51:6164–6172

    Article  Google Scholar 

  • Kanzaki M, Xue X, Reibstein S, Berryman E, Namgung S (2011) Structures of two new high-pressure forms of \(\text{ AlPO}_{4}\) by X-ray powder diffraction and NMR spectroscopy. Acta Crystallogr Sect B Struct Sci 67:30–40

    Article  Google Scholar 

  • Kohn W, Sham LJ (1965) Self-consistent equations including exchange and correlation effects. Phys Rev 140:A1133–A1138

    Article  Google Scholar 

  • Krempl P (2005) Piezoelectricity in quartz analogues. J Phys IV 126:95–100

    Google Scholar 

  • Kruger MB, Jeanloz R (1990) Memory glass: an amorphous material formed from \(\text{ AlPO}_{4}\). Science 249:647–649

    Article  Google Scholar 

  • Louie SG, Froyen S, Cohen ML (1982) Nonlinear ionic pseudopotentials in spin-density-functional calculations. Phys Rev B 26:1738–1742

    Article  Google Scholar 

  • Maradudin AA, Montroll EW, Weiss GH, Ipatova IP (1971) Theory of lattice dynamics in the harmonic approximation, 2nd edn. Solid State Physics, Suppl. 3. Academic Press, New York

    Google Scholar 

  • Miehe G, Graetsch H (1992) Crystal structure of moganite: a new structure type for silica. Eur J Mineral 4:693–706

    Article  Google Scholar 

  • Momma K, Izumi F (2011) VESTA3 for three-dimensional visualization of crystal, volumetric and morphology data. J Appl Cryst 44:1272–1276

    Article  Google Scholar 

  • Monkhorst HJ, Pack JD (1976) Special points for Brillouin-zone integrations. Phys Rev B 13:5188–5192

    Article  Google Scholar 

  • Muraoka Y, Kihara K (1997) The temperature dependence of the crystal structure of berlinite, a quartz-type form of \(\text{ AlPO}_{4}\). Phys Chem Miner 24:243–253

    Article  Google Scholar 

  • Onac BP, White WB (2004) First reported sedimentary occurrence of berlinite (\(\text{ AlPO}_{4}\)) in phosphate-bearing sediments from Cioclovina Cave, Romania. Am Miner 88:1395–1397

    Google Scholar 

  • Otero-de-la-Roza A, Luaña V (2011) Treatment of first-principles data for predictive quasiharmonic thermodynamics of solids: the case of MgO. Phys Rev B 84:024109–024115

    Article  Google Scholar 

  • Pellicer-Porres J, Saitta AM, Polian A, Itié JP, Hanfland M (2007) Six-fold-coordinated phosphorus by oxygen in α-AIPO4 quartz homeotype under high pressure. Nat Mater 6:698–702

    Article  Google Scholar 

  • Perdew JP, Burke K, Ernzerhof M (1996) Generalized gradient approximation made simple. Phys Rev Lett 77:3865–3868

    Article  Google Scholar 

  • Philippot E, Palmier D, Pintard M, Goiffon A (1996) A general survey of quartz and quartz-like materials: packing distortions, temperature, and pressure effects. J Solid State Chem 123:1–13

    Article  Google Scholar 

  • Poswal H, Garg N, Somayazulu M, Sharma SM (2013) Pressure-induced structural transformations in the low-cristobalite form of \(\text{ AlPO}_{4}\). Am Miner 98:285–291

    Article  Google Scholar 

  • Seifert K (1968) Untersuchungen zur druck-kristallchemie der \(\text{ AX}_{2}\)-verbindungen. Fortschr Miner 45:214–280

    Google Scholar 

  • Sharma SM, Garg N, Sikka SK (2000) High-pressure X-ray-diffraction study of α-AIPO4. Phys Rev B 62:8824–8827

    Article  Google Scholar 

  • Sowa H, Reithmayer K, Macavei J, Rieck W, Schulz H, Kupcik V (1990) The crystal structure of berlinite \(\text{ AlPO}_{4}\) at high pressure. J Appl Cryst 192:119–136

    Google Scholar 

  • Stebbins JF, Kim N, Brunet F, Irifune T (2009) Confirmation of octahedrally coordinated phosphorus in \(\text{ AlPO}_{4}\)-containing stishovite by 31P NMR. Eur J Mineral 21:667–671

    Article  Google Scholar 

  • Tichý J, Erhart J, Kittinger E, Přívratská J (2010) Fundamentals of piezoelectric sensorics: mechanical, dielectric, and thermodynamical properties of piezoelectric materials. Springer, Berlin, Heidelberg

  • Tsuchiya J, Tsuchiya T, Wentzcovitch RM (2005) Vibrational and thermodynamic properties of \(\text{ MgSiO}_{3}\) postperovskite. J Geophys Res 110(B02):B02204–B02209

    Google Scholar 

  • Vanderbilt D (1990) Soft self-consistent pseudopotentials in a generalized eigenvalue formalism. Phys Rev B 41:7892–7895

    Article  Google Scholar 

  • Vosko SH, Wilk L, Nusair M (1980) Accurate spin-dependent electron liquid correlation energies for local spin density calculations: a critical analysis. Can J Phys 58:1200–1211

    Article  Google Scholar 

  • Wallace DC (1972) Thermodynamics of crystals. Wiley, New York

    Google Scholar 

  • Wang R (2013) First-principles prediction of ferroelastic phase transition in \(\text{ AlPO}_{4}\). Solid State Commun 155:88–91

    Article  Google Scholar 

  • Wentzcovitch R, Yonggang G, Wu Z (2010) Thermodynamic properties and phase relations in mantle minerals investigated by first principles quasiharmonic theory. In: Wentzcovitch R, Stixrude L (eds) Reviews in Mineralogy and Geochemistry, vol 71. Mineralogical Society of America, Washington, pp 59–98

    Google Scholar 

Download references

Acknowledgments

This study was supported by a Grants-in-Aid for Scientific Research funded by the Ministry of Education, Culture, Sports, Science and Technology of Japan to M.K. and Xianyu Xue. We thank Xianyu Xue for discussions and providing the PCs used for the calculations. R.W. also thanks Benjamin Moulton for discussions.

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  1. Riping Wang

    Present address: Beijing Computational Science Research Center, Beijing, 10084, China

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  1. Institute for Study of the Earth’s Interior, Okayama University, 827 Yamada, Misasa, Tottori, 682-0193, Japan

    Riping Wang & Masami Kanzaki

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  1. Riping Wang
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Correspondence to Riping Wang.

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Wang, R., Kanzaki, M. Phase diagram and thermodynamic properties of AIPO4 based on first-principles calculations and the quasiharmonic approximation. Phys Chem Minerals 42, 15–27 (2015). https://doi.org/10.1007/s00269-014-0695-8

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  • DOI: https://doi.org/10.1007/s00269-014-0695-8

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