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Theoretical study of high-pressure phase stability of NaZr2(PO4)3 via elastic constants and equation of state

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Abstract

Phase stability of \(\mathrm {NaZr_2(PO_4)_3}\) has been studied through density functional theory calculations of elastic constants, equation of state and enthalpies. The changes in elastic constants as a function of pressure show that the ambient rhombohedral (R\(\bar{3}c\)) \(\mathrm {NaZr_2(PO_4)_3}\) becomes unstable above 8 GPa and this instability is driven by a softening of C\(_{44}\) elastic constant through one of the Born stability criteria. High-pressure equation-of-state and enthalpy calculations further show that the ambient rhombohedral (\(R\bar{3}c\)) structure transforms first into another rhombohedral (R3) phase and subsequently to LiZr\(_2\)(PO\(_4\))\(_3\)-type orthorhombic phase at pressures above 6 and 8 GPa respectively which are in agreement with a recent x-ray diffraction study. Analysis of interatomic distances show that LiZr\(_2\)(PO\(_4\))\(_3\)-type orthorhombic structure allows for shorter Na–O and Zr–P bonds at high pressures which appears to enable strong bonding and stability. Calculated formation enthalpy and bulk modulus of the ambient phase of \(\mathrm {NaZr_2(PO_4)_3}\) are found to be in reasonable agreement with the respective experimental values.

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References

  1. L Hagman and P Kierkegaard Acta Chem. Scand. 22 1822 (1968)

    Article  Google Scholar 

  2. T Oota and I Yamai J. Am. Ceram. Soc. 69 1 (1986)

    Article  Google Scholar 

  3. P Tarte, A Rulmont and C Merckaert-Ansay Spectrochim. Acta A 42 1009 (1986).

    Article  ADS  Google Scholar 

  4. R M Hazen, L W Finger, D K Agrawal, H A McKinstry and A J Perrotta J. Mater. Res. 2 329 (1987).

    Article  ADS  Google Scholar 

  5. S Yamanaka, K Yoshioka and M Hattori Solid State Ion. 40-41 43 (1990)

    Article  Google Scholar 

  6. J Alamo Solid State Ion. 63-65 547 (1993)

    Article  Google Scholar 

  7. B E Scheetz, D K Agrawal, E Breval and R Roy Waste Manage. 14 489 (1994)

    Article  Google Scholar 

  8. A K Ivanov-Schitz and A B Bykov Solid State Ion. 100 153 (1997)

    Article  Google Scholar 

  9. I W Donald, B L Metcalfe and R N J Taylor, J. Mater. Sci. 32 5851 (1997)

    Article  ADS  Google Scholar 

  10. V I Petkov, K V Kiryanov, A I Orlova and D B Kitaev J. Therm. Anal. Calorim. 65 381 (2001)

    Article  Google Scholar 

  11. S Nakayama and K Itoh J. Nucl. Sci. Tech. 40 631 (2003)

    Article  Google Scholar 

  12. V I Petkov and E A Asabina Glass Ceram. 61 233 (2004)

    Article  Google Scholar 

  13. A H Naik, N V Thakkar, V R Palkar, S R Dharwadkar, K D S Mudher and V Venugopal Radiochim. Acta 94 335 (2006)

    Article  Google Scholar 

  14. I W Donald, B L Metcalfe, S K Fong, L A Gerrard, D M Strachan and R D Scheele J. Nucl. Mater. 361 78 (2007)

    Article  ADS  Google Scholar 

  15. H Miyazaki, I Ushiroda, D Itomura, T Hirashita, N Adachi and T Ota Jpn. J. Appl. Phys. 47 7262 (2008)

    Article  ADS  Google Scholar 

  16. Z-J Zhang, H-H Chen, X-X Yang, J-T Zhao, G-B Zhang and C-S Shi J. Phys. D Appl. Phys. 41 105503 (2008)

    Article  ADS  Google Scholar 

  17. W J Weber, A Navrotsky, S Stefanovsky, E R Vance and E Vernaz MRS Bull. 34 46 (2009)

    Article  Google Scholar 

  18. C Rashmi, O P Shrivastava, R D Ambashta and P K Wattal Ann. Nucl. Energy 37 103 (2010)

    Article  Google Scholar 

  19. W Meier, C Apblett, D Ingersoll, A McDaniel and J F Ihlefeld J. Electrochem. Soc. 161 A364 (2014)

    Article  Google Scholar 

  20. W Wang, B Jiang, L Hu and S Jiao J. Mater. Chem. A 2 1341 (2014)

    Article  Google Scholar 

  21. B Lang, B Ziebarth and C Elsasser Chem. Mater. 27 5040 (2015)

    Article  Google Scholar 

  22. K Kamali, T R Ravindran, N V ChandraShekar, K K Pandey and S M Sharma J. Solid State Chem. 221 285 (2015)

    Article  ADS  Google Scholar 

  23. R M Hazen, D C Palmer, L W Finger, G D Stucky, W T A Harrison and T E Gier J. Phys. Condens. Matter 6 1333 (1994)

    Article  ADS  Google Scholar 

  24. M Catti, N Morgante and R M Ibberson J. Solid State Chem. 152 340 (2000)

    Article  ADS  Google Scholar 

  25. G Grimvall Thermophysical Properties of Materials (Amsterdam: Elsevier Science) (1999)

    Google Scholar 

  26. Y Le Page and P Saxe Phys. Rev. B 65 104104 (2002)

    Article  ADS  Google Scholar 

  27. G Kresse and J Hafner Phys. Rev. B 47 558 (1993)

    Article  ADS  Google Scholar 

  28. G Kresse and J Furthmuller Phys. Rev. B 54 11169 (1996)

    Article  ADS  Google Scholar 

  29. P E Blochl Phys. Rev. B 50 17953 (1994)

    Article  ADS  Google Scholar 

  30. G Kresse and J Joubert Phys. Rev. B 59 1758 (1999)

    Article  ADS  Google Scholar 

  31. J P Perdew, K Burke and M Ernzerhof Phys. Rev. Lett. 77 3865 (1996)

    Article  ADS  Google Scholar 

  32. P E Blochl, O Jepsen and O K Andersen Phys. Rev. B 49 16223 (1994)

    Article  ADS  Google Scholar 

  33. H J Monkhorst and J D Pack Phys. Rev. B 13 5188 (1976)

    Article  ADS  MathSciNet  Google Scholar 

  34. A Leclaire, J C Monier and B Raveau J. Solid State Chem. 59 301 (1985)

    Article  ADS  Google Scholar 

  35. P Vinet, J H Rose, F Ferrante and J R Smith J. Phys. Condens. Matter 1 1941 (1989)

    Article  ADS  Google Scholar 

  36. K Frey, D J Schmidt, C Wolverton and W F Schneider Catal. Sci. Technol. 4 4356 (2014)

    Article  Google Scholar 

  37. E Calderon, M Gauthier, F Decremps, G Hamel, G Syfosse and A Polian J. Phys. Condens. Matter 19 436228 (2007)

    Article  ADS  Google Scholar 

  38. J F Nye Physical Properties of Crystals (Oxford: Oxford University Press) (1972)

    MATH  Google Scholar 

  39. F Mouhat and F-X Coudert Phys. Rev. B 90 224104 (2014)

    Article  ADS  Google Scholar 

  40. E Gregoryanz, R J Hemley, H Mao and P Gillet Phys. Rev. Lett. 84 3117 (2000)

    Article  ADS  Google Scholar 

  41. M I Mendelev, S Han, D J Srolovitz, G J Ackland, D Y Sun and M Asta Philos. Mag. 83 3977 (2003)

    Article  ADS  Google Scholar 

  42. L Wang, T Maxisch, G Ceder Phys. Rev. B 73 195107 (2006)

    Article  ADS  Google Scholar 

  43. A Droghetti, C D Pemmaraju, and S Sanvito Phys. Rev. B 78 140404R (2008)

    Article  ADS  Google Scholar 

  44. J E Schirber and B Morosin Phys. Rev. B 29 4150 (1984)

    Article  ADS  Google Scholar 

  45. R M Hazen and L W Finger J. Appl. Phys. 56 311 (1984)

    Article  ADS  Google Scholar 

  46. K Lejaeghere, V Van Speybroeck, G Van Oost and S Cottenier Crit. Rev. Solid State 39 1 (2014)

    Article  Google Scholar 

  47. J L F Da Silva, M V Ganduglia-Pirovano and J Sauer Phys. Rev. B 76 125117 (2007)

    Article  ADS  Google Scholar 

  48. J Neugebauer and T Hickel WIREs Comput. Mol. Sci. 3 438 (2013)

    Article  Google Scholar 

  49. T Le Bihan, S Heathman, M Idiri, G H Lander, J M Wills, A C Lawson and A Lindbaum Phys. Rev. B 67 134102 (2003)

    Article  ADS  Google Scholar 

  50. M Cankurtaran, G A Saunders, J R Willis, A Al-Kheffaji and D P Almond Phys. Rev. B 39 2872 (1989)

    Article  ADS  Google Scholar 

  51. N Katagiri, Y Hattori, T Ota and I Yamai J. Ceram. Soc. Jpn. 102 718 (1994)

    Article  Google Scholar 

  52. Q Wang, G A Saunders, D P Almond, M Cankurtaran and K C Goretta Phys. Rev. B 52 3711 (1995)

    Article  ADS  Google Scholar 

  53. S Barzilai, I Halevy and O Yeheskel J. Appl. Phys. 110 043532 (2011)

    Article  ADS  Google Scholar 

  54. Z Wu and R E Cohen Phys. Rev. B 73 235116 (2006)

    Article  ADS  Google Scholar 

  55. M G Del Popolo, C Pinilla and P Ballone J. Chem. Phys. 126 144705 (2007)

    Article  ADS  Google Scholar 

  56. M A Caravaca, J C Mino, V J Perez, R A Casali and C A Ponce J. Phys. Condens. Matter 21 015501 (2009)

    Article  ADS  Google Scholar 

  57. P Haas, F Tran, P Blaha, L S Pedroza, A J R da Silva, M M Odashima and K Capelle Phys. Rev. B 81 125136 (2010)

    Article  ADS  Google Scholar 

  58. J Kohanoff, C Pinilla, T G A Youngs, E Artacho and J M Soler J. Chem. Phys. 135 154505 (2011)

    Article  ADS  Google Scholar 

  59. G Sophia, P Baranek, C Sarrazin, M Rerat and R Dovesi Phase Trans. 86 1069 (2013)

    Article  Google Scholar 

Download references

Acknowledgments

We thank Dr. T. R. Ravindran, Dr. S. Mathijaya and Dr. N. V. Chandra Shekar for fruitful discussions.

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  1. Materials Physics Division, Indira Gandhi Centre for Atomic Research, Kalpakkam, Tamilnadu, 603 102, India

    Ravi Chinnappan & B. K. Panigrahi

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  1. Ravi Chinnappan
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  2. B. K. Panigrahi
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Correspondence to Ravi Chinnappan.

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Chinnappan, R., Panigrahi, B.K. Theoretical study of high-pressure phase stability of NaZr2(PO4)3 via elastic constants and equation of state. Indian J Phys 91, 277–286 (2017). https://doi.org/10.1007/s12648-016-0923-9

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  • DOI: https://doi.org/10.1007/s12648-016-0923-9

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