Semi-Empirical Predictions for Hardness of Rare Earth Pyrochlores; High-Permittivity Dielectrics and Thermal Barrier Coating Materials

  • Rekha Bhati Department of Natural and Applied Sciences, Glocal University, Saharanpur, India
  • Dheerendra Singh Yadav Department of Physics, Ch. Charan Singh P G College Heonra, Etawah, India
  • Preeti Varshney Department of Physics, G.G.I.C., Iglas, Aligarh, India
  • Rajesh Chandra Gupta Department of Physics, B. S. A. College, Mathura, India
  • Ajay Singh Verma Division of Research & Innovation, Department of Applied and Life Sciences, Uttaranchal University, Dehradun, Uttarakhand, India; University Centre for Research and Development, Department of Physics, Chandigarh University, Mohali, Punjab, India
Keywords: Pyrochlores, Plasmon energy, Vicker’s hardness


Herein, we have formulated a simplistic semi-empirical model for Vicker’s hardness of rare earth based pyrochlore compounds. We have considered the  structured 97 pyrochlore compounds for Vicker’s hardness calculations. The plasmon energy (ħωp) depends on basic parameters of the material such as Ne-effective number of free electrons per unit volume participating in plasma oscillations, e-electronic charge and m-mass of an electron. The proposed model predicts that the experimental and theoretical values of Vicker’s hardness increases as plasmon energy of pyrochlore increases. We have found that the calculated values are in better agreement with available experimental and theoretical data, which supports the validity of the model. This model supports the modeling of emerging functional pyrochlore compounds and helps to understand their mechanical properties for excellent thermal stability, superconductivities, batteries, ferroelectricity, water spitting, high ionic conductivity, good photoluminescence, inherent oxygen vacancies, exotic magnetism, and now-a-days most importantly in nuclear waste encapsulation and aerospace industry


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S. Singh, A. Bandyopadhyay, “Crystal growth of magnetic pyrochlore oxides and their structure-property correlations”, in: Pyrochlore Ceramics Properties, Processing, and Applications, edited by A. Chowdhury, 1st edition (Elsevier, 2022). pp. 25.

A. Raza, A. Afaq, M.S. Kiani, M. Ahmed, A. Bakar, and M. Asif, J. Mater. Res. Technol. 18, 5005 (2022).

J. Yang, M. Shahid, M. Zhao, J. Feng, C. Wan, and W. Pan, J. All. Comp. 663, 834 (2016).

J. Feng, B. Xiao, Z.X. Qu, R. Zhou, and W. Pan, Appl. Phys. Lett. 99, 201909 (2011).

C. Kaliyaperumal, A. Shankarakumar, J. Palanisamy, and T. Paramasivam, Mater. Lett. 228, 493 (2018).

G.M. Mustafa, S. Atiq, S.K. Abbas, S. Riaz, and S. Naseem, Ceram. Int. 44, 2170 (2018).

Y. Zhao, N. Li, C. Xu. Y. Li, H. Zhu, P. Zhu, and W. Yang, Adv. Mater. 29, 1701513 (2017).

H. Zhang, K. Haule, and D. Vanderbilt, Phys. Rev. Lett. 118, 026404 (2017).

S. Chen, B. Pan, L. Zeng, S. Luo, X. Wang, and W. Su, RSC Adv. 7, 14186 (2017).

J.S. Gardner, M.J.P. Gingras, and J. E. Greedan, Rev. Mod. Phys. 82, 53 (2010).

Y. Jiang, J.R. Smith, and G.R. Odette, et al., Acta Materialia, 58, 1536 (2010).

J. Wu, X. Wei, N.P. Padture, P.G. Klemens, M. Gell, E. García, P. Miranzo, and M.I. Osendi, Am. Ceram. Soc. 85, 3031 (2002).

B. Liu, J. Wang, Y. Zhou, T. Liao, and F. Li, Acta Mater. 55, 2949 (2007).

Q. Xu, W. Pan, J. Wang, C. Wan, L. Qi, H. Miao, K. Mori, and T. Torigoe, J. Am. Ceram. Soc. 89, 340 (2006).

F.A. Zhao, H.Y. Xiao, X.M. Bai, Z.J. Liu, and X.T. Zu, J. Alloys Compounds 776, 306 (2019).

A. Chartier, C. Meis, J.P. Crocombette, L.R. Corrales, and W.J. Weber, Phys. Rev. B, 67, 174102 (2003).

C.R. Stanek, R.W. Grimes, and L. Minervini, Am. Ceram. Soc. 85, 2792 (2002).

J. Lian, L.M. Wang, S.X. Wang, J. Chen, L.A. Boatner, and R.C. Ewing, Phys. Rev. Lett. 87, 145901 (2001).

M.A. Subramaniam, G. Aravamundan, and G.V.S. Rao, Oxide Pyrochlores – A Review Progress in Solid State Chem. 15, 55 (1983).

X.T. Zu, J. Lian, and R.C. Ewing, J. Phys: Cond. Matt. 19, 346203 (2007).

F. Gao, J. He, E. Wu, S. Liu, D. Yu, D. Li, S. Zhang, and Y. Tian, Phys. Rev. Lett. 91, 015502 (2003).

X. Guo, L. Li, Z. Liu, D. Yu, J. He, R. Liu, B. Xu, et al., J. Appl. Phys. 104, 023503 (2008).

S.-H. Jhi, S.G. Louie, M.L. Cohen, and J. Ihm, Phys. Rev. Lett. 86, 3348 (2001).

J. Yang, M. Shahid, M. Zhao, J. Feng, C. Wan, and W. Pan, J. Alloys Comp. 663, 834 (2016).

J. Feng, B. Xiao, C.L. Wan, Z.X. Qu, Z.C. Huang, J.C. Chen, R. Zhou, and W. Pan, Acta Mater. 59, 1742 (2011).

D.S. Yadav, and S.P. Singh, Phys. Scr. 82, 065705 (2010).

D.S. Yadav, and A.S. Verma, Int. J. Mod. Phys. B, 26, 1250020 (2012).

D.S. Yadav, J. Alloys Comp. 537, 250 (2012).

D.S. Yadav, and D.V. Singh, Phys. Scr. 85, 015701 (2012).

D.S. Yadav, J. Mater. Chem. Phys. 3, 6 (2015).

A.S. Verma, and S.R. Bhardwaj, Phys. Stat. Sol. (b) 243, 2858 (2006).

R.C. Gupta, A.S. Verma, and K. Singh, East Eur. J. Phys. 1, 80 (2021).

R.C. Gupta, A.S. Verma, and K. Singh, East Eur. J. Phys. 1, 89 (2021).

R.C. Gupta, A.S. Verma, and K. Singh, J. Taibah Univ. Sci. 16, 676 (2022).

V. Kumar, V. Jha, and A.K. Shrivastava, Cryst. Res. Technol. 45, 920 (2010).

V. Kumar, G.M. Prasad, and D. Chandra, Phys. Stat. Solidi B, 170, 77 (1992).

V. Kumar, J.K. Singh, and G.M. Prasad, Ind. J. Pure Appl. Phys. 53, 429 (2015).

A.S. Verma, and S.R. Bharadwaj, J. Phys. Cond. Mater. 19, 026213 (2007).

How to Cite
Bhati, R., Yadav, D. S., Varshney, P., Gupta, R. C., & Verma, A. S. (2023). Semi-Empirical Predictions for Hardness of Rare Earth Pyrochlores; High-Permittivity Dielectrics and Thermal Barrier Coating Materials. East European Journal of Physics, (1), 222-227.