A method to predict temperature derivatives of the bulk modulus: A case study for HfB2

Özkan H., Delice S., HASANLI N.

Physica Scripta, vol.97, no.8, 2022 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 97 Issue: 8
  • Publication Date: 2022
  • Doi Number: 10.1088/1402-4896/ac8250
  • Journal Name: Physica Scripta
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Aerospace Database, Chemical Abstracts Core, Compendex, INSPEC, zbMATH
  • Keywords: ultra-high temperature ceramics, HfB2, gruneisen parameter, temperature derivative of the bulk modulus, THERMODYNAMIC PROPERTIES, ELASTIC PROPERTIES, THERMAL-PROPERTIES, ZIRCONIUM, ZRB2, DEPENDENCE, PRESSURE, 1ST-PRINCIPLES, DIBORIDES, HAFNIUM
  • Middle East Technical University Affiliated: Yes


© 2022 IOP Publishing Ltd.Hafnium diboride (HfB2) is an ultra-high temperature ceramic that has attracted increased attention for its fascinating properties. In this study, temperature derivatives of the bulk modulus of HfB2 were calculated from room temperature up to 2273 K by using the relevant theoretical thermodynamic equations for the bulk modulus. The equations used involve the parameters as the enthalpy, thermal expansion and heat capacity in addition to the Anderson Grüneisen parameter. The calculations were performed using the pressure derivative of the bulk modulus for the Anderson Grüneisen parameter and the experimental temperature dependent values for the other parameters of the used equations. Temperature derivatives of the bulk modulus of HfB2 were found to be, −0.012/−0.013 GPa K−1 at 293 K and −0.015/−0.016 GPa K−1 at 2273 K. These values are in good agreement with the corresponding experimental data, and quite close to the corresponding values reported for ZrB2 and TiB2. However, the experimental temperature derivatives of the bulk moduli for the three diborides, TiB2, ZrB2, and HfB2 are quite smaller in magnitude than the corresponding theoretical values. The Grüneisen parameter of HfB2 decreases from 1.2 to about 1.0 with increasing temperature up to about 500 K, and then it has a small variation at higher temperatures. HfB2, with its high strength, high density and small temperature derivatives of the bulk modulus, may be useful for the aerodynamic and nuclear applications. The method presented in our studies is a practical way to predict temperature dependencies of the bulk moduli. This method may be more useful at ultra-high temperatures where the experimental bulk moduli measurements are quite difficult.