Calculation of debye temperature for crystalline structures—a case study on Ti, Zr, and Hf

• Published in: Acta materialia Vol. 49; no. 6; pp. 947 - 961
• Main Authors: Chen, Q, Sundman, B
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier Ltd 02.04.2001; Elsevier Science
• Subjects: Ab initio calculation; bcc phase; Condensed matter: structure, mechanical and thermal properties; cubic transition-metals; Debye temperature; Elastic; elastic-constants; Exact sciences and technology; exchange; generalized gradient approximation; group-iv metals; Lattice dynamics; phonon-dispersion; Physics; stability; Statistical mechanics of lattice vibrations and displacive phase transitions; Thermodynamics; total-energy calculations; zirconium; Debye temperature; Ab initio calculation; Thermodynamics; Elastic; Elastic modulus; Elastic constants; Zirconium; Cubic crystals; Ab initio method; Hafnium; Theoretical study; Titanium; Thermodynamic analysis; Bulk modulus; Crystal structure
• ISSN: 1359-6454; 1873-2453; 1873-2453
• DOI: 10.1016/S1359-6454(01)00002-7

The methods to calculate the Debye temperature from elastic moduli have been reviewed. The approximation approach due to Moruzzi et al. was critically examined by considering experimental elastic constant data for all the cubic elements. It was found that many cubic elements are exceptions with regard to the assumed constant scaling factor for the expression of the average sound velocity in terms of the bulk modulus, and consequently the Debye temperature of a cubic element must be calculated from the knowledge of all the elastic constants of the system. On the other hand, a fairly constant scaling factor has been found to exist for the hexagonal elements. Through the study of experimental data, some empirical relationships have been observed between the high temperature entropy–Debye temperature θ D (0) and the low temperature limit of the Debye temperature θ D (−3). For those structures that are dynamically unstable at low temperatures, we proposed a way to obtain their θ D (0) from the calculated isotropic bulk moduli. The methods have been applied to calculate the Debye temperatures of hcp, bcc, and fcc Ti, Zr, and Hf from their elastic moduli derived from ab initio calculations. The calculated results agree very well with the experimental data.