Debye temperature of CaO under high pressure up to 65.2 GPa

Abstract

In the present work we used the experimental relative volume unit cell and the elastic stiffness constants measured by Speziale et al. (Journal of Geophysical Research, Vol. 111, (2006), pp. B02203 (12 pages)) using the Radial X-Ray Diffraction at high pressure from 5.6 up to 65.2 GPa to investigate the effect of high pressure on the bulk modulus, aggregate shear modulus, elastic wave velocities and Debye temperature of calcium oxide (CaO) ceramic material in cubic rock-salt (B1) phase. Our obtained values show that the bulk modulus increases monotonously with increasing pressure, while the aggregate shear modulus, the mean elastic wave velocity and the Debye temperature of CaO material varied non-linearly and non-monotonously with increasing pressure from 5.6 up to 65.2 GPa.

Quasi-linear correlation between shear and young’s moduli in some polycrystalline ceramics

“…We calculate the Vickers hardness HV of pore-free polycrystalline ceramics according to the following empirical expression: HV = 0.92(G/B) 1.137 G 0.708 [32], [38], whereG is the shear modulus and B is the bulk modulus. Frequently, the elastic moduli of the polycrystalline materials are calculated [39][40][41][42][43][44][45][46][47][48]. Iuga et al [45] have investigated the elastic constants Cij of ceramic crystals using an Ab-initio calculation.…”

Mechanical stability criterions of cubic Na2He up to 500 GPa

“…The evolutions of the Cauchy pressure Cp and the generalized elastic stability criteria under compression in the pressure ranging from 100 to 500 GPa of Na2He compound were presented in Figure1 (curves (a) and (b), respectively). The Debye temperature θD is an essential parameter in solid state physic [19][20][21][22][23]. For cubic crystals, the Debye temperature θD could be calculated using the following expression: [24][25][26], where, Cc = (26.05 ± 0.81) K (m kg N -1 ) 1/2 (the numerical value 26.05 ± 0.81 K (m kg N -1 ) 1/2 is valuable only for with cubic crystals), s is the number of atoms in the unit cell, a is the lattice parameter expressed in m, and M is the atomic weight (arithmetical average of the masses of the species), respectively [24][25][26].…”

Some physical properties of K2TlAsX6 (X = Cl, Br) and CsPbBr3 semiconducting compounds

“…In the past decade, a wide range of semiconductors were known; however, attention was focused on the simplest the III-V and II-VI compounds [1]. Debye temperature θD of material is an essential parameter in solid state physic [2][3][4][5][6], this because it is correlated with many physical properties of solids; such as specific heat, elastic moduli, melting point, and lattice energy [7]. At low temperature, the vibrational excitations arise solely from acoustic vibrations, with consequence the Debye temperature calculated from elastic constants is the same as that determined from the measurements of the specific heat [8].…”

“…First we recalculate the bulk modulus B, shear modulus G, Pugh ratio (B/G), Young modulus E and the Poisson's ratio σ, then the Debye temperature θD. In cubic polycrystalline crystals, the bulk modulus B could be calculated from the elastic constants Cij as follows: B = (C11 + 2C12)/3 [3,13], while the shear modulus G was usually calculated using the Voigt-Reuss-Hill approach, which is expressed as follows: G = (GV + GR)/2 [3,13], where GV is the Voigt shear modulus, while GR is the Reuss shear modulus. The Lamé's first parameter λ is expressed as follows: λ= σE/[(1+σ)(1-2σ)] [14].…”

“…A typical value of σ for ionic materials is 0.25 and G = 0.6B, while for metallic bonded materials σ is typically 0.33 and G = 0.4B [15]. There are different expressions usually used to calculate the Debye temperature θD of crystal from the acoustic wave speed [3,13]. The expression used here is the same like that used in the work [3] for CaO compound (for more details on the calculation of the acoustic wave speed and the Debye temperature θD polycrystalline materials, please see for example the references [3,13]).…”