Ab initiothermodynamics of body-centred cubic and face-centred cubic Cs

Abstract

The equation of state of solid caesium (body-centred cubic (bcc) and face-centred cubic (fcc) structures) is examined theoretically by means of ab initio calculations. The Helmholtz free energies are calculated for pressures (P ) up to 5 GPa and temperatures (T ) in the range 0 300 K. The electronic contributions are calculated within density-functional theory (local density approximation (LDA) and generalized gradient approximation (GGA)), whereas vibrational contributions to energy and entropy are calculated within the quasi-harmonic approximation. The thermal expansion coefficients ( ) of bcc as well as fcc Cs are calculated as functions of P and T . Both phases are predicted to have (P , T ) regimes where is negative. For the fcc phase, goes negative for P above 3.5 GPa (and up to the end of the stability range of the fcc phase) for all T . The value = 3.0 ×10-4 K-1 found for Cs at ambient conditions agrees with experiments, and so does the Debye temperature, 39.5 K. The calculation shows that the bcc fcc transition occurs at P 2.2 GPa and low T , and at a higher pressure, 3 GPa, at room temperature. The fcc phase becomes unstable around 4.3 GPa, where a transverse phonon mode with q along (110) becomes soft. The calculations do not indicate that this transition is isostructural (fcc fcc), a result which is at variance with earlier theoretical and experimental work.

Elemental Metals under Pressure

“…[5,6]. The frequencies obtained for b.c.c.-Cs at the experimental equilibrium volume, V 0 , agree well with other theoretical results [34 to 36] and experiments [37,38] in Table 1.…”

“…The softening of the lattice, also reflected by the rapid decrease of Q D in Fig. 5 slightly larger volumes, does lead to a negative overall Gru È neisen parameter, but the effect does not produce a Van der Waals loop in the isoterms [5,6]. The softening, on the other hand, causes the thermal expansion coefficient to be negative above 3.5 GPa.…”

“…by diagonalizing a dynamical matrix as in usual harmonic theory, but with volume dependent force constants. The force constants are calculated from first principles [5,6]. Having calculated FV; T, we derive the PV; T, and other physical quantities like the thermal expansion coefficient, a, can be calcu-…”

“…by diagonalizing a dynamical matrix as in usual harmonic theory, but with volume dependent force constants. The force constants are calculated from first principles [5,6]. Having calculated FV; T, we derive the PV; T, and other physical quantities like the thermal expansion coefficient, a, can be calculated as function of temperature for fixed pressure or for varying P with chosen values of T. Also, the Gibbs free energy is calculated, and the temperature variation of the coexistence pressure for two phases can be predicted.…”

Atomistic simulation of phonon dispersion for body-centred cubic alkali metals

“…For instance, the phonon dispersion of alkali metals has been calculated by many model methods, such as pair potentials [2][3][4], the general tensor force model [5], the embedded atom method (EAM) [6], analytic EAM (AEAM) [7,8], ab initio [9][10][11][12], and pseudopotential theory [13]. For instance, the phonon dispersion of alkali metals has been calculated by many model methods, such as pair potentials [2][3][4], the general tensor force model [5], the embedded atom method (EAM) [6], analytic EAM (AEAM) [7,8], ab initio [9][10][11][12], and pseudopotential theory [13].…”