A method for handling the extrapolation of solid crystalline phases to temperatures far above their melting point

Abstract

Thermodynamic descriptions in databases for applications in computational thermodynamics require representation of the Gibbs energy of stable as well as metastable phases of the pure elements as a basis to model multi-component systems. In the Calphad methodology these representations are usually based on physical models.Reasonable behavior of the thermodynamic properties of phases extrapolated far outside their stable ranges is necessary in order to avoid that they become stable just because these properties extrapolate badly. This paper proposes a method to prevent crystalline solid phases in multicomponent systems to become stable again when extrapolated to temperatures far above their melting temperature.

Third Generation of Unary Calphad Descriptions and the Avoidance of Re-Stabilized Solid Phases and Unexpected Large Heat Capacity

“…The author entirely agrees that the physical basis (or axiom) of the Equal-Entropy Criterion (EEC) as given in, [10] is truly valid: No solid phase should be more stable than the liquid at high temperature. The Equal-Entropy Temperature (EET) of any solid phase u is defined by…”

“…It is also entirely agreed that certainly at T = EET the thermodynamic description of the solid phase u becomes physically unrealistic. [10] The Calphad method requires the handling of phase u above EET but there is no physical basis for any extrapolation of…”

“…The first serious consequence of this extrapolation method in Ref 4 for Fe is that not only the solid phase BCC becomes stable beyond 3630 K, G BCC (T) \ G Liquid (T) for T [ 3630 K. In addition, liquid becomes less stable compared to all solid phases at high T: G FCC (T) \ G Liquid (-T) for T [ 6320 K, and G HCP (T) \ G Liquid (T) for T [ 7380 K. The authors suggest that, as remedy for this artifact, new software should be used: ''Thus, the Equal-Entropy Criterion (EEC) suggested by Sundman et al [10] must be applied to exclude any solid phase with higher entropy than the liquid phase. If the calculation reaches the Equal-Entropy Temperature (EET) of the solid phase, the software will automatically suspend this solid phase.''…”

Modification of Lu's (2005) high pressure model for improved high pressure/high temperature extrapolations. Part I: Modeling of platinum at high pressure/high temperature

“…A very efficient way of doing this and solving this long standing problem (see e.g. the discussions on the C p of Al above its melting point [56][57][58]) would be the possibility to actually use high pressure in order to stabilize the solid phase and measure the C p above the normal melting point. This is probably difficult experimentally and, as far as we are aware, such measurements do not exist for metallic materials.…”

Calphad Modeling of LRO and SRO Using ab initio Data

“…A new unary database is under development with the aim of including thermodynamic descriptions of pure elements down to 0 K, including the 3rd law for defect free crystalline phases, and improving the approximations made in 1991 for the extrapolations of the solid phases to high T and the liquid phase below its solidification T. Some results from this work are described in [7,[18][19][20][21][22]. In most cases this new unary database will be compatible with the current one in the stable range of the phases and does not require any significant changes in the modeling of the solution phases [20].…”