General Einstein Model

An Einstein model implemented in a general way with multiple Einstein temperatures and accompanying weight functions.

The LNTHETA and THETAF parameters are only available with GES6.

It describes the vibrational contribution to Cp at low and intermediate temperatures.

The model is implemented as:

General Einstein model equation

Where

  • Einstein temperature is the Einstein temperature. ln Einstein temperature is entered as the database parameters LNTHETA1, LNTHETA2, LNTHETA3, LNTHETA4, and LNTHETA5.
  • weight function is a weight function, entered as the database parameters THETAF1, THETAF2, THETAF3, THETAF4, and THETAF5.
  • number of atoms per mole formula unit is the number of atoms per mole formula unit
  • universal gas constant is the universal gas constant
  • temperature is the temperature

Examples of parameters for this model:

PARAMETER LNTHETA1(GRAPHITE,C;0) 298.15 +LN(1953); 6000 N REF0 !

PARAMETER THETAF1(GRAPHITE,C;0) 298.15 +0.484786; 6000 N REF0 !

PARAMETER LNTHETA2(GRAPHITE,C;0) 298.15 +LN(947); 6000 N REF0 !

PARAMETER THETAF2(GRAPHITE,C;0) 298.15 +0.349135; 6000 N REF0 !

PARAMETER LNTHETA3(GRAPHITE,C;0) 298.15 +LN(448); 6000 N REF0 !

PARAMETER THETAF3(GRAPHITE,C;0) 298.15 +0.121463; 6000 N REF0 !

PARAMETER LNTHETA4(GRAPHITE,C;0) 298.15 +LN(193); 6000 N REF0 !

PARAMETER THETAF4(GRAPHITE,C;0) 298.15 +0.0387523; 6000 N REF0 !

PARAMETER LNTHETA5(GRAPHITE,C;0) 298.15 +LN(65); 6000 N REF0 !

PARAMETER THETAF5(GRAPHITE,C;0) 298.15 +0.0058637; 6000 N REF0 !

The Einstein function also can used with the GEIN(THETA) function.

For more information about this see FUNCTION and PARAMETER.

[2001Che] Q. Chen, B. Sundman, Modeling of thermodynamic properties for BCC, FCC, liquid, and amorphous iron. J. Phase Equilibria. 22, 631–644 (2001).

[2018Big] S. Bigdeli, Q. Chen, M. Selleby, A New Description of Pure C in Developing the Third Generation of Calphad Databases. J. Phase Equilibria Diffus. 39, 832–840 (2018).