root/trunk/matml/src/ternary/freenergy.h

/***************************************
  $Header$

  This is the freenergy.h header file with structures and prototypes for
  calculating free energy functions for ternary systems.
  ***************************************/


#ifndef FREENERGY_H
#define FREENERGY_H

typedef struct {
  double C2;     /*+ Ternary concentration variable
                   +latex+$C_2$ ($0\rightarrow1$)
                   -latex-2 (0 -> 1)
                   +*/
  double C3;     /*+ Ternary concentration variable
                   +latex+$C_3$ ($0\rightarrow1-C_2$)
                   -latex-3 (0 -> 1-C2)
                   +*/
  int efunc;     /*+ Index indicating which energy surface (phase) this point
                   is on; a negative value indicates that energy derivatives
                   are not yet calculated. +*/
  double T;      /*+ Temperature at which the free energies and derivatives
                   are valid +*/
  double P;      /*+ Pressure at which the free energies and derivatives are
                   valid, -1 if not valid +*/
  double G;      /*+ Free energy +*/
  double G2;     /*+ Free energy derivative
                   +latex+$\partial G/\partial C_2$
                   -latex-dG/dC2
                   +*/
  double G3;     /*+ Free energy derivative
                   +latex+$\partial G/\partial C_3$
                   -latex-dG/dC3
                   +*/
  double G22;    /*+ Free energy second derivative
                   +latex+$\partial^2 G/\partial C_2^2$
                   +html+ d<sup>2</sup>G/dC2<sup>2</sup>
                   +*/
  double G33;    /*+ Free energy second derivative
                   +latex+$\partial^2 G/\partial C_3^2$
                   +html+ d<sup>2</sup>G/dC3<sup>2</sup>
                   +*/
  double G23;    /*+ Free energy mixed partial second derivative
                   +latex+$\partial^2 G/\partial C_2\partial C_3$
                   +html+ d<sup>2</sup>G/dC2dC3
                   +*/
} energy_point;

typedef struct {
  double coeff; /*+ Coefficient at 0 temperature +*/
  double dcdT;  /*+ Temperature derivative of coefficient +*/
  double n1;    /*+ C1 exponent +*/
  double n2;    /*+ C2 exponent +*/
  double n3;    /*+ C3 exponent +*/
} energy_polynomial; /*+ Polynomial free energy term structure +*/

typedef struct {
  char *name;
  double C2; /*+ Composition at center of this Gaussian term +*/
  double C3; /*+ Composition at center of this Gaussian term +*/
  double G;  /*+ Free energy addition at the Gaussian center +*/
  double w;  /*+ Width of the Gaussian distribution +*/
  double n;  /*+ Exponent of the distribution, currently fixed at 2 +*/
} energy_gaussian; /*+ Gaussian free energy term structure +*/

typedef struct {
  char *name;      /*+ Name of this phase +*/
  double R;        /*+ Ideal gas law constant +*/
  double T0;       /*+ Reference temperature +*/
  double G1_T0;    /*+ Free energy of species 1 at reference temperature +*/
  double G2_T0;    /*+ Free energy of species 2 at reference temperature +*/
  double G3_T0;    /*+ Free energy of species 3 at reference temperature +*/
  double G1_C;     /*+ Species 1 heat capacity +*/
  double G2_C;     /*+ Species 2 heat capacity +*/
  double G3_C;     /*+ Species 3 heat capacity +*/
  double S1;       /*+ Species 1 entropy coefficient (inverse Flory-Huggins relative molar volume) +*/
  double S2;       /*+ Species 2 entropy coefficient +*/
  double S3;       /*+ Species 3 entropy coefficient +*/
  double S4;       /*+ 1-C2 entropy coefficient for square system +*/
  double S5;       /*+ 1-C3 entropy coefficient for square system +*/
  double Omega12;  /*+ Species 1-2 regular solution interaction parameter +*/
  double Omega13;  /*+ Species 1-3 regular solution interaction parameter +*/
  double Omega23;  /*+ Species 2-3 regular solution interaction parameter +*/
  double Omega123; /*+ Species 1-2-3 regular solution interaction parameter +*/
  double Omega234; /*+ Species 2-3-4 regular solution interaction parameter +*/
  double Omega235; /*+ Species 2-3-5 regular solution interaction parameter +*/
  double Omega245; /*+ Species 2-4-5 regular solution interaction parameter +*/
  double Omega345; /*+ Species 3-4-5 regular solution interaction parameter +*/
  double Omega2345;/*+ Species 2-3-4-5 regular solution interaction parameter+*/
  energy_polynomial *poly; /*+ Array of polynomial energy parameter structs +*/
  int n_poly;      /*+ Number of polynomial energy terms +*/
  energy_gaussian *gauss; /*+ Array of Gaussian energy parameter structs +*/
  int n_gauss;     /*+ Number of Gaussian energy terms +*/
} energy_params;   /*+ Free energy parameters structure +*/

typedef enum {
  STANDARD=0,
  WITH_DERIVATIVES=1,
  NO_INFINITY=2,
  WITH_DERIVATIVES_NO_INFINITY=3
} free_energy_flags;

#define TERNARY_INFINITY HUGE_VALF
#define TERNARY_NEGATIVE_INFINITY (-HUGE_VALF)

double free_energy
(double C2, double C3, double T, double P, energy_params *eparams);
int free_energies
(energy_point *points, int n, double T, double P, energy_params *eparams,
 int efunc, free_energy_flags flags);
#if HAVE_LAPACK == yes
int adjust_gaussians
(double T, double P, double *G0, energy_params *eparams, int efunc);
#endif

#endif // FREENERGY_H