Reference_element_method-mathematica_script.txt

G = 4*c1*c2*H12 + 4*c2*c3*H23 + 4*c1*c3*H13 + 4*c1*c4*H14 + 
  4*c2*c4*H24 + 4*c3*c4*H34 + 
  R*T*(c1*Log[c1] + c2*Log[c2] + c3*Log[c3] + c4*Log[c4])

Tmatrix = {{-1, -3^(-1/2), -6^(-1/2)}, {1, -3^(-1/2), -6^(-1/2)}, {0, 
   2*3^(-1/2), -6^(-1/2)}}

#################################
#Select only one element as the reference element!

c4 = 1 - c1 - c2 - c3
Hmatrix4 = D[G, {{c1, c2, c3}, 2}]

c3 = 1 - c1 - c2 - c4
Hmatrix3 = D[G, {{c1, c2, c4}, 2}]

c2 = 1 - c1 - c4 - c3
Hmatrix2 = D[G, {{c1, c3, c4}, 2}]

c1 = 1 - c4 - c2 - c3
Hmatrix1 = D[G, {{c2, c3, c4}, 2}]
####################################


######################################
#Run only one calculation based on the selection of the reference element!

HBarmatrix4 = Dot[Transpose[Tmatrix], Hmatrix4, Tmatrix]
Eigenvectors4 = Eigenvectors[HBarmatrix4]
Eigenvalues4 = Eigenvalues[HBarmatrix4]
Directions4 = Transpose[Dot[Tmatrix, Transpose[Eigenvectors4]]]

HBarmatrix3 = Dot[Transpose[Tmatrix], Hmatrix3, Tmatrix]
Eigenvectors3 = Eigenvectors[HBarmatrix3]
Eigenvalues3 = Eigenvalues[HBarmatrix3]
Directions3 = Transpose[Dot[Tmatrix, Transpose[Eigenvectors3]]]

HBarmatrix2 = Dot[Transpose[Tmatrix], Hmatrix2, Tmatrix]
Eigenvectors2 = Eigenvectors[HBarmatrix2]
Eigenvalues2 = Eigenvalues[HBarmatrix2]
Directions2 = Transpose[Dot[Tmatrix, Transpose[Eigenvectors2]]]

HBarmatrix1 = Dot[Transpose[Tmatrix], Hmatrix1, Tmatrix]
Eigenvectors1 = Eigenvectors[HBarmatrix1]
Eigenvalues1 = Eigenvalues[HBarmatrix1]
Directions1 = Transpose[Dot[Tmatrix, Transpose[Eigenvectors1]]]
######################################

#############
#source data
#(*1:Fe 2:Co 3:Ni 4:Cu*)
c1 = 0.15
c2 = 0.15
c3 = 0.35
c4 = 0.35

H12 = -600
H13 = -1600
H14 = 12900
H23 = -200
H24 = 6400
H34 = 3600
T = 1100
R = 8.314