def __thermal_bulk_modulus(self, T,V,params):
     gr = self.__grueneisen_parameter(params['V_0']/V, params)
     Debye_T = self.__debye_temperature(params['V_0']/V, params)
     K_th = 3.*params['n']*constants.gas_constant*T/V * gr * \
         ((1. - params['q_0'] - 3.*gr)*debye.debye_fn(Debye_T/T)+3.*gr*(Debye_T/T)/(np.exp(Debye_T/T) - 1.)) # EQ B5
     return K_th
 def __thermal_shear_modulus(self, T, V, params):
     gr = self.__grueneisen_parameter(params['V_0']/V, params)
     Debye_T = self.__debye_temperature(params['V_0']/V, params)
     G_th= 3./5. * ( self.__thermal_bulk_modulus(T,V,params) - \
              6*constants.gas_constant*T*params['n']/V * gr * debye.debye_fn(Debye_T/T) ) # EQ B10
     return G_th