def energy_Jam_mgd_powlaw( V_a, T_a, param_d ):
# get parameter values
theta0 = param_d['theta0']
gamma= param_d['gamma0']*(V_a/param_d['V0'])**param_d['q']
theta = param_d['theta0']*np.exp((-1)*(gamma-param_d['gamma0'])/param_d['q'])
T_ref_a = 298 # here we use isothermal reference compression curve
energy_therm_a = 0.12786*(T_a*debye_fun(theta/T_a) - T_ref_a*debye_fun(theta/T_ref_a ))
return energy_therm_a
def entropy(V, T, param_d): #compute the change of entropy d_s
V0 = param_d['V0']
gamma0 = param_d['gamma0']
theta0 = param_d['theta0'] #unit K
thetaV = theta0 * np.exp(gamma0*(1-V/V0))
T0 = 300.0
fcv = param_dic['const']['fcv']
Cv_max_cell = param_dic['const']['Cv_max_cell']
d_s = fcv * Cv_max_cell *(4.0/3*(debye_fun(thetaV/T) - debye_fun(theta0/T0)) - np.log((1.0-np.exp(-thetaV/T))/(1.0-np.exp(-theta0/T0))))
return d_s
def energy_mgd_powlaw( T, Eth, rho,param_dic ):
rho0 = param_dic['Jam_ref']['rho0']#g/cm^3
gamma0 = param_dic['Jam_ref']['gamma0']
theta0 = param_dic['Jam_ref']['theta0'] #unit K
thetaV = theta0 * np.exp(gamma0*(1-rho0/rho))
T0 = 300.0
fcv = param_dic['const']['fcv'] #the ratio of Cvmax/DP
Cv_max_cell = param_dic['const']['Cv_max_cell'] #eV/K/unitcell
energy_therm_a =fcv * Cv_max_cell * (T* debye_fun(thetaV/T) -T0* debye_fun(theta0/T0))
return Eth - energy_therm_a
def energy_mgd_powlaw(V_a, T_a, param_d):
# get parameter values
theta0 = param_d['theta0']
C_DP = param_d['const']['C_DP']
P_factor = param_d['const']['P_factor']
gamma = param_d['gamma0'] * (V_a / param_d['V0'])**param_d['q']
theta = param_d['theta0'] * np.exp(
(-1) * (gamma - param_d['gamma0']) / param_d['q'])
T_ref_a = 300 # here we use isothermal reference compression curve
energy_therm_a = C_DP / atompermol * param_d['const']['Natom'] * (
T_a * debye_fun(theta / T_a) - T_ref_a * debye_fun(theta / T_ref_a))
return energy_therm_a
def findT(T, Pth,rho2):
atompermol = 6.022*(10**23) #at/mol
rho0 = 21.4449 #unit g/cm^3
V_0 = 195*param_d['const']['Natom']/atompermol/rho0*1e24 #unit Ang^3/unitcell
g0 = 2.40
thetaD = 200 #unit K
thetaV = thetaD * np.exp(g0*(1-rho0/rho2))
T0 = 300
fcv = 0.12786/0.12664 #the ratio of Cvmax/DP
kT0 = 1.0/40 #unit eV
unit_conv = 160.217657
return Pth - g0/V_0 * 3 * fcv * kT0 * (T/T0 * debye_fun(thetaV/T) - debye_fun(thetaV/T0)) * unit_conv
def energy_mgd_powlaw(V_a, T_a, param_d):
# get parameter values
theta0 = param_d["theta0"]
C_DP = param_d["const"]["C_DP"]
P_factor = param_d["const"]["P_factor"]
gamma = param_d["gamma0"] * (V_a / param_d["V0"]) ** param_d["q"]
theta = param_d["theta0"] * np.exp((-1) * (gamma - param_d["gamma0"]) / param_d["q"])
T_ref_a = 300 # here we use isothermal reference compression curve
energy_therm_a = (
C_DP
/ atompermol
* param_d["const"]["Natom"]
* (T_a * debye_fun(theta / T_a) - T_ref_a * debye_fun(theta / T_ref_a))
)
return energy_therm_a
def energy_mgd_powlaw( V_a, T_a, param_d ):
# get parameter values
theta0 = param_d['theta0']
C_DP = param_d['const']['C_DP']
P_factor = param_d['const']['P_factor']
gamma= param_d['gamma0']*(V_a/param_d['V0'])**param_d['q']
theta = param_d['theta0']*np.exp((-1)*(gamma-param_d['gamma0'])/param_d['q'])
T_ref_a = 300 # here we use isothermal reference compression curve
energy_therm_a = C_DP/atompermol*param_d['const']['Natom']*(T_a*debye_fun(theta/T_a) - T_ref_a*debye_fun(theta/T_ref_a ))
return energy_therm_a
def findT(T, P,rho):
rho0 = param_dic['Jam_ref']['rho0']
V_0 = rho_to_vol(rho0) #unit Ang^3/unitcell
gamma0 = param_dic['Jam_ref']['gamma0']
theta0 = param_dic['Jam_ref']['theta0'] #unit K
thetaV = theta0 * np.exp(gamma0*(1-rho0/rho))
T0 = 300.0
fcv = param_dic['const']['fcv']
kT300 = param_dic['const']['kT300'] #unit eV
Cv_max_cell = param_dic['const']['Cv_max_cell']
return P - gamma0/V_0 * fcv * Cv_max_cell* T0 * (T/T0 * debye_fun(thetaV/T) - debye_fun(theta0/T0)) * param_dic['const']['P_factor']
def entropy(V, T, param_d):
V0 = param_d['V0']
g0 = 2.40
thetaD = 200.0 #unit K
thetaV = thetaD * np.exp(g0*(1-V/V0))
T0 = 300.0
fcv = 0.12786/0.12664 #the ratio of Cvmax/DP
kT300 = 1.0/40 #unit eV
#entropy = 3*fcv * kT300/300 * param_dic['const']['Natom'] *(4.0/3*debye_fun(thetaV/T) - np.log(1-np.exp(-thetaV/T)))
d_s = 3.0*fcv * kT300/300.0*param_dic['const']['Natom'] *(4.0/3*(debye_fun(thetaV/T) - debye_fun(thetaD/T0)) - np.log((1-np.exp(-thetaV/T))/(1-np.exp(-thetaD/T0))))
return d_s
def energy_mgd_powlaw(T, Eth, rho):
rho0 = 21.4449 # unit g/cm^3
# rho0 = param_dic['const']['rho_Pt']
P_factor = param_dic["const"]["P_factor"]
g0 = 2.40
thetaD = 200.0 # unit K
thetaV = thetaD * np.exp(g0 * (1 - rho0 / rho))
T0 = 300.0
fcv = 0.12786 / 0.12664 # the ratio of Cvmax/DP
kT300 = 1.0 / 40 # unit eV
energy_therm_a = (
3
* fcv
* kT300
/ 300.0
* param_dic["const"]["Natom"]
* (T / T0 * debye_fun(thetaV / T) - debye_fun(thetaV / T0))
* param_dic["const"]["P_factor"]
)
return Eth - energy_therm_a
def energy_mgd_powlaw( T, Eth, rho ):
rho0 = 21.4449 #unit g/cm^3
#rho0 = param_dic['const']['rho_Pt']
P_factor = param_dic['const']['P_factor']
g0 = 2.40
thetaD = 200.0 #unit K
thetaV = thetaD * np.exp(g0*(1-rho0/rho))
T0 = 300.0
fcv = 0.12786/0.12664 #the ratio of Cvmax/DP
kT300 = 1.0/40 #unit eV
energy_therm_a =3*fcv * kT300/300.0 * param_dic['const']['Natom'] * (T/T0 * debye_fun(thetaV/T) - debye_fun(thetaV/T0)) * param_dic['const']['P_factor']
return Eth - energy_therm_a
def entropy(V, T, param_d):
V0 = param_d["V0"]
g0 = 2.40
thetaD = 200.0 # unit K
thetaV = thetaD * np.exp(g0 * (1 - V / V0))
T0 = 300.0
fcv = 0.12786 / 0.12664 # the ratio of Cvmax/DP
kT300 = 1.0 / 40 # unit eV
# entropy = 3*fcv * kT300/300 * param_dic['const']['Natom'] *(4.0/3*debye_fun(thetaV/T) - np.log(1-np.exp(-thetaV/T)))
d_s = (
3.0
* fcv
* kT300
/ 300.0
* param_dic["const"]["Natom"]
* (
4.0 / 3 * (debye_fun(thetaV / T) - debye_fun(thetaD / T0))
- np.log((1 - np.exp(-thetaV / T)) / (1 - np.exp(-thetaD / T0)))
)
)
return d_s
def findT(T, P, rho):
# rho0 = param_dic['const']['rho_Pt']
rho0 = 21.4449 # unit g/cm^3
V0 = rho_to_vol(rho0) # unit Ang^3/unitcell
g0 = 2.40
thetaD = 200.0 # unit K
# thetaV = thetaD * np.exp(g0*(1-rho0/rho))
thetaV = thetaD * np.exp(g0 * (1 - rho0 / rho))
T0 = 300.0
fcv = 0.12786 / 0.12664 # the ratio of Cvmax/DP
kT300 = 1.0 / 40 # unit eV
return (
P
- g0
/ V0
* 3
* fcv
* kT300
/ 300.0
* param_dic["const"]["Natom"]
* T0
* (T / T0 * debye_fun(thetaV / T) - debye_fun(thetaV / T0))
* param_dic["const"]["P_factor"]
)
def findT(T, P,rho):
#rho0 = param_dic['const']['rho_Pt']
rho0 = 21.4449 #unit g/cm^3
V0 = rho_to_vol(rho0) #unit Ang^3/unitcell
g0 = 2.40
thetaD = 200.0 #unit K
#thetaV = thetaD * np.exp(g0*(1-rho0/rho))
thetaV = thetaD * np.exp(g0*(1-rho0/rho))
T0 = 300.0
fcv = 0.12786/0.12664 #the ratio of Cvmax/DP
kT300 = 1.0/40 #unit eV
return P - g0/V0 * 3 * fcv * kT300/300.0* param_dic['const']['Natom'] * T0 * (T/T0 * debye_fun(thetaV/T) - debye_fun(thetaV/T0)) * param_dic['const']['P_factor']
T_P = infer_mgd_temp_P(P-P300,rho,param_dic) print T_P #compute Vinet Energy E300 = energy_vinet(V,param_dic['Jam_ref'],300.0) E_test = energy_vinet(V0,param_dic['Jam_ref'],300.0) mask_a = E > E300 T_E = infer_mgd_temp_E(E-E300,rho,param_dic) print T_E V0 = param_dic['Jam_ref']['V0'] K0 = param_dic['Jam_ref']['K0'] K0p = param_dic['Jam_ref']['K0p'] P_factor = param_dic['const']['P_factor'] rho0 = 21.4449 #unit g/cm^3 g0 = 2.40 thetaD = 200.0 #unit K thetaV = thetaD * np.exp(g0*(1-rho0/rho)) T0 = 300.0 fcv = 0.12786/0.12664 #the ratio of Cvmax/DP kT0 = 1.0/40 #unit eV x = (V/V0)**(1.0/3) #print 'x',x eta = 3.0*(K0p- 1)/2.0 print 'eta', eta energy_a = V0*K0/P_factor*9.0/(eta**2.0) * (1 + (eta*(1-x)-1) * np.exp(eta*(1-x)))/param_dic['const']['avogadro_const'] entropy = 3*fcv * kT0 *(4.0/3*(debye_fun(thetaV/300.0) - debye_fun(thetaD/T0)) - np.log((1-np.exp(-thetaV/300.0))/(1-np.exp(-thetaD/T0)))) from IPython import embed; embed(); import ipdb; ipdb.set_trace() ##########################
x = (V / V0) ** (1.0 / 3)
# print 'x',x
eta = 3.0 * (K0p - 1) / 2.0
print "eta", eta
energy_a = (
V0
* K0
/ P_factor
* 9.0
/ (eta ** 2.0)
* (1 + (eta * (1 - x) - 1) * np.exp(eta * (1 - x)))
/ param_dic["const"]["avogadro_const"]
)
entropy = (
3
* fcv
* kT0
* (
4.0 / 3 * (debye_fun(thetaV / 300.0) - debye_fun(thetaD / T0))
- np.log((1 - np.exp(-thetaV / 300.0)) / (1 - np.exp(-thetaD / T0)))
)
)
from IPython import embed
embed()
import ipdb
ipdb.set_trace()
##########################