add tnmh stuff

2023-05-13 19:23:15 +02:00 · 2023-05-13 19:23:15 +02:00 · 11ed3c16eb
commit 11ed3c16eb
parent 15c959fd71
5 changed files with 40806 additions and 0 deletions
--- a/src/nmreval/dsc/D84_10.0K-min_h.dat
+++ b/src/nmreval/dsc/D84_10.0K-min_h.dat
--- a/src/nmreval/dsc/D84_10.0K-min_h_dTfdT_tau.fit
+++ b/src/nmreval/dsc/D84_10.0K-min_h_dTfdT_tau.fit
@ -0,0 +1,202 @@
+# tau_TNMH=77.93669386254352	beta=0.6334823578561849	x=0.4107577725462226	deltaE=205554.80338165778
+# Temp		dTfdT_data		dTfdT_fit
+1.50007e+02 -1.54659e-03 5.04753e-03
+1.50258e+02 -1.35164e-03 -5.81695e-03
+1.50509e+02 -1.15321e-03 -5.24594e-03
+1.50760e+02 1.33378e-03 -5.19023e-03
+1.51011e+02 -4.19078e-03 -5.23034e-03
+1.51262e+02 -3.69741e-03 -5.32106e-03
+1.51514e+02 -1.17892e-03 -5.44569e-03
+1.51765e+02 -4.26847e-04 -5.59617e-03
+1.52016e+02 1.34823e-03 -5.76806e-03
+1.52267e+02 -8.53837e-04 -5.95864e-03
+1.52518e+02 -3.32957e-03 -6.16618e-03
+1.52769e+02 -3.18265e-03 -6.38951e-03
+1.53021e+02 -9.27941e-04 -6.62778e-03
+1.53272e+02 2.81209e-03 -6.88034e-03
+1.53523e+02 2.53703e-03 -7.14668e-03
+1.53774e+02 2.79565e-03 -7.42632e-03
+1.54025e+02 3.73709e-03 -7.71879e-03
+1.54277e+02 -4.74193e-04 -8.02362e-03
+1.54528e+02 5.53513e-03 -8.34027e-03
+1.54779e+02 5.40911e-03 -8.66813e-03
+1.55030e+02 4.61145e-03 -9.00648e-03
+1.55281e+02 3.12182e-03 -9.35449e-03
+1.55532e+02 6.75992e-03 -9.71118e-03
+1.55784e+02 3.14577e-03 -1.00754e-02
+1.56035e+02 2.59412e-03 -1.04458e-02
+1.56286e+02 -1.54718e-03 -1.08208e-02
+1.56537e+02 1.17037e-04 -1.11987e-02
+1.56788e+02 -2.03614e-03 -1.15774e-02
+1.57039e+02 1.33113e-03 -1.19545e-02
+1.57291e+02 -5.96949e-03 -1.23274e-02
+1.57542e+02 -6.48426e-03 -1.26931e-02
+1.57793e+02 -1.59997e-03 -1.30481e-02
+1.58044e+02 -3.72898e-04 -1.33886e-02
+1.58295e+02 1.30990e-03 -1.37104e-02
+1.58547e+02 4.08780e-03 -1.40088e-02
+1.58798e+02 -7.05642e-03 -1.42784e-02
+1.59049e+02 -2.00584e-03 -1.45134e-02
+1.59300e+02 -1.92937e-03 -1.47073e-02
+1.59551e+02 -6.58517e-04 -1.48531e-02
+1.59802e+02 7.32033e-04 -1.49429e-02
+1.60054e+02 2.36722e-03 -1.49682e-02
+1.60305e+02 -1.17443e-03 -1.49196e-02
+1.60556e+02 4.59116e-04 -1.47868e-02
+1.60807e+02 8.17255e-03 -1.45588e-02
+1.61058e+02 8.48647e-03 -1.42234e-02
+1.61310e+02 7.96560e-03 -1.37674e-02
+1.61561e+02 1.29202e-02 -1.31766e-02
+1.61812e+02 4.84645e-03 -1.24355e-02
+1.62063e+02 1.24679e-02 -1.15274e-02
+1.62314e+02 1.08789e-02 -1.04342e-02
+1.62565e+02 9.31453e-03 -9.13630e-03
+1.62817e+02 1.10428e-02 -7.61265e-03
+1.63068e+02 1.81300e-02 -5.84047e-03
+1.63319e+02 9.70774e-03 -3.79521e-03
+1.63570e+02 1.20566e-02 -1.45035e-03
+1.63821e+02 1.49584e-02 1.22268e-03
+1.64072e+02 1.72350e-02 4.25478e-03
+1.64324e+02 2.03471e-02 7.67928e-03
+1.64575e+02 3.74633e-02 1.15322e-02
+1.64826e+02 2.20722e-02 1.58527e-02
+1.65077e+02 2.90447e-02 2.06828e-02
+1.65328e+02 3.56891e-02 2.60686e-02
+1.65580e+02 4.02175e-02 3.20598e-02
+1.65831e+02 4.99873e-02 3.87108e-02
+1.66082e+02 6.52373e-02 4.60809e-02
+1.66333e+02 5.16469e-02 5.42346e-02
+1.66584e+02 6.50874e-02 6.32432e-02
+1.66835e+02 7.59582e-02 7.31846e-02
+1.67087e+02 8.82617e-02 8.41446e-02
+1.67338e+02 9.75569e-02 9.62183e-02
+1.67589e+02 1.08193e-01 1.09511e-01
+1.67840e+02 1.09727e-01 1.24138e-01
+1.68091e+02 1.30829e-01 1.40230e-01
+1.68342e+02 1.55907e-01 1.57932e-01
+1.68594e+02 1.71526e-01 1.77404e-01
+1.68845e+02 1.87568e-01 1.98829e-01
+1.69096e+02 2.05094e-01 2.22407e-01
+1.69347e+02 2.27806e-01 2.48367e-01
+1.69598e+02 2.58337e-01 2.76962e-01
+1.69850e+02 2.88510e-01 3.08478e-01
+1.70101e+02 3.20528e-01 3.43232e-01
+1.70352e+02 3.57173e-01 3.81577e-01
+1.70603e+02 4.02201e-01 4.23903e-01
+1.70854e+02 4.47497e-01 4.70630e-01
+1.71105e+02 5.06370e-01 5.22210e-01
+1.71357e+02 5.66666e-01 5.79104e-01
+1.71608e+02 6.33707e-01 6.41763e-01
+1.71859e+02 7.08395e-01 7.10580e-01
+1.72110e+02 7.86941e-01 7.85817e-01
+1.72361e+02 8.80202e-01 8.67486e-01
+1.72612e+02 9.72949e-01 9.55178e-01
+1.72864e+02 1.07283e+00 1.04780e+00
+1.73115e+02 1.17098e+00 1.14323e+00
+1.73366e+02 1.26581e+00 1.23794e+00
+1.73617e+02 1.36284e+00 1.32657e+00
+1.73868e+02 1.40164e+00 1.40186e+00
+1.74120e+02 1.45067e+00 1.45520e+00
+1.74371e+02 1.46476e+00 1.47830e+00
+1.74622e+02 1.44706e+00 1.46612e+00
+1.74873e+02 1.40520e+00 1.42006e+00
+1.75124e+02 1.35811e+00 1.34934e+00
+1.75375e+02 1.26322e+00 1.26857e+00
+1.75627e+02 1.20703e+00 1.19227e+00
+1.75878e+02 1.15871e+00 1.12985e+00
+1.76129e+02 1.12062e+00 1.08413e+00
+1.76380e+02 1.09118e+00 1.05315e+00
+1.76631e+02 1.07111e+00 1.03314e+00
+1.76882e+02 1.05191e+00 1.02044e+00
+1.77134e+02 1.04878e+00 1.01241e+00
+1.77385e+02 1.04027e+00 1.00731e+00
+1.77636e+02 1.03275e+00 1.00413e+00
+1.77887e+02 1.02782e+00 1.00219e+00
+1.78138e+02 1.02566e+00 1.00108e+00
+1.78390e+02 1.02147e+00 1.00049e+00
+1.78641e+02 1.01938e+00 1.00020e+00
+1.78892e+02 1.02000e+00 1.00007e+00
+1.79143e+02 1.01835e+00 1.00002e+00
+1.79394e+02 1.01657e+00 1.00001e+00
+1.79645e+02 1.01941e+00 1.00000e+00
+1.79897e+02 1.00523e+00 1.00000e+00
+1.80148e+02 1.00689e+00 1.00000e+00
+1.80399e+02 1.00730e+00 1.00000e+00
+1.80650e+02 1.00768e+00 1.00000e+00
+1.80901e+02 1.00746e+00 1.00000e+00
+1.81152e+02 1.00606e+00 1.00000e+00
+1.81404e+02 1.00202e+00 1.00000e+00
+1.81655e+02 9.93205e-01 1.00000e+00
+1.81906e+02 9.98851e-01 1.00000e+00
+1.82157e+02 1.00478e+00 1.00000e+00
+1.82408e+02 1.00147e+00 1.00000e+00
+1.82660e+02 1.00747e+00 1.00000e+00
+1.82911e+02 9.83522e-01 1.00000e+00
+1.83162e+02 9.90690e-01 1.00000e+00
+1.83413e+02 9.94175e-01 1.00000e+00
+1.83664e+02 9.95883e-01 1.00000e+00
+1.83915e+02 9.92199e-01 1.00000e+00
+1.84167e+02 9.90755e-01 1.00000e+00
+1.84418e+02 9.86480e-01 1.00000e+00
+1.84669e+02 9.93964e-01 1.00000e+00
+1.84920e+02 9.94745e-01 1.00000e+00
+1.85171e+02 9.95895e-01 1.00000e+00
+1.85422e+02 9.97575e-01 1.00000e+00
+1.85674e+02 9.99326e-01 1.00000e+00
+1.85925e+02 9.97579e-01 1.00000e+00
+1.86176e+02 1.00187e+00 1.00000e+00
+1.86427e+02 9.99647e-01 1.00000e+00
+1.86678e+02 1.00026e+00 1.00000e+00
+1.86930e+02 1.00307e+00 1.00000e+00
+1.87181e+02 1.01192e+00 1.00000e+00
+1.87432e+02 9.96247e-01 1.00000e+00
+1.87683e+02 9.98530e-01 1.00000e+00
+1.87934e+02 1.00165e+00 1.00000e+00
+1.88185e+02 1.00562e+00 1.00000e+00
+1.88437e+02 1.01337e+00 1.00000e+00
+1.88688e+02 1.01309e+00 1.00000e+00
+1.88939e+02 9.95564e-01 1.00000e+00
+1.89190e+02 1.00160e+00 1.00000e+00
+1.89441e+02 1.00596e+00 1.00000e+00
+1.89692e+02 1.01222e+00 1.00000e+00
+1.89944e+02 1.00825e+00 1.00000e+00
+1.90195e+02 1.00603e+00 1.00000e+00
+1.90446e+02 1.00770e+00 1.00000e+00
+1.90697e+02 9.89746e-01 1.00000e+00
+1.90948e+02 1.00511e+00 1.00000e+00
+1.91200e+02 1.00621e+00 1.00000e+00
+1.91451e+02 1.00143e+00 1.00000e+00
+1.91702e+02 1.00224e+00 1.00000e+00
+1.91953e+02 1.03274e+00 1.00000e+00
+1.92204e+02 9.87474e-01 1.00000e+00
+1.92455e+02 9.93631e-01 1.00000e+00
+1.92707e+02 9.96782e-01 1.00000e+00
+1.92958e+02 9.99014e-01 1.00000e+00
+1.93209e+02 1.00251e+00 1.00000e+00
+1.93460e+02 1.01135e+00 1.00000e+00
+1.93711e+02 9.92486e-01 1.00000e+00
+1.93962e+02 9.94748e-01 1.00000e+00
+1.94214e+02 9.96729e-01 1.00000e+00
+1.94465e+02 9.99500e-01 1.00000e+00
+1.94716e+02 1.00314e+00 1.00000e+00
+1.94967e+02 1.00767e+00 1.00000e+00
+1.95218e+02 9.92280e-01 1.00000e+00
+1.95470e+02 9.93172e-01 1.00000e+00
+1.95721e+02 9.99065e-01 1.00000e+00
+1.95972e+02 1.00089e+00 1.00000e+00
+1.96223e+02 1.00147e+00 1.00000e+00
+1.96474e+02 1.00277e+00 1.00000e+00
+1.96725e+02 9.93517e-01 1.00000e+00
+1.96977e+02 9.89833e-01 1.00000e+00
+1.97228e+02 1.00075e+00 1.00000e+00
+1.97479e+02 1.00224e+00 1.00000e+00
+1.97730e+02 9.97354e-01 1.00000e+00
+1.97981e+02 9.96498e-01 1.00000e+00
+1.98232e+02 1.01632e+00 1.00000e+00
+1.98484e+02 9.86819e-01 1.00000e+00
+1.98735e+02 1.00374e+00 1.00000e+00
+1.98986e+02 1.00217e+00 1.00000e+00
+1.99237e+02 1.00089e+00 1.00000e+00
+1.99488e+02 1.00215e+00 1.00000e+00
+1.99740e+02 1.01197e+00 1.00000e+00
+1.99991e+02 9.92503e-01 1.00000e+00
--- a/src/nmreval/dsc/D84_DSC_tau.param
+++ b/src/nmreval/dsc/D84_DSC_tau.param
@ -0,0 +1,7 @@
+
+#Heating Rate 	 tau_TNMH 	 beta 			 x 	 deltaE 	 Tg fictive
+1.0000e+01 	 9.0613e+01 	 6.2053e-01 	 3.9548e-01 	 2.0820e+05 	 1.6911e+02
+#Heating Rate 	 tau_TNMH 	 beta 			 x 	 deltaE 	 Tg fictive
+1.0000e+01 	 3.5330e+01 	 6.7660e-01 	 5.2984e-01 	 1.7362e+05 	 1.6934e+02
+#Heating Rate 	 tau_TNMH 	 beta 			 x 	 deltaE 	 Tg fictive
+1.0000e+01 	 7.7937e+01 	 6.3348e-01 	 4.1076e-01 	 2.0555e+05 	 1.6925e+02
--- a/src/nmreval/dsc/TNMH_v0c-tau.py
+++ b/src/nmreval/dsc/TNMH_v0c-tau.py
@ -0,0 +1,197 @@
+# Tool-Naranayaswamy-Moynihan-Hodge model
+# by Florian Pabst 2020
+
+
+import re
+import os
+import sys
+import time
+
+import numpy as np
+import matplotlib.pyplot as plt
+
+from scipy.integrate import quad, cumulative_trapezoid
+from scipy.optimize import curve_fit, fsolve
+from scipy.stats import linregress
+
+from nmreval.data import Points
+
+
+def slope(x, t, m):
+    return t+x*m
+
+
+def tau_k(tau_0, deltaE, temp_k, xx, T_f_km1):
+    return tau_0 * np.exp(xx*deltaE / (R*temp_k) + (1-xx) * deltaE / (R*T_f_km1))
+
+
+# Read data
+dataName = sys.argv[1]
+try:
+    data = np.loadtxt(dataName, skiprows=0).T
+    print("Loading")
+    temp = data[0]
+    heat_capacity = data[1]
+except IndexError:
+    print("File not found")
+    exit()
+
+
+def get_fictive_temperature(pts: Points, glass: tuple[float, float], liquid: tuple[float, float]):
+    min_glass, max_glass = min(glass), max(glass)
+    min_liquid, max_liquid = min(liquid), max(liquid)
+
+    region = pts.copy()
+    region.cut(min_glass, max_liquid)
+
+    glass_regime = (min_glass < region.x) & (region.x < max_glass)
+    regress = linregress(region.x[glass_regime], region.y[glass_regime])
+    glass_extrapolation = regress.slope * region.x + regress.intercept
+
+    region.y -= glass_extrapolation
+
+    liquid_regime = (min_liquid < region.x) & (region.x < max_liquid)
+    regress = linregress(region.x[liquid_regime], region.y[liquid_regime])
+    liquid_extrapolation = regress.slope * region.x + regress.intercept
+
+    real_area = -cumulative_trapezoid(region.y, region.x, initial=0)
+    real_area -= real_area[-1]
+    equivalent_area = cumulative_trapezoid(liquid_extrapolation, region.x, initial=0)
+    equivalent_area -= equivalent_area[-1]
+    equivalent_area *= -1
+
+    return region.x, region.x[np.argmin(np.abs(real_area[:, None] - equivalent_area[None, :]), axis=1)]
+
+
+curve = Points(x=temp, y=heat_capacity, name=dataName)
+
+# First step: Calculate fictive Temperature T_f(T) from Cp data, then dT_f/dT
+
+temperatures, fictiveTemp = get_fictive_temperature(curve, glass=(150, 160), liquid=(190, 200))
+
+# Determine limiting T_f, i.e. T_f at lowest temperature
+initial_Tf = np.mean(fictiveTemp[:20])
+
+rate = curve.value
+
+# Calculate dTf/dT
+with np.errstate(all='ignore'):
+    dTfdT = np.gradient(fictiveTemp, temperatures)
+nan_filter = ~np.isnan(dTfdT)
+temperatures = np.array(temperatures)[nan_filter]
+dTfdT = dTfdT[nan_filter]
+
+
+exponents = []
+taus = []
+temps = [0]
+T_f_ns = []
+R = 8.314
+
+
+def tnmfunc(temperature, tau_g, xx, beta, deltaE):
+    steps = len(temperature)
+    tau = np.zeros(steps)
+    temp_fictive = np.zeros(steps)
+
+    # Initialize first values
+    temp_fictive[0] = temperature[0]
+    tau[0] = relax(temp_fictive[0], temp_fictive[0], tau_g, T_g, deltaE, xx)
+
+    deltaT = np.zeros(steps)
+    deltaT[1:] = np.diff(temperature)
+    delta_t = deltaT * 60 / rate
+    dttau = np.zeros(steps)
+
+    for i in range(1, steps):
+        tau[i] = relax(temperature[i], temp_fictive[i-1], tau_g, T_g, deltaE, xx)
+        dttau[:i] += delta_t[i-1] / tau[i]
+        temp_fictive[i] = np.sum(deltaT[:i] * (1-np.exp(-(dttau[:i])**beta))) + temp_fictive[0]
+        print(i, temperature[i], temp_fictive[i-i], dttau, tau[i], delta_t[i-1], deltaT[i-1])
+
+    return temp_fictive
+
+
+def relax(t, tf, tau_g, t_glass, ea, x):
+    h = ea/R
+    return tau_g * np.exp((x*h / t) + ((1 - x) * h / tf) - h / t_glass)
+
+
+# TNMH Code (adapted from Badrinarayanan's PhD Thesis):
+def tnmfunc2(xdata, tau_0, xx, beta, deltaE):
+    delhR = deltaE/8.314
+    T = []
+    Tf = []
+    t = []
+    delt = []
+    tau = []
+    dttau = []
+    delT = []
+    step = len(xdata)
+    for k in range(0, step):
+        dttau.append(0)
+        T.append(240)
+        Tf.append(240)
+        t.append(0)
+        delt.append(0)
+        tau.append(0)
+        dttau.append(0)
+        delT.append(0)
+    T[1] = xdata[1]
+    Tf[1] = T[1]
+    t[1] = 0
+    delt[1] = 0
+    tau[1] = tau_0 * np.exp((xx*delhR / T[1]) + ((1 - xx)*delhR / Tf[1])-delhR/T_g)
+    dttau[1] = delt[1] / tau[1]
+    delT[1] = 0
+
+    Tfinit = T[1]
+    T_f_ns = [xdata[0]]
+    for i in range(1, step):
+        T[i] = xdata[i]
+        delT[i] = xdata[i] - xdata[i-1]
+        delt[i] = abs(delT[i]) / (rate/60)
+        t[i] = t[i-1] + delt[i]
+        tau[i] = tau_0 * np.exp((delhR*xx / T[i]) + ((1 - xx)*delhR / Tf[i-1])-delhR/T_g)
+        print(tau[i], T[i], Tf[i-1])
+        for j in np.arange(2, i).reshape(-1):
+            dttau[j] = dttau[j] + (delt[i] / tau[i])
+            Tfinit = Tfinit + (delT[j] * (1 - np.exp(- (dttau[j] ** beta))))
+            Tf[i] = Tfinit
+        T_f_ns.append(Tfinit)
+        Tfinit = Tf[1]
+
+    return T_f_ns
+
+
+# Use T_g = T_fictive for tau determination
+T_g = initial_Tf
+
+# Start values
+p0 = [10, 0.5, 0.4, 225085]
+
+
+def fitTNMH(x, tau_0, xx, beta, deltaE):
+    dTNMHdT = []
+    modelTemp = np.append(x[::-1], x[1:])
+
+    TNMH = tnmfunc2(modelTemp, tau_0, xx, beta, deltaE)
+    for i in range(len(modelTemp)-1):
+        dTNMHdT.append((TNMH[i+1]-TNMH[i]) / (modelTemp[i+1]-modelTemp[i]))
+    res = dTNMHdT[len(modelTemp)//2-1:]
+
+    plt.plot(x, res)
+    plt.show()
+
+    return np.array(res)  
+
+
+# Use only every 20th data point to reduce fitting time
+temperaturesInterpol = np.linspace(temperatures[0], temperatures[-1], 20)
+temperaturesInterpol = np.linspace(150, 200, 5)
+dTfdTInterpol = np.interp(temperaturesInterpol, temperatures, dTfdT)
+
+plt.plot(tnmfunc2(temperaturesInterpol, *p0))
+plt.plot(tnmfunc(temperaturesInterpol, *p0))
+plt.show()
+# print(fitTNMH(temperaturesInterpol, *p0))
--- a/src/nmreval/dsc/TNMH_v0c-tau2.py
+++ b/src/nmreval/dsc/TNMH_v0c-tau2.py
@ -0,0 +1,333 @@
+# Tool-Naranayaswami-Moynihan-Hodge model
+# by Florian Pabst 2020
+
+
+import time
+import re
+import os
+import sys
+
+import numpy as np
+import matplotlib.pyplot as plt
+import scipy.odr as odr
+from scipy.integrate import quad
+from scipy.optimize import curve_fit, fsolve
+
+# Read data
+dataName = sys.argv[1]
+try:
+    data = np.loadtxt(dataName,skiprows=0)
+    print("Loading")
+    dataTemp = data[:, 0]
+    dataCp = data[:, 1]
+except IndexError:
+    print("File not found")
+    exit()
+     
+dataOutName = os.path.splitext(str(dataName))[0] + "_Tfict+TNMH.dat"
+
+
+# First step: Calculate fictive Temperature T_f(T) from Cp data, then dT_f/dT
+
+# Find start and end point for glass Cp linear fit
+coordsGl = [(150, -0.126), (160, -0.09)]
+"""
+print("Please click on the left limit for glass Cp linear fit")
+fig, (ax1) = P.subplots(1)
+ax1.set_xlabel('Temperature / K')
+ax1.set_xlim(left=140)
+ax1.set_xlim(right=200)
+ax1.plot(dataTemp,dataCp, 'ro')
+#ax1.legend()
+def onclick(event):
+  ix = event.xdata
+  iy = event.ydata
+  print(ix)
+
+  global coordsGl
+  coordsGl.append((ix, iy))
+    
+  if len(coordsGl) == 1:
+    print('right limit')
+
+  if len(coordsGl) == 2:
+      fig.canvas.mpl_disconnect(cid)
+
+  return coordsGl
+cid = fig.canvas.mpl_connect('button_press_event', onclick)
+P.show()
+"""
+print(coordsGl)
+
+for i in range(0,len(dataTemp)):
+    if dataTemp[i] < coordsGl[0][0]:
+        fitLimitLeft_Gl = i
+    if dataTemp[i] < coordsGl[1][0]:
+        fitLimitRight_Gl = i
+
+# Find start and end point for liquid Cp linear fit
+coordsLq = [(190, 2.07), (200, 1.773)]
+"""
+print("Please click on the left limit for liquid Cp linear fit")
+fig, (ax1) = P.subplots(1)
+ax1.set_xlabel('Temperature / K')
+ax1.set_xlim(left=180)
+ax1.set_xlim(right=250)
+ax1.plot(dataTemp,dataCp, 'ro')
+#ax1.legend()
+def onclick(event):
+  ix = event.xdata
+  iy = event.ydata
+  print(ix)
+
+  global coordsLq
+  coordsLq.append((ix, iy))
+    
+  if len(coordsLq) == 1:
+    print('right limit')
+
+  if len(coordsLq) == 2:
+      fig.canvas.mpl_disconnect(cid)
+
+  return coordsLq
+cid = fig.canvas.mpl_connect('button_press_event', onclick)
+P.show()
+#print(coordsLq)
+"""
+
+for i in range(0, len(dataTemp)):
+    if dataTemp[i] < coordsLq[0][0]:
+        fitLimitLeft_Lq = i
+    if dataTemp[i] < coordsLq[1][0]:
+        fitLimitRight_Lq = i
+
+
+def slope(x, t, m):
+    return t+x*m
+
+
+# Determine glass Cp slope
+res = curve_fit(slope, dataTemp[fitLimitLeft_Gl:fitLimitRight_Gl], dataCp[fitLimitLeft_Gl:fitLimitRight_Gl])
+glassCpParam = res[0]
+
+# Determine liquid Cp slope
+res  = curve_fit(slope, dataTemp[fitLimitLeft_Lq:fitLimitRight_Lq], dataCp[fitLimitLeft_Lq:fitLimitRight_Lq])
+liquidCpParam = res[0]
+
+xLin = np.linspace(coordsGl[0][0], coordsLq[1][0], len(dataTemp))
+
+CpInterpol = np.interp(xLin, dataTemp, dataCp)
+"""
+fig, (ax1) = P.subplots(1)
+ax1.set_xlabel('Temperature / K')
+ax1.set_xlim(left=coordsGl[0][0])
+ax1.set_xlim(right=coordsLq[1][0])
+ax1.set_ylim(bottom=coordsGl[0][1]-0.1)
+ax1.set_ylim(top=coordsLq[1][1]+0.1)
+ax1.plot(dataTemp,dataCp, 'ro')
+ax1.plot(dataTemp,slope(dataTemp,glassCpParam[0],glassCpParam[1]), 'b-')
+ax1.plot(dataTemp,slope(dataTemp,liquidCpParam[0],liquidCpParam[1]), 'b-')
+ax1.plot(xLin,CpInterpol, 'g-')
+P.show()
+"""
+
+
+# Calculate Fictive Temperature for all temperatures in range
+intStart = fitLimitLeft_Gl
+intStop = fitLimitRight_Lq
+
+fictiveTemp = []
+temperatures = []
+for i,tempStart in enumerate(dataTemp):
+    if fitLimitLeft_Gl < i < fitLimitRight_Lq:
+        intStart = i
+
+        integration2 = np.trapz((dataCp[intStart:intStop]-slope(dataTemp[intStart:intStop], glassCpParam[0], glassCpParam[1])), dataTemp[intStart:intStop])
+
+        def integrand1(temp):
+            return slope(temp, liquidCpParam[0], liquidCpParam[1])-slope(temp, glassCpParam[0], glassCpParam[1])
+
+        def fictiveTempEq(x):
+            return quad(integrand1, x, coordsLq[1][0])[0] - integration2
+
+        ficTemp = fsolve(fictiveTempEq, np.array([160]))
+        fictiveTemp.append(ficTemp[0])
+        temperatures.append(tempStart)
+
+
+# Determine limiting T_f, i.e. T_f at lowest temperatures
+def constant(x, t):
+    return t
+
+
+res = curve_fit(constant, temperatures[0:20], fictiveTemp[0:20])
+T_f_0 = res[0]
+print(T_f_0[0])
+
+# Calculate dTf/dT
+dTfdT = []
+temperaturesCut = []
+for i in range(len(temperatures)-1):
+    if (temperatures[i+1]-temperatures[i]) != 0:
+        dTfdT.append((fictiveTemp[i+1]-fictiveTemp[i]) / (temperatures[i+1]-temperatures[i]))
+        temperaturesCut.append(temperatures[i+1])
+
+"""        
+fig, (ax1) = P.subplots(1)
+ax1.set_xlabel('Temperature / K')
+ax1.set_ylabel('Fictive Temperature / K')
+#ax1.set_xlim(left=coordsGl[0][0])
+#ax1.set_xlim(right=coordsLq[1][0])
+#ax1.set_ylim(bottom=coordsGl[0][1]-0.1)
+#ax1.set_ylim(top=coordsLq[1][1]+0.1)
+ax1.plot(temperatures,fictiveTemp, 'ro')
+#ax1.plot(temperatures,(T_f_0+temperatures*0), 'b-')
+ax1.axhline(y=T_f_0[0], color='b', linestyle='-')
+#ax1.plot(temperatures[:-1],dTfdT, 'ro')
+P.show()
+"""
+
+# Second step: Calcualte and Fit TNMH-model
+try:
+    rate = float(str((re.findall(r'\d+\.\d+K', dataName))[0])[:-1])
+    print("\tRate:  %fK-min" % rate)
+except IndexError:
+    rate = int(input("\tPlease enter the heating rate:   "))
+    print("\tRate:  %fK-min" %rate)
+
+
+def tau_k(tau_0, deltaE, T_k, xx, T_f_km1):
+    return tau_0 * np.exp(xx*deltaE/(R*T_k) + (1-xx)*deltaE/(R*T_f_km1))
+    
+
+exponents = []
+taus = []
+temps = [0]
+T_f_ns = []
+markovs = [coordsLq[1][0]]
+R = 8.31
+
+# TNMH Code (adapted from Badrinarayanan's PhD Thesis):
+def tnmfunc2(xdata, tau_0, xx, beta, deltaE):
+    delhR = deltaE/8.314
+    T = []
+    Tf = []
+    t = []
+    delt = []
+    tau = []
+    dttau = []
+    delT = []
+    step = len(xdata)
+    for k in range(0, step):
+        dttau.append(0)
+        T.append(240)
+        Tf.append(240)
+        t.append(0)
+        delt.append(0)
+        tau.append(0)
+        dttau.append(0)
+        delT.append(0)
+    T[1] = xdata[1]
+    Tf[1] = T[1]
+    t[1] = 0
+    delt[1] = 0
+    tau[1] = tau_0 * np.exp((xx*delhR / T[1]) + ((1 - xx)*delhR / Tf[1])-delhR/T_g)
+    dttau[1] = delt[1] / tau[1]
+    delT[1] = 0
+
+    Tfinit = T[1]
+    T_f_ns = [coordsLq[1][0]]
+    for i in range(1, step):
+        T[i] = xdata[i]
+        delT[i] = xdata[i] - xdata[i-1]
+        delt[i] = abs(delT[i]) / (rate/60)
+        t[i] = t[i-1] + delt[i]
+        tau[i] = tau_0 * np.exp((delhR*xx / T[i]) + ((1 - xx)*delhR / Tf[i-1])-delhR/T_g)
+        for j in np.arange(2, i).reshape(-1):
+            dttau[j] = dttau[j] + (delt[i] / tau[i])
+            Tfinit = Tfinit + (delT[j] * (1 - np.exp(- (dttau[j] ** beta))))
+            Tf[i] = Tfinit
+        T_f_ns.append(Tfinit)
+        Tfinit = Tf[1]
+
+    print(T_f_ns[:10])
+    return T_f_ns
+
+
+####################################################
+# Use T_g = T_fictive for tau determination
+T_g = T_f_0[0]
+# or plug in T_half, T_onset, ... from separate evaluation
+
+# Start values
+p0 = [10, 0.5, 0.4, 225085]
+
+
+def fitTNMH(p, x):
+    dTNMHdT = []
+    modelTemp = np.append(x[::-1], x[1:])
+    tau_0, xx, beta, deltaE = p
+    TNMH = tnmfunc2(modelTemp, tau_0, xx, beta, deltaE)
+    for i in range(len(modelTemp)-1):
+        dTNMHdT.append((TNMH[i+1]-TNMH[i]) / (modelTemp[i+1]-modelTemp[i]))
+    res = dTNMHdT[len(modelTemp)//2-1:]
+    return np.array(res)  
+
+
+# Use only every 20th data point to reduce fitting time
+temperaturesInterpol = np.linspace(temperaturesCut[0], temperaturesCut[len(temperaturesCut)-1], 200)
+dTfdTInterpol = np.interp(temperaturesInterpol, temperaturesCut, dTfdT)
+
+ts = time.time()
+model = odr.Model(fitTNMH)
+whichFit = [1, 1, 1, 1]
+odrdata = odr.Data(temperaturesInterpol, dTfdTInterpol)
+myodr = odr.ODR(odrdata, model, beta0=p0, ifixb=whichFit, maxit=3000)
+result = (myodr.run())
+print(result.stopreason)
+p0 = result.beta
+print('TNMH heating Fit:')
+print(p0)
+# print('errors:')
+# print(result.sd_beta)
+ts = time.time()-ts
+print('Time for fit:')
+print(ts)
+tau_0, xx, beta, deltaE = p0
+
+fitResult = fitTNMH(p0, temperaturesInterpol)
+
+"""
+fig, (ax1) = P.subplots(1)
+ax1.set_xlabel('Temperature / K')
+ax1.set_ylabel('Fictive Temperature / K')
+#ax1.set_xlim(left=coordsGl[0][0])
+#ax1.set_xlim(right=coordsLq[1][0])
+#ax1.set_ylim(bottom=coordsGl[0][1]-0.1)
+#ax1.set_ylim(top=coordsLq[1][1]+0.1)
+#ax1.plot(temperatures,fictiveTemp, 'bo')
+#ax1.plot(temperatures,T_f_ns, 'r-')
+ax1.plot(temperaturesCut,dTfdT, 'bo')
+#ax1.plot(temperatures[0:5454],dTNMHdT[0:5454], 'bo')
+#ax1.plot(temperatures[5456:],dTNMHdT[5455:], 'ro')
+#ax1.plot(temperaturesModel[0:99],dTNMHdT[0:99], 'b-')
+#ax1.plot(temperaturesModel[100:199],dTNMHdT[100:199], 'r-')
+ax1.plot(temperaturesInterpol,dTfdTInterpol, 'yo')
+ax1.plot(temperaturesInterpol,fitResult, 'r-')
+P.show()
+"""
+dataOutName = os.path.splitext(str(dataName))[0] + "_dTfdT_tau.fit"
+dataOut = np.column_stack((temperaturesInterpol, dTfdTInterpol, fitResult))
+
+save = 0  # input("Save parameter to file? (yes = 1, no = 0):  ")
+if save == '1':
+    np.savetxt(dataOutName, dataOut, fmt='%1.5e', header="tau_TNMH="+str(tau_0) + "\tbeta="+str(beta) + "\tx="+str(xx) + "\tdeltaE="+str(deltaE) + "\nTemp\t\tdTfdT_data\t\tdTfdT_fit")
+    # Try to determine the heating rate from the data file name (Searching for digits followed by ".")
+    paramName = ((str(dataName)).split("_"))[0] + "_DSC_tau.param"
+    print(paramName)
+    with open(paramName, 'a') as f:
+        f.write('\n#Heating Rate \t tau_TNMH \t beta \t\t\t x \t deltaE \t Tg fictive')
+        f.write('\n')
+        f.write('%1.4e \t %1.4e \t %1.4e \t %1.4e \t %1.4e \t %1.4e' % (rate, tau_0, beta, xx, deltaE, T_g))
+
+