From 11ed3c16eb0eb63b89d6dcd225dfff245ccbe2d6 Mon Sep 17 00:00:00 2001 From: Dominik Demuth Date: Sat, 13 May 2023 19:23:15 +0200 Subject: [PATCH] add tnmh stuff --- src/nmreval/dsc/D84_10.0K-min_h.dat | 40067 ++++++++++++++++ src/nmreval/dsc/D84_10.0K-min_h_dTfdT_tau.fit | 202 + src/nmreval/dsc/D84_DSC_tau.param | 7 + src/nmreval/dsc/TNMH_v0c-tau.py | 197 + src/nmreval/dsc/TNMH_v0c-tau2.py | 333 + 5 files changed, 40806 insertions(+) create mode 100644 src/nmreval/dsc/D84_10.0K-min_h.dat create mode 100644 src/nmreval/dsc/D84_10.0K-min_h_dTfdT_tau.fit create mode 100644 src/nmreval/dsc/D84_DSC_tau.param create mode 100644 src/nmreval/dsc/TNMH_v0c-tau.py create mode 100644 src/nmreval/dsc/TNMH_v0c-tau2.py diff --git a/src/nmreval/dsc/D84_10.0K-min_h.dat b/src/nmreval/dsc/D84_10.0K-min_h.dat new file mode 100644 index 0000000..f008147 --- /dev/null +++ b/src/nmreval/dsc/D84_10.0K-min_h.dat @@ -0,0 +1,40067 @@ +# group: +# name: D84 10.0 (h) +# value: 10.0 +1.1161896727e+02 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+2.9878597684e+02 9.8890932414e-01 +2.9879364401e+02 9.9037972195e-01 +2.9879747759e+02 9.8943250462e-01 +2.9880131117e+02 9.8883066088e-01 +2.9880993673e+02 9.8857419073e-01 +2.9881377032e+02 9.9280757728e-01 +2.9881377032e+02 9.9255110714e-01 +2.9881377032e+02 9.9505762573e-01 +2.9881760390e+02 9.9376503480e-01 +2.9882143748e+02 9.9765304776e-01 +2.9882527106e+02 9.9946881917e-01 +2.9883389663e+02 1.0019753378e+00 +2.9883773021e+02 1.0051726035e+00 diff --git a/src/nmreval/dsc/D84_10.0K-min_h_dTfdT_tau.fit b/src/nmreval/dsc/D84_10.0K-min_h_dTfdT_tau.fit new file mode 100644 index 0000000..a820b99 --- /dev/null +++ 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 diff --git a/src/nmreval/dsc/D84_DSC_tau.param b/src/nmreval/dsc/D84_DSC_tau.param new file mode 100644 index 0000000..974496a --- /dev/null +++ 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 \ No newline at end of file diff --git a/src/nmreval/dsc/TNMH_v0c-tau.py b/src/nmreval/dsc/TNMH_v0c-tau.py new file mode 100644 index 0000000..18107de --- /dev/null +++ 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)) diff --git a/src/nmreval/dsc/TNMH_v0c-tau2.py b/src/nmreval/dsc/TNMH_v0c-tau2.py new file mode 100644 index 0000000..3ac2e0d --- /dev/null +++ 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)) + +