From 37a877a52edd1ea14f2c0d2e8775a05eb02f2218 Mon Sep 17 00:00:00 2001
From: Anton Akhmerov <anton.akhmerov@gmail.com>
Date: Wed, 25 Apr 2018 12:23:18 +0200
Subject: [PATCH] start migrating heat capacity plots
---
code/heat_capacity.py | 56 ++++++++++++++++
docs/figures/zeropoint.svg | 129 -------------------------------------
2 files changed, 56 insertions(+), 129 deletions(-)
create mode 100644 code/heat_capacity.py
delete mode 100644 docs/figures/zeropoint.svg
diff --git a/code/heat_capacity.py b/code/heat_capacity.py
new file mode 100644
index 00000000..ebd054fa
--- /dev/null
+++ b/code/heat_capacity.py
@@ -0,0 +1,56 @@
+import matplotlib
+matplotlib.use('agg')
+from matplotlib import pyplot
+
+import numpy as np
+from scipy.optimize import curve_fit
+from scipy.integrate import quad
+
+import common
+from common import draw_classic_axes
+
+
+# Data from Einstein's paper
+T = [222.4, 262.4, 283.7, 306.4, 331.3, 358.5, 413.0, 479.2, 520.0, 879.7, 1079.7, 1258.0],
+c = [0.384, 0.578, 0.683, 0.798, 0.928, 1.069, 1.343, 1.656, 1.833, 2.671, 2.720, 2.781]
+
+
+def c_einstein(T, T_E=1):
+ x = T_E / T
+ return 3 * x**2 * np.exp(x) / (np.exp(x) - 1)**2
+
+
+def integrand(y):
+ return y**4 * np.exp(y) / (np.exp(y) - 1)**2
+
+
+@np.vectorize
+def c_debye(T, T_D=1):
+ x = T / T_D
+ return 9 * x**3 * quad(integrand, 0, 1/x)[0]
+
+
+def plot_einstein():
+ T = np.linspace(0.01, 3, 500)
+ fig, ax = pyplot.subplots()
+
+ ax.plot(T, c_einstein(T)/3)
+ ax.fill_between(T, c_einstein(T)/3, 1, alpha=0.5)
+
+ ax.set_ylim(bottom=0, top=1.2)
+ ax.set_xlabel('$T$')
+ ax.set_ylabel(r'$\omega$')
+ ax.set_xticks([1])
+ ax.set_xticklabels([r'$\hbar \omega/k_B$'])
+ ax.set_yticks([1])
+ ax.set_yticklabels(['$k_B$'])
+ pyplot.hlines([1], 0, 3, linestyles='dashed')
+ draw_classic_axes(ax)
+ pyplot.savefig('zeropoint.svg')
+
+def main():
+ os.chdir('docs/figures')
+ plot_einstein()
+
+if __name__ == "__main__":
+ main()
diff --git a/docs/figures/zeropoint.svg b/docs/figures/zeropoint.svg
deleted file mode 100644
index 382274fc..00000000
--- a/docs/figures/zeropoint.svg
+++ /dev/null
@@ -1,129 +0,0 @@
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