Added Appendix with calculation of modulus with higher-order interaction, made figure bigger.

1 files changed, 38 insertions, 27 deletions

diff --git a/fig-stiffnesses.gplot b/fig-stiffnesses.gplot
index 24d4e17..c91d0b8 100644
--- a/fig-stiffnesses.gplot
+++ b/fig-stiffnesses.gplot
@@ -8,13 +8,21 @@ cc4 = "#d41159"
 
 Tc = 17.26
 
-a1 = 71.1212
-b1 = 0.0104105
-c1 = 0.00378087
-d1 = 6.2662
+a1 = 71.13597475161484
+b1 = 0.010425748328804992
+c1 = 1665.064389018724
+d1 = 6.283065722894796
+e1 = 14.579664883988315
 
 C10(T) = a1 - b1 * T
-C1(T) = C10(T) / (1 + d1 / (1 + c1 * abs(T - Tc)) / C10(T))
+C1(T) = C10(T) / (1 + 1 / (1 / d1 + abs(T - Tc) / c1) / C10(T))
+C11(T) = C10(T) \
+  + e1**2 / (2 * C10(T)) \
+  + e1**2 * ((T - Tc) / c1) / 12 \
+  - e1**2 * (9 * C10(T) + d1) / (6 * C10(T) * (9 * C10(T) + d1 + C10(T) * d1 * (T - Tc) / c1)) \
+  + d1 * (C10(T) + d1) * (12 * C10(T)**2 + 5 * e1**2) / (12 * C10(T) * ((C10(T) + d1) + C10(T) * d1 * (T - Tc) / c1)**2) \
+  - (24 * C10(T)**2 * d1 + (4 * C10(T) + 9 * d1) * e1**2) / (12 * C10(T) * (C10(T) + d1 + C10(T) * d1 * (T - Tc) / c1))
+C12(T) = T < Tc ? C11(T) : C1(T)
 
 a2 = 144.345
 b2 = 0.019492
@@ -22,11 +30,11 @@ c2 = 120.462
 
 C20(T) = a2 - b2 * T**2 / (c2 + T)
 
-set terminal epslatex size 8.68cm, 6.7cm standalone header \
+set terminal epslatex size 18.00cm, 11.12cm standalone header \
   '\usepackage{xcolor}\definecolor{mathc3}{HTML}{1a85ff}\definecolor{mathc4}{HTML}{d41159}'
 set output "fig-stiffnesses.tex"
 
-set multiplot  layout 2, 2  margins 0.1, 0.88, 0.125, 0.99  spacing 0.01, 0.01
+set multiplot  layout 2, 2  margins 0.075, 0.915, 0.1, 0.99  spacing 0.01, 0.01
 
 set nokey
 
@@ -35,10 +43,10 @@ set mxtics 2
 set mx2tics 2
 set mytics 2
 set my2tics 2
-set format y '\tiny $%1.f$'
-set format y2 '\tiny $%.1f$'
-set format x '\tiny $%.0f$'
-#set format x2 '\tiny $%.0f$'
+set format y '\scriptsize $%1.f$'
+set format y2 '\scriptsize $%.1f$'
+set format x '\scriptsize $%.0f$'
+#set format x2 '\scripsize $%.0f$'
 set format x2 ''
 
 set style rect back fc rgb cc2l
@@ -52,44 +60,47 @@ set x2tics 50, 50, 250 offset 0,-0.5 mirror
 #set x2label '\tiny $T / \mathrm K$' offset 0,-1.0
 set xrange [0:300]
 
-set title '(a)' offset 5,-2.7
-set ylabel '\scriptsize $C_{\mathrm{B_{2\mathrm g}}} / \mathrm{GPa}$' offset 4.3
+set title '(a)' offset 12,-2.7
+set ylabel '$C_{\mathrm{B_{2\mathrm g}}} / \mathrm{GPa}$' offset 3
 set yrange [140:145]
 set ytics 141,1,144 offset 0.5 mirror
-plot "data/c66.dat" using 1:(100 * $2) with lines lw 3 lc rgb cc3, \
+plot "data/c66.dat" using 1:(100 * $2) with lines lw 6 lc rgb cc3, \
      C20(x) dt 3 lw 4 lc rgb cc4
 
-set title '(b)' offset 5,-2.7
+set title '(b)' offset 12,-2.7
 unset ylabel
-set y2label '\scriptsize $C_{\mathrm{B_{1\mathrm g}}} / \mathrm{GPa}$' offset -5 rotate by -90
+set y2label '$C_{\mathrm{B_{1\mathrm g}}} / \mathrm{GPa}$' offset -4 rotate by -90
 set yrange [65.05:65.7]
 set y2tics 62.1,0.1,65.6 offset -0.5 mirror
-plot "data/c11mc12.dat" using 1:(100 * $2) with lines lw 3 lc rgb cc3, \
+plot "data/c11mc12.dat" using 1:(100 * $2) with lines lw 6 lc rgb cc3, \
+     C12(x) dt 1 lw 2 lc black, \
      C1(x) dt 3 lw 4 lc rgb cc4
 
 
+
 unset x2label
 unset x2tics
 
-set title '(c)' offset 5,-2.7
-set xlabel '\scriptsize $T / \mathrm K$\\~' offset 0,0.78
+set title '(c)' offset 12,-2.7
+set xlabel '$T / \mathrm K$\\~' offset 0,0.5
 set xtics 50, 50, 250 offset 0,0.5 mirror
 unset y2tics
 set ytics 63,1,72
 unset y2label
-set ylabel '\scriptsize $\textcolor{mathc3}{C_{\mathrm{B_{1\mathrm g}}}},\textcolor{mathc4}{C_{\mathrm{B_{1\mathrm g}}}^0} / \mathrm{GPa}$' offset 3.7
+set ylabel '$\textcolor{mathc3}{C_{\mathrm{B_{1\mathrm g}}}},\textcolor{mathc4}{C_{\mathrm{B_{1\mathrm g}}}^0} / \mathrm{GPa}$' offset 3
 
 set yrange [64.5:71.5]
-plot "data/c11mc12.dat" using 1:(100 * $2) with lines lw 3 lc rgb cc3, \
+plot "data/c11mc12.dat" using 1:(100 * $2) with lines lw 6 lc rgb cc3, \
      C10(x) dt 3 lw 4 lc rgb cc4
 
 set ylabel ''
-set y2label '\scriptsize $[C^0(C^0/C - 1)]^{-1} / \mathrm{GPa}^{-1}$' offset -5.5 rotate by -90
+set y2label '$\Big[C^0_{\mathrm{B_{1\mathrm g}}}(C^0_{\mathrm{B_{1\mathrm g}}}/C_{\mathrm{B_{1\mathrm g}}} - 1)\Big]^{-1} / \mathrm{GPa}^{-1}$' offset -3 rotate by -90
 
-set title '(d)' offset 5,-2.7
-set format y2 '\tiny $%0.2f$'
-set format y '\tiny $%0.2f$'
+set title '(d)' offset 12,-2.7
+set format y2 '\scriptsize$%0.2f$'
+set format y '\scriptsize$%0.2f$'
 set yrange [0.12:0.38]
 set y2tics 0.15,0.05,0.39 offset -0.7 mirror
-plot "data/c11mc12.dat" using 1:(1 / (C10($1)*(C10($1) / (100 * $2) - 1))) with lines lw 3 lc rgb cc3, \
-     1/(C10(x) * (C10(x) / C1(x) - 1)) dt 3 lw 4 lc rgb cc4
+plot "data/c11mc12.dat" using 1:(1 / (C10($1)*(C10($1) / (100 * $2) - 1))) with lines lw 6 lc rgb cc3, \
+     1/(C10(x) * (C10(x) / C12(x) - 1)) dt 1 lw 2 lc black, \
+     1/(C10(x) * (C10(x) / C1(x) - 1)) dt 2 lw 4 lc rgb cc4