状態方程式

  V_0 = V_{(T = T_0, P=0)}, \\ V = V_{(T = T_0, P)} \\  K_0 = K_{(T=T_0, P=0)}, K'_0 = (\partial K_0 / \partial P)_T,K''_0 = (\partial^2 K_0 / \partial P^2)_T \\  a=\left(\cfrac{V_0}{V}\right)^{1/3} \\
とすると、


2nd-order Birch-Murnaghan
  P_{(T=T_0, V)} = \cfrac{3K_0}{2}  \left( \cfrac{V_0}{V} \right)^{5/3}  \left[ \left( \cfrac{V_0}{V} \right)^{2/3} - 1 \right]  = \cfrac{3K_0 }{2} \left\{a^5 ( a^2 - 1)\right\}


3rd-order Birch-Murnaghan
  P_{(T=T_0, V)} = \cfrac{3K_0}{2}  \left( \cfrac{V_0}{V} \right)^{5/3}  \left[ \left( \cfrac{V_0}{V} \right)^{2/3} - 1 \right]  \left[ 1 + \cfrac{3}{4} (K'_0-4) \left\{ \left(\cfrac{V_0}{V} \right)^{2/3} -1 \right\} \right]\\ \  = \cfrac{3K_0}{2} \left\{a^5 ( a^2 - 1)\right\} \left\{ 1 + \cfrac{3}{4} (K'_0-4) (a^2 -1) \right\}


4th-order Birch-Murnaghan
  P_{(T=T_0, V)} = \cfrac{3K_0}{2}  \left( \cfrac{V_0}{V} \right)^{5/3}  \left[ \left( \cfrac{V_0}{V} \right)^{2/3} - 1 \right]  \left[  1 +  \cfrac{3}{4} (K'_0-4) \left\{ \left(\cfrac{V_0}{V} \right)^{2/3} -1 \right\} +  \cfrac{9K_0 K''_0 + 9{K'_0}^2 - 63K'_0 + 143}{24} \left\{ \left(\cfrac{V_0}{V} \right)^{2/3} -1 \right\}^2  \right]\\ \  = \cfrac{3K_0}{2} \left\{a^5 ( a^2 - 1)\right\} \left\{ 1 + \cfrac{3}{4} (K'_0-4) (a^2 -1)  + \cfrac{9K_0 K''_0 + 9{K'_0}^2 - 63K'_0 + 143}{24} (a^2 -1)^2 \right\}


T-dependence-Birch Murnaghan
  V_{(T,P=0)} = V_{(T_0, P=0)} \exp{\displaystyle\int_{T_0}^T a + b T^2+c/T^2 dT}\\  K_{(T,P=0)} =K_{(T_0, P=0)} + (\partial K_{(T,P=0)}/ \partial T) (T-T_0)


Vinet
  P_{(T=T_0, V)} = 3K_0  \left(\cfrac{V}{V_0}\right)^{-2/3}  \left\{ 1- \left(\cfrac{V}{V_0}\right)^{1/3} \right\}  \exp \left[ \cfrac{3}{2} (K'_0-1) \left\{ 1- \left(\cfrac{V}{V_0}\right)^{1/3} \right\} \right] \\ \  = 3K_0 a^{2} \left\{ 1- 1/a \right\}  \exp \left[ \cfrac{3}{2} (K'_0-1) \left( 1- 1/a \right) \right]


Mie-Grüneisen
  \gamma = \gamma_0 \left( \cfrac{V}{V_0}\right)^q, \ \ \theta = \theta_0 \exp \left( \cfrac{\gamma_0-\gamma}{q} \right)\\  P_{th} =P_{(T, V)} - P_{(T=T_0, V)}= \cfrac{9nz \gamma R} {N_A V \theta^3}  \left\{  T^4 \displaystyle\int_0^{\theta/T} \cfrac{z^3}{\exp{(z)}-1} dz  - T_0^4 \displaystyle\int_0^{\theta/T_0} \cfrac{z^3}{\exp{(z)}-1} dz  \right\} \ \ \ \ {\rm [Pa]}  \\ \\  R:{\rm\ Gas\ constant, 8.314 4621(75) [N\ m\ K^{-1}\ mol^{-1}] }\\  N_A:{\rm\ Avogadro\ constant, 6.02214129(27) \times 10^{23} [mol^{-1}]}\\  z:{\rm\ Number\ of\ formula\ in\ unit\ cell}\\  n:{\rm\ Atoms\ per\ formula}\\  T_0:{\rm\ Standard\ temperature [K]}\\  T:{\rm\ Target\ temperature\ [K]}\\  V_0:{\rm\ Standard\ unit\ cell\ volume\ [m^3]}\\  V:{\rm\ Target\ unit\ cell\ volume\ [m^3]}\\  \theta_{0}:{\rm\ Debye\ Temperature\ at\ standard\ volume\ [K]}\\  \gamma_{0}:{\rm\ Gruneisen\ parameter\ at\ standard\ volume}\\  q:{\rm\ Volume\ dependence\ of\ Gruneisen\ parameter}\\


Pt
  \begin{array}{ccccccccccc}  {\rm\ Author(s) } & K_0 & K'_0 & z & n &T_0\ [K]& V_0\ [A^3]& \theta_0\ [K]&\gamma_0 & q & comment\\  \hline\hline  {\rm\ Matsui\ et\ al.\ (2009)} &273 &5.20 & 4 & 1 & 300 & 60.38 & 230 & 2.70 & 1.10 &V+M\\  {\rm\ Fei\ et\ al.\ (2007)} &277 &5.08(2) & 4 & 1 & 300 & 60.38 & 230 & 2.72(3) & 0.5 &V+M\\  {\rm\ Zha\ et\ al.\ (2008)} &273.5(10) &4.70(6) & 4 & 1 & 300 & 60.38 & 230 & 2.75(3) & 0.25(V/V_0) &V+M\\  \hline  \end{array}


NaCl B2
  \begin{array}{ccccccccccc}  {\rm\ Author(s) } & K_0 & K'_0 &z &n &T_0\ [K]& V_0\ [A^3]& \theta_0\ [K]&\gamma_0 & q & comment \\  \hline\hline  {\rm\ Sakai\ et\ al.\ (2009)} &47.00(46) &4.10(2) & - & - & - & 37.73(4.05)& - & - & - & 3BM \\  {\rm\ Sakai\ et\ al.\ (2009)} &40.40(54) &5.04(4) & - & - & - & 37.73(4.05)& - & - & - & V \\  {\rm\ Ueda\ et\ al.\ (2008)^1} &28.45(31) &5.16(4) & - & - & 300 & 41.115 & - & - & - & V \\  \hline  \end{array}\\  1: Vinet + (\partial P/ \partial T)(T-300), \partial P/ \partial T = 0.00468(4)


NaCl B1
  \begin{array}{cccccccccccc}  {\rm\ Author(s) } & K_0 & K'_0 & K''_0 & z & n &T_0\ [K]& V_0\ [A^3]& \theta_0\ [K]&\gamma_0 & q & comment \\  \hline\hline  {\rm\ Matsui\ et\ al.\ (2012)} &23.7 &5.14(5) &-0.392(21) & 4 & 2 & 300 & - & 279 & 1.56 & 0.96 & 4BM+V \\  {\rm\ Decker\ (1971)^1} &23.70(1) &4.91(1) &-0.267(2) & 4 & 2 & 300 & - & 279 & 1.59 & 0.93 & 4BM+V \\  \hline  \end{array}\\  {\rm\ 1:\ Recalculated\ by\ Matsui\ et\ al.\ (2012)}


Al2O3
  \begin{array}{cccccccccccc}  {\rm\ Author(s) } & K_0 & K'_0 & \partial K_{(T,P=0)}/ \partial T & a & b & c &T_0\ [K]& V_0\ [cm^3/mol]& comment \\  \hline\hline  {\rm\ Dubrovinsky\ et\ al.\ (1998)} &258(2) &4.88(4) &-0.020 & 2.6\times10^{-5} & 1.81(9)\times10^{-9} & -0.67 &300 & 25.59(2) & T-dependence-BM \\  \hline  \end{array}\\


Diamond
  \begin{array}{cccccccccccc}  {\rm\ Author(s) } & K_0 & K'_0 & V_0\ [cm^3/mol]& comment \\  \hline\hline  {\rm\ Occelli\ et\ al.\ (2003)} &446(1) &3.0(1) & 3.4170(8) & 3BM \\  \hline  \end{array}\\