Melting Curves

Simple Simon Curves

Simon curves give the melting curve pressure in a form like

$$p=p_0+a\left[\left(\frac{T}{T_0}\right)^c-1\right]$$

The values here are from Larry E. Reeves, Gene J. Scott, and Stanley E. Babb, Jr., "Melting Curves of Pressure-Transmitting Fluids", The Journal Of Chemical Physics, v. 40, n. 12, 15 June 1964.

Fluid	Formula	$T_0$ [K]	a [Pa]	c	$p_0$ [Pa]
Propane	$C_3H_8$	85.3	7.180e8	1.283	0.0
n-Butane	n-$C_4H_{10}$	134.5	3.634e8	2.210	0.0
n-Pentane	n-$C_5H_{12}$	143.5	6.600e8	1.649	0.0
Isobutane-I	i-$C_4H_{10}$-I	128.2	4.246e8	2.478	0.0
Isobutane-II	i-$C_4H_{10}$-II	160.2	7.942e8	1.571	3.265e8
Isopentane	i-$C_5H_{12}$	112.5	5.916e8	1.563	0.0
Ethylene	$C_2H_{4}$	103.8	3.275e8	1.811	0.0
Propylene-I	$C_3H_{6}$-I	86.0	3.196e8	2.821	0.0
Propylene-II	$C_3H_{6}$-II	109.6	3.064e8	3.871	4.450e8
Refrigerant R12	$CCl_{2}F_2$	117.9	3.288e8	2.231	0.0

Values from Penoncello, IJT, 1995 :

Fluid	Formula	$T_0$ [K]	a [Pa]	c	$p_0$ [Pa]
Cyclohexane	$C_6H_{12}$	279.7	383.4e6	1.41	0.0

Krypton and Xenon

For Krypton and Xenon, the form of the correlation from Michels and Prins, Physica, 1962 is $$\log_{10}(p+A) = C\log_{10} T+B$$

Start with the Reeves form: $$p=p_0+a\left[\left(\frac{T}{T_0}\right)^c-1\right]$$ Left hand side $$p-p_0+a=a\left(\frac{T}{T_0}\right)^c$$ log base 10 both sides, $T_0$ is 1 $$\log_{10}(p-p_0+a)=c\log_{10}T+\log_{10}a$$

Thus from Michels, $a = 10^{B}$, $c = C$, $p_0 = A-10^B$. $p_0$ and $a$ must be multiplied by 101325 to convert to Pa

Carbon Monoxide

For carbon monoxide, the curve comes from Barreiros, JCT, 1982: $$p/MPa = -142.941+0.0195608(T/K)^{2.10747}$$ or in Pa $$p/Pa = -142941000+19560.8(T/K)^{2.10747}$$ with $T_0$ is 1, Reeves form is $$p=p_0+a\left(T^c-1\right)=p_0-a+aT^c$$

Ammonia

For ammonia, the melting line comes from Haar and Gallagher, 1978 $$\theta = 195.48\exp(4\times 10^{-5}\cdot p/atm )$$ where $\theta$ is the temperature in K or alternatively $$p/Pa = \frac{101325}{4\times 10^{-5}}\ln\frac{T/K}{195.48} = 2533125000\ln\frac{T/K}{195.48}$$

Oxygen and Parahydrogen

For oxygen and parahydrogen, melting curves of the form $$p = A + BT^C$$ with T in K, p in MPa. With $T_0$ of 1, Reeves form is $$p=p_0-a+aT^c$$ Thus $a=B$, $c = C$, $p_0=A+B$, multiply A and B by 1e6 as given

Expanded Simon Curves

$$\frac{p_m}{p_t} - 1= \sum_i{a_i\left[\left(\frac{T}{T_c}\right)^{t_i}-1\right]}$$

Fluid	Reference	$T_t$ [K]	$T_{max}$ [K]	$p_t$ [Pa]	$a_1$	$t_1$	$a_2$	$t_2$	$a_3$	$t_3$
Argon	Tegeler, 1999	83.8058	??	68891	-7476.2665	1.05	9959.0613	1.275
Ethane	Buecker and Wagner, 2006	90.368	195	1.14	2.23626315e8	1.0	1.05262374e8	2.55
n-Butane	Buecker and Wagner, 2006	134.895	??	0.653	5.585582364e8	2.206
Isobutane	Buecker and Wagner, 2006	113.73	??	0.0219	1.953637130e9	6.12
Nitrogen	Span, 2000	63.151	??	12523	12798.61	1.78963
Fluorine	de Reuck, 1990	53.4811	??	252	988043.478261	2.1845
Methane	Setzmann, 1991	90.6941	??	11696	2.47568e4	1.85	-7.36602e3	2.1
Ethylene-I	Smukala, 2000	103.989	110.369	122.65	2947001.84	2.045
Ethylene-II	Smukala, 2000	110.369	???	46.8e6	6.82693421	1.089

$$\frac{p_m}{p_t} - 1= \sum_i{a_i\left[\left(\frac{T}{T_c}\right)-1\right]^{t_i}}$$

Fluid	Reference	$T_t$ [K]	$T_{max}$ [K]	$p_t$ [Pa]	$a_1$	$t_1$	$a_2$	$t_2$	$a_3$	$t_3$
Methanol	de Reuck, 1993	175.61	??	0.187	5.330770e9	1	4.524780e9	3/2	3.888861e10	4
Carbon dioxide (CO2)	Span, 1996	216.592	??	51795	1955.5390	1	2055.4593	2

Water

For water, from http://www.iapws.org/relguide/MeltSub2011.pdf

$$\rho/\rho_{0}=a_i\left(\frac{T}{T_0}-1\right)^{c_i}$$

ln of both sides $$\ln(\rho/\rho_{0})=c_i\ln\left(\frac{T}{T_0}-1\right)+\ln a_i$$