Simon–Glatzel equation
   HOME

TheInfoList



OR:

The Simon–Glatzel equation is an empirical correlation describing the pressure dependence of the melting temperature of a
solid Solid is one of the State of matter#Four fundamental states, four fundamental states of matter (the others being liquid, gas, and Plasma (physics), plasma). The molecules in a solid are closely packed together and contain the least amount o ...
. The pressure dependence of the melting temperature is small for small pressure changes because the volume change during fusion or melting is rather small. However, at very high pressures higher melting temperatures are generally observed as the liquid usually occupies a larger volume than the solid making melting more thermodynamically unfavorable at elevated pressure. If the liquid has a smaller volume than the solid (as for ice and liquid water) a higher pressure leads to a lower melting point.


The equation and its variations

: T_m = T_\text \left( \frac + 1 \right)^ T_\text and P_\text are normally the temperature and the pressure of the
triple point In thermodynamics, the triple point of a substance is the temperature and pressure at which the three phases (gas, liquid, and solid) of that substance coexist in thermodynamic equilibrium.. It is that temperature and pressure at which the subli ...
, but the normal melting temperature at atmospheric pressure are also commonly used as reference point because the normal melting point is much more easily accessible. Typically P_\text is then set to 0. a and b are component-specific parameters. The Simon–Glatzel equation can be viewed as a combination of the
Murnaghan equation of state The Murnaghan equation of state is a relationship between the volume of a body and the pressure to which it is subjected. This is one of many state equations that have been used in earth sciences and shock physics to model the behavior of matter u ...
and the Lindemann law, and an alternative form was proposed by J. J. Gilvarry (1956): T_m = T_\text \left(K_0^ \frac + 1 \right)^ where K_0 is general K at P = 0, K_0^ is pressure derivative K at P = 0, \gamma is Grüneisen ratio, and f is the coefficient in Morse potential.


Example parameters

For
methanol Methanol (also called methyl alcohol and wood spirit, amongst other names) is an organic chemical and the simplest aliphatic alcohol, with the formula C H3 O H (a methyl group linked to a hydroxyl group, often abbreviated as MeOH). It is a ...
the following parameters can be obtained: The reference temperature has been ''T''ref = 174.61 K and the reference pressure ''P''ref has been set to 0 kPa. Methanol is a component where the Simon–Glatzel works well in the given validity range.


Extensions and generalizations

The Simon–Glatzel equation is a monotonically increasing function. It can only describe the melting curves that rise indefinitely with increasing pressure. It may fail to describe the melting curves with a negative pressure dependence or local maximums. A damping term that asymptotically slopes down under pressure, D(P) = \exp c(P - P_\text)/math> (''c'' is another component-specific parameter), is introduced by Vladimir V. Kechin to extend the Simon–Glatzel equationKechin V. V., J. Phys. Condens. Matter, 1995, 7, 531–535 so that all melting curves, rising, falling, and flattening, as well as curves with a maximum, can be described by a unified equation: T_m = F(P)\cdot D(P) where F(P) is the Simon–Glatzel equation (rising) and D(P) is the damping term (falling or flattening). The unified equation may be rewritten as: T_m = T_\text \left( \frac + 1 \right)^\cdot \exp c (P - P_\text)/math> This form predicts that all solids have a maximum melting temperature at a positive or (fictitious) negative pressure.


References

{{DEFAULTSORT:Simon-Glatzel equation Phase transitions Equations Thermodynamics