# Melting point vs pressure

In my physics-class, I was told that,

"The melting point of the same substance changes under different pressure. But it can change in two different manner"

There are 2 different ways it can change:

$$(1)$$ For higher pressure , the melting point will be lower (Like water)
$$(2)$$ For higher pressure , the melting point will be higher.

Also ,

$$(1)$$ This case happens for those substances which decrease in Volume when changing from a solid to a liquid.
$$(2)$$ This case happens for those substances which increase in Volume when changing from a solid to a liquid.

I have two questions

$$(a)$$ Can someone give me some more examples of of substances for case $$(1)$$ and case $$(2)$$ . [I couldn't find any except 'water' that was told in my physics class]
$$(b)$$ Why does melting point vs pressure depend on Volume change Like this ?

• There are a variety of elements with denser liquids at the melting point. These include Si, Ge, Sb, Bi, and others. There are then a number of non-elemental materials as well. Nov 9, 2020 at 16:39
• Are you familiar with the concept that, for a phase change of a pure substance, the change in Gibbs free energy is equal to zero? If so, are you familiar with the Clapeyron equation for a phase change? Nov 9, 2020 at 17:02

(b) Among the theoretical criteria for melting, the Lindemann and Born criteria are those most frequently used as a basis to analyse the melting conditions:

• The Lindemann criterion states that melting occurs because of vibrational instability, e.g. crystals melt when the average amplitude of thermal vibrations of atoms is relatively high compared with interatomic distances. The Lindemann melting criterion is supported by experimental data both for crystalline materials and for glass-liquid transitions in amorphous materials.
• The Born criterion is based on a rigidity catastrophe caused by the vanishing elastic shear modulus, i.e. when the crystal no longer has sufficient rigidity to mechanically withstand the load.

(a) Every material has its own phase diagram where you can see how the pressure affects phase transitions. Unfortunately I don't know many such examples, however there is one interesting material GdN (Gadolinium nitride) (see image below). I've also read that carbon has similar effects under significant pressure (see image below). There are even more bizzare cases than that, for example helium (see image below). 