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I am interested in the underlying physics of the concept of a melting point, a temperature at which an object tends to gain enough energy to break the bonds that hold it together and be in a liquid state. Or the other way around, a freezing point.

What I am interested is... Since temperature is basically a measure of the kinetic energy of particles within, when they actually start to vibrate enough they break apart. And the changes in temperature in the surrounding medium is due to them transferring heat during "impact" with the solid object, be it air or some other medium at a certain temperature.

So, if we know all that, why do we depend upon experimental data? Why isn't there some logical way to deduce what is the melting point of some matter under some variable pressure?

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""melting point, a temperature at which an object tends to gain enough energy to break the bonds that hold it together "" This is an erronous statement. When "bonds holding together breake", as a result the solid woulf vaporize! On melting, only a small part of the bonds break, the interatomar diestances increse a liitle bit just to allow some movement. Because solids theories are very coarse, one can estimate melting points at best. –  Georg Oct 29 '11 at 19:43
there are too much variables in this analysis that it might not be feasible to calculate theoretically the melting point. This is a type of macroscopic feature of matter that its always better to calculate it form experiment. –  Vineet Menon Oct 30 '11 at 15:18
""that its always better to calculate it form experiment."" Aha, "calculating from experiment". ROFL. I'd just read the thermometer. –  Georg Oct 30 '11 at 16:59
@Georg..."reading a thermometer" is a part of an experiment!!! –  Vineet Menon Oct 31 '11 at 4:50
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It is not possible to perform reliable ab-initio computations of melting phase transitions. Simple reason being that such computations need to cover the thermodynamic (large size, many particle) limit to access the loss of long rang order. We simply lack the computational resources to do so.

What is possible, is to apply semi-empirical rules to estimate melting temperatures (google "Lindemann's criterion").

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