Question: how to calculate the energy of crystal

[hymeme]

Dear all, I am recently dealing with crystals. There is one question which puzzles me a lot. How to calculate the energy of crystals? For example, tungsten oxide has severl polymorphs such as alpha, beta , and gamma. What is the energy difference among them. Hope you can help with this question. Thanks a lot!

 

[Vagn]

Usually, density functional theory is used to predict structures from first principles. An example for WO₃ would be this paper.

 

[hymeme]

Usually, density functional theory is used to predict structures from first principles. An example for WO₃ would be this paper.

thank you! From the paper, the value of the band gap various a lot for one specific phase. Does that mean such difference in structure is not the key factor which enfluences the energy much.(we synthesized WO3 experimentaly, but not familar with the theory. )

 

[ZapperZ]

There is a lot of ambiguity in your question.

First of all, what exactly do you mean by "energy of a crystal"? It is hard to know if you want the bonding energy of a particular crystal configuration, the electronic binding energy, etc. In fact, you thank Vagn for giving you a paper that theoretically derived the band structure of a crystal. Is the electronic band structure what you actually meant by "energy of a crystal"?

So what exactly are you looking for here?

Zz.

 

[hymeme]

ZapperZ, Thank you very much for the thoughtful reply. My question is not clear because I am not a physicist and not familiar with this area. This question occurred to me when we were synthesizing WO3 nanoparticles. At different temperature, the phase of the product is different. So I was wondering that different phase must have different energy level. I have hard time to find the right method to characterize such 'energy'. Band structure is good to know. But it will be best if there is another simple way.