Hallo Payal,

high elasticity (young module) means a high ratio of reset force and extension or a high potential energy in the case of extension. On the other hand, a high melting temperature corresponds to a high kinetic energy of the atoms (molecules). If you want to melt a solid the attractive forces must be overcome. So higher the elasticity, so higher the energy for melting. This is of course only a rough estimation because the strain at the melting point is different for the materials.

The relationship between elasticity and dielectric constant is me unknown. I assume, the dipolmoment which correlates with inneratomic forces is responsible for this effect. So "higher" the polarization so stronger the forces between the atoms that is elasticity correlates with dielectric constant.

Best wishes to you

R. Mitdank

Hallo Payal again,

I found the following article in nature from

Haiming Lu & Xiangkang Meng

Scientific Reports | 5:16939 | DOI: 10.1038/srep16939

Correlation between band gap, dielectric constant, Young’s modulus and melting temperature of GaN nanocrystals and their size and shape dependences

I hope, it helps

Thank you so much sir for your detailed explanation. I have gone through this article but i could not understand the physical meaning behind their correlation. One more thing i want to clarify that is greater is the Young's modulus of a solid, higher would be the potential energy needed to stretch the solid means higher would be the band gap. Am i getting the right thing? Similarly, high melting point means higher would be the energy needed for melting, greater would be the band gap? Please let me know whether i am getting the right concept or not? 

Dear Payal,

I found still a publication which could help you:

Journal of Electronic Materials, Vol. 26, No. 2, 1997

B.R. NAG Calcutta University, 92 Acharya Prafulla Chandra Road, Calcutta -700009, India

An Empirical Relation Between the Melting Point and the Direct Bandgap of Semiconducting Compounds

It is from your country, so I hope, they can better answer your questions than I.

Thank you Sir.

Hi,

In general, you might think that a high Young modulus correlates with a high potential which implies stronger forces among ions, which will also be true for the melting point. As far as the band gap is concerned, the same type of hand waving arguments may  apply....Simple thinking but I hope it helps

Thank you Sir. But, i want to know that is there any universal dependence of melting point on band gap. The papers mentioned above have correlated band gap with melting pt., Young's modulus on the basis of the size dependence of the crystal and also on the the systems having common anions. But, can we correlate band gap and melting point of any two systems?   

Sorry, I do not know the precise answer to your question...

Its ok Sir. 

Thanks.

Young's modulus and band gap are, for the most part, entirely uncorrelated.  In some specific systems, some trends might be observed as a function of some variable.  Treat these as qualitative and not as universal.

Young's modulus is related to chemical bond energies (more specifically, the pair-potentials, which are used in MD simulations), and also the crystal structure.  Band gap is a quantum-mechanical value that is the difference in energy between the valence and conduction bands of the electron orbitals.

So, sorry, but there is no universal physical relationship between the two – primarily because the two material constants are the product of differing physical phenomena/interactions.

Thank you so much sir.

Dear Payal and Mark (Zurbuchen),

at this point I have to agree with Mark. The two are really unrelated when we can accept / can use the "adiabatic approximation" (Ascrfoft, Mermin book I think) , that is we can treat atoms and electrons separately, with electrons moving in a static potential of the atoms. The situation becomes different when we allow the posasibility that the system is strongly correlated (strong interactions between the electrons and atoms), kind of analogue to Landau Fermi liquid, for example in viscous liquids. 

But these are admittedly  just speculations, so stick (at least for the time being) with Mark's explanation. 

There might be though some correlation in the case of materials with strong optical non-linearities ?!

With best regards

Petr

For such a correlation you need to restrict yourself to a certain class of materials. For example, all metals have zero band gap but can have rather low or very high melting points: for wolfram it's 3695 K (3422 °C), for gallium it's just 302.9 K (29.8 °C).

Dear Payal,

Jan-Martin Wagner's point is very relevant also. Perhaps one should start there in the search.

Petr

Thank you so much all for your valuable discussions.