Melting points of finite-sized materials

[wangasu]

Hi, does anybody know why the melting points of materials drop down when its size gets smaller down to nano-scale? For a nano particle set in another high-melting-point material, how does its Tm go?

 

[lalbatros]

probably linked with surface tension effects

Fine materials thermodynamics must take surface energy into account.
This leads to surface tension and many other effects.

But unfortunately I cannot tell more. Try to find books on materials thermodynamics.

 

[Gokul43201]

Hi, does anybody know why the melting points of materials drop down when its size gets smaller down to nano-scale?

Roughly speaking, the surface to volume ratio being high for a cluster makes it melt at a lower temperature. This is true of most metals and non-metallic isolated clusters that have been studied, except for tin and gallium, which exhibit the reverse behavior. There is as yet (I'm not up to date on this, but as of a couple yrs ago) no theoretical basis for this anomaly in Sn and Ga..

For a nano particle set in another high-melting-point material, how does its Tm go?

Most measurements are done on surface deposited nanoparticles (since these are easier to study) but even in bulk embedded clusters the depression of melting point, T(bulk) - Tm , is inversely proportional to the cluster radius. The reason for the lowering of Tm in bulk embedded clusters is simply that large mismatch at the interface leads to poor bonding between the cluster and the matrix, thereby making the interface susceptible to melting just like a surface is.

 

[wangasu]

thanks, lalbatros and Gokul43201, the lowering of melting point in small-size materials reminds me of the cases in binary alloys, where the eutectic point is invariably lower than those of the two pure components. i guess it might follows the same explanation. Anyway, I have a feeling that, so far, the explanations largely stay in phenomenology and thermodynamic discussion. it might be more interesting to continue to ask why the increasing effect of free surface or mismatched interface leads to the lowing of Tm? do you have any idea about it?

 

[Gokul43201]

it might be more interesting to continue to ask why the increasing effect of free surface or mismatched interface leads to the lowing of Tm? do you have any idea about it?

This is actually well understood and is, in fact not exactly as you (or I, previously) have stated it.

For one thing, there usually is not a distinct Tm (just like in a eutectic), and instead there is a two phase region bounded by a solidus below and a liquidus above (particularly in the smaller cluster sizes).

Second, the melting is often parametrized in terms of the mobilities in the atoms. Surface/interface atoms have higher mobilities than interior atoms, so very often you see something called "surface melting".

There's more stuff happening here than I've bothered to keep myself familiar with, but I'm sure you will find good references if you hunt around some. I know there have been tons of DFT-based calculations that do a reasonable job of predicting mobilities and thermodynamic behavior - but there really isn't much of an intuitive understanding to be gained from them.

The anomalous behavior observed in Ga in not more than a couple of years old, and as yet, I don't think there have been measurements made on several elements.