It is known that the melting point of metals viz. Au, Ag erc. decrease on reducing the size of the particles. I see from the published curve that the melting point of Ag which is about 960 C become incredibly smaller with the size reduction. For a size of 5 nm the the melting point of Ag is about 530 C. Incedible! But there are theories and simulation that supports this number.

Melting tempewrature of nanoparticles depend from size of particle. With decreasing size of particles, it was decreasing melting temperature. In some materials melting temperature may be 2 time less than bulk materials.

The main reason for the depression of the melting points of materials on size reduction can be understood by invoking the ratio of the surface atoms to the total number atoms of the partcle. In bulk this number is negligible whereas in small nanoparticles are are quite considerable compared to the total number. Now the bonding of the at the atoms at surface is much weaker because they do have the full coordination and there are dangling bonds. So the surace is suppoed to melt more easily than bulk. This is even more so at the edge and corner of a particle if they have any. We can easily calcultate the ratio of the surace to the total number of particles and we know the size variation of the ratio and therefore the scaling law. This scaling law is the same for the melting point. Thus the melting point of a solid decreases at first rather slowly then more rapidly and becomes zero for size zero because a single particle has no melting point any more!   

Yes, melting point depend from ratio of surface atoms to bulk. It also will depend from crystalline structure of materials. On surface part the distance between atoms are more than in central part/ Because itin heating process the probability of evaropation such atoms are higer, than in central part.

Thanks a lot Mr.Muradov and Mr.Chatterji. Your answers were really useful

Dear Nima Jafari,

The reasoning in the above answers is as far as I can see, related to Gibbs-Thomson effects and is at least partly kinetical. I dare to make a humble remark. As soon as melting has occurred in an assembly of crystalline nanoparticles at the above predicted melting temperatures, the temperature of the liquid formed shows a remarkable undercooling as compared to the bulk solidification/melting temperature. Otherwise stated, the just formed liquid is  from a thermodynamical point of view, strongly  unstable. This unstability can be annihilated by solidification via a heterogenous nucleation as provided by the remaining nanocrystallites. It might be that the behaviour of one single nanocrystallite differs from the behaviour of an assembly of nanocrystallites.

The best piece of literature for this topic is most likely the following:

"Thermodynamic theory of size dependence of melting temperature in metals" by Couchman and Jesser, Nature 1977. 

In the article, this topic is discussed in terms of the fundamental thermodynamic parameters and they support the theory with experimental data. 

Dear Nima,

Melting temperature depends upon the particle size of silver nano particles. Nano silver means Silver Nanoparticles. I think melting temperature may be just around 110-115 degree centigrade. Melting point of silver is high around 961 degree centigrade, but when silver conjugates and becomesilver nano particle as a free nanoparticle, they have a different melting temperature (usually much lower) tdue to the absence cohesive energy is lost between the nanoparticle and substrate.it is easier to break the crystal structure by applying lesser thermal agitation. So, for most nanomaterials melting pointdecreases with smaller size it is assumed.

Come with physics, Gibbs-Thomson effects, it implies that crystalline structure becomes with less in weight and electron rapid in moverment, cohesive bond is lost here and subsequently enthalpy getting down. Hence temperature slowly melts to lower critical point than the bulk crystal structure.

Ashish