Dear Adel Iligan,

Superheating of metals above their melting point Tm can occur under certain circumstances and for a given material the degree of superheating varies with the heating rate and the microstructural details such as the amount of grain boundaries, of defects and of free surfaces present.

The nucleation of melt from a solid can be treated very similarly to the nuclation of crystals from a melt during cooling. In both cases nucleation may be homogeneous and/or heterogeneous. Heterogeneous nucleation generally aids nucleation and hence decreases the amount of superheating/undercooling. Heterogeneous nucleation of the melt upon heating can occur at any kind of lattice defect or imperfection (grain boundaries, dislocations, free surfaces). In a crystal with a low density of defects and low free surface area in which homogeneous nucleation prevails the melting point will be higher compared to a defect-rich crystal with many heterogeneous nucleation sites.

A potential asymmetry between superheating and undercooling is caused by the differences in the variations of the thermodynamic quantities (such as entropy) of the liquid and crystal with temperature. Various criteria for melting/crystallization have been suggested, such as equal entropies or densities of both phases at the transformation points. The review article by Mei, Lu, Progress in Materials Science 52 (2007) 1175–1262 is very helpful to get an overview.

Because the entropy, volume, etc. of the liquid and crystal vary in different ways below and above the equilibrium melting point Tm, the degrees of superheating and undercooling are typically not equal.

Dear Adel Iligan,

Superheating of metals above their melting point Tm can occur under certain circumstances and for a given material the degree of superheating varies with the heating rate and the microstructural details such as the amount of grain boundaries, of defects and of free surfaces present.

The nucleation of melt from a solid can be treated very similarly to the nuclation of crystals from a melt during cooling. In both cases nucleation may be homogeneous and/or heterogeneous. Heterogeneous nucleation generally aids nucleation and hence decreases the amount of superheating/undercooling. Heterogeneous nucleation of the melt upon heating can occur at any kind of lattice defect or imperfection (grain boundaries, dislocations, free surfaces). In a crystal with a low density of defects and low free surface area in which homogeneous nucleation prevails the melting point will be higher compared to a defect-rich crystal with many heterogeneous nucleation sites.

A potential asymmetry between superheating and undercooling is caused by the differences in the variations of the thermodynamic quantities (such as entropy) of the liquid and crystal with temperature. Various criteria for melting/crystallization have been suggested, such as equal entropies or densities of both phases at the transformation points. The review article by Mei, Lu, Progress in Materials Science 52 (2007) 1175–1262 is very helpful to get an overview.

Because the entropy, volume, etc. of the liquid and crystal vary in different ways below and above the equilibrium melting point Tm, the degrees of superheating and undercooling are typically not equal.

In polycrystalline metals and alloys the  melting starts at the grain boundaries well below the equilibrium coexistence temperature of solid and liquids phases.  As far as I remember  this temperature differential in copper is about  500 C.  I don't  think that these super heating or cooling phenomenon in bulk systems have nothing to do with the equilibrium thermodynamics arguments stated above, but solely it is related to the kinetics of the homogeneous nucleation problem, which  is even today  lacking  of any  sound theoretical treatments on the contrary to  the growth stage, where very sophisticated  non equilibrium theory is available.  One needs to do experiments on melting  similar the one performed by Late Professor Turnbull  on  small droplets of mercury  in 1948 to prove the supercooling is a fact but not fairy tail!    Regards. 

It would depend on whether the melting transition was exo or endothermic.

Dear Lawrence do you mean there are matters in the nature, which have negative heat of fusion?   May be you also mean entropy of fusion is also negative! since they are connected  by absolute temperature!! according to Max Born Best Regards.

With one known  acception is 'Helium-3 has a negative enthalpy of fusion at temperatures below 0.3 K. Helium-4 also has a very slightly negative enthalpy of fusion below 0.8 K. This means that, at appropriate constant pressures, these substances freeze with the addition of heat.[2]

My guess is here: this apparent anomalous behavior lies in the definitions of the  thermodynamic quantities at this spooky temperature range for the spooky matters, which may have even negative absolute spin or angular momentum temperatures!! 

I can also prove using the equation for the solubility of solid in liquid that if the heat of fusion would be negative the temperature of solid is greater than the fusion temperature?^Superheating?? '

Remark: Ideal Solution 'activity is replaced by the mole fraction'

Solubility  of solid in liquids:  ''Ideal solution '

Ln X2 = - Delta Hofuz /R [ 1/T-1/Tfus ]  which is negative since  x2 EQL  1,

Therefore  Delta Hofus /R [ 1/T-1/Tfus ]   > 0  Then If  Hofus > 0    T <  Tfus   Supercooling

   IF    Hofus   < 0  Then  T > Tfus      Superheating . EQD   

In the case of nonideal solutions    x2 is replaced by the activity coefficient, which is also  EQL  unity. Therefore the results will not change.

Usually, metals show premelting at surfaces and (sometimes) at grain boundaries. This means, that a thin melt layer can appear at the surface already below the bulk melting point. When the bulk melting point is approached from below, the melt layer thickness increases and diverges at the melting temperature. Hence one cannot overheat the metal, as melting will always start from surfaces and interfaces. 

There are however exceptions, and one case are {111} surfaces of lead. A crystal that is surrounded only by such surfaces can even be overheated above the bulk melting point [J. J. Metois and J. C. Heyraud, J. Phys. France 50, 3175 (1989)]. The overheating range is typically low; in this example 3K have been reached.

According to my experimental records, I noticed ONLY a difference of behaviours between grain boundaries, and free surface!!t, not a SINGLE metal behaviour.... you should think in that sense...

One shouldn't compare the behavior of surface or interface layers 2D (van der Waals & Guggenheim model)  with the bulk matrix 3D  since they are  represented by  completely different thermodynamic characteristic functions. Surface phases  involve not only bi-product of  stress and strain tensors but  also enjoy with an additonal  term, which is a double inner product of surface stress  and  strain  tensors  ( it  is replaced by area versus surface tension product in isotropic simple cases) .  The heat of fusion per mole for surface phase  might be different then the bulk phase.

But I normally expect  that the number of bonds to be relaxed (fusion) or  to be broaken (sublimation) much less then the ones occupying normal lattice sites. 

I never  compared behavior of surface with the bulk matrix 3D !!! but in my panoply of experiment, everytime I begun to consider the bulk matrix 3D surface odd surface behaviour falsed the result .... Dear tarik, people want to help you not retracing the same errors. so if you wish to give lessons, try to focus on the following: how to study, separately (in the same sample) SURFACE and BULK  behaviours..... if you suceed, I will be your voluntee student.

best wishes