SuperHeating and Phase Coexistence in NaNoparticles

1
SuperHeating and Phase Coexistence in
NaNoparticles

• Hasan Kurt

2
Introduction

• The thermodynamics of small systems
• Classical example
• Melting Point of Free Nanoparticles
• Exceptions
• Lead and Gallium

3
Superheating (SM)

• Surface Melting (below Tc)
• A liquid layer on the surface is generally
  observed, thickness diverges logarithmically as T
  ? Tc

4
Nonmelting (NM)

• For low energy metal surfaces
• Pb (111)
• Al (111) (100)
• Au (111)
• Surface melting is not observed and often surface
  can be heated above Tc

5
Isolated Nanoparticle

• The internal relaxation time is less than the
  time for equilibration with the environment.
• Such a particle will follow a microcanonical
  caloric curve, where the transition between solid
  and liquid phases will generally occur via
  solid-liquid phase coexistence, even if the
  particle has only NM facets.

6
Isolated Nanoparticle

• In a small particle, the cost of forming the
  solid-liquid interface during phase coexistence
  is comparable to its total energy.
• This can lead to
• S-bend in the microcanonical caloric curve,
• negative heat capacities,
• the avoidance of phase coexistence entirely, or
• dynamic coexistence between fully solid and fully
  liquid states.

7
Isolated Nanoparticle

• Phase coexistence in clusters with NM facets will
  be particularly unfavorable.
• Coexistence has been observed in molecular
  dynamics simulations of such clusters.
• The transition between the solid and solid-liquid
  coexisting state is ?rst-order rather than
  continuous

8
MCD Theory

• Microcanonical Critical Droplet Theory
• Model Geometries for coexisting clusters
• Total Surface Energy

9
MCD Theory

• Any coexisting state in a cluster with NM
  surfaces will be unstable for hlth

10
MCD Theory
Assuming that the density is unchanged at
melting. es and el are the energy densities of
the solid and liquid respectively.
11
MCD Theory

• The entropy density of the solid region.
• sl(el) is the entropy density of liquid.
• c is the heat capacity at Tc.

12
MCD Theory

• 3.5nm Al cluster (9590 atoms)
• ?? -2.3 meV/Å
• ??/ ?SL -0.23
• h 8Å
• on set of coexistence
• h19.8 Å gt h

13
MCD Theory Results

• The cluster does not start to melt until TgtTC.
• In SM case, a solid cluster begins to melt below
  Tc because it can convert an increment of surface
  energy into latent heat.
• In NM case, the cluster will not melt until it is
  favorable to melt a finite volume with h gt h.

14
MCD Theory Results

• MCD theory predicts that the superheating effect
  will peak at a cluster radius of 5.5nm.
• As radius increases, the melting temperature
  converges to Tc.
• With previous parameters, for R lt 3.4nm,
  coexisting state is always unstable.
• Model also neglects the size dependence of
  properties such as the latent heat of melting.

15
Conclusion

• Theoretical evidence for superheating in
  nanoclusters with NM surface facets in the
  microcanonical ensemble.
• The superheating is associated with a minimum
  stable liquid volume, which requires first order
  transition at onset of Tm.

16
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