Melting-point depression
The decrease in melting temperature can be on the order of tens to hundreds of degrees for metals with nanometer dimensions.
[1][2][3] Melting-point depression is most evident in nanowires, nanotubes and nanoparticles, which all melt at lower temperatures than bulk amounts of the same material.
The melting temperature of a nanoparticle decreases sharply as the particle reaches critical diameter, usually < 50 nm for common engineering metals.
[1][2][4] Melting point depression is a very important issue for applications involving nanoparticles, as it decreases the functional range of the solid phase.
Nanoparticles are currently used or proposed for prominent roles in catalyst, sensor, medicinal, optical, magnetic, thermal, electronic, and alternative energy applications.
[7][8] The melting temperature is estimated from the beam intensity, while changes in the diffraction conditions to indicate phase transition from solid to liquid.
This method allows direct viewing of nanoparticles as they melt, making it possible to test and characterize samples with a wider distribution of particle sizes.
More recently, researchers developed nanocalorimeters that directly measure the enthalpy and melting temperature of nanoparticles.
[4] Nanocalorimeters provide the same data as bulk calorimeters, however, additional calculations must account for the presence of the substrate supporting the particles.
A narrow size distribution of nanoparticles is required since the procedure does not allow users to view the sample during the melting process.
The increased surface-to-volume ratio means surface atoms have a much greater effect on the chemical and physical properties of a nanoparticle.
However, recent work indicates the melting point of semiconductor and covalently bonded nanoparticles may have a different dependence on particle size.
Researchers have demonstrated that Equation 3 more accurately models melting point depression in covalently bonded materials.
Three of the four models detailed below derive the melting temperature in a similar form using different approaches based on classical thermodynamics.
If the LDM is true, a solid nanoparticle should function over a greater temperature range than other models predict.
Where: σsv=solid-vapor interface energy The liquid shell nucleation model (LSN) predicts that a surface layer of atoms melts prior to the bulk of the particle.
The distinct intersection of the potentials means the LSN predicts a sharp, unmoving interface between the solid and liquid phases at a given temperature.
The exact thickness of the liquid layer at a given temperature is the equilibrium point between the competing Landau potentials.
Where: d0=atomic diameter The liquid nucleation and growth model (LNG) treats nanoparticle melting as a surface-initiated process.
The model calculations show that the liquid phase forms at lower temperatures for smaller nanoparticles.
Once the liquid phase forms, the free energy conditions quickly change and favor melting.
The bond-order-length-strength (BOLS) model employs an atomistic approach to explain melting point depression.
The BOLS model calculates the melting temperature for individual atoms from the sum of their cohesive bonds.
The BOLS model and the core–shell structure have been applied to other size dependencies of nanostructures such as the mechanical strength, chemical and thermal stability, lattice dynamics (optical and acoustic phonons), Photon emission and absorption, electronic colevel shift and work function modulation, magnetism at various temperatures, and dielectrics due to electron polarization etc.
Quantitative information, such as the energy level of an isolated atom and the vibration frequency of individual dimer, has been obtained by matching the BOLS predictions to the measured size dependency.
Facets, edges and deviations from a perfect sphere all change the magnitude of melting point depression.
Equation 7 gives a general shape-corrected formula for the theoretical melting point of a nanoparticle-based on its size and shape.
Where: c=materials constant The shape parameter is 1 for a sphere and 3/2 for a very long wire, indicating that melting-point depression is suppressed in nanowires compared to nanoparticles.
However, measurement of the properties of a freestanding nanoparticle remains impossible, so the extent of the interactions cannot be verified through an experiment.
In fact it, has been shown that size-induced instability of Fe-C mixtures represents the thermodynamic limit for the thinnest nanotube that can be grown from Fe nanocatalysts.
