Melting Temperature Of Nanocrystals Research Articles

Gibbs free energy approach to calculate the thermodynamic properties of copper nanocrystals

Based on the thermodynamic and thermophysical properties of bulk materials, Gibbs free energy for nanocrystals is obtained and used to study the size-dependent melting point depression phenomenon. On the basis of size effects on the melting temperature of nanocrystals, thermodynamic properties of Cu nanocrystals, such as the specific heat capacity, the Debye temperature and the diffusion activation energy are investigated. Conversely, reliable predictions of these thermodynamic properties further verify the proposed approach.

Size Dependence of Optical Properties in Semiconductor Nanocrystals

An extension of the classic thermodynamic theory to nanometer scale has generated a new interdisciplinary theory - nanothermodynamics. It is the critical tool for the investigation of the size-dependent physicochemical properties in nanocrystals. A simple and unified nanothermodynamic model for the melting temperature of nanocrystals has been established based on Lindemann’s criterion for the melting, Mott’s expression for the vibrational melting entropy, and Shi’s model for the size dependence of the melting point. The developed model has been extensively verified in calculating a variety of size- and dimensionality-dependent phase transition functions of nanocrystals. In this work, such a model was extended to explain the underlying mechanism behind the bandgap energy enhancement and Raman red shifts in semiconductor nanocrystals by (1) investigating the crystal size r, dimensionality d, and constituent stoichiometry x dependences of bandgap energies Eg in semiconductor quantum dots (QDs) and quantum wires (QWs); and (2) revealing the origin of size effect on the Raman red shifts in low dimensional semiconductors by considering the thermal vibration of atoms. For Eg, it is found that: (1) Eg increases with a decreasing r for groups IV, III-V and II-VI semiconductors and the quantum confinement effect is pronounced when r becomes comparable to the exciton radius; (2) the ratio of Eg(r, d)QWs/Eg(r, d)QDs is size-dependent, where Eg(r, d) denotes the change in bandgap energy; (3) the crystallographic structure (i.e. zinc-blende and wurtzite) effect on Eg of III-V and II-VI semiconductor nanocrystals is limited; and (4) for both bulk and nanosized III-V and II-VI semiconductor alloys, the composition effects on Eg are substantial, having a common nonlinear (bowing) relationship. For the Raman red shifts, the lower limit of vibrational frequency was obtained by matching the calculation results of the shifts with the experimental data of Si, InP, CdSe, CdS0.65Se0.35, ZnO, CeO2, as well as SnO2 nanocrystals. It shows that: (1) the Raman frequency (r) decreases as r decreases in both narrow and wide bandgap semiconductors; (2) with the same r, the sequence of size effects on (r) from strong to weak is nanoparticles, nanowires, and thin films; and (3) the Raman red shift is caused by the size-induced phonon confinement effect and surface relaxation. These results are consistent with experimental findings and may provide new insights into the size, dimensionality, and composition effects on the optical properties of semiconductors as well as fundamental understanding of high-performance nanostructural semiconductors towards their applications in optoelectronic devices.

Size-, Shape-, and Dimensionality-Dependent Melting Temperatures of Nanocrystals

On the basis of a model for size-dependent cohesive energy, the size, shape, and dimensionality effects on melting temperatures of nanocrystals are modeled in a unified form. The model predicts that the melting temperature Tm(D,d,λ) decreases with reducing size D and dimensionality d or increasing shape factor λ. For nanoparticles with the same D values, there is Tm(icosahedron) > Tm(sphere or cube) > Tm(octahedron) > Tm(tetrahedron). Moreover, the ratio of depression of Tm(D,d,λ) is about 1:2λwire:3λparticle for thin films, nanowires, and nanoparticles when D is large enough, for example, 6 nm. The model is found to be in accordance with available experimental, MD simulation, and other theoretical results for Au, Ag, Ni, Ar, Si, Pb, and In nanocrystals.

Modeling cohesive energy and melting temperature of nanocrystals

A model has been developed to account for the size dependent cohesive energy and melting temperature of nanocrystals. This model can deal with the thermodynamic properties of nanoparticles (spherical and non-spherical), nanowires and nanofilms with free surface or non-free surface (embedded in a matrix). The cohesive energy depression of nanocrystals has been predicted, and the conditions of superheating are obtained. It is found that the present theoretical results are consistent with the available experimental values.

Melting enthalpy depression of nanocrystals based on surface effect

Takagi was the first to demonstrate that ultrafine metallic particles melt below their corresponding bulk melting temperature in 1954 [1]. Now it is known that the melting temperatures of all nanocrystals, including metals [2, 3], semiconductors [4, 5] and organic nanocrystals [6, 7], depend on their size and this has been explained in terms of various models related to interface energy [8]. This size effect is experimentally also observed on the melting enthalpy [2, 6]. However, none of the above models can interpret sizedependent melting enthalpy of nanocrystals directly [8]. Knowledge of thermodynamic parameter are important for complete understanding of melting transition of nanocrystals and will deepen our insight into the size effect on melting. Therefore, a direct consideration on the size-dependence of melting enthalpy is needed. In this contribution, a simple physical model for the size-dependent melting enthalpy of nanocrystals in terms of the effect of bond number and bond energy of surface atoms of nanocrystals and that of the corresponding liquids on the internal energy of the system is developed. Combining with Mott’s expression for the vibrational entropy of melting for metallic crystals, size-dependent melting temperature of metallic nanocrystals is also predicted. The model predictions correspond well to the latest experimental results of indium nanocrystals. We consider that size-dependent melting enthalpy H (r ) is additive where r denotes radius of nanoparticles and nanowires, or half thickness of thin films,

Two limits of melting temperatures of nanocrystals

It is demonstrated that the melting temperature of nanocrystals embedded in a matrix exhibit two asymptotic limits as the size of the nanocrystal reaches its smallest value. The lower limit of melting temperatures is related to the disappearance of size-dependent entropy of melting and is considered as the lowest glass transition temperature which is located between Kauzmann temperature and glass transition temperature. The upper limit of a nanocrystal embedded in a matrix is determined by the ratio between the bulk melting temperature of the embedded nanocrystal and that of the matrix. The predicted thermodynamic melting temperature range and the lowest glass transition temperature are supported by available experimental evidences.