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.     

Bond theory model to study cohesive energy,thermal expansion coefficient and specific heat of nanosolids

The fraction of surface atoms and the dangling bonds on the surface affect the thermodynamical properties of the nanostructured solids. A bond theory model is extended to study the size dependent thermodynamical properties at nanoscale. The theory is applied to analysis the size and shape dependence of cohesive energy, thermal expansion coefficient and specific heat of Ag, Au, Cu and Se nanosolids. The relaxation factor is incorporated at low dimension of nanosolids, which is expressed as the ratio of dangling bonds and the total bonds of atoms. It is predicted that the cohesive energy decreases with decrease in particle size. On the same ground, the model is proposed to analyze the thermal expansion coefficient and specific heat of the nanomaterials. It is reported that the thermal expansion coefficient and specific heat increase as particle size decreases. The predictions agree well with available experimental or simulation results.     

Thermodynamics approach of the formation of Ni catalyst particles for carbon nanotubes growth

Size-dependent thermodynamic parameters, such as Gibbs free energy, enthalpy and entropy, for the transition of a Ni nanofilm to catalyst particles for subsequent carbon nanotube growth have been explored. In this investigation, we consider the derived equations of the size-dependent melting temperature of nanosolids based on our previous works. Using this thermodynamic approach, it is found that the diameter of Ni particles is 3 times greater than the thickness of the original film. From the critical and stable sizes of transformed Ni nanoparticles, a minimum film thickness for transformation of film to nanoparticles was obtained. Our predictions are in good agreement with experimental results.     

Critical thermodynamic evaluation and optimization of the Fe-Mg-O system

A complete literature review, critical evaluation and thermodynamic modeling of the phase diagrams and thermodynamic properties at 1 bar total pressure of all oxide phases in the Fe-Mg-O system are presented. Optimized model equations for the thermodynamic properties of all phases are obtained which reproduce all available thermodynamic and phase equilibrium data within experimental error limits from 25 °C to above the liquidus temperatures at all compositions and oxygen partial pressures. The complex phase relationships in the system have been elucidated and discrepancies among the data have been resolved. The database of the model parameters can be used along with software for Gibbs energy minimization in order to calculate any type of phase diagram section. Sublattice models, based upon the compound energy formalism, were used for the spinel, pyroxene, olivine and monoxide phases. The use of physically reasonable models means that the models can be used to predict properties, phase equilibria, and cation site distributions in composition and temperature regions where data are not available.     

Modeling of size and shape dependent band gap,dielectric constant and phonon frequency of semiconductor nanosolids

A bond theory model is extended to study the size and shape dependent optoelectronics properties of semiconductors solids at nanoscale. On structural miniaturization down to nano scale, the optical parameters no longer remain stable but become tunable. The fraction of surface atoms and the dangling bonds on the surface affects the properties of semiconductors at nanoscale. The theory is applied to study the size and shape dependent energy band gap, dielectric constant and phonon frequency of TiO₂, CdS, CdSe, Si and GaN semiconductor nanosolids. We incorporated the relaxation factor, defined as the ratio of dangling bonds and the total bonds of atoms at nano scale. It is predicted that as the energy band increases with decrease in size, the effect becomes more when shape changes from spherical to tetrahedral. The model projects a decrease in phonon frequency and dielectric constants of semiconductor nanostructured materials with decrease in particle size. A good agreement between predicted results and the available experimental data is projected.     

Empirical correlation between melting temperature and cohesive energy of binary Laves phases

A list of 143 binary Laves phases with their melting temperature and melting type is collected, and used to study a correlation between melting temperature and cohesive energy. It is found that the melting temperature of Laves phases is roughly proportional to its cohesive energy calculated by Miedema's empirical model from their intrinsic atomic properties. The average predicted error of melting temperature of compounds is as low as 8.0%. This empirical rule is consistent with the result of the universal binding energy theory of solids.     

Finite size effect on critical transition temperature of superconductive nanosolids

A simple and unified model is developed for finite size effect on the critical transition temperature of superconductive nanosolids, which is based on the size-dependent Debye temperature of crystals within the McMillan expression. In the model, two material and structure dependent parameters of D₀ and α are used, which, respectively, are the critical size at which all atoms of a low-dimensional material are located on its surface, and the ratio of the mean square vibrational amplitude between surface atoms and interior atoms, In light of this model, the critical transition temperatures of superconductive nanosolids can decrease or increase with the dropping size of nanosolids depending on the bond strength changes of interfacial atoms. The predicated results are consistent with the available experimental results for superconductors MgB₂ and Nb thin films, Bi and Pb granular thin films and nanoparticles, Al thin films and nanoparticles.     

Size effect in the melting and freezing behaviors of Al/Ti core-shell nanoparticles using molecular dynamics simulations

The thermal stability of Ti@Al core/shell nanoparticles with different sizes and components during continuous heating and cooling processes is examined by a molecular dynamics simulation with embedded atom method. The thermodynamic properties and structure evolution during continuous heating and cooling processes are investigated through the characterization of the potential energy, specific heat distribution, and radial distribution function(RDF). Our study shows that, for fixed Ti core size, the melting temperature decreases with Al shell thickness, while the crystallizing temperature and glass formation temperature increase with Al shell thickness. Diverse melting mechanisms have been discovered for different Ti core sized with fixed Al shell thickness nanoparticles. The melting temperature increases with the Ti core radius. The trend agrees well with the theoretical phase diagram of bimetallic nanoparticles. In addition, the glass phase formation of Al–Ti nanoparticles for the fast cooling rate of 12 K/ps, and the crystal phase formation for the low cooling rate of 0.15 K/ps. The icosahedron structure is formed in the frozen 4366 Al–Ti atoms for the low cooling rate.     

Shape and size dependent thermophysical properties of nanocrystals

A theoretical model based on thermodynamic variables is employed in the present work to study the thermophysical properties of nanomaterials of different shapes and sizes. The model proposed by Qi and Wang [19] is applied to determine the cohesive energy of nanomaterial. The number of atoms on the surface to the total number of atoms in nanosolid is considered in terms of shape factor (α) and size of nanocrystal. The variation of cohesive energy?(E_cn?), melting temperature?(T_mN), Debye temperature (θ_DN), Specific heat capacity (C_pN), and Energy band gap (E_gN?) is studied for spherical, regular tetrahedral, regular hexahedral and regular octahedral nanocrystals. The cohesive energy, melting temperature and Debye temperature are found to decrease as the grain size is reduced. However, the energy band gap and specific heat capacity are found to increase with decrease of grain size of nanomaterial. The results achieved in the present study are compared with the available experimental and also with those calculated from other theoretical models. The consistency between the present calculated results and the results reported earlier confirms the validity of the present model theory to explain the shape and size dependence of thermophysical properties of nanomaterials.     

The phases of two-dimensional matter,their transitions,and solid-state stability: A perspective via computer simulation of simple atomic systems

An extensive computer simulation investigation of the structure, thermodynamics and phase stability of the two-dimensional Lennard-Jones system is presented, with special emphasis on the low-pressure melting regime of the phase diagram. This investigation includes isobaric-isothermal Monte Carlo simulations of the various phases of the two-dimensional Lennard-Jones system and of the melting and vaporization processes in configuration space, the isodensity-isothermal Monte Carlo simulations of two-phase coexistence between crystal and liquid and between liquid and vapor, the determination of the phase diagram, the establishment of the thermodynamic melting temperature, and the determination of the physical significance of the Kosterlitz-Thouless-Feynman dislocation model for melting in relation to the stability of the crystalline phase. I conclude that th phase diagram of the Lennard-Jones system in two dimensions is qualitatively similar to that in three dimensions. Finally, I present a new simulation method for doing molecular dynamics at constant pressure and/or constant temperature, and employ this method to study the temporal-spatial evolution of two-dimensional melting and vaporization.     

Size, shape and structure dependent cohesive energy and phase stability of metallic nanocrystals

A model to account for the size, shape and structure dependent cohesive energy of metallic nanocrystals is developed in this contribution. It is predicted that the cohesive energy of nanocrystals decreases with decreasing the crystal size in specific shape, and decreases with increasing the shape factor in specific size. Furthermore, the model can be applied to predict the size and shape dependent phase stability of nanocrystal. To take Cr nanocrystal as an example, we found that there exists FCC structure for Cr crystal (the bulk structure is BCC) when the crystal size is small enough, and critical size of phase transition ranges from 249 to 824 atoms due to crystal shape variation, which is consistent with the corresponding experimental results.     

Shape effect on the size and dimension dependent order-disorder transition temperatures of bimetallic alloys

Chemically ordered bimetallic nanocrystals may be promising candidates for the future magnetic-storage applications. In order to theoretically understand the order-disorder transition in nanoscale, a model based on the previous result for the size and dimension dependent melting temperature is developed to describe the effects of sizes, shapes and dimensions on order-disorder transition temperatures (T_OD) of bimetallic alloys. The results show that T_OD drops as size decreases, shape factor increases and dimension decreases. Also, the shape effect on T_OD cannot be neglected. Among these effects on T_OD, size is the strongest, while shape is the weakest. All these conclusions have been compared and confirmed by the recent simulations and experiments.     

Effect of voids and pressure on melting of nano-particulate and bulk aluminum

Molecular dynamics simulations are performed using isobaric–isoenthalpic (NPH) ensembles to study the effect of internal defects in the form of voids on the melting of bulk and nano-particulate aluminum in the size range of 2–9 nm. The main objectives are to determine the critical interfacial area required to overcome the free energy barrier for the thermodynamic phase transition, and to explore the underlying mechanisms for defect-nucleated melting. The inter-atomic interactions are captured using the Glue potential, which has been validated against the melting temperature and elastic constants for bulk aluminum. A combination of structural and thermodynamic parameters, such as the potential energy, Lindemann index, translational-order parameter, and radial-distribution functions, are employed to characterize the melting process. The study considers a variety of void shapes and sizes, and results are compared with perfect crystals. For nano aluminum particles smaller than 9 nm, the melting temperature is size dependent. The presence of voids does not impact the melting properties due to the dominancy of nucleation at the surface, unless the void size exceeds a critical value beyond which lattice collapse occurs. The critical void size depends on the particle dimension. The effect of pressure on the particulate melting is found to be insignificant in the range of 1–300 atm. The melting behavior of bulk aluminum is also examined as a benchmark. The critical interfacial area required for the solid–liquid phase transition is obtained as a function of the number of atoms considered in the simulation. Imperfections such as voids reduce the melting point. The ratio between the structural and thermodynamic melting points is 1.32. This value is comparable to the ratio of 1.23 for metals like copper.     

Molecular alloys as phase change materials (MAPCM) for energy storage and thermal protection at temperatures from 70 to 85 °C

Molecular alloys, that combine a relatively high heat of melting with a suitable melting temperature adapted to the application temperature, are excellent materials for thermal protection and for thermal energy storage. Of special interest is the fact that, by making alloys of molecular materials; the range of melting can be adjusted over a range of temperatures. The present paper reports on the design of MAPCMs to be used for energy storage and thermal protection at temperatures from 70 to 85 °C. The aim is to use these materials for thermal protection in the catering sector in order to avoid proliferation of micro organisms; the minimal temperature required is higher than 65 °C. The work illustrates how some fundamental studies are helpful in choosing the right composition that is able to work at the temperature required for an application. Several molecular alloys using the n-alkanes are elaborated and characterized. The preparation of mixed crystals, their crystallographic and thermodynamic properties and stability, phase change behaviour, and their use in practical applications are reported.     

Cohesive energy and physical properties of nanocrystals

Recently, a lattice-type-sensitive model, free of any adjustable parameter, for the size dependence of the cohesive energy of nanocrystals (nanodisks, -films, -wires and -particles) has been developed, taking into account the effects of the averaged structural and energetic properties of their surface and volume. These effects are related to the first- and second-nearest-neighbor atomic interactions. Now, considering the intimate relation between cohesive energy and other physical properties of materials, the recently obtained formula for the cohesive energy of nanocrystals has been applied to the cases of melting point (In, Bi, Si and Ag), evaporation temperature (Ag and Au), vacancy formation energy (Au), diffusion activation energy (Au), surface energy (Au, Al and Na), liquid–vapor interfacial energy (Al and Na), Curie temperature (Pb), Debye temperature (Au and Fe) and band gap energy (Si) of nanocrystals. In general, good agreement between the present model and the data has been obtained. Moreover, the surface-area-difference (SAD) model has been derived as a first-order approximation of the present model.     

Phase diagram of trivalent and pentavalent patchy particles

We compute the equilibrium phase diagram of two simple models for patchy particles with three and five patches in a very broad range of pressure and temperature. The phase diagram presents low-density crystal structures which compete with the fluid phase. The phase diagram of the five-patch model shows re-entrant melting, in analogy with the previously studied four-patch case, a metastable gas-liquid critical point and a stable, high-density liquid. The three-patch model shows a stable gas-liquid critical point and, in the region of temperatures where equilibration is numerically feasible, a stable liquid phase, suggesting the possibility that in this small valence model the liquid retains its thermodynamic stability down to the vanishing range limit.     

Pressure-induced antiferromagnetism in ferromagnetic Fe51.5Rh48.5 alloy

The pressure-temperature magnetic phase diagram based on electrical resistivity measurements was determined for Fe-Rh alloys, ferromagnetic down to 4.2 K, from room temperature to the Curie point (750 K) and for pressure up to 100 kbar. A pressure-induced first order ferromagnetic-antiferromagnetic phase transition line was found with an inhomogeneous, mixed phase existing at pressures lower than 50 kbar. A new, qualitative model is proposed to explain the phase transitions, the absence of magnetic moment on Rh atoms in the AF state and the shape of the p-T diagram. The model is based on the excitonic antiferromagnetism of semimetallic Fe-Rh and it is connected with the pecularities of the electroni structure and the shape of the Fermi surface.     

Ga含量对Mn2-xNiGa1+x结构和磁性的影响

系统研究了铁磁性形状记忆合金Mn_{2 -x}NiGa_1+x的结构、磁性和有序化转变. 研究表明: 随着Ga含量的增加, Mn_{2 -x}NiGa_1+x的母相结构由Hg₂CuTi 型逐渐转变到Cu₂MnAl型Heusler结构. 母相的晶格常数先增加后降低, 当x=0.3时达到最大值. 0.3 ≤x ≤0.8时, 材料除呈现Heusler结构的主相之外, 还出现了Ni₂In型六角相. 过渡金属中3d电子之间交换相互作用的减弱, 导致Mn_2-xNiGa_1+x主相的居里温度由Mn₂NiGa的590 K逐渐降低至Ga₂MnNi的220 K左右; 当x=0.6–0.8时, Ni₂In型六角相的居里温度与主相的居里温度出现分离. Ga对Mn的替代引起合金中原子间耦合作用的变化, 导致低温下Mn_{2 -x}NiGa_1+x的饱和磁化强度先增加后降低, 即x≤0.4时呈上升趋势, x>0.4时急剧下降. 差热分析结果显示, 随着x从0增加到1, 样品熔化温度逐渐降低, B2相到Heusler相的转变温度先降低后增加.     

Structure and magnetic properties of rare earth small particles

Fine gadolinium, terbium and holmium particles are shown to change their crystal structure when their dimensions become less than 30 nm. In newly formed cubic phase magnetic ordering was not found down to helium temperatures. A correlation between the particle size and paramagnetic Curie temperature has been observed for holmium.     

Structure changes in gallium near its melting point

The electrical resistivity as a function of temperature was measured for gallium samples annealed above the melting point and cooled down to −100°C. The observed phase transition temperatures depend on the temperature of the annealing in the liquid state. The complete phase diagram in (T_ann, T_cr) coordinates was constructed. Neutron diffraction measurements are consistent with the phase diagram obtained from the electrical resistivity data.