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.     

Dynamical signatures of ‘phase transitions’: Chaos in finite clusters

Finite clusters of atoms or molecules, typically composed of about 50 particles (and often as few as 13 or even less) have proved to be useful prototypes of systems undergoing phase transitions. Analogues of the solid-liquid melting transition, surface melting, structural phase transitions and the glass transition have been observed in cluster systems. The methods of nonlinear dynamics can be applied to systems of this size, and these have helped elucidate the nature of the microscopic dynamics, which, as a function of internal energy (or ‘temperature’) can be in a solidlike, liquidlike, or even gaseous state. The Lyapunov exponents show a characteristic behaviour as a function of energy, and provide a reliable signature of the solid-liquid melting phase transition. The behaviour of such indices at other phase transitions has only partially been explored. These and related applications are reviewed in the present article.     

Melting of isolated tin nanoparticles

The melting of isolated neutral tin cluster distributions with mean sizes of about 500 atoms has been investigated in a molecular beam experiment by calorimetrically measuring the clusters' formation energies as a function of their internal temperature. For this purpose the possibility to adjust the temperature of the clusters' internal degrees of freedom by means of the temperature of the cluster source's nozzle was exploited. The melting point of the investigated tin clusters was found to be lowered by 125 K and the latent heat of fusion per atom is reduced by 35% compared to bulk tin. The melting behavior of the isolated tin clusters is discussed with respect to the occurrence of surface premelting.     

Superheating and induced melting at semiconductor interfaces

We present ab initio density-functional simulations of the state of several semiconductor surfaces at temperatures near the bulk melting temperatures. We find that the solid-liquid phase-transition temperature at the surface can be altered via a microscopic (single-monolayer) coating with a different lattice-matched semiconducting material. Our results show that a single-monolayer GaAs coating on a Ge(110) surface above the Ge melting temperature can dramatically reduce the diffusion coefficient of the germanium atoms, going so far as to prevent melting of the bulk layers on the 10 ps time scale. In contrast, a single-monolayer coating of Ge on a GaAs(110) surface introduces defects into the bulk and induces melting of the top layer of GaAs atoms 300 K below the GaAs melting point. To our knowledge, these calculations represent the first ab initio investigation of the superheating and induced melting phenomena.     

Melting, premelting, and structural transitions in size-selected aluminum clusters with around 55 atoms

Heat capacities have been determined for unsupported aluminum clusters, Al49(+) - Al63(+), from 150 to 1050 K. Peaks in the heat capacities due to melting occur between 450 and 650 K (well below the bulk melting point of 933 K). The peaks for Al+51 and Al+52 are bimodal, suggesting the presence of a premelting transition where the surface of the clusters melts around 100 K before the core. For clusters with n > 55 the melting temperatures suddenly drop, and there is a dip in the heat capacities due to a transition between two solid forms before the clusters melt.     

Surface energy and surface proton order of ice Ih

Ice Ih is comprised of orientationally disordered water molecules giving rise to positional disorder of the hydrogen atoms in the hydrogen bonded network of the lattice. Here we arrive at a first principles determination of the surface energy of ice Ih and suggest that the surface of ice is significantly more proton ordered than the bulk. We predict that the proton order-disorder transition, which occurs in the bulk at approximately 72 K, will not occur at the surface at any temperature below surface melting. An order parameter which defines the surface energy of ice Ih surfaces is also identified.     

Na(n)(5<=n<=10)小团簇相变

采用紧密结合的分子动力学模型,对Na(n)(5<=n<=10)小团簇的键长涨落、势能、热容量等熔化性质在50K到1500K温区进行了模拟研究,结果表明：它们发生两次相变,一种在230K到300K的温度范围内,依次有块体玻璃态转变;一种在550K到870K温度段,依次经历了熔化相变.同时也得到随着团簇体系的减小,势能由下向上排列的曲线,即体系的势能由低变高.     

Modeling the cohesive energy and melting point of nanoparticles by their average coordination number

We present a relation between the average coordination number and the cohesive energy for nanoparticles that shows that the ratio of nanoparticles cohesive energy to the bulk value is equal to the ratio of the nanoparticles average coordination number to that of the bulk. We consider the effect of lattice and surface packing factors on the average coordination numbers of the atoms in the nanoparticle. The melting temperature of nanoparticles has been calculated from the obtained relation for cohesive energy, and predictions for the cohesive energy and melting temperature of the nanoparticles have been compared with other theoretical models and available experimental data and the results of molecular dynamics simulations.     

Molecular dynamics simulation of the melting of a twist Σ=5 grain boundary

The existence of a possible grain boundary disordering transition of the melting type in a =5 (001) twist boundary of aluminium bicrystal below the melting temperature was investigated using a constant pressure molecular dynamics simulation. The calculated melting temperature T _cm of the bulk Al is about 960 K. The total internal energy, the structure factor, and the pair distribution function were calculated at different layers across the grain boundary. The mean atomic volume, the grain boundary energy, and the thermal expansion coefficients were also calculated using the same simulation method. This simulation also allows us to image the grain boundary structure at different temperatures. The equilibrium grain boundary structure at 300 K retains the periodicity of the coincident site lattice, so that the lowest energy structure corresponds to the coincident site arrangement of the two ideal crystals. With increasing temperature, the total internal energy of the atoms for both the perfect crystal and the grain boundary increases, as do the number of layers in the grain boundary. The grain boundary core exists and the perfect crystal structure still exists outside the grain boundary at 0.9375 T _cm. However, two atomic layers of the equilibrium grain boundary structure at 0.9375 T _cm lose the coincident site lattice periodicity and attain a structure with liquid-like disorder. Therefore, partial melting of the grain boundary has occurred at the temperature above 0.9375 T _cm which is in agreement with the experimental results.     

Hot and solid gallium clusters: too small to melt

A novel multicollision induced dissociation scheme is employed to determine the energy content for mass-selected gallium cluster ions as a function of their temperature. Measurements were performed for Ga(+)(n) (n=17 39, and 40) over a 90-720 K temperature range. For Ga+39 and Ga+40 a broad maximum in the heat capacity-a signature of a melting transition for a small cluster-occurs at around 550 K. Thus small gallium clusters melt at substantially above the 302.9 K melting point of bulk gallium, in conflict with expectations that they will remain liquid to below 150 K. No melting transition is observed for Ga+17.     

X-ray study of molecular oxygen adsorbed on graphite

We have performed a detailed X-ray diffraction study of O₂ adsorbed on UCAR-ZYX and Le Carbon Lorraine vermicular exfoliated graphite between 15 and 50 K. At least four phases of physisorbed oxygen are found. The monolayer δ phase consists of a centered parallelogram lattice, with the molecular axes parallel to the graphite surface. The data are consistent with a triple point at 26 K. The melting transition at a coverage of one monolayer appears to be first order. At higher coverages the molecules undergo a lying-down to standing-up transition; the higher coverage ζ phase froms an approximately triangular lattice with the molecular axes perpendicular to the graphite surface. Satellite peaks around the (1, 0) Bragg peak indicate, however, that this cannot be a simple triangular lattice; possible explanations include successively incommensurate layers or a sinusoidal density modulation. For coverages in the two-layer region the ζ phase modulation peaks disappear at 37 K, and at 40 K the adsorbed oxygen appears to undergo a first order melting transition into a fluid phase. With increasing coverage, the 2D X-ray diffraction profiles and phase boundaries do not connect smoothly onto those of the 3D α and β phases. At low temperatures (T < 30 K) the ζ phase always coexists with bulk crystallites; for temperatures near the 2D melting transition the 3D peaks are not observable. These data, taken together with the heat capacity results, suggest a wetting transition with only the bilayer lamellar phase or bulk O₂ being stable at low temperatures.     

Atomistic simulations for the non-equilibrium surface premelting and melting of Nb(1 1 0) plane

In the present paper molecular dynamics (MD) simulations have been preformed to investigate the surface melting process and microscopic mechanism of Nb(1 1 0) plane in the atomic scale with a modified analytic embedded atom method (MAEAM). On the basis of the MD relaxation dependence of averaged internal energy and layer structure factor at given temperatures, the melting point of the sample has been estimated to be 2510 K. Then by the above results the Nb(1 1 0) plane melting process has been approximately divided into two stages: first the layer-by-layer premelting phase in the surface region and then a simultaneous abrupt melting transition for the inner layers. According to the variation of the averaged internal energy of the inner atomic layer, the melting latent heat has been calculated and the result is in good agreement with the experimental value. The simulated snapshots of atomic configuration for Nb(1 1 0) plane have indicated that the dynamically microscopic mechanism of melting nucleation during the melting transition.     

Studies of pulsed laser melting and rapid solidification using amorphous silicon

Pulsed laser melting of ion implantation-amorphized silicon layers, and the subsequent solidification of undercooled liquid silicon, have been studied experimentally and theoretically. Measurements of the time of the onset of melting of amorphous silicon layers, during an incident laser pulse, have been combined with measurements of the duration of melting, and with modified melting model calculations to demonstrate that the thermal conductivity, K_a, of amorphous silicon is very low (K_a0.02 W/cm K). K_a is also found to be the dominant parameter determining the dynamical response of amorphous silicon to pulsed laser radiation; the latent heat of fusion and melting temperature of amorphous silicon are relatively unimportant. Transmission electron microscopy indicates that bulk (volume) nucleation occurs directly from the highly undercooled liquid silicon that can be prepared by pulsed laser melting of amorphous silicon layers at low laser energy densities. A modified thermal melting model has been constructed to simulate this effect and is presented. Nucleation of crystalline silicon apparently occurs at a nucleation temperature, T_n, that is higher than the temperature, T_a, of the liquid-to-amorphous phase transition. The model calculations demonstrate that the release of latent heat by bulk nucleation occurring during the melt-in process is essential to obtaining agreement with experimentally observed depths of melting. These calculations also show that this release of latent heat accompanying bulk nucleation can result in the existence of buried molten layers of silicon in the interior of the sample after the surface has solidified. It is pointed out that the occurrence of bulk nucleation implies that the liquid-to-amorphous phase transition (produced using picosecond or ultraviolet nanosecond laser pulses) cannot be explained by purely thermodynamic considerations.     

Determining surface free energies of crystals with highly disordered surfaces from simulation

A method for calculating surface free energies by gradually creating slabs from a simulation of bulk crystals is tested for three low index faces of a Lennard-Jones crystal at temperatures up to the melting point. The path by which the interactions between atoms in different slabs are turned off must be chosen with care; here it is done in three stages, first the interaction energy is reduced until the well in the pair potential is considerably less than kT, then the effective particle sizes are reduced and finally the interaction energy is reduced to zero. The results show a slow and steady decrease in the surface free energy with temperature, while both the surface energy and the surface entropy increase rapidly when the upper layers of the crystal disorder. There is no evidence for a first order surface roughening transition although the (111) surface shows a sharper onset of disorder than do the (110) and (100) surfaces.     

Thermodynamics of melting of lithium,potassium and rubidium at high pressures

Volume measurements of liquid and solid Li, K and Rb in the vicinity of their melting curves have been carried out using a piston piezometer method. From the experimental results the volume, entropy and internal energy changes upon melting of the metals are calculated. The obtained data are analyzed along with the results for Na and Cs.It is stated that the anomalies in the melting curves of K, Rb and Cs are most probably connected with a s-d electron transition.     

MEAM势与Tersoff势比较研究——碳化硅熔化与凝固行为

运用分子动力学方法对比模拟研究了碳化硅的体熔化、表面熔化和晶体生长过程.分别采用MEAM 势和Tersoff势两种势函数描述碳化硅.结果表明:体熔化时,两种势函数描述的SiC的原子平均能量、 Lindemann指数和结构有序参数与温度的变化关系相似,但MEAM势对应的体熔点(4250 K)比Tersoff势(4750 K) 的要高.表面熔化时,两种势函数描述的SiC在相同的过热度下熔化速度相近;而在相同的温度条件下,MEAM 作用的SiC表面熔化速度更快.这是由于MEAM势SiC的热力学熔点(3338 K)低于Tersoff势SiC的热力学熔点 (3430 K)的缘故.两种势函数作用的SiC在晶体生长方面差异很大.MEAM势SiC的晶体生长速度与过冷度有关, 过冷度约为400 K时晶体生长速度最快.但Tersoff势SiC晶体却在过冷度为0—1000 K的范围内均不能生长. 综合考虑,MEAM势比Tersoff势能更好地描述碳化硅的熔化和凝固行为.     

小尺寸铝纳米团簇的相变行为

采用分子动力学方法模拟了半径从0.3–1.3 nm变化的小尺寸铝纳米团簇的熔化、凝固行为. 基于势能-温度曲线、热容-温度曲线分析, 获得了熔点、凝固点与尺寸的依变关系, 并利用表面能理论、小尺寸效应开展了现象分析.研究表明, 铝团簇原子数小于80时, 熔点和凝固点的尺寸依赖性出现无规律的异常变化; 而大于该原子数, 熔、凝固点则随着团簇尺寸的减小而单调下降; 当原子数为27时, 团簇熔点高于块材熔点近40 K. 同时, 铝纳米团簇呈现出凝固滞后现象, 即凝固点低于熔点. 关键词： 纳米团簇 熔点 凝固点 分子动力学     

Evolution of small copper clusters and dissociative chemisorption of hydrogen

The structural evolution of small copper clusters of up to 15 atoms and the dissociative chemisorption of H2 on the minimum energy clusters are studied systematically using density functional theory. The preferred copper sites for chemisorption are identified and the transition state structures and activation barriers for clusters four to nine atoms are determined and found to be inconsistent with the empirical Bronsted-Evans-Polanyi relationship. The physicochemical properties of the clusters are computed and compared with the bulk and surface values. The results indicate that a phase transition must occur in the going from cluster to bulk.     

Computer study of the temperature dependence of physical properties of noncrystalline silicon nanoparticles

Variations in the structure and kinetic properties of vitreous and amorphous Si₄₀₀ nanoparticles upon heating from 300 to 1700 K are studied by molecular dynamics. The nanoparticle density increases with temperature and approaches the density of bulk solid silicon. A transition from a unimodal to a bimodal distribution of bond lengths is observed upon heating. This transition is more pronounced in the case of the vitreous nanoparticle. The average bond length in the amorphous nanoparticle is, as a rule, larger than that in the vitreous one, and the average number of bonds per atom is lower than that in the vitreous nanoparticle for nearly all studied temperatures. Negative values of the excess potential energy correspond to middle concentric layers of nanoparticles. Liquid layers form in the surface region of nanoparticles in the vicinity of the melting transition. A kinetic test indicating the beginning of nanoparticle melting is formulated.     

Thermodynamic properties of noble metal clusters:molecular dynamics simulation

The thermodynamics properties of noble metal clusters Au_N, Ag_N, Cu_N, and Pt_N (N = 80, 106, 140, 180, 216, 256, 312, 360, 408, 500, 628, 736, and 864) are simulated by micro-canonical molecular dynamics simulation technique. The potential energy and heat capacities change with temperature are obtained. The results reveal that the phase transition temperature of big noble metal clusters (N ⩾ 312 for Au, 180 for Ag and Cu, and 360 for Pt) increases linearly with the atom number slowly and approaches gently to bulk crystals. This phenomenon indicates that clusters are intermediate between single atoms and molecules and bulk crystals. But for the small noble clusters, the phase transition temperature changes irregularly with the atom number due to surface effect. All noble metal clusters have negative heat capacity around the solid-liquid phase transition temperature, and hysteresis in the melting/freezing circle is derived in noble metal clusters.