Size-dependent Binary Eutectic Phase Diagram And Computer Simulation

There is another world between the macroscopic one and the microscopic one,the mesoscopic world of the nanosystem where many special phenomena occur. Theresearch on such state changes of condensed matter as melting and freezing is veryimportant. Takagi in 1954 demonstrated for the first time that ultrafine metallicparticles melt below their corresponding bulk melting temperature. It is now knownthat the melting temperature of all kinds of low-dimensional crystals, includingmetals, semiconductors and organic crystals, depends on their sizes. The meltingtemperatures could be higher or lower than the corresponding bulk ones dependingon the surface states of low-dimensional materials. The study on superheating andsurface stress related to surface phenomena is significant to stability of nanosizeddevice.To understand the above problems, the essential way lies in the transition frommicroscopic properties of the material or the macroscopic ones to the mesoscopicones. Thermodynamics is a simple method to study the transition from macroscopicworld to the mesoscopic one. The application of thermodynamics to nanomaterialsreveals that a new branch of thermodynamics appears, i.e., nanothermodynamics.Although there are relatively extensive investigations on the size-dependent meltingof nanocrystals, it has not been accompanied by the necessary investigation of thesize-dependent thermodynamics of nanocrystals. A clear cognizance of thesize-dependent thermodynamic function will help us to know more about thesize-dependent energy transition law in the mesoscopic world. And it will stimulatethe application of thermodynamics to the small system composed of hundreds of orthousands of atoms as well.In the aspect of theoretical research, since the presence of computer,computation abilities develop with astonishing speed, and improve the developmentof related scientific calculations. In 50 years of 20C, people introduced computer tomaterial calculation and design, and then it became a new subject. Recently, with thedevelopment of modern scientific theory and the rapid progress of compute ability,material calculation and design become the most active branches in the materialscience. The main research methods are focused on first-principle method, andempirical potential molecular dynamic method et al. Empirical potential moleculardynamic methods are computationally simple but functionally simplex.First-principle method, free of any adjustable parameter, is the most importantmethod, which gets the electrical structure by solving the Schr?dinger equation, butrequired high computational performance.The phase diagram is important to industry application. The study of nanophasediagram may deepen the understanding for phase transition theory and extendpossible industry application fields. However, a systematic study on phase equilibriaamong nanometer sized components related to phase diagrams is limited. Sincenanophase equilibrium is metastable in nature (when temperature approaches meltingtemperature, the growth of nanocrystals is quicker, which leads to a continuouschange of the size), direct experimental measurements are difficult to obtain.Therefore, theoretical work may be an alternative method to study nanophasediagram. It is well known that some thermodynamic quantities related to meltingGibbs free energy, such as melting temperature and melting enthalpy of components,are basic quantities to describe phase diagram. Moreover, atomic interaction energyamong components needs to be determined for regular solution. For nanophasediagram, the size effect of the above quantities should be considered. According togeneral quantum chemistry consideration, the model for size-dependent atomicinteraction energy among components is developed and the model predicts thethermodynamic quantity linearly decreases with 1/D (D denotes the size ofnanocrytals). Combing with the size-dependent melting temperature and meltingenthalpy, the related quantities can be obtained according to the basic equations foreutectic and therefore, the size-dependent phase diagram can be obtained. As the sizeof components decreases, the temperatures of solidus and liquidus curves drop andthe area of the two-phase zone in the continuous solution binary phase diagramdecreases.Dynamical diffusion properties distinguish the liquid phase from the solid phaseof a material. Atoms in a solid will not self-diffuse in the absence of defects. On theother hand, in the liquid the atoms will diffuse away from their original positions.Many properties of a material, such as the bond energy and force constants, directlyaffect the rate at which atoms will diffuse. The knowledge of D(T) plays importantrole in the design of metallurgical and solidification processes such as in castingindustry. However, experimental measurement of D in liquid metals is a difficult taskbecause of the high sensitivity of the phenomenon to external perturbations such asconvection effects. Through combining Egry′s expression for η and an γlv(T) function,a semi-empirical expression for D(T)/D(Tm) of liquid metals is established. Themodel predictions correspond to available experimental and MD simulations results.Computer is the most important tool of simulation. The more powerfulcomputer we have, the more efficient our works are. As the PC platform developedfurther, the performance gap between a Supercomputer and a cluster became smaller.Beowulfs have been developed especially to give research facilities the computingspeed they need. It mainly comes down to in this situation is that a process is beingparallelized. No two Beowulfs are exactly the same in the word. Beowulfs can beconfigured flexibly, by combining different of softwares. Beowulf clusters arescalable performance clusters based on commodity hardware, on a private systemnetwork, with open source software (Linux) infrastructure. By building Beowulfcluster, our computational ability is greatly improved.