Thermophysical properties of stable and metastable liquid copper and nickel by molecular dynamics simulation

Molecular dynamics simulation combined with an embedded atom method (EAM) potential was applied to the calculation of the specific heat and the diffusion coefficient for superheated and undercooled liquid copper and nickel as functions of temperature. The system contains 108,000 atoms. The calculated results show that the enthalpy increases linearly with the rise of temperature. There are no breaks at their melting temperatures of 1356 and 1726 K. It is found that the calculated specific heats of Cu and Ni are 32.75 and 36.11 J/mol/K respectively. The calculated mean square displacements increase linearly with calculated time. The diffusion coefficients are exponentially dependent on temperature. Moreover, the calculated results are in good agreement with the reported experimental results for the specific heat and diffusion coefficient.     

Elastic continuum theory of bulk and surface-atom mean square displacements of hexagonal crystals

The mean square displacements of particles in a semi-infinite hexagonal elastic continuum with a free (0001) surface are calculated using a Green's function method in the high temperature limit.     

Exploring the surface permeability of nanoporous particles by pulsed field gradient NMR

A new method to determine the surface permeability of nanoporous particles is proposed. It is based on the comparison of experimental data on tracer exchange and intracrystalline molecular mean square displacements as obtained by the PFG NMR tracer desorption technique with the corresponding solutions of the diffusion equation via dynamical Monte Carlo simulations. The method is found to be particularly sensitive in the "intermediate" regime, when the influence of intracrystalline diffusion and surface resistances of the nanoporous crystal on molecular transport are comparable and the conventional method fails. As an example, the surface permeabilities of two samples of zeolite NaCaA with different crystal sizes are determined with methane, as a probe molecule, at room temperature.     

Thermal expansion near plane and stepped surfaces

A theory of the thermal expansion of the plane and (11n) stepped surfaces of fcc crystals is presented. The temperature dependent relaxations arise from cubic anharmonic terms in the crystal potential energy. We show that the thermal expansion depends on the positions of the atoms with respect to the steps and is greatest for the atom of the upper corner. The knowledge of these new atomic positions at each temperature allows us to calculate new atomic force constants and then new vibrational properties at this temperature. The application is made for a Ni crystal for which we give the corrections, due to the thermal expansion, on the mean square displacements of stepped surface atoms. The variation with temperature of the optical modes due to a light monolayer is also presented.     

Theory of surface atom mean square displacements in chromium

The temperature dependence of the mean square displacements for atoms on the (100) and (110) surfaces of chromium has been studied theoretically using the harmonic approximation. Calculations were carried out for crystals with periodic boundary conditions in two directions and free boundary conditions in the third direction using a Born-van Karman model with central interactions up to third nearest neighbors and non-central angular stiffness interaction between nearest and next nearest neighbors. The values of the force constants were chosen to give good fits to the elastic constants and to the bulk phonon dispersion curves in the three major directions [100], [110] and [111]. The ratio of the mean-square displacements at a surface to that in the bulk was calculated as a function of temperature for both the (100) and (110) surfaces. The theoretical, results are compared with the available experimental data from low-energy electron diffraction.     

Visualization of 50 MHz Surface Acoustic Wave Propagation Using Stroboscopic Phase-Shift Interferometry

A Stroboscopic phase-shift interferometry has been developed to visualize surface acoustic wave (SAW) propagation on SAW devices quantitatively. The developed interferometry is a Fizeau-type one with a multi-mode semiconductor laser diode and an optical isolator. With the laser light illuminating stroboscopically, observed interference intensity gives information about average displacements of the vibrations. Fifty MHz SAW propagation on the surface of the SAW device has been measured with the interferometry. Distribution of the SAW along the propagation path has been observed, whose amplitude is 3 nm (p-p). Repetition accuracy evaluated with the root mean square method is 1/2500 of the laser wavelength. The system is useful for estimating and improving performances of micro-devices.Presented at 1996 International Workshop on Interferometry (IWI ‘96), August 27-29, Saitama, Japan.     

Melting evolution and diffusion behavior of vanadium nanoparticles

Molecular dynamics calculations have been performed to study the melting evolution, atomic diffusion and vibrational behavior of bcc metal vanadium nanoparticles with the number of atoms ranging from 537 to 28475 (diameters around 2–9 nm). The interactions between atoms are described using an analytic embedded-atom method. The obtained results reveal that the melting temperatures of nanoparticles are inversely proportional to the reciprocal of the nanoparticle size, and are in good agreement with the predictions of the thermodynamic liquid-drop model. The melting process can be described as occurring in two stages, firstly the stepwise premelting of the surface layer with a thickness of 2–3 times the perfect lattice constant, and then the abrupt overall melting of the whole cluster. The heats of fusion of nanoparticles are also inversely proportional to the reciprocal of the nanoparticle size. The diffusion is mainly localized to the surface layer at low temperatures and increases with the reduction of nanoparticle size, with the temperature being held constant. The radial mean square vibration amplitude (RMSVA) is developed to study the anharmonic effect on surface shells.     

Mode coupling approximation in a model of structural phase transitions with infinite range interaction

The long-time value of the displacement-displacement correlation function and the mean square displacements are calculated within the ⁴-lattice model with infinite range interaction by use of a mode coupling approximation. Their temperature dependence is compared with exact results. While the mean square displacements (zero decoupling times) agree with exact results except the low temperature range for weak coupling, the long time correlations from MCA (infinite decoupling times) are wrong. Even a separation of the displacement function into two parts representing the two different time scales is of no use since the distribution function doesn't separate.     

Accuracy evaluation in temperature‐dependent EXAFS measurements of CdTe

The evaluation of uncertainty in temperature‐dependent EXAFS measurements is discussed, considering the specific case of a recent experiment performed on CdTe. EXAFS at both Cd and Te K‐edges was measured at different times and at different beamlines in a temperature range from 5 to 300 K. Attention is focused on the nearest‐neighbours parameters: bond thermal expansion, parallel and perpendicular mean‐square relative displacements and the third cumulant. Different causes of uncertainty, a comparison of experimental results with theoretical models, the difference between EXAFS and crystallographic thermal expansions and the meaning of the third cumulant are discussed.     

Dynamical motion of adatoms and their neighbours at the Ni(111) surface

We have calculated mean square displacements and one atom spectral densities for the adatoms H, O, S, Ni, and their neighbours on a Ni(111) surface. The adatoms are isolated on the substrate. They lie at a site of three-fold symmetry. The upward shift in frequency of the adatom's normal mode of vibration perpendicular to the surface (a shift from the value on an infinitely massive substrate) has been calculated. A simple analytical formula is obtained by means of which the shift can be estimated for any adatom —surface combination.     

Molecular dynamics simulations of the melting of Al–Ni nanowires

Molecular dynamics (MD) simulations were performed to investigate the influence of nickel (Ni) composition and nanowire thickness on the thermal properties of Al-x%Ni (at%) nanowires using the embedded atom model (EAM) potential. The melting of the nanowire was characterised by studying the temperature dependence of the cohesive energy and mean square displacement. The effect of the nanowire thickness on the cohesive energy, melting temperature, heat capacity as well as latent heat was studied in canonical ensemble. Moreover, the crystal stability of Al, Al-20%Ni, Al-40%Ni, Al-60%Ni, Al-80%Ni, Al₃Ni, Ni₃Al and Ni nanowires was studied at different temperatures using mean square displacement and cohesive energy.     

Study of low energy noble gas ion reflection from monocrystalline surfaces; Influence of thermal vibrations of the surface atoms: II. Calculational evaluation of the sensitivity for model parameters and possibilities for estimation

The sensitivity of the characteristics of low energy noble gas ion reflection from monocrystalline surfaces for thermal properties of the target atoms has been investigated by computer simulation. In addition the uncertainties in comparing experimental results with calculations, introduced by a not well-known interaction potential, have been examined. The calculations have been carried out for 6 keV Ar⁺ ions reflected from a vibrating Cu〈100〉 chain. To achieve the above presented object we varied the mean square value $\text{u}{}^2$ and the correlation coefficients of the atomic thermal displacements. The used ion-atom interaction potential (a Thomas-Fermi potential in the Molière approximation) has been varied by changing the screening length aF. Under certain conditions the shape of the energy spectra of specularly reflected particles depends pronouncedly on both $\text{u}{}^2$ and aF. The effects are the most pronounced for scattering angles between about 20° and 30°. The angular distribution shows also a distinct and simultaneous sensitivity for the used potential and the target-temperature. A most interesting feature is the occurrence of a QT peak at higher temperatures, resulting from quasi triple collisions from surface “thermal pit” structures. At a given scattering angle the cut-off temperature of this QT peak can be related to the mean square displacements of the involved atoms. This cut-off temperature appears to be (almost) independent from the used potential, allowing an estimation of $\text{u}{}^2$. The intensity of the QS peak and the QD peak depend exclusively on the mean square differences of thermal displacements of neighbouring atoms. Correlated atomic displacements have some influence on the angular distributions and on the QT peak intensity. Possibilities to estimate model quantities are discussed briefly.     

晶体相场法研究预变形对熔点附近六角相/正方相相变的影响

应用双模晶体相场模型计算二维相图,并模拟了在熔点附近预变形和保温温度对六角相晶界演化以及六角相/正方相相变的影响.研究发现:在相变初期,当预变形为零、保温温度离熔点很近时在晶界发生缺陷诱发预熔;增大预变形,变形与缺陷的交互作用在熔点附近诱发预熔;随着预变形的进一步增大,变形在畸变处同时诱发液相和正方相,且预变形越大、保温温度越接近熔点,液相生长越明显,反之正方相生长明显.持续保温使得畸变能释放,晶粒最终完全转变为平衡正方相.模拟结果表明:预变形六角相在熔点附近保温时,由于晶界固有缺陷和预变形双重作用使得原子无序度增加,从而在晶界或其他缺陷处产生液相,待能量释放后晶粒再转变成平衡正方相,进而延缓了六角相/正方相相变时间.     

Response of an open curved thin shell to a random pressure field arising from a turbulent boundary layer

A method is presented to predict the root mean square displacement response of an open curved thin shell structure subjected to a turbulent boundary-layer-induced random pressure field. The basic formulation of the dynamic problem is an efficient approach combining classic thin shell theory and the finite element method, in which the finite elements are flat rectangular shell elements with five degrees of freedom per node. The displacement functions are derived from Sanders’ thin shell theory. A numerical approach is proposed to obtain the total root mean square displacements of an open curved thin structure in terms of the cross spectral density of random pressure fields. The cross spectral density of pressure fluctuations in the turbulent pressure field is described using the Corcos formulation. Exact integrations over surface and frequency lead to an expression for the total root mean square displacement response in terms of the characteristics of the structure and flow. An in-house program based on the presented method was developed. The total root mean square displacements of a curved thin blade subjected to turbulent boundary layers were calculated and illustrated as a function of free stream velocity and damping ratio. A numerical implementation for the vibration of a cylinder excited by fully developed turbulent boundary layer flow was presented. The results compared favorably with those obtained using software developed by Lakis and Païdoussis (J. Sound Vib. 25 (1972) 1–27) using cylindrical elements and a hybrid finite element method.     

Effect of atomic displacements in covalent solids

In covalent materials the electronic wave functions are very sensitive even to small displacements, while with displacements of increasing magnitude the stability of the covalent bond gradually decreases and eventually another type of bond becomes more favourable. This has consequences for some of the properties of covalent solids even at low temperature and produces significant changes with increasing temperature and on melting.     

高温下镜面纯Fe的表面质量研究

研究了真空状态下保温60min不同退火温度对镜面纯铁的表面粗糙度、表面形貌及晶粒取向的影响。结果表明:在纯铁的多晶型性转变温度点以下,面均方根粗糙度随退火温度的升高而缓慢增大;在多晶型性转变温度及以上发生突变,从面均方根粗糙度为4~5nm的镜面突变到700nm;用扫描电子显微镜(SEM)观察样品表面,发现在810℃出现再结晶细小晶粒。研究了原材料及860~960℃之间几个温度点的X射线衍射{200}晶面极图,结果发现:晶粒在860℃开始择优取向,随温度升高,取向越来越明显;再结晶对表面粗糙度的影响不大,晶粒的择优取向使得晶粒在不同方向的膨胀系数不同,以及多晶型性转变导致体积的变化使得晶粒之间挤压造成晶粒之间的凹凸不平和表面较深较粗的晶界,这是造成粗糙度突变的主要原因。     

Qualitative Aspects of Melting Transition on Fractals

The melting instability on fractals is discussed qualitatively under the Lindemann's hypothesis. The density of elastic vibrational states originating from phonon and elastic fraction modes is used to calculate the mean square displacement of lattice constitutents, and the transition temperature is estimated for fractal aggregates with different dimensionalities of elastic fractons.     

Temperature dependence of specular and non-specular leed beams from Cu3 Au

The temperature dependence of intensities of the prominent diffraction peaks in the specular (00) and one non-specular ($\text{11}$) beam from the (100) surface of Cu₃Au have been measured in the range of 300 to 673 K. The effective Debye temperature associated with the specular beam appears to increase continuously with energy below 50 eV but varies discontinuously at high energies. For the ($\text{11}$) beam, which was available only in the higher energy range of 65 to 136 eV, the effective Debye temperature varies discontinuously with energy. Parallel and normal components of the Debye temperature were deduced from the two sets of data from which it appears that the two mean square displacements are approximately equal, compared to the harmonic approximation which indicates a difference of 30 percent. The log of peak intensity versus temperature (Debye plot) deviates from the straight line at 60° below the disordering temperature for all beams and all energies.     

Theory of diffusion in premelting systems

Summary The diffusion in premelting films and surfaces is described by the Fokker-Planck equation with a periodic potential whose amplitude depends on the temperature and vanishes at the bulk melting temperature. The self-part of the dynamic structure factor is calculated and the results are compared with neutron scattering data from CH₄ premelting films adsorbed on MgO and with atom scattering data from the (110) surface of Pb. In honour of Prof. Fausto Fumi on the occasion of his retirement from teaching.     

Surface energy and pressure of diamond and silicon nanocrystals

Based on the pair potential of interatomic interaction, we study the dependence of various properties of diamond and silicon nanocrystals with a free surface on size, surface shape, and temperature. A model nanocrystal has the form of a parallelepiped faceted by {100} planes with a square base. The number of atoms N in the nanocrystals is varied from 5 to infinity. The Debye temperature, Gruneisen parameter, specific surface energy, isochoric derivative of specific surface energy with respect to temperature, and surface pressure are calculated as a function of the size and shape of diamond and silicon nanocrystals at temperatures ranging from 20 K to the melting point. The surface pressure P _sf(N) ∼ N ^−1/3 is much lower than the pressure calculated by the Laplace formula for similar nanocrystals for given values of density, temperature, and number of atoms. As the temperature increases from 20 K to the melting point, the isotherm P _sf(N) lowers and changes the shape of the dependence on N; at high temperatures, it goes to the region of extension of small nanocrystals of diamond and silicon.