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.     

Thermal expansion of amorphous Zr Al Cu Ni in the vicinity of the glass transition

The thermal expansion of non-crystalline Zr₆₅Al_7.5Cu_17.5 Ni₁₀ has been studied in the range of the glass transition and in the undercooled liquid using a dilatometric device. The measuring technique used permits reliable experimental results up to 40 K above the glass transition temperature. The linear thermal expansion coefficient obtained is almost constant in the glassy state with a value of . It discontinuously increases at the glass transition temperature yielding a value of in the undercooled liquid. The results are compared with specific heat measurements of the amorphous material in this temperature range and are interpreted in the framework of a cluster model. Received 5 March 1999 and received in final form 11 June 1999     

Approximate energies and thermal properties of a position-dependent mass charged particle under external magnetic fields

We solve the Schr?dinger equation with a position-dependent mass(PDM) charged particle interacted via the superposition of the Morse-plus-Coulomb potentials and is under the influence of external magnetic and Aharonov–Bohm(AB) flux fields. The nonrelativistic bound state energies together with their wave functions are calculated for two spatially-dependent mass distribution functions. We also study the thermal quantities of such a system. Further, the canonical formalism is used to compute various thermodynamic variables for second choosing mass by using the Gibbs formalism. We give plots for energy states as a function of various physical parameters. The behavior of the internal energy, specific heat, and entropy as functions of temperature and mass density parameter in the inverse-square mass case for different values of magnetic field are shown.     

Crack motion in viscoelastic solids: The role of the flash temperature

We present a simple theory of crack propagation in viscoelastic solids. We calculate the energy per unit area, G(v), to propagate a crack, as a function of the crack tip velocity v. Our study includes the non-uniform temperature distribution (flash temperature) in the vicinity of the crack tip, which has a profound influence on G(v). At very low crack tip velocities, the heat produced at the crack tip can diffuse away, resulting in very small temperature increase: in this “low-speed” regime the flash temperature effect is unimportant. However, because of the low heat conductivity of rubber-like materials, already at moderate crack tip velocities a very large temperature increase (of order of 1000 K) can occur close to the crack tip. We show that this will drastically affect the viscoelastic energy dissipation close to the crack tip, resulting in a “hot-crack” propagation regime. The transition between the low-speed regime and the hot-crack regime is very abrupt, which may result in unstable crack motion, e.g. stick-slip motion or catastrophic failure, as observed in some experiments. In addition, the high crack tip temperature may result in significant thermal decomposition within the heated region, resulting in a liquid-like region in the vicinity of the crack tip. This may explain the change in surface morphology (from rough to smooth surfaces) which is observed as the crack tip velocity is increased above the instability threshold.     

Energy distributions of clusters cooled by thermal radiation

Particles that cool radiatively in vacuum reach a limiting energy distribution, defined by the low energy dielectric function, the heat capacity and time. We find that in a finite time, both mean temperature and the width of the distribution converge to powerlaws in time, and that the ratio of the two reach a constant value which depends on the heat capacity and the photon absorption cross section. Further, both the photon emission rate and the ratio of width to mean energy of the distribution show surprising similarities with the analogous results for cooling by particle evaporation.     

Quantum heat engines, the second law and Maxwell's daemon

We introduce a class of quantum heat engines which consists of two-energy-eigenstate systems, the simplest of quantum mechanical systems, undergoing quantum adiabatic processes and energy exchanges with heat baths, respectively, at different stages of a cycle. Armed with this class of heat engines and some interpretation of heat transferred and work performed at the quantum level, we are able to clarify some important aspects of the second law of thermodynamics. In particular, it is not sufficient to have the heat source hotter than the sink, but there must be a minimum temperature difference between the hotter source and the cooler sink before any work can be extracted through the engines. The size of this minimum temperature difference is dictated by that of the energy gaps of the quantum engines involved. Our new quantum heat engines also offer a practical way, as an alternative to Szilard's engine, to physically realise Maxwell's daemon. Inspired and motivated by the Rabi oscillations, we further introduce some modifications to the quantum heat engines with single-mode cavities in order to, while respecting the second law, extract more work from the heat baths than is otherwise possible in thermal equilibria. Some of the results above are also generalisable to quantum heat engines of an infinite number of energy levels including 1-D simple harmonic oscillators and 1-D infinite square wells, or even special cases of continuous spectra.     

Low-temperature specific heat spectra considering nonextensive long-range correlated quasiperiodic DNA molecules

We consider the low-temperature specific heat spectra of long-range correlated quasiperiodic DNA molecules using a q-gaussian distribution, and compare them with those considering the Boltzmann-Gibbs distribution. The energy spectra are calculated using the one-dimensional Schrödinger equation in a tight-binding approximation with the on-site energy exhibiting long-range disorder and non-random hopping amplitudes. We focus our attention at the low temperature region, where the specific heat spectra presents a logarithmic-periodic oscillations as a function of the temperature T around a mean value given by a characteristic dimension of the energy spectrum.     

First-principles study of the anisotropic thermal expansion of hcp metals Be and Y

A first-principles study of the anisotropic thermal expansion of hcp metals Be and Y is reported. According to quasiharmonic approximation, the phonon spectra were computed at a set of lattice parameters using the pseudopotential plane wave method with the local density approximation in the framework of the density functional perturbation theory. The free energies were obtained according to the calculated phonon spectra and thermal properties such as specific heat at constant volume (pressure) were calculated. The electronic contribution to specific heat was found important to metal Y not only at very low temperature but also over room temperature. The calculated results are in good agreement with available experimental data in a wide range of temperature.     

LiH的热力学性质及分子内部运动对体系热力学性质的影响

利用基于密度泛函理论的第一性原理平面波超软赝势方法,计算了LiH在零温零压下的晶格常数、体弹模量,计算结果与实验值和其他理论计算值符合得较好.通过准谐德拜模型计算了LiH在压强为0-80GPa、温度为0-2000K范围内,体积膨胀率、热涨系数、德拜温度及定容热容随压强和温度的变化关系.最后,以代数方法（AM）和势能变分法(PVM)为基础,运用统计热力学理论计算了LiH分子内部运动对体系热力学性质的影响.     

Studies of bosons in optical lattices in a harmonic potential

We present a theoretical study of Bose condensation and specific heat of non-interacting bosons in finite lattices in harmonic potentials in one, two, and three dimensions. We numerically diagonalize the Hamiltonian to obtain the energy levels of the systems. Using the energy levels thus obtained, we investigate the temperature dependence, dimensionality effects, lattice size dependence, and evolution to the bulk limit of the condensate fraction and the specific heat. Some preliminary results on the specific heat of fermions in optical lattices are also presented. The results obtained are contextualized within the current experimental and theoretical scenario.     

Low-temperature properties of ferromagnetic-antiferromagnetic double layer superlattices

Low-temperature magnetic properties of a Heisenberg model consisting of ferro- and antiferromagnetic layer superlattices are studied by using spin-wave theory and retarded Green's function method. The four-sublattice magnetizations and internal energy and specific heat at low temperature are calculated. The results of various physical quantities are shown for different sets of intra- and interplane coupling interactions. There is a crossover between sublattice magnetizations in each layer is affected by quantum fluctuations, thermal fluctuations and frustration of spins.     

Time and temperature dependence of the specific heat of non-crystalline solids within the tunneling model

We propose a new way to introduce the measuring time in the Tunneling Model of non-crystalline solids. We have obtained a time dependent relation for the specific heat which can be used without limits in time or temperature. We prove that under the usual assumptions of the standard Tunneling Model and without free parameters one can understand quantitatively the experimentally observed time and temperature dependence of the specific heat and heat release experiments on vitreous silica over ten orders of magnitude in time. We also discuss the influence of conductions electrons on the time dependent specific heat. Time dependent experiments could provide useful information on the interaction of Tunneling Systems with conduction electrons.     

Storage of electromagnetic field energy in matter

The partitioning, uniqueness and form of field energy stored in matter, and its properties as a state function, is established. Consequently, the first and second laws apply to the nonfield and field parts of the internal energy as separate entities. This provides a bridge between thermodynamics and the classical theory of electromagnetism. Presentation of the temperature as the sum of nonfield and field contributions is used to establish field dependent barriers to temperature decrease toward the absolute zero, and the existence of field induced temperature jumps. These temperature jumps appear at the instant the field is switched on, or turned off. The partitioning of field and nonfield energies is illustrated for a specific case of an ideal gas, and the heat absorbed by the field is derived in terms of difference in adiabatic magnetization. Finally, the current, restrictive, form of electromagnetic field energy density is redefined with respect to the effect of field energy stored outside the system boundaries. Received 6 June 2000 / Received in final form 26 March 2002 Published online 24 September 2002 RID="a" ID="a"e-mail: zimmels@tx.technion.ac.il     

Low temperature specific heat and thermal conductivity of bulk metallic glass (Cu50Zr50)94Al6

The low temperature specific heat and thermal conductivity of (Cu₅₀Zr₅₀)₉₄Al₆ bulk metallic glass have been studied experimentally. A low temperature anomaly in the specific heat is observed in this alloy. It is also found that in addition to Debye oscillators, the localized vibration modes whose vibration density of state has a Gaussian distribution should be considered to explain the low temperature phonon specific heat anomaly. The phonon thermal conductivity dependence on temperature for the sample does not show apparent plateau characteristics as other glass materials do; however, the influence of the resonant scattering from the localized modes on the lattice thermal conductivity is prominent in the bulk metallic glass at low temperatures.     

Specific heat at low temperature due to negative U centres in disordered solids

The negativeU-Anderson model is considered and energy spectrum is obtained using the Gorkov’s decoupling scheme for one-electron Green’s function. The correlation of localized electron pair (bipolaron) is explicitly taken into account in this scheme. The electronic specific heat of disordered solids with negativeU-centres and having a distribution of negativeU is then calculated. At low temperature the specific heat shows linear temperature dependence, and this linearT-term is a combined effect of distributedU and of the existence of localized electron pairs.     

Quantum vibrational partition function in the non-extensive Tsallis framework

The quantum vibrational partition function has been obtained in the Tsallis statistics framework for the entropic index, q, between 1 and 2. The effect of non-extensivity on the population of states and thermodynamic properties have been studied and compared with their corresponding values obtained in the Boltzmann-Gibbs (BG) statistics. Our results show that the non-extensive partition function of harmonic oscillator at any temperature is larger than its corresponding values for an extensive system and that their differences increase with temperature and entropic index. Also, the number of accessible states increases with q but, compared to the BG statistics, the occupation number decreases for low energy levels while the population of the higher energy levels increases. The internal energy and heat capacity have also been obtained for the non-extensive harmonic oscillator system. Results indicate that the heat capacity is greater than its corresponding value in the extensive (BG) system at low temperatures but that this trend is reversed at higher temperatures.     

Thermodynamic properties of ZnSe under pressure and with variation in temperature

The thermodynamic properties of Zn Se are obtained by using quasi-harmonic Debye model embedded in Gibbscode for pressure range 0–10 GPa and for temperature range 0–1000 K. Helmholtz free energy, internal energy, entropy,Debye temperature, and specific heat are calculated. The thermal expansion coefficient along with Gruneisen parameter are also calculated at room temperature for the pressure range. It is found that internal energy is pressure dependent at low temperature, whereas entropy and Helmholtz free energy are pressure sensitive at high temperature. At ambient conditions,the obtained results are found to be in close agreement to available theoretical and experimental data.     

Finite temperature theory of metastable anharmonic potentials

The decay rate for a particle in a metastable cubic potential is investigated in the quantum regime by the Euclidean path integral method in semiclassical approximation. The imaginary time formalism allows one to monitor the system as a function of temperature. The family of classical paths, saddle points for the action, is derived in terms of Jacobian elliptic functions whose periodicity sets the energy-temperature correspondence. The period of the classical oscillations varies monotonically with the energy up to the sphaleron, pointing to a smooth crossover from the quantum to the activated regime. The softening of the quantum fluctuation spectrum is evaluated analytically by the theory of the functional determinants and computed at low T up to the crossover. In particular, the negative eigenvalue, causing an imaginary contribution to the partition function, is studied in detail by solving the Lamè equation which governs the fluctuation spectrum. For a heavvy particle mass, the decay rate shows a remarkable temperature dependence mainly ascribable to a low lying soft mode and, approaching the crossover, it increases by a factor five over the predictions of the zero temperature theory. Just beyond the peak value, the classical Arrhenius behavior takes over. A similar trend is found studying the quartic metastable potential but the lifetime of the latter is longer by a factor ten than in a cubic potential with same parameters. Some formal analogies with noise-induced transitions in classically activated metastable systems are discussed.     

Low temperature glassy properties of disordered crystals

Low temperature measurements of specific heat, thermal conductivity, dielectric dispersion, ultrasonic dispersion and other properties have disclosed that a variety of disordered crystals exhibit the same anomalous behavior as found in amorphous solids. The anomalies arise from localized excitations having broad spectra in both energy and equilibration time. In some disordered crystals, these spectra may be changed systematically by varying the disorder present. The physical origin of the excitations, in crystals or glasses, lacks a satisfactory theoretical explanation. It is expected that the crystalline systems will be more amenable to theoretical study. The crystalline solids found to harbor the excitations include, at this time, certain fast-ion conductors, ferroelectrics, metallic alloys, and rotationally disordered solids.     

Some theoretical considerations in modeling laser-induced incandescence at low-pressures

Laser-induced incandescence (LII) of nanoparticles at low pressures has received some attention in recent years as a particle sizing technique or a technique for inferring the mean value of the absorption function of the particle material. In this paper, we are concerned with some fundamental issues in the theory of LII with particular attention paid to those encountered at very low pressures. The commonly adopted Rayleigh approximation for particle laser energy absorption and subsequent thermal emission is critically evaluated against the Mie solution in the range of size parameter relevant to LII. The Rayleigh approximation can cause significant error in particle laser energy absorption rate, especially when shorter wavelengths are used, and potentially in the particle temperature inferred from the two-color LII. We also demonstrate that claims that low-pressure LII can be used for particle sizing are flawed, due to the use of an incorrect expression for radiation heat loss rate from the particles in this regime, and unjustified neglect of particle sublimation heat loss. Using the currently best available carbon sublimation rate expression and physical parameters, the relative importance of heat conduction, thermal radiation, and sublimation heat loss from an isolated carbon particle was investigated for different ambient pressures, particle temperatures and particle diameters. To ensure particle radiation heat loss is dominant over conduction and sublimation the ambient pressure and the particle temperature should be kept respectively lower than 10^-4 atm and below about 2800 K. Under these conditions the effective temperature of a particle ensemble containing non-aggregated polydisperse primary particles to the power of -4 is proportional to the mean value of the particle absorption function, provided the particles are in the Rayleigh regime in the near infrared. The effect of aggregation on particle absorption and emission is briefly discussed. PACS 44.10.+i; 44.40.+a; 61.46Df