Crystal growth by dynamic gradient reserval techniques — III. Pure thermodynamic derivation of growth conditions

The thermodynamic derivation of the growth condition requires no kinetic growth constants. Kinetics appear only in the form of activation barriers. Complicated Δ G-pathways can principally be reduced to an easily understandable model of square wave functions.     

Autodiffusion dans les alliages concentres fer-palladium

Measurements of the diffusion coefficients of ³⁹Fe and ¹⁰³Pd in various iron-palladium alloys (between 0 and 100at.% iron) between 1100 and 1250°C, have shown that the activation energies for selfdiffusion for the two tracers are practically equal, independent of composition.The values obtained are very close to those corresponding to the activation energy of chemical diffusion. This result is in good agreement with the fact that the thermodynamic activities of iron and palladium have small temperature dependance and that the vacancy flow, as calculated with the model of Manning, is rather small.In spite of a strong ordering tendency in the solid solution of Fe-Pd, as indicated by a thermodynamic calculation, this model allows to calculate, with the aid of the measured self-diffusion coefficients, various parameters, such as the correlation factors for both iron and palladium, the vacancy correlation factors, and the atomic jump frequencies.     

Chemical tension and global equilibrium in VLS nanostructure growth process: from nanohillocks to nanowires

We formulate a global equilibrium model to describe the growth of one-dimensional nanostructures in the VLS process by including also the chemical tension in addition to the physical tensions, i.e. surface energies. The chemical tension derives from the Gibbs free energy change due to the growth of a crystal layer of an elementary thickness. The system global equilibrium is arrived at via the balance of the static physical tensions and the dynamic chemical tension. The model predicts and provides conditions for the growth of nanowires of all sizes exceeding a lower thermodynamic limit. The model also predicts the conditions distinguishing the growth of nanohillocks from nanowires. These predictions will allow the verification of the model by future experiments specifically designed for this purpose. PACS 81.07.-b; 82.60.-s; 05.70.Np; 68.35.Md; 68.03.Cd     

A simulation model of biofilms with autonomous cells: I. Analysis of a two-dimensional version

We introduce a single-cell based simulation model of biofilm growth. Each microbial cell is modelled as an autonomous agent whose behavior is controlled by thermodynamic parameters, mechanical properties, physiological rules and environmental conditions. In the two-dimensional version presented here, a cell is represented by a closed chain of self-avoiding beads linked together using the bond fluctuation algorithm. The cell is thus controlled both by the rigidity of its membrane and a pressure difference. The model is complemented by key features such as the explicit presence of nutrient diffusion and flow, the processes of cell-division and cell-death, and the attractive interactions between the cell and the surface on which the colony grows. Tuning the parameters of the model can lead to the growth and maturation of various types of biofilms. In this first article, we describe the main properties of a two-dimensional version of the model, and we discuss the extension to three dimensions.     

Self-organization in systems of treadmilling filaments

The cytoskeleton is an important substructure of living cells, playing essential roles in cell division, cell locomotion, and the internal organization of subcellular components. Physically, the cytoskeleton is an active polar gel, that is, a system of polar filamentous polymers, which is intrinsically out of thermodynamic equilibrium. Active processes are notably involved in filament growth and can lead to net filament assembly at one end and disassembly at the other, a phenomenon called treadmilling. Here, we develop a framework for describing collective effects in systems of treadmilling filaments in the presence of agents regulating filament assembly. We find that such systems can self-organize into asters and moving filament blobs. We discuss possible implications of our findings for subcellular processes.     

A comparative analysis of linear,nonlinear and improved nonlinear thermodynamic models of voltage-dependent ion channel kinetics

The linear, nonlinear and improved nonlinear thermodynamic models of the voltage-dependent ion channels were proposed to deduce the exact functional form of the rate constants. In this context, we present a comparative analysis of the linear, nonlinear and improved nonlinear thermodynamic models of voltage-dependent channel kinetics based on the sodium activation experimental data of Cav3.1 channel. We also provide some insight on the assumptions used to derive the thermodynamic models of the channels and show that the improved nonlinear thermodynamic model provides a simple and physically plausible approach to describe the behavior of the voltage-dependent ion channels.     

Contribution a la theorie atomique de la diffusion chimique

Here we present an analysis and a development of the atomic theory of chemical diffusion as proposed by Manning for a binary system a/b.The general expression for the flux of a tracer in a concentration gradient is first established. This expression of the flux is identified with that deduced in the phenomenological theory. Thus a relationship between the partial correlation factors of vacancies with each of the a and b species is obtained.The effect of “vacancy flow” can be described in terms of these correlation factors. Thus the vacancy flow on species A leads to a correlation of the vacancy jumps with species B and vice versa.We shall see that the Nernst-Einstein equation can be extended to the case of chemical diffusion and that the ratio of the intrinsic diffusion coefficients is equal to the ratio of the mean jump frequencies W_A and W_B.Also, the activation energies of intrinsic diffusion coefficients are related very simply to the activation enthalpies of atomic jumps.In conclusion, we shall see that chemical diffusion in a binary system a/b can be completely described if either the thermodynamic factor and the coefficients of self diffusion, or the thermodynamic factor and the coefficients of intrinsic diffusion are known as functions of the concentration.     

Thermodynamic limit for classical systems with Coulomb interactions in a constant external field

We introduce a new method for studying the thermodynamic limit for systems of particles with Coulomb interactions. The method is based on calculating the potential energy of the Coulomb interactions from the electric or magnetic fields in the system rather than from the energy of the individual particle — particle interactions. We are able to include the effects of a constant external field being imposed at the boundary of the system. The difficulties associated with Coulomb potentials being not even weakly tempered are overcome by imposing the boundary condition that at the boundary of the region containing the particles, the electric or magnetic field has normal component equal to that of the applied field. We prove that the thermodynamic free energy density exists and is independent of the sequence of regions used to define the limit. We introduce sequences of regions all of the same shape and show that for these sequences of regions the thermodynamic free energy density is independent of shape. Finally, we prove that the thermodynamic free energy is a convex function of the density of particles and of the applied field.     

Migration and proliferation dichotomy in tumor-cell invasion

We propose a two-component reaction-transport model for the migration-proliferation dichotomy in the spreading of tumor cells. By using a continuous time random walk (CTRW), we formulate a system of the balance equations for the cancer cells of two phenotypes with random switching between cell proliferation and migration. The transport process is formulated in terms of the CTRW with an arbitrary waiting-time distribution law. Proliferation is modeled by a standard logistic growth. We apply hyperbolic scaling and Hamilton-Jacobi formalism to determine the overall rate of tumor cell invasion. In particular, we take into account both normal diffusion and anomalous transport (subdiffusion) in order to show that the standard diffusion approximation for migration leads to overestimation of the overall cancer spreading rate.     

Socio-economical dynamics as a solvable spin system on co-evolving networks

We consider social systems in which agents are not only characterized by their states but also have the freedom to choose their interaction partners to maximize their utility. We map such systems onto an Ising model in which spins are dynamically coupled by links in a dynamical network. In this model there are two dynamical quantitieswhich arrange towards a minimum energy state in the canonical framework:the spins, s_i, and the adjacency matrix elements, c_ij.The model is exactly solvable because microcanonical partition functions reduce to productsof binomial factors as a direct consequence of the c_ij minimizing energy. We solve the system for finite sizes and for the two possible thermodynamic limits and discussthe phase diagrams.     

Fluctuations of the phase difference across an array of Josephson junctions in superfluid 4He near the lambda Transition

We present a formal thermodynamic treatment of superfluid flow in a Josephson junction. We show that the current i(s) and the phase difference phi are thermodynamic conjugate variables. We derive quantitative expressions for the rms fluctuations of i(s) and phi. Also, we discuss the thermodynamic stability and the thermal activation to the phase-slip region. We apply the developed formalism to show why an array of apertures in 4He can exhibit the Josephson effect near the lambda transition despite strong thermal fluctuations.     

Phase-field model for multiphase systems with different thermodynamic factors

A modified phase-field model for quantitative simulations of low-speed phase transitions in multiphase systems is proposed, which takes into account the difference between thermodynamic factors in all the phases. The presented model is based on the quantitative phase-field concept developed by Steinbach et al. [I. Steinbach, F. Pezolla, B. Nestler, M. Seeelberg, R. Prieler, G.J. Schmitz, J.L.L. Rezende, A phase field concept for multiphase systems, Physica D 94 (1996) 135] for multiphase systems allowing to consider the multiphase transition as a superposition of pairwise interactions between two phases. We complete this approach and develop a model, which uses parameters derived from chemical free energy functions of individual phases evaluated from experimental data by the CALPHAD method Lukas et al. (2007) [17]. Because the thermodynamic factors are different in various phases we need to evaluate a special form of total chemical free energy function of a multiphase mixture and use it in the phase-field model. It is shown, that for the developed model the thin-interface asymptotic and the anti-trapping term developed previously for the solidification of pure substances can be applied. The model is verified by an example of the Al-Ni system whose peritectic structural morphology during the directional solidification is investigated. The suggested model can be also extended to multicomponent systems.     

Thermodynamic investigation of yield-stress models for amorphous polymers

A thermodynamic study of the yield process in amorphous polymers is proposed to investigate four yield theories: the Eyring model and its linearized form, the cooperative model and the Argon model. For a poly(methyl methacrylate) (PMMA) and a polycarbonate (PC), the corresponding apparent activation volumes and apparent activation energies are calculated and compared for a wide range of temperatures and strain rates. For the cooperative model, we show that the secondary molecular relaxation is a key parameter in the explanation of the specific mechanical behaviour of glassy polymers at low temperatures and at high strain rates. For the three other models, thermodynamic inconstancies were found and these are discussed.     

Growth kinetics of polymer crystals in bulk

Temperature-dependent measurements of spherulite growth rates carried out for i-polystyrene, poly(ε -caprolactone) and linear polyethylene show that the controlling activation barrier diverges at a temperature which is 14K, 22K and 12K, respectively, below the equilibrium melting points. We discuss the existence of such a “zero growth temperature” T _zg in the framework of a recently introduced thermodynamic multiphase scheme and identify T _zg with the temperature of a (hidden) transition between the melt and a mesomorphic phase which mediates the crystal growth. The rate-determining step in our model of crystal growth is the attachment of chain sequences from the melt onto the lateral face of a mesomorphic layer at the growth front. The necessary straightening of the sequence prior to an attachment is the cause of the activation barrier. A theory based on this view describes correctly the observations. With a knowledge of T _zg it is possible to fully establish the nanophase diagram describing the stability ranges of crystalline and mesomorphic layers in a melt. An evaluation of data from small-angle X-ray scattering, calorimetry and optical growth rate measurements yields heats of transition and surface free energies of crystals and mesophase layers, as well as the activation barrier per monomer associated with the chain stretching. According to the theory, the temperature dependence of the crystallization rate is determined by both the activation energy per monomer and the surface free energy of the preceding mesomorphic layer. Data indicate that the easiness of crystallization in polyethylene is first of all due to a particularly low surface free energy of the mesomorphic layer.     

Two-dimensional normal grain growth: topological aspects

Normal grain growth in polycrystals is an important example of a capillarity driven coarsening phenomenon where topological structure of the system plays a major role. The process is practically important and attracts much interest, in particular in two-dimensional (2D) polycrystals because of the growing technological importance of thin polycrystalline films. In the present paper we discuss various approaches to normal grain growth in 2D polycrystals. We stay mostly within the framework of the uniform boundary model. This model provides a reasonable simplification leading to the Von Neumann-Mullins relation that relates the rate of growth of an individual grain to its local topology. Comparing different approaches—relatively simple mean-field theories, more sophisticated models incorporating real topology, and computer simulations adequately reproducing local equations of motion—we identify the principal factors responsible for different features of the phenomenon.     

非线性过程控制系统传感器故障检测新方法

针对电厂热力系统故障检测和定位准确性低的问题,提出了基于鲁棒输入训练网络(Robust Input-training Network, RITN)的传感器故障检测模型。采用带参数限制项的目标函数对网络进行训练,并在测试目标函数中引入影响因子,增加了模型训练精度,抑制了网络计算过程故障数据对正常值的影响,减小了残差污染,提高了模型准确性。以某300MW电厂热力系统20组测点为对象进行算例分析,通过反复的实验,结果表明,该模型能够更加准确的对非线性系统故障点进行检测和分离,并更加精确重构各变量真实值,验证了该模型用于非线性过程传感器故障检测的有效性和可靠性。     

计入固液界面作用的润滑热力学模型与分析

摩擦与润滑过程是典型的能量耗散过程, 在机理上与非平衡热力学中的熵增、耗散结构等理论颇有相似之处. 通过热力学分析可以对一些典型的摩擦磨损过程做出合理的机理揭示与推测. 本文利用热力学理论对典型的润滑过程进行了建模分析. 采用分离压模型表征和计入了微尺度下的固液界面作用, 揭示分析了润滑热力学模型与润滑状态Stribeck曲线的联系. 从分析计算结果来看, 润滑Stribeck曲线的摩擦系数最低点与系统热力学上的熵增率最低点具有相当好的对应关系, 而润滑状态从弹流润滑向薄膜润滑的转变过程, 可以用耗散结构理论加以机理解释. 文中的热力学模型和方法能够有效地体现出润滑过程中多物理要素跨尺度非线性耦合的作用, 对实际工程与实验有着重要的指导作用.     

Microscopic systems with and without Coulomb interaction, fragmentation and phase transitions in finite nuclei

We test the influence of the Coulomb interaction on the thermodynamic and cluster generation properties of a system of classical particles described by different lattice models. Numerical simulations show that the Coulomb interaction produces essentially a shift in temperature of quantities like the specific heat but not qualitative changes. We also consider a cellular model. The thermodynamic properties of the system are qualitatively unaltered. Received: 7 November 2000 / Accepted: 17 May 2001