Kinetic Phase Diagrams Research Articles

Construction of kinetic phase diagrams

It is a noted fact that the composition of a mixed solid phase grown at non-equilibrium can deviate from the equilibrium composition due to the very low diffusion rate in the solid phase. We present an analytical model for the determination of the kinetic composition of a binary solid phase that is growing from a solution at a given supersaturation, giving rise to kinetic phase diagrams. The model is derived for growth at rough surfaces but is expected to apply also to growth at non-roughened surfaces. Kinetic phase diagrams for different undercooling and excess energy parameters are presented and discussed. If the interaction parameters, describing the excess free energy, are large the model equations can have two stable solutions, which implies the simultaneous growth of two solid phases with different compositions. This kinetic phase separation depends on the undercooling and the composition dependence of the attachment probabilities.

Thermodynamic Limits and Kinetic Probabilities During Homogeneous Nucleation in Liquid Ag-Cu Alloys

Novel kinetic phase diagrams for homogeneous nucleation during nun-equilibrium solidification of Ag-Cu alloys were evolved by stochastic modelling. The allowable undercoolings and the composition of the primary nucleating phase at any cooling rate and liquid composition could be read from these diagrams, The calculated values were found to lie within the thermodynamically permissible limits determined through construction of non-isothermal metastability held diagrams.

Computational model of nonequilibrium phase transitions in a Si-Ge system

A computational model of a Si-Ge system melting and solidification induced by pulsed-laser irradiation is presented in the paper. Phase transitions in the system are modeled using the theory of transition states so that undercooling or overheating of the interface and kinetic phase diagrams are taken into account. The computational solution of the mathematical model is performed using the Galerkin finite element method in a one-dimensional approximation and the moving boundary problem is solved by a front-fixing technique. In a practical application of the model, the melting and solidification of both Si-Ge alloys of various composition and thin Ge layers on the Si bulk induced by ArF excimer laser are simulated. The results of numerical simulations are compared with the available experimental data.

Scalings of A + B Reaction Kinetics due to Anisotropic Confinements

We report on the diffusion-limited A + B reaction in highly anisotropic spaces. In addition to the highly non-classical behavior of the density of reactants predicted for isotropic spaces, we observe a dimensional crossover in A + B → 0 reactions due to the geometrical compactness of the tubular 2- and 3-dimensional spaces (baguettelike structures). For slabs, we find the crossover time Tc. = Wα, which scales as , where a, b and β are given by the earlier and the late time inverse density scalings of ρ− 1 ˜-, ta and ρ−1 - tbWβ, respectively. We also obtain a critical width W, below which the chemical reaction progresses without traversing a 2- or 3-dimensional Ovchinnikov-Zeldovich reaction regime. We find that there exist different hierarchies of dimensionally forced crossovers, depending on the initial conditions and geometric restrictions. Kinetic phase diagrams are employed and exponents are given for the A + B elementary reactions in various euclidean geometries. Monte-Carlo simulations illustrate some of the kinetic hierarchies.

Combined pressure/heat-induced inactivation of butyrylcholinesterase

The combined effects of pressure and temperature on the activity of butyrylcholinesterase (BuChE) were investigated in the pressure range from 10 −3 to 5 kbar and temperature range from −10°C to 70°C. Inactivation of the enzyme showed a complex dependence on pressure and temperature. Under moderate pressures (1–3 kbar) at temperatures 40–65°C BuChE was resistant to heat inactivation; under other conditions of pressure and temperature, the action of both parameters was synergistic and caused inactivation. Results allowed to construct a pressure-temperature kinetic phase diagram for the enzyme inactivation. The elliptic diagram for the irreversible transition active→inactive BuChE as a function of both pressure and temperature has a positive angular coefficient. This indicates that pressure acts as a stabilizer of BuChE against heat denaturation.

Kinetic phase diagram for CO oxidation on Pt(210): Pattern formation in the hysteresis and oscillation regions

The reactive behavior of catalytic CO oxidation on Pt(210) is studied by means of combined reaction rate measurements and photoelectron emission microscopy (PEEM). These methods allow an investigation of the phenomena at macroscopic and mesoscopic level, respectively. The external control parameters (flow rate, CO and oxygen partial pressures, surface temperature and scanning rates of pressure and temperature) are systematically varied to reveal various reactive regions in parameter space. The macroscopic measurements for a given temperature and flow rate (under isothermal conditions) show that lower pressures lead to a pronounced clockwise hysteresis in the production rate of CO2, while increasing pressures cause a systematic narrowing leading to a crossing of the two hysteresis branches into a region of counterclockwise hysteresis. A further pressure increase leads to macroscopic temporal oscillations. Mesoscopic spatiotemporal oscillations appear at the same conditions. The resulting macroscopic isothermal kinetic phase diagram exhibits a cross-shaped characteristic similar to that previously obtained for the Pd(110) surface. The mesoscopic lateral distribution of CO and oxygen adsorbed on the surface is monitored with the photoelectron emission microscope during the reaction at isothermal conditions and different constant oxygen pressures. The observed mesoscopic spatiotemporal patterns, such as islands, waves, target patterns and spirals, are correlated via the external control parameters with different regions in the macroscopic isothermal phase diagram. The results are compared with previous data of CO oxidation on other surfaces, like Pd(110) and Pt(110).

Growth of minute barium ferrite single crystals from a Na 2OB 2O 3 flux system

Mono-sized minute single crystals of barium ferrite were grown from a Na 2O solvent containing B 2O 3. A kinetic phase diagram of the BaFe 12O 19Na 2O system containing 5 wt% of B 2O 3 was prepared for the crystal growth. In the solution containing more than 60 wt% Na 2O components, octahedral crystals of three types were encountered, two of which appear to represent two different types of pseudomorphic transformation.

Scaling model of annihilation-diffusion kinetics for charged particles with long-range interactions.

We propose a general scaling model for the diffusion-annihilation reaction ${A}_{+}+{A}_{\ensuremath{-}}\ensuremath{\rightarrow}\ensuremath{\emptyset}$ with long-range power-law interactions. The presented scaling arguments lead to the finding of three different regimes, depending on the space dimensionality $d$ and the long-range force power exponent $n$. The obtained kinetic phase diagram agrees well with existing simulation data and approximate theoretical results.

Growth of island films from binary melts or a vapor phase at the ostwald ripening stage under non-isothermal conditions

A theory on the growth of island films from binary melts or a vapor phase under non-isothermal conditions is developed. A system in which the growth of island films takes place is thermally isolated, and both diffusion and temperature fields exist in the system. Temperature fields are formed due to evolution of the latent heat of crystallization or the heat of sublimation. The diffusion and temperature fields and self-consistent with each other. A full set of equations describing this process is derived. By solution of this set of equations, the rules governing the variation of the mean radius and the island density in time with different mechanisms for mass or heat transfer were found. It is shown that islands grow due to two processes, diffusional or thermal. One of these processes, namely, the diffusional one, is related to a variation in the supersaturation, while the thermal process occurs due to a change in the overcooling. It is also shown that the rate of island growth is determined by the factor that relates coefficients of the diffusion and thermal conductivity. Kinetic phase diagrams for binary systems are defined. A distribution relating the size of islands to their composition is obtained for the island films growing from binary systems, which gives rise to a continuous range of solid solutions in the solid state. The law of the variation of composition with time is found. Open systems are discussed in the second part of the work. The possibility of controlling the processes of growth of islands by means of sinks (sources) of heat or air is demonstrated. A model of growth of island film assemblies from melts having the eutectic composition is constructed. The possibility of controlling the structure or composition of continuous films is demonstrated.

Rapid dendritic growth in undercooled Ag-Cu melts

The results of measurements of the reciprocal recalescence rise time (Δt) −1 of undercooled melts of an Ag-Cu alloy with 65 at.% Cu are presented. It is shown that (Δt) −1 is a semiquantitative measure of the growth rate. In agreement with observations already made on alloys with other compositions in this binary system, the growth rate as a function of the undercooling rises sharply at an undercooling corresponding to the T 0 temperature. This behaviour can be explained in the framework of the theories of rapid dendritic growth, when the kinetic displacements of the solidus and liquidus are taken into account. A simple empirical expression for this kinetic effect is proposed. For the Ag-65 at.% Cu alloy the predictions of the theory are expressed as a plot of growth rate against undercooling and also in the form of a kinetic phase diagram. The predictions are in good qualitative agreement with the experimental results.

Assessment of the physical state of stratospheric aerosols by use of emulsions in the construction of kinetic phase diagrams

Assessment of the physical state of stratospheric aerosols by use of emulsions in the construction of kinetic phase diagrams

Kinetic phase transitions and bistability in a model surface reaction I. Monte Carlo simulations

We have performed Monte Carlo simulations for a model of the surface-catalyzed 2A + B 2 → 2AB reaction in which the surface reaction rate and the A surface diffusion rate are finite. The kinetic phase diagram for this model contains two poisoned phases and a reactive phase, separated by a continuous and a discontinuous kinetic phase transition. Above the discontinuous transition there is a region of near bistability in which the poisoned phase is stable and the reactive phase is strongly metastable. This regime exists in a very narrow band of impingement rates when there is no diffusion but becomes much broader when surface diffusion is fast. We present MC measurements of the range of the bistability when the diffusion and reaction rates are similar. The A diffusion rate is found to affect the bistable regime dramatically. The physical origin of this effect and its relation to experiments is analyzed. We further quantify the effects of diffusion on this reaction by measuring the surface lifetime and mobility of adsorbed A particles.

Characterization of Buffer Layers for SiC CVD

Silicon Carbide has been grown by rapid thermal carbonization of (100) and (111) Si surfaces at atmospheric pressure using 1 lpm hydrogen (H 2 ) as a carrier gas and propane (C 3 H 8 ) with concentrations ranging from 0.025-1.5%. RHEED investigations have shown single crystalline SiC as well as additional phases depending on the propane concentration. A set of kinetic phase diagrams were determined. The chemical nature was examined by AES. At concentrations below 0.1% additional silicon and an increasing number of defects were found. The growth on (100) substrates has shown a change in orientation toward (111). Above 0.6% a carbon rich polycrystalline layer covering completely the surface was formed. The carbon has both graphitic and carbidic nature. The graphitic content could be decreased by post deposition H 2 annealing without changing the polycrystalline nature of this top layer. Best crystallinity were found at 1250 °C, 0.15% propane and 30-90 s.

Nonequilibrium phase diagrams in the PbCl2−AgCl eutectic system

It is well-known that eutectics do not necessarily grow at the eutectic temperature, or with the eutectic composition. Thus, the eutectic point can be shifted due to nonequilibrium conditions in the system. This fact was observed in many experiments. We try to explain this behaviour on base of the study of phase transformation kinetics. We construct the kinetic phase diagrams of PbCl2−AgCl within the framework as of the nucleation theory as of the theory of growth on the phase interface. Our models are based on the molecular model of the difference of chemical potential of components for the liquid and solid phases. The proposed model describes the position of the eutectic point very well and is practically applied for the study of nonequilibrium directional growth in the PbCl2−AgCl system.

Oscillating Catalytic CO Oxidation on a Platinum Field Emitter Tip: Determination of a Reactive Phase Diagram by Field Electron Microscopy

A [111]-oriented Pt field emitter tip is used to study bistability and oscillations of CO oxidation by field electron microscopy (FEM) under low-pressure conditions ( p O 2 = 4 × 10 −4 Torr, p CO = 8 × 10 −8 to 4 × 10 −5 Torr) in the temperature range 240 to 450 K. A kinetic phase diagram can be established, obtained on an FEM level with ≍2 nm lateral resolution. Below T ≍ 300 K a region of bistability prevails, and above T ≍ 300 K an oscillatory regime is obtained, thus yielding a cross-shaped phase diagram. These phenomena are surface plane specific and visible at the {011} planes of Pt and their surroundings.

Thermal treatment and analysis

Heating and/or cooling of substances is one of the oldest and basic methods for preparing materials with defined properties. This always leaves a definitive fingerprint of the thermal history. Beside knowing the structure we need to specify such materials by their thermodynamic behaviour, i.e., stability/metastability, phase relations and transitions, particularly establishing corresponding characteristic points. All this can be based on ordinary thermodynamics but its validity must be approved for non-equilibrium conditions of temperature changes where equilibrium and kinetic effects overlap. The slower the phase transition proceeds the greater is the deviation of the system state (kinetic curve) from its equilibrium state (equilibrium background). This makes possible to locate the actual phase boundary between two states investigated, resulting in the so-called kinetic phase diagrams. Most of modern technologies are intentionally based on non-equilibrium phenomena in order to create metastable/nonstable phases of specific properties. In this sense thermal analysis is understand as the method for determining the sample state on the basis of the sample interactions with the surroundings whose intensive parameters are controlled. Temperature is here considered as a basic parameter that connects all thermophysical measurements and thermal treatments.

Calculations of the phase interface constitution during the non-equilibrium growth of binary eutectics

It is well-known that eutectics do not necessarily grow at the eutectic temperature, or with the eutectic composition. Thus, the eutectic point can be shifted due to nonequilibrium conditions in the system. This fact was observed in many experiments. We try to explain this behaviour on the basis of the study of phase transformation kinetics. We construct the kinetic phase diagrams within the framework of the nucleation theory as well as of the theory of growth on the phase interface. Our models are based on the molecular model of the difference in chemical potential of components for the liquid and solid phases. The proposed model describes the position of the eutectic point very well.

Kinetics of nucleation in eutectic PbCl 2-AgCl system

Results of the space experiments show the shift of the eutectic point in the PbCl 2-AgCl system in the direction of the higher concentration of AgCl with an increase of the undercooling of the melt. In our paper we endeavour to explain this phenomenon on the basis of the study of nucleation kinetics in the system. Using the statistical methods of calculations of the probability of first critical nucleus creation in the system, a kinetic phase diagram is constructed, which corresponds to the experimental data. A molecular model (based on the energy of intermolecular binding) of the difference of chemical potential in liquid and solid phase is proposed in our work. This model describes the position of the eutectic point and the shape of the liquidus line in the equilibrium phase diagram very well.

Kinetic phase diagrams for the monomer–dimer surface reaction: Unification of mean-field and lattice–gas behavior

We provide a unified discussion of kinetic phase transitions for mean-field and lattice–gas treatments of the monomer–dimer surface reaction. For high surface mobilities, kinetics is typically well described by mean-field rate equations. These reveal bistability over a range of monomer adsorption rates which diminishes with increasing nonreactive monomer desorption rate d, and vanishes at some critical d=dc. Relative stability in the bistable region is determined from the behavior of chemical waves corresponding to the displacement of one stable state by the other. Their evolution is determined via appropriate reaction–diffusion equations. Conventional diffusion terms are modified here to reflect the influence of the presence of one species on diffusion of the other. We determine equistability (i.e., discontinuous transition) points for d≤dc, and thus construct a kinetic phase diagram including a spinodal line. For lower surface mobilities, analysis of lattice–gas models reveals qualitatively analogous behavior. The key difference is that for lower mobilities, spontaneous fluctuations are effective in automatically selecting the most stable state, i.e., in reducing metastability, and thus producing discontinuous transitions.

Comment on "Kinetic phase diagram for crystal growth: A (1+1)-dimensional model"

A Comment on the Letter by R. Phillips and D. C. Chrzan, Phys. Rev. Lett. 67, 220 (1991).Received 8 August 1991DOI:https://doi.org/10.1103/PhysRevLett.68.2854©1992 American Physical Society