Chemistry and Physics Faculty Working Papers

Nonisothermal relaxation in a nonlocal medium

Alexander Umantsev et al. — Thu, 21 Feb 2013 12:33:24 PST

A study is made of the thermodynamics of a non-local medium whose evolution is governed not only by the temperature and pressure, but also by the field of a relaxation parameter. For solid-state materials which undergo a phase transition, such a relaxation parameter is the order parameter. Heat transport equations are derived together with a thermodynamic inequality which must be satisfied during relaxation. The motion of an interphase boundary during a first-order phase transition is investigated. It is shown that, if the width of the boundary exceeds a critical value, there are steady-state conditions under which the new phase formed in an exothermal transition may be at a temperature above the equilibrium temperature.

Modeling the evolution of a dendritic structure

Alexander Umantsev — Thu, 21 Feb 2013 12:25:50 PST

The authors give the results of mathematical modeling of the evolution of a dendritic structure with the aid of the model proposed in Ref. I. They show that, as also in experiment, on the side surface of the model dendrite secondary branches form and develop into the side structure. They make a detailed investigation of its evolution in the process of growth. They show that as time passes the side structure becomes coarser. They study the changes in the dendritic structure in relation to the supercooling. With increasing supercooling the structure becomes denser, then changes to a cellular form, and finally, when the supercooling is greater than one, there is a transition to globular growth forms. A comparison is made with the experimental results.

Mathematical model of growth of dendrites in a supercooled melt

Alexander Umantsev et al. — Thu, 21 Feb 2013 12:18:19 PST

Motion of a plane front during crystallization

Alexander Umantsev — Thu, 21 Feb 2013 12:10:56 PST

Many authors have studied the growth rates of crystals with a plane front. It is known that, if the advance of the boundary is determined by deviation of its state from equilibrium, then various regimes can be realized in the system, depending on the external conditions. ^1,2 However, they have not yet been obtained as different solutions of a single problem. In our work, the integral equation representing normal growth of a crystal is solved by means of an asymptotic expansion by the method of Laplace. In the second part we construct an algorithm for obtaining numerical solutions to the problem of solidification, and compare these with the analytical results.

Thermal Effects of Interface Motion in Crystallization

Alexander Umantsev — Thu, 03 May 2012 13:37:50 PDT

This paper discusses two thermal effects of crystallization, which may be of interest for the community of molecular dynamics modelers. The first effect deals with the problem of motion of a plane interface in the system with internal cooling. It provides a simple recipe for identification of the kinetic coefficient of growth as a function of the measurable quantities, which does not require direct measurement of the interfacial temperature during the crystallization. The second effect deals with a heat-trapping effect, which consists in the crystallization of a solid phase from the supercooled liquid when the temperature of the crystallized solid is above the melting point.

Calibration of the Egret Gamma Ray Telescope With a Back-Scattered Laser Beam

John Richard Mattox — Wed, 23 Nov 2011 10:29:51 PST

One of the three co-aligned gamma ray telescopes to be placed in orbit aboard the Gamma Ray Observatory is EGRET, the energetic gamma ray experiment telescope. EGRET will measure celestial gamma rays in the energy range 20 - 24,000 MeV. The telescope uses conversion foils and a spark chamber to resolve gamma ray direction and is triggered by a directionally sensitive pair of plastic scintillator arrays. An 8" thick N aI(TI) spectrometer below the spark chamber yields information about the gamma ray energy. The sensitive area is 20 times larger than previous instruments of its type. A full sky survey is expected to resolve ~10 extragalactic and ~100 galactic point gamma ray sources. Diffuse gamma ray emission will also be examined.

A calibration of the telescope to determine efficiency, angular resolution and energy resolution as a function of gamma ray energy and arrival direction is necessary to analyze the flight data. EGRET received a calibration gamma ray exposure with a back-scattered laser beam. Gamma rays were produced by the compton scattering of frequency-doubled YAG laser photons from a high energy electron beam. The SLAC beam was constructed originally to produce 20 GeV gamma rays. Modifications were made to operate over the energy range required for calibration. The beam was operated at ten gamma ray energies between 15 MeV (0.65 Ge V electron energy) and 10 GeV (22.4 GeV electron energy). The back-scattered gamma rays were collimated to produce an energy spectrum of ~15% FWHM.

The beam intensity used was ~0.3 gamma rays per machine pulse. The intensity was monitored primarily by placing a 15 cm thick plastic scintillator in the beam to convert and detect a known fraction of the gamma rays . The response of the NaI(TI) spectrometer in EGRET was also used for beam intensity monitoring.

A large sample of photomultiplier tubes was evaluated for use with the energy spectrometer. Absolute measurements of gain indicate that the scintillation efficiency of NaI(TI) is at least 17±2% - significantly higher than has been previously assumed. The gain was monitored during high anode current. A temporary gain increase of ~10% was noted for 52% of the photomultipliers, while 33% showed a temporary gain decrease of the same magnitude.

On the Origin of Biological Functions

Alexander Umantsev — Wed, 23 Nov 2011 10:29:50 PST

We consider the problem of structure and functions of the first forms of living matter and present a hypothesis that they were formed through a physico-chemical process known as dendritic crystallization. According to this hypothesis the branching, dendritic structures helped build living systems by lending them functions so that organic chemical evolution is just one natural consequence of the evolution of matter in the universe. We conclude that a self-replicating biological system with adaptation emerged from simple molecules using completely abiotic mechanism of formation, which acted simultaneously or intermittently at different places on the early Earth and created similar structures everywhere. The dendritic hypothesis of origin of the functions explains similarities in the living systems and supports the assumption of a ‘second genesis of life’. The dendritic scenario does not need carbon/phosphorus-based solutes in water-based solutions, which may have
important implications for exobiology and extraterrestrial origin-of-life scenarios. An experiment to test the hypothesis is suggested.

Thermodynamic Stability of Transition States in Nanosystems

Alexander Umantsev — Wed, 23 Nov 2011 10:29:49 PST

We present a theory which shows that, in a closed system of fixed volume capable of undergoing a phase transition, the transition state can be thermodynamically stable against the bulk phases if a certain material parameters criterion is fulfilled. In a small system below the critical size the transition state turns into a globally stable phase that can be observed experimentally. This effect is analogous to stabilization of icosahedral structures in clusters of certain sizes and energies. Stabilization of the transition state in small systems of limited resources allows us to conjecture that, in the case of a melting/freezing transition in pure substances, this state corresponds to an amorphous phase. Although unstable in open systems, this phase may be observed experimentally due to slow kinetics of its decomposition at low temperatures. The material-parameters criterion should help experimenters select the materials for the experimental verification of the phenomenon. In the present paper we consider thin films where the phase separation is permitted only parallel to the plane of the film. The calculations, however, hold true for 3D small systems: e.g., nanoparticles.

Correlations of Physiological Activities in Nocturnal Cheyne–Stokes respiration

Alexander Umantsev et al. — Wed, 23 Nov 2011 10:29:48 PST

We have conducted a power–spectrum–density (PSD) analysis of the distinct sleep stages of a previously diagnosed nocturnal Cheyne–Stokes patient (NCSR) and studied the correlations of different physiological activities. This is the first study where the correlations were analyzed separately for different sleep stages and the influence of arousals was completely eliminated. Mathematical analysis of the polysomnographical records revealed clear indicators of the disorder in the form of large peaks in a very-low frequency range of ƒ ˜ 0.02 Hz. We have shown existence of the significant entrainment of the cerebral and cardiac activities with respiration during different stages of sleep in the patient. The entrainment is highly pronounced in light (stage 2) and deep (stage 3) sleep, but is significantly less pronounced in rapid eye movement sleep. A correlation functions analysis revealed that the correlations between the central activities and respiration attain maximum at negative lag times. Lagging of respiration behind the central activities favors the central hypothesis of generation of NCSR. On the basis of comparison of PSD plots of a NCSR patient and a healthy patient we speculate that the vasomotor center of a NCSR patient assumes the control function in the respiratory control system. Clinical applications of the findings of the study may lead to the development of novel low-cost methods of diagnostic of NCSR based on easy-to-obtain electrocardiogram or electroencephalogram records of patients and emergence of some forms of “substitution therapy”.

Continuum Theory of Carbon Phases

Alexander Umantsev et al. — Wed, 23 Nov 2011 10:29:46 PST

We constructed a continuum theory of carbon phases based on the Landau theory of phase transitions. Our theory ties up many seemingly unrelated data on the carbon system. Transformations between graphite, diamond, and liquid-carbon are described by the Landau– Gibbs free-energy which depends on two order parameters: crystallization and structural. The barrier-height and gradient-energy coefficients were calculated from the nucleation data obtained in the studies of diamond/graphite and diamond/liquid-carbon systems. The boundary of the absolute stability of the graphitic phase was interpreted as the spinodal point of the free-energy, which allowed us to calculate the pressure dependence of the barrier-height coefficient. The continuum model yielded a value of 1.66 J/m2 for the graphite/liquid-carbon interface energy, which continues the trend of the elements of Group IV. We also analyzed stability of nanostructured amorphous carbon and interpreted it as the transition state of the free-energy function. This conjecture helped us to explain results of the experiments on the focused ion-beam irradiation of CVD-diamond nanofilms. The present theory may be used for the large-scale modeling of graphite and diamond crystallization; it can also be extended to include other structural modifications of carbon or an entirely different element such as silicon.

Identification of Material Parameters for Continuum Modeling of Phase Transformations In Multicomponent Systems

Alexander Umantsev — Wed, 23 Nov 2011 10:29:45 PST

The continuum (field theoretic) method has become the method of choice for multiscale structure-formation modeling of very different phase transformations in the past decade. One of the challenges in application of the method to transformations in real materials is to obtain the mesoscopic parameters, which characterize the thermodynamic system of interest. Significant progress has been made in the case of pure systems; however, one would like to know what changes need to be made in the case of binary or multicomponent systems. We consider an exactly solvable case of the linear multicomponent system undergoing a phase transformation and derive equations that relate parameters of the continuum method, like barrier height, gradient energy, and relaxation coefficients, to the measurable quantities, like interface energy, interfacial thickness, and kinetic coefficient. We find that the contribution of chemical interactions in the system can be expressed as the renormalization of the barrier-height parameter of the continuum method and replacement of the latent heat with the chemical modulus. Atomic-scale simulations data for a solid/liquid transition in a binary Cu-Ni system were chosen for comparison with the theory and the fitting yields the estimates for the continuum-method parameters. Analysis of the temperature dependence of the interfacial energy allowed us to shed light on the magnitudes of the internal energy and entropy contributions into the solid/liquid interface.

Modeling of Intermediate Phase Growth

Alexander Umantsev — Wed, 23 Nov 2011 10:29:44 PST

We introduced a continuum method for modeling of intermediate phase growth and numerically simulated three common experimental situations relevant to the physical metallurgy of soldering: growth of intermetallic compound layer from an unlimited amount of liquid and solid solders and growth of the compound from limited amounts of liquid solder. We found qualitative agreements with the experimental regimes of growth in all cases. For instance, the layer expands in both directions with respect to the base line when it grows from solid solder, and grows into the copper phase when the solder is molten. The quantitative agreement with the sharp-interface approximation was also achieved in these cases. In the cases of limited amounts of liquid solder we found the point of turnaround when the compound/solder boundary changed the direction of its motion. Although such behavior had been previously observed experimentally, the simulations revealed important information: the turnaround occurs approximately at the time of complete saturation of solder with copper. This result allows us to conclude that coarsening of the intermetallic compound structure starts only after the solder is practically saturated with copper.

Thermal effects of phase transformations: A review

Alexander Umantsev — Wed, 23 Nov 2011 10:29:43 PST

All the stages of phase transformations in materials, nucleation, growth, and coarsening, are subject to thermal effects that stem from the redistribution of energy in the system, like release of latent heat, and heat conduction. The thermal effects change the rate and outcome of the transformation and may result in the appearance of unusual states or phases, in particular in nanosystems. This review will cover the attempts of researchers to build a comprehensive theory of thermal effects in different phase transformations. Although the dynamical Ginzburg–Landau (continuum) approach will be used for the analysis of the effects, they are robust and conceivably independent of the theoretical method employed. On general physical grounds a possibility of an oscillatory regime in nucleation is considered and evolution equations for the interfacial motion are derived. The equations show that there are two distinctly different sets of thermal effects of interface motion: one set originates from the existence of the Gibbs–Duhem thermodynamic force on the interface, which has opposite directions compared to the velocity of the interface in the cases of continuous and discontinuous transitions, resulting in a heat trapping effect for the latter and a drag effect for the former. The other set of thermal effects stems from the existence of the surface internal energy and the necessity to carry it over together with the moving interface. As a result, temperature double layers accompany moving domain boundaries after a continuous transition or the surface creation and dissipation effect appear after a discontinuous one. An unusual, novel phase that may appear in isolated nanosystems (adiabatic nanophase) is described. Several experiments are suggested for the verification of the thermal effects in different material systems.

Growth from a hypercooled melt near absolute stability

Alexander Umantsev et al. — Wed, 23 Nov 2011 10:29:42 PST

Adaptive chaos: Mild disorder may help

Alexander Golbin et al. — Wed, 23 Nov 2011 10:29:40 PST

We have qualitatively analyzed different cases of human disorders and displacement activities of animals and hypothesize that some of them are examples of low-dimensional dynamical chaos in biological organisms. We also considered a biological organism in the framework of the control system theory and found that chaotic regime in one subsystem may be compensating for the loss of chaos in another subsystem for the sake of stability of the whole system. According to the hypothesis chaotic behavior of different organs sets in a human body as an alternative to serious diseases or even death. The principle of compensation was applied to different physiological systems with chaotic regimes to explain the adaptive nature of chaos there. Implications of the mechanism of adaptive chaos for sleep diseases, e.g., enuresis, and other potentially life threatening disorders of humans, e.g., RLS, are discussed in connection with the possibility to use these ideas for improved treatment strategies. The main conclusion is that adaptive disorders with chaotic symptoms should not be aggressively treated; if adaptive disorders are overtreated, the whole organism may be thrown into a more regular state, which eventually will lead to a chronic disease or even death.

Thermal effects in dynamics of interfaces

Alexander Umantsev — Wed, 23 Nov 2011 10:29:39 PST

Dynamical Ginzburg–Landau theory is applied to the study of thermal effects of motion of interfaces that appear after different phase transitions. These effects stem from the existence of the surface thermodynamic properties and temperature gradients in the interfacial transition region. Thermal effects may be explained by the introduction of a new thermodynamic force exerted on the interface, called here Gibbs–Duhem force, and the internal energy density flux through the interface. The evolution equations for the interfacial motion are derived. For the experimental verification of the thermal effects during continuous ordering the expression is derived for the amplitude of temperature waves.

Adiabatic phase transformations in confinement

Alexander Umantsev — Wed, 23 Nov 2011 10:29:38 PST

The phase diagram of small one-component particles has been analyzed under conditions of thermal insulation, i.e., conservation of energy. In large isolated systems the absolute stability belongs to heterogeneous states with phase separation. However, for small particles the global stability analysis shows a considerable extension of the single-phase regions into a two-phase zone of the phase diagram. Moreover, for very fine particles with sizes only 5-20 times exceeding interfacial thickness, phase separation does not occur at all and the equilibrium is achieved on homogeneous transition states that can never be obtained in bulk samples because of their absolute instability. The thermodynamic and dynamical explanations are presented. This type of a small-particle phase diagram may be relevant to the theory of amorphization, magnetocaloric effect, and nanophase composite materials where small particles or thin whiskers, capable of undergoing a transition, are immersed into a poorly conducting matrix. In case of small particles of solid solution, where mass conservation replaces the conservation of energy, present results predict the appearance of new stable phases with compositions deeply inside the miscibility gap.

Thermodynamic stability of phases and transition kinetics under adiabatic conditions

Alexander Umantsev — Wed, 23 Nov 2011 10:29:36 PST

A study of equilibrium states of a thermodynamic system whose evolution is governed not only by the temperature, but also by the ordering field is carried out. It is found that an adiabatically insulated system may have a new type of nonuniform state of equilibrium which is inhomogeneousin temperature.T he comparison is made of the stability conditions in isothermal and adiabatic systems. The steady motion of an interface boundary during a firstorder phase transition is investigated. It is shown, that depending upon the values of the diffusion coefficients, different regimes can exist. For small thermal diffusivity, the temperature of the final phase after the exothermal transition can be above the equilibrium point. The kinetic problem is reformulated to a dynamical system, and a numerical procedure to solve the latter is presented.N umerical results are discussedi n comparison with analytic ones

Early stages of soldering reactions

R A. Lord et al. — Wed, 23 Nov 2011 10:29:35 PST

An experiment on the early stages of intermetallic compound layer growth during soldering and its theoretical analysis were conducted with the intent to study the controlling factors of the process. An experimental technique based on fast dipping and pulling of a copper coupon in liquid solder followed by optical microscopy allowed the authors to study the temporal behavior of the sample on a single micrograph. The technique should be of value for different areas of metallurgy because many experiments on crystallization may be described as the growth of a layer of intermediate phase. Comparison of the experimental results with the theoretical calculations allowed one to identify the kinetics of dissolution as the rate-controlling mechanism on the early stages and measure the kinetic coefficient of dissolution. A popular model of intermetallic compound layer structure coarsening is discussed.

Thermal Effects of Interfacial Dynamics

Alexander Umantsev — Wed, 23 Nov 2011 10:29:34 PST

Dynamical Ginzburg-Landau theory is applied to the study of thermal effects of motion of interfaces that appear after different phase transitions. These effects stem from the existence of the surface internal energy, entropy and temperature gradients in the interfacial transition region. Evolution equations for the interfacial motion are derived. For the experimental verification of the thermal effects the expression is derived for the amplitude of temperature waves during continuous ordering.