Thermal Jumps Research Articles

Defect production and annealing induced by electronic energy loss in pure metal

This work reports on the theoretical studies of defect production and annealing induced by electronic energy loss S e in pure metal. The selected metal was α-iron in which irradiation effects produced by swift heavy ions have been well studied experimentally by Dunlop et al. [Nucl. Instr. and Meth. B 90 (1994) 330]. According to thermal spike model in metals and taking into account the principles of ion–solid interactions and thermal atomic jumps and migrations in solid, we have done numerical calculations of spatial distributions of vacancies and interstitials created by nuclear collisions, concentration-dependent thermal migration and recombination of existed defects and thermal defect generation for given swift heavy ion irradiations. The calculated results suggested that threshold S e values for defect annealing and production were about 15 and 38 keV/nm which are in agreement with experiments. The comparison of damage efficiencies deduced from our numerical calculations with experimental ones have shown that S e induced defect production and annealing in pure metal can be a result of thermal transient process.

A shear transformation in the a-b plane of YBa 2Cu 3O 7−δ from the superconducting onset

The discontinuities or jumps in the crystallographic thermal expansion coefficients across the superconducting to normal phase boundary have been reported to contain opposite signs and nearly equal magnitudes between the a and b crystal axes. A shear transformation is shown to account for almost all of the thermal expansion jumps in a coordinate system that is rotated by π 4 about the c axis. The heat capacity, the shear thermal expansion coefficient and the elastic compliance matrix jumps in this rotated coordinate are related using second order phase transformation thermodynamics for a solid. The lattice motion for the shear transformation involves a single coupled displacement. A shear stress that gives a pure shear strain displacement will change T c in this crystal. The thermal expansion jumps when restricted to contain no volume terms have been emphasized in this paper. This shear thermal expansion is found to interact with the lattice through the orthorhombic shear compliance of ( s 11+ s 22−2 s 12).

Monte Carlo Study of the Phase Stability of Ordered F.C.C. Phases under Irradiation

The order-disorder transition in a binary fcc Ising-crystal with competing thermal and ballistic jumps, as is found e.g. under irradiation with high energy particles is studied by a Monte-Carlo technique. The state of order is characterized by a four-dimensional order parameter X the relative A-occupation of the four simple cubic sublattices (each consisting of Ω atoms) into which the fcc lattice may be decomposed. In a mean-field approximation, the transition rates w(X→X′) between neighbouring states of order can be found. By integrating a trajectory in the order parameter space stochastically, i.e. with a suitable Monte-Carlo-method, the respective probability P(X) each state of order Xcan be computed. For a large system this yields a stochastic potential \( \varphi \left( {{\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{X}}} \right) = \frac{1}{\Omega }{\text{ }}\log {\text{ }}P\left( {{\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{X}}} \right){\text{ }} \). The simulation algorithm is based on a method proposed some years ago by Gillespie [8], where one computes the probability for the system to leave its current state through a “reaction channel” μ, in our case a transition between two special sublattices, after a delay time r. Integration yields the total time in a certain state X, i.e. its probability.

Antisite Defects and Nonequilibrium Phase Transition in Intermetallics

Among the many point defects in crystalline solids, antisite defects play a key role in the stability of intermetallics. Such defects are either thermal equilibrium defects or are introduced by some external forcing.There are, indeed, many examples where intermetallics or compound semiconductors are “driven,” i.e., sustained in nonequilibrium configurations by external forcing. Good examples include the following:∎ Intermetallics in alloys under irradiation, like FeZr2 in Zircalloy used as a cladding material in pressurized water nuclear reactors, or any of the compounds produced by ion implantation or ion beam mixing (atoms are continuously forced to change lattice sites because of replacement collsions). See, for example, Reference 1.∎ Intermetallics in superalloys under cyclic fatigue (γ′ precipitates in persistent slip bands undergo sustained shearing, and sometimes redissolves).∎ Intermetallics during high-energy ball milling, a promising technique to stabilize nonequilibrium phases.∎ Ordered compounds when formed by vapor phase deposition.In such compounds, atoms are forced to leave their optimum local surroundings by nuclear collisions, shearing, fracturing, and welding respectively, or land on a surface at a random position, while thermal jumps tend to restore some degree of local atomic order. For simplicity, we call such compounds “driven systems” or “driven intermetallics.” Indeed, such systems are driven away from the usual thermodynamic equilibrium by a permanent dynamical forcing (nuclear collisions, plastic shear, etc.).

Thermal hydraulic jump: theory and experiment

A thermally stratified internal hydraulic jump in a fresh water ambient, which has a temperature equal to or greater than 4 °C, is investigated theoretically and experimentally. The thermal jump solutions obtained using a nonlinear buoyancy function are compared with the density jump solutions obtained using a linear buoyancy function. The study reveals considerable difference between thermal and density jump behaviour in a range of temperature above 4 °C. The error of treating a thermal jump as a density jump is found to increase with Froude number and temperature difference and decrease with ambient temperature. Thermal jump-experiments are conducted at ambient water temperatures of 4 °C and 16 °C. The two sets of experiments have identical Froude number, Reynolds number and temperature difference. Experimental observations compare favourably with the thermal jump theory. The analysis of temperature fluctuations suggests that ambient temperature is also modifying the internal mixing characteristics of thermal jumps.

Nonequilibrium transitions in driven AB3 compounds on the fcc lattice: A multivariate master-equation approach.

We studied the order-disorder transition in an Ising-type alloy on a fcc lattice with ${\mathit{AB}}_{3}$ stoichiometry with atomic exchanges due to two competing processes: thermally activated jumps and ballistic jumps, as, for example, is the case under irradiation with high-energy particles. The latter favor disordered configurations, while the former tend to restore a certain degree of order. The state of order is described by a four-dimensional parameter, the occupation of the four simple cubic sublattices into which the fcc lattice may be decomposed. In a mean-field approximation the kinetic equations for the evolution of this order parameter can be found. For a stochastic description, the master equation for the probability of a given state of order is approximated using Kubo's ansatz. The resulting partial differential equation is solved taking advantage of symmetry properties of the order-parameter space. A dynamical-equilibrium phase diagram is constructed, and it is shown that new phases, not found under thermal conditions, can be stabilized for a certain model for the saddle-point energy of the thermal jumps.

Cation (63Ni) diffusion in YBa2Cu3O7- delta epitaxial films.

The diffusion of $^{63}\mathrm{Ni}$ has been measured in ${\mathrm{YBa}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{7\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\delta}}}$ epitaxial thin films on (100) ${\mathrm{SrTiO}}_{3}$ substrates in the 550--650 \ifmmode^\circ\else\textdegree\fi{}C range (orthorhombic phase) in ${\mathrm{O}}_{2}$ pressure of 1 bar, keeping \ensuremath{\delta} in the 0.3--0.4 range. The diffusion behavior is described by D=1.3 exp[(-2.7 eV)/kT] ${\mathrm{cm}}^{2}$/sec and is many orders of magnitude slower than anion (oxygen) diffusion reported in the literature. A diffusion mechanism involving thermal vacancies and atomic jumps in diagonal directions of the type 〈110〉, 〈301〉, and 〈031〉 is proposed for long-range diffusion of cations occupying the Cu sites.

Cascade size effects on phase stability under irradiation: A stochastic description

Abstract Cascade size may affect phase stability under irradiation because of two distinct contributions: the replacement to displacement cross-section ratio depends on the deposited energy density; ballistic jumps which tend to disorder ordered compounds occur by bursts, while thermal jumps which restore long range order occur one by one. The latter effect cannot be handled by standard rate theory. A stochastic treatment of the problem, based on a Fokker Planck approximation of the relevant master equation is summarized. It is shown that the possible values of the long range order parameter under irradiation are not affected by the size of the cascade but that the respective stability of the former is cascade size sensitive. As a consequence, the stability diagram of phases under irradiation varies with the size of the cascades. A numerical example of this is given for the B2 structure.

Luminescence différée d'une solution organique vitreuse photoactivée et transition vitreuse

A general kinetic theory is used to explain the shapes of photoionized sample luminescence curves perturbed by thermal jumps (Δ ∼ 1 K, rise time ∼ 1 s). The samples studied are photoactivated organic vitreous solutions of TMPD/MCH 10−3 M and TMPD/3-MP 10−3 M. The experiments are performed within a temperature range (63–91 K) which includes the glass transition temperature Tg. It is shown that there is a slow diffusion of the trapped electrons towards the cation and competition between thermal detrapping and tunneling. The tunneling/thermal detrapping ratio Y is not time dependent during an isothermal luminescence and is only slowly temperature dependent if T ≤ Ty. Ty is very close to Tg. For T > Ty, Y decreases rapidly with T. The activation energy for thermal detrapping shows a maximum when the temperature reaches [Formula: see text] The glass transition temperature Tg may therefore be defined empirically as:[Formula: see text]Finally we obtain a glassy matrix relaxation time, τ, which decreases with T.

Luminescence de recombinaison consecutive a la photoionisation d'une solution organique vitreuse-nouvelle methode experimentale

In this paper, we describe a new experimental method which is used to determine the effect of temperature on the mechanisms related to the detrapping of electrons trapped in a glass. The studied samples are organic vitreous solutions of an aromatic molecule (TMPD) inside a non-polar glass (3-MP or MCH). The intensity of the isothermal luminescence (ITL) following the photoionization of the sample at 77K is increased when applying thermal jumps ΔT≲2K (the rise time is ⋍s). A general kinetical theory is used to explain the shapes of the luminescence curves perturbed by thermal jumps. It is shown that the experimental observations can be explained in terms of a slow diffusion of the trapped electrons towards a tunneling detrapping zone. When applying a thermal jump ΔT, the intensity of luminescence is multiplied by X such as: X = exp ΔT T E kT + Y 1+Y . This relationship is in good agreement with experience. The thermal detrapping activation energy E and the tunnelling effect ratio Y can be determined through this formula. The shapes of the kinetic curves at T = 77K and T = 77·50K are compared in the case of 3-MP glassy samples (near the glass transition, T g = 77K). It is concluded that there is a slow diffusion of trapped electrons (as it was already shown); the diffusion activation energy ( E d = 0·65eV) is found to be very close to viscosity activation energy ( E = 0·65eV) as given by Willard. This last result seems to support the hypothesis according to which the diffusion of trapped electrons is the consequence of the diffusion of the trapping cavities (at T g ).

Thermo-acoustical waves in linear thermo-elastic materials

Coupled waves of thermal and mechanical jumps in linear thermo-elastic materials are analysed. General linear anisotropic constitutive equations of thermo-elastic materials are derived from the Clausius-Duhem inequality and Vernotte's heat conduction law is adopted. The waves are defined to have jumps in acceleration and in temperature rate and the four-dimensional thermo-acoustical propagation condition is obtained. The differential equations which govern the variation of the wave amplitudes are obtained. For waves in linear isotropic thermo-elastic materials, there are four principal waves. Two shear waves are purely mechanical and propagate with constant amplitude, while two thermo-longitudinal waves have different propagation velocities: one is larger and other smaller than the purely mechanical longitudinal wave velocity, and their amplitudes decay, in general, exponentially in time.

Electron-phonon interaction, microscopic mechanism and properties of ferroelectric phase transitions

The vibronic theory of ferroelectric phase transitions is reviewed and the essential contribution of electron-phonon interaction into the microscopic origin of the ferroelectricity is demonstrated. In the narrow-gap (semiconducting) systems the soft mode is caused by interband vibronic interaction and the temperature dependencies are essentially determined by band occupation numbers. In a general case the phonon anharmonicity must also be taken into account. In the large-gap dielectric systems (BaTiO3) this mechanism leads to a negative value of the square of an initial anomalously small frequency. The thermal jumps of electrons are now absent and the temperature dependencies (and the stabilization of the crystal) are essentially determined by the phonon anharmonicity. A theory for hydrogen-containing ferroelectrics with proton-proton, proton-phonon and phonon-phonon interactions taken into account is also developed. The main properties and characteristics of phase transitions in the mentioned scheme are considered. The semiempirical test of the theory leads to reasonable results. Semiconducting properties of ferroelectrics are analysed: the influence of nonequilibrium carriers and impurities on Tc, and the dependence of the forbidden gap on temperature in BaTiO3.

Ionic diffusion in membranes

A fundamental approach to calculate the diffusion of ions through membranes is introduced. The membran eis considered as a heterogeneous structure with molecules that can have a selective affinity for a certain class of diffusing ions. To diffuse through a membrane an ion must become associated with, or dissolved into, at least one component of that membrane. Diffusion is produced by thermal jumps from one molecular site to another. It is assumed that the electric field can change the binding properties between ions and membrane molecules. The kinetics of the conductances are calculated from the chemical kinetic theory. The calculations are compared to the squid axon data and the unknown parameters are adjusted to fit the data curves. The results are very satisfactory. The calculated activation energies correspond to the measuredQ 10 in the squid axon. The calculated and measured action potentials are quite similar.