Diffusionless crystal growth in a eutectic system during rapid solidification

Experiments on nonequilibrium rapid eutectic growth are surveyed. The applicability limits of the modern theoretical models describing rapid solidification of binary systems are assessed. A problem of rapid eutectic growth when the local equilibrium is violated in the solute diffusion field (in the bulk liquid and at the solid-liquid interface) is formulated. An analytical solution to the problem of rapid lamellar eutectic growth under local nonequilibrium conditions in the solute diffusion field is found. It is shown that the diffusion-limited growth of a eutectic pattern ceases as soon as a chemically homogeneous crystalline phase begins to grow when the critical point V=V _D is achieved (V is the solid-liquid interface velocity and V _D is the solute diffusion speed in the bulk liquid). At V ≥ V _D, eutectic decomposition is suppressed and the nascent homogeneous crystalline phase has the initial (nominal) chemical composition of the binary system.     

晶体熔解和凝固实验的小改进

将一团蓬松的细铁丝或铜丝先放到试管的底端,以增加海波的导热性能,使海波在48℃开始熔解,直到全部熔解温度仍保持48℃.     

Thermodynamically stable states in eutectic systems

It is shown that in a binary system in which the liquid-solid phase transition is described by a eutectic phase diagram, there are temperature and concentration regions in the liquid state with different thermodynamic stability. These regions are separated by bell-shaped decay and spinodal curves. Zh. Tekh. Fiz. 67, 7–12 (April 1997)     

Asymmetrical contribution of eutectic growth kinetics on the coupled growth behaviour in rapid eutectic solidification

The interface undercooling in classical eutectic growth theories consists of solute and curvature undercooling with different expression formats. However, a significant difference in interface kinetic coefficients arises for a disordered non-facetted solid solution and an ordered facetted intermetallic compound in that different growth kinetics govern the attachment kinetics at the solid–liquid interface, which correspond to a typical eutectic reaction with a solid solution and an intermetallic compound as its terminal eutectic phases. Following the pioneering work of Jackson and Hunt (Trans. Metall. Soc. AIME 236 1129 (1966) ), the kinetic undercooling is supplemented to interface undercooling and two eutectic phases are considered separately so as to diagnose the effect of the asymmetrical contribution of kinetic undercooling on the coupled eutectic growth behaviour. Further analysis indicates that it is the asymmetrical contribution of kinetic undercoolings of the facetted and non-facetted phases that enables the coupled eutectic composition shift to the facetted phase side so as to weaken the solute undercooling of the facetted phase and balance the kinetic contribution in the rapid solidification of coupled eutectics.     

Liquidus curves for eutectic systems

The liquidus curves of the Na-K system are calculated from conformal solution theory, the input consisting of thermodynamic data for pure Na and K, plus an interchange energy characteristic of the solution.     

Solubility of solid phases in eutectic systems

A problem which takes into account the temperature dependence of interfacial energy is solved in order to describe quasi-equilibrium lines of solid-phase solubility in eutectic systems. The chosen reference point is the point of the eutectic horizontal corresponding to the limiting solubility of the second component in the solid solution. An expression is obtained which makes it possible to equate empirical values of solubility and to almost exactly represent its temperature path for the eutectic systems examined.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 40–45, October, 1986.     

Computer simulations of heterogeneous crystal growth of atomic systems

The systematic study of the mechanisms of heterogeneous crystal growth has proven somewhat difficult. Here we briefly review previous work in this area. We then report a novel molecular dynamics simulation methodology that has been developed to enable the creation of steady-state crystal growth–melting. We employ this methodology to examine BCC and FCC 001, 011 and 111 crystal faces of systems of spherical particles interacting through Lennard-Jones and inverse sixth-power potentials. Various growth–melting conditions are explored involving different temperature gradients and velocities. Profile functions of various quantities across the interface have been recorded; as measured in the moving frame by the present approach, these functions are effectively averaged over the molecular detail of the interface and become smooth. This characteristic allows for new ways of interpreting profile functions like the energy and local structural order parameters. We find that when the derivative of these profile functions is taken with respect to the z dimension, we obtain consistent peaks that characterize the freezing–melting interfaces. Consequently, the position and width of an interface are easily identified. The interfacial widths calculated show that it is somewhat dependent on the temperature gradient but no dependence on the growth velocity was observed. The interfacial widths are found to decrease in the order 001?>?011?>?111. Furthermore we determine interfacial tensions, which arise directly out of our methodology. We are able to demonstrate that ordering and disordering are distinct and different processes occurring at both the melting and freezing interfaces.     

Contact melting in layered film systems of the eutectic type

The existing concepts of the mechanism of eutectic melting have been developed on the basis of the study of melting in the Sn-Bi film system. This paper reports on the experimental results indicating the possibility of visualizing an increase in the solubility of components in the Sn-Bi system with increasing temperature and the existence of a critical thickness of the film of one of the components below which no eutectic melting occurs.     

Self-consistent diffusion-controlled growth of nuclei from eutectic solutions

A study is made of the dynamics of self-consistent motion and growth of spherical new-phase nuclei from a eutectic melt. The growth rate of nuclei is shown to be proportional to supersaturation in both components. Motion of a single nucleus in a concentration-gradient field and of a pair of nuclei in a self-consistent concentration field is investigated. The velocity of motion of the nucleus as a whole has been established to depend on the key parameters of the problem, namely, supersaturation, radii of the nuclei, and their separation. The force of mutual attraction between nuclei is estimated, and it is shown to be inversely proportional to the fifth power of their separation. Fiz. Tverd. Tela (St. Petersburg) 40, 1615–1618 (September 1998)     

Faceting transitions in crystal growth and heteroepitaxial growth in the anisotropic phase-field crystal model

We modify the anisotropic phase-field crystal model(APFC),and present a semi-implicit spectral method to numerically solve the dynamic equation of the APFC model.The process results in the acceleration of computations by orders of magnitude relative to the conventional explicit finite-difference scheme,thereby,allowing us to work on a large system and for a long time.The faceting transitions introduced by the increasing anisotropy in crystal growth are then discussed.In particular,we investigate the morphological evolution in heteroepitaxial growth of our model.A new formation mechanism of misfit dislocations caused by vacancy trapping is found.The regular array of misfit dislocations produces a small-angle grain boundary under the right conditions,and it could significantly change the growth orientation of epitaxial layers.     

Spectral element method in time for rapidly actuated systems

In this paper, the spectral element (SE) method is applied in time to find the entire time-periodic or transient solution of time-dependent differential equations. The time-periodic solution is computed by enforcing periodicity of the element set. Of particular interest are periodic forcing functions possessing high frequency content. To maintain the spectral accuracy for such forcing functions, an h-refinement scheme is employed near the semi-discontinuity without increasing the number of degrees of freedom.Time discretization by spectral elements is applied initially to a standard form of a set of linear, first-order differential equations subject to harmonic excitation and an excitation admitting rapid variation. Other case studies include the application of the SE approach to parabolic and hyperbolic partial differential equations. The first-order form of these equations is obtained through semi-discretization using conventional finite-element, spectral element and finite-difference schemes. Element clustering (h-refinement) is applied to maintain the high accuracy and efficiency in the region of the forcing function admitting rapid variation. The convergence in time of the method is demonstrated. In some cases, machine precision is obtained with 25 degrees of freedom per cycle. Finally the method is applied to a weakly nonlinear problem with time-periodic solution to demonstrate its future applicability to the analysis of limit-cycle oscillations in aeroelastic systems.     

Modeling elasticity in crystal growth

A new model of crystal growth is presented that describes the phenomena on atomic length and diffusive time scales. The former incorporates elastic and plastic deformation in a natural manner, and the latter enables access to time scales much larger than conventional atomic methods. The model is shown to be consistent with the predictions of Read and Shockley for grain boundary energy, and Matthews and Blakeslee for misfit dislocations in epitaxial growth.     

Formation of composite structures in eutectic systems in the presence of electromigration

It is shown that alloys in the liquid-solid state formed during contact melting in multicomponent systems contain separately existing solid phases. The application of a dc electric current during contact melting intensifies the process and provides control of the shape, sizes, and migration direction of inclusions.     

Quantum mechanics of rapidly and periodically driven systems

This review deals with the dynamics of quantum systems that are subject to high frequency external perturbations. Though the problem may look hopelessly time-dependent, and poised on the extreme opposite side of adiabaticity, there exists a ‘Kapitza Window’ over which the dynamics can be treated in terms of effective time-independent Hamiltonians. The consequent results are important in the context of atomic traps as well as quantum optic properties of atoms in intense and high-frequency electromagnetic fields.