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Yayın Theoretical calculation of the kinetic coefficient of normal crystal growth(Trans Tech Publications Ltd, 2004) Dimitrov, Ventzislav IvanovAn expression for the velocity u of migration of a diffuse simple crystal-melt interface has been derived on the basis of the theory of atomic mobility in supercooled liquids: u = K-0 (T / T-m) DeltaT, where DeltaT = T-m - T the undercooling below the melting point T-m; K-0 is the kinetic coefficient of atomic attachment, which is used in models of crystal growth. It has been calculated for a number of metals. u(max) = K0Tm / 4 is the theoretical limit of the velocity of crystal growth. For a number of FCC metals the theoretical limit of crystal growth has been found to be of order of 200 m/s. The crystal growth kinetics has been shown to be limited by the atomic self-diffusion in the interface, for which the strong dependence on the orientation of the crystal/melt interface has been explained.Yayın Breakdown of the Stokes-Einstein relation in supercooled liquids(Trans Tech Publications Ltd, 2004) Dimitrov, Ventzislav IvanovBreakdown of the Einstein-Stokes relation in undercooled liquids is one of the unsolved problems in the theory of liquids. The self-diffusion coefficient follows the temperature dependence of the Einstein-Stokes equation D = kT / 6pietar at high temperatures but only down to approximately 1.2T(g) (T-g - glass-temperature). Below 1.2T(g) the temperature behavior of the diffusion coefficient is weaker than 1/eta. In the present study we show that this is a consequence of increasing correlations in the Brownian motion of the constituting particles of the liquid. We derive a relation, which includes the Einstein-Stokes equation as a limiting case for high temperatures.Yayın Theory of fluidity of liquids, glass transition, and melting(Elsevier B.V., 2006-03-01) Dimitrov, Ventzislav IvanovThis is a presentation of a rigorous theory of fluidity of liquids, glass transition and melting of solids in the frame of an asymmetric double well potential model. Potential wells are doubled time to time by the local density fluctuations caused by the thermal longitudinal waves. The average frequency of doubling of potential wells is equal to the frequency of the most energetic waves which obey a law similar to Wein's displacement law in black body radiation. Based on the equilibrium thermodynamic theory of fluctuations and the displacement law, a law of linear pre-diffusion mean-square displacement of particles in a solid is derived: the mean-square displacement of molecules within their potential wells increases linearly with temperature. It is shown that when this is broken-down (where the mean-square displacement at a certain temperature rapidly changes its slope as a function of temperature) glass devitrifies and crystal melts, and all possible solid-liquid transitions of a substance occur at the same critical mean-square displacement: any solid (not only crystals) transforms into liquid when the mean-square displacement, as a fraction of the average intermolecular distance, acquires a certain universal critical value - the same for different substances. It is proved that molecules in a liquid perform specific Brownian motion. The average jump distance is a function of temperature and it is much smaller than the nearest intermolecular distances. At a certain temperature, shown to be the Kauzmann temperature, the average jump distance of Brownian motion becomes equal to zero: the supercooled liquid undergoes glass transition. The transition was proven to be a phase transition of the fourth order: the free energy of the system and its first, second and third derivatives are all continuous functions, but its fourth derivative with respect to temperature is discontinuous. Molecular mobility, diffusion and viscosity are obtained as functions of temperature.Yayın Interpretation of the glass transition temperature from the point of view of molecular mobility(Springer, 2005) Dimitrov, Ventzislav IvanovGlass transition has been one of the biggest challenges in condensed matter physics during the last century: in spite of significant progress we still cannot explain the sudden solidification of undercooled liquids on the atomic scale. The liquid state itself is one of the less developed branches of condensed matter physics. The theoretical concepts of atomic mobility, diffusion and viscosity in liquids are not in good agreement with experiments. In the present paper we attempt to answer this challenge by describing the thermal motion of the native molecules of the liquid as Brownian motion. On the basis of this theory we have derived general expressions for the atomic mobility, mu, self-diffusion, D, and viscosity, eta for liquids. In dependence on a reduced temperature t, the mobility is expressed as mu = mu(0)m(t) for t >= 0 and mu = 0 for t <= 0 where mu(0) is the mobility at the jamming point of the liquid, and m(t) is defined by t = m/(1 - e(-m)). The reduced temperature t = gamma T-2/gamma T-2(c)c is determined by a quantity gamma accounting for the anharmonicity of interparticle interactions in the liquid state. At the special values gamma(c) and T-c the mobility becomes zero, i.e. the equilibrium glass transition occurs when the reduced temperature becomes equal to 1.Yayın The liquid–glass transition – is it a fourth order phase transition?(Elsevier Science, 2005-09-01) Dimitrov, Ventzislav IvanovThe liquid-glass transition is analyzed using a theory of Brownian motion in liquids recently developed by the author. It is shown that if a liquid could be cooled in quasi-static process and still avoids crystallization it would transform into a stable non-crystalline solid, which would be a normal thermodynamic phase. This hypothetical phase transition is neither first nor second order. At equilibrium transition temperature the free energy of the system and its first, second and third derivatives are all continuous functions, but its fourth derivative with respect to temperature is discontinuous. Therefore, the equilibrium liquid to non-crystalline solid transition may be considered a fourth order phase transition. The temperature of this phase transition, T-K, which coincides approximately with the Kauzmann temperature, is below the standard glass transition temperature T, (When the temperature decreases below T-g, the viscosity increases above 10(13) dPa s.) When the temperature decreases below T-K, the system becomes an ideal solid because the molecular mobility becomes zero and the viscosity becomes infinite if we neglect vacancy-like mechanisms of mobility. This hypothetical quasi-static transition is physically unobservable because the real liquid-glass transition must be done at a cooling rate high enough to suppress the growth of nanocrystals, which makes the liquid-glass transformation a non-equilibrium complicated phenomenon. Understanding this ideal phase transition is a first step towards describing the real liquid-glass transition from first principles.Yayın Fluctuation theory of the liquid-glass transition(Trans Tech Publications Ltd, 2004) Dimitrov, Ventzislav IvanovThe glassy state and the character of the liquid-glass transition from undercooled liquid to amorphous solid is one of the biggest challenges of our time. In spite of significant progress we still cannot explain accurately the sudden solidification of undercooled liquids on the atomic scale. In the present paper we present an analytical theory of the dependence of the glass transition temperature on the rate of cooling: the glass transition temperature increases with increasing cooling rate but does not exceed some upper limit. At almost zero cooling rates (hypothetical reversible transformation of the liquid into glass) the glass transition temperature reduces to a critical temperature, similar to a phase transition temperature.Yayın A model of AlN layer formation during ion nitriding of Al(Springer-Verlag, 2004-11) Dimitrov, Ventzislav IvanovA diffusion model of AlN layer formation by ion nitriding of Al is proposed based on the analysis of atomic transport during the process. This model is reduced to the following. Implantation of N ions to the surface of the specimen, named the reaction zone; extraction of Al from the substrate; diffusion transport of Al to the reaction zone through an AlN layer formed during the process; formation and growth of AlN in the reaction zone; sputtering of the AlN layer. Equations controlling the growth process have been obtained.
