From nucleation and coarsening to coalescence in metastable liquids

Abstract

<jats:p>The transition of a metastable liquid (supersaturated solution or supercooled melt) occurring from the intermediate stage (where the crystals nucleate and grow) to the concluding stage (where the larger particles evolve at the expense of the dissolution of smaller particles) is theoretically described, with allowance for various mass transfer mechanisms (reaction on the interface surface, volume diffusion, grain-boundary diffusion, diffusion along the dislocations) arising at the stage of Ostwald ripening (coalescence). The initial distribution function (its ‘tail’) for the concluding stage (forming as a result of the evolution of a particulate assemblage during the intermediate stage) is taken into account to determine the particle-size distribution function at the stage of Ostwald ripening. This modified distribution function essentially differs from the universal Lifshitz–Slyozov (LS) solutions for several mass transfer mechanisms. Namely, its maximum lies below and is shifted to the left in comparison with the LS asymptotic distribution function. In addition, the right branch of the particle-size distribution lies above and is shifted to the right of the LS blocking point. It is shown that the initial ‘tail’ of the particle-size distribution function completely determines its behaviour at the concluding stage of Ostwald ripening. The present theory agrees well with experimental data.</jats:p> <jats:p>This article is part of the theme issue ‘Patterns in soft and biological matters’.</jats:p>

The influence of non-stationarity and interphase curvature on the growth dynamics of spherical crystals in a metastable liquid

“…Therefore, expression (3.31) can be used as the initial distribution function when describing the concluding stage of a phase transformation (the stages of Ostwald ripening, coagulation or their combined occurrence [25–27,33,36,53,65]). Let us also especially note that expression (3.31) coincides with the simplified theory [68,69] previously developed for an idealized form of the coefficient D of mutual Brownian diffusion.…”

“…(b) The 'tail' of the particle-radius distribution function This subsection is devoted to the question of how the phase transformation process transforms from the intermediate stage (when the system metastability w is not small enough) to the concluding one (when the supercooling is small enough, w 1). To describe this transition, we need to find the 'tail' of the distribution function (3.17) and then use the previously developed analytical approach [64][65][66][67][68][69] for the stage of Ostwald ripening.…”

Ostwald ripening in the presence of simultaneous occurrence of various mass transfer mechanisms: an extension of the Lifshitz–Slyozov theory

“…To find such a 'tail', it is necessary to determine the particle size distribution function at the intermediate stage of the phase transformation, and then, considering its asymptotic behaviour at large times, determine the 'tail'. This 'tail' is found analytically in our previous papers [20][21][22] for supersaturated solutions and supercooled melts. Using the initial condition thus found for the distribution function, we can describe the process of formation of the universal state of a dispersed system based on a previously developed theory for the volume diffusion mechanism [23], as well as for the grain boundary diffusion, diffusion along the dislocations and reaction on the interface surface [24,25].…”

Nucleation and growth dynamics of ellipsoidal crystals in metastable liquids

“…Second, the present theory of evolution of an ensemble of ellipsoidal particles during the intermediate stage should be extended to the final stage when such processes as Ostwald ripening, coagulation and disintegration of particles are capable to occur. This can be done by analogy with the already developed theories of this stage for spherical crystals [70][71][72][73][74][75][76][77][78][79][80][81][82][83]. Third, the theory under consideration makes sense to expand with allowance for the shift in the phase transition temperature due to the Gibbs-Thomson effect and the attachment kinetics of atoms to the interphase boundaries of evolving crystals [84,85].…”