Crystal growth rates in supercooled atomic liquid mixtures

Abstract

Crystallization is a fundamental process in materials science, providing the primary route for the realization of a wide range of novel materials. Crystallization rates are considered also to be useful probes of glass-forming ability. [1][2][3]. At the microscopic level, crystallization is described by the classical crystal nucleation and growth theories [4, 5], yet in general solid formation is a far more complex process. Particularly the observation of apparently different crystal growth regimes in many binary liquid mixtures greatly challenges our understanding of crystallization [1, 6-12]. Here, we study by experiments, theory, and computer simulations the crystallization of supercooled mixtures of argon and krypton, showing that crystal growth rates in these systems can be reconciled with existing crystal growth models only by explicitly accounting for the non-ideality of the mixtures. Our results highlight the importance of thermodynamic aspects in describing the crystal growth kinetics, providing a major step towards a more sophisticated theory of crystal growth.The classical crystal nucleation and growth theories describe the microscopic steps by which a solid phase spontaneously forms in the supercooled liquid at some temperature T below melting.Homogeneous crystal nucleation is the process of the formation by thermal fluctuations of a small, localized nucleus of the newly ordered phase in the metastable liquid [4]. Once the nucleus has reached its critical size, it grows at a rate that within the kinetic theory of crystal growth is givenwhere f ≤ 1 is a geometrical factor representing the fraction of atomic collisions with the crystal surface that actually contribute to the growth, a(T ) is a characteristic interatomic spacing that can be identified with the lattice constant, ν(T ) is the crystal addition rate at the crystal/liquid interface, ∆S m is the molar entropy of fusion, R is the universal gas constant, and ∆G(T ) = G L (T ) − G C (T ) is the difference in liquid (L) and crystal (C) molar Gibbs free energies. In the Wilson-Frenkel (WF) theory [13], the crystal addition rate is proportional to the atomic diffusivity D(T ), ν WF (T ) = 6D(T )/Λ 2 (T ), and hence exhibits the strong temperature dependence associated with an activated process. Here, Λ(T ) = ca(T ) is an average atomic displacement that we assume to be proportional to a(T ), with c being a dimensionless parameter. In the collision-limited (CL) scenario [14], the crystal addition rate is proportional to the average thermal velocity of the particles, ν CL (T ) = 3k B T /m/Λ(T ), where k B is Boltzmann's constant and m is the particle's mass, and represents the extreme case in which there is no activation barrier for ordering.At the microscopic level, the WF and CL models can be characterized by limiting time scales

Probing the dynamics of Cu nanoparticle growth inside metal-organic frameworks upon electron beam irradiation

“…(1). As in case of the complicated process of growth of the crystals [23], one can observe a good agreement between the growth theory and the experimental results. This allows us to speculate on relatively classical microscopic-level processes of the crystalline NP growth inside MOF from its constituent parts due to breaking of the bonds between metal ions and organic linkers.…”

“…5a and b). Hence, we model the growth of Cu NPs using classical growth theory with JMAK equation [33]: (1) Where V NP is the volume of Cu NP formed, V Cu max the maximum volume of Cu that can be formed, K and n the JMAK coefficients [23]. The first JMAK coefficient K is expressed by:…”

“…Indeed, such post-processing initiates the deformation of framework backbone and breaking of chemical bonds [19] leading to formation of amorphous glassy compounds [12], nanocomposites [20] and nanoparticles (NPs) with different optial properties [13,14,21]. Herein, compared to investigating mechanisms of nucleation and growth of initial MOFs [1] and different inorganic NPs [22][23][24], the kinetics of formation of NPs from constituent parts of MOFs remain unexplored.…”

“…1a) to initiate the nucleation and growth of crystalline metallic NPs with tunable size from ⁓2 nm to ⁓100 nm. The process of the NPs growth, captured in real time, demonstrates the evolution of their size, shape and spatial distribution and can be analyzed by classical kinetic theory taking into account the phase transformation [23,24].…”

Crystallization of Supercooled Liquids: Self-Consistency Correction of the Steady-State Nucleation Rate

“…Hereby, both general thermodynamic aspects and the details of the kinetics of aggregation of ambient phase particles to the newly evolving crystalline phase are of fundamental importance. In the theoretical analysis of these problems, several problems remain unsolved [ 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 ]. Here, we will consider in detail one particular issue that was already formulated in the first stages of development of the classical theory of nucleation and growth processes (CNT) [ 28 ], but has been widely neglected in applications.…”