Anomalous dynamics of interstitial dopants in soft crystals

Abstract

The dynamics of interstitial dopants govern the properties of a wide variety of doped crystalline materials. To describe the hopping dynamics of such interstitial impurities, classical approaches often assume that dopant particles do not interact and travel through a static potential energy landscape. Here we show, using computer simulations, how these assumptions and the resulting predictions from classical Eyring-type theories break down in entropically stabilized body-centered cubic (BCC) crystals due to the thermal excitations of the crystalline matrix. Deviations are particularly severe close to melting where the lattice becomes weak and dopant dynamics exhibit strongly localized and heterogeneous dynamics. We attribute these anomalies to the failure of both assumptions underlying the classical description: (i) The instantaneous potential field experienced by dopants becomes largely disordered due to thermal fluctuations and (ii) elastic interactions cause strong dopant-dopant interactions even at low doping fractions. These results illustrate how describing nonclassical dopant dynamics requires taking the effective disordered potential energy landscape of strongly excited crystals and dopantdopant interactions into account.anomalous dynamics | doping | crystals D oping pure crystalline solids with small amounts of interstitial impurities is a widely used method to enhance material properties such as heat and electric conductivity (1-4) or to tailor mechanical properties (5). Prototypical examples include the introduction of carbon atoms in iron crystals to make steel or the doping of plastic crystals with Li ions to create solid-state batteries (4). To ensure longevity of doped materials, it is essential that the spatial homogeneity and transport dynamics of the dopants within the crystal are well controlled and understood. Although theories and models are abundant (5-11), it remains unclear how large thermal excitations of the matrix lattice affect the dynamics of dopants. This becomes of particular interest during the processing of doped crystals, where they are heated close to or beyond their melting point. For example in body-centered cubic (BCC) iron doped with carbon, significant deviations from the exponential increase of diffusivity with temperature, expected from Arrhenius' law, are observed close to the melting temperature where lattice excitations are strong (12). Whereas doping is typically performed to tailor material properties at the macroscopic scale, these enhanced properties emerge from the dynamics and interactions between dopants at the scale of individual atoms (13). In classical theories for dopant dynamics, impurity particles are described as hopping through a potential energy landscape that is set by a perfect lattice symmetry, with transition rates governed by the energy barriers between adjacent interstitial sites and their occupancy (6,7,14). In reality, thermal fluctuations of atoms away from their equilibrium lattice positions will randomize the instantaneous potential energy l...

Soft Crystals: Flexible Response Systems with High Structural Order

“…This term has also been used for organic molecular crystals with low melting points or those with plasticity . In other papers, the crystalline state near the melting point is called the soft crystal state . In these examples, the term is used for a mechanically “soft” state of crystals.…”

“…In addition, the theoretical prediction of crystal structures has attracted many researchers’ interests and has developed remarkably recently . Computer simulations exploring the dynamics of the self‐organization of crystals and doped crystalline materials have also been reported recently . These theoretical approaches are expected to be important tools for the understanding and design of sophisticated soft crystals.…”

“…[8] In other papers, the crystalline state near the melting point is called the soft crystal state. [9] In these examples, the term is used for a mechanically "soft" state of crystals. On the other hand, as oftcrystal phase is knowna so ne of the liquid crystal phases:t he smecticp hase (SmE), which has al ayered structure and restricted molecular motion.…”

“…[4a, 36] Computer simulations exploring the dynamics of the self-organization of crystals and doped crystalline materials have also been reported recently. [9,37] These theoretical approaches are expectedt ob ei mportant tools for the understanding and design of sophisticated soft crystals.…”

Diffusion and interactions of interstitials in hard-sphere interstitial solid solutions

“…1 Examples of such solid solutions can be found in the atomic realm but also in colloidal systems. [2][3][4][5][6][7][8][9][10][11][12] Over the last decades, colloidal "hard spheres" have provided an excellent model system to investigate a variety of problems in condensed matter physics, such as glass transitions, [13][14][15] crystal nucleation, [16][17][18][19][20][21] and optimal packings. [22][23][24][25] Likewise, binary mixtures of hard spheres provide a simple model system to study solid solutions.…”