Glassy Interfacial Dynamics of Ni Nanoparticles: Part II Discrete Breathers as an Explanation of Two-Level Energy Fluctuations

Stringlet excitation model of the boson peak

The boson peak (BP), a low-energy excess in the vibrational density of states over the Debye contribution, is often identified as a characteristic of amorphous solid materials. Despite decades of efforts, its microscopic origin still remains a mystery. Recently, it has been proposed, and corroborated with simulations, that the BP might stem from intrinsic localized modes involving one-dimensional (1D) string-like excitations ("stringlets"). We build on a theory originally proposed by Lund that describes the localized modes as 1D vibrating strings, but we specify the stringlet size distribution to be exponential, as observed in simulations. We provide an analytical prediction for the BP frequency ωBP in the temperature regime well below the observed glass transition temperature Tg. The prediction involves no free parameters and accords quantitatively with prior simulation observations in 2D and 3D model glasses based on inverse power law potentials. The comparison of the string model to observations is more uncertain when compared to simulations of an Al-Sm metallic glass material at temperatures well above Tg. Nonetheless, our stringlet model of the BP naturally reproduces the softening of the BP frequency upon heating and offers an analytical explanation for the experimentally observed scaling with the shear modulus in the glass state and changes in this scaling in simulations of glass-forming liquids. Finally, the theoretical analysis highlights the existence of a strong damping for the stringlet modes above Tg, which leads to a large low-frequency contribution to the 3D vibrational density of states, observed in both experiments and simulations.

A closer examination of the nature of atomic motion in the interfacial region of crystals upon approaching melting

Although crystalline materials are often conceptualized as involving a static lattice configuration of particles, it has recently become appreciated that string-like collective particle exchange motion is a ubiquitous and physically important phenomenon in both the melting and interfacial dynamics of crystals. This type of collective motion has been evidenced in melting since early simulations of hard disc melting by Alder et al. [Phys. Rev. Lett. 11(6), 241-243 (1963)], but a general understanding of its origin, along with its impact on melting and the dynamics of crystalline materials, has been rather slow to develop. We explore this phenomenon further by focusing on the interfacial dynamics of a model crystalline Cu material using molecular dynamics simulations where we emphasize the geometrical nature and spatial extent of the atomic trajectories over the timescale that they are caged, and we also quantify string-like collective motion on the timescale of the fast β-relaxation time, τf, i.e., "stringlets." Direct visualization of the atomic trajectories in their cages over the timescale over which the cage persists indicates that they become progressively more anisotropic upon approaching the melting temperature Tm. The stringlets, dominating the large amplitude atomic motion in the fast dynamics regime, are largely localized to the crystal interfacial region and correspond to "excess" modes in the density of states that give rise to a "boson peak." Moreover, interstitial point defects occur in direct association with the stringlets, demonstrating a link between classical defect models of melting and more recent studies of melting emphasizing the role of this kind of collective motion.

The initiation of shear band formation in deformed metallic glasses from soft localized domains

It has long been thought that shear band (SB) formation in amorphous solids initiates from relatively "soft" regions in the material in which large-scale non-affine deformations become localized. The test of this hypothesis requires an effective means of identifying "soft" regions and their evolution as the material is deformed to varying degrees, where the metric of "softness" must also account for the effect of temperature on local material stiffness. We show that the mean square atomic displacement on a caging timescale ⟨u²⟩, the "Debye-Waller factor," provides a useful method for estimating the shear modulus of the entire material and, by extension, the material stiffness at an atomic scale. Based on this "softness" metrology, we observe that SB formation indeed occurs through the strain-induced formation of localized soft regions in our deformed metallic glass free-standing films. Unexpectedly, the critical strain condition for SB formation occurs when the softness (⟨u²⟩) distribution within the emerging soft regions approaches that of the interfacial region in its undeformed state, initiating an instability with similarities to the transition to turbulence. Correspondingly, no SBs arise when the material is so thin that the entire material can be approximately described as being "interfacial" in nature. We also quantify relaxation in the glass and the nature and origin of highly non-Gaussian particle displacements in the dynamically heterogeneous SB regions at times longer than the caging time.

Unraveling the Atomic Structure of Bulk Binary Ga-Te Glasses with Surprising Nanotectonic Features for Phase-Change Memory Applications

Binary Ge-Te and ternary Ge-Sb-Te systems belong to flagship phase-change materials (PCMs) and are used in nonvolatile memory applications and neuromorphic computing. The working temperatures of these PCMs are limited by low-T glass transition and crystallization phenomena. Promising high-T PCMs may include gallium tellurides; however, the atomic structure and transformation processes for amorphous Ga-Te binaries are simply missing. Using high-energy X-ray diffraction and Raman spectroscopy supported by first-principles simulations, we elucidate the short- and intermediate-range order in bulk glassy Ga_xTe_1-x, 0.17 ≤ x ≤ 0.25, following their thermal, electric, and optical properties, revealing a semiconductor-metal transition above melting. We also show that a phase change in binary Ga-Te is characterized by a very unusual nanotectonic compression with the high internal transition pressure reaching 4-8 GPa, which appears to be beneficial for PCM applications increasing optical and electrical contrast between the SET and RESET states and decreasing power consumption.

Localization model description of the interfacial dynamics of crystalline Cu and [Formula: see text] metallic glass nanoparticles

Many of the special properties of nanoparticles (NPs) and nanomaterials broadly derive from the significant fraction of particles (atoms, molecules or segments of polymeric molecules) in the NP interfacial region in which the interparticle interactions are characteristically highly anharmonic in comparison to the bulk material. This leads to relatively large mean square particle displacements relative to the material interior, often resulting in a strong increase interfacial mobility and reactivity in both crystalline and glass NPs. The 'Debye-Waller factor', or the mean square particle displacement [Formula: see text] on a ps 'caging' timescale relative to the square of the average interparticle distance [Formula: see text], provides an often experimentally accessible measure of the strength of this anharmonic interaction. The Localization Model (LM) of the dynamics of condensed materials relates this thermodynamic property to the structural relaxation time [Formula: see text], determined from the intermediate scattering function, without any free parameters. Moreover, the LM allows for the prediction of the diffusion coefficient D when combined with the 'decoupling' or Fractional Stokes-Einstein relation linking [Formula: see text] to D. In the current study, we employed classical molecular dynamics simulation to investigate the structural relaxation and diffusion of model [Formula: see text] metallic glass and Cu crystalline NPs with different sizes. As with previous studies validating the LM on model bulk and crystalline materials, and for the interfacial dynamics of thin crystalline and metallic glass films, we find the LM model also describes the interfacial dynamics of model crystalline metal (Cu) and metallic glass ([Formula: see text] NPs to a good approximation, further confirming the generality of the model.

Localization model description of the interfacial dynamics of crystalline Cu and Cu64Zr36 metallic glass films

Recent studies of structural relaxation in Cu-Zr metallic glass materials having a range of compositions and over a wide range of temperatures and in crystalline UO₂ under superionic conditions have indicated that the localization model (LM) can predict the structural relaxation time τ_α of these materials from the intermediate scattering function without any free parameters from the particle mean square displacement ⟨r²⟩ at a caging time on the order of ps, i.e., the "Debye-Waller factor" (DWF). In the present work, we test whether this remarkable relation between the "fast" picosecond dynamics and the rate of structural relaxation τ_α in these model amorphous and crystalline materials can be extended to the prediction of the local interfacial dynamics of model amorphous and crystalline films. Specifically, we simulate the free-standing amorphous Cu₆₄Zr₃₆ and crystalline Cu films and find that the LM provides an excellent parameter-free prediction for τ_α of the interfacial region. We also show that the Tammann temperature, defining the initial formation of a mobile interfacial layer, can be estimated precisely for both crystalline and glass-forming solid materials from the condition that the DWFs of the interfacial region and the material interior coincide.

Repetition and pair-interaction of string-like hopping motions in glassy polymers

The dynamics of many glassy systems are known to exhibit string-like hopping motions each consisting of a line of particles displacing one another. By using the molecular dynamics simulations of glassy polymers, we show that these motions become highly repetitive back-and-forth motions as temperature decreases and do not necessarily contribute to net displacements. Particle hops which constitute string-like motions are reversed with a high probability, reaching 73% and beyond at low temperature. The structural relaxation rate is then dictated not by a simple particle hopping rate but instead by the rate at which particles break away from hopping repetitions. We propose that disruption of string repetitions and hence also structural relaxations are brought about by pair-interactions between strings.

Comparative Study of the Collective Dynamics of Proteins and Inorganic Nanoparticles

Molecular dynamics simulations of ubiquitin in water/glycerol solutions are used to test the suggestion by Karplus and coworkers that proteins in their biologically active state should exhibit a dynamics similar to 'surface-melted' inorganic nanoparticles (NPs). Motivated by recent studies indicating that surface-melted inorganic NPs are in a 'glassy' state that is an intermediate dynamical state between a solid and liquid, we probe the validity and significance of this proposed analogy. In particular, atomistic simulations of ubiquitin in solution based on CHARMM36 force field and pre-melted Ni NPs (Voter-Chen Embedded Atom Method potential) indicate a common dynamic heterogeneity, along with other features of glass-forming (GF) liquids such as collective atomic motion in the form of string-like atomic displacements, potential energy fluctuations and particle displacements with long range correlations ('colored' or 'pink' noise), and particle displacement events having a power law scaling in magnitude, as found in earthquakes. On the other hand, we find the dynamics of ubiquitin to be even more like a polycrystalline material in which the α-helix and β-sheet regions of the protein are similar to crystal grains so that the string-like collective atomic motion is concentrated in regions between the α-helix and β-sheet domains.

Understanding the cooperative atomic motion and shape change of ultrasmall Au nanoparticles below the premelting temperature

Surface melting is widely observed in crystalline materials, which has a significant influence on their interfacial properties.

String model for the dynamics of glass-forming liquids

We test the applicability of a living polymerization theory to describe cooperative string-like particle rearrangement clusters (strings) observed in simulations of a coarse-grained polymer melt. The theory quantitatively describes the interrelation between the average string length L, configurational entropy Sconf, and the order parameter for string assembly Φ without free parameters. Combining this theory with the Adam-Gibbs model allows us to predict the relaxation time τ in a lower temperature T range than accessible by current simulations. In particular, the combined theories suggest a return to Arrhenius behavior near Tg and a low T residual entropy, thus avoiding a Kauzmann "entropy crisis."

Influence of string-like cooperative atomic motion on surface diffusion in the (110) interfacial region of crystalline Ni

Although we often think about crystalline materials in terms of highly organized arrays of atoms, molecules, or even colloidal particles, many of the important properties of this diverse class of materials relating to their catalytic behavior, thermodynamic stability, and mechanical properties derive from the dynamics and thermodynamics of their interfacial regions, which we find they have a dynamics more like glass-forming (GF) liquids than crystals at elevated temperatures. This is a general problem arising in any attempt to model the properties of naturally occurring crystalline materials since many aspects of the dynamics of glass-forming liquids remain mysterious. We examine the nature of this phenomenon in the "simple" case of the (110) interface of crystalline Ni, based on a standard embedded-atom model potential, and we then quantify the collective dynamics in this interfacial region using newly developed methods for characterizing the cooperative dynamics of glass-forming liquids. As in our former studies of the interfacial dynamics of grain-boundaries and the interfacial dynamics of crystalline Ni nanoparticles (NPs), we find that the interface of bulk crystalline Ni exhibits all the characteristics of glass-forming materials, even at temperatures well below the equilibrium crystal melting temperature, Tm. This perspective offers a new approach to modeling and engineering the properties of crystalline materials.

Origin and nature of spontaneous shape fluctuations in "small" nanoparticles

Normally chemically inert materials such as Au have been found to be catalytically active in the form of particles whose size is about 1 nm. Direct and indirect observations of various types of metal nanoparticles (NPs) in this size range, under catalytically relevant conditions for fuel-cell operation and catalysis, have indicated that such "small" particles can exhibit large spontaneous shape fluctuations and significant changes in shape and chemical activity in response to alterations in environmental conditions. NPs also normally exhibit facile coalescence when in proximity, impacting their stability and reactivity in applications. We perform molecular dynamics simulations on Ni nanoparticles, a commonly used NP in catalytic applications and carbon nanotube growth, in the ≈1 nm size regime where large-scale shape fluctuations have been observed experimentally. An analysis of the large-scale shape fluctuations observed in our simulations of these "small" NPs indicates that they are accompanied by collective motion of Ni atoms through the NP center, and we quantify these dynamic structures and their impact on NP shape. In contrast, stringlike collective atomic motion is confined to the NP interfacial region of NPs having a diameter greater than a few nanometers, and correspondingly, the overall NP shape remains roughly spherical, a case studied in our prior Ni NP simulations. Evidently, the large spontaneous NP shape fluctuations reflect a change in character of the collective atomic dynamics when the NPs become critically small in size.