High density amorphous form and polyamorphic transformations of silicon

Microscopic mechanisms of pressure-induced amorphous-amorphous transitions and crystallisation in silicon

Some low-coordination materials, including water, silica, and silicon, exhibit polyamorphism, having multiple amorphous forms. However, the microscopic mechanism and kinetic pathway of amorphous-amorphous transition (AAT) remain largely unknown. Here, we use a state-of-the-art machine-learning potential and local structural analysis to investigate the microscopic kinetics of AAT in silicon after a rapid pressure change. We find that the transition from low-density-amorphous (LDA) to high-density-amorphous (HDA) occurs through nucleation and growth, resulting in non-spherical interfaces that underscore the mechanical nature of AAT. In contrast, the reverse transition occurs through spinodal decomposition. Further pressurisation transforms LDA into very-high-density amorphous (VHDA), with HDA serving as an intermediate state. Notably, the final amorphous states are inherently unstable, transitioning into crystals. Our findings demonstrate that AAT and crystallisation are driven by joint thermodynamic and mechanical instabilities, assisted by preordering, occurring without diffusion. This unique mechanical and diffusion-less nature distinguishes AAT from liquid-liquid transitions.

Relationship between diffraction peak, network topology, and amorphous-forming ability in silicon and silica

The network topology in disordered materials is an important structural descriptor for understanding the nature of disorder that is usually hidden in pairwise correlations. Here, we compare the covalent network topology of liquid and solidified silicon (Si) with that of silica (SiO2) on the basis of the analyses of the ring size and cavity distributions and tetrahedral order. We discover that the ring size distributions in amorphous (a)-Si are narrower and the cavity volume ratio is smaller than those in a-SiO2, which is a signature of poor amorphous-forming ability in a-Si. Moreover, a significant difference is found between the liquid topology of Si and that of SiO2. These topological features, which are reflected in diffraction patterns, explain why silica is an amorphous former, whereas it is impossible to prepare bulk a-Si. We conclude that the tetrahedral corner-sharing network of AX2, in which A is a fourfold cation and X is a twofold anion, as indicated by the first sharp diffraction peak, is an important motif for the amorphous-forming ability that can rule out a-Si as an amorphous former. This concept is consistent with the fact that an elemental material cannot form a bulk amorphous phase using melt quenching technique.

Time-dependent principal component analysis: A unified approach to high-dimensional data reduction using adiabatic dynamics

Systematic reduction of the dimensionality is highly demanded in making a comprehensive interpretation of experimental and simulation data. Principal component analysis (PCA) is a widely used technique for reducing the dimensionality of molecular dynamics (MD) trajectories, which assists our understanding of MD simulation data. Here, we propose an approach that incorporates time dependence in the PCA algorithm. In the standard PCA, the eigenvectors obtained by diagonalizing the covariance matrix are time independent. In contrast, they are functions of time in our new approach, and their time evolution is implemented in the framework of Car-Parrinello or Born-Oppenheimer type adiabatic dynamics. Thanks to the time dependence, each of the step-by-step structural changes or intermittent collective fluctuations is clearly identified, which are often keys to provoking a drastic structural transformation but are easily masked in the standard PCA. The time dependence also allows for reoptimization of the principal components (PCs) according to the structural development, which can be exploited for enhanced sampling in MD simulations. The present approach is applied to phase transitions of a water model and conformational changes of a coarse-grained protein model. In the former, collective dynamics associated with the dihedral-motion in the tetrahedral network structure is found to play a key role in crystallization. In the latter, various conformations of the protein model were successfully sampled by enhancing structural fluctuation along the periodically optimized PC. Both applications clearly demonstrate the virtue of the new approach, which we refer to as time-dependent PCA.

Tension-compression asymmetry in amorphous silicon

Hard and brittle materials usually exhibit a much lower strength when loaded in tension than in compression. However, this common-sense behaviour may not be intrinsic to these materials, but arises from their higher flaw sensitivity to tensile loading. Here, we demonstrate a reversed and unusually pronounced tension-compression asymmetry (tensile strength exceeds compressive strength by a large margin) in submicrometre-sized samples of isotropic amorphous silicon. The abnormal asymmetry in the yield strength and anelasticity originates from the reduction in shear modulus and the densification of the shear-activated configuration under compression, altering the magnitude of the activation energy barrier for elementary shear events in amorphous Si. In situ coupled electrical tests corroborate that compressive strains indeed cause increased atomic coordination (metallization) by transforming some local structures from sp³-bonded semiconducting motifs to more metallic-like sites, lending credence to the mechanism we propose. This finding opens up an unexplored regime of intrinsic tension-compression asymmetry in materials.

Liquid-Liquid Phase Transitions in Silicon

We use computationally simple neutral pseudoatom ("average atom") density functional theory (DFT) and standard DFT to elucidate liquid-liquid phase transitions (LPTs) in liquid silicon. An ionization-driven transition and three LPTs including the known LPT near 2.5  g/cm^{3} are found. They are robust even to 1 eV. The pair distributions functions, pair potentials, electrical conductivities, and compressibilites are reported. The LPTs are elucidated within a Fermi liquid picture of electron scattering at the Fermi energy that complements the transient covalent bonding picture.

Structural Ordering in Liquid Gallium under Extreme Conditions

The atomic-scale structure, melting curve, and equation of state of liquid gallium has been measured to high pressure (p) and high temperature (T) up to 26 GPa and 900 K by in situ synchrotron x-ray diffraction. Ab initio molecular dynamics simulations up to 33.4 GPa and 1000 K are in excellent agreement with the experimental measurements, providing detailed insight at the level of pair distribution functions. The results reveal an absence of dimeric bonding in the liquid state and a continuous increase in average coordination number n[over ¯]_{Ga}^{Ga} from 10.4(2) at 0.1 GPa approaching ∼12 by 25 GPa. Topological cluster analysis of the simulation trajectories finds increasing fractions of fivefold symmetric and crystalline motifs at high p-T. Although the liquid progressively resembles a hard-sphere structure towards the melting curve, the deviation from this simple description remains large (≥40%) across all p-T space, with specific motifs of different geometries strongly correlating with low local two-body excess entropy at high p-T.

Tunable Anelasticity in Amorphous Si Nanowires

In situ bending tests of amorphous Si nanowires (a-Si NWs) found different elastic behavior depending on whether they were straight or curved to begin with. The axially straight NWs exhibit pure elastic deformation; however, the axially curved NWs exhibit obvious anelastic behavior when they are bent in the direction of original curvature. On the basis of STEM-EELS analysis, we propose that the underlying mechanism for this anelastic behavior is a bond-switching assisted redistribution of the nonuniform density (structure) in the curved NWs under the inhomogeneous stress field. This mechanism was further supported by the fact that the originally straight a-Si NWs also display similar anelasticity with the as-grown curved NWs after focused ion beam irradiation that can cause nonuniform structure distribution. As compared to what has been reported in other 1D materials, the anelasticity of a-Si NWs can be tuned by modifying their morphology, controlling the loading direction, or irradiating them via ion beam. Our findings suggest that a-Si NWs could be a promising material in the nanoscale damping systems, especially the semiconductor nanodevices.

In situ spectroscopic study of the plastic deformation of amorphous silicon under non-hydrostatic conditions induced by indentation

Indentation-induced plastic deformation of amorphous silicon (a-Si) thin films was studied by in situ Raman imaging of the deformed contact region of an indented sample, employing a Raman spectroscopy-enhanced instrumented indentation technique. Quantitative analyses of the generated in situ Raman maps provide unique, new insight into the phase behavior of as-implanted a-Si. In particular, the occurrence and evolving spatial distribution of changes in the a-Si structure caused by processes, such as polyamorphization and crystallization, induced by indentation loading were measured. The experimental results are linked with previously published work on the plastic deformation of a-Si under hydrostatic compression and shear deformation to establish a sequence for the development of deformation of a-Si under indentation loading. The sequence involves three distinct deformation mechanisms of a-Si: (1) reversible deformation, (2) increase in coordination defects (onset of plastic deformation), and (3) phase transformation. Estimated conditions for the occurrence of these mechanisms are given with respect to relevant intrinsic and extrinsic parameters, such as indentation stress, volumetric strain, and bond angle distribution (a measure for the structural order of the amorphous network). The induced volumetric strains are accommodated solely by reversible deformation of the tetrahedral network when exposed to small indentation stresses. At greater indentation stresses, the increased volumetric strains in the tetrahedral network lead to the formation of predominately five-fold coordination defects, which seems to mark the onset of irreversible or plastic deformation of the a-Si thin film. Further increase in the indentation stress appears to initiate the formation of six-fold coordinated atomic arrangements. These six-fold coordinated arrangements may maintain their amorphous tetrahedral structure with a high density of coordination defects or nucleate as a new crystalline β-tin phase within the a-Si network.

Dynamics and Diffusion Mechanism of Low-Density Liquid Silicon

A first-order phase transition from a high-density liquid to a low-density liquid has been proposed to explain the various thermodynamic anomies of water. It also has been proposed that such liquid-liquid phase transition would exist in supercooled silicon. Computer simulation studies show that, across the transition, the diffusivity drops roughly 2 orders of magnitude, and the structures exhibit considerable tetrahedral ordering. The resulting phase is a highly viscous, low-density liquid silicon. Investigations on the atomic diffusion of such a novel form of liquid silicon are of high interest. Here we report such diffusion results from molecular dynamics simulations using the classical Stillinger-Weber (SW) potential of silicon. We show that the atomic diffusion of the low-density liquid is highly correlated with local tetrahedral geometries. We also show that atoms diffuse through hopping processes within short ranges, which gradually accumulate to an overall random motion for long ranges as in normal liquids. There is a close relationship between dynamical heterogeneity and hopping process. We point out that the above diffusion mechanism is closely related to the strong directional bonding nature of the distorted tetrahedral network. Our work offers new insights into the complex behavior of the highly viscous low density liquid silicon, suggesting similar diffusion behaviors in other tetrahedral coordinated liquids that exhibit liquid-liquid phase transition such as carbon and germanium.

Pressure-Induced Amorphization and a New High Density Amorphous Metallic Phase in Matrix-Free Ge Nanoparticles

Over the last two decades, it has been demonstrated that size effects have significant consequences for the atomic arrangements and phase behavior of matter under extreme pressure. Furthermore, it has been shown that an understanding of how size affects critical pressure-temperature conditions provides vital guidance in the search for materials with novel properties. Here, we report on the remarkable behavior of small (under ~5 nm) matrix-free Ge nanoparticles under hydrostatic compression that is drastically different from both larger nanoparticles and bulk Ge. We discover that the application of pressure drives surface-induced amorphization leading to Ge-Ge bond overcompression and eventually to a polyamorphic semiconductor-to-metal transformation. A combination of spectroscopic techniques together with ab initio simulations were employed to reveal the details of the transformation mechanism into a new high density phase-amorphous metallic Ge.

Polyamorphism in tetrahedral substances: Similarities between silicon and ice

Tetrahedral substances, such as silicon, water, germanium, and silica, share various unusual phase behaviors. Among them, the so-called polyamorphism, i.e., the existence of more than one amorphous form, has been intensively investigated in the last three decades. In this work, we study the metastable relations between amorphous states of silicon in a wide range of pressures, using Monte Carlo simulations. Our results indicate that the two amorphous forms of silicon at high pressures, the high density amorphous (HDA) and the very high density amorphous (VHDA), can be decompressed from high pressure (∼20 GPa) down to the tensile regime, where both convert into the same low density amorphous. Such behavior is also observed in ice. While at high pressure (∼20 GPa), HDA is less stable than VHDA, at the pressure of 10 GPa both forms exhibit similar stability. On the other hand, at much lower pressure (∼5 GPa), HDA and VHDA are no longer the most stable forms, and, upon isobaric annealing, an even less dense form of amorphous silicon emerges, the expanded high density amorphous, again in close similarity to what occurs in ice.

Cluster formation, waterlike anomalies, and re-entrant melting for a family of bounded repulsive interaction potentials

We introduce a family of bounded repulsive potentials, which we call the cut ramp potential, obtained by cutting a linear ramp potential at different heights. We find that for the uncut ramp potential the system shows a region of anomalous re-entrant melting (a negative slope of the melting line in the temperature-pressure phase diagram), with waterlike anomalies in the same pressure range. At high pressure the melting line recovers a positive slope, a feature that we associate with the formation of clusters of particles separated by a more or less density-independent distance, the cluster separation, which is approximately equal to the ramp width sigma1. As the ramp is cut at lower and lower heights, the region of anomalous behavior shrinks and eventually disappears while at the same time the formation of clusters becomes more favored, as it is energetically less unfavorable for particles to "climb up" the ramp. We relate the occurrence of anomalous behavior to the reduced efficacy of the soft repulsive length scale with increasing pressure. The clustering phenomenon partially restores this efficacy, giving rise to an approximately constant distance sigma1 between the clusters. Our results may be useful to better understand the phase behavior of macromolecules as well as that of substances with nondirectional interactions that are capable of displaying liquid polymorphism.

Unusual phase behavior of one-component systems with two-scale isotropic interactions

We study the phase behavior of systems of particles interacting through pair potentials with a hard core plus a soft repulsive component. We consider several different forms of soft repulsion, including a square shoulder, a linear ramp and a quasi-exponential tail. The common feature of these potentials is the presence of two repulsive length scales, which may be the origin of unusual phase behaviors such as polyamorphism both in the equilibrium liquid phase and in the glassy state, water-like anomalies in the liquid state and anomalous melting at very high pressures.

Structural and thermodynamic properties of different phases of supercooled liquid water

Computer simulation results are reported for a realistic polarizable potential model of water in the supercooled region. Three states, corresponding to the low density amorphous ice, high density amorphous ice, and very high density amorphous ice phases are chosen for the analyses. These states are located close to the liquid-liquid coexistence lines already shown to exist for the considered model. Thermodynamic and structural quantities are calculated, in order to characterize the properties of the three phases. The results point out the increasing relevance of the interstitial neighbors, which clearly appear in going from the low to the very high density amorphous phases. The interstitial neighbors are found to be, at the same time, also distant neighbors along the hydrogen bonded network of the molecules. The role of these interstitial neighbors has been discussed in connection with the interpretation of recent neutron scattering measurements. The structural properties of the systems are characterized by looking at the angular distribution of neighboring molecules, volume and face area distribution of the Voronoi polyhedra, and order parameters. The cumulative analysis of all the corresponding results confirms the assumption that a close similarity between the structural arrangement of molecules in the three explored amorphous phases and that of the ice polymorphs I(h), III, and VI exists.

Structural and dynamical heterogeneity in deeply supercooled liquid silicon

We report on a first-principles molecular-dynamics study of structural and dynamical heterogeneity in supercooled liquid silicon. We find that highly tetrahedral configurations are intermittently formed and that spatially heterogeneous dynamics is concurrently induced in the deeply supercooled state (1000 K). This heterogeneity is responsible for the anomalous structural relaxation characterized by the stretched-exponential function. The temporal structural fluctuation is found to give rise to the 1/f dependence in the corresponding power spectral density. In a moderately supercooled state (1600 K), the structural and dynamical heterogeneity is quite weak, in contrast to the deeply supercooled state. The applicability of the Stillinger-Weber potential to the deeply supercooled state is also discussed.

Fluid-phase behavior of binary mixtures in which one component can have two critical points

We investigate theoretically the binary fluid-phase behavior of mixtures in which one water-like component can have two critical points. We consider three equal-sized nonpolar solutes that differ in the strength of their dispersive interactions (a1 < a2 < a3, where a denotes the van der Waals attractive parameter). In each case, we compare the phase behavior predicted using two sets of parameters for water: one giving rise to a pure component low-temperature liquid-liquid transition terminating at a critical point (two-critical-point parameter set), and one in which no such second critical point exists (singularity-free parameter set). Regardless of the parameter values used, we find five mixture critical lines. Using the two-critical-point parameter set, we find that a critical line originates at water's second critical point for aqueous mixtures involving solutes 1, 2, or 3. For mixtures involving solutes 1 or 2, this line extends towards low pressures and high temperatures as the solute mole fraction increases, and is closely related to the critical line originating at water's ordinary vapor-liquid critical point: these two critical lines are loci of upper and lower consolute points corresponding to the same liquid-liquid transition. In mixtures involving solute 2, the critical locus emanating from water's second critical point is shifted to higher temperatures compared to mixtures involving solute 1, and extends up to T approximately 310 K at moderate pressures (ca. 200 bars). This suggests the possibility of an experimentally accessible manifestation of the existence of a second critical point in water. For binary mixtures involving solutes 1 or 2, changing the water parameters from the two critical points to the singularity-free case causes the disappearance of a lower consolute point at moderate pressures. For binary mixtures involving solute 3, the differences between two-critical-point and singularity-free behaviors occur only in the experimentally difficult-to-probe low-temperature and high-pressure region.

Polyamorphism in a metallic glass

A metal, or an alloy, can often exist in more than one crystal structure. The face-centred-cubic and body-centred-cubic forms of iron (or steel) are a familiar example of such polymorphism. When metallic materials are made in the amorphous form, is a parallel 'polyamorphism' possible? So far, polyamorphic phase transitions in the glassy state have been observed only in glasses involving directional and open (such as tetrahedral) coordination environments. Here, we report an in situ X-ray diffraction observation of a pressure-induced transition between two distinct amorphous polymorphs in a Ce(55)Al(45) metallic glass. The large density difference observed between the two polyamorphs is attributed to their different electronic and atomic structures, in particular the bond shortening revealed by ab initio modelling of the effects of f-electron delocalization. This discovery offers a new perspective of the amorphous state of metals, and has implications for understanding the structure, evolution and properties of metallic glasses and related liquids. Our work also opens a new avenue towards technologically useful amorphous alloys that are compositionally identical but with different thermodynamic, functional and rheological properties due to different bonding and structural characteristics.

How does tetrahedral structure grow in liquid silicon upon supercooling?

We present an extensive set of isothermal-isobaric first-principles molecular-dynamics simulations of liquid silicon over a temperature range of 950-1700 K. We find that the tetrahedral order gradually grows upon cooling to approximately 1200 K, but that the growth accelerates significantly below approximately 1200 K. This growth process gives rise to anomalous changes in density and liquid structure upon supercooling. In particular, we find that the atomic coordination number remains constant to approximately 1200 K and then begins to decrease below approximately 1200 K, which resolves the existing controversy regarding liquid structure in the supercooled regime [T. H. Kim, Phys. Rev. Lett. 95, 085501 (2005)10.1103/PhysRevLett.95.085501].

Anomalous diffusivity in supercooled liquid silicon under pressure

We perform isothermal-isobaric first-principles molecular-dynamics simulations to investigate the dynamics of liquid silicon (l-Si) under pressure. We find that the self-diffusion coefficient increases with increasing pressure in the deeply supercooled state. This anomalous diffusivity is attributed to the formation of locally tetrahedral configurations which on average reduces the diffusivity at low pressures. Densification hinders the formation of the tetrahedral configurations, thus the diffusivity increases with increasing pressure. The tetrahedral configurations frequently formed at low pressures may be viewed as fragments of the low-density form of l-Si . It is therefore conceivable that transformations between two distinct liquids, low- and high-density liquids, locally occur in deeply supercooled l-Si . The present findings indicate the profound generality of the dynamics in liquids with a tetrahedral network such as water.

Electronic-enthalpy functional for finite systems under pressure

We introduce the notion of electronic enthalpy for first-principles structural and dynamical calculations of finite systems under pressure. An external pressure field is allowed to act directly on the electronic structure of the system studied via the ground-state minimization of the functional E+PV(q), where V(q) is the quantum volume enclosed by a charge isosurface. The Hellmann-Feynman theorem applies, and assures that the ionic equations of motion follow an isoenthalpic dynamics. No pressurizing medium is explicitly required, while coatings of environmental ions or ligands can be introduced if chemically relevant. We apply this novel approach to the study of group-IV nanoparticles during a shock wave, highlighting the significant differences in the plastic or elastic response of the diamond cage under load, and their potential use as novel nanostructured impact-absorbing materials.

Formation of high density amorphous ice by decompression of ice VII and ice VIII at 135 K

Monte Carlo computer simulations of ice VII and ice VIII phases have been undertaken using the four-point transferable intermolecular potential model of water. By following thermodynamic paths similar to those used experimentally, ice is decompressed resulting in an amorphous phase. These phases are compared to the high density amorphous phase formed upon compression of ice Ih and are found to have very similar structures. By cooling liquid water along the water/Ih melting line a high density amorphous phase was also generated.

Amorphous silicon exhibits a glass transition

Amorphous silicon is a semiconductor with a lower density than the metallic silicon liquid. It is widely believed that the amorphous-liquid transition is a first-order melting transition. In contrast to this, recent computer simulations and the experimental observation of pressure-induced amorphization of nanoporous silicon have revived the idea of an underlying liquid-liquid phase transition implying the existence of a low-density liquid and its glass transition to the amorphous solid. Here we demonstrate that during irradiation with high-energy heavy ions amorphous silicon deforms plastically in the same way as conventional glasses. This behaviour provides experimental evidence for the existence of the low-density liquid. The glass transition temperature for a timescale of 10 picoseconds is estimated to be about 1,000 K. Our results support the idea of liquid polymorphism as a general phenomenon in tetrahedral networks.