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Amorphous and crystalline forms of silicon are well-known, tetrahedrally coordinated semiconductors. High-pressure studies have revealed extensive polymorphism among various metallic crystal structures containing atoms in six-, eight- and 12-fold coordination. Melting silicon at ambient or high pressure results in a conducting liquid, in which the average coordination is greater than four (ref. 3). This liquid cannot normally be quenched to a glass, because of rapid crystallization to the diamond-structured semiconductor. Solid amorphous silicon is obtained by synthesis routes such as chemical or physical vapour deposition that result in a tetrahedrally bonded semiconducting state. It has long been speculated that the amorphous solid and the liquid could represent two polymorphic forms of the amorphous state that are linked by density- or entropy-driven transformations. Such polyamorphic transitions are recognized to occur among several different types of liquid and glassy systems. Here we present experimental evidence for the occurrence of a density-driven polyamorphic transition between semiconducting and metallic forms of solid amorphous silicon. The experiments are combined with molecular dynamics simulations that map the behaviour of the amorphous solid on to that of the liquid state.

Structurally disordered materials continue to pose fundamental questions [1][2][3][4] , including that of how different disordered phases ("polyamorphs") can coexist and transform from one to another 5-9 . As a widely studied case, amorphous silicon (a-Si) forms a fourfold-coordinated, covalent network at ambient conditions and much higher-coordinated, metalliclike phases under pressure 10-12 . However, a detailed mechanistic understanding of the structural transitions in disordered silicon has been lacking, due to intrinsic limitations of even the most advanced experimental and computational techniques. Here, we show how atomistic machine-learning (ML) models can break through this long-standing barrier, describing liquid-amorphous and amorphous-amorphous transitions with quantum-mechanical accuracy for a system of 100,000 atoms (ten-nanometre length scale). Our simulations reveal a three-step transformation sequence for a-Si under increasing external pressure. First, polyamorphic low-and high-density amorphous (LDA and HDA) regions are found to coexist, rather than appearing sequentially. Then, we observe a structural collapse into a distinct, very-high-density amorphous (VHDA) phase. Finally, our simulations indicate the transient nature of this VHDA phase: it rapidly nucleates crystallites, ultimately leading to the formation of a poly-crystalline structure, consistent with experiments [13][14][15] but not seen in earlier simulations 11,[16][17][18] . An ML model for electronic densities of states (DOS) confirms the onset of metallicity during VHDA formation and subsequent crystallisation. These results shed new light on liquid and amorphous states of silicon, and, in a wider context, they exemplify a holistic, ML-driven approach to predictive materials mod-

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Phase transitions in the liquid state can be related to pressure-driven fluctuations developed in the density (i.e., the inverse of the molar volume; ρ = 1/V) or the entropy (S(T)) rather than by gradients in the chemical potential (μ(X), where X is the chemical composition). Experiments and liquid simulation studies now show that such transitions are likely to exist within systems with a wide range of chemical bonding types. The observations permit us to complete the trilogy of expected liquid state responses to changes in P and T as well as μ(X), as is the case among crystalline solids. Large structure-property changes occurring within non-ergodic amorphous solids as a function of P and T are also observed, that are generally termed 'polyamorphism'. The polyamorphic changes can map on to underlying density- or entropy-driven L-L transitions. Studying these phenomena poses challenges to experimental studies and liquid simulations. Experiments must be carried out over a wide P-T range for in situ structure-property determinations, often in a highly metastable regime. It is expected that L-L transitions often occur below the melting line, so that studies encounter competing crystallization phenomena. Simulation studies of liquid state polyamorphism must involve large system sizes, and examine system behaviour at low T into the deeply supercooled regime, with distance and timescales long enough to sample characteristic density/entropy fluctuations. These conditions must be achieved for systems with different bonding environments, that can change abruptly across the polyamorphic transitions. Here we discuss opportunities for future work using simulations combined with neutron and x-ray amorphous scattering techniques, with special reference to the behaviour of two polyamorphic systems: amorphous Si and supercooled YO-AlO liquids.

A combination of in situ high-pressure neutron diffraction at pressures up to 17.5(5) GPa and molecular dynamics simulations employing a many-body interatomic potential model is used to investigate the structure of cold-compressed silica glass. The simulations give a good account of the neutron diffraction results and of existing x-ray diffraction results at pressures up to ~60  GPa. On the basis of the molecular dynamics results, an atomistic model for densification is proposed in which rings are "zipped" by a pairing of five- and/or sixfold coordinated Si sites. The model gives an accurate description for the dependence of the mean primitive ring size ⟨n⟩ on the mean Si-O coordination number, thereby linking a parameter that is sensitive to ordering on multiple length scales to a readily measurable parameter that describes the local coordination environment.

Wilson, M., Wilding, M. C., Daisenberger, D., Machon, D., Cabrera, R. Q. (2007). High-pressure x-ray scattering and computer simulation studies of density-induced polyamorphism in silicon. Physical Review B: Condensed Matter and Materials Physics, 75 (22). Sponsorship: ESRFA low- to high-density pressure-driven phase transition in amorphous silicon is investigated by synchrotron x-ray diffraction in the diamond anvil cell. Complementary atomistic molecular dynamics computer simulations provide insight into the underlying structural transformations and allow us to interpret the structure factors obtained from experiment. During compression the form of the scattering function S(Q) changes abruptly at 13.5 GPa, indicating significant structural rearrangement in the amorphous solid. In particular, the first peak in S(Q) shifts to larger Q values. The changes are correlated with the occurrence of a low- to high-density (LDA-HDA) polyamorphic transition observed previously using Raman scattering and electrical conductivity measurements. The data are analyzed to provide real space (pair distribution function) information. The experimental data are compared with results from molecular dynamics (MD) simulations using a modified Stillinger-Weber many-body potential energy function in order to extract structural information on the densified amorphous material. We deduce that the polyamorphic transition involves an abrupt increase in the proportion of 5- and 6-coordinate Si atoms. The overall structure of the HDA polyamorph can be related to that of the LDA form by creation of highly-coordinated "defects" within the tetrahedrally-bonded LDA network. However classical and quantum MD simulations indicate that an even higher density amorphous state might exist, based on structures that resemble the densely-packed metallic polymorphs of crystalline Si.publishersversionPeer reviewe

A representation of the short-range repulsion energy in an ionic system is described which allows for the fact that an ion may be compressed by its neighbours. The total energy of the system is expressed in a pairwise additive form, but the interionic interactions have a many-body character. The form of this representation and the parameters required to represent MgO and CaO are obtained from recent ab-initio electronic structure calculations. The fact that the representation is transferable between crystals with different coordination number is demonstrated by direct comparison with ab-initio results on the different crystal types. Comparison with experimental results on the equation of state of different isomorphs and on the location of the pressure of the transition between them confirms the accuracy of the ab-initio results and of the potential derived from them in representing perfect crystal properties. A computationally efficient molecular dynamics (MD) scheme may be derived for this representation. The additional degrees of freedom which represent the varying ionic radii are constrained to their adiabatic values in the course of the simulation by an adaptation of Car and Parrinello’s method. The MD scheme is used to examine whether an ab-initio parameterized potential model which allows for the spherical compression of an oxide ion by its neighbours and for dipole polarization effects is a sufficiently good representation of the interactions in MgO to allow an accurate calculation of the phonon dispersion curves.