First-order structural phase transitions are common in crystalline solids, whereas first-order liquid-liquid phase transitions (that is, transitions between two distinct liquid forms with different density and entropy) are exceedingly rare in pure substances But recent theoretical and experimental studies have shown evidence for such a transition in several materials, including supercooled water and liquid carbon Here we report an in situ X-ray diffraction observation of a liquid-liquid transition in phosphorus, involving an abrupt, pressure-induced structural change between two distinct liquid forms In addition to a known form of liquid phosphorus--a molecular liquid comprising tetrahedral P4 molecules--we have found a polymeric form at pressures above 1 GPa Changing the pressure results in a reversible transformation from the low-pressure molecular form into the high-pressure polymeric form The transformation is sharp and rapid, occurring within a few minutes over a pressure range of less than 002 GPa During the transformation, the two forms of liquid coexist These features are strongly suggestive of a first-order liquid-liquid phase transition

A first-order liquid–liquid phase transition in phosphorus

Despite their lack of long-range translational and orientational order, covalent amorphous solids can exhibit structural order over both short and medium length scales, the latter reaching to 20 A or so. Medium-range order is difficult to measure experimentally and to interpret unambiguously, but a variety of techniques have allowed several types of characteristic structural ordering to be identified and their origin elucidated.

Medium-range structural order in covalent amorphous solids

It is proposed that the first sharp diffraction peak (FSDP) in the structure factor of network glasses and liquids is a pre-peak in the concentration-concentration structure factor due to the chemical ordering of interstitial voids around cation-centred clusters in the structure. This model can predict quantitatively the positions of the FSDP for a wide range of oxide and chalcogenide glasses and liquids, and can also successfully rationalize the anomalous temperature and pressure behaviour of the FSDP intensity, as well as the effect of the incorporation of network modifiers.

https://iopscience.iop.org/article/10.1088/0953-8984/4/38/003/pdf

The origin of the first sharp diffraction peak in the structure factor of covalent glasses and liquids

The structural origin of the first sharp diffraction peak (FSDP), a prepeak in the structure factor of network-forming amorphous materials which exhibits anomalous behaviour with respect to temperature, pressure and composition, is ascribed to the structural ordering of interstitial voids. This void-based model gives a quantative description of the behaviour of the FSDP. The real-space quasi-periodicity in the structure of amorphous network materials necessary to produce an FSDP as a pseudo-Bragg peak has been identified in an ultra-large model of a-Si. This extended-range order is found to result from the propagation of short-range order (second-neighbour correlations) in the case of a-Si, or of medium-range order (fourth-neighbour correlations) in the case of AX 2 -type materials.

Extended-range order, interstitial voids and the first sharp diffraction peak of network glasses

The Structure factors of molten AgCl, AgBr and AgI have been obtained by neutron scattering measurements at two different temperatures in order to investigate the local structure and its temperature dependence. The partial structural parameters such as a partial coordination number and an inter ionic distance have been determined by curve fitting analysis. Molten silver halides are found to have tetrahedral coordination of the local order near the melting points. The local order for molten AgCl and AgBr is broken with increasing temperature, while that for molten AgI is preserved even at high temperature. This suggests that the bonding in molten AgI has more covalent character than that in molten AgCl and AgBr.

Structural Study of Molten Silver Halides by Neutron Diffraction

Structure factor Sm(Q) of liquids of simple tetrahedral molecules X4 has been calculated as a function of ζ, where ζ is a ratio of the intermolecular atomic spacing L to the intramolecular atomic spacing l, i.e., ζ=L/l, under constraints of a fixed preferred orientation between the nearest neighbors and a fixed packing fraction of uncorrelated molecules. It turned out that the Sm(Q) depends strongly on the ratio ζ. An important feature of the calculated Sm(Q)’s is an appearance of a new peak at low Q region and its rapid growth with increasing ζ. The characteristic features of the experimental Sm(Q)’s of liquids P4 and VCl4 can be reasonably reproduced by the present simple calculation with ζ=1.64 for liquid P4 and 1.14 for liquid VCl4. These values of ζ are simply interpreted by the molecular size and intramolecular atomic spacing of each molecule.

M. Misawa

Papers

Structure factor of X4 tetrahedral molecular liquids: Competition between intramolecular and intermolecular atomic spacings