Reverse Monte Carlo (RMC) modelling is a general method of structural modelling based on experimental data. RMC modelling can be applied to many different sorts of data, simultaneously if wished. Powder and single-crystal neutron diffraction (including isotopic substitution), x-ray diffraction (including anomalous scattering) and electron diffraction, extended x-ray absorption fine structure and nuclear magnetic resonance (magic angle spinning and second moment) have already been used to provide data. RMC modelling can also be applied to many different types of system - liquids, glasses, polymers, crystals and magnetic materials. This article outlines the RMC method and discusses some of the common misconceptions about it. It is stressed that RMC models are neither unique nor `correct'. However, they are often useful for aiding our understanding either of the structure itself, or of the relationships between local structure and other physical properties. Examples are given and the possibilities for further development of the RMC method are discussed.

http://slapper.apam.columbia.edu/bib/papers/mcgre_jpcm01.pdf

Reverse Monte Carlo modelling

The problem of those discernible features of the intermediate range order (IRO) which can be attributed to the first sharp diffraction peak (FSDP) observed in the structure factor of many liquid and glassy materials is approached by treating this peak as a distinct feature. It is found, by considering the measured partial structure factors, S αβ ( k ), for molten ZnCl 2 , GeSe 2 , MgCl 2 , NiBr 2 and Nil 2 and the measured total structure factors, F ( k ), for glassy SiO 2 , PS 4 and liquid CCl 4 , that the propensity of the FSDP to have a prominent effect on the underlying features of the IRO depends noticeably on the system type. Specifically, the FSDP confers a marked oscillatory character of periodicity 2π/ k 1 (where k 1 is the FSDP position) on the IRO when the local structural units, which give rise to the density fluctuations on the IRO scale, exist as stable entities for a timescale τ ≫ 5 × 10 -12 s. The FSDP therefore accounts for the discernible features of the underlying IRO for the viscous glass forming liquids ZnCl 2 and GeSe 2 , for the glasses SiO 2 and PS 4 , and for the molecular liquid CCl 4 . The influence of the FSDP on the IRO is less pronounced for molten MgCl 2 and is negligible for molten NiBr 2 and Nil 2 , both of which have a high cation mobility which leads to a relative instability of the Ni 2+ centred structural units. The effect on the FSDP of temperature and pressure are briefly considered as are the development of the FSDP in molten ZnX 2 (when X is changed from Cl to I to Br) and the minimum size of r -space model which is required if the FSDP is to be accurately predicted.

Real Space Manifestation of the First Sharp Diffraction Peak in the Structure Factor of Liquid and Glassy Materials

A systematic analysis of those liquid binary 2:1 systems (denoted MX$\_{2}$), for which experimental partial structure factors are available from the isotopic substitution method in neutron diffraction, is made using the Bhatia-Thornton (BT) formalism. Particular attention is paid to the origin of the first sharp diffraction peak (FSDP), which occurs in the measured diffraction patterns for some of the MX$\_{2}$ systems, since it appears, from recent studies, that this feature is a signature of directional bonding. It is found that FSDPS can occur in all three BT partial structure factors S$\_{\alpha \beta}$(k). A FSDP feature in the concentration-concentration partial structure factor S$\_{\text{CC}}$(k) is not, however, pronounced except in the case of MgCl$\_{2}$ and the glass forming network melts ZnCl$\_{2}$ and GeSe$\_{2}$ To the extent that these systems can be regarded as ionic melts a FSDP in S$\_{\text{CC}}$(k) implies a non-uniformity in the charge distribution on the scale of the intermediate-range order (IRO). The structure of molten GeSe$\_{2}$ is compared with the structures of molten ZnCl$\_{2}$, glassy GeS$\_{2}$ and glassy SiO$\_{2}$. Although the GeSe$\_{2}$ and ZnCl$\_{2}$ melts have different short-range order, there are similarities in the observed IRO which can be attributed to the arrangement of the electropositive species M. The essential features of the measured total structure factor for glassy GeS$\_{2}$ can be reproduced by using the molten GeSe$\_{2}$ S$\_{\alpha \beta}$(k). This result lends support to the notion that the S$\_{\alpha \beta}$(k) for liquid GeSe$\_{2}$ (and ZnCl$\_{2}$) are characteristic of both the liquid and glassy states of other network glass forming systems. The structures of molten GeSe$\_{2}$ (or ZnCl$\_{2}$) and glassy SiO$_{2}$ are, however, found to be different. The observed discrepancies are largest in the region of the FSDP which signifies pronounced differences in the nature of the IRO for these systems.

The structure of molten and glassy 2:1 binary systems: An approach using the Bhatia-Thornton formalism

The occurrence of polyanions in a group of liquid ionic alloys, viz. alloys of the alkali metals with 13, 14, 15 and 16 elements (post-transition-metal groups 3, 4, 5 and 6), is discussed. It is shown that there are strong parallels with the corrresponding crystalline phases, in which polyanions such as .Pb4/4 , .Sb /1 and .Te2/2 exist, known for a long time as 'Zintl ions'. Little evidence exists for remnants of the diamond-lattice-type Zintl ion in liquid alkali-group-13 alloys, but in the alloys of Tl with K, Rb and Cs very long-range superstructures have been found, which are related to the occurrence of large, compact, polyhedral clusters in many crystalline phases. A stability rule, first proposed by Geertsma, relating the stability of the polyanions to the size of the cations, is universally observed. Furthermore it is shown that the range of the superstructure in the liquid is with remarkable precision proportional to the intercluster distance in the corresponding solids. The interpretation of the experimental data in terms of polyanion formation is discussed critically. There remains a paradox. Some sharp experimental features (superstructure peaks and maxima in the resistivities and stability functions) seem to indicate that the Zintl ions in the liquid are near perfect whereas specific heat results and ab initio computer simulations clearly show that the structure of the liquid is seriously blurred.

https://iopscience.iop.org/article/10.1088/0953-8984/8/34/003/pdf

Polyanions in liquid ionic alloys: a decade of research

The atomic structures in equilibrium and supercooled liquids of Zr${}_{80}$Pt${}_{20}$ were determined as a function of temperature by in situ high-energy synchrotron diffraction studies of the levitated liquids (containerless processing) using the beamline electrostatic levitation (BESL) technique. The presence of a pronounced pre-peak at q \ensuremath{\sim} 1.7 \AA{}${}^{\ensuremath{-}1}$ in the static structure factor indicates medium-range order (MRO) in the liquid. The position and intensity of the pre-peak remain constant with cooling, indicating that the MRO is already present in the liquid above its melting temperature. An analysis of the liquid atomic structures obtained using the Reverse Monte Carlo method utilizing both the structure factor $S$($q$) from x-ray diffraction experiments and the partial pair-correlation functions from ab initio molecular dynamics simulations show that the pre-peak arises from a Pt-Pt correlation that can be identified with icosahedral short-range order around the Pt atoms. The local atomic ordering is dominated by icosahedral-like structures, raising the nucleation barrier between the liquid and these phases, thus assisting glass formation.

/pdf/short-and-medium-range-order-in-zr-80-pt-20-liquids-3a6ov2gay9.pdf

Short- and medium-range order in Zr 80 Pt 20 liquids

The structural properties of liquid equiatomic alkali-metal--lead alloys APb, with A=Na, K, Rb, and Cs, have been studied with neutron diffraction. The experimental data are reduced to the neutron-weighted total structure factors S(Q) and radial distribution functions n(r). In all the systems studied, S(Q) is characterized by a first sharp diffraction peak (FSDP) at Q\ensuremath{\sim}1 A\r{} $^{\mathrm{\ensuremath{-}}1}$ and n(r) by structure in the first coordination shell at r=3--4 A\r{}, both features indicating the presence of polyatomic structural units. Two types of structural models have been fitted to the experimental data, both based on consideration of such units: the random packing of structural units model, and the reference interaction site model. The structures of the units are derived from powder-diffraction measurements made with the same instrument on solid polycrystalline samples. Allowing for a slight expansion of the units on melting and using physically reasonable values for the adjustable parameters, both models give satisfactory agreement with the experimental data and are used to give the partial structure factors and pair distribution functions. Inelastic-scattering measurements have been made on one system, liquid KPb, using a spectrometer at the same source. These yield a value for the mean diffusion constant, D=1.2\ifmmode\pm\else\textpm\fi{}0.2\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}5}$ ${\mathrm{cm}}^{2}$/sec, and a smoothly varying inelastic scattering spectrum with no indication of excitations of a molecular character. The FSDP remains well defined when the inelastic scattering is integrated over small energy transfers, indicating a lifetime of ${10}^{\mathrm{\ensuremath{-}}13}$ sec or longer for the intermediate-range order responsible for this peak.

Structural-properties of liquid alkali-metal lead alloys - napb, kpb, rbpb, and cspb

The structure factors of liquid equiatomic KSn and CsSn alloys have been determined by neutron diffraction. A distinct peak at about 1 A${\mathrm{\r{}}}^{\mathrm{\ensuremath{-}}1}$, the first sharp diffraction peak (FSDP), occurs in all measured structure factors. The temperature dependence of the structure has been studied for KSn: apart from the FSDP, whose position shifts toward smaller wave vector and magnitude decreases with increasing temperature, the structure factor remains essentially unaltered. The radial distribution function clearly shows three maxima in the first coordination shell. The simultaneous presence of the FSDP and several maxima in the first coordination shell are indications of formation of polyatomic species in the liquid. Application of two simple structural models, taking into account the presence of structural units, yields reasonable agreement with the measured structure factors.

Structure of liquid equiatomic KSn and CsSn.

A molecular-dynamics computer simulation is used to determine velocity and current-density autocorrelation functions for a liquid system consisting of K{sup +} and Pb{sub 4}{sup 4{minus}} ions. The calculated structure of this system is in excellent agreement with that determined experimentally for liquid KPb alloys. The calculations provide an interpretation for recent inelastic-neutron-scattering results, which do not show any distinct vibrational modes characteristic of Pb{sub 4}{sup 4{minus}} tetrahedra.

H. T. J. Reijers

Papers

Structural-properties of liquid alkali-metal lead alloys - napb, kpb, rbpb, and cspb

Structure of liquid equiatomic KSn and CsSn.

Atomic motions in liquid KPb: A molecular-dynamics investigation.