First-neighbour Distances Research Articles

Local structure in high-entropy transition metal diborides

Studies on high-entropy materials often speculate about the effects of lattice distortion and disorder on characteristics such as hardness, thermal expansion, and electronic properties. Notwithstanding the ongoing race to discover new compositions, investigations of the local structure at the atomic level remain sparse at best. Additionally, assessments of the homogeneity of the distribution of metals within the lattice sites are often restricted to techniques such as energy dispersive spectroscopy which might lead to an inaccurate picture of the bulk material. Herein, we report an extensive and systematic study of a class of emerging high-entropy ceramics that uses a combination of high-resolution synchrotron powder diffraction and extended X-ray absorption fine structure analysis. Our data are consistent with a random distribution of atoms with local strain around the d-metals sites, which describes the bulk structure of these materials. Moreover, a linear trend is observed between the average structure and the first-neighbour distances, regardless the number (from 3 to 5) and type (Ti, Zr, Nb, Hf, Ta, Mo, W) of metals that constitute the high-entropy ceramic, which suggests that any description of properties for such materials need to go beyond the simple dichotomy of long-range order and local structure.

Structural and electronic changes in graphite fluorides as a function of fluorination rate: An XRS, PDF and DFT study

In the present paper, graphite fluoride compounds CxF with various degrees of fluorination (x = 4, 2 and 1), i.e., with different C-F bonding characteristics, were systematically investigated using X-ray Raman Spectroscopy (XRS) and X-ray and neutron diffraction by means of Pair Distribution Function (PDF) analysis. For both techniques, ab-initio calculations allow the experimental results and structural/bonding assignments to be explained and/or confirmed. Presented here for the three stoichiometries are results for the carbon and fluorine first-neighbour distances, the evolution of the electronic band structure due to the change of the carbon hybridization upon fluorination, and also the nature of the final states for 1s core-electron excitations. Since fluorination is limited by the diffusion of fluorine in the carbon lattice, the process is less effective in the bulk, where a graphitic core remains. The cross-checked XRS, PDF data and Density Functional Theory (DFT) simulations appear also to be a powerful method to highlight the presence of a residual graphitic core, even at the highest fluorine content, in such semi-disordered and structurally complex compounds.

Cation distribution of Mn-Zn ferrite nanoparticles using pair distribution function analysis and resonant X-ray scattering

Mn-Zn ferrite nanoparticles were synthesized by chemical co-precipitation method and analysed using X-ray synchrotron diffraction data. Pair distribution function (PDF) analysis was used to probe the local structure and revealed that the first-neighbour distances of Fe-Fe and Mn-Zn in the 3.0 up to 3.5 Å range are different from the ones usually reported in the literature. For the sample with the best magnetic behaviour, resonant X-ray scattering (RXS) using three energies close to the absorption edges of Mn, Zn and Fe was applied to determine the cation distribution which explained the previous result from PDF analysis.

Structure and Electronic Properties of Amorphous Ge–Pd Alloys Manifesting the Metal-Insulator Transition. I. Atomic Structure and Electrical Conductivity

Amorphous Ge 100- x Pd x alloy films are prepared with an Ar-ion-beam sputtering technique over wide ranges of compositions (0≤ x ≤49.4 and 73.3≤ x ≤80.7). Their atomistic structures are studied with a grazing-incidence X-ray diffraction technique. The first-neighbour interatomic distance, r 1 , and the coordination number, N 1 , are evaluated from the analysis of total radial distribution function, R D F ( r ), derived from the diffraction data. For low Pd concentrations ( x x c ). The metal-insulator transition (Anderson transition) takes place at 10.2< x c <11.5 in this system.

Pressure-induced phase transition in icosahedral Al–Li–Cu quasicrystals

Abstract We report in-situ extended X-ray absorption fine-structure (EXAFS) studies of icosahedral Al6Li3Cu quasicrystals, without any aluminium excess, under a high pressure in quasihydrostatic conditions. The EXAFS experiments have been performed at the Cu K absorption edge from ambient pressure up to 33 GPa and give the variation in the average distance of fist neighbours around copper atoms against pressure. This average distance decreases monotonically with increasing pressure up to 12 GPa, remains almost constant up to 20 GPa and then increases. This increase in the interatomic distance is interpreted as the fingerprint of a phase transition. The relative first-neighbour distance has been fitted, up to 12 GPa, by a Murnaghan equation of state so that the zero-pressure bulk modulus is B 0 = 71 GPa for a first derivative B′0 = 6. This B 0 local value found around copper atoms is close to the overall bulk modulus of pure aluminium. After release of the pressure, the Al6Li3Cu quasicrystal shows spectacular 'metastable' properties.

X-ray absorption and diffraction spectroscopy of icosahedral Al-Cu-Fe quasicrystals under high pressure

Abstract We report in-situ extended X-ray absorption fine structure (EXAFS) and X-ray diffraction studies of quasicrystals under high pressure quasihydrostatic conditions. The EXAFS and diffraction experiments are combined for the first time to give a joint evolution of the short-range and long-range atomic order with pressure. EXAFS experiments performed at the Fe and Cu K absorption edges have been carried out for an icosahedral Al62Cu25.5Fe12.5 alloy from ambient pressure up to about 8 GPa (Fe edge) or 35 GPa (Cu edge). The local order around Fe and Cu atoms has thus been obtained as a function of pressure. X-ray diffraction patterns have been obtained for the same quasicrystal up to 35 GPa and these have given a variation in the 6D lattice parameter with pressure. A remarkable result is that the quasicrystal remains icosahedral up to the highest pressure. The evolution of the 6D lattice parameter and of the first-neighbour distances has provided values of the zero-pressure bulk modulus and of its firs...

A nearly free-electron model of the pair potential in molten copper

An effective interionic pair potential in liquid copper at 1393 K was extracted from the neutron-diffraction data using an iterative fitting procedure based on the modified hypernetted-chain approach. The procedure involved extensive molecular-dynamics simulation using a system of 16384 particles. The potential, constructed within the framework of the nearly-free-electron approximation, is based on the Dagens-Rasolt-Taylor model, and it is repulsive and positive around the first-neighbour distance. The proposed potential when used in molecular-dynamics calculations reproduces, within the limit of experimental accuracy, the structure factor measured by neutron diffraction, including the long-wavelength region of the structure factor and the isothermal compressibility limit, as well as the experimental value of the self-diffusion coefficient. The bridge function of liquid copper derived from the simulation data is compared with a hard-sphere fluid bridge function obtained in the context of the modified hypernetted-chain approximation.

A local order study of molten LiNbO3 by neutron diffraction

The total structure factor S(Q) and the total pair correlation function G(r) of liquid LiNbO3 have been investigated by neutron diffraction. The temperature dependence of the scattered intensity has been measured in the range of momentum transfer 0.3 AA-1 < Q < 16.2 AA-1 and the range of temperature 1623 K > T > 1490 K including an undercooling domain. A large variation of S(Q) with temperature was never observed. From an analysis of G(r) made with reference to the crystalline LiNbO3 structure, it was possible to confirm a local ordering similar to the crystalline one. The assumption of a change in the Nb coordination in the liquid near solidification is unfounded. The Nb atom remains octahedrally coordinated up to one hundred degrees above the melting point. The values of the first-neighbour distances r1Nb-O, r1O-O and r1Li-O and the coordination numbers nLi-O and nO-O can be explained by the presence of NbO6 octahedra bonded together by Li atoms in the melt.

Three-body distribution function in liquids: the case of liquid gallium

The first report of an X-ray absorption spectroscopy (XAS) study of liquid gallium, carried out at several temperatures in liquid and crystalline phases and in the supercooled state, is presented. Data analysis has shown the presence of two resolved first-neighbour distances and a detectable signal due to three-body configurations.

Solute-and-dumbbell defect diffusion in b.c.c. lattices

Abstract Defect and solute diffusion coefficients, namely D I and D B∗, are calculated for a b.c.c. lattice when diffusion occurs by a dumbbell mechanism. Two possible symmetries of the defect are envisaged, together with all the jump frequencies invoked so far to interpret the experimental data. For simplicity and tractability, only the binding energy of the mixed dumbbell is taken into account; all the interaction energies of a solute-defect complex when separated by a first-neighbour distance or more are ignored. The full correlation effect of the infinite lattice is taken into account using a double Fourier-Laplace transform. Unlike the vacancy case, the defect concentration C I does not enter D B∗ in a simple multiplicative way; the self-diffusion coefficient D A∗ is not equal to f 0 C I D I, where f 0 is the correlation factor for self-diffusion, because the average jump length of an atom is not equal to the jump length of the defect; finally, the isotope effect is a complicated function of the jump frequencies and cannot be restated in the simple form f 0 ΔK.

Sphere and distance models for binary disordered systems

Abstract First-neighbour geometrical models are presented and shown to provide a good approximation for the structural description of binary disordered systems with metallic, covalent or ionic bonding. Sphere mixture models taking into account atomic size and chemical order effects are first studied and analytical expressions for the partial coordination numbers are derived which only involve packing fraction, diameter ratio, concentration and chemical order parameter. Relations between the concentration thresholds separating different chemical order regimes and site percolation theory are established. Close-packed sphere mixtures are finally shown to be a good representation of liquid or glassy alloys. Hole sphere models are then introduced and shown to provide a satisfactory approximation to the structure of loose-packed covalent glasses of silicon and germanium. Finally, first-neighbour distance models are presented and the variations of their partial structure factors with non-additivity parameter are...

Analysis of EXELFS modulations in EELS above the K-shell of silicon at 1 MeV in the HVEM

EXELFS experiments performed at 1 MeV in a high-voltage electron microscope (HVEM) under relatively straightforward conditions on several types of Si thin films have been analysed. It has been observed that the presence of a contamination layer, such as oxide or carbide, drastically affects the EXELFS oscillations past the Si K-edge. The visibility of the second neighbour distance of silicon is not clearly seen in specimens which are composed of several phases, and the expected accuracy of ± 0.05 A in the first-neighbour distance is not reached. Depending on the K-range chosen for analysis, the structural information arising from the weakly present phase can be enhanced or removed. Finally, we show that the thicker specimens after HF cleaning give best results because of the small relative amount of oxide. In that case, however, the calculated distances for the first two

A mossbauer study of 119Sn in alloys of iron with Si, Al and Rh: interaction potentials and phase diagrams

Mossbauer spectra of 119Sn at a concentration of 0.2% in alloys of iron with Si, Al and Rh are presented. The strength of some of the interaction potentials between Sn and Si, Al and Rh are obtained, and some details of the iron-rich corner of the ternary phase diagrams elucidated. In alloys of iron with silicon and aluminium, the interaction potentials are found to be large and positive, in agreement with the Miedema-Krolas and size-mismatch theories. The authors find that in both these alloy systems, the presence of tin in concentrations as low as 0.2% strongly lowers the value of the concentration of the alloying element at which order states of Fe3Si and Fe3Al appear. In the iron-rhodium alloys, they find a potential at the first-neighbour distance between Sn and Rh atoms of -32 meV, in fair agreement with the Miedema-Krolas prediction of -84 meV. At the second-neighbour distance the potential cannot be determined. For Rh concentrations greater than 3%, an intermetallic compound is formed in which 119Sn has a positive hyperfine field of 57 kOe and an isomer shift 0.1 mm s-1 less than is found at 119Sn in iron.

A diffraction investigation of some NiTa metallic alloy glasses

X-ray and neutron diffraction measurements have been made on three NiTa metallic glasses, Ni55Ta45, Ni62Ta38 and Ni67Ta33. The total structure factors have been derived and the curves obtained with neutrons found to be particularly well defined. The total radial distribution functions (RDF) obtained are discussed in relation to models of close packing and to the stable crystalline phases in the NiTa alloy system. A derivation of the partial structure factors has been made for the Ni55Ta45 glass by an approximate method. The results of this suggest there is a progressively broadened distribution through the Ni-Ni, Ni-Ta and Ta-Ta first-neighbour distances which allows the form of the first peak in the total RDF to be understood. The broadening and expansion of particularly the Ta-Ta first-neighbour distances in the glassy state is consistent with the kind of local order which exists in the Ni2Ta and mu -NiTa crystalline phases. The possible identification of glassy NiTa alloys as disordered Frank-Kaspar phases, or alternatively as structurally relaxed 'soft sphere' assemblies, is discussed.

Neutron-diffraction study of hydrogenated and deuterated CuTi amorphous alloys

Neutron-diffraction experiments have been performed on amorphous CuxTi1-x (x=0.67,0.50,0.35) alloys charged either with hydrogen or deuterium. The variation of the interference functions and pair-correlation functions have been studied as a function of copper and hydrogen or deuterium concentration. The results obtained of non-hydrogenated alloys confirm the existence of chemical order. First-neighbour distances are determined and can be well compared with those in corresponding crystalline phases. The good contrast between copper and titanium on the one hand and between hydrogen and deuterium on the other allows one to identify individual metal-hydrogen correlations. Their positions in the total pair-correlation functions are very close to those found in crystalline hydrides and show that Ti3 tetrahedra are preferred hydrogenation sites in the concentration range studied.

Effective interatomic pair potentials in liquid polyvalent metals from observed structure data

A method which is based on the random phase approximation (RPA) and Monte Carlo (MC) computer simulation is applied to liquid Mg, Zn, Ca, Sr, Ba, Al, In and Pb to extract the effective pair potential nu eff(r) using the experimental structure factor a(k) near the melting point. For Zn, Al, In and Pb the nu eff(r) thus obtained have a markedly raised principal minimum, while for Mg, Ca, Sr and Ba they display a conventional attractive well at the first-neighbour distance. They present results, though not fully quantitative, give good support to the recent analysis by Jacucci and Taylor (1981) in which one expects the interatomic potential to be repulsive at the first-neighbour distance for simple metals with a high density of conduction electrons.

Impurity migration stimulated by generation and recombination of Frenkel pair.

The defect-witness behaviour at generation and sloping of neighbouring unstable Frenkel pairs in the b.c.c. iron was studied by the computer simulation method. It is shown that a helium atom always jumps when it is located on the first-neighbour distances to a branch of a Frenkel pair recombination zone. But a less mobile defect-witness ( a vacancy ) does not leave its site under analogical conditions. It is concluded that the influence of the Frenkel pair as a stimulator of mobile defect migrations is limited in space though the mechanism of such stimulation exists.

The nature of an interionic potential in the near-neighbour region in a simple metal

It is pointed out that calculated interionic potentials for simple metals with a high density of conduction electrons may or may not contain a term of the form exp(- eta R)/R depending on the choice of dielectric function. The presence of such a term can have a large effect on the potential in the near-neighbour region, removing the attractive well at the first-neighbour distance. The authors' analysis suggests that for rs<2.5 one can expect an interionic potential to be repulsive at the first-neighbour distance but that at larger values of rs it should display the more conventional attractive behaviour at that distance.

Investigation of disorder effects in amorphous GaAs and GaP by EXAFS

Disorder effects in amorphous GaAs and GaP are investigated by EXAFS measurements at the K edge of Ga and As for GaAs and of Ga only for GaP, performed with the DCI synchrotron radiation at LURE. The samples are unannealed films with controlled stoichiometry prepared by flash-evaporation under ultrahigh-vacuum conditions. In the case of GaAs, the EXAFS data are analysed by a classical Fourier filtering technique, using crystalline powders as a reference material. The results are compared with those obtained in the same experiments on evaporated amorphous Ge films. No contribution from second neighbours can be detected in either set of amorphous data. The mean first-neighbour distances around Ga and As absorbing atoms are found to be identical, in contrast to previous observations, and larger than the crystalline distance by 0.01 AA only. The spread of these distances around their mean value, deduced from the EXAFS amplitudes, supports the conclusion that the amorphous GaAs samples are chemically ordered. In the case of GaP, the EXAFS data are compared with computed model curves constructed within different assumptions about chemical disorder characteristics. From the study of the amplitude, there is some indication of the presence of Ga-Ga wrong bonds, with a length slightly larger than the Ga-P normal bonds. The difficulties in EXAFS analysis related to disorder are discussed.

Soft X-ray absorption and EXAFS on the K edge of aluminium

The authors report EXAFS (extended X-ray absorption fine structure) measurements performed in the 1000-2500 eV range using synchrotron radiation delivered by the ACO storage ring (LURE). The K edge EXAFS spectra of Al in elemental aluminium and alpha alumina have been analysed; it is shown that accurate measurements of the first-neighbour distances are possible even for low-Z atoms. In the case of the metal, the authors emphasise the importance of the screening of the core hole potential in the first 150 eV part of the spectrum.