Layer Structure Factor Research Articles

Quantitative analysis of diffuse X-ray scattering in partially transformed 3C-SiC single crystals

The X-ray scattering of partially transformed 3C-SiC single crystals is considered in detail. Extended diffuse scattering streaks, originating from stacking faults (SFs) lying in the {111} planes, are clearly observed in the wide-range reciprocal-space maps. The intensity distribution along the diffuse streaks is simulated with a model including the contributions of the diffuse scattering originating from the SFs [based on the pioneering theoretical description given by Kabra, Pandey & Lele (1986).J. Mater. Sci.21, 1654–1666], the coherent scattering emanating from untransformed areas of the crystals and all θ-dependent terms that affect the scattered intensity (the layer structure factor, the irradiated volume and the polarization of the beam). The quantitative simulation of the diffuse streaks reveals that the transformation occurs through the glide of partial dislocations and allows one to derive the transformation level. It is shown that the 3C polytype is indeed unstable at high temperature. However, it is further shown that defect-free 3C-SiC single crystals remain stable at temperatures where 3C-SiC is known to be usually unstable (2173 K). The origin of this apparent stability is very likely of kinetic nature,i.e.the lack of crystalline defects inhibits the transformation.

Atomistic simulations for the non-equilibrium surface premelting and melting of Nb(1 1 0) plane

In the present paper molecular dynamics (MD) simulations have been preformed to investigate the surface melting process and microscopic mechanism of Nb(1 1 0) plane in the atomic scale with a modified analytic embedded atom method (MAEAM). On the basis of the MD relaxation dependence of averaged internal energy and layer structure factor at given temperatures, the melting point of the sample has been estimated to be 2510 K. Then by the above results the Nb(1 1 0) plane melting process has been approximately divided into two stages: first the layer-by-layer premelting phase in the surface region and then a simultaneous abrupt melting transition for the inner layers. According to the variation of the averaged internal energy of the inner atomic layer, the melting latent heat has been calculated and the result is in good agreement with the experimental value. The simulated snapshots of atomic configuration for Nb(1 1 0) plane have indicated that the dynamically microscopic mechanism of melting nucleation during the melting transition.

Molecular dynamics simulation of surface melting behaviours of the V(110) plane

The modified analytic embedded-atom method and molecular dynamics simulations are applied to the investigation of the surface premelting and melting behaviours of the V(110) plane by calculating the interlayer relaxation, the layer structure factor and atomic snapshots in this paper. The results obtained indicate that the premelting phenomenon occurs on the V(110) surface at about 1800K and then a liquid-like layer, which approximately keeps the same thickness up to 2020K, emerges on it. We discover that the temperature 2020K the V(110) surface starts to melt and is in a completely disordered state at the temperature of 2140K under the melting point for the bulk vanadium.

Surface melting of close-packed Mg(0001)

Using molecular dynamics simulations and an analytic embedded-atom method, an investigation of the surface anharmonicity for the close-packed surface of Mg(0001) is presented in the temperature range from 0 K to its bulk melting temperature. The temperature dependences of the surface phonon frequencies, the mean square vibrational amplitudes of surface atoms and the layer structure factor have been calculated. The calculated results are in good agreement with the experimental data available. Surface melting of the closed-packed Mg(0001) is predicted by the calculation of the layer structure factor, and a liquid-like layer is observed from the simulation of its microstructure. The possible mechanism for the anomalous behavior is discussed.

Anharmonic effects on B2–FeAl(1 1 0) surface: A molecular dynamics study

Using molecular dynamics simulations and the analytic embedded-atom method (AEAM), the surface anharmonicity of B2–FeAl(1 1 0) has been studied in the temperature range from 0 K to 1400 K. The temperature dependence of the interlayer spacing, mean square vibrational amplitudes, surface phonon frequencies and line-widths, and layer structure factor have been calculated. The obtained results indicate that the anharmonic effects are small in the temperature range from 0 K to 900 K. The temperature dependences of the interlayer spacing indicates that the rippling effect of the B2–FeAl(1 1 0) surface is exhibited by the contraction of Fe surface atoms and the expansion of Al atoms, which persists at high temperatures. The temperature dependence of the layer structure factors shows that the B2–FeAl(1 1 0) surface does not disorder until the temperature of 1300 K.

Surface melting of close‐packed Mg(0001), compared with Al(111)

AbstractUsing molecular dynamics simulations and an analytic embedded‐atom method, a comparative study of the surface anharmonicity for the close‐packed surface of Mg(0001) and Al(111) is presented in the temperature range from 0 K to their melting temperatures. The temperature dependences of the surface phonon frequencies, the mean square vibrational amplitudes of surface atoms and the layer structure factor are calculated. The calculated results are in good agreement with the available experimental data. Although with the same atomic arrangement for the top layer, Al(111) preserves its crystalline order in the temperature range considered, and Mg(0001) exhibits surface melting. The possible mechanism for the different melting behaviors of the two surfaces is discussed. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Melting mechanisms of Nb(111) plane with molecular dynamics simulations

Using the modified analytic embedded-atom method, the premelting and melting process of the low-index plane of niobium (111) is studied with molecular dynamics simulations. The physical properties of this plane, including the layer atomic density function, the layer structure factor and the radial distribution function, are calculated in order to systematically investigate the complex microstructure evolution of the (111) plane with temperature. The results indicate that there exists a premelting phenomenon on the (111) surface of niobium at lower temperature and it has melted entirely at some temperature below the corresponding melting point of the prefect crystal. In addition, the premelting atomic fraction of this plane is fitted with the corresponding temperature to obtain the surface premelting activation energy which is able to estimate the premelting phenomena and the disordering progress of the plane.

Anharmonic effects on Be(0 0 0 1): A molecular dynamics study

Using molecular dynamics simulations and a modified analytic embedded atom method (MAEAM), the anharmonic effects of Be(0 0 0 1) surface have been studied in the temperature range from 0 K to 1400 K. The temperature dependence of the interlayer separation, mean square vibrational displacement, phonon frequencies and phonon line width, and layer structure factor are calculated. The obtained results for temperature dependence of interlayer separation and mean square displacement show that the anharmonic effects are small in the temperature range from 0 K to 1100 K. The calculated layer order parameters indicate that Be(0 0 0 1) surface loses its long-range translational order, but do not premelt up to 50 K below the bulk melting point. The surface disordering may result from strongly contracted c/ a ratio of Be.

Temperature dependence of atomic relaxation and vibrations for the vicinal Ni(9 7 7) surface: a molecular dynamics study

Using molecular dynamics simulations and a modified analytic embedded-atom method (MAEAM), the relaxations and vibrations of Ni(9 7 7) surface are studied in the temperature range of 100–1500 K, The calculated results for the temperature dependence of phonon frequencies, line-width and the mean square amplitude show that the anharmonic effects are small for temperatures up to 900 K. The calculated interlayer separation for the first and second surface decreases, and the distance along the x direction increases between the topmost and second surface, with increasing temperature. In addition, the calculated layer structure factor indicates that the Ni(9 7 7) surface is well ordered and does not premelt up to a temperature of 1700 K.

Ein einfacher Weg, Strukturinformation aus den diffusen Reflexen von Kristallen mit eindimensionaler Lagenfehlordnung zu erhalten

One-dimensionally disordered crystals consisting of layers that are equal with one another but stacked with displacement faults show sharp reflexions and diffuse streaks on their diffraction patterns. From the sharp reflexions alone an averaged structure (with fractional site-occupation factors) can be deduced. To obtain the real layer structure, the diffuse streaks have to be of considered. A simple experimental and mathematical procedure is described which enables their use without the need of measuring integrated streak intensities or streaks analysing the diffuse intensity profiles. Essentially, one has to measure the intensities of equal portions Δζ at equal positions ζ on different diffuse streaks; the values can be used directly, as they are proportional to the squared value of the layer structure factor. Additionally, a procedure is described for the measurement of the diffuse streak intensity profile on a four-circle diffractometer.

A study of a long-spacing mica-like mineral

AbstractAn interstratified clay mineral from Surges Bay, Tasmania, described by Cole & Carthew (1953) as containing a random stacking of illite and montmorillonite in the ratio of 3:2 and a regular stacking of illite and montmorillonite in the ratio of 1 : 1 is re-examined, after purification, and a new interpretation is made of the X-ray diffraction effects in terms of a single complex stacking model. The Fourier transform method of analysis used with an appropriate layer structure factor shows that the interstratification is produced by a three component stacking of 18% single mica layers (A), 10% double mica layers (ĀĀ) and 72% allevardite-like layers (ĀB̄) in which the A and ĀĀ layers are never together. This leads to the conclusion that the near regular interstratification of the mineral is due to structural and/or compositional variation from layer to layer within the parent crystals as suggested by Sudo, Hayashi & Shimoda (1962) to explain similar mineral types occurring in Japan.

Fourier transform methods for studying x-ray scattering from lamellar systems

A simple method based on Fourier transforms is described, for calculating X-ray diffraction effects due to interstratified mixtures of layers. The method is exact, and allows the following factors to be taken into account: crystallite size (including cases where the crystallites all not all of the same size), degree of randomness, variation of layer structure factor.