Total Interference Functions Research Articles

Liquid structure of N-butyl- N-methylpyrrolidinium bis-(trifluoromethanesulfonyl) amide ionic liquid studied by large angle X-ray scattering and molecular dynamics simulations

Large angle X-ray scattering of the N-butyl- N-methylpyrrolidinium bis-(trifluoromethanesulfony) amide (P 14 +TFSA −) ionic liquid was measured at 298 K. The total interference function i LAXS( s) and the total pair correlation function G LAXS( r) were successfully obtained. The i LAXS( s) was analyzed in terms of the intra-molecular geometries of the conformational isomers of the P 14 + and TFSA − ions based on the crystal structures, the inter-molecular correlation function G inter LAXS( r) and the inter-molecular radial distribution function as the form D inter LAXS( r) − 4 πr 2 ρ 0 were evaluated. With D inter LAXS( r) − 4 πr 2 ρ 0, the inter-molecular correlation peaks at 3.5, 4.5 and 5–6 Å evidently appeared as the short range interaction, while considerable long range interactions were found as the broad peaks at 10 and 15 Å. Molecular dynamics simulations of the ionic liquid based on the effective pairwise potentials were carried out. The X-ray total interference function derived from the MD simulations i MD( s) was in agreement with the experimental one. According to the inter-molecular partial atom–atom correlation functions from MD simulations, the observed peaks at 3.5, 4.5 and 5–6 Å can be predominantly ascribed to the closest atom–atom correlations between the P 14 + and TFSA – ions such as C···O and C···F. In the inter-molecular partial atom–atom correlation function between terminal methyl carbons of the butyl chain in the P 14 + ion, a peak at 4.0 Å was found as the inter-molecular correlation, suggesting that the ionic liquid shows an alkyl chain aggregation, which is similar to that observed for 1-alkyl-3-methylmidazolium ionic liquids.

Noncooperative iterative MMSE beamforming algorithms for ad hoc networks

An asynchronous unicast ad hoc network is considered, where each node i is equipped with a receive/transmit beam-former pair (W/sub i/, g/sub i/) designed under a quality-of-service (QoS) SNR constraint. It is first shown that the minimum sum-power beamformers for the network satisfy a weak duality condition, in which the pairs ((g/sub i//sup opt/)*, (W/sub i//sup opt/)*) achieve the same sum power as the primal network. However, the optimum receive beamformer w/sub i//sup opt/ is not in general equal to (g/sub i//sup opt/)*, in contrast to the case of cellular and time-division duplexing networks. Iterative minimum mean-square error (IMMSE) beamforming algorithms are then proposed in which w/sub i/ = g/sub i/* is enforced. These algorithms are shown to be instances of the Power Algorithm in which gi is the maximizing eigenvector of an SNR-related objective matrix. The IMMSE algorithm can also be viewed as a noncooperative beamforming game, in which the payoff includes normalized SNR, and the tax is related to interference caused at other nodes. The existence of fixed points (Nash equilibria) is proved for IMMSE. Furthermore, fixed points of IMMSE are shown to satisfy the first-order necessary conditions for optimization using a network Lagrangian. The IMMSE game is modified to yield a sequential distortionless-response beamforming algorithm, which is shown to be convergent using a Total Interference Function. Extensive simulation results illustrate that IMMSE yields better power efficiency than a greedy noncooperative SNR-maximizing game.

Effects of near-neighbor correlations on the diffuse scattering from a one-dimensional paracrystal

The one-dimensional paracrystal model is generalized by folding the lattice sites with objects whose scattering lengths or sizes and separation display a spatial correlation from cell to cell. A general theory to calculate the diffuse scattering and the scattering-length autocorrelation function is developed. The investigated models of coupling along the paracrystalline chain are the correlations between (i) the sizes of the scatterers, (ii) the sizes of scatterers and their separations, and (iii) the sizes of scatterers and the fluctuation of their separation distances. In the first case (i), the size of a scatterer is, on average, linked to that of its neighbors. As a result, a continuous transition from the total lack of size correlation (known as decoupling approximation or DA) to the scattering from monodisperse domains (local monodisperse approximation or LMA) is obtained. In the second case of correlation (ii), the mean interobject distance is assumed to depend on the respective sizes of nearest neighbors. Depending on the introduced correlation parameter, aggregation or hard-core-type effects can be accounted for. Surprisingly, in some cases, it is possible to find a peak in the scattering curve without any structure in the total interference function. The size-separation correlations may also dramatically reduce the scattering intensity close to the origin compared to the completely uncorrelated case. The last model (iii) foresees a coupling between the sizes of neighboring objects and the variance of the separation between neighbors. Within this model, on average along the chain, the fluctuations of distances between scatterers become dependent on the respective sizes of neighbors, while the mean distance between objects remains constant.

Computation of total and partial structure factors, coordination number, and compressibility with self- and mutual-diffusion coefficients of Hg-In alloy.

Hg-In alloy consisting of Hg, which shows several anomalous features in its properties and In, has been studied with a square-well attractive tail as an interaction potential between the atoms in the amalgam. The partial and the total interference functions have been computed with the Lebowitz hard-sphere mixture solution for the Percus-Yevick equation with an attractive square-well potential over a hard-sphere mixture. In addition, the Bhatia-Thoronton correlation functions have also been calculated. From the partial structure factors the number of nearest neighbors has been calculated. All the computed results have been found to be in very good agreement with the x-ray diffraction results obtained by Halder and Wagner (Z. Naturforsch. 22a, 1489 (1967)) except at 62% atomic fraction of indium. All these results were computed purely from the potential parameters of the pure metals. The alloy is found to show a shoulder in the S/sub N//sub C/(K) cross correlation function. This may be due to either compound formation or internal segregation, even though the metals mix freely at all concentrations. The compressibilities at various concentrations of In have been computed from the Kirkwood-Buff formula. The diffusion coefficients have been calculated from Helfand's linear-trajectory principle. The self-diffusion coefficients as evaluated correctlymore » predict them for both metals because of the attractive wells associated with these metals. Thus Hg, in spite of its heavy mass, has a comparatively higher diffusion coefficient than In, which has a lower mass. The melt appears to form a regular solution, as predicted by Bearman and Jones.« less

Structural investigations of amorphised iron and nickel by high-fluence metalloid ion implantation

Boron, phosphorus and arsenic ions have been implanted into evaporated iron and nickel thin films at room temperature, and the implantation-induced microstructure has been investigated by high-voltage electron microscopy and transmission high energy electron diffraction. The metal films were implanted with ions into a constant dose of 1*1017 and 5*1017 ions/cm2 respectively at energy of 50 keV. An amorphous layer was produced by boron and phosphorus ion implantation. Information on the atomic structure of the amorphous layers was obtained from the elastically diffracted electron intensity. On the basis of the correct scattering curves, the total interference function and the pair correlation function were determined. Finally, the atomic arrangement of the implantation-induced amorphous layers is discussed and structure produced by ion irradiation is compared with amorphous structures formed with other techniques.

Diffraction analysis of metallic, semiconducting and inorganic glasses

Recent advances in both diffraction theory and experiments have led to the determination of the topological and chemical short-range order in metallic, semiconducting and inorganic glasses. The introduction of the variable wavelength experiments in x-ray diffraction (energy-dispersive x-ray diffraction) and in neutron diffraction (time-of-flight measurements with polychromatic neutrons) has extended the reciprocal space to the values of K = ( 4π γ ) sinϑ as high as 40 Å −1. These extended diffraction data have yielded high resolution radial distribution functions for such glasses. The structure of two-component systems, consisting of elements 1 and 2 (binary alloys), is characterized by three partial structure factors S NN (K), S CC (K), and S NC (K) which describe interference functions I 11 (K), I 22 (K) and I 12 (K), or the topological short-range order, the chemical short-range order, and the correlation between number density and concentration, respectively. These partial functions can be evaluated from three total interference functions obtained by (1) isomorphous substitution of one or both elements, (2) isotopic substitution (for neutrons), (3) three different radiations (x-rays, neutrons, and electrons), (4) anomalous dispersion, and/or (5) polarized neutrons for magnetic materials. Three special cases facilitate the evaluation of the partial interference functions or structure factors: (1) x-ray or neutron experiments on two-component systems with elements i, whose coherent scattering amplitudes f i are similar, will yield the topological shortrange order S NN(K) = c 1 2I 11(K) + c 2 2I 22(K) + 2c 1c 2I 12(K) where c i is the atomic concentration of element i. (2) If we choose a system for which c 1f 1 + c 2f 2 = 0, (zero-alloy), we can directly determine the chemical short-range order S CC(K) = c 1c 2{1 + c 1c 2[I 11(K) +I 22(K) − 2I 12(K)]}. (3) If the coherent scattering amplitude f 2 of element 2 is zero (null-element), then we obtain directly the partial interference function I 11(K). Examples of recent attempts to determine the partial interference functions I ij(K) and their corresponding atomic distribution functions ϱ ij(r) will be given for metallic, semiconducting and inorganic glasses.

Meaning of the concentration independent partial interference functions of liquid bianry systems

Abstract The procedure of obtaining the concentration independent partial interference functions Iij(k) which was applied in many articles for the analysis of diffraction experiments on liquid metall alloys is reproduced for the model system of hard spheres. As in the real alloys the functions Iij(k) allow one to reconstruct the total interference functions of the system in the wide range of compositions. However, Iij(k) differ in an essential way from the true partial functions Iij(k) of the model system. Thus, although for every real binary alloy it is possible to find (in a variety of ways) the concentration independent functions Iij(k), they have no clear physical interpretation and, in any case, do not represent the true partial interference functions of the system

An X-ray diffraction investigation of molten copper-indium alloys by the partial interference function method

Total interference functions from alloys of copper with 25.5, 50.0 and 75.0 at% indium have been obtained by X-ray diffraction at 700 degrees C. The assumption of concentration independence of the partial interference functions appears to be valid from the calculation of the partial function between copper and indium, ICuIn(K). For the three alloys, the first peak of ICuIn(K) occurs at 2.85, 2.79 and 2.76AA-1, respectively, with very slight change in general shape. These peak positions are closer to that of pure copper, at 3.00 AA-1, than pure indium, at 2.28AA-1. Thus the alloy behaves in a similar way to those containing groups I and IV elements (eg Au-Sn and Cu-Sn).

Atomic distributions in liquid copper-tin alloys

Abstract Molten copper-tin alloys have been studied by X-ray diffraction, using a focusing theta-theta diffraetometer and Mo-Kα radiation (monochromator in the diffracted beam). Five alloys with 20, 35, 45, 55 and 78 atomic percent Sn, and pure Cu and Sn were measured at temperatures about 20 °C above the liquidus, and at 1100 °C. The total interference functions I(K), where K = 4π sin θ/δ, were obtained from the observed scattered intensities Ia(K) per atom and the theoretical atomic scattering factors. Splitting of the first peak in I(K) has been observed in the Cu-55 at% Sn alloy at the liquidus temperature. The partial interference functions Itj(K) at the liquidus temperature and at 1100°C were evaluated (assuming that they are independent of atomic concentration) using the five total I(K) of the alloys. The functions Iij(K) are in reasonable agreement with those obtained by Enderby, North and Egelstaff from neutron diffraction data of a Cu-45 at % Sn alloy. The reduced partial distribution functions ...

Temperature Dependence of the Total Interference Functions of Liquid Cu-Sn Alloys

The total interference function I (K), which is a weighted sum of the partial interference functions, and the corresponding weighted distribution function have been calculated from the elastic x-ray scattering of liquid Cu-Sn alloys with 20 and 22.5 at.% Sn measured at temperatures between 800 and 1160\ifmmode^\circ\else\textdegree\fi{}C. The total I(K) of the alloys show a slight decrease in the position ${K}_{1}=\frac{4\ensuremath{\pi}({sin\ensuremath{\theta}}_{1})}{\ensuremath{\lambda}}$ and in height of the first peak with increasing temperature [${K}_{1}=2.88$ ${\mathrm{\AA{}}}^{\ensuremath{-}1}$ and $\mathrm{I}({K}_{1})=3.05$ at 800\ifmmode^\circ\else\textdegree\fi{}C, and ${K}_{1}=2.86$ ${\mathrm{\AA{}}}^{\ensuremath{-}1}$ and $\mathrm{I}({K}_{1})=2.50$ at 1160\ifmmode^\circ\else\textdegree\fi{}C]. On using the total $\mathrm{I}(K)$ in the Faber-Ziman theory of electrical resistivity ${\ensuremath{\rho}}_{R}$ and thermoelectric power $Q$ of binary liquid alloys, one obtains theoretical values of ${\ensuremath{\rho}}_{R}$ and $Q$ which decrease slightly with increasing temperature in agreement with the experimental results of Roll and Motz and Howe, respectively.

Partial Interference and Atomic Distribution Functions of Liquid Silver—Tin Alloys

The x-ray scatterings from liquid Ag–Sn alloys previously measured at temperatures 100°C above the respective liquidus temperatures have been reanalyzed. The total-interference functions (also called structure factors) I(K), where K=4π sinθ/λ, were first refined and then used to calculate the partial-interference functions Iij(K), assuming that they are approximately independent of the atomic concentrations. The least-squares analysis with five different atomic concentrations of Sn, i.e., 18.5, 25, 36.5, 50, and 68.5 at.%, yielded three Iij(K). The Fourier transform of Iij(K) leads to the partial radial distribution function (RDF)=4πr2ρij(r)/cj, and the reduced distribution function Gij(r)=4πr[ρij(r)/cj—ρ0], where ρij(r) is the partial radial density, cj is the atomic concentration of the j-atoms and ρ0 is the average atomic density. Thus calculated Iij(K) and Gij(r) were used to reproduce the measured I(K) and their corresponding G(r), and a remarkably good agreement was found between the measured and calculated values. Judging from the observed agreement, it can be concluded that for liquid Ag–Sn alloys the partial ISnSn(K), IAgAg(K), and ISnAg(K) are not influenced by the relative abundance of the elements. The resistivity of the alloys obtained with Iij(K) and the pseudopotential elements Ui(K) agrees well with those measured experimentally.