Warren-Cowley Short-range Order Parameters Research Articles

Atomic and magnetic short-range order in a Pt–8.8 at. % Mn spin-glass alloy

The x-ray and neutron diffuse scattering intensities from a disordered Pt--8.8 at. % Mn spin-glass alloy were measured to obtain information about structural fluctuations due to atomic and magnetic short-range order. Diffuse maxima have been observed at the (100), (110) and their equivalent positions. Additional diffuse scatterings are also found at $(1/2,1/2,1/2)$ and its equivalent positions on the x-ray and neutron diffraction patterns at room temperature. Warren-Cowley atomic short-range order (ASRO) parameters were obtained by analyzing the x-ray diffuse intensity data. The correlation length has been deduced to be about $15\AA{}$ from estimating the reconstructed diffuse intensity distribution using the ASRO parameters determined experimentally. The neutron scattering result shows that a magnetic diffuse maximum appears at around $(1/2,0,0).$ The magnetic peak disappears at temperature far above the freezing temperature ${T}_{\mathrm{g}}$ at which a cusp-type peak is observed in the magnetic susceptibility measurement. The origin of the diffuse scattering is discussed in terms of a spin-density wave (SDW) induced by a Fermi surface nesting effect. The spin-glass-like behavior of Pt-Mn alloys is interpreted by the model of dynamically fluctuating SDW clusters as proposed for other metallic spin-glass alloys.

A Study of Short-Range Order in an F.C.C.-Based Stoichiometric A0.5B0.5 Solid Solution

In this paper the nature of the relationships between the low-index Warren-Cowley short-range order (SRO) parameters in a face centered cubic (f.c.c.) stoichiometric A0.5B0.5 binary alloy is discussed. A region of allowed combinations of SRO parameters describing ordering in two nearest coordination spheres is demonstrated and its connection with the Clapp-Moss diagram is explored. Evolution paths of ordering in the SRO space obtained by Monte Carlo simulation using an Ising model with first- and second-nearest-neighbor pairwise interaction parameters are presented and discussed. A method is proposed for the estimation of the interaction parameters from the initial behavior of the evolution path of a disordered system.

A Study of Short-Range Order in an F.C.C.-Based Stoichiometric A0.5B0.5 Solid Solution

In this paper the nature of the relationships between the low-index Warren-Cowley short-range order (SRO) parameters in a face centered cubic (f.c.c.) stoichiometric A 0.5 B 0.5 binary alloy is discussed. A region of allowed combinations of SRO parameters describing ordering in two nearest coordination spheres is demonstrated and its connection with the Clapp-Moss diagram is explored. Evolution paths of ordering in the SRO space obtained by Monte Carlo simulation using an Ising model with first- and second-nearest-neighbor pairwise interaction parameters are presented and discussed. A method is proposed for the estimation of the interaction parameters from the initial behavior of the evolution path of a disordered system.

Ordering of Substoichiometric δ-TiCx Phase in Ti–V–C Alloys

Several Ti–V–C alloys have been studied by transmission electron microscopy (TEM) after cooling from the melt, with special attention paid to ordering processes taking place in the highly substoichiometric (Ti,V)Cx phase. The effects of both short and long range ordering in the carbon sublattice are observed in selected area electron diffraction patterns. The Warren-Cowley short range order parameters have been evaluated from the intensity distribution in reciprocal space. More complex models for the intensity distribution are then developed and the effects on the predicted short range order parameters are discussed.

Ordering of Substoichiometric δ-TiCx Phase in Ti–V–C Alloys

Several Ti-V-C alloys have been studied by transmission electron microscopy (TEM) after cooling from the melt, with special attention paid to ordering processes taking place in the highly substoichiometric (Ti,V)C x phase. The effects of both short and long range ordering in the carbon sublattice are observed in selected area electron diffraction patterns. The Warren-Cowley short range order parameters have been evaluated from the intensity distribution in reciprocal space. More complex models for the intensity distribution are then developed and the effects on the predicted short range order parameters are discussed.

The type of order in Cu–10 at.% Au—evidence from the diffuse scattering of X-rays

In a recent publication, Kuhlmann et al. ( Acta mater., 1997, 45, 3319) claimed Cu–10 at.% Au to be long-range ordered at temperatures above 473 K and as high as 723 K. This is in contrast to the generally accepted phase diagram where this region is attributed to the range of solid solutions. To clarify this problem, a three-dimensional diffuse X-ray scattering experiment was performed at room temperature on a Cu–10 at.% Au single crystal aged at 573 K. The Warren–Cowley short-range order parameters derived from this experiment show conclusively that only short-range order is present. Effective pair interaction parameters determined by the inverse Monte-Carlo method are somewhat different from those obtained for Cu–25 at.% Au in the short-range ordered state.

Diffuse scattering of Ni [sbnd]Al

A Ni 8.9 at.% Al single crystal was aged at 775 K for one day to establish a state of thermal equilibrium and subsequently quenched to room temperature where it was investigated by diffuse neutron scattering. In the elastic coherent scattering, short-range order scattering was separated from linear displacement scattering. An abundance analysis of nearest and next-nearest configurations in crystals modelled on the basis of 21 Warren-Cowley short-range order parameters obtained from the experiment yields no signs for characteristic elements of the D7 structure (which has been suggested on the basis of electronic structure calculations), but for the L1 2 structure of the γ′ phase. A set of effective pair interaction parameters is found from the experimental data by using inverse Monte Carlo techniques. This set is not appropriate for estimating the temperature of congruent melting of Ni 3Al, presumably because the experimental effective pair interaction parameters depend on composition and/or temperature.

Local atomic order and individual pair displacements of Fe46.5Ni53.5 and Fe22.5Ni77.5 from diffuse x-ray scattering studies.

We have recovered the local atomic structures in a fcc ${\mathrm{Fe}}_{46.5}$${\mathrm{Ni}}_{53.5}$ solid solution near an equilibrium temperature of 600 \ifmmode^\circ\else\textdegree\fi{}C with an improved version of the recently demonstrated three x-ray energy (3\ensuremath{\lambda}) method. We have also reevaluated the 3\ensuremath{\lambda} data from a ${\mathrm{Fe}}_{22.5}$${\mathrm{Ni}}_{77.5}$ crystal which significantly changed the results. Both the Warren-Cowley short-range order parameters \ensuremath{\alpha} and the first moment of the mean static displacements for Fe-Fe, Fe-Ni, and Ni-Ni pairs are recovered. Comparisons of the \ensuremath{\alpha}'s from ${\mathrm{Fe}}_{22.5}$${\mathrm{Ni}}_{77.5}$ with neutron-scattering results show good agreement, and both compositions have \ensuremath{\alpha}'s with a strong similarity to those from ${\mathrm{Cu}}_{3}$Au quenched from above the ordering temperature. Displacements from the average lattice of less than 0.001 \AA{} can be recovered. For both ${\mathrm{Fe}}_{46.5}$${\mathrm{Ni}}_{53.5}$ and ${\mathrm{Fe}}_{22.5}$${\mathrm{Ni}}_{77.5}$ the average Fe-Fe first-neighbor distance of 2.564(5) \AA{} is much larger than the average derived from the lattice spacing for the alloys and is independent of concentration. However, the Ni-Ni, first-neighbor distance follows the average lattice, and the Fe-Ni first-neighbor distances are smaller than average. Both the Ni-Ni and Fe-Ni first-neighbor distances increase with Fe concentration. The relatively large and strongly chemically specific bond distances observed here may be a more meaningful concept for understanding the magnet properties of these Ni-rich alloys than the relative lesser change in volume of the Fe atom. \textcopyright{} 1996 The American Physical Society.

Short range order and atomic interactions in Al-7 and 17 at% Zn single crystals

Short range order (SRO) in Al Zn ( c = 7 and 17at%) single crystals has been measured by the neutron diffuse scattering technique at temperatures above the miscibility gap. The Warren-Cowley short range order parameters have been obtained by least-squares fit. The results are used to calculate effective chemical interactions by an inverse Monte Carlo method. The introduction of atomic size effects in the system is discussed. The Monte Carlo simulations of a lattice distorted by elastic interactions are compared with experimental results and with point defect approximations. In the concentration range considered, the elastic effects can explain the observed changes in effective pair interactions.

Short-range order in Ni-Pt alloys

Electron and X-ray diffraction patterns were taken from four different Ni1-xPtx alloys, with x=0.25, 0.35, 0.44 and 0.50, to understand the existence and shape of the diffuse intensity, which gives us information about structural fluctuations. A peculiar shape of diffuse scattering has been observed at 100 and 110 and their equivalent positions in the patterns, the shape of the diffuse intensity at the 100 position changing with Pt content in the alloys. The shape of the diffuse intensity at the 100 position for the x=0.25 alloy is rod-like, but the shape is nearly spherical for the x=0.50 alloy. The X-ray diffuse scattering intensities were measured from the x=0.50 single-crystal alloy at room temperature, and the Warren-Cowley short-range order parameters were determined after analysing the data. The correlation length has been deduced to be about 19 AA from estimating the inverse of the full width at half-maximum of the diffuse peak.

Structure and magnetism of fcc Pd-Mn alloys.

To understand the relationship between the structure and magnetism of fcc Pd-Mn spin-glass disordered alloys, we have measured the lattice parameters, electron diffraction (ED) patterns, x-ray diffuse scattering intensity, and magnetic susceptibilities. The lattice parameters of the ${\mathrm{Pd}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Mn}}_{\mathit{x}}$ alloys show a nonlinear increase with composition for 0\ensuremath{\le}x\ensuremath{\le}0.25. Peculiar diffuse scattering has been observed at the 100, 110, and the equivalent positions on ED patterns in the composition range from x=0.15 to 0.25. Warren-Cowley short-range order (SRO) parameters from a single crystal of the x=0.25 alloy were obtained by analyzing the x-ray diffuse intensity. Extra diffuse maxima were observed at 1/2,1/2,1/2 and equivalent positions, in addition to the diffuse scattering described above, and their intensity is 20% of that at the 100 position. A correlation length has been deduced to be about 10 \AA{} from estimating the reconstructed diffuse intensity distribution using the SRO parameters determined experimentally. A magnetic phase diagram has been constructed from measuring the freezing temperature (${\mathit{T}}_{\mathit{g}}$). ${\mathit{T}}_{\mathit{g}}$ shows a peculiar dependence for a Mn content below x=0.05, above which it increases monotonically up to x=0.17, and then rises dramatically up to x=0.25. The paramagnetic Curie temperature (FTHETA) is negative for all the compositions, which indicates that the antiferromagnetic interactions are influential. Ordered-structure experiments indicate that the values of ${\mathit{T}}_{\mathit{c}}$ are very low for alloy compositions of x0.244.

Recovery of SRO Parameters and Pairwise Atomic Displacements in a Fe46.5Ni53.5 Alloy

AbstractResonant (anomalous) x-ray scattering is used to alter the contrast between atoms nearby in the periodic table to recover local pair correlations. Both Warren-Cowley short-range order parameters and chemically specific interatomic distances are recovered from diffusely scattered x-ray intensities measured at three different x-ray energies (3λ method). Analysis of the statistical and systematic errors shows that the average values for the number and kinds of first nearest neighbors are recovered to about one atom in one hundred and their interatomic distances to about ±0.002 Å.

A study of the local atomic structure in Hg0.80Cd0.20Te using x-ray diffuse scattering

The local atomic arrangements in a commercial n-type wafer of Hg0.8Cd0.8Te were investigated by measuring the diffuse x-ray scattering in two volumes in reciprocal space. A change in contrast between the two measurements was achieved by making one volume measurement at 12037 eV and a second volume measurement at 12270 eV, i.e., near the HgLIII edge. The difference between these two measurements yielded intensity only due to Hg–Hg, Hg–Te, and Hg–Cd pair interactions. In all three patterns, peak-like features were apparent at the forbidden Bragg peak positions on thermal diffuse scattering ridges that joined major Bragg reflections; these are primarily attributed to second order displacement effects on the mixed cation sublattice. The first two Warren–Cowley short-range order parameters were determined to be α½½0 = −0.050(26) and α110 = 0.118(35). Simulations of the structure revealed small ordered regions with a preference for 3:1 Hg–Cd near-neighbor configurations. The near-neighbor Hg–Te bonds contract from that calculated from the average crystal's lattice parameter, and this Hg–Te distance is less than the distance in HgTe.

X-Ray and Neutron Diffraction of Amorphous Nickel-Zirconium-Alloys as Prepared in Different Ways

Abstract The structure of amorphous NiχZr100-χ-alloys (Χ= 30, 31, 34, 63.7, and 65), which were produced by melt spinning (MS), mechanical alloying (MA), and sputtering (SP) was studied by X-ray- and neutron diffraction yielding structure factors, pair correlation functions, coordination numbers, atomic distances, and Warren-Cowley chemical short range order parameters. The atomic arrangement within the first coordination sphere is independent of the method of preparation while in the second and higher spheres it differs between the MS- and the MA-alloys on the one side and the SP-specimens on the other side. Thus one understands that some physical properties of the different specimens differ

First-principles study of short range order and instabilities in Au [sbnd]Cu, Au [sbnd]Ag and Au [sbnd]Pd alloys

Interaction energies derived from first-principles total energy calculation are used together with the Cluster Variation Method in order to study phase diagrams, ordering instabilities and the Fourier spectrum of the Warren-Cowley short range order parameters for Au Cu, Au Ag and Au Pd alloys. The present study is carried out using both the tetrahedron and the tetrahedron-octahedron approximations of the CVM. It is shown that the tetrahedron approximation predicts the wrong Fourier spectrum for the SRO parameters although it gives qualitatively correct phase diagrams. In particular, the tetrahedron approximation fails to reproduce the expected maxima in the fluctuation spectrum at the 〈1,0,0〉-type reciprocal space vectors, characteristics of L1 0 and L1 2 ordering systems. The correct features of the k-space fluctuation spectrum is obtained in the tetrahedron-octahedron approximation.

X-ray diffuse scattering study of G.P. zones in Al-4 at.% Zn

A wide-angle X-ray diffuse scattering experiment (using synchrotron radiation) has been conducted on two Al-4 at.% Zn samples, one aged 3 h and the other 168 h at 353 K. Values obtained for the Warren-Cowley short range order parameters and first order static displacements are given. The short range order parameters were used to generate a 32 × 32 × 32 unit cell model. The zones in the simulation have rough interfaces and show no faceting. The diameter for transformation from spherical to ellipsoidal zones has been found to occur at 20–25 Å. Also from the simulation, it was found that the interior of the zone is nearly all Zn. This amount of Zn is much greater than that predicted from the metastable miscibility gap. If the interface of the zone and matrix is included, the Zn concentration is found to be close to the value predicted by the lever rule. The strains for the short aging treatment decrease steadily with increased atomic distance. Those for Zn-Zn pairs are expansive along the 〈100〉 but are compressive along the 〈 110〉 directions. The reverse is true for the Al-Zn pairs. The strains for the long aging treatment show the same trends for the first neighbor pairs, but then oscillate about zero while decreasing in amplitude with increasing distance.

Wave vector dependent kinetics of short-range ordering in 62Ni 0.765Fe 0.235, studied by neutron diffuse scattering

In situ measurements of the diffuse elastic neutrons scattering from a short-range ordered 62Ni 0.765Fe 0.235 single crystal were carried out during annealing, along three high symmetrical lines of the reciprocal space. Transient as well as equilibrium measurements were done in order to elucidate the kinetic behaviour of the short range order in this alloy as the disorder to order transition is approached. The relaxation time of intensity variation was measured at several points of the reciprocal space near 001. as a function of temperature. The kinetic behaviour is correctly described by the linear theory of continuous transformation provided that more than one interaction potential is used. The values of the interdiffusion coefficient obtained in this way, and its activation energy, suggest a modification of the interdiffusion mechanism due to the proximity of the annealing temperature to the transition temperature. The Warren-Cowley short-range order parameters α lmn were approximated by a least square fit using a Lorenzian and corrective terms to describe the intensity halo. During the kinetic evolution, the smaller is the distance r lmn , the more rapid is the variation of α lmn . The correlation length for short-range order varies with the same relaxation time as the intensity at the maximum. I(001).

Atomic and magnetic short-range order in PdMn

Nuclear diffuse neutron scattering measurements, are performed on PdMn. The Warren-Cowley atomic short-range order parameters alpha /sub /i are determined up to the third neighbour (i=1,2,3) for four different heat treatments of the specimen. Additional triple-axis neutron scattering measurements show a large inelastic contribution at room temperature. Susceptibility measurements are also carried out on these specimens, and these show a large dependence of the spin-glass freezing temperature Tf on the specimen treatments. The magnetic correlation function chi (T)T is determined from the high-temperature (T>Tf) susceptibility and analysed with a configuration group model which includes the measured Warren-Cowley parameters. From this analysis the exchange parameters J/sub /i are calculated up to the sixth neighbour.

Neutron scattering study of short-range clustering in CuNi(Fe) alloys

The thermodynamic equilibrium state of short-range clustering and the kinetics of short-range clustering are studied for two CuNi(Fe) alloys by means of neutron scattering. The first four Warren-Cowley short-range order parameters are determined for different equilibrium states of a Ni-32 at.% Cu alloy between 648 and 973K. The coherent spinodal temperature Tc,s is determined for a Ni-32 at.% Cu alloy (Tc, s=(500+or-25)K) and for a Ni-30 at.% Cu-5 at.% Fe alloy (Tc,s=(675+or-24)K). It is shown that for the compositions investigated the conventional linearised theory is valued for the relaxation of short-range clustering only for those cases where the degrees of clustering in the initial and final states do not differ too much. A procedure proposed recently for the dynamical scaling of the structure function during spinodal decomposition is also tested for the structure functions measured during the short-range clustering process. It is found that the procedure does not provide useful results for the dynamics of short-range clustering.