J.B. Cohen

The structure of G.P. I zones in Al-1.7 at.% Cu

Abstract The diffuse X-ray scattering has been measured from a single crystal of Al-1.7 at.% Cu, aged to contain G.P. I zones. A new method has been employed to separate the contributions from clustering from those due to atomic displacements. Computer simulations with 108,000 atoms were employed to examine the local atomic arrangements. The zones are a mixture of single (001) planes ≈ 100% copper and multilayer regions and with the nearest-neighbor spacing near that of the matrix. There is no significant copper concentration in the matrix. The Al (100) planes near the zone collapse toward it, the displacement decreasing more rapidly (with increasing distance from the zone) than in Gerolds model. A model recently derived from EXAFS data is shown to be inconsistent with the X-ray data.

The defect arrangement in (non-stoichiometric) β′-NiAl

Abstract X-ray scattering similar to that for the diffuse omega state in Ti and Zr alloys has been detected with Ni 1+(−) x Al 1± x , and is strongest for non-stoichiometric compositions. A new method of analyzing diffuse X-ray scattering has been applied to the data to separate the effects of local order and atomic displacements. The defects (Ni vacancies in Al-rich alloys, Ni atoms on the AI sublattice for Ni-rich compositions) are locally ordered, exhibiting a strong tendency to avoid the same species at the first neighbor distance of their sublattice. The proposed theories of homogeneous nucleation of omega phase do not satisfactorily explain the data. Heterogeneous nucleation by collapse around a point defect appears to be more appropriate (that is, the trapping of phonon states by such defects). This is similar to the proposal by Kuan and Sass for Ti and Zr alloys, but their requirement of one per cent quenched in vacancies is eliminated because it is shown that substitutional atoms provide suitable nucleation sites.

Local atomic arrangements in the solid solution Al-1.7 at.% Cu, at 793 K

Abstract The absolute diffuse X-ray intensity, scattered from a crystal of Al-1.7 at.% Cu, was measured in the solid solution region at 793 K. This intensity was separated into terms associated with local order and those due to displacements of atoms from the sites of the average lattice. Computer simulations with the measured short-range order parameters and for a pseudo-random alloy were compared. The actual alloy has few isolated Cu atoms, compared to the random configuration. Instead the Cu is present in small composition fluctuations; more than half the solute content is in tiny plate-like regions which resemble the larger G.P. zones that form upon quenching and aging. Also, the density of these embryonic regions is similar to the zone density for short aging times. Therefore, there is no apparent nucleation barrier for zone formation. The electrical resistivity immediately after quenching can be calculated from the cluster population and the result agrees with experiment. The pair potentials in the system were determined from the X-ray scattering.

The G.P. zones in AlCu alloys—II

Abstract Measurements on an absolute scale of the diffuse X-ray scattering by an aged single crystal of Al-1.94 at.% Cu have been made at a synchrotron source. Aging times were chosen to correspond to a mixture of G.P.1 and G.P.2 states, and to G.P.2 itself. The results indicate that the transition is in reality a coarsening reaction. There is not a unique structure for G.P.2 different than that for G.P.1. The G.P.1 state is a mixture of almost pure Cu single layer and multilayer platelets with their broad faces parallel to {100} planes of the Al-rich matrix. With increased aging time, these regions thicken and the number of single layer regions decreases. The so-called extra reflections in the G.P.2 state are actually thickness fringes. The strains around a multilayer zone are similar for all aging treatments, oscillate with distance from a zone, and are ~10% near the zone boundary, where the A1 planes collapse toward the zone.

The chemical and elastic contributions to the free energy of a Au-Ni alloy above the miscibility gap

Abstract The coupling parameters in the Cook-deFontaine microscope theory for the free energy of solid solutions have been evaluated for Au-40 at.% Ni, at 1023 K above the miscibility gap, by combining results from neutron inelastic and X-ray diffuse scattering from the same single crystal. The thermodynamic quantities calculated from this theory are in good agreement with available data. The chemical energy in this system favors ordering, but clustering occurs (and precipitation below the miscibility gap) because of the elastic energy. This elastic component has a minimum at 1023 K for a wavelength of 6–7 A, which is the initial coherent precipitate spacing that forms on aging. The minimum in elastic energy results from a maximum in the phonon dispersion, which, in turn, probably occurs due to electron screening.

Clustering in a AuNi alloy above the miscibility gap

Abstract Quantitative measurements of the diffuse X-ray scattering from a Au-40 at.% Ni crystal were made at 1023°K, just above the miscibility gap. These data were separated into contributions due to local atomic arrangements and those due to atomic displacements from the average lattice. With these results and computer simulation, it has been found that approximately 60% of the Ni is in fluctuations that resemble platelets on (100) planes, and 〈100〉 rods, with a spacing (6–7 A) similar to the clusters that are found after quenching and aging. There is little preference for nearest-neighbors to cluster or order, and the clustering arises due to the competition of the interactions in higher neighbor shells and elastic energy. The elastic response of this material is controlled primarily by the Au-atom interactions. The Ni atoms are displaced from lattice points by large amounts, reducing their interaction.

Measurements of the ordering instability in binary alloys

Abstract The coherent instability temperatures for continuous ordering have been determined for various binary alloys from absolute intensities of X-ray diffuse scattering. The measured Tinstability are 358.2, 211.4 and 627.6°C for alloys of Cu3Au, Cu81.5Au18.5 and CoPt3 respectively. A comparison is made of these values to mean field theories and to recent calculations of the Cu-Au phase diagram by means of the cluster-variation method, including nearest-neighbor tetrahedra.

Premonitory effects in Cu3Au near the order-disorder transformation

Abstract Just above the order—disorder critical temperature (T c) in Cu3Au several unusual effects have been reported: (1) The ratio of diffuse intensity at the 003 position to that at the 001 decreases markedly. (2) There is a sudden increase in the total diffuse X-ray scattering due to mean-square displacements. (3) Phonon groups broaden. (4) Optical modes appear. Additional details of these effects are described here. Also it is shown that: (5) there are no significant changes in the phonon dispersion curves; and (6) there is a marked increase in (quasi-static) anharmonic interactions (which were observed in the X-ray diffraction pattern). All of these unusual effects are interpreted as arising from long-lived fluctuations above T c, like the low temperature ordered phase. The results suggest these fluctuations contain a high density of thick antiphase boundary.

Phonon dispersion and the thermodynamic properties of a Au-Ni alloy

Abstract Phonon dispersion for Au-40 at.% Ni has been measured above the miscibility gap (≈1023 K). The nearest-neighbor force constants are considerably reduced compared to those for the pure components, whereas those for more distant neighbors are enhanced, implying an increased long-range phonon-electron interaction in the alloy. The overall effect is a structural softening which accounts quantitatively for the measured excess entropy. For phonon modes near the Brillouin zone boundary there is an additional softening, which appears to be due to shielding by electrons (from the 3d band of Ni) in the vicinity of the Fermi surface. These effects are more difficult to detect after quenching, due to the decrease of phonon lifetimes resulting from distortions associated with solute clustering.

Pre-transition phenomena in an iron-nickel alloy

Abstract X-ray diffraction from an Fe-30.5Ni single crystal has been examined to obtain information on the vibrational state of the sample prior to the martensite transformation. The measurements included integrated intensities of Bragg peaks as well as diffuse scattering along several directions in reciprocal space. Data were obtained from room temperature to within approximately 1°K of the transformation temperature. Previous reports of an increase in the mean-square atomic displacements on approaching M s (determined with Mossbauer techniques) were not confirmed by measurements of the integrated X-ray diffraction peaks. The results of this study reveal a decrease in the mean-squared amplitude of vibration with temperature which is in close agreement with that predicted by harmonic theory. Diffuse X-ray scattering, examined to sample the temperature dependence of particular vibrational modes, gave no indication of softening of short wavelength modes. However, these measurements did reveal a softening of long wavelength (100) [100] modes as the sample approached the M s temperature. The softening of this mode provides a Bain distortion which can lead to a lattice instability near defects as predicted by localized soft mode theories. Such an instability can be viewed as one mechanism by which a martensite nucleus is formed.