Small-angle neutron scattering study of dislocations in deformed single-crystal copper

Abstract

Small-angle neutron scattering measurements of deformed single-crystal copper have been performed over a wave-vector transfer range of 0.0655 <__ Q < 1.32 nm -l. The measurements included four samples deformed in compression at room temperature along the [110] direction to 6.8, 15.6, 35.0 and 54.3% reduction in thickness and an undeformed reference sample. The response of the reference sample followed the Porod law at lowest (Q and was, at least in part, the result of scattering from the external surfaces of the sample. The radially averaged net cross sections were found to increase with increasing deformation, while the power-law exponent n (dZ'/d~ ~x 1/Q '~) decreased from 7t _~ 3 to n ~ 2.2 with increasing deformation. The scattering response of the two most deformed samples was noticeably anisotropic. Analysis of this anisotropy revealed strong 1/Q 2 scattering perpendicular to the { 111 } dislocation slip planes, in agreement with the theoretical work of Seeger [J. . Phys. (1959), 30, 629--637]. The decrease in the radially averaged power-law exponent is therefore attributed to strong 1/Q 2 behavior at the highest levels of deformation. Bulk-averaged edge dislocation densities that varied systematically from approximately 1 × 10 ~° to 5 × 101° cm -2 were obtained from the measured data. Appl

Survey of background scattering from materials found in small-angle neutron scattering

“…13 is probably dominated by scattering from the dislocation structures as predicted by calculations made by Schmatz et al (1974) and seen in more recent experimental results on copper by Heuser (1994). Scattering from isolated edge dislocations of random orientation should follow the power law I(q) ' q À3 .…”

Small-angle neutron scattering correlation functions of bulk magnetic materials

“…3], this results in dAE M =d / q Àn with n ranging between 6 and 8 . We emphasize that other models for the anisotropy-field microstructure may result in different power-law exponents of dAE M =d; in particular, the h 2 ðqÞ that are related to the long-range stress fields of dislocations are expected to give rise to asymptotic power laws that are different from the Porod exponent (Seeger, 1959;Heuser, 1994;Thomson et al, 1999;Maxelon et al, 2001;Long & Levine, 2005). This is, however, the subject of further investigations.…”

Entropy of solidHe4: The possible role of a dislocation-induced glass

“…Neutron-scattering experiments may measure dislocation densities. 41 To test our theory for a dislocated solid 4 He, such experiments should be done within the pressure cell. 42 One way to differentiate between glassy effects and a true thermodynamic s is to measure the frequency dependence of s .…”