Severe matrix deformation has been examined at an early stages of age hardening in a polycrystalline Brush 25 alloy containing Cu-11.5at% Be-0.23at% Co aged at 200o C and 315o C. It leads to strong diffuse scattering and gives special diffraction effects. Aging at 200oC, introduces larger changes in the diffraction profiles than at 315oC. Quantitative interpretation requires a separation of diffracted intensity into Bragg peaks, static diffuse scattering, and quasilines. The latter originates from the severely distorted zone about precipitates.
The kinematical diffraction theory for both the high and low lattice distortions due to precipitates has been developed by Krivoglaz [1] but, however, until recently, not enough attention had been paid to the most interesting intermediate region where the strong enough Bragg peaks and diffuse scattering can be observed simultaneously in a form of special doublets. This case cannot be evaluated analytically and numerical calculations must be used.
A model of general ellipsoidal shape of precipitate was suggested for the derivation of displacement field with the aid of the Green function calculations. Subsequently, total diffraction profiles were generated and compared to the experimental data. Good agreement was achieved for the samples aged at 315o C. However, the whole procedure requires extensive calculations and it is time consuming which makes the refinement of the model parameters (size, shape and concentration of precipitates) difficult.
Therefore, simplified anisotropic elastic models for the atomic displacement field about coherent disk shaped precipitate provide quantitative estimates of the atomic displacement field in the surrounding matrix. The evaluation is based on calculation of the static Debye-Waller factors (2M) and quasiline shifts for different concentrations and dimensions of precipitates and their comparison with the values obtained by fitting of three Pearson functions to the experimental profiles. The unambiguous fitting can be done by constraining the intensities according to the partitioning formula and knowing that the peak width is increasing in a sequence : Bragg - static diffuse - quasiline. Two elastic models were considered for calculations - single disks and [101] stair step pairs of the precipitates with the {100} habit planes
Large anisotropy of both 2M factors and quasiline shifts was observed for the sample aged at 200o C. It indicates larger distortion in the [100] than the [111] direction. It could only be explained by the near surface preferred orientation of precipitate habit planes parallel to the free surface, i.e. the largest deformation perpendicular to it. Disk diameters range from 48 to 64Å with a thickness of 2.9Å after 16 to 64 hrs at 200o and the [101] stair step pair model best fits the experimental results. Quasiline shifts were successfully used along with Vegards Law to extend the metastable GP zone boundary to 200o C.
1. M.A. Krivoglaz: Difrakciya rentgenovskich luchey i neitronov
v neideal'nych kristallach. Naukova Dumka. Kiev. 1983.
2. C.R. Houska: Acta Cryst., A49 (1993) 771-781.