Stress Annealing Induced Diffuse Scattering from Ni 3 (Al, Si) Precipitates R.I. BARABASH, G.E. ICE, E.A. KARAPETROVA, and P. ZSCHACK Diffuse scattering caused by L 1 2 type Ni 3 (Al, Si) precipitates after stress annealing of Ni-Al-Si alloys is studied. Peculiarities of diffuse scattering in the asymptotic region as compared to the Huang scattering region are discussed. Coupling between the stress annealing direction and the precipitate shape is demonstrated. Experimental reciprocal space maps (RSMs) are compared to theoretical ones. Oscillations of diffuse scattering due to Ni 3 (Al, Sc) precipitates are observed. The strengths of the precipitates are estimated from the analysis of the diffuse scattering oscillations. DOI: 10.1007/s11661-011-0937-z Ó The Minerals, Metals & Materials Society and ASM International (outside the USA) 2011 I. INTRODUCTION X-RAY and neutron diffuse scattering was used in many studies to access the fundamental properties of materials and defects in them. [1–39] The grouping of point defects into clusters, microscopic pores, coherent precipitates, dislocation loops, and other organized structures changes the character of the local strain field and results in a redistribution of diffuse scattering intensity. The diffuse scattering depends on both the local and the average lattice distortions. The average distortion is related to the static Debye–Waller factor (DWF). Peculiarities of diffuse scattering are distinct for defects corresponding to different ranges of static DWF. A qualitative classification of defects with respect to their influence on diffuse scattering and reciprocal space was developed by Krivoglaz. [1] This classification is based on an analysis of the static DWF exponent, e -2W . Defects can be described as belonging to one of two kinds. A. Defects of the First Kind In crystals with defects of the first kind, the intensity from the Bragg peaks is redistributed into broad diffuse intensity. In addition, the Bragg peaks remain sharp like those of perfect crystals, but become weaker and can be displaced from their reciprocal space location without defects. For this reason, both the Bragg and diffuse scattering can be simultaneously observed in the dif- fraction pattern. Usually, the intensity of the diffuse component I D increases and the intensity of the Bragg component I 0 decreases with defect concentration c. B. Defects of the Second Kind In crystals with defects of the second kind, long-range spatial correlations of atomic sites are lost and the Bragg term becomes meaningless. Sharp Bragg reflections of perfect crystals are replaced by broad peaks, which can be anisotropic in reciprocal space. Whether a defect is of the first or second kind depends on the behavior of the DWF exponent, 2W, at large distances from the defect (q Þ¥). It should be noted that the DWF has a complicated dependence on the details of the distortion fields near a defect. As a first approximation, [1] 2W ¼ ReT 1 ffi c lim q)1 X tss 0 1  cos Qu ss 0 t ð Þ ½  1 þ 1 f / st þ / s 0 t ð Þ   ½1 Here, T ¥ is the correlation function for defects at large distances (q Þ¥), c is the concentration of defects, f is the structure factor of the average crystal, Q is the momentum transfer for certain (hkl) reflections, u ss’t is the difference between displacements in two scattering cells s and s¢ caused by the defect located in position t, and u st and u s’t describe structure amplitude changes of scattering cells s and s¢ caused by the defect located in the position t. We note that for dislocations, changes in structure amplitudes are small and the behavior of the 2W depends mainly of the asymptotic behavior of the displacement field created by the dislocation. With defects there are two possibilities: 2W is either finite at large distances or 2W tends to infinity at large distances. It was shown [1–6] that if the displacements fall off faster, then 1  r 3=2 ; the value 2W is finite, and the defects belong to the first kind. If the displacements decrease lower than1  r 3=2 ; the value 2W Þ¥ and these defects are of the second kind. In this study, we report the diffuse scattering analysis of stress-annealing-induced coherent Ni 3 (Al,Sc) precip- itates, which correspond to the first kind defects (Figure 1). As described previously, these defects cause diffuse scattering, I D (Q), that exists together with R.I. BARABASH, Research Staff Member, and G.E. ICE, Division Director, are with Oak Ridge National Laboratory, Oak Ridge, TN 37831. Contact e-mail: barabashr@ornl.gov E.A. KARAPETROVA, Senior Scientific Associate, and P. ZSCHACK, Senior Research Staff Member, are with the Materials Science and Technology Division, Advanced Photon Source, Argonne, IL 60439. Manuscript submitted March 21, 2011. Article published online November 12, 2011 METALLURGICAL AND MATERIALS TRANSACTIONS A VOLUME 43A, MAY 2012—1413