Two Length Scales and Crossover Behavior in the Critical Diffuse Scattering fromV2H

Abstract

We have observed two length scales in a V 2 H crystal above the b 1 -b 2 phase transition. A sharp Lorentzian profile in the critical diffuse scattering was superimposed on a broader one for a low-energy x-ray experiment in reflection, while no sharp component appeared in transmission at high energy. For the sharp component, we extracted tricritical exponents n 1 and g 1 at small reduced temperatures t, where fluctuations are coherent over large distances. For larger t, where the correlation length is comparable to an effective defect size, there is a crossover to altered exponents. [S0031-9007(98)07111-7] PACS numbers: 64.60. Cn, 61.10.Nz, 61.72.Hh, 64.60.Fr The interstitial alloy V 2 H presents an excellent system to study the "two length-scale" issue first seen in SrTiO 3 by Andrews [1] who found, in a high resolution x-ray diffraction study, a narrow Lorentzian-squared peak in the critical diffuse scattering (CDS) on top of a broad Lorentzian in contradiction to theories of critical phenomena. Systematic studies of perovskites, e.g., SrTiO 3 , KMnF 3 , RbCaF 3 (see [2][3][4] and references in McMorrow et al. [5]), as well as magnetic scattering from Tb [6,7] and Ho [8] have led to the conclusion that the narrow component of the CDS (second length scale) arises from a skin layer of several mm extending below the surface, while the bulk material still shows normal critical behavior (see, e.g., references in Cowley [9] and Wang et al. [4]). Neumann et al. [10] observed that the sharp component in SrTiO 3disappears in a high-energy synchrotron x-ray experiment in transmission geometry which probed the "true" bulk behavior. However, the sharp component of the CDS still remained when the corner of the crystal was illuminated, thereby probing the behavior of a defective near-surface region, estimated by Rütt et al.[3] to be less than 100 mm. A transmission electron microscopy study of SrTiO 3 by Wang et al. [4] directly reveals structural defects in this skin layer, namely, dislocations, whose density decreased with increasing depth from the surface, which were thereby considered responsible for the second length scale. They also discuss the expected shift in the critical temperature due to defect strain (see also [9]). Two length scales have also been seen by Gehring et al. [11] in a neutron study of a 1 mm Ho film grown on a Y buffer, suggesting that the two may coexist within this small volume.In this Letter, we report on a second length scale and crossover behavior in the critical diffuse scattering from V 2 H above the order-disorder phase transition b 1 -b 2 . We first probed both the bulk and the skin layer, using lowenergy x-ray diffraction in reflection geometry and, in a separate experiment, the true bulk using high-energy diffraction in transmission geometry. In V 2 H, we find a transition on cooling from a regime in which the two length scales are observable at higher reduced temperatures, t T ͞T C 2 1, to one showing only the sharp component at lower t. This sharp component can best be fit with a sin...

Depth-dependent ordering, two-length-scale phenomena, and crossover behavior in a crystal featuring a skin layer with defects

“…Systematic studies of many materials in which twolength-scale behavior has been found, [6][7][8][9][10][11][12][13][14][15][16] including previous studies of V 2 H, 4 have concluded that the narrow central peak of the CDS only occurs in the scattering from a defective "skin layer," that is a region of the material that starts a few hundred angstrom below the surface and extends several tens of micrometer below the surface. However, to the best of our knowledge, the two-length-scale behavior in V 2 H is different from that which has been observed in any other material, because in V 2 H the phase transition in the bulk is a firstorder transition.…”

“…However, to the best of our knowledge, the two-length-scale behavior in V 2 H is different from that which has been observed in any other material, because in V 2 H the phase transition in the bulk is a firstorder transition. In the skin layer, instead, the ordering is more complicated as found experimentally by a number of unusual phenomena including: ͑1͒ diffuse scattering which, as the temperature is lowered toward a critical value, consists of a broad peak that changes only slightly with temperature and a narrow central peak with an amplitude that diverges; 4 ͑2͒ an effective critical temperature T c ͑y͒ for the behavior of the central peak that changes with the depth y below the surface and extrapolates to a temperature T c ϱ that always exceeds the bulk transition temperature T 0 ; 5 ͑3͒ a crossover in the universal critical behavior shown by the central peak from three-dimensional mean-field critical behavior to a different universality class as the temperature increases from T c ͑y͒; 4,5 ͑4͒ a narrow two-phase region and a weak first-order transition observed at temperatures T 0 ͑y͒ slightly below the critical value. 17 In order to explain these experimental findings we present a theory which accounts for the distribution of defects experimentally detected: 3 edge dislocations occur mostly in the skin layer, accumulating near the surface; they are arranged in arrays of parallel lines which we refer to as "walls;" each wall consists of lines that are oriented in either of the two directions parallel to the surface; the walls extend into the crystal and are thus oriented in either of the two directions perpendicular to the surface.…”

“…Indeed, with high-resolution x-ray diffraction measurements, we have previously found that V 2 H has two-length-scale and associated behavior that is depth dependent. 4,5 These measurements were performed in both reflection and transmission geometries, allowing us to compare the behavior of the crystal at different depths. In this paper, we propose a theoretical explanation of these experimental results that accounts for the depth dependence of the observed behavior.…”

X-ray scattering study of two length scales in the critical fluctuations ofCuGeO3

“…Such studies can be regarded as a systematic exploration of the effects of point defects on the CuGeO 3 structural phase transition. Thus, as a byproduct of our Cu 1−x (Zn,Mg) x GeO 3 phase diagram studies, we also are able to test the hypothesis that the long length scale fluctuations are caused by point defects 10 . Fig.…”

“…Moreover, even if the idea that the second length scale originates from defects is taken for granted, there exists additional complexity because the defects can either be point defects or line defects such as dislocations. A recent study suggests that point defects are responsible for the occurrence of the second length scale 10 . The dislocation theory, on the other hand, has been less favored.…”