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...

Using x-ray diffuse scattering, we investigate the critical behavior of an order-disorder phase transition in a defective "skin layer" of V 2 H. In the skin layer, there exist walls of dislocation lines oriented normal to the surface. The density of dislocation lines within a wall decreases continuously with depth. We find that, because of this inhomogeneous distribution of defects, the transition effectively occurs at a depth-dependent local critical temperature. A depth-dependent scaling law is proposed to describe the corresponding critical ordering behavior.

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