Sample-Shape-Dependent Phase Transition of Hydrogen in Niobium

Abstract

diffraction intensity in plane is of the order of |% of the incident beam 0 Strong vicinal out-of-plane peaks recorded in scans using a larger detector acceptance angle (1.4°) indicate that the total diffractive scattering may be a substantial fraction of I 0 as expected for an estimated surface Debye temperature of 360 K" 5 There is some indication that a hard-wall potential with a weak attractive well is appropriate for this scattering system 0 The different structural models which have been proposed for the Si(lll) 7x7 reconstruction 7 " 9 are expected to generate quite different intensity sequences versus 9 r for the range of incident conditions we reporto Consequently, we think that the data we present here are sufficient to give each model a critical test, x R a E. Schlier and H. E. Farnsworth, J. Chem. Phys. The a-a' phase transition of H in Nb resembles a gas-liquid transition of a real gas. 1 ' 2 In this transition the lattice retains its original bcc symmetry, and the phases are only distinguishable by their different lattice expansions. This transition and similar transitions in PdH (Ref. 3) and PdAgH (Ref. 4) are still under discussion,, 5,6They have often been treated as textbook examples of a lattice gas , 7 • 8 and the interaction energy, responsible for the phase transition, is introduced as a suitable parameter proportional to the measured critical temperature T c . In contrast to the lattice-gas model the real lattice is deformable and the interstitially dissolved protons set up long-range distortion fields. 9 " 11 The a-a' 3£, 917 (19593£, 917 ( ) j J 0 . Technol. 15, 423 (1978. 4 M. J. Cardillo and G. E. Becker, Phys. Rev. Lett. 40, 1148Lett. 40, (1978.Assuming 0 D surface =j(9 D bulk , with 0 D bulk =543 K [B. W. Batterman and D. R 0 Chipman, Phys. Rev. 127, 690 (1962)1, we estimate a reduction in the total diffraction intensities to I/IQ^ 10-20%, for a range of the He/Si attractive well depth of 10-20 meV. 6 E. Grimmelmann and J. C. Tully, private communication. 7 J.transition has therefore been attributed to an elastic interaction via this lattice distortion induced by the protons. 12 ' 13 The model of elastic interaction leads in turn to the concept of macroscopic elastic modes 14 ' 15 caused by internal stress produced by the inhomogeneous hydrogen density variation in a coherent lattice. At T c only a few modes become unstable which depend upon the sample geometry through the fulfillment of the elastic boundary condition. Therefore, the study of the shape dependence of the phase transition is a crucial test of the validity of the elastic interaction as the main contribution to the attractive part of the energy. Nb samples (single crystals, wires, and foils)The coherent OL-GL' phase transiton of H in Nb has been studied in several sample shapes. The samples were loaded in situ with the critical hydrogen concentration of 0.31 H/Nb above T C =171°C and slowly cooled. Below T c a coherent macroscopic spinodal decomposition takes place. By x-ray scattering and examination of the relaxed c...

Effect of deformation on low-temperature deuteride precipitation in single crystal niobium

“…These efforts were found to be in reasonable agreement with the known phase diagram [2]. On the experimental side, coherent and incoherent hydrogen precipitation in Nb has been observed by in situ x-ray diffraction [3,4]. One especially interesting aspect of this work was the observation of sample-shape-dependent hydrogen concentration modes within the coherent portion of the α-α phase diagram [4], consistent with earlier theoretical work [2,5].…”

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“…An effect of this type was noted by Larché and Cahn [75] who pointed out that if spinodal decomposition takes place in in an isotropic crystal with uniform elastic constants the equilibrium state can have the two phases on opposite faces of the film, and because of the elastic misfit the film will bend. This effect has indeed been observed, in the α − α ′ phase separation of Nb-H [160,155]. In these experiments, the hydrogen-rich α ′ phase was found on the outer side of simply curved specimen foils.…”

H-H interactions in Nb/W(110) superlattices

“…in single crystals of Nb by Zabel and Peisl. 2 H solubility measurements in thin metal films have also been used to address the relation between finite-size effects and elastic boundary conditions. 3,4 The thicknesses of the films were typically in the range: 10Ϫ1000 nm.…”