The Debye-Waller factor and the diffusion process for hydrogen in Nb, Ta, and V single crystals investigated by neutron spectroscopy
Tóm tắt
Quasielastic scattering of slow neutrons on hydrogen diffusing in theα-phase of NbH0.02, TaH0.13 and VH0.07 single crystals was investigated in a wide range of temperatures and scattering vectorsQ (0.5≦Q≦2.5 Å−1). The incoherent scattering lawS
d
(Q,ω) for four different diffusion models was consistently compared with the measured lineshapes. At elevated temperatures one had to introduce correlated jumps to describe the experimental data, whereas at room temperature a model with jumps between adjacent sites is sufficient. The integrated quasielastic intensityI(Q) obtained from the fit ofS
d
(Q,ω) with the measured spectra follows an isotropic Debye-Waller factor with mean square amplitudes 〈u
2〉=0.02–0.04 Å2 for H in Ta (20°C–500°C), and 〈u
2〉=0.03–0.04 Å2 for H in Nb (20°C–300°C). For H in V,I(Q) obtained from the analysis of the quasielastic scattering deviates from a normal Debye-Waller factor behaviour. This effect is assumed to be due to the flight process between the interstitial sites. On the other hand, a normal Debye-Waller factor was obtained from theQ-dependence of the inelastic scattering of the band modes, with values of 〈u
2〉=0.02–0.04 Å2 (135°C–500°C). The observed values of 〈u
2〉 were compared with theoretical calculations.
Tài liệu tham khảo
Chudley, C.T., Elliott, R.: J. Proc. Phys. Soc.77, 353 (1961)
Springer, T.: Investigation of diffusive motions in solids and liquids, Springer Tracts in Modern Physics64, 55 (1972) and Springer, T., in Topics in Current Physics3 (S. Lovesey and T. Springer, ed.) 1977
Gissler, W., Alefeld, G., Springer, T.: J. Phys. Chem. Solids31, 2361 (1970)
Kistner, G., Rubin, R., Sosnowska, I.: Phys. Rev. Lett.27, 1576 (1971)
Stump, N., Gissler, W., Rubin, R.: Phys. Stat. Sol. (b)54, 295 (1972)
Gissler, W., Jay, B., Rubin, R., Vinhas, L.A.: Phys. Lett.43A, 279 (1973)
Wakabayashi, N., Alefeld, B., Kehr, K.W., Springer, T.: Sol. Stat. Comm.15, 503 (1974)
Bauer, G.S.: Dissertation Universität Bochum, JUL-Bericht JUL 1158 and Bauer, G., Seitz, E., Horner, H., Schmatz, W.: Sol. Stat. Comm.17, 161 (1975)
Rush, J., Livingston, R.C., de Graaf, L.A., Flotow, H.E., Rowe, J.M.: J. Chem. Phys.59, 6570 (1973)
Rowe, J.M., Rush, J.J., Flotow, H.E.: Phys. Rev. B9, 5039 (1974)
Alefeld, B., Kehr, K.W., Springer, T., Lottner, V., Heim, A., Wakabayashi, N.: J. Low. Temp. Physics (USSR)1, 638 (1975)
Rowe, J.M., Sköld, K., Flotow, H.E., Rush, J.J.: J. Phys. Chem. Sol.32, 41 (1971)
de Graaf, L.A., Rush, J.J., Flotow, H.E., Rowe, J.M.: J. Chem. Phys.56, 4574 (1972)
Sköld, K., Nelin, G.: J. Phys. Chem. Solids28, 2369 (1967)
Rowe, J.M., Rush, J.J., de Graaf, L.A., Ferguson, G.A.: Phys. Rev. Lett.29, 1250 (1972)
Carlile, C.J., Ross, D.K.: Sol. Stat. Comm.15, 1923 (1974)
Nelin, G., Sköld, K.: J. Phys. Chem. Sol.36, 1175 (1975)
Rowe, J.M., Rush, J.J., de Graaf, L.A., Ferguson, G.A.: Phys. Rev. Lett.32, 1087 (1974)
Gissler, W., Stump, N.: Physica65, 109 (1973)
Lottner, V., Heim, A., Kehr, K.W., Springer, T.: IAEA Symposium on Neutron Inelastic Scattering, Vienna,2, 339 (1977)
Sjölander, A.: Arkiv Fysik14, 315 (1958)
Dederichs, P.H., Lehmann, C., Schober, H.R., Scholz, A., Zeller, R.: Journal Nucl. Materials69/70, 176 (1978)
Schober, H.R., Lottner, V.: to be published
Kley, W.: Z. Naturf.21a, 1770 (1966) (Suppl.)
Carstanjen, H.D., Sizmann, R.: Ber. Bunsenges. Phys. Chem.76, 1223 (1972), and Antonini, M., Carstanjen, H.D.: Phys. Stat. Sol. (a)34, K153 (1976)
Blässer, G., Peretti, J.: Proc. Int. Conf. on Vac. and Interstitials KFA/Jülich JUL-Conf-2,2, 886 (1968)
Kutner, R., Sosnowska, I.: J. Phys. Chem. Sol.38, 741 and 747 (1977)
Gissler, W., Rother, H.: Physica50, 380 (1970)
for a detailed presentation of this model with more recent experiments see Lottner, V., Haus, J.W., Heim, A., Kehr, K.W.: submitted J. Phys. Chem. Solids
Vineyard, G.H.: Phys. Rev.96, 93 (1954)
Copley, J.R.D.: Comp. Phys. Comm.7, 289 (1974)
Völkl, J., Alefeld, G.: Diffusion in Solids: Recent Developments, ed. by A.S. Novick and J.J. Burton, New York, London: Academic Press 1975
Völkl, J.: Ber. Bunsenges. Phys. Chemie76, 797 (1972)
Wipf, H., Alefeld, G.: Phys. Stat. Sol. (a)23, 175 (1974)
Richter, D., Alefeld, B., Heidemann, A., Wakabayashi, N.: J. Phys. F. Metal Phys.7, 569 (1977)
Völkl, J., Bauer, H.G., Freudenberg, U., Kokinidis, M., Lang, G., Steinhauser, K.A., Alefeld, G.: Proc. 6th Int. Conf. Friction and Ultrasonic Attenuation in Cryst. Sol., Tokyo (1977)
Stoneham, A.M.: J. Nucl. Materials69/70, 109 (1978) and Birnbaum, H.K., Flynn, C.P.: Phys. Rev. Lett.37, 25 (1976)