Short-Range Order and Static Displacements in Polycrystalline Ni-13.1at. %W Alloy

Abstract:

A methodology accounting for the contributions of static displacements of atoms to X-ray diffuse scattering by binary solid solutions with a face-centered cubic lattice was proposed. By microscopic accounting of static displacements of the atoms on the particular shell, we identified short- range order parameters on the first eight shells of Ni-13.1at. %W alloy from the intensity of X-ray diffuse scattering. The Fourier transform of static displacement of the atoms on every considered shell was calculated with the De Launay model using expressions of elements of dynamical matrix and Fourier transforms of quasi elastic forces, which are calculated by the pseudopotential method.

• Periodical: Solid State Phenomena (Volume 271)
• Pages: 98-105
• DOI: https://doi.org/10.4028/www.scientific.net/SSP.271.98
• Online since: January 2018
• Authors: Lhkamsuren Enkhtor*, Ragchaa Galbadrakh, Valentin Silonov
• Keywords: Dynamical Matrix, Interatomic Quasi Elastic Forces, Short-Range Order, Static Displacement Of Atoms, X-Rays Diffuse Scattering

References

[1] G.M. Mc Magnus, Short-range order in some nickel-base alloys, J. Appl. Phys. 6 (1965) 3631-3633.

[2] A.A. Katsnelson, S.A. Alimov, P.S. Dajaev, V.M. Silonov, N.N. Stupina, Local ordering and electrical resistance of Ni-W and Pd-Co alloys (in Russian), Fizika Metallov and Metallovedenie, 26 (1968) 987-995.

[3] A.M. Ammons, J.E. Spruiell, Local arrangements in nickel-10 atomic percent tungsten alloy, J. Appl. Phys. 39 (1968) 3681-3688.

DOI: 10.1063/1.1656840

[4] B.E. Warren, B.L. Averbach, B.W. Roberts, Atomic Size Effect in the X-ray Scattering by Alloys, J. Appl. Phys. 22 (1951) 1493-(1946).

[5] V.I. Iveronova, A.A. Katsnelson, Short-range order in solid solutions (in Russian), Nauka, Moscow, (1977).

[6] V.M. Silonov, Investigation of atomic ordering in Ni-W, Ni-Mo, Ni3(Fe, W) and Ni3(Fe, Mo) system, Dissertation of Ph. D thesis (in Russian), Moscow, (1973).

[7] V.M. Silonov, L. Enkhtor, Debye characteristic temperature, short-range order and stability of solid solution Ni-6 at. %W (in Russian), Fizika Metallov and Metallovedenie, 80 (1993) 79-85.

[8] V.M. Silonov, T.V. Skorobogatova, L. Enkhtor, Experimental and theoretical study of short-range order in diluted solid solutions of Ni-W (in Russian), Vestnik Moskovskogo Universiteta, Ser. 3. Fizika i astronomya 6 (2004) 47-49.

[9] A.A. Katsnelson, O.V. Krisko, V.M. Silonov, T.V. Skorobogatova, Accounting of atomic displacements in diffuse scattering by polycrystalline FCC and BCC alloys (in Russian), Dep. v VINITI, №4751 (1984) 1-64.

[10] M.A. Krivoglaz, X-ray and neutron diffraction in nonideal crystals, Softcover reprint of the original 1st ed., Springer, (2011).

[11] G.H. Begbie, M. Born, Thermal scattering of X-rays by crystals. I. Dynamical foundation, Proc. Roc. Soc. A. 188 (1947) 179-188.

[12] L. Enkhtor, V.M. Silonov, Short-range order in solid solutions of iron-rhenium, Journal of Surface Investigation. X-Ray, Synchrotron and Neutron Techniques, 9 (2015) 1005-1011.

DOI: 10.1134/s1027451015050250

[13] L. Enkhtor, V.M. Silonov, An ordering in Ni-13. 1 at. %W solid solution (in Russian), Perspektivnie materiali 6 (2011) 5-9.

[14] G. L. Squires, The relation between the interatomic forces and the frequencies for symmetry phonons in cubic crystals, Arkiv Physics 25(1963) 21-32.

[15] H.E. Cook, D. De Fontane, On the elastic free energy of solid solutions-I. Microscopic theory, Acta Metallurgica 17 (1969) 915-924.

DOI: 10.1016/0001-6160(69)90112-6

[16] J De Launay, The theory of specific heats and lattice vibrations, Solid State Physics, 2 (1956) 219-303.

[17] R. Shyam, S.C. Upadhyaya, J.C. Upadhyaya, First-Principles Calculation of the Lattice Dynamics of the Co0. 92Fe0. 08 Alloy, Phys. Status Solidi B, 161 (1990) 565-574.

DOI: 10.1002/pssb.2221610211

[18] L. Enkhtor, V.M. Silonov, R. Galbadrakh. New general equation for calculations of elements of dynamical matrix and elastic constants of BCC and FCC metals. Intern. Jour. Adv. Res. in Phys. Sci. 24 (2015) 10-14.

[19] V.M. Silonov, S. Rodin, L. Enkhtor. Calculation of elastic constants of many composed solid solutions (in Russian), Vestnik Moskovskogo Universiteta. Ser. 3. Fizika i astronomya, 3 (2000) 28-30.