Abstract
In 1926 Hume Rothery discovered that for some simple alloys the electron to atom ratio e/a is a stability determining factor. We applied this energy band effect or Hume-Rothery rule to the quasicrystalline series Al80Mn20-xFex. The isomer shift of the Mössbauer spectra shows a maximum at x=9, where e/a=1.76. This strongly indicates a relatively low s-electron density, in agreement with the energy band effect.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
D. Shechtman, I. Blech, D. Gratias and H.W. Cahn, Phys. Rev. Lett. 53 (1984) 1951.
M. Gardner, Sci. Am. 236 (1977) 110.
N.G. de Bruijn, Proc. K. Ned. Akad. Wet. Ser. A 84 (1981) 39, 84 (1981) 53.
W. Hume-Rothery, J. Inst. Met. 35 (1926) 295.
P.J. Schurer, R.D. Werkman, F. van der Woude, I.L.L./CODEST workshop on quasicrystalline materials, Grenoble, (World Scientific, Singapore, 1988) ed. J.M. Dubois and C. Janot, 75.
L.J. Swartzendruber, D. Shechtman, L. Bendersky and J.W. Cahn, Phys. Rev. B32 (1985) 1383.
M. Eibschutz, H.G. Chen and J.J. Hauser, Phys. Rev. Lett. 56 (1986) 169.
P.J. Schurer, B. Koopmans, F. van der Woude and P. Bronsveld, Solid State Comm. 59 (1986) 619.
P.J. Schurer, B. Koopmans and F. van der Woude, Phys. Rev. B37 (1988) 507.
P.M.L.O. Scholte, M. Tegze and F. van der Woude, to be published.
W.B. Pearson, The crystal Chemistry and Physics of Metals and Alloys (Wiley, New York, 1972) Chap. 3.
A.R. Miedema and A.K. Niessen, Cohesion in Metals (North-Holland Publishing, Amsterdam), to be published.
E.A. Stern, Y. Ma and C.E. Bouldin, Phys. Lev. Lett. 55 (1985) 2172.
A. Sadoc, A.M. Flank, P. Lagarde, P. Sainfort and P. Bellisent, J. de Phys. (Paris) 47 (1986) 873.
J.B. Boyce, J.C. Mikkelson Jr., F. Bridges and T. Egami, Phys. Rev. B33 (1986) 7314.
A. Sadoc, P. Lagarde and P. Sainfort, Int. J. of Modern Physics B1 (1987) 133.
A. Sadoc, A.M. Flank, P. Lagarde, and J.M. Dubois, I.L.L./CODEST workshop on quasicrystalline materials, Grenoble (World Scientific, Singapore, 1988) eds. J.M. Dubois and C. Janot, 148.
J.C. Lasjaunias, C. Berger, K. Hasselbach, C. Paulsen, G. Foucaudot and J.C. Griéco, I.L.L./CODEST workshop on quasicrystalline materials, Grenoble, (World Scientific, Singapore, 1988) eds. J.M. Dubois and C. Janot, 389.
F.C. Frank and J. Kasper, Acta Crystallogr. 11 (1958) 184; 12 (1959) 483.
H. Jones, Proc. Phys. Soc. A47 (1937) 250.
A.P. Blandin, in Phase Stability in Metal and Alloys, ed. P.S. Rudman, J. Stringer and R.I. Jaffee, (McGraw-Hill, New York, 1967) p. 115.
V. Heine, in the Physics of Metals, ed. J.M. Ziman, (Cambridge University Press, 1969) Vol. 1.
D. Stroud and N.W. Ashcroft, J. Phys. F: Metal Phys. 1 (1971) 113.
R. Evans, P. Lloyd and S.M. Mujibar Rahman, J. Phys. F: Metal Phys. 9 (1979) 1939.
A.P. Smith and N.W. Ashcroft, Phys. Rev. Lett. 59 (1987) 1365.
P.A. Bancel and P.A. Heiney, Phys. Rev. B33 (1986) 7922.
B. Koopmans, P.J. Schurer, F. van der Woude and P. Bronsveld, Phys. Rev. B35 (1987) 3005.
G.V. Raynor, Progress in Metal Physics 1 (1949) 1.
L. Pauling, Phys. Rev. 54 (1938) 899.
A. Traverse and E. Beling, I.L.L./CODEST workshop on quasicrystalline materials, Grenoble, (World Scientific, Singapore, 1988), eds. J.M. Dubois and C. Janot, 399.
D.L. Ederer, R. Schaefer, K.-L. Tsang, C.H. Chang, T.A. Callcott and E.T. Arakawa, Phys. Rev. B37 (1988) 8594.
K. Wang, P. Garoche and Y. Galvayrad, I.L.L./CODEST workshop on quasicrystalline materials, Grenoble, (World Scientific, Singapore, 1988) eds. J.M. Dubois and C. Janot, 372.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Werkman, R.D., Schurer, P.J., Vincze, I. et al. Are quasicrystals hume-rothery alloys?. Hyperfine Interact 45, 409–414 (1989). https://doi.org/10.1007/BF02405907
Issue Date:
DOI: https://doi.org/10.1007/BF02405907