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Factors Governing the Structure of Intermetallic Phases

  • F. Laves (a1)


A review of the crystal structures of the elements shows some prevailing tendencies of atomic arrangement. These are discussed as space, symmetry, and connection principles. Counteracting temperature and bond factors can be recognized.

The same principles and factors are responsible for the formation of alloy structures, taking into account additional factors due to the component's similarities and dissimilarities in size and electronegativity.

Similarity favors solid solution and dissimilarity favors compound formation. A q compound is here defined as a phase in a q-component system not connected with any other phase of the system by continuous solid solution. Similarly a q structure is defined as a structure type which needs only q components to be formed (considering present-day knowledge). For example, the binary compound Mg17Al12 has the elementary (1 ™) structure of α-manganese. As a rule, q compounds tend to form p structures with q > p.

A discussion of q structures with q = 1, 2, and 3 is given in some detail on the basis of known representatives to show: (1) the competition of geometrical principles and physicochemical factors in determining atomic arrangements of alloys; and (2) the value of rules for making guesses on the probable occurrence of compounds and their chemical composition in polycomponent systems yet unknown.



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1. Laves, F., “Crystal Structure and Atomic Size,” Theory of Alloy Phases, Am. Soc. for Metals, Cleveland, 1956, pp. 124-198.
2. Kasper, J. S., “Atomic and Magnetic Ordering in Transition Metal Structures,” Theory of Alloy Phases, Am. Soc. for Metals, Cleveland, 1956, pp. 264-279.
3. Frank, F. C. and Kasper, J. S., “Complex Alloy Structures Regarded as Sphere Packings. I. Definition and Bask Principles,” Acta Cryst. 11: 184191, 1958; II. “Analysis and Classification of Representative Structures,” 12; 483-499, 1959.
4. Zintl, E. and Woltersdorf, G., “Gitterstruktur von LiAl,” Z. Elektrochem. 41; 877879, 1935.
5. Böhm, B. and Klemm, W., “Zur Kenntnis des Verhaltens der Alkalimetalle zueinander,” Z. anorg. u. allgem. Chem. 243: 6985, 1940.
6. Goldschmidt, H. J., “The Phase Constitutions of Some Niobium-Bearing and Associated Transition Metal Systems,” J. Less Common Metals 2: 138153, 1960.
7. Laves, P. and Witte, H., “Der Einfluss von Valenzelcktronen auf die Kristallstruktur-ternarer Mg-Legierungen,” Metallwirtschaft 15: 840842, 1936.
8. Laves, F., Z. Kristall. (to be published).
9. Laves, F. and Wallbaum, H. J., “Ueber einige neue Vertreter des NiAs-Typs und ihré kristallchemische Bedeutung,” Z. angew. Mineral. 4: 1746, 1941.
10. Bvauer, G. and Mitius, A., “Die Kristallstvuktur des ThSi2,” Z, anorg. u. allgem, Chem. 249: 325335, 1942.
11. Schulze, G. E. R., “Dichte und Raumerfullung bei interrnetalllschen Verbindungen, insbesondere Laves-Phasen,” Z. Kristall. 115: 261268, 1961.
12. Laves, F., “Zintl's Arbeiten uber die Chemie und Struktur von Legkrungen,” Naturzviss. 29: 244254, 1941.
13. Mooscr, E. and Pearson, W. E., “The chemical bond in semiconductors,” J. Electronics 6, 629645, 1956, pp. 117; Progress in Semiconductors, Vol. 5, Heywood Comp., London, 1960, pp. 103-139.
14. Hume-Rothery, W., “Nature, Properties, and Formation of Intermetallic Compounds,“J. InH. Metals 35: 295-361, 1926.
15. Witte, H., “Der Gültigkeitsberekh der Hume-Rotheryschen Regel,” Metallwirtsthaft 16: 237245, 1937.
16. Beck, P. and. co-workers (only few of his papers can be quoted here): 1, K. R. Gupta, N. S. Rajan and P. A. Beck, “Effect of Si and Al on the Stability of Certain Sigma Phases,” Trans. Met. Soc, AIME 21S: 1960; 2. B. N. Das and P. A. Beck, “Relationship Between the Mu Phase and the Sigma Phase in the Mo-Mm-Co System,” Trans, Met. Soc, AIME 218: 1960.
17. Parthé, E., “Contributions to the Nowotny Phases,” Acta Cryst. 10: 768769, 1957; E. Parthe” and J. T. Norton, “Crystal Structures of Zr5Ge3, Ta5Ge3, and Cr5Ge3,” Acta Cryst. II; 14-17, 1958.
18. Stadelmaier, H. H., “Ueber ternäre Verbindungen von Ucbergangsmetall, B-Metall und Metalloid,” Z. Metallkunde 52: 758762, 1961; “Ternary Carbides of the Transition Metals Ni, Co, Fe, Mn with Zn and Sn,” Acta Met. 7: 415-419, 1959.
19. Brown, P. J., “The Structure of α (V-Al),” Acta Cryst. 10: 133135, 1957.
20. Smith, J. F. and Ray, A. E., “The Structure of V4Al23,” Acta Cryst. 10: 169172, 1957; see in addition Acta Cryst. 13: 876-884, 1960.
21. Slater, J. C., “Band Theory of Bonding in Metals,” Theory of Alloy Phases, Am. Soc. for Metals, Cleveland, 1956, pp. 1-12.

Factors Governing the Structure of Intermetallic Phases

  • F. Laves (a1)


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