Abstract
1/1, 3/2, 5/3, 7/4, 9/5, 11/6, 13/7 ... (2n – 1)/n ... 2/1 is a monotonic sequence1 tending to the limiting value 2/1 when n is increased indefinitely. This sequence is a systematic representation of the ratio of the number of free valency electrons to atoms in the well-known Hume-Rothery2 series of electronic compounds.
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References
Bromwich, T. J. I'a., "The Theory of Infinite Series" (London: Macmillan and Co., Ltd.).
Hume-Rothery, W., "The Structure of Metals and Alloys" (Institute of Metals).
Mott, N. F., and Jones, H., "The Theory of the Properties of Metals and Alloys" (Oxford: Clarendon Press).
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Bradley, A. J., Lipson, H., and Goldschmidt, H. J., J. Inst. Metals, 63, 149 (1938).
Konobeevsky, S., J. Inst. Metals, 63, 161 (1938).
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BRADLEY, A. Electron–Atom Ratios in Alloy Phases as a Monotonic Sequence. Nature 163, 683–684 (1949). https://doi.org/10.1038/163683a0
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DOI: https://doi.org/10.1038/163683a0
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