Slater–Pauling rule
In condensed matter physics, the Slater–Pauling rule states that adding an element to a metal alloy will reduce the alloy's saturation magnetization by an amount proportional to the number of valence electrons outside of the added element's d shell.[1] Conversely, elements with a partially filled d shell will increase the magnetic moment by an amount proportional to number of missing electrons. Investigated by the physicists John C. Slater[2] and Linus Pauling[3] in the 1930s, the rule is a useful approximation for the magnetic properties of many transition metals.
Application[edit]
The use of the rule depends on carefully defining what it means for an electron to lie outside of the d shell. The electrons outside a d shell are the electrons which have higher energy than the electrons within the d shell. The Madelung rule (incorrectly) suggests that the s shell is filled before the d shell. For example, it predicts Zinc has a configuration of [Ar] 4s2 3d10. However, Zinc's 4s electrons actually have more energy than the 3d electrons, putting them outside the d shell. Ordered in terms of energy, the electron configuration of Zinc is [Ar] 3d10 4s2. (see: the n+ℓ energy ordering rule)
| Element | Electron configuration | Magnetic valence | Predicted moment per atom |
|---|---|---|---|
| Tin | [Kr] 4d10 5s2 5p2 | -4 | -4 |
| Aluminum | [Ne] 3s2 3p1 | -3 | -3 |
| Zinc | [Ar] 3d10 4s2 | -2 | -2 |
| Copper | [Ar] 3d10 4s1 | -1 | -1 |
| Palladium | [Kr] 4d10 | 0 | 0 |
| Cobalt | [Ar] 3d7 4s2 | +1 | +1 |
| Iron | [Ar] 3d6 4s2 | +2 | +2 |
| Manganese | [Ar] 3d5 4s2 | +3 | +3 |
The basic rule given above makes several approximations. One simplification is rounding to the nearest integer. Because we are describing the number of electrons in a band using an average value, the s and d shells can be filled to non-integer numbers of electrons, allowing the Slater–Pauling rule to give more accurate predictions. While the Slater–Pauling rule has many exceptions, it is often a useful as an approximation to more accurate, but more complicated physical models.
Building on further theoretical developments done by physicists such as Jacques Friedel,[4] a more widely applicable version of the rule, known as the generalized Slater–Pauling rule was developed.[5][6]
See also[edit]
References[edit]
- ^ Kittel, Charles (2005). Introduction to Solid State Physics (8th ed.). United States: John Wiley & Sons. p. 335-336. ISBN 0-471-41526-X.
- ^ Slater, J. C. (1936-06-15). "The Ferromagnetism of Nickel. II. Temperature Effects". Physical Review. 49 (12). American Physical Society (APS): 931–937. Bibcode:1936PhRv...49..931S. doi:10.1103/physrev.49.931. ISSN 0031-899X.
- ^ Pauling, Linus (1938-12-01). "The Nature of the Interatomic Forces in Metals". Physical Review. 54 (11). American Physical Society (APS): 899–904. Bibcode:1938PhRv...54..899P. doi:10.1103/physrev.54.899. ISSN 0031-899X.
- ^ Friedel, J. (1958). "Metallic alloys". Il Nuovo Cimento. 7 (S2). Springer Science and Business Media LLC: 287–311. Bibcode:1958NCim....7S.287F. doi:10.1007/bf02751483. ISSN 0029-6341. S2CID 189771420.
- ^ Williams, A.; Moruzzi, V.; Malozemoff, A.; Terakura, K. (1983). "Generalized Slater-Pauling curve for transition-metal magnets". IEEE Transactions on Magnetics. 19 (5). Institute of Electrical and Electronics Engineers (IEEE): 1983–1988. Bibcode:1983ITM....19.1983W. doi:10.1109/tmag.1983.1062706. ISSN 0018-9464.
- ^ Malozemoff, A. P.; Williams, A. R.; Moruzzi, V. L. (1984-02-15). ""Band-gap theory" of strong ferromagnetism: Application to concentrated crystalline and amorphous Fe- and Co-metalloid alloys". Physical Review B. 29 (4). American Physical Society (APS): 1620–1632. Bibcode:1984PhRvB..29.1620M. doi:10.1103/physrevb.29.1620. ISSN 0163-1829.
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