Slater–Pauling rule

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In [[condensed matter physics]], the '''Slater–Pauling rule''' states that adding a element to a [[Alloy|metal alloy]] will be reduce the alloy's [[Saturation (magnetic)|saturation magnetization]] by an amount proportional to the number of [[valence electrons]] outside of the added element's [[Electron shell|d shell]].<ref>Liquid error: wrong number of arguments (given 1, expected 2)</ref> 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]]<ref>Liquid error: wrong number of arguments (given 1, expected 2)</ref> and [[Linus Pauling]]<ref>Liquid error: wrong number of arguments (given 1, expected 2)</ref> in the 1930's, the rule is a useful approximation for the magnetic properties of many [[transition metals]].

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 [[Aufbau_principle#Madelung_energy_ordering_rule|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: [[Aufbau_principle#The_n_+_ℓ_energy_ordering_rule|the n+ℓ energy ordering rule]])

{| class="wikitable" style="text-align:center;"
|+ Slater–Pauling rule (nearest integer)
|-
! Element !! [[Electron configurations of the elements (data page)|Electron configuration]] !! Magnetic valence !! Predicted [[Magnetic moment|moment]] per atom
|-
| [[Tin]] || [Kr] 4d¹⁰ 5s² 5p²|| -4 || -4 <math>\mu_\mathrm{B}</math>
|-
|[[Aluminum]] || [Ne] 3s² 3p¹ || -3 || -3 <math>\mu_\mathrm{B}</math>
|-
| [[Zinc]] || [Ar] 3d¹⁰ 4s² || -2 || -2 <math>\mu_\mathrm{B}</math>
|-
| [[Copper]] || [Ar] 3d¹⁰ 4s¹ || -1 || -1 <math>\mu_\mathrm{B}</math>
|-
| [[Palladium]] || [Kr] 4d¹⁰ || 0 || 0 <math>\mu_\mathrm{B}</math>
|-
| [[Cobalt]]|| [Ar] 3d⁷ 4s² || +1 || +1 <math>\mu_\mathrm{B}</math>
|-
| [[Iron]] || [Ar] 3d⁶ 4s² || +2 || +2 <math>\mu_\mathrm{B}</math>
|-
| [[Manganese]] || [Ar] 3d⁵ 4s² || +3 || +3 <math>\mu_\mathrm{B}</math>
|}

The basic rule given above makes several approximations. One simplification is rounding to the nearest integer. Because we are describing the number of [[Electronic band structure|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 [[Heuristic|useful as an approximation]] to more accurate, but more complicated physical models.

==See also==
* [[Spin states (d electrons)]]
* [[Ferromagnetism]]
* [[Metallic bonding]]

==References==


[[Category:Electric and magnetic fields in matter]]
[[Category:Magnetism]]
[[Category:Electronic band structures]]

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