Umklapp process

Umklapp process [′u̇m‚kläp ‚prä·səs]

(solid-state physics)

The interaction of three or more waves in a solid, such as lattice waves or electron waves, in which the sum of the wave vectors is not equal to zero but, rather, is equal to a vector in the reciprocal lattice. Also known as flip-over process.

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Umklapp process

A concept in the theory of transport properties of solids which has to do with the interaction of three or more waves in the solid, such as lattice waves or electron waves. In a continuum, such interactions occur only among waves described by wave vectors k ₁, k ₂, and so on, such that the interference condition, given by Eq. (1), is satisfied.

(1) 

The sign of k depends on whether the wave absorbs or emits energy. Since ℏ k is the momentum of a quantum (or particle) described by the wave, Eq. (1) corresponds to conservation of momentum. In a crystal lattice further interactions

(2) 

occur, satisfying Eq. (2), where b is any integral combination of the three inverse lattice vectors b _i, defined by a · b _j = 2&pgr;δ_ij, the a 's being the periodicity vectors. The group of processes described in Eq. (2) are the Umklapp processes or flip-over processes, so called because the total momentum of the initial particles or quanta is reversed. See Crystal