Not to be confused with the Born Rule

Born rule

The Born rule is a law of quantum mechanics which gives the probability that a measurement on a quantum system will yield a given result. It is named after its originator, the physicist Max Born. The Born rule is one of the key principles of quantum mechanics...

 in Quantum Mechanics

Quantum mechanics

Quantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...

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The Cauchy–Born rule or Cauchy-Born approximation states that in a crystalline solid subject to a small strain

Deformation (mechanics)

Deformation in continuum mechanics is the transformation of a body from a reference configuration to a current configuration. A configuration is a set containing the positions of all particles of the body...

, the positions of the atoms within the crystal lattice follow the overall strain of the medium. This approximation generally holds for face-centered and body-centered cubic crystal system

Cubic crystal system

In crystallography, the cubic crystal system is a crystal system where the unit cell is in the shape of a cube. This is one of the most common and simplest shapes found in crystals and minerals....

s. For complex lattices such as diamond

Diamond

In mineralogy, diamond is an allotrope of carbon, where the carbon atoms are arranged in a variation of the face-centered cubic crystal structure called a diamond lattice. Diamond is less stable than graphite, but the conversion rate from diamond to graphite is negligible at ambient conditions...

, however, the rule has to be modified to allow for internal degrees of freedom between the sublattices.