Neumann’s principle in crystallography

E458004

crystallographic principle physical principle

Neumann’s principle in crystallography is a fundamental rule stating that the symmetry elements of any physical property of a crystal must include the symmetry elements of the crystal’s point group.

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Observed surface forms (1)

Surface form	Occurrences
Neumann’s principle	47

Statements (47)

Predicate	Object
instanceOf	crystallographic principle ⓘ physical principle ⓘ
appliesTo	crystals ⓘ physical properties of crystals ⓘ
appliesToPropertyType	conductivity tensors ⓘ dielectric properties ⓘ elastic properties ⓘ magnetic properties ⓘ optical properties ⓘ piezoelectric properties ⓘ thermal expansion ⓘ
assumes	crystal described by a point group ⓘ
category	symmetry principle in physics ⓘ
constraintType	symmetry constraint ⓘ
coreStatement	The symmetry elements of any physical property of a crystal must include the symmetry elements of the crystal’s point group. ⓘ
domainOfApplication	linear response properties ⓘ nonlinear optical properties ⓘ
field	crystallography ⓘ materials science ⓘ solid-state physics ⓘ
holdsFor	all 32 crystallographic point groups ⓘ
implies	degeneracies in physical properties follow crystal symmetry ⓘ forbidden tensor components must vanish ⓘ physical property symmetry cannot be lower than crystal point group symmetry ⓘ
involvesConcept	anisotropy ⓘ crystal point group ⓘ material symmetry ⓘ symmetry elements ⓘ tensor properties ⓘ
mathematicalFormulation	property tensors must be invariant under all symmetry operations of the crystal point group ⓘ
namedAfter	Franz Ernst Neumann NERFINISHED ⓘ
relatedTo	Curie’s principle NERFINISHED ⓘ representation theory of point groups ⓘ tensor transformation laws ⓘ
relatesSymmetryOf	physical properties ⓘ
relatesSymmetryTo	crystal point group symmetry ⓘ
status	widely accepted in crystallography ⓘ
usedFor	constraining physical property tensors ⓘ determining allowed tensor components ⓘ predicting anisotropy of physical properties ⓘ
usedIn	crystal optics ⓘ elasticity theory of crystals ⓘ group-theoretical analysis of crystals ⓘ magnetocrystalline anisotropy analysis ⓘ materials characterization ⓘ piezoelectricity analysis ⓘ
validFor	equilibrium physical properties ⓘ

Referenced by (1)

Full triples — surface form annotated when it differs from this entity's canonical label.

Franz Ernst Neumann → notableWork → Neumann’s principle in crystallography ⓘ