Miller indices conventions

E591488

crystallographic notation system scientific convention

Miller indices conventions are the standardized crystallographic notation rules used to label and describe crystal planes and directions in a crystal lattice.

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Observed surface forms (1)

Surface form	Occurrences
Miller indices	1

Statements (48)

Predicate	Object
instanceOf	crystallographic notation system ⓘ scientific convention ⓘ
appliesTo	Bravais lattices NERFINISHED ⓘ crystal lattice ⓘ
assumes	choice of crystallographic axes ⓘ
basedOn	reciprocal of intercepts with crystallographic axes ⓘ
clarifies	orientation of cleavage planes ⓘ slip systems in crystals ⓘ texture and preferred orientation in polycrystals ⓘ
compatibleWith	14 Bravais lattice types ⓘ
definesNotation	Miller indices for directions [u v w] ⓘ Miller indices for planes (h k l) ⓘ families of directions ⟨u v w⟩ ⓘ families of planes {h k l} ⓘ
distinguishes	planes from directions by bracket style ⓘ
enables	comparison of crystallographic data across publications ⓘ
field	crystallography ⓘ
includesRule	direction indices [u v w] are proportional to components of a vector in lattice coordinates ⓘ direction indices are reduced to the smallest set of integers with the same ratio ⓘ if a plane is parallel to an axis its intercept is taken as infinity and the corresponding index is zero ⓘ indices are integers with no common factor other than 1 ⓘ negative indices are written with a bar over the number ⓘ parallel planes share the same Miller indices ⓘ plane indices are proportional to reciprocals of axis intercepts ⓘ the origin is not considered an intercept when determining indices ⓘ
introducedIn	19th century ⓘ
namedAfter	William Hallowes Miller NERFINISHED ⓘ
relatedTo	Miller–Bravais indices in hexagonal systems ⓘ reciprocal lattice ⓘ zone axis notation ⓘ
standardizedBy	International Union of Crystallography NERFINISHED ⓘ
supports	systematic indexing of diffraction peaks ⓘ
usedFor	describing crystal directions ⓘ describing crystal planes ⓘ labeling lattice directions ⓘ labeling lattice planes ⓘ
usedIn	X-ray diffraction analysis ⓘ crystal structure determination ⓘ electron diffraction ⓘ materials science ⓘ metallurgy ⓘ neutron diffraction ⓘ semiconductor crystallography ⓘ solid-state physics ⓘ
usesBracketsType	angle brackets ⟨u v w⟩ for families of symmetry-equivalent directions ⓘ curly brackets {h k l} for families of symmetry-equivalent planes ⓘ round brackets (h k l) for individual planes ⓘ square brackets [u v w] for individual directions ⓘ

Referenced by (2)

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

Commission on Crystallographic Nomenclature → worksOn → Miller indices conventions ⓘ

Bragg's law → relatedConcept → Miller indices conventions ⓘ

this entity surface form: Miller indices