Miller indices conventions
E591488
Miller indices conventions are the standardized crystallographic notation rules used to label and describe crystal planes and directions in a crystal lattice.
All labels observed (2)
| Label | Occurrences |
|---|---|
| Miller indices | 1 |
| Miller indices conventions canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T6387703 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Miller indices conventions Context triple: [Commission on Crystallographic Nomenclature, worksOn, Miller indices conventions]
-
A.
International Tables for Crystallography
International Tables for Crystallography is a comprehensive, authoritative multi-volume reference work that provides standardized data, symmetry information, and methodologies essential for crystallographic research and practice.
-
B.
Neumann’s principle in crystallography
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.
-
C.
Bragg's law
Bragg's law is a fundamental equation in X-ray crystallography that relates the angles at which X-rays are diffracted by crystal lattice planes to the spacing between those planes.
-
D.
Debye–Scherrer method
The Debye–Scherrer method is an X-ray powder diffraction technique used to determine the crystal structure and lattice parameters of polycrystalline materials.
-
E.
Alexander–Briggs notation
Alexander–Briggs notation is a classical system for naming and classifying knots in knot theory, assigning each distinct knot a unique label based on its crossing number and order in knot tables.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Miller indices conventions Target entity description: Miller indices conventions are the standardized crystallographic notation rules used to label and describe crystal planes and directions in a crystal lattice.
-
A.
International Tables for Crystallography
International Tables for Crystallography is a comprehensive, authoritative multi-volume reference work that provides standardized data, symmetry information, and methodologies essential for crystallographic research and practice.
-
B.
Neumann’s principle in crystallography
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.
-
C.
Bragg's law
Bragg's law is a fundamental equation in X-ray crystallography that relates the angles at which X-rays are diffracted by crystal lattice planes to the spacing between those planes.
-
D.
Debye–Scherrer method
The Debye–Scherrer method is an X-ray powder diffraction technique used to determine the crystal structure and lattice parameters of polycrystalline materials.
-
E.
Alexander–Briggs notation
Alexander–Briggs notation is a classical system for naming and classifying knots in knot theory, assigning each distinct knot a unique label based on its crossing number and order in knot tables.
- F. None of above. chosen
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 ⓘ |
How these facts were elicited
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Instruction
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Input
Subject: Miller indices conventions Description of subject: Miller indices conventions are the standardized crystallographic notation rules used to label and describe crystal planes and directions in a crystal lattice.
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.
this entity surface form:
Miller indices