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LatticeSystem—Wolfram Documentation

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LatticeSystem

Related Interpreter »
Named lattice systems.

Entity["LatticeSystem",name] or

represents an entity of type "LatticeSystem".

[prop]

gives the value of a specified property.

[{propi,…}]

gives the value of a list of properties.

EntityClass["LatticeSystem",{propispeci,…}]

represents a class of entities with values of propi defined by speci.

Sample Entities

  • …

Properties

  • AlternateNamesalternate names
    AngleRelationsangle relations
    BravaisLatticesBravais lattice
    CrystalFamilycrystal family
    CrystallographicPointGroupscrystallographic point groups
    CrystallographicSpaceGroupscrystallographic space groups
    CrystalSystemscrystal system
    EdgeRelationsedge relations
    EntityClassesentity classes
    EntityTypeListentity type list
    Namename
    RequiredPointGroupSymmetriesrequired point group symmetry
    UnitCellVolumeunit cell volume

Details

  • "LatticeSystem" entities consist of the seven named lattice systems in three dimensions: cubic, hexagonal, monoclinic, orthorhombic, rhombohedral, tetragonal and triclinic.
  • A lattice system is a class of lattices with the same set of lattice point groups.
  • Some properties are available for the "LatticeSystem" entity type as a whole and can be given using the form EntityValue["LatticeSystem",property]. Such properties include:
  • "Properties"the list of available properties
    "PropertyCanonicalNames"the standard names of available properties
    "SampleEntities"a sample list of available entities (typically of length 10)
    "SampleEntityClasses"a sample list of available entity classes (typically of length 10)
    "EntityCount"number of entities available
    "Entities"the list of available entities
    "EntityCanonicalNames"the standard names of available entities
    "EntityClasses"the list of available entity classes
    "EntityClassCanonicalNames"the standard names of available entity classes
    "PropertyClasses"the list of available property classes
    "PropertyClassCanonicalNames"the standard names of available property classes
    "PropertyCount"number of properties available
  • The following annotations can be used in the third argument of EntityValue["LatticeSystem",property,annotation]:
  • "Source"source information for the property
    "Date"the date associated with the entity-property value (if any)
    "EntityAssociation"an association of entities and entity-property values
    "PropertyAssociation"an association of properties and entity-property values
    "EntityPropertyAssociation"an association in which the specified entities are keys, and values are a nested association of properties and entity-property values
    "PropertyEntityAssociation"an association in which the specified properties are keys, and values are a nested association of entities and entity-property values
    "Dataset"a dataset in which the specified entities are keys, and values are an association of property names and entity-property values
  • The following annotations can be used in the second argument of EntityValue[property,annotation]:
  • "Qualifiers"the list of possible qualifiers for the property
    "QualifierValues"the list of possible values that can be given to each qualifier
    "DefaultQualifierValues"the list of default values for the property's qualifiers
    "Description"a brief textual description of the property
    "Definition"a detailed textual definition of the property
    "PhysicalQuantity"the physical quantity associated with the entity-property value
    "Unit"the unit associated with the entity-property value
  • A qualifier value of Automatic indicates that an applicable format of values can be used; e.g. for the "Date" qualifier, this includes a proper date or date span.

Examples

Basic Examples  (4)

Use for entity discovery:

Wolfram Language code: ["hexagonal lattice system"]
Wolfram Language code: Entity["LatticeSystem", "Hexagonal"]

Find a property value for an entity:

Wolfram Language code: Entity["LatticeSystem", "Orthorhombic"]["UnitCellVolume"][a, b, c][q]

Retrieve a dataset of all available properties for an entity:

Wolfram Language code: Entity["LatticeSystem", "Triclinic"]["Dataset"]

Retrieve lattice systems corresponding to the triclinic crystal family:

Wolfram Language code: EntityClass["CrystalSystem", "CrystalFamily" -> "Triclinic"]//EntityList