A class containing the Point Groups for a crystal. More...

#include <PointGroup.h>

Inheritance diagram for Mantid::Geometry::PointGroup:

Public Types
enum class	CrystalSystem { Triclinic , Monoclinic , Orthorhombic , Tetragonal , Hexagonal , Trigonal , Cubic }

enum class	LatticeSystem { Triclinic , Monoclinic , Orthorhombic , Tetragonal , Hexagonal , Rhombohedral , Cubic }

Public Types inherited from Mantid::Geometry::Group
enum	CoordinateSystem { Orthogonal , Hexagonal }

enum	GroupAxiom { Closure , Identity , Inversion , Associativity }

Public Member Functions
CrystalSystem	crystalSystem () const

std::vector< Kernel::V3D >	getEquivalents (const Kernel::V3D &hkl) const
	Returns a vector with all equivalent hkls. More...

std::string	getName () const
	Name of the point group. More...

Kernel::V3D	getReflectionFamily (const Kernel::V3D &hkl) const
	Returns the same hkl for all equivalent hkls. More...

std::string	getSymbol () const
	Hermann-Mauguin symbol. More...

bool	isEquivalent (const Kernel::V3D &hkl, const Kernel::V3D &hkl2) const
	Return true if the hkls are in same group. More...

LatticeSystem	latticeSystem () const

	PointGroup (const std::string &symbolHM, const Group &group, const std::string &description="")
	Protected constructor - can not be used directly. More...

Public Member Functions inherited from Mantid::Geometry::Group
bool	containsOperation (const SymmetryOperation &operation) const
	Returns true if the group contains the supplied operation. More...

bool	fulfillsAxiom (GroupAxiom axiom) const
	Checks whether a certain group axiom is fulfilled, can be used as a more fine-grained alternative to isGroup(). More...

CoordinateSystem	getCoordinateSystem () const
	Returns the axis system of the group (either orthogonal or hexagonal). More...

std::vector< SymmetryOperation >	getSymmetryOperations () const
	Returns a vector with all symmetry operations. More...

	Group ()
	Default constructor. Creates a group with one symmetry operation (identity). More...

	Group (const std::string &symmetryOperationString)
	Uses SymmetryOperationFactory to create a vector of symmetry operations from the string. More...

	Group (const std::vector< SymmetryOperation > &symmetryOperations)
	Constructs a group from the symmetry operations in the vector, duplicates are removed. More...

bool	isGroup () const
	Returns whether the group fulfills the four group axioms. More...

bool	isInvariant (const Kernel::DblMatrix &tensor, double tolerance=1e-8) const
	Returns true if the tensor is invariant under the group operations. More...

bool	operator!= (const Group &other) const
	Returns true if groups are different from eachother. More...

Group	operator* (const Group &other) const
	Multiplication operator of two groups. More...

std::vector< Kernel::V3D >	operator* (const Kernel::V3D &vector) const
	Returns a unique set of Kernel::V3D resulting from applying all symmetry operations, vectors are wrapped to [0, 1). More...

bool	operator== (const Group &other) const
	Returns true if both groups contain the same set of symmetry operations. More...

size_t	order () const
	Returns the order of the group, which is the number of symmetry operations. More...

virtual	~Group ()=default

Protected Member Functions
std::vector< Kernel::V3D >	getAllEquivalents (const Kernel::V3D &hkl) const
	Generates a set of hkls. More...

CrystalSystem	getCrystalSystemFromGroup () const
	Returns the CrystalSystem determined from symmetry elements. More...

LatticeSystem	getLatticeSystemFromCrystalSystemAndGroup (const CrystalSystem &crystalSystem) const
	Returns the LatticeSystem of the point group, using the crystal system. More...

Protected Member Functions inherited from Mantid::Geometry::Group
bool	associativityHolds () const
	Checks that associativity holds, i.e. More...

bool	eachElementHasInverse () const
	Returns true if the inverse of each element is in the group. More...

CoordinateSystem	getCoordinateSystemFromOperations (const std::vector< SymmetryOperation > &symmetryOperations) const
	Returns the axis system based on the given symmetry operations. More...

bool	hasIdentity () const
	Returns true if the group has the identity element. More...

bool	isClosed () const
	Returns true if the group is closed, i.e. all elements of G * G are in G. More...

void	setSymmetryOperations (const std::vector< SymmetryOperation > &symmetryOperations)
	Assigns symmetry operations, throws std::invalid_argument if vector is empty. More...

Protected Attributes
CrystalSystem	m_crystalSystem

LatticeSystem	m_latticeSystem

std::string	m_name

std::string	m_symbolHM

Protected Attributes inherited from Mantid::Geometry::Group
std::vector< SymmetryOperation >	m_allOperations

CoordinateSystem	m_axisSystem

std::set< SymmetryOperation >	m_operationSet

Detailed Description

A class containing the Point Groups for a crystal.

Author: Vickie Lynch

Date: 2012-02-02

Definition at line 31 of file PointGroup.h.

Member Enumeration Documentation

◆ CrystalSystem

enum class Mantid::Geometry::PointGroup::CrystalSystem

strong

Enumerator
Triclinic
Monoclinic
Orthorhombic
Tetragonal
Hexagonal
Trigonal
Cubic

Definition at line 33 of file PointGroup.h.

◆ LatticeSystem

enum class Mantid::Geometry::PointGroup::LatticeSystem

strong

Enumerator
Triclinic
Monoclinic
Orthorhombic
Tetragonal
Hexagonal
Rhombohedral
Cubic

Definition at line 35 of file PointGroup.h.

Constructor & Destructor Documentation

◆ PointGroup()

Mantid::Geometry::PointGroup::PointGroup	(	const std::string &	symbolHM,
		const Group &	group,
		const std::string &	description = `""`
	)

Protected constructor - can not be used directly.

Definition at line 68 of file PointGroup.cpp.

References getCrystalSystemFromGroup(), getLatticeSystemFromCrystalSystemAndGroup(), m_crystalSystem, and m_latticeSystem.

Member Function Documentation

◆ crystalSystem()

CrystalSystem Mantid::Geometry::PointGroup::crystalSystem ( ) const

inline

Definition at line 43 of file PointGroup.h.

Referenced by export_PointGroup(), getLatticeSystemFromCrystalSystemAndGroup(), and Mantid::Geometry::operator<<().

◆ getAllEquivalents()

std::vector< V3D > Mantid::Geometry::PointGroup::getAllEquivalents ( const Kernel::V3D & hkl ) const

protected

Generates a set of hkls.

This method applies all transformation matrices to the supplied hkl and puts them into a vector, which is returned in the end. For special reflections such as 100 or 110 or 111, the vector may contain duplicates that need to be filtered out.

The symmetry operations need to be set prior to calling this method by a call to PointGroup::setTransformationMatrices.

Parameters

hkl	:: Arbitrary hkl

Returns: :: vector of hkls.

Definition at line 97 of file PointGroup.cpp.

References Mantid::Geometry::Group::m_allOperations.

Referenced by getEquivalents(), getReflectionFamily(), and isEquivalent().

◆ getCrystalSystemFromGroup()

PointGroup::CrystalSystem Mantid::Geometry::PointGroup::getCrystalSystemFromGroup ( ) const

protected

Returns the CrystalSystem determined from symmetry elements.

This method determines the crystal system of the point group. It makes use of the fact that each crystal system has a characteristic set of symmetry elements. The requirement for the cubic system is for example that four 3-fold axes are present, whereas one 3-fold axis indicates that the group belongs to the trigonal system.

Returns: Crystal system that the point group belongs to.

Definition at line 116 of file PointGroup.cpp.

References Cubic, Hexagonal, Mantid::Kernel::SingletonHolder< T >::Instance(), Mantid::Geometry::Group::m_allOperations, Monoclinic, Orthorhombic, Tetragonal, Triclinic, and Trigonal.

Referenced by PointGroup().

◆ getEquivalents()

std::vector< V3D > Mantid::Geometry::PointGroup::getEquivalents ( const Kernel::V3D & hkl ) const

Returns a vector with all equivalent hkls.

Returns all equivalent reflections for the supplied hkl.

This method returns a vector containing all equivalent hkls for the supplied one. It depends on the internal state of the pointgroup object (e.g. which symmetry operations and therefore, which transformation matrices are present). This internal state is unique for each concrete point group and is set in the constructor.

The returned vector always contains a set of unique hkls, so for special hkls like (100), it has fewer entries than for a general hkl. See also PointGroup::getEquivalentSet.

Parameters

hkl	:: Arbitrary hkl

Returns: :: std::vector containing all equivalent hkls.

Definition at line 38 of file PointGroup.cpp.

References getAllEquivalents().

◆ getLatticeSystemFromCrystalSystemAndGroup()

PointGroup::LatticeSystem Mantid::Geometry::PointGroup::getLatticeSystemFromCrystalSystemAndGroup ( const CrystalSystem & crystalSystem ) const

protected

Returns the LatticeSystem of the point group, using the crystal system.

This function uses the crystal system argument and the coordinate system stored in Group to determine the lattice system. For all crystal systems except trigonal there is a 1:1 correspondence, but for trigonal groups the lattice system can be either rhombohedral or hexagonal.

Parameters

crystalSystem :: CrystalSystem of the point group.

Returns: LatticeSystem the point group belongs to.

Definition at line 170 of file PointGroup.cpp.

References crystalSystem(), Cubic, Mantid::Geometry::Group::getCoordinateSystem(), Mantid::Geometry::Group::Hexagonal, Hexagonal, Monoclinic, Orthorhombic, Rhombohedral, Tetragonal, and Triclinic.

Referenced by PointGroup().

◆ getName()

std::string Mantid::Geometry::PointGroup::getName ( ) const

inline

Name of the point group.

Definition at line 39 of file PointGroup.h.

Referenced by export_PointGroup().

◆ getReflectionFamily()

V3D Mantid::Geometry::PointGroup::getReflectionFamily ( const Kernel::V3D & hkl ) const

Returns the same hkl for all equivalent hkls.

Returns the same V3D for all equivalent hkls.

This method is closely related to PointGroup::getEquivalents. It returns the same V3D for all hkls of one "family". For example in a cubic point group it will return (100) for (001), (010), (0-10), etc.

It can be used to generate a set of symmetry independent hkls, useful for example in powder diffraction.

Parameters

hkl	:: Arbitrary hkl

Returns: :: hkl specific to a family of index-triplets

Definition at line 61 of file PointGroup.cpp.

References getAllEquivalents().

◆ getSymbol()

std::string Mantid::Geometry::PointGroup::getSymbol ( ) const

Hermann-Mauguin symbol.

Definition at line 75 of file PointGroup.cpp.

References m_symbolHM.

Referenced by export_PointGroup(), and Mantid::Geometry::operator<<().

◆ isEquivalent()

bool Mantid::Geometry::PointGroup::isEquivalent	(	const Kernel::V3D &	hkl,
		const Kernel::V3D &	hkl2
	)		const

Return true if the hkls are in same group.

Definition at line 77 of file PointGroup.cpp.

References getAllEquivalents().

◆ latticeSystem()

LatticeSystem Mantid::Geometry::PointGroup::latticeSystem ( ) const

inline

Definition at line 44 of file PointGroup.h.

Referenced by export_PointGroup(), and Mantid::Geometry::operator<<().

Member Data Documentation

◆ m_crystalSystem

CrystalSystem Mantid::Geometry::PointGroup::m_crystalSystem

protected

Definition at line 62 of file PointGroup.h.

Referenced by PointGroup().

◆ m_latticeSystem

LatticeSystem Mantid::Geometry::PointGroup::m_latticeSystem

protected

Definition at line 63 of file PointGroup.h.

Referenced by PointGroup().

◆ m_name

std::string Mantid::Geometry::PointGroup::m_name

protected

Definition at line 61 of file PointGroup.h.

◆ m_symbolHM

std::string Mantid::Geometry::PointGroup::m_symbolHM

protected

Definition at line 60 of file PointGroup.h.

Referenced by getSymbol().

The documentation for this class was generated from the following files:

Framework/Geometry/inc/MantidGeometry/Crystal/PointGroup.h
Framework/Geometry/src/Crystal/PointGroup.cpp

Public Types

Public Member Functions

Protected Member Functions

Protected Attributes

Detailed Description

Member Enumeration Documentation

◆ CrystalSystem

◆ LatticeSystem

Constructor & Destructor Documentation

◆ PointGroup()

Member Function Documentation

◆ crystalSystem()

◆ getAllEquivalents()

◆ getCrystalSystemFromGroup()

◆ getEquivalents()

◆ getLatticeSystemFromCrystalSystemAndGroup()

◆ getName()

◆ getReflectionFamily()

◆ getSymbol()

◆ isEquivalent()

◆ latticeSystem()

Member Data Documentation

◆ m_crystalSystem

◆ m_latticeSystem

◆ m_name

◆ m_symbolHM