A class for representing space groups, inheriting from Group. More...

#include <SpaceGroup.h>

Inheritance diagram for Mantid::Geometry::SpaceGroup:

Public Member Functions
template<typename T >
std::vector< T >	getEquivalentPositions (const T &position) const

PointGroup_sptr	getPointGroup () const
	Returns the point group of the space group. More...

Group_const_sptr	getSiteSymmetryGroup (const Kernel::V3D &position) const
	Returns the site symmetry group. More...

std::string	hmSymbol () const
	Returns the stored Hermann-Mauguin symbol. More...

bool	isAllowedReflection (const Kernel::V3D &hkl) const
	Returns whether the given reflection is allowed or not in this space group. More...

bool	isAllowedUnitCell (const UnitCell &cell) const
	Convenience function for checking compatibility of a cell metric with the space group, see Group::isInvariant. More...

size_t	number () const
	Returns the stored space group number. More...

	SpaceGroup (size_t itNumber, std::string hmSymbol, const Group &group)
	Constructor. 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 Attributes
std::string	m_hmSymbol

size_t	m_number

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

CoordinateSystem	m_axisSystem

std::set< SymmetryOperation >	m_operationSet

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

enum	GroupAxiom { Closure , Identity , Inversion , Associativity }

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...

Detailed Description

A class for representing space groups, inheriting from Group.

SpaceGroup-objects represent a space group, which is a set of symmetry operations. Along with storing the operations themselves, which is realized through inheriting from Group, SpaceGroup also stores a number (space group number according to the International Tables for Crystallography A) and a Hermann-Mauguin-symbol.

SpaceGroup may for example be used to generate all equivalent positions within the unit cell:

SpaceGroup_const_sptr group;

V3D position(0.13, 0.54, 0.38);
std::vector<V3D> equivalents = group->getEquivalentPositions(position);

The class should not be instantiated directly, see SpaceGroupFactoryImpl instead.

Author: Michael Wedel, Paul Scherrer Institut - SINQ

Date: 03/10/2014

Definition at line 46 of file SpaceGroup.h.

Constructor & Destructor Documentation

◆ SpaceGroup()

Mantid::Geometry::SpaceGroup::SpaceGroup	(	size_t	itNumber,
		std::string	hmSymbol,
		const Group &	group
	)

Constructor.

This constructor creates a space group with the symmetry operations contained in the Group-parameter and assigns the given number and symbol.

Parameters

itNumber	:: Space group number (ITA)
hmSymbol	:: Herman-Mauguin symbol for the space group
group	:: Group that contains all symmetry operations (including centering).

Definition at line 27 of file SpaceGroup.cpp.

Member Function Documentation

◆ getEquivalentPositions()

template<typename T >

std::vector< T > Mantid::Geometry::SpaceGroup::getEquivalentPositions ( const T & position ) const

inline

Definition at line 53 of file SpaceGroup.h.

References position.

◆ getPointGroup()

PointGroup_sptr Mantid::Geometry::SpaceGroup::getPointGroup ( ) const

Returns the point group of the space group.

This method uses PointGroupFactory to create the point group of the space- group. Becausethe factory is used for construction, a new object is returned each time this method is called.

Returns: :: PointGroup-object.

Definition at line 84 of file SpaceGroup.cpp.

References Mantid::Kernel::SingletonHolder< T >::Instance().

Referenced by export_SpaceGroup().

◆ getSiteSymmetryGroup()

Group_const_sptr Mantid::Geometry::SpaceGroup::getSiteSymmetryGroup ( const Kernel::V3D & position ) const

Returns the site symmetry group.

The site symmetry group contains all symmetry operations of a space group that leave a point unchanged. This method probes the symmetry operations of the space group and constructs a Group-object using them.

Parameters

position :: Coordinates of the site.

Returns: :: Site symmetry group.

Definition at line 98 of file SpaceGroup.cpp.

References Mantid::Geometry::getWrappedVector(), Mantid::Geometry::Group::m_allOperations, and position.

◆ hmSymbol()

std::string Mantid::Geometry::SpaceGroup::hmSymbol ( ) const

Returns the stored Hermann-Mauguin symbol.

Definition at line 34 of file SpaceGroup.cpp.

References m_hmSymbol.

Referenced by Mantid::Geometry::PointGroupFactoryImpl::createPointGroupFromSpaceGroup(), export_SpaceGroup(), and Mantid::Geometry::operator<<().

◆ isAllowedReflection()

bool Mantid::Geometry::SpaceGroup::isAllowedReflection ( const Kernel::V3D & hkl ) const

Returns whether the given reflection is allowed or not in this space group.

Space groups that contain translational symmetry cause certain reflections to be absent due to the contributions of symmetry equivalent atoms to the structure factor cancelling out. This method implements the procedure described in ITA [1] to check whether a reflection is allowed or not according to the symmetry operations in the space group. Please note that certain arrangements of atoms can lead to additional conditions that can not be determined using a space group's symmetry operations alone. For these situations, Geometry::CrystalStructure can help.

[1] International Tables for Crystallography (2006). Vol. A, ch. 12.3, p. 832

Parameters

hkl	:: HKL to be checked.

Returns: :: true if the reflection is allowed, false otherwise.

Definition at line 53 of file SpaceGroup.cpp.

References fabs, Mantid::Geometry::Group::m_allOperations, and Mantid::Kernel::V3D::scalar_prod().

◆ isAllowedUnitCell()

bool Mantid::Geometry::SpaceGroup::isAllowedUnitCell ( const UnitCell & cell ) const

Convenience function for checking compatibility of a cell metric with the space group, see Group::isInvariant.

Definition at line 73 of file SpaceGroup.cpp.

References Mantid::Geometry::UnitCell::getG(), and Mantid::Geometry::Group::isInvariant().

Referenced by export_SpaceGroup().

◆ number()

size_t Mantid::Geometry::SpaceGroup::number ( ) const

Returns the stored space group number.

Definition at line 31 of file SpaceGroup.cpp.

References m_number.

Referenced by export_SpaceGroup().

Member Data Documentation

◆ m_hmSymbol

std::string Mantid::Geometry::SpaceGroup::m_hmSymbol

protected

Definition at line 76 of file SpaceGroup.h.

Referenced by hmSymbol().

◆ m_number

size_t Mantid::Geometry::SpaceGroup::m_number

protected

Definition at line 75 of file SpaceGroup.h.

Referenced by number().

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

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

Public Member Functions

Protected Attributes

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ SpaceGroup()

Member Function Documentation

◆ getEquivalentPositions()

◆ getPointGroup()

◆ getSiteSymmetryGroup()

◆ hmSymbol()

◆ isAllowedReflection()

◆ isAllowedUnitCell()

◆ number()

Member Data Documentation

◆ m_hmSymbol

◆ m_number