CASM::Lattice Class Reference

#include <Lattice.hh>

Inheritance diagram for CASM::Lattice:

Detailed Description

Definition at line 31 of file Lattice.hh.

Public Types
typedef Eigen::Matrix3d::ColXpr	LatVec
typedef Eigen::Matrix3d::ConstColXpr	ConstLatVec

Public Member Functions
	Lattice (const Eigen::Vector3d &vec1, const Eigen::Vector3d &vec2, const Eigen::Vector3d &vec3)
	Lattice (const Eigen::Ref< const Eigen::Matrix3d > &lat_mat=Eigen::Matrix3d::Identity())
LatVec	operator[] (Index i)
	Get i'th lattice vector as column expression. More...
ConstLatVec	operator[] (Index i) const
	Get i'th lattice vector as column expression. More...
std::tuple< LatVec, LatVec, LatVec >	vectors ()
std::tuple< ConstLatVec, ConstLatVec, ConstLatVec >	vectors () const
Lattice	scaled_lattice (double scale) const
	Return scaled copy of this lattice (Note: Volume will be scaled by scale^3) More...
double	angle (Index i) const
	Return angle between lattice vectors (*this)[(i+1)%3] and (*this)[(i+2)%3], in degrees. More...
double	length (Index i) const
	Return length of i'th lattice vector. More...
double	vol () const
	Return signed volume of this lattice. More...
Eigen::MatrixXd const &	voronoi_table () const
	Return voronoi table, which specifies outward-pointing normals of Lattice Voronoi cell. outward-pointing normals are given as rows of the matrix, and defined such that if (voronoi_table()*coord.cart()).maxCoeff()>1, then 'coord' is outside of the voronoi cell. More...
double	inner_voronoi_radius () const
	Radius of the largest sphere that fits wholly within the voronoi cell. More...
const Eigen::Matrix3d &	lat_column_mat () const
	3x3 matrix with lattice vectors as its columne More...
const Eigen::Matrix3d &	inv_lat_column_mat () const
	Inverse of Lattice::lat_column_mat() It is the transformation matrix 'C2F', such that f = C2F * c where 'c' is Cartesian coordinate/vector and 'f' and 'f' is fractional coordinate/vector. More...
Array< int >	calc_kpoints (Array< int > prim_kpoints, Lattice prim_lat)
Lattice	get_reciprocal () const
	Return reciprocal lattice. More...
void	generate_point_group (SymGroup &point_group, double pg_tol=TOL) const
	Populate. More...
template<typename SymOpIterator , typename SymOpOutputIterator >
SymOpOutputIterator	find_invariant_subgroup (SymOpIterator begin, SymOpIterator end, SymOpOutputIterator result, double pg_tol=TOL) const
	Output the SymOp that leave this lattice invariant. More...
void	find_invariant_subgroup (const SymGroup &super_group, SymGroup &sub_group, double pg_tol=TOL) const
	populate More...
bool	is_canonical (double tol=TOL) const
	Check if Lattice is in the canonical form. More...
bool	is_canonical (const SymGroup &pg, double tol=TOL) const
	Check if Lattice is in the canonical form. More...
SymOp	to_canonical (double tol=TOL) const
	Returns the operation that applied to *this returns the canonical form. More...
SymOp	to_canonical (const SymGroup &pg, double tol=TOL) const
	Returns the operation that applied to *this returns the canonical form. More...
SymOp	from_canonical (double tol=TOL) const
	Returns the operation that applied to the canonical form returns *this. More...
SymOp	from_canonical (const SymGroup &pg, double tol=TOL) const
	Returns the operation that applied to the canonical form returns *this. More...
Lattice	canonical_form (double tol=TOL) const
	Returns the canonical equivalent Lattice, using the point group of the Lattice. More...
Lattice	canonical_form (const SymGroup &pg, double tol=TOL) const
	Returns the canonical equivalent Lattice, using the provided point group. More...
void	generate_supercells (Array< Lattice > &supercell, const SymGroup &effective_pg, const ScelEnumProps &enum_props) const
	Populate. More...
template<typename T >
Lattice	make_supercell (const Eigen::Matrix< T, 3, 3 > &trans_mat) const
	make a supercell of this lattice. Equivalent to Lattice(lat_column_mat()*trans_mat) More...
Lattice	get_reduced_cell () const
	Find the lattice vectors which give most compact unit cell Compactness is measured by how close lat_column_mat().transpose()*lat_column_mat() is to a diagonal matrix. More...
void	print_voronoi_table (std::ostream &stream) const
double	min_voronoi_radius () const
	Radius of largest sphere that totally fits inside the voronoi cell. More...
double	max_voronoi_measure (const Eigen::Vector3d &pos, Eigen::Vector3d &lattice_trans) const
int	voronoi_number (const Eigen::Vector3d &pos) const
Eigen::Vector3i	enclose_sphere (double radius) const
template<typename CoordType , typename CoordType2 >
Array< CoordType >	gridstruc_build (double max_radius, double min_radius, Array< CoordType > basis, CoordType2 lat_point)
	Make a grid of lattice sites such that min_radius <= distance <= max_radius from. More...
void	read (std::istream &stream)
void	print (std::ostream &stream, int _prec=8) const
bool	is_equivalent (const Lattice &RHS, double tol) const
	Are two lattices the same, even if they have different lattice vectors. More...
bool	operator< (const Lattice &RHS) const
	Compare two Lattice. More...
bool	is_supercell_of (const Lattice &tile, Eigen::Matrix3d &multimat, double _tol=TOL) const
	Matrix that relates two lattices (e.g., strain or slat) More...
bool	is_supercell_of (const Lattice &tile, const Array< SymOp > &symlist, Eigen::Matrix3d &multimat, double _tol=TOL) const
bool	is_supercell_of (const Lattice &tile, double _tol=TOL) const
	Checks if lattice is a supercell of tile, applying operations from symlist. More...
bool	is_supercell_of (const Lattice &tile, const Array< SymOp > &symlist, double _tol=TOL) const
Lattice	box (const Lattice &prim, const Lattice &scel, bool verbose=false) const
	Return a lattice with diagonal matrix that fits around starting lattice. More...
Lattice &	make_right_handed ()
	Flip c vector if it's on the wrong side of a-b plane – return (*this) More...
bool	is_right_handed () const
	Check if the lattice is right handed. More...
Eigen::Vector3i	get_millers (Eigen::Vector3d plane_normal, double tolerance=TOL) const
	Given a normal vector, a Vector3 containing the miller indeces for the lattice is generated. More...
Lattice	get_lattice_in_plane (Eigen::Vector3i millers, int max_vol=20) const
	Generates a lattice with vectors a and b parallel to the plane described by the miller indeces. More...
Array< double >	pg_converge (double large_tol)
void	pg_converge (double small_tol, double large_tol, double increment)
void	symmetrize (const SymGroup &relaxed_pg)
	Force this lattice to have symmetry of group. More...
void	symmetrize (double _tol)
	Force this lattice to have symmetry of point group calculated based on tolerance. More...
bool	operator> (const Lattice &B) const
bool	operator<= (const Lattice &B) const
bool	operator>= (const Lattice &B) const
bool	operator== (const Lattice &B) const
bool	operator!= (const Lattice &B) const

Static Public Member Functions
static Lattice	fcc ()
	Construct FCC primitive cell of unit volume. More...
static Lattice	bcc ()
	Construct BCC primitive cell of unit volume. More...
static Lattice	cubic ()
	Construct simple cubic primitive cell of unit volume. More...
static Lattice	hexagonal ()
	Construct cubic primitive cell of unit volume. More...

Protected Member Functions
const Lattice &	derived () const
bool	_ne (const Lattice &B) const

Private Member Functions
bool	_eq (const Lattice &RHS) const
	Are lattice vectors identical for two lattices, within TOL. More...
void	_generate_voronoi_table () const
	populate voronoi information. More...

Private Attributes
friend	Comparisons< Lattice >
double	m_inner_voronoi_radius
Eigen::MatrixXd	m_voronoi_table
Eigen::Matrix3d	m_lat_mat
Eigen::Matrix3d	m_inv_lat_mat

Related Functions
(Note that these are not member functions.)
Lattice	replace_vector (const Lattice &lat, const Eigen::Vector3d &new_vector, double tol)
	Returns a minimum volume Lattice obtainable by replacing one Lattice vector with tau. More...
Eigen::Matrix3i	canonical_hnf (const Eigen::Matrix3i &T, const SymGroup &effective_pg, const Lattice &ref_lattice)
	Return canonical hermite normal form of the supercell matrix. More...

Member Typedef Documentation

typedef Eigen::Matrix3d::ConstColXpr CASM::Lattice::ConstLatVec

Definition at line 34 of file Lattice.hh.

typedef Eigen::Matrix3d::ColXpr CASM::Lattice::LatVec

Definition at line 33 of file Lattice.hh.

Constructor & Destructor Documentation

CASM::Lattice::Lattice	(	const Eigen::Vector3d &	vec1,
		const Eigen::Vector3d &	vec2,
		const Eigen::Vector3d &	vec3
	)

Definition at line 27 of file Lattice.cc.

CASM::Lattice::Lattice

(

const Eigen::Ref< const Eigen::Matrix3d > &

lat_mat = Eigen::Matrix3d::Identity()

)

Construct Lattice from a matrix of lattice vectors, where lattice vectors are columns (e.g., lat_mat is equivalent to coord_trans[FRAC])

Construct Lattice from a matrix of lattice vectors, where lattice vectors are columns (e.g., lat_mat is equivalent to lat_column_mat())

Definition at line 38 of file Lattice.cc.

Member Function Documentation

bool CASM::Lattice::_eq ( const Lattice &  RHS ) const

private

Are lattice vectors identical for two lattices, within TOL.

Are lattice vectors identical for two lattices.

Definition at line 1024 of file Lattice.cc.

void CASM::Lattice::_generate_voronoi_table ( ) const

private

populate voronoi information.

Definition at line 563 of file Lattice.cc.

bool CASM::Comparisons< Lattice >::_ne ( const Lattice &  B ) const

inlineprotectedinherited

Definition at line 56 of file Comparisons.hh.

double CASM::Lattice::angle

(

Index

i

)

const

Return angle between lattice vectors (*this)[(i+1)%3] and (*this)[(i+2)%3], in degrees.

Definition at line 99 of file Lattice.cc.

Lattice CASM::Lattice::bcc ( )

static

Construct BCC primitive cell of unit volume.

Definition at line 57 of file Lattice.cc.

Lattice CASM::Lattice::box	(	const Lattice &	prim,
		const Lattice &	scel,
		bool	verbose = false
	)		const

Return a lattice with diagonal matrix that fits around starting lattice.

Array< int > CASM::Lattice::calc_kpoints	(	Array< int >	prim_kpoints,
		Lattice	prim_lat
	)

Calculates the kpoint mesh for a supercell lattice given the kpoint mesh for the primitive lattice

Definition at line 161 of file Lattice.cc.

Lattice CASM::Lattice::canonical_form

(

double

tol = TOL

)

const

Returns the canonical equivalent Lattice, using the point group of the Lattice.

• To specify different symmetry, see canonical_equivalent_lattice

Definition at line 289 of file Lattice.cc.

Lattice CASM::Lattice::canonical_form	(	const SymGroup &	pg,
		double	tol = TOL
	)		const

Returns the canonical equivalent Lattice, using the provided point group.

Definition at line 298 of file Lattice.cc.

Lattice CASM::Lattice::cubic ( )

static

Construct simple cubic primitive cell of unit volume.

Definition at line 69 of file Lattice.cc.

const Lattice & CASM::Comparisons< Lattice >::derived ( ) const

inlineprotectedinherited

Definition at line 48 of file Comparisons.hh.

Eigen::Vector3i CASM::Lattice::enclose_sphere

(

double

radius

)

const

Gives a scaling of the lattice vectors such that after scaling, The eight parallelipipeds touching the origin enclose a sphere of given radius

This function, given a linearly independent set of lattice vectors, finds the dimensions along the unit cell vectors such that a sphere of given radius fits within a uniform grid of 2dim[1]x2dim[2]x2dim[3] lattice points centered at the origin.

The algorithm works by getting the normal (e.g. n1) to each pair of lattice vectors (e.g. a2, a3), scaling this normal to have length radius and then projecting this normal parallel to the a2,a3 plane onto the remaining lattice vector a1. This will tell us the number of a1 vectors needed to make a grid to encompass the sphere.

Definition at line 626 of file Lattice.cc.

Lattice CASM::Lattice::fcc ( )

static

Construct FCC primitive cell of unit volume.

Definition at line 45 of file Lattice.cc.

template<typename SymOpIterator , typename SymOpOutputIterator >

SymOpOutputIterator CASM::Lattice::find_invariant_subgroup	(	SymOpIterator	begin,
		SymOpIterator	end,
		SymOpOutputIterator	result,
		double	pg_tol = TOL
	)		const

Output the SymOp that leave this lattice invariant.

Definition at line 77 of file Lattice_impl.hh.

void CASM::Lattice::find_invariant_subgroup	(	const SymGroup &	super_group,
		SymGroup &	sub_group,
		double	pg_tol = TOL
	)		const

populate

Parameters

sub_group	with subset of
super_group	that leaves this lattice invariant
sub_group	should be empty

Definition at line 222 of file Lattice.cc.

SymOp CASM::Lattice::from_canonical

(

double

tol = TOL

)

const

Returns the operation that applied to the canonical form returns *this.

Returns the operation that applied to *this returns the canonical form.

Definition at line 273 of file Lattice.cc.

SymOp CASM::Lattice::from_canonical	(	const SymGroup &	pg,
		double	tol = TOL
	)		const

Returns the operation that applied to the canonical form returns *this.

Returns the operation that applied to *this returns the canonical form.

Definition at line 280 of file Lattice.cc.

void CASM::Lattice::generate_point_group	(	SymGroup &	point_group,
		double	pg_tol = TOL
	)		const

Populate.

Parameters

point_group	with the point group of this lattice
point_group	should be empty
pg_tol	can be increased to find point group of lattice vectors that are slightly distorted due to numerical noise

Definition at line 304 of file Lattice.cc.

void CASM::Lattice::generate_supercells	(	Array< Lattice > &	supercell,
		const SymGroup &	effective_pg,
		const ScelEnumProps &	enum_props
	)		const

Populate.

Generate super Lattice.

Parameters

supercell	with symmetrically distinct supercells of this lattice Superlattices are enumerated with volumes
min_prim_vol	<= volume <=
max_prim_vol
effective_pg	is a group that should either be equivalent to the full point group of this lattice or be a subgroup of that full point group

Use SupercellEnumerator to enumerate possible HNF transformation matrices. Unique supercells are identified by applying point group operations and keeping the supercell if the HNF is 'canonical', meaning that the HNF indices in order H00, H11, H22, H12, H02, H01 are the lexicographically greatest.

The supercell that is inserted in the 'supercell' container is the niggli cell, rotated to a standard orientation (see standard_orientation function).

See PrimcClex::generate_supercells for information on dims and G.

Definition at line 410 of file Lattice.cc.

Lattice CASM::Lattice::get_lattice_in_plane	(	Eigen::Vector3i	millers,
		int	max_vol = 20
	)		const

Generates a lattice with vectors a and b parallel to the plane described by the miller indeces.

Using miller indeces, the intercept of the plane is calculated. All intercepts are multiplied by a factor such that their values are integers. This corresponds to the plane being shifted so that it lands on three lattice sites. Using these lattice sites new vectors A and B that lie on the desired plane can be constructed. The choice of vector C is somewhat arbitrary. get_lattice_in_plane will first construct C to be the shortest most orthogonal vector possible. The user is then given the option to make C more orthogonal to A and B in exchange for a greater length. The returned lattice will be the one containing the most orthogonal C that is still smaller than max_vol

Definition at line 717 of file Lattice.cc.

Eigen::Vector3i CASM::Lattice::get_millers	(	Eigen::Vector3d	plane_normal,
		double	tolerance = TOL
	)		const

Given a normal vector, a Vector3 containing the miller indeces for the lattice is generated.

Definition at line 694 of file Lattice.cc.

Lattice CASM::Lattice::get_reciprocal

(

)

const

Return reciprocal lattice.

Definition at line 149 of file Lattice.cc.

Lattice CASM::Lattice::get_reduced_cell

(

)

const

Find the lattice vectors which give most compact unit cell Compactness is measured by how close lat_column_mat().transpose()*lat_column_mat() is to a diagonal matrix.

This function finds the reduced cell from the given primitive cell.

First, the translation vectors of the primitive cell are determined, then reduced. The Bravais lattice is determined using Niggli's transformations. The method used to determine the basis vectors are to find body and face diagonals across the cell. The vectors satisfying these main conditions can be found by ensuring: i) the shortest face diagonal is not shorter than the longest edge of the same face ii) the shortest body diagonal is not shorter than the longest edge of the cell

This is accomplished by enumerating the skew matrices (identity matrix with one of the off-diagonal terms =1 or =-1). This will replace one of the lattice vectors with the face diagonal corresponding to that linear combination. If the length of any of the new skewed lattice vectors is shorter than the length of the original cell, it is replaced. All skew matrices have determinants equal to 1, which preserves the volume of the original cell.

Definition at line 442 of file Lattice.cc.

template<typename CoordType , typename CoordType2 >

Array< CoordType > CASM::Lattice::gridstruc_build	(	double	max_radius,
		double	min_radius,
		Array< CoordType >	basis,
		CoordType2	lat_point
	)

Make a grid of lattice sites such that min_radius <= distance <= max_radius from.

Parameters

lat_point

This function generates a grid of points between max_radius and min_radius. Additionally, it also fills up the points with a basis

Definition at line 15 of file Lattice_impl.hh.

Lattice CASM::Lattice::hexagonal ( )

static

Construct cubic primitive cell of unit volume.

Definition at line 75 of file Lattice.cc.

double CASM::Lattice::inner_voronoi_radius ( ) const

inline

Radius of the largest sphere that fits wholly within the voronoi cell.

Definition at line 98 of file Lattice.hh.

const Eigen::Matrix3d& CASM::Lattice::inv_lat_column_mat ( ) const

inline

Inverse of Lattice::lat_column_mat() It is the transformation matrix 'C2F', such that f = C2F * c where 'c' is Cartesian coordinate/vector and 'f' and 'f' is fractional coordinate/vector.

Definition at line 113 of file Lattice.hh.

bool CASM::Lattice::is_canonical

(

double

tol = TOL

)

const

Check if Lattice is in the canonical form.

Definition at line 235 of file Lattice.cc.

bool CASM::Lattice::is_canonical	(	const SymGroup &	pg,
		double	tol = TOL
	)		const

Check if Lattice is in the canonical form.

Definition at line 242 of file Lattice.cc.

bool CASM::Lattice::is_equivalent	(	const Lattice &	RHS,
		double	tol
	)		const

Are two lattices the same, even if they have different lattice vectors.

Are lattice vectors identical for two lattices.

Definition at line 1002 of file Lattice.cc.

bool CASM::Lattice::is_right_handed

(

)

const

Check if the lattice is right handed.

Definition at line 1096 of file Lattice.cc.

bool CASM::Lattice::is_supercell_of	(	const Lattice &	tile,
		Eigen::Matrix3d &	multimat,
		double	_tol = TOL
	)		const

Matrix that relates two lattices (e.g., strain or slat)

Checks if lattice is a supercell of tile, acting on multiplication matrix. Check is performed applying operations from symlist

Definition at line 655 of file Lattice.cc.

bool CASM::Lattice::is_supercell_of	(	const Lattice &	tile,
		const Array< SymOp > &	symlist,
		Eigen::Matrix3d &	multimat,
		double	_tol = TOL
	)		const

Definition at line 645 of file Lattice.cc.

bool CASM::Lattice::is_supercell_of	(	const Lattice &	tile,
		double	_tol = TOL
	)		const

Checks if lattice is a supercell of tile, applying operations from symlist.

Definition at line 664 of file Lattice.cc.

bool CASM::Lattice::is_supercell_of	(	const Lattice &	tile,
		const Array< SymOp > &	symlist,
		double	_tol = TOL
	)		const

Definition at line 670 of file Lattice.cc.

const Eigen::Matrix3d& CASM::Lattice::lat_column_mat ( ) const

inline

3x3 matrix with lattice vectors as its columne

Definition at line 104 of file Lattice.hh.

double CASM::Lattice::length

(

Index

i

)

const

Return length of i'th lattice vector.

Definition at line 93 of file Lattice.cc.

Lattice & CASM::Lattice::make_right_handed

(

)

Flip c vector if it's on the wrong side of a-b plane – return (*this)

A lattice is considered right handed when the determinant of the lattice vector matrix is positive. This routine will flip the sign of all the lattice vectors if it finds that the determinant is negative

Definition at line 681 of file Lattice.cc.

double CASM::Lattice::max_voronoi_measure	(	const Eigen::Vector3d &	pos,
		Eigen::Vector3d &	lattice_trans
	)		const

Given cartesian vector 'pos', returns double v_dist and populates 'lattice_trans'. v_dist is the fractional number of half lattice-planes along 'lattice_trans' between 'pos' and the lattice plane that passes through the origin. lattice_trans is a lattice translation that is normal to a face of the voronoi cell and translating pos to 'pos-lattice_trans' will yield a translationally-equivalent vector between the -1 and +1 half-plane. v_dist is maximized over all faces of the voronoi cell.

Definition at line 530 of file Lattice.cc.

double CASM::Lattice::min_voronoi_radius

(

)

const

Radius of largest sphere that totally fits inside the voronoi cell.

bool CASM::Comparisons< Lattice >::operator!= ( const Lattice &  B ) const

inlineinherited

Definition at line 41 of file Comparisons.hh.

bool CASM::Lattice::operator<

(

const Lattice &

RHS

)

const

Compare two Lattice.

• First compares is_niggli(*this, TOL) with is_niggli(RHS, TOL)
• Then compares via standard_orientation_compare(this->lat_column_mat(), RHS.lat_column_mat(), TOL)

Definition at line 1013 of file Lattice.cc.

bool CASM::Comparisons< Lattice >::operator<= ( const Lattice &  B ) const

inlineinherited

Definition at line 29 of file Comparisons.hh.

bool CASM::Comparisons< Lattice >::operator== ( const Lattice &  B ) const

inlineinherited

Definition at line 37 of file Comparisons.hh.

bool CASM::Comparisons< Lattice >::operator> ( const Lattice &  B ) const

inlineinherited

Definition at line 25 of file Comparisons.hh.

bool CASM::Comparisons< Lattice >::operator>= ( const Lattice &  B ) const

inlineinherited

Definition at line 33 of file Comparisons.hh.

LatVec CASM::Lattice::operator[] ( Index  i )

inline

Get i'th lattice vector as column expression.

Definition at line 56 of file Lattice.hh.

ConstLatVec CASM::Lattice::operator[] ( Index  i ) const

inline

Get i'th lattice vector as column expression.

Definition at line 61 of file Lattice.hh.

Array< double > CASM::Lattice::pg_converge

(

double

large_tol

)

Definition at line 351 of file Lattice.cc.

void CASM::Lattice::pg_converge	(	double	small_tol,
		double	large_tol,
		double	increment
	)

Definition at line 369 of file Lattice.cc.

void CASM::Lattice::print	(	std::ostream &	stream,
		int	_prec = 8
	)		const

Definition at line 129 of file Lattice.cc.

void CASM::Lattice::print_voronoi_table

(

std::ostream &

stream

)

const

void CASM::Lattice::read

(

std::istream &

stream

)

Definition at line 116 of file Lattice.cc.

Lattice CASM::Lattice::scaled_lattice

(

double

scale

)

const

Return scaled copy of this lattice (Note: Volume will be scaled by scale^3)

Definition at line 87 of file Lattice.cc.

void CASM::Lattice::symmetrize

(

const SymGroup &

relaxed_pg

)

Force this lattice to have symmetry of group.

Parameters

relaxed_pg

Applies all operations of given SymGroup to the lattice and averages out the lattice vectors, changing your lattice to perfectly match with the SymGroup.

Definition at line 1038 of file Lattice.cc.

void CASM::Lattice::symmetrize

(

double

tol

)

Force this lattice to have symmetry of point group calculated based on tolerance.

Parameters

_tol

Same as the other symmetrize routine, except this one assumes that the symmetry group you mean to use is the point group of your lattice within a certain tolerance.

Definition at line 1087 of file Lattice.cc.

SymOp CASM::Lattice::to_canonical

(

double

tol = TOL

)

const

Returns the operation that applied to *this returns the canonical form.

Definition at line 249 of file Lattice.cc.

SymOp CASM::Lattice::to_canonical	(	const SymGroup &	pg,
		double	tol = TOL
	)		const

Returns the operation that applied to *this returns the canonical form.

Definition at line 261 of file Lattice.cc.

std::tuple<LatVec, LatVec, LatVec> CASM::Lattice::vectors ( )

inline

Definition at line 65 of file Lattice.hh.

std::tuple<ConstLatVec, ConstLatVec, ConstLatVec> CASM::Lattice::vectors ( ) const

inline

Definition at line 69 of file Lattice.hh.

double CASM::Lattice::vol ( ) const

inline

Return signed volume of this lattice.

Definition at line 83 of file Lattice.hh.

int CASM::Lattice::voronoi_number

(

const Eigen::Vector3d &

pos

)

const

return number of voronoi cell faces that 'pos' is on, within +/- TOL 0 indicates that 'pos' is within the voronoi cell, and the origin is the nearest lattice site -1 indicates that 'pos' is outside the voronoi cell, and there is a lattice site closer than the origin Values of 1<=n<=7 indicate that there n lattice sites equally as close as the origin

Definition at line 541 of file Lattice.cc.

Eigen::MatrixXd const& CASM::Lattice::voronoi_table ( ) const

inline

Return voronoi table, which specifies outward-pointing normals of Lattice Voronoi cell. outward-pointing normals are given as rows of the matrix, and defined such that if (voronoi_table()*coord.cart()).maxCoeff()>1, then 'coord' is outside of the voronoi cell.

Definition at line 90 of file Lattice.hh.

Friends And Related Function Documentation

Eigen::Matrix3i canonical_hnf ( const Eigen::Matrix3i &  T, const SymGroup &  effective_pg, const Lattice &  ref_lattice  )

related

Return canonical hermite normal form of the supercell matrix.

Returns

Eigen::Matrix3i of H in canonical form

Parameters

T	A supercell matrix (Eigen::Matrix3i), such that S = U*T, where S is the superlattice and U the unit lattice, as column vector matrices
ref_lattice	The lattice the transformation matrix T is meant to be acting on
effective_pg	Group of symmetry operations to use for determining whether a canonical HNF matrix has been found. This is probably the point group of a structure or configuration Canonical form is such that T is in Hermite normal form (as from CASM::hermite_normal_form), and the unrolled coefficients [a f e] [0 b d] -> abcdef [0 0 c] form the highest lexicographic order when considering equivalent superlattices by point group operations.

• Equivalent superlattices can be obtained using point group operations: S' = op*S = U*H*V, where V is integer and has determinant +/- 1
• Substituting S = U*T, we have op*U*T = U*H*V.
• Or H*V = U.inverse*op*U*T, which is the hermite normal form of U.inverse*op*U*T
• So T is canonical if it is in hermite normal form and for all point group operations it has a higher lexicographic order than the resulting H

Definition at line 653 of file SupercellEnumerator.cc.

Lattice replace_vector ( const Lattice &  lat, const Eigen::Vector3d &  new_vector, double  tol  )

related

Returns a minimum volume Lattice obtainable by replacing one Lattice vector with tau.

• No guarantee on the result being canonical in any way

Definition at line 1214 of file Lattice.cc.

Member Data Documentation

friend CASM::Lattice::Comparisons< Lattice >

private

Definition at line 253 of file Lattice.hh.

double CASM::Lattice::m_inner_voronoi_radius

mutableprivate

Definition at line 261 of file Lattice.hh.

Eigen::Matrix3d CASM::Lattice::m_inv_lat_mat

private

Definition at line 269 of file Lattice.hh.

Eigen::Matrix3d CASM::Lattice::m_lat_mat

private

Definition at line 269 of file Lattice.hh.

Eigen::MatrixXd CASM::Lattice::m_voronoi_table

mutableprivate

Definition at line 262 of file Lattice.hh.

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

• /Users/bpuchala/Work/codes/CASMcode_v0.2.X_reference/include/casm/crystallography/Lattice.hh
• /Users/bpuchala/Work/codes/CASMcode_v0.2.X_reference/include/casm/crystallography/Lattice_impl.hh
• /Users/bpuchala/Work/codes/CASMcode_v0.2.X_reference/src/casm/crystallography/Lattice.cc
• /Users/bpuchala/Work/codes/CASMcode_v0.2.X_reference/src/casm/crystallography/SupercellEnumerator.cc