Lattice

Detailed Description

Relates to Lattice.

Modules
	Lattice Enumerators
	Enumerates Lattice.

Classes
class	CASM::xtal::Lattice
class	CASM::xtal::LatticeIsEquivalent
	Lattice comparisons. More...
class	CASM::xtal::StrainCostCalculator
class	CASM::xtal::NiggliRep

Functions
double	CASM::xtal::volume (const Lattice &lat)
	Returns the volume of a Lattice. More...
std::pair< bool, Eigen::Matrix3d >	CASM::xtal::is_superlattice (const Lattice &scel, const Lattice &unit, double tol)
	Check if scel is a superlattice of unitcell unit and some integer transformation matrix T. More...
std::istream &	CASM::xtal::operator>> (std::istream &in, const Lattice &lattice_in)
Lattice	CASM::xtal::make_superduperlattice (const Lattice &lat1, const Lattice &lat2)
	returns Lattice that is smallest possible superlattice of both input Lattice More...
Eigen::Matrix3d	CASM::xtal::cart2frac (const Eigen::Ref< const Eigen::Matrix3d > &cart_mat, const Lattice &lat)
	Returns 'frac_mat' which is transformation of 'cart_mat' if cart_vec_after = cart_mat*cart_vec then frac_vec_after = frac_mat*frac_vec where cart_vec = lat.lat_column_mat()*frac_vec and cart_vec_after = lat.lat_column_mat()*frac_vec_after. More...
Eigen::Matrix3d	CASM::xtal::frac2cart (const Eigen::Ref< const Eigen::Matrix3d > &frac_mat, const Lattice &lat)
	Returns 'cart_mat' which is transformation of 'frac_mat' if cart_vec_after = cart_mat*cart_vec then frac_vec_after = frac_mat*frac_vec where cart_vec = lat.lat_column_mat()*frac_vec and cart_vec_after = lat.lat_column_mat()*frac_vec_after. More...
template<typename IntegralType , int Options = 0>
Lattice	CASM::xtal::make_superlattice (const Lattice &lat, const Eigen::Matrix< IntegralType, 3, 3, Options > &transf_mat)
	Returns a super Lattice. Transformation matrix must be integer. More...
Lattice	replace_vector (const Lattice &lat, const Eigen::Vector3d &new_vector, double tol)
	Returns a minimum volume Lattice obtainable by replacing one Lattice vector. More...

Function Documentation

cart2frac()

Eigen::Matrix3d CASM::xtal::cart2frac ( const Eigen::Ref< const Eigen::Matrix3d > &  cart_mat, const Lattice &  lat  )

inline

Returns 'frac_mat' which is transformation of 'cart_mat' if cart_vec_after = cart_mat*cart_vec then frac_vec_after = frac_mat*frac_vec where cart_vec = lat.lat_column_mat()*frac_vec and cart_vec_after = lat.lat_column_mat()*frac_vec_after.

Definition at line 258 of file Lattice.hh.

frac2cart()

Eigen::Matrix3d CASM::xtal::frac2cart ( const Eigen::Ref< const Eigen::Matrix3d > &  frac_mat, const Lattice &  lat  )

inline

Returns 'cart_mat' which is transformation of 'frac_mat' if cart_vec_after = cart_mat*cart_vec then frac_vec_after = frac_mat*frac_vec where cart_vec = lat.lat_column_mat()*frac_vec and cart_vec_after = lat.lat_column_mat()*frac_vec_after.

Definition at line 270 of file Lattice.hh.

is_superlattice()

std::pair< bool, Eigen::Matrix3d > CASM::xtal::is_superlattice	(	const Lattice &	scel,
		const Lattice &	unit,
		double	tol
	)

Check if scel is a superlattice of unitcell unit and some integer transformation matrix T.

Check if scel is a superlattice of unitcell unit and some integer transformation matrix T

Definition at line 836 of file Lattice.cc.

make_superduperlattice()

Lattice CASM::xtal::make_superduperlattice	(	const Lattice &	lat1,
		const Lattice &	lat2
	)

returns Lattice that is smallest possible superlattice of both input Lattice

Definition at line 783 of file Lattice.cc.

make_superlattice()

template<typename IntegralType , int Options = 0>

Lattice CASM::xtal::make_superlattice	(	const Lattice &	lat,
		const Eigen::Matrix< IntegralType, 3, 3, Options > &	transf_mat
	)

Returns a super Lattice. Transformation matrix must be integer.

Definition at line 287 of file Lattice.hh.

operator>>()

std::istream& CASM::xtal::operator>>	(	std::istream &	in,
		const Lattice &	lattice_in
	)

replace_vector()

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.

• No guarantee on the result being canonical in any way

Definition at line 812 of file Lattice.cc.

volume()

double CASM::xtal::volume ( const Lattice &  lat )

inline

Returns the volume of a Lattice.

Small class that describes a superlattice. Contains the superlattice, the primitive tiling unit, and the integer transformation matrix to convert from the tiling unit to the superlattice.

Returns

volume of the Lattice

Parameters

lat

a Lattice

Definition at line 281 of file Lattice.hh.