#include <BiCrystal.h>

Inheritance diagram for oILAB::BiCrystal< dim >:

Public Member Functions
LatticeVector< dim >	shiftTensorA (const LatticeVector< dim > &d) const

LatticeVector< dim >	shiftTensorB (const LatticeVector< dim > &d) const

	BiCrystal (const Lattice< dim > &A, const Lattice< dim > &B, const bool &useRLLL=false)
	Constructs a bicrystal from two lattices \(\mathcal A \) and \(\mathcal B \) by computing the parallel bases \(\textbf A^\\|, \textbf B^\\|, \textbf C^\\|, \textbf D^\\|\) for lattices \(\mathcal A, \mathcal B, \mathcal C, \mathcal D\), respectively. If the flag useRLLL is .true., then the bases of CSL and DSCL are reduced using the LLL algorithm.

LatticeVector< dim >	getLatticeVectorInA (const LatticeVector< dim > &v) const

LatticeVector< dim >	getLatticeVectorInB (const LatticeVector< dim > &v) const

LatticeVector< dim >	getLatticeVectorInD (const LatticeVector< dim > &v) const

LatticeDirection< dim >	getLatticeDirectionInC (const LatticeVector< dim > &v) const

LatticeDirection< dim >	getLatticeDirectionInD (const LatticeVector< dim > &v) const

ReciprocalLatticeDirection< dim >	getReciprocalLatticeDirectionInA (const ReciprocalLatticeVector< dim > &v) const

ReciprocalLatticeDirection< dim >	getReciprocalLatticeDirectionInB (const ReciprocalLatticeVector< dim > &v) const

ReciprocalLatticeDirection< dim >	getReciprocalLatticeDirectionInC (const ReciprocalLatticeVector< dim > &v) const

ReciprocalLatticeDirection< dim >	getReciprocalLatticeDirectionInD (const ReciprocalLatticeVector< dim > &v) const

template<int dm = dim>
std::enable_if< dm==2\|\|dm==3, std::map< IntScalarType, Gb< dm > > >::type	generateGrainBoundaries (const LatticeDirection< dim > &d, int div=30) const
	Given a tilt axis \(\textbf d\), that belongs to lattices \(\mathcal A\) or \(\mathcal B\), this function generate a set of tilt GBs. CURRENTLY ONLY WORDS FOR DIMENSION 3.

template<int dm = dim>
std::enable_if< dm==2\|\|dm==3, std::vector< LatticeVector< dim > > >::type	box (std::vector< LatticeVector< dim > > &boxVectors, const double &orthogonality, const int &dsclFactor, std::string filename="", bool orient=false) const

Public Member Functions inherited from oILAB::RationalMatrix< dim >
	RationalMatrix (const MatrixDimD &R)

	RationalMatrix (const MatrixDimI &Rn, const IntScalarType &Rd)

	RationalMatrix (const MatrixDimI &Rn, const MatrixDimI &Rd)

MatrixDimD	asMatrix () const

Public Member Functions inherited from oILAB::SmithDecomposition< dim >
	SmithDecomposition (const MatrixNi &A)

const MatrixNi &	matrixU () const

const MatrixNi &	matrixD () const

const MatrixNi &	matrixV () const

const MatrixNi &	matrixX () const

const MatrixNi &	matrixY () const

Data Fields
const Lattice< dim > &	A

const Lattice< dim > &	B

const MatrixDimI	M
	Integer matrix that connects the bases \( \textbf A^{\\|} \) and \( \textbf C^{\\|} \) of lattices \(\mathcal A\) and the CSL \(\mathcal C\), respectively: \( \textbf C^{\\|} = \textbf A^{\\|} \textbf M\).

const MatrixDimI	N
	Integer matrix that connects the bases \( \textbf B^{\\|} \) and \( \textbf C^{\\|} \) of lattices \(\mathcal B\) and the CSL \(\mathcal C\), respectively: \( \textbf C^{\\|} = \textbf B^{\\|} \textbf N\).

const IntScalarType	sigmaA
	Signed ratio of the unit cell volume of \(\mathcal C\) to that of \(\mathcal A\). \( \Sigma_{\mathcal A} = \det(\textbf M)\).

const IntScalarType	sigmaB
	Signed ratio of the unit cell volume of \(\mathcal C\) to that of \(\mathcal B\): \( \Sigma_{\mathcal B} = \det(\textbf N)\).

const int	sigma
	\( \Sigma = \|\Sigma_{\mathcal A}\|\) if \( \Sigma_{\mathcal A} = \Sigma_{\mathcal B}\), else \( \Sigma = 0 \)

const Lattice< dim >	csl
	CSL lattice \(\mathcal C\).

const Lattice< dim >	dscl
	DCSL lattice \(\mathcal D\).

const Lattice< dim >	Ap
	Lattice \(\mathcal A\) with basis \(\textbf A^\\|\).

const Lattice< dim >	Bp
	Lattice \(\mathcal B\) with basis \(\textbf B^\\|\).

const MatrixDimI	LambdaA
	Shift tensor \(\Lambda_{\mathcal A}:\mathbb Z_{\mathcal D} \to \mathbb Z_{\mathcal D}\) describes the shift in the CSL when lattice \(\mathcal A\) is shifted by a DSCL vector.

const MatrixDimI	LambdaB
	Shift tensor \(\Lambda_{\mathcal B}:\mathbb Z_{\mathcal D} \to \mathbb Z_{\mathcal D}\) describes the shift in the CSL when lattice \(\mathcal B\) is shifted by a DSCL vector.

Data Fields inherited from oILAB::RationalMatrix< dim >
const MatrixDimI &	integerMatrix

const IntScalarType &	mu

Private Types
typedef LatticeCore< dim >::IntScalarType	IntScalarType

typedef LatticeCore< dim >::VectorDimD	VectorDimD

typedef LatticeCore< dim >::MatrixDimD	MatrixDimD

typedef LatticeCore< dim >::VectorDimI	VectorDimI

typedef LatticeCore< dim >::MatrixDimI	MatrixDimI

Static Private Member Functions
static MatrixDimI	getM (const RationalMatrix< dim > &rm, const SmithDecomposition< dim > &sd)

static MatrixDimI	getN (const RationalMatrix< dim > &rm, const SmithDecomposition< dim > &sd)

static MatrixDimI	getLambdaA (const MatrixDimI &M, const MatrixDimI &N)

static MatrixDimI	getLambdaB (const MatrixDimI &M, const MatrixDimI &N)

static MatrixDimD	getCSLBasis (const Lattice< dim > &A, const Lattice< dim > &B, const SmithDecomposition< dim > &sd, const MatrixDimI &M, const MatrixDimI &N)

static MatrixDimD	getDSCLBasis (const Lattice< dim > &A, const Lattice< dim > &B, const SmithDecomposition< dim > &sd, const MatrixDimI &M, const MatrixDimI &N)

Private Attributes
const Lattice< dim >	cslp
	Lattice \(\mathcal C\) with basis \(\textbf C^\\|\).

const Lattice< dim >	dsclp
	Lattice \(\mathcal D\) with basis \(\textbf D^\\|\).

const MatrixDimI	dscl2dsclp
	Maps integer coordinates w.r.t \(\textbf D\) basis to integer coordinates w.r.t parallel basis \(\textbf D^\\|\).

const MatrixDimI	csl2cslp
	Maps integer coordinates w.r.t \(\textbf C\) basis to integer coordinates w.r.t parallel basis \(\textbf C^\\|\).

Detailed Description

template<int dim>
class oILAB::BiCrystal< dim >

Class template that computes the coincident-site-lattice (CSL) of two parent lattices using the Smith Normal Form [1].

[1] Coincidence Lattices and Associated Shear Transformations

Examples: testCoincidentRotations.cpp, testGb.cpp, testGb3d.cpp, testGenerateGBs.cpp, testMoire.cpp, and testSNF.cpp.

Definition at line 25 of file BiCrystal.h.

Member Typedef Documentation

◆ IntScalarType

template<int dim>

typedef LatticeCore<dim>::IntScalarType oILAB::BiCrystal< dim >::IntScalarType

private

Definition at line 28 of file BiCrystal.h.

◆ MatrixDimD

template<int dim>

typedef LatticeCore<dim>::MatrixDimD oILAB::BiCrystal< dim >::MatrixDimD

private

Definition at line 30 of file BiCrystal.h.

◆ MatrixDimI

template<int dim>

typedef LatticeCore<dim>::MatrixDimI oILAB::BiCrystal< dim >::MatrixDimI

private

Definition at line 32 of file BiCrystal.h.

◆ VectorDimD

template<int dim>

typedef LatticeCore<dim>::VectorDimD oILAB::BiCrystal< dim >::VectorDimD

private

Definition at line 29 of file BiCrystal.h.

◆ VectorDimI

template<int dim>

typedef LatticeCore<dim>::VectorDimI oILAB::BiCrystal< dim >::VectorDimI

private

Definition at line 31 of file BiCrystal.h.

Constructor & Destructor Documentation

◆ BiCrystal()

template<int dim>

oILAB::BiCrystal< dim >::BiCrystal	(	const Lattice< dim > &	A,
		const Lattice< dim > &	B,
		const bool &	useRLLL = `false`
	)

Constructs a bicrystal from two lattices \(\mathcal A \) and \(\mathcal B \) by computing the parallel bases \(\textbf A^\|, \textbf B^\|, \textbf C^\|, \textbf D^\|\) for lattices \(\mathcal A, \mathcal B, \mathcal C, \mathcal D\), respectively. If the flag useRLLL is .true., then the bases of CSL and DSCL are reduced using the LLL algorithm.

Parameters

[in] Lattices \(\mathcal A \) and \(\mathcal B \), and useRLLL flag

Returns: A bicrystal object

Definition at line 161 of file BiCrystal.cpp.

Member Function Documentation

◆ box()

template<int dim>

template<int dm>

template std::vector< LatticeVector< 3 > > oILAB::BiCrystal< dim >::box< 3 >	(	std::vector< LatticeVector< dim > > &	boxVectors,
		const double &	orthogonality,
		const int &	dsclFactor,
		std::string	filename = `""`,
		bool	orient = `false`
	)		const

This function outputs/prints a 2D bicrystal (two lattices that form the GB and the CSL) bounded by a box defined using two input box vectors. The box vectors have to be linearly independent lattice vectors. The function optimizes boxVectors[0] to make the box as orthogonal as possible depending on the orthogonality parameter.

Template Parameters

dm	dimension (int)

Parameters

boxVectors	two linearly independent lattice vectors.
orthogonality	(double) a value in the interval \([0,1]\).
filename	(optional) name of the output file
orient	(optional) While printing to a file, orient the system such that one of the box sides is along the global x axis. This flag does not influence the returning configuration, only the configuration printed to the file.

Returns: lattice points of the bicrystal (along with the CSL) bounded by the box (std::vector<LatticeVector<2>>).

Definition at line 520 of file BiCrystal.cpp.

◆ generateGrainBoundaries()

template<int dim>

template<int dm>

template std::map< BiCrystal< 3 >::IntScalarType, Gb< 3 > > oILAB::BiCrystal< dim >::generateGrainBoundaries< 3 >	(	const LatticeDirection< dim > &	d,
		int	div = `30`
	)		const

Given a tilt axis \(\textbf d\), that belongs to lattices \(\mathcal A\) or \(\mathcal B\), this function generate a set of tilt GBs. CURRENTLY ONLY WORDS FOR DIMENSION 3.

Template Parameters

dm

Parameters

d	- LatticeDirection that describes the tilt axis
div	- parameter to span the GBs

Returns: A data structure that stores GBs sorted in increasing order of their inclination angle.

Examples: testGenerateGBs.cpp.

Definition at line 466 of file BiCrystal.cpp.

◆ getCSLBasis()

template<int dim>

BiCrystal< dim >::MatrixDimD oILAB::BiCrystal< dim >::getCSLBasis	(	const Lattice< dim > &	A,
		const Lattice< dim > &	B,
		const SmithDecomposition< dim > &	sd,
		const MatrixDimI &	M,
		const MatrixDimI &	N
	)

staticprivate

Definition at line 82 of file BiCrystal.cpp.

◆ getDSCLBasis()

template<int dim>

BiCrystal< dim >::MatrixDimD oILAB::BiCrystal< dim >::getDSCLBasis	(	const Lattice< dim > &	A,
		const Lattice< dim > &	B,
		const SmithDecomposition< dim > &	sd,
		const MatrixDimI &	M,
		const MatrixDimI &	N
	)

staticprivate

Definition at line 133 of file BiCrystal.cpp.

◆ getLambdaA()

template<int dim>

BiCrystal< dim >::MatrixDimI oILAB::BiCrystal< dim >::getLambdaA	(	const MatrixDimI &	M,
		const MatrixDimI &	N
	)

staticprivate

Definition at line 42 of file BiCrystal.cpp.

◆ getLambdaB()

template<int dim>

BiCrystal< dim >::MatrixDimI oILAB::BiCrystal< dim >::getLambdaB	(	const MatrixDimI &	M,
		const MatrixDimI &	N
	)

staticprivate

Definition at line 62 of file BiCrystal.cpp.

◆ getLatticeDirectionInC()

template<int dim>

LatticeDirection< dim > oILAB::BiCrystal< dim >::getLatticeDirectionInC ( const LatticeVector< dim > & v ) const

Outputs lattice direction in the CSL \(\mathcal C\) that is parallel to the inputted vector \(\textbf v\) that belongs to one of the four lattices, \(\mathcal A\), \(\mathcal B\), \(\mathcal C\), or \(\mathcal D\),

Parameters

v	- lattice vector

Returns: LatticeDirection in \(\mathcal C\)

Examples: testGb3d.cpp, and testGenerateGBs.cpp.

Definition at line 306 of file BiCrystal.cpp.

◆ getLatticeDirectionInD()

template<int dim>

LatticeDirection< dim > oILAB::BiCrystal< dim >::getLatticeDirectionInD ( const LatticeVector< dim > & v ) const

Outputs lattice direction in the DSCL \(\mathcal D\) that is parallel to the inputted vector \(\textbf v\) that belongs to one of the four lattices, \(\mathcal A\), \(\mathcal B\), \(\mathcal C\), or \(\mathcal D\),

Parameters

v	- lattice vector

Returns: LatticeDirection in \(\mathcal D\)

Examples: testGenerateGBs.cpp.

Definition at line 336 of file BiCrystal.cpp.

◆ getLatticeVectorInA()

template<int dim>

LatticeVector< dim > oILAB::BiCrystal< dim >::getLatticeVectorInA ( const LatticeVector< dim > & v ) const

Outputs lattice vector in lattice \(\mathcal A\) that is equal to the inputted vector \(\textbf v\) that belongs to \(\mathcal A\) or \(\mathcal C\)

Parameters

v	- lattice vector

Returns: LatticeVector in \(\mathcal A\)

Definition at line 238 of file BiCrystal.cpp.

◆ getLatticeVectorInB()

template<int dim>

LatticeVector< dim > oILAB::BiCrystal< dim >::getLatticeVectorInB ( const LatticeVector< dim > & v ) const

Outputs lattice vector in lattice \(\mathcal B\) that is equal to the inputted vector \(\textbf v\) that belongs to \(\mathcal B\) or \(\mathcal C\)

Parameters

v	- lattice vector

Returns: LatticeVector in \(\mathcal B\)

Definition at line 256 of file BiCrystal.cpp.

◆ getLatticeVectorInD()

template<int dim>

LatticeVector< dim > oILAB::BiCrystal< dim >::getLatticeVectorInD ( const LatticeVector< dim > & v ) const

Outputs lattice vector in lattice \(\mathcal D\) that is equal to the inputted vector \(\textbf v\) that belongs to \(\mathcal A\), \(\mathcal B\), \(\mathcal C\), or \(\mathcal D\)

Parameters

v	- lattice vector

Returns: LatticeVector in \(\mathcal D\)

Definition at line 274 of file BiCrystal.cpp.

◆ getM()

template<int dim>

BiCrystal< dim >::MatrixDimI oILAB::BiCrystal< dim >::getM	(	const RationalMatrix< dim > &	rm,
		const SmithDecomposition< dim > &	sd
	)

staticprivate

Definition at line 17 of file BiCrystal.cpp.

◆ getN()

template<int dim>

BiCrystal< dim >::MatrixDimI oILAB::BiCrystal< dim >::getN	(	const RationalMatrix< dim > &	rm,
		const SmithDecomposition< dim > &	sd
	)

staticprivate

Definition at line 29 of file BiCrystal.cpp.

◆ getReciprocalLatticeDirectionInA()

template<int dim>

ReciprocalLatticeDirection< dim > oILAB::BiCrystal< dim >::getReciprocalLatticeDirectionInA ( const ReciprocalLatticeVector< dim > & v ) const

Outputs reciprocal lattice direction in the dual lattice \(\mathcal A^*\) that is parallel to the inputted reciprocal vector \(\textbf v\) that belongs to one of the four dual lattices, \(\mathcal A^*\), \(\mathcal B^*\), \(\mathcal C^*\), or \(\mathcal D^*\),

Parameters

v	- lattice vector

Returns: ReciprocalLatticeDirection in \(\mathcal A^*\)

Definition at line 342 of file BiCrystal.cpp.

◆ getReciprocalLatticeDirectionInB()

template<int dim>

ReciprocalLatticeDirection< dim > oILAB::BiCrystal< dim >::getReciprocalLatticeDirectionInB ( const ReciprocalLatticeVector< dim > & v ) const

Outputs reciprocal lattice direction in the dual lattice \(\mathcal B^*\) that is parallel to the inputted reciprocal vector \(\textbf v\) that belongs to one of the four dual lattices, \(\mathcal A^*\), \(\mathcal B^*\), \(\mathcal C^*\), or \(\mathcal D^*\),

Parameters

v	- lattice vector

Returns: ReciprocalLatticeDirection in \(\mathcal B^*\)

Definition at line 370 of file BiCrystal.cpp.

◆ getReciprocalLatticeDirectionInC()

template<int dim>

ReciprocalLatticeDirection< dim > oILAB::BiCrystal< dim >::getReciprocalLatticeDirectionInC ( const ReciprocalLatticeVector< dim > & v ) const

Outputs reciprocal lattice direction in the dual lattice \(\mathcal C^*\) that is parallel to the inputted reciprocal vector \(\textbf v\) that belongs to one of the four dual lattices, \(\mathcal A^*\), \(\mathcal B^*\), \(\mathcal C^*\), or \(\mathcal D^*\),

Parameters

v	- lattice vector

Returns: ReciprocalLatticeDirection in \(\mathcal C^*\)

Examples: testGenerateGBs.cpp.

Definition at line 400 of file BiCrystal.cpp.

◆ getReciprocalLatticeDirectionInD()

template<int dim>

ReciprocalLatticeDirection< dim > oILAB::BiCrystal< dim >::getReciprocalLatticeDirectionInD ( const ReciprocalLatticeVector< dim > & v ) const

Outputs reciprocal lattice direction in the dual lattice \(\mathcal D^*\) that is parallel to the inputted reciprocal vector \(\textbf v\) that belongs to one of the four dual lattices, \(\mathcal A^*\), \(\mathcal B^*\), \(\mathcal C^*\), or \(\mathcal D^*\),

Parameters

v	- lattice vector

Returns: ReciprocalLatticeDirection in \(\mathcal D^*\)

Definition at line 425 of file BiCrystal.cpp.

◆ shiftTensorA()

template<int dim>

LatticeVector< dim > oILAB::BiCrystal< dim >::shiftTensorA ( const LatticeVector< dim > & d ) const

Definition at line 449 of file BiCrystal.cpp.

◆ shiftTensorB()

template<int dim>

LatticeVector< dim > oILAB::BiCrystal< dim >::shiftTensorB ( const LatticeVector< dim > & d ) const

Definition at line 457 of file BiCrystal.cpp.

Field Documentation

◆ A

template<int dim>

const Lattice<dim>& oILAB::BiCrystal< dim >::A

Examples: testGb3d.cpp, and testGenerateGBs.cpp.

Definition at line 52 of file BiCrystal.h.

◆ Ap

template<int dim>

const Lattice<dim> oILAB::BiCrystal< dim >::Ap

Lattice \(\mathcal A\) with basis \(\textbf A^\|\).

Examples: testMoire.cpp.

Definition at line 110 of file BiCrystal.h.

◆ B

template<int dim>

const Lattice<dim>& oILAB::BiCrystal< dim >::B

Definition at line 53 of file BiCrystal.h.

◆ Bp

template<int dim>

const Lattice<dim> oILAB::BiCrystal< dim >::Bp

Lattice \(\mathcal B\) with basis \(\textbf B^\|\).

Examples: testMoire.cpp.

Definition at line 114 of file BiCrystal.h.

◆ csl

template<int dim>

const Lattice<dim> oILAB::BiCrystal< dim >::csl

CSL lattice \(\mathcal C\).

Examples: testGb.cpp, testGb3d.cpp, testGenerateGBs.cpp, and testMoire.cpp.

Definition at line 102 of file BiCrystal.h.

◆ csl2cslp

template<int dim>

const MatrixDimI oILAB::BiCrystal< dim >::csl2cslp

private

Maps integer coordinates w.r.t \(\textbf C\) basis to integer coordinates w.r.t parallel basis \(\textbf C^\|\).

Definition at line 97 of file BiCrystal.h.

◆ cslp

template<int dim>

const Lattice<dim> oILAB::BiCrystal< dim >::cslp

private

Lattice \(\mathcal C\) with basis \(\textbf C^\|\).

Definition at line 83 of file BiCrystal.h.

◆ dscl

template<int dim>

const Lattice<dim> oILAB::BiCrystal< dim >::dscl

DCSL lattice \(\mathcal D\).

Examples: testGb.cpp, testGenerateGBs.cpp, and testMoire.cpp.

Definition at line 106 of file BiCrystal.h.

◆ dscl2dsclp

template<int dim>

const MatrixDimI oILAB::BiCrystal< dim >::dscl2dsclp

private

Maps integer coordinates w.r.t \(\textbf D\) basis to integer coordinates w.r.t parallel basis \(\textbf D^\|\).

Definition at line 92 of file BiCrystal.h.

◆ dsclp

template<int dim>

const Lattice<dim> oILAB::BiCrystal< dim >::dsclp

private

Lattice \(\mathcal D\) with basis \(\textbf D^\|\).

Definition at line 87 of file BiCrystal.h.

◆ LambdaA

template<int dim>

const MatrixDimI oILAB::BiCrystal< dim >::LambdaA

Shift tensor \(\Lambda_{\mathcal A}:\mathbb Z_{\mathcal D} \to \mathbb Z_{\mathcal D}\) describes the shift in the CSL when lattice \(\mathcal A\) is shifted by a DSCL vector.

Examples: testGenerateGBs.cpp, testMoire.cpp, and testSNF.cpp.

Definition at line 119 of file BiCrystal.h.

◆ LambdaB

template<int dim>

const MatrixDimI oILAB::BiCrystal< dim >::LambdaB

Shift tensor \(\Lambda_{\mathcal B}:\mathbb Z_{\mathcal D} \to \mathbb Z_{\mathcal D}\) describes the shift in the CSL when lattice \(\mathcal B\) is shifted by a DSCL vector.

Examples: testSNF.cpp.

Definition at line 124 of file BiCrystal.h.

◆ M

template<int dim>

const MatrixDimI oILAB::BiCrystal< dim >::M

Integer matrix that connects the bases \( \textbf A^{\|} \) and \( \textbf C^{\|} \) of lattices \(\mathcal A\) and the CSL \(\mathcal C\), respectively: \( \textbf C^{\|} = \textbf A^{\|} \textbf M\).

Definition at line 58 of file BiCrystal.h.

◆ N

template<int dim>

const MatrixDimI oILAB::BiCrystal< dim >::N

Integer matrix that connects the bases \( \textbf B^{\|} \) and \( \textbf C^{\|} \) of lattices \(\mathcal B\) and the CSL \(\mathcal C\), respectively: \( \textbf C^{\|} = \textbf B^{\|} \textbf N\).

Definition at line 63 of file BiCrystal.h.

◆ sigma

template<int dim>

const int oILAB::BiCrystal< dim >::sigma

\( \Sigma = |\Sigma_{\mathcal A}|\) if \( \Sigma_{\mathcal A} = \Sigma_{\mathcal B}\), else \( \Sigma = 0 \)

Examples: testCoincidentRotations.cpp, testGb3d.cpp, and testGenerateGBs.cpp.

Definition at line 78 of file BiCrystal.h.

◆ sigmaA

template<int dim>

const IntScalarType oILAB::BiCrystal< dim >::sigmaA

Signed ratio of the unit cell volume of \(\mathcal C\) to that of \(\mathcal A\). \( \Sigma_{\mathcal A} = \det(\textbf M)\).

Examples: testMoire.cpp, and testSNF.cpp.

Definition at line 68 of file BiCrystal.h.

◆ sigmaB

template<int dim>

const IntScalarType oILAB::BiCrystal< dim >::sigmaB

Signed ratio of the unit cell volume of \(\mathcal C\) to that of \(\mathcal B\): \( \Sigma_{\mathcal B} = \det(\textbf N)\).

Examples: testMoire.cpp, and testSNF.cpp.

Definition at line 73 of file BiCrystal.h.

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

include/Lattices/BiCrystal.h
src/Lattices/BiCrystal.cpp

Public Member Functions

Data Fields

Private Types

Static Private Member Functions

Private Attributes

Detailed Description

Member Typedef Documentation

◆ IntScalarType

◆ MatrixDimD

◆ MatrixDimI

◆ VectorDimD

◆ VectorDimI

Constructor & Destructor Documentation

◆ BiCrystal()

Member Function Documentation

◆ box()

◆ generateGrainBoundaries()

◆ getCSLBasis()

◆ getDSCLBasis()

◆ getLambdaA()

◆ getLambdaB()

◆ getLatticeDirectionInC()

◆ getLatticeDirectionInD()

◆ getLatticeVectorInA()

◆ getLatticeVectorInB()

◆ getLatticeVectorInD()

◆ getM()

◆ getN()

◆ getReciprocalLatticeDirectionInA()

◆ getReciprocalLatticeDirectionInB()

◆ getReciprocalLatticeDirectionInC()

◆ getReciprocalLatticeDirectionInD()

◆ shiftTensorA()

◆ shiftTensorB()

Field Documentation

◆ A

◆ Ap

◆ B

◆ Bp

◆ csl

◆ csl2cslp

◆ cslp

◆ dscl

◆ dscl2dsclp

◆ dsclp

◆ LambdaA

◆ LambdaB

◆ M

◆ N

◆ sigma

◆ sigmaA

◆ sigmaB