occ::crystal::UnitCell Class Reference

This class represents a unit cell of a crystal lattice. More...

#include <unitcell.h>

Public Member Functions
	UnitCell ()
	UnitCell (double a, double b, double c, double alpha, double beta, double gamma)
	UnitCell (const Vec3 &lengths, const Vec3 &angles)
	UnitCell (const Mat3 &vectors)
	Construct from a matrix of lattice vectors (columns = a, b, c).
double	a () const
	the length of the a-axis in Angstroms
double	b () const
	the length of the b-axis in Angstroms
double	c () const
	the length of the c-axis in Angstroms
double	alpha () const
	angle \(\alpha\), i.e. the angle between the b- and c-axes in radians
double	beta () const
	angle \(\beta\), i.e. the angle between the a- and c-axes in radians
double	gamma () const
	angle \(\gamma\), i.e. the angle between the a- and b-axes in radians
double	volume () const
	Volume of the unit cell in cubic Angstroms.
Mat3	metric_tensor () const
Mat3	reciprocal_metric_tensor () const
void	set_a (double a)
	Set the length of the a-axis.
void	set_b (double b)
	Set the length of the b-axis.
void	set_c (double c)
	Set the length of the c-axis.
void	set_alpha (double alpha)
	Set the angle of between the b- and c-axes.
void	set_beta (double beta)
	Set the angle of between the a- and c-axes.
void	set_gamma (double gamma)
	Set the angle of between the a- and b-axes.
bool	is_cubic () const
	Check if cubic i.e. \( a=b=c, \alpha=\beta=\gamma \).
bool	is_triclinic () const
	Check if triclinic i.e.
bool	is_monoclinic () const
	Check if monoclinic i.e.
bool	is_orthorhombic () const
	Check if orthorhombic i.e.
bool	is_tetragonal () const
	Check if tetragonal i.e.
bool	is_rhombohedral () const
	Check if rhombohedral i.e.
bool	is_hexagonal () const
	Check if hexagonal i.e.
bool	is_orthogonal () const
	Check if orthogonal i.e. \(\alpha = \beta = \gamma = 90^\circ\).
std::string	cell_type () const
	String representing the type of cell e.g. "monoclinic".
auto	to_cartesian (const Mat3N &coords) const
	Convert a given matrix of coordinates from fractional to Cartesian.
Mat3	adp_adhoc_direct () const
	Calculate the direct matrix for ADP transformations.
Mat3	adp_adhoc_inverse () const
	Calculate the inverse matrix for ADP transformations.
Mat6N	to_fractional_adp (const Mat6N &adp) const
	Convert ADPs from Cartesian to fractional coordinates.
Mat6N	to_cartesian_adp (const Mat6N &adp) const
	Convert ADPs from fractional to Cartesian coordinates.
auto	to_fractional (const Mat3N &coords) const
	Convert a given matrix of coordinates from Cartesian to fractional.
auto	to_reciprocal (const Mat3N &coords) const
	Convert a given matrix of coordinates from Cartesian to fractional.
const auto &	direct () const
	The direct matrix of this unit cell (columns are lattice vectors)
const auto &	reciprocal () const
	The reciprocal matrix of this unit cell (columns are reciprocal lattice vectors)
const auto &	inverse () const
	The inverse matrix of this unit cell (rows are reciprocal lattice vectors)
auto	a_vector () const
	the \(\bf{a}\) lattice vector
auto	b_vector () const
	the \(\bf{b}\) lattice vector
auto	c_vector () const
	the \(\bf{c}\) lattice vector
auto	a_star_vector () const
	the \(\bf{a^*}\) vector in reciprocal lattice
auto	b_star_vector () const
	the \(\bf{b^*}\) vector in reciprocal lattice
auto	c_star_vector () const
	the \(\bf{c^*}\) vector in reciprocal lattice
const auto &	lengths () const
	Vector of lengths \((a, b, c)\).
const auto &	angles () const
	Vector of lengths \((a, b, c)\).
HKL	hkl_limits (double d_min) const
	Return the maximum fractional coordinates \((h,k,l)\) needed to enclose a sphere of size d_min.

Static Public Member Functions
static UnitCell	from_lattice_vectors (const Mat3 &vectors)
	Construct from a matrix of lattice vectors (columns = a, b, c) while preserving the input direct matrix exactly.

Detailed Description

This class represents a unit cell of a crystal lattice.

A UnitCell describes the lattice vectors of a 3D crystal structure, including the 6 (possibly unique) parameters lengths \((a,b,c)\) and angles \((\alpha, \beta, \gamma)\). It also serves as a utility class for coordinate transforms, and other conversions and checks.

Constructor & Destructor Documentation

UnitCell() [1/4]

occ::crystal::UnitCell::UnitCell

(

)

UnitCell() [2/4]

occ::crystal::UnitCell::UnitCell	(	double	a,
		double	b,
		double	c,
		double	alpha,
		double	beta,
		double	gamma
	)

UnitCell() [3/4]

occ::crystal::UnitCell::UnitCell	(	const Vec3 &	lengths,
		const Vec3 &	angles
	)

UnitCell() [4/4]

occ::crystal::UnitCell::UnitCell

(

const Mat3 &

vectors

)

Construct from a matrix of lattice vectors (columns = a, b, c).

The matrix is canonicalized: only (a, b, c, α, β, γ) are extracted and the direct matrix is rebuilt in the conventional orientation (a along x, b in the xy plane). This loses the original basis orientation.

Member Function Documentation

a()

double occ::crystal::UnitCell::a ( ) const

inline

the length of the a-axis in Angstroms

a_star_vector()

auto occ::crystal::UnitCell::a_star_vector ( ) const

inline

the \(\bf{a^*}\) vector in reciprocal lattice

a_vector()

auto occ::crystal::UnitCell::a_vector ( ) const

inline

the \(\bf{a}\) lattice vector

adp_adhoc_direct()

Mat3 occ::crystal::UnitCell::adp_adhoc_direct

(

)

const

Calculate the direct matrix for ADP transformations.

This method computes the ad hoc direct matrix used specifically for transforming Anisotropic Displacement Parameters (ADPs).

Returns

Mat3 representing the ADP direct transformation matrix

adp_adhoc_inverse()

Mat3 occ::crystal::UnitCell::adp_adhoc_inverse

(

)

const

Calculate the inverse matrix for ADP transformations.

This method computes the ad hoc inverse matrix used specifically for transforming Anisotropic Displacement Parameters (ADPs).

Returns

Mat3 representing the ADP inverse transformation matrix

alpha()

double occ::crystal::UnitCell::alpha ( ) const

inline

angle \(\alpha\), i.e. the angle between the b- and c-axes in radians

angles()

const auto & occ::crystal::UnitCell::angles ( ) const

inline

Vector of lengths \((a, b, c)\).

b()

double occ::crystal::UnitCell::b ( ) const

inline

the length of the b-axis in Angstroms

b_star_vector()

auto occ::crystal::UnitCell::b_star_vector ( ) const

inline

the \(\bf{b^*}\) vector in reciprocal lattice

b_vector()

auto occ::crystal::UnitCell::b_vector ( ) const

inline

the \(\bf{b}\) lattice vector

beta()

double occ::crystal::UnitCell::beta ( ) const

inline

angle \(\beta\), i.e. the angle between the a- and c-axes in radians

c()

double occ::crystal::UnitCell::c ( ) const

inline

the length of the c-axis in Angstroms

c_star_vector()

auto occ::crystal::UnitCell::c_star_vector ( ) const

inline

the \(\bf{c^*}\) vector in reciprocal lattice

c_vector()

auto occ::crystal::UnitCell::c_vector ( ) const

inline

the \(\bf{c}\) lattice vector

cell_type()

std::string occ::crystal::UnitCell::cell_type

(

)

const

String representing the type of cell e.g. "monoclinic".

direct()

const auto & occ::crystal::UnitCell::direct ( ) const

inline

The direct matrix of this unit cell (columns are lattice vectors)

from_lattice_vectors()

static UnitCell occ::crystal::UnitCell::from_lattice_vectors ( const Mat3 &  vectors )

static

Construct from a matrix of lattice vectors (columns = a, b, c) while preserving the input direct matrix exactly.

Use this when the basis orientation matters (e.g. derivatives under affine strain) and must not be silently rotated via (a, b, c, α, β, γ) reconstruction.

gamma()

double occ::crystal::UnitCell::gamma ( ) const

inline

angle \(\gamma\), i.e. the angle between the a- and b-axes in radians

hkl_limits()

HKL occ::crystal::UnitCell::hkl_limits

(

double

d_min

)

const

Return the maximum fractional coordinates \((h,k,l)\) needed to enclose a sphere of size d_min.

Returns

HKL of the limits bounding a given sphere

inverse()

const auto & occ::crystal::UnitCell::inverse ( ) const

inline

The inverse matrix of this unit cell (rows are reciprocal lattice vectors)

is_cubic()

bool occ::crystal::UnitCell::is_cubic

(

)

const

Check if cubic i.e. \( a=b=c, \alpha=\beta=\gamma \).

is_hexagonal()

bool occ::crystal::UnitCell::is_hexagonal

(

)

const

Check if hexagonal i.e.

\( a = b, a \ne c, \alpha = 90^\circ , \gamma = 120^\circ \)

is_monoclinic()

bool occ::crystal::UnitCell::is_monoclinic

(

)

const

Check if monoclinic i.e.

\( a \ne b \ne c, \alpha = \gamma = 90^\circ \ne \beta \)

is_orthogonal()

bool occ::crystal::UnitCell::is_orthogonal ( ) const

inline

Check if orthogonal i.e. \(\alpha = \beta = \gamma = 90^\circ\).

is_orthorhombic()

bool occ::crystal::UnitCell::is_orthorhombic

(

)

const

Check if orthorhombic i.e.

\( a \ne b \ne c, \alpha = \beta = \gamma = 90^\circ \)

is_rhombohedral()

bool occ::crystal::UnitCell::is_rhombohedral

(

)

const

Check if rhombohedral i.e.

\( a = b = c, \alpha = \beta = \gamma \ne 90^\circ \)

is_tetragonal()

bool occ::crystal::UnitCell::is_tetragonal

(

)

const

Check if tetragonal i.e.

\( a = b, a \ne c, \alpha = \beta = \gamma = 90^\circ \)

is_triclinic()

bool occ::crystal::UnitCell::is_triclinic

(

)

const

Check if triclinic i.e.

\( a \ne b \ne c, \alpha \ne \beta \ne \gamma \)

lengths()

const auto & occ::crystal::UnitCell::lengths ( ) const

inline

Vector of lengths \((a, b, c)\).

metric_tensor()

Mat3 occ::crystal::UnitCell::metric_tensor ( ) const

inline

reciprocal()

const auto & occ::crystal::UnitCell::reciprocal ( ) const

inline

The reciprocal matrix of this unit cell (columns are reciprocal lattice vectors)

reciprocal_metric_tensor()

Mat3 occ::crystal::UnitCell::reciprocal_metric_tensor ( ) const

inline

set_a()

void occ::crystal::UnitCell::set_a

(

double

a

)

Set the length of the a-axis.

Parameters

a	new length of the a-axis in Angstroms

Note

Will update other dependent values e.g. volume etc. No checking is performed.

set_alpha()

void occ::crystal::UnitCell::set_alpha

(

double

alpha

)

Set the angle of between the b- and c-axes.

Parameters

alpha

new angle between the b- and c-axes in radians

Note

Will update other dependent values e.g. volume etc. No checking is performed.

set_b()

void occ::crystal::UnitCell::set_b

(

double

b

)

Set the length of the b-axis.

Parameters

b	new length of the b-axis in Angstroms

Note

Will update other dependent values e.g. volume etc. No checking is performed.

set_beta()

void occ::crystal::UnitCell::set_beta

(

double

beta

)

Set the angle of between the a- and c-axes.

Parameters

beta	new angle between the a- and c-axes in radians

Note

Will update other dependent values e.g. volume etc. No checking is performed.

set_c()

void occ::crystal::UnitCell::set_c

(

double

c

)

Set the length of the c-axis.

Parameters

c	new length of the c-axis in Angstroms

Note

Will update other dependent values e.g. volume etc. No checking is performed.

set_gamma()

void occ::crystal::UnitCell::set_gamma

(

double

gamma

)

Set the angle of between the a- and b-axes.

Parameters

gamma

new angle between the a- and b-axes in radians

Note

Will update other dependent values e.g. volume etc. No checking is performed.

to_cartesian()

auto occ::crystal::UnitCell::to_cartesian ( const Mat3N &  coords ) const

inline

Convert a given matrix of coordinates from fractional to Cartesian.

Parameters

coords

Mat3N of fractional coordinates

Returns

Mat3N of Cartesian coordinates

to_cartesian_adp()

Mat6N occ::crystal::UnitCell::to_cartesian_adp

(

const Mat6N &

adp

)

const

Convert ADPs from fractional to Cartesian coordinates.

This method transforms a set of Anisotropic Displacement Parameters (ADPs) from fractional (ad-hoc) basis to Cartesian coordinate system.

Parameters

adp	Mat6N of ADPs in fractional coordinates

Returns

Mat6N of ADPs in Cartesian coordinates

to_fractional()

auto occ::crystal::UnitCell::to_fractional ( const Mat3N &  coords ) const

inline

Convert a given matrix of coordinates from Cartesian to fractional.

Parameters

coords

Mat3N of Cartesian coordinates

Returns

Mat3N of fractional coordinates

to_fractional_adp()

Mat6N occ::crystal::UnitCell::to_fractional_adp

(

const Mat6N &

adp

)

const

Convert ADPs from Cartesian to fractional coordinates.

This method transforms a set of Anisotropic Displacement Parameters (ADPs) from Cartesian to the fractional (ad-hoc) coordinate system.

Parameters

adp	Mat6N of ADPs in Cartesian coordinates

Returns

Mat6N of ADPs in fractional coordinates

to_reciprocal()

auto occ::crystal::UnitCell::to_reciprocal ( const Mat3N &  coords ) const

inline

Convert a given matrix of coordinates from Cartesian to fractional.

Parameters

coords

Mat3N of Cartesian coordinates

Returns

Mat3N of fractional coordinates

volume()

double occ::crystal::UnitCell::volume ( ) const

inline

Volume of the unit cell in cubic Angstroms.

---

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

• /home/runner/work/occ/occ/include/occ/crystal/unitcell.h