pyxtal.lattice module
- class pyxtal.lattice.Lattice(ltype, volume=None, matrix=None, PBC=[1, 1, 1], **kwargs)[source]
Bases:
object
Class for storing and generating crystal lattices. Allows for specification of constraint values. Lattice types include triclinic, monoclinic, orthorhombic, tetragonal, trigonal, hexagonal, cubic, spherical, and ellipsoidal. The last two are used for generating point group structures, and do not actually represent a parallelepiped lattice.
- Parameters:
ltype – a string representing the type of lattice (from the above list)
volume – the volume, in Angstroms cubed, of the lattice
matrix – matrix in 3*3 form
PBC – A periodic boundary condition list, where 1 is periodic, Ex: [1, 1, 1] -> 3d periodicity, [0, 0, 1] -> periodic at z axis
kwargs –
various values which may be defined. If none are defined, random ones will be generated. Values will be passed to generate_lattice. Options include: area: The cross-sectional area (in Ang^2). Only for 1D crystals thickness: The cell’s thickness (in Angstroms) for 2D crystals unique_axis: The unique axis for certain symmetry (and especially
layer) groups. Because the symmetry operations are not also transformed, you should use the default values for random crystal generation
- random: If False, keeps the stored values for the lattice geometry
even upon applying reset_matrix. To alter the matrix, use set_matrix() or set_para
- ’unique_axis’: the axis (‘a’, ‘b’, or ‘c’) which is not symmetrically
equivalent to the other two
- ’min_l’: the smallest allowed cell vector. The smallest vector must
be larger than this.
- ’mid_l’: the second smallest allowed cell vector. The second
smallest vector must be larger than this.
- ’max_l’: the third smallest allowed cell vector. The largest cell
vector must be larger than this.
- ’allow_volume_reset’: a bool stating whether or not the volume
should be reset during each crystal generation attempt
- add_vacuum(coor, frac=True, vacuum=15, PBC=[0, 0, 0])[source]
Adds space above and below a 2D or 1D crystal.
- Parameters:
coor – the relative coordinates of the crystal
vacuum – the amount of space, in Angstroms, to add above and below
PBC – A periodic boundary condition list, Ex: [1,1,1] -> full 3d periodicity, [0,0,1] -> periodicity along the z axis
- Returns:
The transformed lattice and coordinates after the vacuum is added
- check_mismatch(trans, l_type, tol=1.0, a_tol=10)[source]
check if the lattice mismatch is big after a transformation This is mostly used in supergroup function QZ: to fix ===============
- Parameters:
trans – 3*3 matrix
l_type – lattice_type like orthrhombic
tol – tolerance in a, b, c
a_tol – tolerance in alpha, beta, gamma
- Returns:
True or False
- find_transition_to_orthoslab(c=(0, 0, 1), a=(1, 0, 0), m=5)[source]
Create the slab model with an approximate orthogonal box shape
- classmethod from_matrix(matrix, reset=True, shape='upper', ltype='triclinic', PBC=[1, 1, 1], **kwargs)[source]
Creates a Lattice object from a 3x3 cell matrix. Additional keywords are available. Unless specified by the keyword random=True, does not create a new matrix upon calling reset_matrix. This allows for a random crystals with a specific choice of unit cell.
- Parameters:
matrix – a 3x3 real matrix (numpy array or nested list) for the cell
ltype – the lattice type (“cubic, tetragonal, etc.”). Also can be - “spherical”, confines points to lie within a sphere, - “ellipsoidal”, points to lie within an ellipsoid (about z axis)
PBC – A periodic boundary condition list, where 1 is periodic Ex: [1,1,1] -> full 3d periodicity, [0,0,1] -> periodicity at z.
kwargs – various values which may be defined. Random ones if None Values will be passed to generate_lattice. Options include: area: The cross-sectional area (in Ang^2) for 1D crystals `thickness: The cell’s thickness (in Ang) for 2D crystals unique_axis: The unique axis for layer groups. random: If False, keeps the stored values for the lattice geometry even applying reset_matrix. To alter the matrix, use set_matrix() or set_para ‘unique_axis’: the axis (‘a’, ‘b’, or ‘c’) which is unique. ‘min_l’: the smallest allowed cell vector. ‘mid_l’: the second smallest allowed cell vector. ‘max_l’: the third smallest allowed cell vector.
- Returns:
a Lattice object with the specified parameters
- classmethod from_para(a, b, c, alpha, beta, gamma, ltype='triclinic', radians=False, PBC=[1, 1, 1], factor=1.0, **kwargs)[source]
Creates a Lattice object from 6 lattice parameters. Additional keyword arguments are available. Unless specified by the keyword random=True, does not create a new matrix upon calling reset_matrix. This allows for generation of random crystals with a specific choice of unit cell.
- Parameters:
a – The length (in Angstroms) of the unit cell vectors
b – The length (in Angstroms) of the unit cell vectors
c – The length (in Angstroms) of the unit cell vectors
alpha – the angle (in degrees) between the b and c vectors
beta – the angle (in degrees) between the a and c vectors
gamma – the angle (in degrees) between the a and b vectors
ltype – the lattice type (“cubic, tetragonal, etc.”). Also available are “spherical”, which confines generated points to lie within a sphere, and “ellipsoidal”, which confines generated points to lie within an ellipse (oriented about the z axis)
radians – whether or not to use radians (instead of degrees) for the lattice angles
PBC – A periodic boundary condition list, where 1 means periodic, 0 means not periodic. Ex: [1,1,1] -> full 3d periodicity, [0,0,1] -> periodicity along the z axis
kwargs –
various values which may be defined. If none are defined, random ones will be generated. Values will be passed to generate_lattice. Options include: area: The cross-sectional area (in Angstroms squared). Only used
to generate 1D crystals
- thickness: The unit cell’s non-periodic thickness (in Angstroms).
Only used to generate 2D crystals
- unique_axis: The unique axis for certain symmetry (and especially
layer) groups. Because the symmetry operations are not also transformed, you should use the default values for random crystal generation
- random: If False, keeps the stored values for the lattice geometry
even upon applying reset_matrix. To alter the matrix, use set_matrix() or set_para
’unique_axis’: the axis (‘a’, ‘b’, or ‘c’) which is unique ‘min_l’: the smallest allowed cell vector. ‘mid_l’: the second smallest allowed cell vector. ‘max_l’: the third smallest allowed cell vector.
- Returns:
a Lattice object with the specified parameters
- generate_matrix()[source]
Generates a 3x3 matrix for a lattice based on the lattice type and volume
- get_permutation_matrices()[source]
Return the possible permutation matrices that donot violate the symmetry
- get_transformation_matrices()[source]
Return possible transformation matrices that donot violate the symmetry
- optimize_multi(iterations=5)[source]
Optimize the lattice if the cell has a bad inclination angles
- Parameters:
iterations – maximum number of iterations
force – whether or not do the early termination
- Returns:
the optimized lattice
- search_transformation(lat_ref, d_tol=1.0, f_tol=0.1)[source]
search the closest match to the reference lattice object
- Parameters:
lat_ref – reference lattice object
d_tol – tolerance in angle
f_tol
a_tol
- Returns:
a two steps of transformation matrix if the match is possible
- search_transformations(lat_ref, d_tol=1.0, f_tol=0.1)[source]
search the closest match to the reference lattice object
- Parameters:
lat_ref – reference lattice object
d_tol – tolerance in angle
f_tol
a_tol
- Returns:
a two steps of transformation matrix if the match is possible
- swap_angle(random=True, ids=None)[source]
If the angle is not 90. There will be two equivalent versions e.g., 80 and 100.
- pyxtal.lattice.gaussian(min, max, sigma=3.0)[source]
Choose a random number from a Gaussian probability distribution centered between min and max. sigma is the number of standard deviations that min and max are away from the center. Thus, sigma is also the largest possible number of standard deviations corresponding to the returned value. sigma=2 corresponds to a 95.45% probability of choosing a number between min and max.
- Parameters:
min – the minimum acceptable value
max – the maximum acceptable value
sigma – the number of standard deviations between the center and min/max
- Returns:
a value chosen randomly between min and max
- pyxtal.lattice.generate_cellpara(ltype, volume, minvec=1.2, minangle=0.5235987755982988, max_ratio=10.0, maxattempts=100, **kwargs)[source]
Generates the cell parameter (a, b, c, alpha, beta, gamma) according to the space group symmetry and number of atoms. If the spacegroup has centering, we will transform to conventional cell setting. If the generated lattice does not meet the minimum angle and vector requirements, we try to generate a new one, up to maxattempts times.
- Parameters:
volume – volume of the conventional unit cell
minvec – minimum allowed lattice vector length (among a, b, and c)
minangle – minimum allowed lattice angle (among alpha, beta, and gamma)
max_ratio – largest allowed ratio of two lattice vector lengths
maxattempts – the maximum number of attempts for generating a lattice
kwargs – a dictionary of optional values. These include: ‘unique_axis’: the axis (‘a’, ‘b’, or ‘c’) which is unique. ‘min_l’: the smallest allowed cell vector. ‘mid_l’: the second smallest allowed cell vector. ‘max_l’: the third smallest allowed cell vector.
- Returns:
a 6-length array representing the lattice of the unit cell. If generation fails, outputs a warning message and returns empty
- pyxtal.lattice.generate_cellpara_0D(ltype, volume, area=None, minvec=1.2, max_ratio=10.0, maxattempts=100, **kwargs)[source]
Generates a cell parameter (a, b, c, alpha, beta, gamma) according to the point group symmetry and number of atoms. If the generated lattice does not meet the minimum angle and vector requirements, we try to generate a new one, up to maxattempts times.
- Parameters:
num – number of the Rod group
volume – volume of the lattice
area – cross-sectional area of the unit cell in Angstroms squared. If set to None, a value is chosen automatically
minvec – minimum allowed lattice vector length (among a, b, and c)
max_ratio – largest allowed ratio of two lattice vector lengths
maxattempts – the maximum number of attempts for generating a lattice
kwargs – a dictionary of optional values. Only used for ellipsoidal lattices, which pass the value to generate_lattice. They include: ‘unique_axis’: the axis (‘a’, ‘b’, or ‘c’) which is unique. ‘min_l’: the smallest allowed cell vector. ‘mid_l’: the second smallest allowed cell vector. ‘max_l’: the third smallest allowed cell vector.
- Returns:
a 3x3 matrix representing the lattice vectors of the unit cell. If generation fails, outputs a warning message and returns empty
- pyxtal.lattice.generate_cellpara_1D(ltype, volume, area=None, minvec=1.2, minangle=0.5235987755982988, max_ratio=10.0, maxattempts=100, **kwargs)[source]
Generates a cell parameter (a, b, c, alpha, beta, gamma) according to the rod group symmetry and number of atoms. If the rod group has centering, we will transform to conventional cell setting. If the generated lattice does not meet the minimum angle and vector requirements, we try to generate a new one, up to maxattempts times.
- Note: The monoclinic Rod groups have different unique axes. Groups 3-7
have unique axis a, while 8-12 have unique axis c. We use periodic axis c for all Rod groups.
- Parameters:
num – number of the Rod group
volume – volume of the lattice
area – cross-sectional area of the unit cell in Angstroms squared. If set to None, a value is chosen automatically
minvec – minimum allowed lattice vector length (among a, b, and c)
minangle – minimum allowed lattice angle (among alpha, beta, and gamma)
max_ratio – largest allowed ratio of two lattice vector lengths
maxattempts – the maximum number of attempts for generating a lattice
kwargs – a dictionary of optional values. These include: ‘unique_axis’: the axis (‘a’, ‘b’, or ‘c’) which is unique. ‘min_l’: the smallest allowed cell vector. ‘mid_l’: the second smallest allowed cell vector. ‘max_l’: the third smallest allowed cell vector.
- Returns:
a 6-length array representing the lattice of the unit cell. If generation fails, outputs a warning message and returns empty
- pyxtal.lattice.generate_cellpara_2D(ltype, volume, thickness=None, minvec=1.2, minangle=0.5235987755982988, max_ratio=10.0, maxattempts=100, **kwargs)[source]
Generates the cell parameter (a, b, c, alpha, beta, gamma) according to the layer group symmetry and number of atoms. If the layer group has centering, we will transform to conventional cell setting. If the generated lattice does not meet the minimum angle and vector requirements, we try to generate a new one, up to maxattempts times.
- Note: The monoclinic layer groups have different unique axes. Groups 3-7
have unique axis c, while 8-18 have unique axis a. We use non-periodic axis c for all layer groups.
- Parameters:
num – International number of the space group
volume – volume of the lattice
thickness – 3rd-dimensional thickness of the unit cell. If set to None, a thickness is chosen automatically
minvec – minimum allowed lattice vector length (among a, b, and c)
minangle – minimum allowed lattice angle (among alpha, beta, and gamma)
max_ratio – largest allowed ratio of two lattice vector lengths
maxattempts – the maximum number of attempts for generating a lattice
kwargs – a dictionary of optional values. These include: ‘unique_axis’: the axis (‘a’, ‘b’, or ‘c’) which is unique. ‘min_l’: the smallest allowed cell vector. ‘mid_l’: the second smallest allowed cell vector. ‘max_l’: the third smallest allowed cell vector.
- Returns:
a 6-length representing the lattice vectors of the unit cell. If generation fails, outputs a warning message and returns empty
- pyxtal.lattice.matrix2para(matrix, radians=True)[source]
Given a 3x3 matrix representing a unit cell, outputs a list of lattice parameters.
- Parameters:
matrix – a 3x3 array or list, where the first, second, and third rows represent the a, b, and c vectors respectively
radians – if True, outputs angles in radians. If False, outputs in degrees
- Returns:
a 1x6 list of lattice parameters [a, b, c, alpha, beta, gamma]. a, b, and c are the length of the lattice vectos, and alpha, beta, and gamma are the angles between these vectors (in radians by default)
- pyxtal.lattice.para2matrix(cell_para, radians=True, format='upper')[source]
Given a set of lattic parameters, generates a matrix representing the lattice vectors
- Parameters:
cell_para – a 1x6 list of lattice parameters [a, b, c, alpha, beta, gamma]. a, b, and c are the length of the lattice vectos, and alpha, beta, and gamma are the angles between these vectors. Can be generated by matrix2para
radians – if True, lattice parameters should be in radians. If False, lattice angles should be in degrees
format – a string (‘lower’, ‘symmetric’, or ‘upper’) for the type of matrix to be output
- Returns:
a 3x3 matrix representing the unit cell. By default (format=’lower’), the a vector is aligined along the x-axis, and the b vector is in the y-z plane
- pyxtal.lattice.random_shear_matrix(width=1.0, unitary=False)[source]
Generate a random symmetric shear matrix with Gaussian elements. If unitary is True, normalize to determinant 1
- Parameters:
width – the width of the normal distribution to use when choosing values. Passed to np.random.normal
unitary – whether or not to normalize the matrix to determinant 1
- Returns:
a 3x3 numpy array of floats
- pyxtal.lattice.random_vector(minvec=[0.0, 0.0, 0.0], maxvec=[1.0, 1.0, 1.0], width=0.35, unit=False)[source]
Generate a random vector for lattice constant generation. The ratios between x, y, and z of the returned vector correspond to the ratios between a, b, and c. Results in a Gaussian distribution of the natural log of the ratios.
- Parameters:
minvec – the bottom-left-back minimum point which can be chosen
maxvec – the top-right-front maximum point which can be chosen
width – the width of the normal distribution to use when choosing values. Passed to np.random.normal
unit – whether or not to normalize the vector to determinant 1
- Returns:
a 1x3 numpy array of floats