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 crosssectional 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

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 crosssectional 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 crosssectional area (in Angstroms squared). Only used
to generate 1D crystals thickness: The unit cell’s nonperiodic 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_lattice
(ltype, volume, minvec=1.2, minangle=0.5235987755982988, max_ratio=10.0, maxattempts=100, **kwargs)[source]¶ Generates a lattice (3x3 matrix) 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 3x3 matrix representing the lattice vectors of the unit cell. If generation fails, outputs a warning message and returns empty

pyxtal.lattice.
generate_lattice_0D
(ltype, volume, area=None, minvec=1.2, max_ratio=10.0, maxattempts=100, **kwargs)[source]¶ Generates a lattice (3x3 matrix) according to the spacegroup 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. Note: The monoclinic Rod groups have different unique axes. Groups 37
have unique axis a, while 812 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 – crosssectional 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_lattice_1D
(ltype, volume, area=None, minvec=1.2, minangle=0.5235987755982988, max_ratio=10.0, maxattempts=100, **kwargs)[source]¶ Generates a lattice (3x3 matrix) according to the spacegroup 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. Note: The monoclinic Rod groups have different unique axes. Groups 37
have unique axis a, while 812 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 – crosssectional 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 3x3 matrix representing the lattice vectors of the unit cell. If generation fails, outputs a warning message and returns empty

pyxtal.lattice.
generate_lattice_2D
(ltype, volume, thickness=None, minvec=1.2, minangle=0.5235987755982988, max_ratio=10.0, maxattempts=100, **kwargs)[source]¶ Generates a lattice (3x3 matrix) according to the spacegroup symmetry and number of atoms. If the layer group has centering, we will use the 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 37
have unique axis c, while 818 have unique axis a. We use nonperiodic axis c for all layer groups.Parameters:  num – International number of the space group
 volume – volume of the lattice
 thickness – 3rddimensional 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 3x3 matrix 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 xaxis, and the b vector is in the yz 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 bottomleftback minimum point which can be chosen
 maxvec – the toprightfront 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