#!/usr/bin/env python
# mech2d is free software: you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
# mech2d is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
# You should have received a copy of the GNU General Public Licensea
# along with mech2d. If not, see <http://www.gnu.org/licenses/>.
import math
import numpy as np
from pymatgen.symmetry.analyzer import SpacegroupAnalyzer
[docs]class Bravais2D:
"""
2D bravais lattice obj to check the lattice type
Args
a: (float) The magnitude of the first primitive vector (default is 1.0).
b: (float) The magnitude of the second primitive vector (default is 1.0).
angle: (float) The angle between the two primitive vectors; can't be 0 or 180 degrees (default is 120.0).
centered: (bool) True if the lattice is a centered rectangular (default is False).
numpoints: (int) The number of desired points to plot and must be a square number larger than 4;
will be the number of 'non-centered' points if centered rectangular lattice (default is 16).
plot: (bool) If True, will plot the lattice (default is True).
a_vec: (numpy array) The first primitive vector.
b_vec: (numpy array) The second primitive vector.
lattice: (str) The name of the type of Bravais lattice (depends on a, b, angle, and centered).
unit_cell_area: (float) The area of the unit cell.
Functions:
plot: Creates a 2D scatter plot.
"""
def __init__(self, struct , eps_r=0.2, eps_a=1.0, numpoints=16):
"""
:param a: (float) The magnitude of the first primitive vector (default is 1.0).
:param b: (float) The magnitude of the second primitive vector (default is 1.0).
:param angle: (float) The angle between the two primitive vectors; can't be 0 or 180 degrees (default is 120.0).
:param degrees: (bool) If True, the angles are in degrees and if False, the angles are in radians
(default is True).
:param centered: (bool) True if the lattice is a centered rectangular (default is False).
:param numpoints: (int) The number of desired points to plot and must be a square number larger than 4;
will be the number of 'non-centered' points if centered rectangular lattice (default is 16).
:param plot: (bool) If True, will plot the lattice (default is True).
"""
self.struct= struct
lattice= struct.lattice.abc
self.a = lattice[0]
self.b = lattice[1]
self.eps_r= eps_r
self.eps_a= eps_a
self.centered = self._get_centered()
self._numpoints = numpoints
self.angle = struct.lattice.gamma
def _get_centered(self):
#spa=SpacegroupAnalyzer(self.struct)
if len(self.struct) != len(self.struct.get_primitive_structure()):
centered=True
else:
centered=False
return centered
@property
def a_vec(self):
return np.array([self.a, 0])
@property
def b_vec(self):
return np.array([self.b*math.cos(self.angle), self.b*math.sin(self.angle)])
@property
def lattice_type(self):
#print(self.centered)
#print(self.struct.lattice.parameters)
#if (abs(self.angle - 90)> self.eps_a) and (not self.centered):
if (abs(self.a - self.b)> self.eps_r) and (abs(self.angle - 90)> self.eps_a) and (not self.centered):
return "Oblique"
elif (abs(self.a - self.b)> self.eps_r) and (abs(self.angle - 90)<= self.eps_a) and self.centered:
return "CenteredRectangular"
elif (abs(self.a - self.b)> self.eps_r) and (abs(self.angle - 90)<= self.eps_a) and (not self.centered):
return "Rectangular"
elif (abs(self.a - self.b)<= self.eps_r) and ((abs(self.angle - 120)<= self.eps_a) or (abs(self.angle - 60) <= self.eps_a ) ) and (not self.centered):
return "Hexagonal"
#elif (abs(self.a - self.b)<= self.eps_r) and (abs(self.angle - 90)<=self.eps_a) and (not self.centered):
elif (abs(self.a - self.b)<= self.eps_r) and (abs(self.angle - 90)<=self.eps_a) :
return "Square"
elif (abs(self.angle - 90)> self.eps_a) and (not self.centered):
return "Oblique"
else:
raise Exception("Invalid combination of a, b, angle, and/or centered.")
@property
def unit_cell_area(self):
return self.a*self.b*math.sin(self.angle)
@property
def numpoints(self):
val = round(self._numpoints**0.5, 0)**2
if val == self._numpoints and val >= 9:
return self._numpoints
else:
raise Exception("numpoints must be a square number greater than or equal to 9.")
def __find_points(self):
""" Finds all the x and y coordinates of the lattice.
:return: (list(list)) x, y
"""
def f(start, stop, x_list, y_list):
for j in np.arange(start, stop):
for i in np.arange(start, stop):
vec = i*self.a_vec + j*self.b_vec
x_list.append(vec[0])
y_list.append(vec[1])
return x_list, y_list
p = int(self.numpoints**0.5)
x, y = f(0, p, [], [])
if self.centered:
x, y = f(0.5, p - 1, x, y)
return x, y
def __unit_cell(self, x, y):
""" Finds the x and y coordinates for the unit cell.
:param x: (list) The x coordinates of the lattice points.
:param y: (list) The y coordinates of the lattice points.
:return: (list(list()) x, y
"""
root = int(self.numpoints**0.5)
return (x[0], x[1], x[1+root], x[root], x[0]), (y[0], y[1], y[1+root], y[root], y[0])
[docs] def plot(self):
import matplotlib.pyplot as plt
""" Creates a 2D scatter plot. """
x, y = self.__find_points()
fig = plt.figure()
ax = fig.add_subplot(111)
angle = "%.2f"%(self.angle)
title = "Bravais Lattice: " + self.lattice_type
variables = "\n|a| = " + "%.3f"%(self.a) + ", |b| = " + "%.3f"%(self.b) + ", \u03b8 = " + angle + "\u00b0"
scaling = "\n(Axes may be scaled differently)"
ax.set_title(title + variables + scaling)
ax.scatter(x, y, label="Lattice Points")
ax.plot(*self.__unit_cell(x, y), color="darkorange", label="Unit Cell")
plt.legend(loc="best")#.set_draggable(True)
plt.show()
if __name__=='__main__':
from pymatgen.core import Structure
from glob import glob
fs=glob("../tests/configs/*.vasp")
structs=[Structure.from_file(f) for f in fs]
for i,struct in enumerate(structs[:-2]):
print('-'* 20)
print(fs[i])
brav2 = Bravais2D(struct)
#print(struct.lattice)
print(brav2.lattice_type)
brav2.plot()