category

academic_codes/others/2021.07.19_calculate_reciprocal_lattice_vectors/calculate_reciprocal_lattice_vectors.py

@@ -0,0 +1,45 @@
+"""
+This code is supported by the website: https://www.guanjihuan.com
+The newest version of this code is on the web page: https://www.guanjihuan.com/archives/15978
+"""
+
+import numpy as np
+from math import *
+
+def main():
+    a1 = [0, 1]
+    a2 = [1, 0]
+    b1, b2 = calculate_two_dimensional_reciprocal_lattice_vectors(a1, a2)
+    print(b1, b2)
+
+
+def calculate_one_dimensional_reciprocal_lattice_vector(a1):
+    b1 = 2*pi/a1
+    return b1
+
+
+def calculate_two_dimensional_reciprocal_lattice_vectors(a1, a2):
+    a1 = np.array(a1)
+    a2 = np.array(a2)
+    a1 = np.append(a1, 0)
+    a2 = np.append(a2, 0)
+    a3 = np.array([0, 0, 1])
+    b1 = 2*pi*np.cross(a2, a3)/np.dot(a1, np.cross(a2, a3))
+    b2 = 2*pi*np.cross(a3, a1)/np.dot(a1, np.cross(a2, a3))
+    b1 = np.delete(b1, 2)
+    b2 = np.delete(b2, 2)
+    return b1, b2
+
+
+def calculate_three_dimensional_reciprocal_lattice_vectors(a1, a2, a3):
+    a1 = np.array(a1)
+    a2 = np.array(a2)
+    a3 = np.array(a3)
+    b1 = 2*pi*np.cross(a2, a3)/np.dot(a1, np.cross(a2, a3))
+    b2 = 2*pi*np.cross(a3, a1)/np.dot(a1, np.cross(a2, a3))
+    b3 = 2*pi*np.cross(a1, a2)/np.dot(a1, np.cross(a2, a3))
+    return b1, b2, b3
+
+
+if __name__ == '__main__':
+    main()

academic_codes/others/2021.07.19_calculate_reciprocal_lattice_vectors/calculate_reciprocal_lattice_vectors_with_guan.py

@@ -0,0 +1,22 @@
+import guan
+import sympy
+
+a1 = [0, 1]
+a2 = [1, 0]
+b1, b2 = guan.calculate_two_dimensional_reciprocal_lattice_vectors(a1, a2)
+print(b1, b2, '\n')
+
+print('bases in the real space')
+a = sympy.symbols('a')
+a1 = sympy.Matrix(1, 2, [3*a/2, sympy.sqrt(3)*a/2])
+a2 = sympy.Matrix(1, 2, [3*a/2, -sympy.sqrt(3)*a/2])
+print('a1:')
+sympy.pprint(a1)
+print('a2:')
+sympy.pprint(a2)
+print('\nbases in the reciprocal space')
+b1, b2 = guan.calculate_two_dimensional_reciprocal_lattice_vectors_with_sympy(a1, a2)
+print('b1:')
+sympy.pprint(b1)
+print('b2:')
+sympy.pprint(b2)

academic_codes/others/2021.07.19_calculate_reciprocal_lattice_vectors/calculate_reciprocal_lattice_vectors_with_sympy.py

@@ -0,0 +1,55 @@
+"""
+This code is supported by the website: https://www.guanjihuan.com
+The newest version of this code is on the web page: https://www.guanjihuan.com/archives/15978
+"""
+
+import sympy
+
+
+def main():
+    print('bases in the real space')
+    a = sympy.symbols('a')
+    a1 = sympy.Matrix(1, 2, [3*a/2, sympy.sqrt(3)*a/2])
+    a2 = sympy.Matrix(1, 2, [3*a/2, -sympy.sqrt(3)*a/2])
+    print('a1:')
+    sympy.pprint(a1)
+    print('a2:')
+    sympy.pprint(a2)
+    print('\nbases in the reciprocal space')
+    b1, b2 = calculate_two_dimensional_reciprocal_lattice_vectors_with_sympy(a1, a2)
+    print('b1:')
+    sympy.pprint(b1)
+    print('b2:')
+    sympy.pprint(b2)
+
+
+def calculate_one_dimensional_reciprocal_lattice_vector_with_sympy(a1):
+    b1 = 2*sympy.pi/a1
+    return b1
+
+
+def calculate_two_dimensional_reciprocal_lattice_vectors_with_sympy(a1, a2):
+    a1 = sympy.Matrix(1, 3, [a1[0], a1[1], 0])
+    a2 = sympy.Matrix(1, 3, [a2[0], a2[1], 0])
+    a3 = sympy.Matrix(1, 3, [0, 0, 1])
+    cross_a2_a3 = a2.cross(a3)
+    cross_a3_a1 = a3.cross(a1)
+    b1 = 2*sympy.pi*cross_a2_a3/a1.dot(cross_a2_a3)
+    b2 = 2*sympy.pi*cross_a3_a1/a1.dot(cross_a2_a3)
+    b1 = sympy.Matrix(1, 2, [b1[0], b1[1]])
+    b2 = sympy.Matrix(1, 2, [b2[0], b2[1]])
+    return b1, b2
+
+
+def calculate_three_dimensional_reciprocal_lattice_vectors_with_sympy(a1, a2, a3):
+    cross_a2_a3 = a2.cross(a3)
+    cross_a3_a1 = a3.cross(a1)
+    cross_a1_a2 = a1.cross(a2)
+    b1 = 2*sympy.pi*cross_a2_a3/a1.dot(cross_a2_a3)
+    b2 = 2*sympy.pi*cross_a3_a1/a1.dot(cross_a2_a3)
+    b3 = 2*sympy.pi*cross_a1_a2/a1.dot(cross_a2_a3)
+    return b1, b2, b3
+
+
+if __name__ == '__main__':
+    main()