Powder Patterns¶

In [2]:

import numpy as np
import matplotlib.pyplot as plt
np.set_printoptions(precision=2, suppress=True)

import numpy as np import matplotlib.pyplot as plt np.set_printoptions(precision=2, suppress=True)

In [4]:

def Rx(theta):
    return np.array(
    [
        [1, 0, 0,],
        [0, np.cos(theta), -np.sin(theta),],
        [0, np.sin(theta), np.cos(theta),],
    ])

def Rx(theta): return np.array( [ [1, 0, 0,], [0, np.cos(theta), -np.sin(theta),], [0, np.sin(theta), np.cos(theta),], ])

In [5]:

def Ry(theta):
    return np.array(
    [
        [np.cos(theta), 0, np.sin(theta),],
        [0, 1, 0,],
        [-np.sin(theta), 0, np.cos(theta),],
    ])

def Ry(theta): return np.array( [ [np.cos(theta), 0, np.sin(theta),], [0, 1, 0,], [-np.sin(theta), 0, np.cos(theta),], ])

In [6]:

def Rz(theta):
    return np.array(
    [
        [np.cos(theta), -np.sin(theta), 0],
        [np.sin(theta), np.cos(theta), 0,],
        [0, 0, 1],
    ])

def Rz(theta): return np.array( [ [np.cos(theta), -np.sin(theta), 0], [np.sin(theta), np.cos(theta), 0,], [0, 0, 1], ])

In [7]:

def euler_rotate(tensor, alpha, beta, gamma):
    return  (
          Rz(alpha)
        @ Ry(beta)
        @ Rz(gamma)
        @ tensor
        @ Rz(-gamma)
        @ Ry(-beta)
        @ Rz(-alpha)
    )

def euler_rotate(tensor, alpha, beta, gamma): return ( Rz(alpha) @ Ry(beta) @ Rz(gamma) @ tensor @ Rz(-gamma) @ Ry(-beta) @ Rz(-alpha) )

In [8]:

csa = 2 * np.pi * np.diag([30, 0, -30])
xscale = list(range(-200, 200))
powder = np.zeros(len(xscale))

for i, beta in enumerate(np.linspace(0, np.pi, 512)):
    intensity = abs(np.sin(beta))
    for gamma in np.linspace(0, 2*np.pi, 512):
        freq = euler_rotate(csa, 0, beta, gamma)[2, 2]
        place = int(np.floor(freq) - 200)
        powder[place] += intensity

csa = 2 * np.pi * np.diag([30, 0, -30]) xscale = list(range(-200, 200)) powder = np.zeros(len(xscale)) for i, beta in enumerate(np.linspace(0, np.pi, 512)): intensity = abs(np.sin(beta)) for gamma in np.linspace(0, 2*np.pi, 512): freq = euler_rotate(csa, 0, beta, gamma)[2, 2] place = int(np.floor(freq) - 200) powder[place] += intensity

In [9]:

fig, ax = plt.subplots()
ax.plot(np.array(xscale), powder.real)

plt.show()

fig, ax = plt.subplots() ax.plot(np.array(xscale), powder.real) plt.show()

Q1¶

• Make csa patterns for different anisotropies and asymmetries

In [11]:

# your answer here

# your answer here

Q2¶

• Make the Pake pattern for dipole-dipole coupling. What is the difference between the calculation you do for CSA and dipole-dipole coupling?

In [10]:

dipole = 2 * np.pi * np.diag([10, 10, -20])
xscale = list(range(-150, 150))
powder = np.zeros(len(xscale))

# continue here

dipole = 2 * np.pi * np.diag([10, 10, -20]) xscale = list(range(-150, 150)) powder = np.zeros(len(xscale)) # continue here

In [ ]: