Create Bragg_angle.py

physics/Bragg_angle.py

@@ -0,0 +1,64 @@
+"""
+Find the Bragg angle of a crystal given the wavelength of radiation, distane between the planes of crystal and the order of diffraction.
+
+In many areas of science, Bragg's law, Wulff–Bragg's condition, or Laue–Bragg interference are a special case of Laue diffraction,
+giving the angles for coherent scattering of waves from a large crystal lattice.
+It describes how the superposition of wave fronts scattered by lattice planes leads to a strict relation between the wavelength and scattering angle.
+This law was initially formulated for X-rays, but it also applies to all types of matter waves including neutron and electron waves if there are a large number of atoms,
+as well as visible light with artificial periodic microscale lattices.
+
+Reference: https://en.wikipedia.org/wiki/Bragg%27s_law
+
+"""
+
+import math
+
+
+def bragg_angle(distance: float, n: int, wavelength: float) -> float:
+    """
+    Calculate the Bragg diffraction angle in degrees.
+
+    The Bragg diffraction angle is given by
+    sin(θ) = (n * λ) / (2 * d)
+
+    Parameters:
+    distance (float): Distance between crystal planes (in meters).
+    n (int): Order of reflection.
+    wavelength (float): Wavelength of the radiation (in meters).
+
+    Returns:
+    float: The Bragg diffraction angle θ in degrees.
+
+    Example:
+    >>> bragg_angle(2.2e-10, 1, 2.2e-10)
+    30.0
+
+    >>> bragg_angle(5.0e-10, 2, 1.0e-10)
+    11.5
+
+    >>> bragg_angle(4.0e-10, 1, 8.0e-10)
+    90.0
+
+    # Test case for an invalid sine value that is out of range
+    >>> bragg_angle(1e-10, 2, 3e-10)
+    Traceback (most recent call last):
+        ...
+    ValueError: The calculated sine value is out of the valid range.
+    """
+
+    sine_theta = (n * wavelength) / (2 * distance)
+
+    if sine_theta > 1 or sine_theta < -1:
+        raise ValueError("The calculated sine value is out of the valid range.")
+
+    theta_radians = math.asin(sine_theta)
+
+    theta_degrees = math.degrees(theta_radians)
+
+    return round(theta_degrees, 1)
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod(verbose=True)