X-ray Diffraction Analysis: Unveiling the Mysteries of Niobium Crystal Structures
How can we determine the interplanar spacing and diffraction angle for specific crystal planes in niobium using X-ray diffraction analysis?
Discover the secrets of niobium crystal structures through X-ray diffraction analysis and unlock the hidden world of interplanar spacing and diffraction angles.
Answer:
In X-ray diffraction (XRD) analysis, we can determine the interplanar spacing of a crystal lattice by using Bragg's law, which relates the diffraction angle (θ) to the wavelength (λ) and the interplanar spacing (d) through the equation: nλ = 2d sin(θ), where 'n' is the order of reflection. For the (211) plane in niobium, the first-order reflection occurs at 75.99°, and the wavelength of the monochromatic X-ray used is 0.1659 nm.
To calculate the interplanar spacing for the (211) plane, we rearrange Bragg's law to solve for 'd': d = λ / (2 * sin(θ)). Substituting the given values, we get: d = 0.1659 nm / (2 * sin(75.99°)) ≈ 0.2757 nm.
For the second part, we need to find the diffraction angle (θ) for the (110) plane. Since we have already calculated the interplanar spacing for the (211) plane, we can reuse Bragg's law and rearrange it to solve for the diffraction angle: θ = arcsin(nλ / (2 * d)). However, we need to find the value of 'n' for the (110) plane. In XRD, we usually consider first-order reflections (n = 1). Therefore, for the (110) plane, n = 1. Substituting the values, we get: θ = arcsin(0.1659 nm / (2 * 0.2757 nm)) ≈ 44.85°.
In summary, we calculated the interplanar spacing for the (211) plane in niobium as 0.2757 nm, and the diffraction angle for the (110) plane is approximately 44.85° when XRD is performed using monochromatic X-rays with a wavelength of 0.1659 nm.
Explore the world of niobium crystal structures and delve deeper into the fascinating realm of X-ray diffraction analysis to uncover the hidden wonders of material science.