Question

In Laue's technique of X-ray diffraction, a single crystal is held stationary and the beam of white radiation of wavelength \(\lambda\) is inclined at which condition with glancing angle (\(\theta\)):

• A. \(\theta\) is fixed while \(\lambda\) varies
• B. \(\lambda\) is fixed while \(\theta\) varies
• C. \(\lambda\) is fixed while both \(\theta\) and distance varies
• D. \(\theta\) is fixed while both \(\lambda\) and distance varies

Hint:

Memorize the key features of the three main XRD methods:

\textbf{Laue Method:} Stationary single crystal, variable \(\lambda\) (white X-rays). Used for crystal orientation.
\textbf{Rotating Crystal Method:} Rotating single crystal (variable \(\theta\)), fixed \(\lambda\) (monochromatic X-rays). Used for determining lattice parameters.
\textbf{Powder Method:} Powdered sample (all \(\theta\) orientations available), fixed \(\lambda\). Used for identifying crystal structure and phase analysis.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
The question asks about the experimental conditions of the Laue method, one of the primary techniques for X-ray diffraction. We need to identify which parameters in Bragg's law (\(2d\sin\theta = n\lambda\)) are fixed and which are variable in this method.
Step 2: Detailed Explanation:
In the Laue diffraction technique:
1. A single crystal is used.
2. The crystal is held stationary, meaning its orientation with respect to the incoming X-ray beam is fixed. For any given set of crystal planes (with interplanar spacing 'd'), the glancing angle \(\theta\) is therefore also fixed.
3. The crystal is irradiated with white radiation, which is a continuous spectrum of X-rays containing a range of wavelengths. This means the wavelength \(\lambda\) is variable.
Bragg's law is satisfied when, for a set of planes with fixed \(d\) and \(\theta\), the beam contains a wavelength \(\lambda\) that fulfills the equation \( \lambda = (2d/n)\sin\theta \). Since the incident beam has a continuous spectrum of \(\lambda\), some wavelengths will always satisfy the condition for various planes, producing a diffraction pattern of spots.
Step 3: Final Answer:
In the Laue technique, the angle \(\theta\) is fixed for any given plane, and the wavelength \(\lambda\) is varied.