Bragg Equation For Distance Between Planes Of Atoms In Crystal Lattice Calculator

Bragg Equation:

\[ d = \frac{n \cdot \lambda}{2 \cdot \sin(\theta)} \]

Interplanar Spacing (d):

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1. What is Bragg's Equation?

Bragg's Law describes the relationship between the interplanar spacing in a crystal lattice and the angle of incidence at which X-rays are diffracted. It is fundamental to X-ray crystallography and materials science for determining crystal structures.

2. How Does the Calculator Work?

The calculator uses Bragg's equation:

\[ d = \frac{n \cdot \lambda}{2 \cdot \sin(\theta)} \]

Where:

\( d \) — Interplanar spacing (nm)
\( n \) — Order of diffraction
\( \lambda \) — Wavelength of X-ray (m)
\( \theta \) — Bragg's angle (radians)

Explanation: The equation relates the distance between crystal planes to the diffraction pattern observed when X-rays interact with the crystal structure.

3. Importance of Interplanar Spacing Calculation

Details: Calculating interplanar spacing is crucial for identifying crystal structures, determining lattice parameters, and understanding material properties in crystallography and materials science research.

4. Using the Calculator

Tips: Enter the order of diffraction as a positive integer, wavelength in meters, and Bragg's angle in radians. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is the order of diffraction?
A: The order of diffraction (n) refers to which diffraction maximum is being considered, with n=1 for the first order, n=2 for the second order, etc.

Q2: Why is the angle measured in radians?
A: The trigonometric functions in programming languages typically use radians. You can convert from degrees to radians using: radians = degrees × π/180.

Q3: What are typical wavelength values for X-rays?
A: X-ray wavelengths typically range from 0.01 to 10 nanometers (1×10⁻¹¹ to 1×10⁻⁸ meters), with Cu Kα radiation at about 1.54×10⁻¹⁰ m being commonly used.

Q4: What factors affect interplanar spacing?
A: Interplanar spacing depends on the crystal structure, lattice parameters, and the specific crystallographic planes being considered.

Q5: Can this calculator be used for electron diffraction?
A: While the Bragg equation form is similar, electron wavelengths are much shorter and the calculations may require relativistic corrections for high-energy electrons.