Interplanar Distance in Orthorhombic Crystal Lattice Calculator

Interplanar Spacing Formula:

\[ d = \sqrt{\frac{1}{\frac{h^2}{a^2} + \frac{k^2}{b^2} + \frac{l^2}{c^2}}} \]

Miller Index along x-axis (h):

Miller Index along y-axis (k):

Miller Index along z-axis (l):

Lattice Constant a:

Lattice Constant b:

Lattice Constant c:

Interplanar Spacing (d):

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1. What is Interplanar Spacing?

Interplanar spacing is the distance between adjacent and parallel planes of atoms in a crystal lattice. It is a fundamental parameter in crystallography that helps determine the arrangement of atoms in crystalline materials and is crucial for X-ray diffraction analysis.

2. How Does the Calculator Work?

The calculator uses the interplanar spacing formula for orthorhombic crystals:

\[ d = \sqrt{\frac{1}{\frac{h^2}{a^2} + \frac{k^2}{b^2} + \frac{l^2}{c^2}}} \]

Where:

\( d \) — Interplanar spacing (m)
\( h, k, l \) — Miller indices along x, y, and z axes
\( a, b, c \) — Lattice constants along x, y, and z axes (m)

Explanation: The formula calculates the perpendicular distance between parallel crystal planes in an orthorhombic lattice system, where the three lattice constants are different and all angles are 90 degrees.

3. Importance of Interplanar Spacing Calculation

Details: Accurate interplanar spacing calculation is essential for X-ray diffraction studies, material characterization, determining crystal structures, and understanding material properties at the atomic level.

4. Using the Calculator

Tips: Enter Miller indices as integers (h, k, l ≥ 0) and lattice constants in meters (a, b, c > 0). All values must be valid positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What are Miller indices?
A: Miller indices are a notation system in crystallography that represent the orientation of crystal planes using three integers (h, k, l).

Q2: Why is interplanar spacing important in X-ray diffraction?
A: Interplanar spacing determines the diffraction angles in X-ray patterns through Bragg's law, allowing identification of crystal structures.

Q3: What is an orthorhombic crystal system?
A: An orthorhombic crystal system has three mutually perpendicular axes of different lengths (a ≠ b ≠ c) with all angles equal to 90 degrees.

Q4: Can this calculator be used for other crystal systems?
A: This specific formula is for orthorhombic systems. Other crystal systems (cubic, tetragonal, etc.) have different interplanar spacing formulas.

Q5: What are typical values for lattice constants?
A: Lattice constants are typically in the range of 0.1-1.0 nanometers (1.0×10⁻¹⁰ to 1.0×10⁻⁹ meters) for most crystalline materials.