Interplanar Distance In Monoclinic Crystal Lattice Calculator

Interplanar Spacing Formula:

\[ d = \sqrt{\frac{1}{\frac{\frac{h^2}{a^2} + \frac{k^2 \sin^2(\beta)}{b^2} + \frac{l^2}{c^2} - \frac{2hl \cos(\beta)}{ac}}{\sin^2(\beta)}}} \]

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:

Lattice Parameter Beta (β):

radians

Interplanar Spacing (d):

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1. What Is Interplanar Distance In Monoclinic Crystal Lattice?

Interplanar spacing (d-spacing) is the distance between adjacent parallel planes of atoms in a crystal lattice. In monoclinic crystals, this distance depends on the Miller indices (h,k,l) and the lattice parameters (a, b, c, β).

2. How Does The Calculator Work?

The calculator uses the formula for monoclinic crystals:

\[ d = \sqrt{\frac{1}{\frac{\frac{h^2}{a^2} + \frac{k^2 \sin^2(\beta)}{b^2} + \frac{l^2}{c^2} - \frac{2hl \cos(\beta)}{ac}}{\sin^2(\beta)}}} \]

Where:

\( d \) — Interplanar spacing (m)
\( h, k, l \) — Miller indices
\( a, b, c \) — Lattice constants (m)
\( \beta \) — Angle between a and c axes (radians)

Explanation: This formula accounts for the unique geometry of monoclinic crystal systems where β ≠ 90°.

3. Importance Of Interplanar Spacing Calculation

Details: Calculating interplanar spacing is crucial for X-ray diffraction analysis, material characterization, and understanding crystal structure properties.

4. Using The Calculator

Tips: Enter Miller indices as integers, lattice constants in meters, and β angle in radians. All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What is a monoclinic crystal system?
A: A crystal system where a ≠ b ≠ c, α = γ = 90°, and β ≠ 90°.

Q2: Why are Miller indices important?
A: Miller indices describe the orientation of crystal planes and are essential for calculating interplanar spacing.

Q3: How to convert degrees to radians?
A: Multiply degrees by π/180 (approximately 0.0174533).

Q4: What are typical values for lattice constants?
A: Lattice constants are typically in the range of 10⁻¹⁰ to 10⁻⁹ meters (Ångströms to nanometers).

Q5: Can this calculator be used for other crystal systems?
A: No, this specific formula is designed for monoclinic crystals. Other crystal systems have different formulas.