Miller Indices Calculator
Calculate the interplanar spacing (d-spacing) and Bragg diffraction angle (2-theta) for planes in a cubic crystal lattice.
Calculation Parameters
Input your parameters below.
Calculated Result
Expert Tip
Make sure all values are in the correct units to ensure mathematically precise chemical results.
How this Calculator Works
This calculator allows you to solve Miller Indices problems dynamically. Adjust the input parameters using the sliders or selection menu below:
- Lattice Parameter (a, Å) (Range: 2.0 to 8.0, Default: 3.615)
- Index h (Dropdown selection, Default: 1)
- Index k (Dropdown selection, Default: 1)
- Index l (Dropdown selection, Default: 1)
- X-ray Wavelength (λ, Å) (Range: 0.5 to 3.0, Default: 1.5418)
The results are computed instantly and updated in the results panel on the right.
Formula & Methodology
Where:
- Lattice Parameter: Parameter value.
- Index h: Parameter value.
- Index k: Parameter value.
- Index l: Parameter value.
- X-ray Wavelength: Parameter value.
Step-by-Step Calculation Example
To calculate Miller Indices manually, follow these steps:
- Identify the input parameters. For example:
- Lattice Parameter (a, Å) = 3.615
- Index h = 1
- Index k = 1
- Index l = 1
- X-ray Wavelength (λ, Å) = 1.5418
- Apply the formula:
d = a / √(h² + k² + l²)
- Verify the calculated value which is updated instantly in the results panel on the right.
Frequently Asked Questions
What are Miller indices (hkl)? ▼
Miller indices are a notation system in crystallography for lattice planes in crystal lattices, expressed as integer reciprocals of intercepts.
How do you find Miller indices from fractional intercepts? ▼
Take the reciprocals of plane intercepts on x, y, z axes, then clear fractions to obtain the smallest set of integers (h k l).
What does an intercept at infinity (∞) yield in Miller indices? ▼
An intercept at infinity means the plane is parallel to that axis; its reciprocal 1/∞ = 0.