Lattice Parameter Calculator

The Lattice Parameter Calculator determines the atomic spacing in crystalline materials from X-ray diffraction (XRD) data — a core measurement in materials science used to identify crystal structures and detect strain. Select your crystal system (Cubic, Tetragonal, Hexagonal, or Orthorhombic), enter your peak position (2θ), X-ray wavelength, order of reflection, and Miller indices (h, k, l) to calculate the lattice constant (a). Secondary outputs include d-spacing, Bragg angle (θ), and Q value.

°

Peak position from XRD diffractogram

Å

Cu Kα = 1.5418 Å (default)

Å

For direct lattice constant calculation

Results

Lattice Constant (a)

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d-spacing

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Bragg Angle (θ)

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Q Value

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Frequently Asked Questions

What is a lattice parameter in crystallography?

A lattice parameter is the physical dimension of unit cells in a crystal lattice. It defines the size and shape of the repeating unit in a crystal structure, typically measured in Angstroms (Å).

How do I calculate lattice constant from XRD data?

Use Bragg's law (nλ = 2d sinθ) to first calculate d-spacing from the peak position. Then apply the appropriate formula based on crystal system and Miller indices to determine the lattice constant.

What wavelength should I use for Cu Kα radiation?

The standard wavelength for Cu Kα radiation is 1.5418 Å, which is the default value in most XRD calculations. This is the most commonly used X-ray source in diffractometers.

What are Miller indices and why are they important?

Miller indices (h, k, l) are three integers that define the orientation of crystal planes. They are essential for calculating lattice parameters as different planes give different d-spacing values.

Which crystal system should I select for my material?

Choose based on your material's symmetry: cubic for simple metals, hexagonal for materials like graphite or zinc, tetragonal for materials like tin, and orthorhombic for more complex structures.

What is the difference between 2θ and θ in XRD?

2θ is the diffraction angle measured in XRD experiments, while θ is the Bragg angle (half of 2θ). Most XRD software reports 2θ values, which is what you should enter in the calculator.

How accurate are the calculated lattice parameters?

Accuracy depends on peak position precision, wavelength calibration, and sample quality. Typical accuracy is ±0.001 Å for well-defined peaks with proper instrument calibration.