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Use our lattice constant calculator to find lattice size from XRD data or d-spacing. Get clear steps, key formulas, and fast results.
| Formula | Meaning |
|---|---|
| n*lambda = 2d sin(theta) | Bragg's law |
| d = n*lambda / (2 sin(theta)) | Interplanar spacing from diffraction data |
| a = d x sqrt(h^2+k^2+l^2) | Cubic lattice constant from spacing and Miller indices |
Need to find a crystal's lattice constant? Our lattice constant calculator makes it easy. Enter your data and get a clear result. You can use XRD data or known d-spacing. The tool does the math for you.
Think of a crystal as a neat grid. Each point marks a place for atoms. The lattice constant tells you the size of its cell. This value helps you study how atoms fit together.
A lattice constant calculator finds the size of a crystal's unit cell. For a cubic crystal, all three sides have the same length. This length is called the lattice constant, or a.
You can use this tool in physics, chemistry, and material science. It helps students, lab teams, and researchers check crystal data with ease.
The right formula depends on your input data.
XRD stands for X-ray diffraction. It helps find the space between crystal planes.
First, use Bragg's law:
nλ = 2d sin(θ)
To find d-spacing:
d = nλ / (2 sin(θ))
Then find the cubic lattice constant:
a = d × √(h² + k² + l²)
Here, n is the diffraction order, λ is the X-ray wavelength, and θ is the Bragg angle. The letters h, k, and l are Miller indices.
If your data gives 2θ, divide that angle by two first.
If you know d-spacing, use this formula:
a = d × √(h² + k² + l²)
This method skips the X-ray data step. It works for cubic crystals.
Choose a method. Pick XRD or direct d-spacing.
Enter your data. Add the wavelength and angle, or enter d.
Set the plane. Enter the h, k, and l values.
Check your units. Use the right unit for each value.
Get your result. Read the lattice constant and the steps.
The tool handles the math and unit changes. Check your input before you use the result.
Suppose the X-ray wavelength is 0.15418 nm. The measured 2θ angle is 43.36°. The plane has Miller indices (1, 1, 1), and n = 1.
First, find the Bragg angle:
θ = 43.36° / 2 = 21.68°
Next, find d:
d = 0.15418 / [2 × sin(21.68°)]
d ≈ 0.2087 nm
Now find a:
a = 0.2087 × √(1² + 1² + 1²)
Lattice constant: a ≈ 0.3615 nm, or 3.615 Å.
This is an example of how to determine lattice constant from XRD data.
Our lattice parameter calculator makes crystal math less of a chore. Use it to find a lattice constant from XRD data or d-spacing. It also shows the key steps and formulas. For best results, use the correct units and crystal type.
It is a length that describes a crystal's unit cell. Its value depends on the crystal and its structure.
For a cubic crystal, use:
ρ = ZM / (Nₐa³)
Here, Z is the number of atoms per unit cell, M is molar mass, Nₐ is Avogadro's constant, and a is the lattice constant. Use matching units for all values.
It is the edge length of a cubic unit cell. In a cubic crystal, a = b = c.
Yes. XRD data can give d-spacing. You can then find the lattice constant with the right crystal formula.
No. A lattice parameter table lists values for chosen materials and conditions. Values can vary with heat, pressure, and crystal makeup.