X-ray Diffraction Peak Position Calculator
Predict where an X-ray diffraction peak (2θ) will appear, from a d-spacing directly or from a cubic lattice parameter and Miller indices.
📊 What is an X-ray Diffraction Peak Position Calculator?
An X-ray diffraction peak position is the angle 2θ at which a detector records a diffraction peak for a given set of crystal planes, determined by combining a crystal's geometry with Bragg's law, nλ = 2d sinθ. This calculator predicts that peak position two ways: directly from a known d-spacing, or, for cubic crystals, straight from a lattice parameter a and Miller indices (h,k,l), skipping the intermediate lookup step entirely.
Materials scientists and X-ray diffraction lab technicians use peak position prediction constantly. A researcher planning a powder XRD scan on a new cubic material estimates where the strongest reflections will fall before ever collecting data, so they know what 2θ range to scan. A student verifying a textbook problem checks that a computed lattice parameter reproduces the experimentally observed peak positions. A phase-identification workflow compares a full table of predicted peaks for a candidate cubic phase against an unknown sample's measured pattern.
A common point of confusion is forgetting that 2θ, not θ, is what a diffractometer actually reports, this calculator always shows both so results translate directly to instrument software output. Another subtlety, shared with Bragg's law itself, is that not every reflection has a valid peak position: if nλ/2d exceeds 1 for a given d-spacing and wavelength, that reflection simply does not diffract, and this calculator flags that clearly rather than returning a meaningless angle.
This calculator is useful for planning powder XRD experiments, for crystallography and materials science coursework, and as a fast way to generate a predicted peak table for a cubic material's diffraction pattern.
📐 Formula
📖 How to Use This Calculator
Steps
💡 Example Calculations
Example 1 — Silicon's (111) Peak from Lattice Parameter
From a + hkl: a = 5.43 Å (silicon), (h,k,l) = (1,1,1), λ = 1.5406 Å (Cu-Kα), n = 1
Example 2 — Copper's (200) Peak from Lattice Parameter
From a + hkl: a = 3.615 Å (copper), (h,k,l) = (2,0,0), λ = 1.5406 Å, n = 1
Example 3 — Direct d-Spacing Input
From d-spacing: d = 3.1350 Å, λ = 1.5406 Å, n = 1
❓ Frequently Asked Questions
🔗 Related Calculators
How do you predict where an X-ray diffraction peak will appear?
Find the d-spacing for the reflection (from a cubic lattice parameter and Miller indices, d=a/√(h²+k²+l²), or measured directly), then apply Bragg's law: 2θ = 2·arcsin(nλ/2d). This calculator does both steps in one place.
What is 2θ in X-ray diffraction?
2θ is the angle between the incident and diffracted X-ray beams, the angle a diffractometer detector actually scans and reports. It is exactly twice the Bragg angle θ used inside nλ=2d sinθ.
How do I find the peak position from a and Miller indices?
For a cubic crystal, first compute d = a/√(h²+k²+l²) from the lattice parameter a and Miller indices (h,k,l), then apply 2θ = 2·arcsin(nλ/2d). For example, silicon (a=5.43 Å) at (111): d = 5.43/√3 ≈ 3.135 Å, giving 2θ ≈ 28.447° with Cu-Kα radiation.
Why does this calculator show a table of multiple peaks?
Real X-ray diffraction patterns show many peaks from different (hkl) planes, not just one. The predicted peak table lets you check an entire simulated pattern for a cubic material at once, useful for comparing against an experimental powder XRD trace during phase identification.
What does it mean if a reflection has 'no peak' in the table?
It means nλ/2d exceeds 1 for that reflection at your chosen wavelength, no real angle satisfies Bragg's law, so that reflection simply cannot be observed. This typically happens for high-index reflections (small d-spacing) combined with a relatively long wavelength.
What wavelength should I use for a typical lab XRD measurement?
Cu-Kα radiation at λ ≈ 1.5406 Å is the standard laboratory X-ray source and is the default here. Mo-Kα (≈0.7107 Å) is common for single-crystal work needing shorter wavelengths, and Co-Kα (≈1.7902 Å) is often used for iron-containing samples to avoid fluorescence.
How is this different from the Bragg Law Calculator?
The Bragg Law Calculator solves nλ=2d sinθ for θ, d, or λ given the other two, working entirely in terms of a known d-spacing. This calculator is built specifically for predicting peak positions from a cubic lattice parameter and Miller indices directly, and adds a full table of predicted 2θ positions across common reflections in one step.
How is this different from the d-Spacing from Miller Indices Calculator?
The d-Spacing from Miller Indices Calculator stops at d, covering cubic, tetragonal, and orthorhombic systems. This calculator is focused specifically on cubic crystals and carries the calculation one step further, converting that d directly into the actual diffraction peak position 2θ, plus a full predicted-pattern table.
Can I use a non-integer diffraction order n?
No, the diffraction order n must be a positive integer (1, 2, 3, ...). n=1 is the primary reflection off a given set of planes; higher orders correspond to additional harmonics of the same planes appearing at larger angles, as long as nλ/2d stays at or below 1.
Does this calculator work for non-cubic crystals?
The 'from lattice parameter + hkl' mode assumes a cubic system, where a single lattice parameter a determines d for every reflection. For tetragonal, orthorhombic, or other systems, first find d using the d-Spacing from Miller Indices Calculator, then switch to this calculator's 'from d-spacing' mode to get the peak position.