Intro to X-Ray Diffraction (XRD)
What XRD actually measures
At a high level, XRD measures how X-rays interact with periodically arranged atoms in a crystal.
Because the atoms are arranged in a repeating pattern, X-rays scatter in a predictable way, producing diffraction peaks.
Read those peaks correctly, and you get structural information. Read them sloppily, and you’ll be confidently wrong.
Why battery people care about XRD
Battery materials are structural materials. Graphite, LCO, NMC, LFP, and other electrode materials work because atoms occupy particular positions, with particular spacings, and those positions change during synthesis, cycling, aging, and degradation.
XRD is valuable because it can tell you whether a material is crystalline, which phases are present, and whether the lattice is expanding, contracting, ordering, or distorting. In layered intercalation materials, those structural changes can track lithium content closely enough to become a powerful quantification tool.
The basic logic chain is simple:
structure changes → lattice parameters change → plane spacing changes → diffraction peak positions change
That is the entire game.
The concepts you need before reading an XRD pattern
Crystallinity
Crystallinity is the degree of structural order in a material. A crystal has an atomic arrangement that repeats over long distances. Better order produces sharper, more interpretable diffraction peaks. Poor order or amorphous structure gives broad or missing peaks.
Unit cell
The unit cell is the smallest repeating building block of a crystal. The entire crystal structure can be generated by repeating this unit in three dimensions. When we talk about structural changes in XRD, we are often talking about changes to this repeating unit.
Unit Cell
Lattice parameters
Lattice parameters, usually written as a, b, and c, define the size and shape of the unit cell. If lithium is inserted or removed, transition metals change oxidation state, or layers shift, these parameters can change. When they change, diffraction peaks can move.
d-spacing
d-spacing is the spacing between crystallographic planes. XRD is fundamentally telling you about these spacings. Each diffraction peak corresponds to a specific family of planes, and if that spacing changes, the peak position changes.
Bragg’s law: the peak-position equation
For conventional angle-dispersive XRD, the key relationship is Bragg’s law:
In most lab XRD discussions, you can think in terms of first-order diffraction, where n = 1.
What matters is this:
λ is the X-ray wavelength (typically λ ≈ 1.54 Å)*
θ is the diffraction angle
d is the spacing between crystallographic planes
*In most lab-based XRD systems, the X-ray wavelength is fixed, and the most common source is Cu Kα radiation, with λ ≈ 1.54 Å.
If the X-ray wavelength is fixed, then a change in d must appear as a change in angle. Larger d-spacing shifts a peak to lower angle. Smaller d-spacing shifts a peak to higher angle.
That is the physical meaning of a peak shift.
Miller indices: which planes are you looking at?
Miller indices, written as (hkl), label families of crystallographic planes. They tell you which planes produced a given diffraction peak.
Miller Indices
So “a peak moved” is not enough. The first real question is: which peak?
Relating d-spacing to lattice parameters
Once you know which planes produced a peak, you can connect the measured d-spacing to the unit cell dimensions.
For hexagonal crystal systems (NMC, LCO, graphite), a commonly used relationship is:
This equation connects the measured d-spacing (d) to the Miller indices (hkl) and lattice parameters (a,b,c; for hexagonal materials a=b). That is one of the bridges between a diffraction peak and an actual structural interpretation.
So if lithium extraction changes the layer spacing and changes the lattice parameters, d changes. Then the diffraction angle changes through Bragg’s law. That is how XRD uncovers structural changes.
What XRD is actually measuring in practice
A standard powder XRD experiment measures intensity as a function of diffraction angle, usually reported as intensity versus 2θ. The sample contains many crystallites in many orientations. Whenever a set of planes satisfies the diffraction condition, the detector records intensity at that angle.
The resulting pattern gives you:
peak position, which relates to d-spacing and lattice parameters
peak intensity, which depends on crystallinity, preferred orientation, occupancy, and geometry
peak width and shape, which can reflect crystallite size, strain, disorder, and instrumental broadening
Why this matters for battery materials
Layered battery materials are especially well suited to XRD because electrochemistry changes the lattice in measurable ways. In graphite, interlayer spacing evolves with lithiation. In layered oxides such as LCO and NMC, lithium removal changes transition metal oxidation state and alters slab spacing and unit-cell dimensions. You can find our collection of crystallographic information files (.cif files) here for your own XRD analysis.
These structural responses can be tracked through diffraction peak movement and modeled quantitatively.
What comes next
This first piece is the foundation: crystals, unit cells, lattice parameters, d-spacing, Miller indices, and the equations that connect them.
The next parts can build from here into:
angle-dispersive versus energy-dispersive XRD
peak assignment and refinement
using XRD to quantify lithium content in real battery materials
Because yes, you can get from a peak shift to lithium content (in NMC). But only after you work for it.
Some Resources We Love:
A comprehensive review paper on XRD
Unit cells and different structures explained