Mechanica Labs
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Mechanica Labs

Crystallography and mineral sensing

Every mineral is a crystal. Its atoms repeat in a lattice with a particular symmetry, and that symmetry shows up in how the mineral bends X‑rays and polarized light. We build machine learning models that identify minerals from these measurements, and we make sure we can see how they reach an answer.

  • Na
  • Cl
  • a = 5.640 Å
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Fig. 1 The rock-salt structure, shared by halite (NaCl), sylvite (KCl) and galena (PbS). Two kinds of ion alternate along every edge of the cube, and the cube repeats in every direction. The ions are drawn to scale for each mineral.

Reading a lattice with X‑rays

When X‑rays pass through a crystal, every plane of atoms reflects a little of the beam. Reflections from neighbouring planes travel slightly different distances. At most angles they arrive out of step and cancel. At a few angles the extra distance is a whole number of wavelengths, the reflections line up, and the detector records a peak. This is Bragg’s law, 2d sin θ = nλ.

A diffractometer sweeps through the angles and records these peaks. Their positions give the spacing of the lattice. Their heights depend on which atoms sit where.

d θ 2d sin θ = nλ

Intensity

2θ (°)

  • Previous mineral
Fig. 2 Powder diffraction patterns calculated for copper X‑rays. On the left, the second ray travels an extra 2d sin θ, shown in colour. Halite and sylvite share a structure, so their peaks come in the same order. In sylvite, potassium and chlorine scatter X‑rays almost equally, and several peaks, starting with the first, nearly disappear. Peak positions follow Bragg’s law. Peak heights are approximate.

Minerals under the microscope

X‑ray diffraction reads a powder. A microscope reads the rock as it is, grain by grain. A thin section is a slice of rock ground down to about 30 micrometres, thin enough for light to pass through. Under a petrographic microscope each mineral has its own look: its colour, how much it stands out, and how its brightness changes between crossed polarizers as the stage turns. Mineralogists use these cues to identify grains by eye, and they are the cues an image model has to learn.

  • Quartz
  • Plagioclase
  • Biotite
  • Garnet
  • Opaque (sulfide)

Click a grain to see what identifies it.

Fig. 3 A simulated thin section. Switch between plane-polarized light and crossed polarizers, and turn the stage. Between crossed polarizers most grains go dark four times in each turn, garnet stays dark at every angle, and the opaque grains are black in both. The grain labels show what an image model is trained to produce.

Machine learning on thin-section images is an active field. One recent public dataset has more than 100,000 grains labelled by experts across 25 minerals, and models that see both plane-polarized and cross-polarized images do better than models that see only one. What we want to know is whether such models rely on the cues a mineralogist uses, or on shortcuts that will fail on the next mine’s rocks.

What the models do

A sample from a mine is rarely one mineral. Its diffraction pattern mixes several, with peaks that overlap and noise on top, and its thin section has hundreds of grains. Identifying them by hand is slow. We train models to predict a crystal’s lattice and its space group, which is the complete list of symmetries the crystal has, and to estimate which minerals a sample contains. Microscope images are the natural next input.

The models are built to respect symmetry. A crystal turned around in the instrument is still the same crystal, so the model’s answer should not change when it is turned.

Why interpretability matters here

A space group is a group in exactly the sense used in our interpretability work. The methods we use to find the algorithm inside a network trained on group multiplication can be used to check what a crystallography model has learned. A geologist should be able to confirm that a model reported pyrite because of pyrite’s peaks, or because of how the grain looks under the microscope, and not because of something in the noise.

Mineral content is also one of the properties that geometallurgical models use to predict how ore will behave in the plant. That is where this work meets our work on deep mine systems.