Notation for crystal planes and directions.
Miller indices (hkl) describe crystal planes by the reciprocals of axis intercepts (cleared of fractions); [uvw] denotes directions. Families like {111} are equivalent planes. They are used for slip systems, diffraction and anisotropy.
The (111) plane is the close-packed slip plane in FCC metals.
Miller indices name crystal planes and directions, which is needed to read texture, X-ray results and slip behaviour.
Notation for crystal planes and directions.
Miller indices name crystal planes and directions, which is needed to read texture, X-ray results and slip behaviour.
Reciprocals of the intercepts of a plane with the crystal axes, cleared of fractions, written as a bracketed set of integers.
Planes use parentheses and directions use square brackets, so the two are distinguished in written notation.
Typical applications include identifying the planes that slip in a copper crystal, reading an X-ray diffraction peak to find a plane spacing and describing the orientation of a grain in a textured sheet.
Study "Crystal structures" first (topic 3 of 100 in Materials & Chemical). It covers the groundwork this topic builds on.
Intercepts 1/h,1/k,1/l. Close-packed planes slip easily. Negative indices with bars.
The (111) plane is the close-packed slip plane in FCC metals.
The next topic is "Packing factor and density", which builds directly on this one.
It is classed as Beginner in Materials & Chemical (topic 4 of 100). It is an entry-level topic. It relies only on basic school mathematics and the ideas introduced earlier in this discipline.
Want to practise? Open the interactive course for quick checks, quizzes, simulations and progress tracking.