How to Find Plane Intersection in FCC Lattice Primitive Unit Cell

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SUMMARY

The discussion focuses on determining the intersection of a plane defined by Miller indices (hkl) within a face-centered cubic (FCC) lattice's primitive unit cell. The user seeks clarification on how to find the corresponding Miller indices (h1k1l1) for the plane's intersection with the unit cell. Key insights include the necessity of defining both the plane and the vectors consistently and recognizing that the plane normal is orthogonal to any vector in the plane. Understanding these concepts is crucial for solving the problem accurately.

PREREQUISITES
  • Understanding of Miller indices in crystallography
  • Familiarity with face-centered cubic (FCC) lattice structures
  • Knowledge of vector mathematics and geometric interpretations
  • Ability to apply mathematical definitions of planes and normals
NEXT STEPS
  • Study the mathematical representation of planes in crystallography
  • Learn about the geometric properties of face-centered cubic lattices
  • Explore vector operations related to plane intersections
  • Investigate the derivation of Miller indices for various crystal structures
USEFUL FOR

Students in materials science, crystallography researchers, and anyone studying solid-state physics who requires a deeper understanding of plane intersections in crystal lattices.

td21
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Homework Statement


Consider a plane (hkl) in a fcc lattice, show the correspond miller indices (h1k1l1) in the primitive unit cell.


Homework Equations





The Attempt at a Solution


so (hkl) intersect a/h,a/k,a/l in the fcc lattice right?
but in the primitive unit cell of fcc, i cannot determine the plane's intersection.
Are there any formula for this?
Thanks.
 
Physics news on Phys.org
You need to find the intersection of a plane with 3 different vectors. Just be careful to define both the plane and the vectors using the same conventions. If you don't remember how to define the plane, think about the fact that the plane normal is (obviously) normal to any vector lying in the plane, and write that statement mathematically.
 

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