Question about crystallography

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    Crystallography
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SUMMARY

The discussion focuses on the application of translational symmetry in crystallography, specifically regarding body-centered cubic (BCC) and face-centered cubic (FCC) lattices. The translational vector T = m*a + n*b + p*c, where a, b, and c are primitive lattice vectors and m, n, p are integers, is questioned in its ability to connect lattice points, particularly the central point in BCC structures. The user seeks clarification on how this vector can be utilized to reach non-corner lattice points, emphasizing the need for a deeper understanding of lattice structures and primitive vectors.

PREREQUISITES
  • Understanding of crystallography concepts, particularly lattice structures.
  • Familiarity with translational symmetry in crystal systems.
  • Knowledge of primitive vectors and their role in defining lattice points.
  • Basic comprehension of Bravais lattices, including BCC and FCC types.
NEXT STEPS
  • Study the properties of Bravais lattices in detail, focusing on BCC and FCC structures.
  • Learn about the derivation and application of primitive vectors in crystallography.
  • Explore the concept of translational symmetry and its implications in crystal structures.
  • Investigate the mathematical representation of lattice points and their connections in various crystal systems.
USEFUL FOR

Students and researchers in materials science, physicists studying crystallography, and anyone interested in the mathematical foundations of crystal structures will benefit from this discussion.

Shan K
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Hi,
I am now studying crystall structure and stucked in a question. Any kind of help will be highly appreciated.
In crystall structure talking about translational symmetry they said that for any crystall a translational vector of the kind ,
T = m*a + n*b + p*c
where a,b,c are primitive length. and n, m, p are integers,
can connect any two lattice points , but my question is if the lattice is of bcc or fcc type how this vector connects any two lattice points in them with taking n,m,p as integers ?
Because they will have a lattice point in between the eight corners of the cube, then how can we connect that point (the middle one for body centered cubic) from the corner of the cube by mean of this vector.
As taking m,n,p as integers we can go from a corner but not in the middle .
Thank You
 
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The edges of the cube in BCC or FCC are not primitive vectors.
 

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