Matrices of simple face and cubic centered cubic lattice

In summary, the matrices represent the lattice vectors for simple cubic, volume centered cubic, and face centered cubic structures. These structures have specific positions for the atoms based on the lattice vectors and the matrices help define those positions.
  • #1
Petar Mali
290
0
[tex]S=
\begin{bmatrix} a & 0 & 0 \\ 0 & a & 0 \\ 0 & 0 & a \end{bmatrix}
[/tex]

for simple cubic


[tex]I=
\begin{bmatrix} -\frac{a}{2} & \frac{a}{2} & \frac{a}{2} \\ \frac{a}{2} & -\frac{a}{2} & \frac{a}{2} \\ \frac{a}{2} & \frac{a}{2} & -\frac{a}{2} \end{bmatrix}
[/tex]

for volume centered cubic

[tex]F=
\begin{bmatrix} 0 & \frac{a}{2} & \frac{a}{2} \\ \frac{a}{2} & 0 & \frac{a}{2} \\ \frac{a}{2} & \frac{a}{2} & 0 \end{bmatrix}
[/tex]

for face centered cubic

I don't see any logic for this matrices? How can I get this? I can axcept that simple is P because minimum distance between neighbors is [tex]a[/tex]. But But what with the other two matrices?
 
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  • #2
How are these matrices defined?
 
  • #3
Those matrices have the lattice vectors as rows (or columns, since they are symmetric). If you have a cube with side length a and one corner at the origin, then integer combinations of those vectors give you the lattice points. I'm not sure what your question is. Look at FCC. You have one atom at each corner, so points like (a,0,0) and (0,a,0), etc. Then at the center of each face, so points like (a/2,a/2,0) and (a/2,0,a/2). Those points come from adding those vectors together.
 

1. What are matrices of simple face and cubic centered cubic lattice?

Matrices of simple face and cubic centered cubic lattice refer to the arrangement of atoms or particles in a three-dimensional crystal structure. In simple face lattice, atoms are arranged in a repeating pattern of squares, while in cubic centered cubic lattice, atoms are arranged in a repeating pattern of cubes.

2. How are matrices of simple face and cubic centered cubic lattice different from each other?

The main difference between these two types of lattices lies in their arrangement of atoms. In simple face lattice, each atom is surrounded by four neighboring atoms, while in cubic centered cubic lattice, each atom is surrounded by eight neighboring atoms.

3. What are the applications of matrices of simple face and cubic centered cubic lattice?

Matrices of simple face and cubic centered cubic lattice have various applications in materials science and engineering. They are commonly used in the study of crystal structures, as well as in the design and development of new materials with specific properties.

4. How are matrices of simple face and cubic centered cubic lattice represented mathematically?

Matrices of simple face and cubic centered cubic lattice are represented by a three-dimensional array of numbers, where each number represents the position of an atom in the lattice. These matrices can also be represented using mathematical equations, such as the Bravais lattice and the lattice vectors.

5. Can matrices of simple face and cubic centered cubic lattice be used to create complex structures?

Yes, matrices of simple face and cubic centered cubic lattice can be used to create complex structures by combining multiple lattices together. This allows for the creation of new materials with unique properties, such as increased strength or conductivity, by manipulating the arrangement of atoms in the lattice.

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