# Reciprocal lattice for FCC and diffraction peaks

• Taylor_1989
In summary, the speaker's issue is more with the steps to approach a problem rather than the actual calculations. They are seeking confirmation on their approach to calculating the reciprocal lattice of an FCC structure and are unsure if their question is considered introductory or advanced physics.
Taylor_1989
Homework Statement
For a FCC crystal describe all the reciprocal lattice points corresponding to the first two diffraction peaks.
Relevant Equations
$$F_{\left(hkl\right)=\sum f\:e^{2\pi i\left(h\hat{x}+k\hat{y}+l\hat{z}\right)}}$$
My issue is more with the steps to approach rather than the calculations. I was just wondering if someone could confirm my approach to be correct.

As it asking for the reciprocal lattice of an FCC I assume this would mean I need to use the points on the BCC to calculate the geometrical structure factor and then from this a use the first two diffraction planes for a FCC which are {111} and {200} into the geometrical structure factor?

Also not really sure if this is classed as a intro to physics or advance physics question. If it is advance how could I move to that forum?

Yes, your approach is correct. This type of question is usually classified as an introductory physics question, but if you need help from advanced physicists, you can post your question in the Advanced Physics section of the forum.

## 1. What is the reciprocal lattice for FCC?

The reciprocal lattice for FCC (face-centered cubic) is a mathematical construct that describes the spatial arrangement of points in reciprocal space corresponding to the points in real space of an FCC crystal structure. It is a three-dimensional lattice with an FCC unit cell and reciprocal lattice vectors perpendicular to the planes of the FCC lattice.

## 2. How is the reciprocal lattice for FCC related to diffraction peaks?

The reciprocal lattice for FCC is directly related to the diffraction peaks observed in x-ray or electron diffraction patterns. The reciprocal lattice vectors correspond to the diffraction spots on the pattern, and the distance between the diffraction spots is inversely proportional to the spacing of the planes in the crystal lattice.

## 3. How do you calculate the reciprocal lattice vectors for FCC?

The reciprocal lattice vectors for FCC can be calculated using the equation bi = 2πaj x ak/V, where bi is the i-th reciprocal lattice vector, aj and ak are the lattice vectors of the FCC unit cell, and V is the volume of the unit cell.

## 4. What is the significance of the diffraction peaks in the reciprocal lattice for FCC?

The diffraction peaks in the reciprocal lattice for FCC have a one-to-one correspondence with the points in the real lattice, and their position and intensity provide important information about the crystal structure, such as the size and shape of the unit cell, the symmetry of the crystal, and the arrangement of atoms within the unit cell.

## 5. How does the reciprocal lattice for FCC differ from that of other crystal structures?

The reciprocal lattice for FCC differs from that of other crystal structures in terms of the number and arrangement of the reciprocal lattice points. For example, the reciprocal lattice for BCC (body-centered cubic) has more points than that of FCC, while the reciprocal lattice for hexagonal close-packed (HCP) structures has fewer points and a different arrangement. However, the basic principles of reciprocal lattice and diffraction peaks apply to all crystal structures.

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