# Nearest Neighbor lattice question

• USI
In summary, the element in question has a face-centred cubic lattice with a basis group of two atoms at 000 and 1/4 1/4 1/4, with a lattice constant of 3.55Angstroms. The separation of nearest neighbor atoms is 1.54Angstroms, and each atom has 6 next-nearest neighbors and 12 second-nearest neighbors at distances of lattice constant and 2^(1/2) * lattice constant, respectively.
USI

## Homework Statement

An element crystalises in a face-centred cubic lattice with a basis group of two atoms at 000 and 1/4 1/4 1/4. The lattice constant is 3.55Angstroms.

i) what is the separation of nearest neighbor atoms
ii) how many nearest and second nearest neighbors does each atom have.

attempt

i) The nearest neighbor distance is just going to be from the 000 atom to the one 1/4 1/4 1/4 away from it? Which gives
$$\sqrt{3(\frac{1}{4}a)^3} = 1.54Angstroms$$

ii) If the guess for part i is right then each atom will have one nearest neighbor. I can't get my head around the second nearest neighbors.

Any help appreciated, thanks.

see attachment...

1) distance = 1/2*(2)^(1/2) * lattice constant
2) 6 next-nearest neighbors at distance of lattice constant

#### Attachments

• fcc.jpg
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## 1. What is a Nearest Neighbor lattice?

A Nearest Neighbor lattice is a type of lattice structure in which each point is connected to its closest neighboring points. This is a commonly used structure in scientific studies, particularly in materials science and physics.

## 2. How is a Nearest Neighbor lattice constructed?

A Nearest Neighbor lattice is typically constructed by arranging points in a regular pattern, such as a square or hexagonal grid, and then connecting each point to its nearest neighbors. The number of nearest neighbors can vary depending on the specific lattice structure.

## 3. What are the properties of a Nearest Neighbor lattice?

The properties of a Nearest Neighbor lattice depend on the specific lattice structure being studied. However, some common properties include high symmetry, uniformity, and periodicity. These properties make Nearest Neighbor lattices useful in modeling physical systems and understanding their behavior.

## 4. What are the applications of Nearest Neighbor lattices?

Nearest Neighbor lattices have a wide range of applications in various fields of science and engineering. They are commonly used to model crystal structures, study the behavior of materials, and simulate physical systems. They are also used in computer graphics and image processing algorithms.

## 5. How is the concept of Nearest Neighbor lattices related to machine learning?

In machine learning, Nearest Neighbor lattices refer to a type of data structure used for storing and organizing data points. This structure allows for efficient searching and classification of data, making it a useful tool in various machine learning algorithms. Nearest Neighbor lattices are also used in the popular k-nearest neighbor (k-NN) classification algorithm.

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