# Solid State | Lattice constant | BCC -> HCP

• heycoa
In summary, the conversation discusses the transformation of sodium from bcc to hcp at a specific temperature and the calculation of the hcp lattice constant. The speaker mentions that they haven't gone over this topic in class and suggests finding information on the shape of a unit cell, number of atoms per unit cell, and volume of a unit cell in terms of the lattice constant to solve the problem. They also mention the importance of maintaining constant density during the transformation.
heycoa

## Homework Statement

Sodium transforms from bcc to hcp at about T=23K. Assuming that the density remains fixed and the c/a ratio is ideal (1.633), calculate the hcp lattice constant a, given that the lattice constant a'=4.23 Angstrom in the cubic phase

## Homework Equations

I can't find any equations regarding this

## The Attempt at a Solution

We haven't gone over this in class so I don't even know where to begin.

Using your text or the internet, you should be able to find the following information for bcc and hcp:

1. Shape of a unit cell.

2. Number of atoms per unit cell.

3. Volume of a unit cell in terms of the lattice constant(s). (If you can't find formulas for this, see if you can derive the volumes using geometry and the known shape of the unit cell.)

Think about the condition required for the density not to change in going from bcc to hcp.

## 1. What is the lattice constant of a solid state BCC structure?

The lattice constant, also known as the lattice parameter, of a solid state body-centered cubic (BCC) structure is the distance between two adjacent lattice points in the unit cell. It is typically denoted by the symbol "a" and is dependent on the atomic radius and packing of the atoms in the crystal lattice.

## 2. How does the lattice constant of a BCC structure differ from that of a HCP structure?

The lattice constant of a hexagonal close-packed (HCP) structure is typically smaller than that of a BCC structure because the atoms in an HCP structure are more closely packed together. This results in a more efficient use of space and a shorter distance between lattice points in the unit cell.

## 3. Is there a relationship between the lattice constant and the physical properties of a material?

Yes, the lattice constant can affect the physical properties of a material such as its density, melting point, and thermal conductivity. A smaller lattice constant typically results in a denser and stronger material, while a larger lattice constant can result in a more ductile material.

## 4. How can the lattice constant be determined experimentally?

The lattice constant can be determined experimentally using techniques such as X-ray diffraction or electron diffraction. These methods involve measuring the angles and intensities of diffracted X-rays or electrons from a crystal lattice and using mathematical equations to calculate the lattice constant.

## 5. Can the lattice constant of a material be changed?

Yes, the lattice constant of a material can be changed through processes such as alloying, heat treatment, and mechanical deformation. These methods can alter the arrangement and spacing of atoms in the crystal lattice, resulting in a change in the lattice constant and potentially affecting the material's properties.

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