# Volume vs pressure in solids

• fluidistic
In summary, when compressing a solid like iron, there will be a phase transition from alpha to gamma. As pressure is further increased, the amount of gamma iron will also increase until it becomes the dominant phase. This transition is typically smooth and continuous, but there may be discontinuities in state functions. It is possible to obtain different phases, such as bcc, by compressing an fcc phase and reducing the interatomic distance. This behavior is similar to that of a van der Waals gas, as described by the Maxwell construction.

#### fluidistic

Gold Member
I wonder what happens when one compresses a solid, let's say iron. In thermodynamics state functions are all smooth and differentiable, in other words V(P,T) would have no discontinuity.
Let's assume that we have an iron phase alpha at room temperature and pressure. We compress the rod up to many giga bars. At one moment, I guess, there will be a phase transition. There will be iron gamma (or any other phase) in very few percentage compared to iron alpha. We further increase the pressure, there will be more and more iron gamma until eventually we reach an iron alpha-free iron, i.e. it transformed into iron gamma entirely. And if we increase more and more the pressure it will again suffer a "smooth" phase transition. Is this correct?
I wonder what happens with the volume at any pressure. If there some discontinuity when there are phase transitions?
If I have a phase fcc at start and I increase the pressure, can I obtain a bcc phase after? I would like to have a description at the molecular level, if possible. For example if I have an fcc phase at start, I compress and the only effect would be to reduce the interatomic distance, until there's a change of phase to bcc. Some parts of the original crystal would change from fcc to bcc and the bcc unit cell will have a much lesser length than the fcc one. I am not sure this is possible/correct, I wonder what really happens.
Only curiosity, not an assignment question.
Thank you guys!

Yes, it is typical that state functions are discontious or have discontinous derivatives at phase transition.
The situation that you have a mixture of two phases (gamma and alpha iron) is also typical. You may want to have a look at the discussion of the van der Waals gas in any intro thermodynamics book, namely the so called Maxwell construction.

1 person
DrDu said:
Yes, it is typical that state functions are discontious or have discontinous derivatives at phase transition.
The situation that you have a mixture of two phases (gamma and alpha iron) is also typical. You may want to have a look at the discussion of the van der Waals gas in any intro thermodynamics book, namely the so called Maxwell construction.

Ah I see... yeah I remember what happened in the Van der Waals gas, I didn't realize it could apply to solids too.

## 1. What is the relationship between volume and pressure in solids?

The relationship between volume and pressure in solids is known as the "bulk modulus." This refers to the measure of a material's resistance to compression when subjected to an external force. In general, as pressure increases, the volume of a solid will decrease due to the particles being forced closer together.

## 2. How does temperature affect the volume and pressure of solids?

As temperature increases, the volume and pressure of solids also increase. This is because as temperature rises, the particles within a solid gain more energy and begin to vibrate more, causing them to take up more space and exert more pressure on their surroundings.

## 3. Can volume and pressure be changed independently in solids?

No, volume and pressure in solids are directly related and cannot be changed independently. Any change in one will result in a corresponding change in the other. For example, increasing pressure will decrease volume and vice versa.

## 4. How do different types of solids behave under pressure?

The behavior of solids under pressure depends on their composition and structure. Some solids, such as metals, are more malleable and can be compressed without breaking. Others, like ceramics, are more brittle and may shatter under pressure. The bulk modulus of a solid also plays a role in its behavior under pressure.

## 5. What real-world applications involve the study of volume and pressure in solids?

The study of volume and pressure in solids has many practical applications. For example, understanding the behavior of materials under pressure is crucial in fields such as engineering, materials science, and geology. It is also important in industries such as construction, where the strength and stability of materials under pressure are essential.