# What is difference among the consepts: bulk free energy, cohesive energy, Gibbs free energy, binding energy?

I am working on size dependent surface energy of metals. I need to know the different energies between the atoms. Different papers use different energies but their meanings seem alike, therefore they confuse me a lot.

The concepts I confuse are:

• bulk free energy,
• cohesive energy,
• Gibbs free energy,
• binding energy

Can someone tell me the correct definitions of them and show their differences in detail?

First of all, there are two general types of free energy: Gibbs and Helmholtz. Helmholtz free energy is $F=U-TS$, whereas the Gibbs free energy has an additional term that accounts for the work done on the environment by the system, $G=F+pV$. If you're modelling a system in a vacuum or a gas, say, then you'd typically use Helmholtz, whereas in a solution you'd use Gibbs.
Now imagine you have an infinite number of atoms, all separated by an infinite distance from each other. You then bring them all together to form an infinitely large crystal (i.e. there are no surfaces). The change in internal energy $U$ per atom (or per molecule) is the cohesive energy, while the change in the free energy (typically per unit volume or per unit cell) is the bulk free energy.