Depending on the conditions under which you operate, another thermodynamic potential decides which processes may happen spontaneously. For an isolated system that would be the maximization of entropy, while for a closed system with constant pressure it is the minimization of the Gibbs free energy which is calculated by

G=H-TS=F+pV=U+pV-TS

If you want to relate it to microscopic behaviour, the approach is the same as for other potentials: you need to calculate the partition function (sum of states) and then its derivative. From the canonical Q, you get

G=-kT lnQ + kTV(dlnQ/dV)

The Gibbs free energy serves as an indicator to determine if spontaneous processes will occur.

defined by

G = H – TS

The expression describing Gibbs free energy change consists of ΔH−TΔS.

The expression defines Gibbs free energy through its three components of enthalpy (H) and temperature (T), and entropy (S).

The process proceeds spontaneously when the Gibbs free energy is negative, but positive values indicate energy requirements for the process to occur.

The field of material science depends on Gibbs free energy to predict the occurrence of various processes in its systems.

· A phase transition will occur or not under given temperature and pressure conditions because the value of ΔG plays a crucial role in such determinations. At phase transitions, ΔG is zero.

· The material will easily form when the chemical reactions yield a negative ΔG value.

· A stable material emerges when thermal energy cancels out with disorder processes since lower values of ΔG indicate greater material stability.

Gibbs free energy is a thermodynamic quantity that determines whether a process or reaction will occur spontaneously. It is defined as:

G= H−TS

where:

• H is enthalpy (total heat content),
• T is absolute temperature (in Kelvin),
• S is entropy (measure of disorder).

A process occurs spontaneously if the change in Gibbs free energy (ΔG) is negative:

ΔG=ΔH−TΔS

• If ΔG0: The process is non-spontaneous.
• If ΔG=0: The system is at equilibrium.

*Spontaneous: "Spontaneously" means that a process happens on its own without needing an external energy input.

Importance in Material Science

Gibbs-free energy is crucial in material science because it governs phase stability, reaction feasibility, and material transformations.

a. Phase Stability and Phase Diagrams

• A solid is said to be in equilibrium when it is in the most stable state, i.e., shows no desire to change of its own forever and ever at the given set of conditions.
• At a constant temperature and pressure, a solid will be in stable or true equilibrium if it has the lowest possible value of the Gibbs free energy, G.
• If the material has the highest possible G, then it will be in unstable equilibrium, and any infinitely small change in arrangement in atoms will produce a finite/ irreversible change in its state.
• If the materials are in a local minimum state in free energy but do not have the lowest possible value of G, then it will be in a metastable equilibrium. It can stay there indefinitely but, if it acquires sufficient energy then it will change to its most stable state.

b. Chemical Reactions and Alloy Formation

• The feasibility of chemical reactions (e.g., oxidation, reduction, decomposition) depends onΔG.
• In alloy systems, phase formation and solubility limits are determined by Gibbs free energy minimization.

c. Corrosion and Oxidation Resistance

• Gibbs free energy predicts whether a metal will corrode in a given environment.
• If ΔG for oxidation is negative, the metal will corrode spontaneously; otherwise, it remains stable.
• This helps in designing corrosion-resistant materials (e.g., stainless steel, coatings).

In conclusion, Gibbs free energy is fundamental in understanding material behavior, guiding material design, and predicting phase stability, reaction feasibility, and thermodynamic efficiency in various applications.