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‘Free energy’ is a function of the internal energy of a system and the randomness (disorder) of the atoms/molecules within it, which we call ‘entropy’. Gibbs free energy combines these two quantities into one singe value which can be used to determine whether a phase transformation will occur, and if it will be spontaneous or nonspontaneous.
In this section of AllAboutEngineering, we will explore Gibbs free energy further, showing how equations which relate to it can be used and what the results mean. First, some background:
In the 1870s, Josiah Willard Gibbs first coined the term “available energy”, relating to the amount of energy within a given system. He published a paper in 1973 which explored how his equations could be used to predict the behaviour of systems both uniquely and combined. As will be explained later on in this section, the quantity (which would later take his name) is to do with the energy associated with a chemical reaction that can be used to do work within the system. Gibbs free energy values are obtained by summing together the total enthalpy (H) and the product of the entropy (S) and temperature (T) of a system. This is simply expressed by the following equation:
G = H – TS
A more complete form of the equation, factoring in other quantities and thermodynamic properties, such as pressure and volume, is shown below:
G = U + PV – TS
This is obtained simply in the knowledge that entropy is the sum of a system’s internal energy and the total product of pressure and volume, also shown below:
H = U + PV
The availability and presence of Gibbs free energy influences the local phase transformations within a material. This energy comes from two contributing sources as follows, both of which will be explained in more detail throughout this section:
1. Free energy difference between solid and liquid phases, also known as ‘volume free energy, Gv.
2. Formation of the solid-liquid boundary during solidification transformation, referred to as ‘surface free energy’.
Assumptions to be made when considering simple solidification of pure metals include:
· Nuclei of solid phase form in the interior of the liquid.
· Atoms cluster together to form a packing arrangement similar to that which is found in the solid phase.
· Each radius is spherical.
Equilibrium solidification of metals will be covered during this section, however for clarity, an alternative is shown below. This begins to explain how the nucleation process occurs, and illustrates the key stages using the solidification of water to ice as a more familiar example.
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