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Lecture 16: 10.31.03 Phase changes and phase diagrams of single-component materials (continued)

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Today:

An example: walking along lines of constant temperature or pressure in a single-component phase diagram 2

Second-order phase transitions 4

First-order vs. second-order phase transitions 4

The glass transition2 4

Order-disorder transitions 5

References 6

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Reading:

Supplementary Reading: -

Planning Notes:

HOMEWORK PROBLEMS:

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An example: walking along lines of constant temperature or pressure in a single-component phase diagram

• Consider now how the free energy varies as we move along a line of a single-component phase diagram at constant pressure or constant temperature:

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o First, let’s move along a line of constant pressure P = PB:

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o Now let’s consider what happens if we move along a line of constant temperature, varying the pressure:

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▪ Does this diagram violate the rules for the shape of free energy curves we derived previously?

Second-order phase transitions

First-order vs. second-order phase transitions

• The phase transitions we have focused on thusfar- melting of a crystalline solid, boiling of a liquid, or structural transformations of allotropes from one crystal structure to another are known as first-order transitions. The order is noted by whether the transition is accompanied by a discontinuity in a first-, second-, or higher-order derivative of the Gibbs free energy. DISCUSSED IN CALLEN AND DILL.

o As we’ve just discussed, in the process of melting of a crystalline solid, the free energy is continuous; there is no discontinuous jump from one value of free energy in the solid to some distinctly higher (or lower) free energy in the liquid. However, we saw back in lecture 6 the entropy and enthalpy do have a discontinuity- the entropy/enthalpy of melting. At temperatures just below the melting point, the entropy is significantly lower than at temperature just above the melting point. Because the entropy is a first derivative of G:

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o …we refer to this as a first-order phase transition. Such a discontinuity is the ‘fingerprint’ of a first-order thermodynamic transition.

• In addition to first-order transitions, there are two prevalent types of second-order phase transitions. As you will expect, the second-order phase transitions occur with a discontinuity in a thermodynamic quantity which is a second derivative of the Gibbs free energy. The two second-order transitions of interest are the glass transition and order-disorder transitions.

The glass transition2

• We’ve learned in Structure the clear differences between crystalline and amorphous materials- and that solids can have either an ordered or disordered structure.

o The enthalpy of melting is thermal energy stored in a crystalline solid that is released on melting to the disordered, liquid state. As we saw earlier, there is also typically a discontinuity in the volume of materials when crystalline solids melt to the liquid state (also a first derivative of G with respect to pressure!).

o Now, what will happen if we have a disordered (amorphous) material that becomes liquid? Will there be a dramatic volume change at some point when a glass is heated? The answer is no- there is no volume discontinuity on heating an amorphous solid. There is however, a break in the slope of the volume vs. temperature:

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(Zallen2)

o

Order-disorder transitions

•

References

1. Carter, W. C. 3.00 Thermodynamics of Materials Lecture Notes (2002).

2. Zallen, R. The Physics of Amorphous Solids (John Wiley & Sons, New York, 1983) 304 pp.

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