When studying entropy in terms of order and disorder, we can consider the total entropy, $S$ for a material at a temperature, $T$ to consist of two components:

1. Thermal entropy: The entropy by virtue of the thermal energy supplied to the material. Given by the Clausius equation from the classical notion of entropy $$S = \int_{0}^{T} \frac{dq}{T}$$
2. Configurational Entropy: The entropy by virtue of multiple possible distinct 'arrangements' of the constituent particles of the material. Given by the Boltzmann formula from the statistical notion of entropy: $$S = k \ln (W)$$

It is clear that the first component is meant to capture disorder due to thermal motion (such as vibration) of the constituent atoms (or other particles). Similarly, the second is meant to capture disorder due to multiple possible atomic permutations corresponding to the same thermodynamic state.

However, this appears to become a hairy distinction when we consider the physical changes which might occur in a real substance with temperature:

1. An ionic solid like $\text{Na} \text{Cl}$ might start to see the breakage of an increasing number of bonds and breakdown of its strict order with higher temperature.
2. A substance like ice might undergo a phase transformation to become water in the liquid phase.

etc

I have been told the configurational entropy should strictly depend on the composition of the system so that we have say $S = -R \cdot (X_{A} \ln(X_{A}) + X_{B} \ln(X_{B}))$ for a binary solid solution. This would imply that the configurational entropy should not change and the entropy generated in the above examples is entirely thermal.

However, I cannot help but think that changes of these kinds should increase the space of possible configurations leading to increased configurational entropy.

Thus, I am asking about the proper classification for entropy generated by changes of this kind. Maybe I getting confused by the "configurational" in the name and there is some method by which we can show that the supposedly increased configuration space is already accounted for in the thermal entropy.

[I understand that the Boltzmann and Clausius formulae are supposed to be equivalent and that the heat supplied to the system during a transformation increases the thermal entropy. So this should(?) be possible since we want to avoid double counting of entropy changes.]

Is there some way to deal with these cases given the above definitions? If not, is there some well-accepted convention for assigning the entropy? Or do these notions break down entirely when we consider, say, phase transformations?

When studying entropy in terms of order and disorder, we can consider the total entropy, $S$ for a material at a temperature, $T$ to consist of two components:

1. Thermal entropy: The entropy by virtue of the thermal energy supplied to the material. Given by the Clausius equation from the classical notion of entropy $$S = \int_{0}^{T} \frac{dq}{T}$$
2. Configurational Entropy: The entropy by virtue of multiple possible distinct 'arrangements' of the constituent particles of the material. Given by the Boltzmann formula from the statistical notion of entropy: $$S = k \ln (W)$$

It is clear that the first component is meant to capture disorder due to thermal motion (such as vibration) of the constituent atoms (or other particles). Similarly, the second is meant to capture disorder due to multiple possible atomic permutations corresponding to the same thermodynamic state.

However, this appears to become a hairy distinction when we consider the physical changes which might occur in a real substance with temperature:

1. An ionic solid like $\text{Na} \text{Cl}$ might start to see the breakage of an increasing number of bonds and breakdown of its strict order with higher temperature.
2. A substance like ice might undergo a phase transformation to become water in the liquid phase.

etc

I have been told the configurational entropy should strictly depend on the composition of the system so that we have say $S = -R \cdot (X_{A} \ln(X_{A}) + X_{B} \ln(X_{B}))$ for a binary solid solution. This would imply that the configurational entropy should not change and the entropy generated in the above examples is entirely thermal.

However, I cannot help but think that changes of these kinds should increase the space of possible configurations leading to increased configurational entropy.

Thus, I am asking about the proper classification for entropy generated by changes of this kind. Maybe I getting confused by the "configurational" in the name and there is some method by which we can show that the supposedly increased configuration space is already accounted for in the thermal entropy.

[I understand that the Boltzmann and Clausius formulae are supposed to be equivalent and that the heat supplied to the system during a transformation increases the thermal entropy. So this should(?) be possible since we want to avoid double counting of entropy changes.]

Is there some way to deal with these cases given the above definitions? If not, is there some well-accepted convention for assigning the entropy? Or do these notions break down entirely when we consider, say, phase transformations?

Alternatively, is it correct to say that the configurational entropy (as defined above) has increased with temeprature in such cases?