Thermo inconsistencies in LatticeSolidPhase

[speth]

Problem description

The phase does not satisfy basic thermodynamic identities. Some of these are due to #1309, but I think the discrepancies here may be a separate bug.

I am also suspicious of the implementation of activities and activity coefficients for this phase, which has some unusual behavior that is not documented in any way.

Steps to reproduce

Thermo identities:

>>> import cantera as ct
>>> p = ct.Solution('test/data/thermo-models.yaml', 'Li7Si3_and_interstitials')
>>> p.TP = 725, 50 * ct.one_atm
>>> p.h, p.u + p.P * p.v
-2066297.4664435755 -2077226.57539485  # should be equal
>>> p.chemical_potentials
[-4.62330156e+08 -4.56142503e+07  5.03718894e+05]
>>> p.partial_molar_enthalpies - p.T * p.partial_molar_entropies
[-4.62330156e+08 -4.66072353e+07  2.92167222e+04]

The discrepancy between h and u + Pv seems to grow with pressure.

Activities:

>>> p.X = [0.2, 0.5, 0.3]
>>> p.activity_coefficients
array([1., 1., 1.])
>>> p.activities
array([1.   , 0.625, 0.375])  # should equal X * activity_coefficients

System information

• Cantera version: 2.6.0 or main at 1ab81ac

Additional context

This was discovered as part of #1299, which implements Cantera/enhancements#114.

[speth]

The docstring of the LatticeSolidPhase notes a rather peculiar modeling choice:

 * The mole fraction vector is redefined within the LatticeSolidPhase object.
 * Each of the mole fractions sum to one on each of the sublattices.  The
 * routine getMoleFraction() and setMoleFraction() have been redefined to use
 * this convention.

However, while the phase attempts to override getMoleFractions(), the base class method Phase::getMoleFractions is not virtual. This leads to some surprising behavior, where calls to getMoleFractions from within the LatticeSolidPhase class will use LatticeSolidPhase::getMoleFractions, any external calls from a base class pointer will use Phase::getMoleFractions. I believe that this is the reason for the problem with computing consistent activities and activity coefficients.

I do not think it makes sense to have a phase where the sum of the mole fractions does not equal 1, and I think this needs to be changed to use a definition for mass and mole fractions that satisfies normal expectations.