    ### Derived Variable

Derived variables (also referred to as partial derivatives) are functions defined through certain mathematical expressions of state variables. The Thermo-Calc software uses a dot "." notation between two state variables to define and evaluate derived variables. For example:

HM.T

is the heat capacity for the system at either constant pressure (if pressure is a condition) or constant volume (if volume is a condition).

HM(phase).T

is the heat capacity for a phase at either constant pressure (if pressure is a condition) or constant volume (if volume is a condition).

VM.T

is the thermal expansion of the system (already multiplied by the total volume).

VM(phase).T

is the thermal expansion of a phase (already multiplied by its molar volume).

VM.P

is the isothermal compressibility of the system (already multiplied by the total volume).

VM(phase).P

is the isothermal compressibility of a phase (already multiplied by its molar volume).

T.X(component)

is the slope of a phase boundary on a T-X(component) phase diagram with respect to mole fraction of the component in the system.

T.W(component)

is the slope of a phase boundary on a T-W(component) phase diagram with respect to mass of the component in the system.

Additional derived variables, such as the activity coefficient of a component in the system and the partition coefficient of a component between two phases, can be defined as follows:

ACR(component)/X(component)
X(phase1,component)/X(phase2,component)

In a substitutional phase, such as gas and liquid, the activity coefficient of a species can be calculated as follows:

ACR(species,phase)/Y(phase,species)

The activity coefficient and the chemical potential of a species in a phase that has more than one sublattice (e.g., carbon in FCC or BCC) is not well defined, however, if the reference state for the phase species is defined as the "pure species".