M. T. Yin and M. L. Cohen Phys. Rev. B26, 5668 (1982) Zero ...

Zero is arbitrary.M. T. Yin and M. L. Cohen
Phys. Rev. B26, 5668 (1982)

Theoretical ground state energy
versus volume curves,

used to predict high pressure
allotropic phase transitions.

Reference volume is diamond-structure Si at P=0

Pure state 1 at V* (square box) Energy versus volume at T=0

is unstable. The stable state (schematic)
(circle) lies below at the same

volume, on the common tangent

line. It is a mixture of pure 1 and

pure 2. According to the “lever rule,”
the fraction of 1 is (V*-V2)/(V1-V2),
and the fraction of 2 is

(V1-V*)/(V1-V2). The work done on
The system in compressing from

V1 to V2 is just the energy
difference E2-E1. The enthalpy H=E+pV
is the same (H1=H2) when the pressure,
p=–dE/dV, equals the common tangent.

The physical parts (i.e. positive pressure –dE/dV) of
the curves of E vs V can be transformed into H vs P.
The graph at the left does exactly that for the curves
shown above. The unit of energy D is chosen as the

difference E2-E1 between the minima of the energy
curves for states 2 and 1. Equilibrium corresponds to
the state of least enthalpy at a given P, and volume

is given by dH/dP, a decreasing function of P.

Duclos, Vohra, and Ruoff, McMahon, Nelmes, Wright, & Allan
Phys. Rev. B 41, 12021 (1990) Phys. Rev. B 50, 739 (1994)

Renata M. Wentzcovitch
Dept. of Chem. Eng. &
Materials Science,
Univ. of Minnesota

Perovskite Rutile New phase
ABX3 BX2 ABX3

“usual” solid-liquid-gas case

Redrawn by hand to show P vertical, T horizontal metallic cerium
King, Lee, Harris, Smith
Phys. Rev. B 1, 1380 (1970).