THERMODYNAMIC MODELING OF NON-CONVERGENT ORDERING IN ORTHOPYROXENES -A COMPARISON OF CLASSICAL AND LANDAU APPROACHES

The excess Gibbs free energy due to non-convergent ordering is describ ed by a Landau expansion in which configurational and non-configuratio nal entropy contributions are separated: G(L) = -hQ(t) + 1/2 a(T - T* c Q(t)2 + 1/n e(n) Q(t)n - TS(conf.)ord Neglecting higher order terms in Q(t), this expansion is formally equivalent to the reciprocal solut ion model for the distribution of Fe2+ and Mg over the non-equivalent M1 and M2 sites of orthopyroxenes: G(ord) = -1/2[DELTAG(exch)0 - (L(M1 )G - L(M2)G)X] Q(t) +1/4[DELTAG(rec)0 - (L(M2)G + L(M1)G)]Q(t)2 - TS(c onf.)ord The Q(t) term describes a temperature and composition-depende nt thermodynamic field that prevents the crystal from attaining full d isorder at a finite temperature. The X term models the dependence of t he field on composition. It causes the isotherms in a Roozeboom diagra m X(Fe)M2 vs. X(Fe)M1 to be asymmetric. The Q(t)2 term incorporates ne arest-neighbour interactions. Higher order interactions are accounted for by the Q(t)n term, which is not routinely foreseen in the reciproc al solution model. The critical temperature Tc is interpreted as a ra tio of enthalpy and entropy contributions to the free energy, DELTAG(r ec)0, of a reciprocal reaction Tc = DELTAH(rec)0 - (L(M1)H + L(M2)H)/ DELTAS(rec)0 - (L(M1)S + L(M2)S). The comparison of Landau and classic al approaches is extended to convergent ordering models which are show n to be incorporated in expressions for non-convergent ordering.