. 2020 Feb 17;47(3):15. doi: 10.1007/s00269-020-01085-8

Table 1.

Excess thermodynamic properties of the investigated binaries

	Observed	DFT-calculated					a^id
	max∆H^mix (kJ/mol)	max∆H^mix (kJ/mol)	W^H_AB (kJ/mol)	W^H_BA (kJ/mol)	W^S^vib_AB (J/mol/K)	W^S^vib_BA (J/mol/K)	a^id
NaCl–KCl	4.5^b	4.75^a	16.45^a	22.01^a	8.73^c	8.73^c	a_NaCl^id = X_Na a_KCl^id = X_K
Pyrope–grossular (Py–Gr)	9.6^d	9.3^a	32.72^a	44.50^a	− 7.4^e	27.9^e	a_Py^id = X_Mg³ a_Gr^id = X_Ca³
MgO–CaO	–	19.2^a	65.24^a	86.84^a	10.8^a	10.8^a	a_MgO^id = X_Mg a_CaO^id = X_Ca
Low albite–microcline (Ab–Mic)	8.1^f	6.5^a	20.59^a	31.30^a	9.1^g	9.1^g	a_Ab^id = X_Na a_Mic^id = X_K
Diopside–jadeite (Di–Jd)	7.8^h	7.0^a	27.98^a	27.98^a	2.54ⁱ	2.54ⁱ	a_Di^id = X_Ca^M2X_Mg^M1 a_Jd^id = X_Na^M2 X_Al^M1 T > 1350 Kⁿ
Diopside–CaTs (Di–CaTs)	6.0^k	6.0^j	7.70^j	37.44^j	0^l	0^l	a_Di^id = X_Mg^M1 (X_Si^T)² a_CaTs^id = 4X_Al^M1X_Al^TX_Si^T + SRO^o
Glaucophane–tremolite (Glau–Tre)	16.0^m	18.5^a	78.58^a	72.91^a	11.73ⁱ	11.73ⁱ	a_Glau^id = (X_Na^M4)²(X_Al^M2)² a_Tre^id = (X_Ca^M4)²(X_Mg^M2)² + SRO^p

max∆H^mix is the heat of mixing at the mole fraction where it is at its maximum. DFT-derived values are compared to observed ones. W^H_AB and W^H_BA are the enthalpic interaction parameters of the asymmetric Margules mixing model, ∆H^mix = (1 − X_B) X_B²W^H_AB + (1 − X_B)²X_BW^H_BA, of the A–B binary. W^S^vib_AB and W^S^vib_BA are the interaction parameters for the vibrational excess entropy, ∆S_vib^exc = (1-X_B) X_B²W^Svib_AB + (1-X_B)²X_BW^Svib_BA. To calculate the excess Gibbs energy of mixing, use W^G = W^H– T W^S and G^exc = (1 − X_B) X_B²W^G_AB + (1 − X_B)²X_BW^G_BA. Ideal mixing is defined in the last column (a^id). To define the solvus, the use of a configurational excess entropy is needed in most cases, which is, however, not listed because it is only valid at the solvus temperatures and may vanish at higher temperatures

^aDFT methods using LDA functional, this study

^bSolution calorimetry (Barrett and Wallace 1954)

^cLow-temperature calorimetry (Benisek and Dachs 2013)

^dSolution calorimetry (Newton et al. 1977)

^eLow-temperature calorimetry (Dachs 2006)

^fSolution calorimetry (Hovis 2017)

^gLow-temperature calorimetry (Benisek et al. 2014)

^hSolution calorimetry (Wood et al. 1980)

ⁱAccording to Benisek and Dachs (2012)

^jDFT methods using a partly disordered CaTs endmember

^kSolution calorimetry (Newton et al. 1977; Benisek et al. 2007)

^lLow-temperature calorimetry (Etzel et al. 2007)

^mDerived from line broadening in IR according to Etzel and Benisek (2008)

ⁿAt T < 1350 K, short-range ordering is present and at T < 1000 K, long-range ordering exists (Fleet et al. 1978)

^oShort-range ordering is present; see for example Benisek et al. (2007)

^pPossible short-range ordering is present, this study