Estimating Free Energies of Formation of Titanate (M_𝟐Ti_𝟐O_𝟕) and Zirconate (M_𝟐Zr_𝟐O_𝟕) Pyrochlore Phases of Trivalent Lanthanides and Actinides

Table 3

Thermochemical cycles used to calculate formation enthalpies (Δ𝐻^0𝑓)^a, formation entropies (Δ𝑆^0𝑓), and formation energies (Δ𝐺^0𝑓,)^b from the elements. A complete cycle is shown using RE₂Ti₂O₇ as an example. All calculations are at temperature (𝑇) equal to 25°C (298.15 K).

Δ𝐻1	2RE (cr, 298 K) + 3/2O2 (g, 298 K) → RE2O3 (cr, 298 K)
Δ𝐻2	Ti (cr, 298 K) + O2 (g, 298 K) → TiO2 (cr, 298 K)
Δ𝐻^0𝑓	= Δ𝐻𝑓−OX+ Δ𝐻1+Δ𝐻2
	= [2RE + 2Ti] (cr, 298 K) + 7/2O2 (g, 298 K) → RE2Ti2O7 (cr, 298 K)
Δ𝑆1	2RE (cr, 298 K) + 3/2O2 (g, 298 K) → RE2O3 (cr, 298 K)
Δ𝑆2	Ti (cr, 298 K) + O2 (g, 298 K) → TiO2 (cr, 298 K)
Δ𝑆^0𝑓	= Δ𝑆𝑓−OX+ Δ𝑆1+Δ𝑆2
	= [2RE + 2Ti] (cr, 298 K) + 7/2O2 (g, 298 K) → RE2Ti2O7 (cr, 298 K)
Δ𝐺^0𝑓	=Δ𝐻^0𝑓−TΔ𝑆^0𝑓

^a Thermodynamic cycles for all solids are shown in Table 2. ^bData are reported in Table 4.