International Scholarly Research Notices

Research Article

Estimating Free Energies of Formation of Titanate ( M 𝟐 T i 𝟐 O 𝟕 ) and Zirconate ( M 𝟐 Z r 𝟐 O 𝟕 ) Pyrochlore Phases of Trivalent Lanthanides and Actinides

Table 2

Thermochemical cycles used to calculate formation enthalpies from elements for M2Ti2O7 ( Δ 𝐻 0 𝑓 , M 2 T i 2 O 7 ) , M2Zr2O7 ( Δ 𝐻 0 𝑓 , M 2 Z r 2 O 7 ) , M2(ZrO3)3, ( Δ 𝐻 0 𝑓 , M 2 ( Z r O 3 ) 3 ) , M2(TiO3)3, and ( Δ 𝐻 0 𝑓 , M 2 ( T i O 3 ) 3 ) solids at 25°C (298.15 K).
Δ 𝐻 1 2RE (cr, 298.15 K) + 3/2O2 (g, 298.15 K) → RE2O3
(cr, 298.15 K)
Δ 𝐻 2 Ti (cr, 298.15 K) + O2 (g, 298.15 K) → TiO2
(cr, 298.15 K)
Δ 𝐻 3 Zr (cr, 298.15 K) + O2 (g, 298.15 K) → ZrO2
(cr, 298.15 K)
Δ 𝐻 0 𝑓 , M 2 T i 2 O 7 = Δ 𝐻 𝑓 , M 2 T i 2 O 7 − O X + Δ 𝐻 1 + 2 Δ 𝐻 2
= [2RE + 2Ti] (cr, 298.15 K) + 7/2O2 (g, 298.15 K) → RE2Ti2O7 (cr, 298.15 K)
Δ 𝐻 0 𝑓 , M 2 Z r 2 O 7 = Δ 𝐻 𝑓 , M 2 Z r 2 O 7 − O X + Δ 𝐻 1 + 2 Δ 𝐻 3
= [2RE + 2Zr] (cr, 298.15 K) + 7/2O2 (g, 298.15 K) → RE2Zr2O7 (cr, 298.15 K)
Δ 𝐻 0 𝑓 , M 2 ( Z r O 3 ) 3 = 𝐻 0 𝑓 , M 2 ( Z r O 3 ) 3 − O X + Δ 𝐻 1 + 3 Δ 𝐻 3
Δ 𝐻 0 𝑓 , M 2 ( T i O 3 ) 3 = 𝐻 0 𝑓 , M 2 ( T i O 3 ) 3 − O X + Δ 𝐻 1 + 3 Δ 𝐻 2