Appendices of Advocat, hart, Berger, Lacambe and Bonnetier

APPENDICES OF

Solubility study of Ti,Zr-based ceramics designed to immobilise long-lived radionuclides

Gilles Leturcq, Thierry Advocat, Kaye Hart, Gilles Berger, Jacques Lacombe and Armand Bonnetier

Appendix 1: Thermodynamic data from literature ñ solid species

Chemical species G_f° (kJ/mol) H_f° (kJ/mol) S_f° (J/mol K) Cp (J/mol K) Reference

Al₂O₃
Al(OH)₃
Al₂TiO₅
BaO
BaAl₂O₄
BaSiO₃
Ba₂SiO₄
BaSi₂O₅
Ba₂Si₃O₈
BaTiO₃
Ba₂TiO₄
BaZrO₃
CaO
CaAl₂O₄
Ca₂Al₂O₅
Ca₃Al₂O₆
CaSiO₃ (wollastonite)
Ca₂SiO₄ (olivine)
Ca₃SiO₅
CaAl₂SiO₆ (pyroxene)
CaAl₂Si₂O₈ (anorthite)
Ca2Al2SiO7
Ca₃Al₂Si₃O₁₂
CaTiO₃ (perovskite)
Ca₃Ti₂O₇
Ca₄Ti₃O₁₀
CaTiSiO₅ (titanite)
CaZrO₃
CaZrTi₂O₇ (zirconolite)
SiO₂
TiO₂ (rutile)
TiO₂ (anatase)
Zr(OH)₄ (c)
ZrO₂ (zirconia)
ZrSiO₄ (zircon)
-1582.26
-1156.40
-2489.23
-525.35
-2212.37
-1540.31
-2175.14
-2410.97
-3963.07
-1572.44
-2132.90
-1694.68
-603.51
-2208.82
-2801.42
-3411.79
-1549.66
-2198.59
-2783.90
-3122.04
-4002.22
-3782.86
-6280.41
-1575.2
-3751.01
-5386.85
-2461.78
-1681.06
-3514.6
-856.44
-889.41
-883.00
-1547.97
-1039.72
-1909.33
-1675.70
-1294.63
-2635.5
-553.54
-2325.89
-1623.60
-2287.80
-2548.06
-4184.80
-1659.80
-2243.00
-1779.46
-635.09
-2326.30
-2958
-3587.80
-1634.94
-2315.22
-2929.20
-3298.20
-4227.90
-3981.50
-6646.16
-1660.6
-3950.50
-5671.66
-2603.30
-1766.90
-3713.8
-910.86
-944.75
-938.72
-1720.5
-1097.46
-2023.80
50.92
68.44
109.6
70.42
148.53
109.6
176.1
153.13
258.20
107.90
196.60
124.68
38.07
114.22
127.09
205.90
81.92
120.79
168.60
141.40
199.28
210.00
241.42
93.64
234.70
328.44
129.20
100.08
193.3
41.46
50.29
49.91
129.7
50.36
84.03
79.03
91.76
136.40
47.28
125.07
90.00
134.89
134.21
224.60
102.47
152.63
100.71
42.12
120.79
164.35
209.70
85.27
126.65
171.88
165.7
211.31
205.43
323.14
97.65
239.32
337.81
138.95
96.57
211.9
44.59
55.10
55.27
56.19
98.74
Cox et al. (1989)
Phillips et al. (1988)
Babushkin et al. (1985)
Barin (1989)
Barin (1989)
Barin (1989)
Barin (1989)
Barin (1989)
Barin (1989)
Barin (1989)
Barin (1989)
Barin (1989)
Barin (1989)
Barin (1989)
Barin (1989)
Barin (1989)
Barin (1989)
Barin (1989)
Barin (1989)
Barin (1989)
Barin (1989)
Barin (1989)
Barin (1989)
Wagman et al.(1982)
Barin (1989)
Barin (1989)
Barin (1989)
Barin (1989)
Putnam et al. (1999)
Barin (1989)
Barin (1989)
Phillips et al. (1988)
Babushkin et al. (1985)
Chase et al. (1985)
Barin (1989)

Appendix 2: Thermodynamic data - aqueous species

Chemical species G_f° (kJ/mol) H_f° (kJ/mol) Reference

H₂O
OH^-
Al³⁺
Al(OH)²⁺
Al(OH)₂⁺
Al(OH)_3aq
Al(OH)₄^-
Ca²⁺
Ti⁴⁺
Ti(OH)₂²⁺
Ti(OH)₃⁺
Ti(OH)_4aq
Ti(OH)₅^-
ZrO²⁺
-237.14
-157.20
-488.7
-696.3
-903.7
-1109.2
-1305.6
-552.90
-391.60
-861.47
-1084.92
-1308.37
-1531.32
-840.62
-285.83
-230.03
-537.2
-769.0
-1014.2
-1251.8
-1495.8
-543.1
-449.80
-976.20
-1229.40
-1482.50
-1735.60
-933.50
Cox et al. (1989)
Phillips et al. (1988)
Castet et al. (1993)
Castet et al. (1993)
Castet et al. (1993)
Castet et al. (1993)
Castet et al. (1993)
Phillips et al. (1988)
Phillips et al. (1988)
Phillips et al. (1988)
Phillips et al. (1988)
Phillips et al. (1988)
Phillips et al. (1988)
Latimer (1952)

Reaction log K 25fbC Reference

Zr⁴⁺ + H₂O 5f Zr(OH)³⁺ + H⁺
Zr⁴⁺ + 2H₂O 5f Zr(OH)₂²⁺ + 2H⁺
Zr⁴⁺ + 3H₂O 5f Zr(OH)₃⁺ + 3H⁺
Zr⁴⁺ + 4H₂O 5f Zr(OH)_4aq + 4H⁺
Zr⁴⁺ + 5H₂O 5f Zr(OH)₅^- + 5H⁺
ZrO₂ + 4H⁺ 5f Zr⁴⁺ + 2H₂O
0.3
-1.7
-5.1
-9.7
-16.0
-1.9

Allard et al. (1980) ;
Baes and Mesmer (1986)

Chemical species G_f° (kJ/mol) H_f° (kJ/mol) Reference

Zr⁴⁺
Zr(OH)³⁺
Zr(OH)₂²⁺
Zr(OH)₃⁺
Zr(OH)_4aq
Zr(OH)₅^-
-554.83
-793.64
-1019.34
-1237.04
-1447.89
-1649.05
-610.71
-880.45
-1135.36
-1381.24
-1619.40
-1846.59

this study

Appendix 3: Chemical reactions for the formation of perovskite from oxide reactants and associated free energy and enthalpy of formation.

Chemical reaction 44G_f - 44G_r
kJ/mol
44H_f - 44H_r
kJ/mol

CaO + TiO₂5f CaTiO₃
CaAl₂O₄ + TiO₂5f CaTiO₃ + Al₂O₃
CaTiSiO₅5f CaTiO₃ + SiO₂
BaTiO₃ + CaO 5f CaTiO₃ + BaO
CaZrO3 + TiO₂5f CaTiO₃+ ZrO₂
CaTiSiO₅ + ZrO₂5f CaTiO₃ + ZrSiO₄
CaSiO₃ + CaZrO₃ + TiO₂ 5f CaTiO₃ + ZrSiO₄ + CaO
CaSiO₃ + TiO₂5f CaTiO₃ + SiO₂
CaSiO₃ + BaZrO₃ + TiO₂ 5f CaTiO₃ + ZrSiO₄ + BaO
CaZrTi₂O₇ 5f CaTiO₃+ ZrO₂ + TiO₂
2 CaTiSiO₅ 5f CaTiO₃+ CaSiO₃ + SiO₂ + TiO₂
BaTiO₃ + CaSiO₃ 5f CaTiO₃+ BaSiO₃
BaTiO₃ + CaZrO₃ 5f CaTiO₃+ BaZrO₃
CaSiO₃ + CaZrTi₂O₇ 5f 2 CaTiO₃+ ZrSiO₄
BaO + CaO + 2 TiO₂ 5f CaTiO₃+ BaTiO₃
CaO + CaZrTi₂O₇ 5f CaTiO₃+ CaZrO₃ + TiO₂
(1/3) Ca₃Ti₂O₇ + (1/3) TiO₂ 5f CaTiO₃
(1/2) Ca₃Ti₂O₇ 5f CaTiO₃+ (1/2) CaO
(1/3) Ca₄Ti₃O₁₀ 5f CaTiO₃ + (1/3) CaO
(1/4) Ca₄Ti₃O₁₀ + (1/4) TiO₂ 5f CaTiO₃
-1492.92
-1515.97
-1605.34
-1650.60
-1530.74
-1592.18
-1607.29
-1582.62
-1699.08
-1585.47
-1628.05
-1581.79
-1558.81
-1577.46
-1335.23
-1547.65
-1546.80
-1573.75
-1594.45
-1569.07
-1579.84
-1595.35
-1692.45
-1741.34
-1614.19
-1676.96
-1687.7
-1668.83
-1781.80
-1671.59
-1716.06
-1671.14
-1647.25
-1662.47
-1418.33
-1637.24
-1631.75
-1657.71
-1678.86
-1654.10

AVERAGE -1569 -1654

Appendix 3: Chemical reactions for the formation of zirconolite from oxide reactants and associated free energy and enthalpy of formation.

Chemical reaction 44G_f - 44G_r
kJ/mol
44H_f - 44H_r
kJ/mol

CaTiO₃ + ZrO₂ + TiO₂ 5f CaZrTi₂O₇
2 TiO₂ + CaO + ZrO₂ 5f CaZrTi₂O₇
TiO₂ + CaTiSiO₅ + ZrO₂ 5f CaZrTi₂O₇ + SiO₂
TiO₂ + CaTiO₃ + ZrSiO₄ 5f CaZrTi₂O₇+ SiO₂
TiO₂ + CaTiSiO₅ + ZrSiO₄ 5f CaZrTi₂O₇ + 2 SiO₂
2 TiO₂ + CaSiO₃ + ZrO₂ 5f CaZrTi₂O₇ + SiO₂
BaZrO3 + 2 TiO₂ + CaO 5f CaZrTi₂O₇ + BaO
BaTiO₃ + CaZrO₃ + TiO₂ 5f CaZrTi₂O₇ + BaO
CaZrO₃ + 2 TiO₂ 5f CaZrTi₂O₇
CaZrO₃ + CaTiO₃ + TiO₂ 5f CaZrTi₂O₇+ CaO
CaTiO₃ + CaTiSiO₅ + ZrO₂ 5f CaZrTi₂O₇ + CaSiO₃
2 CaTiO₃ + ZrSiO₄ 5f CaZrTi₂O₇ + CaSiO₃
CaAl₂O₄ + 2 TiO₂ + ZrO₂ 5f CaZrTi₂O₇ + Al₂O₃
BaTiO₃ + TiO₂ + ZrO₂ + CaAl₂O₄ 5f CaZrTi₂O₇ + BaAl₂O₄
BaTiO₃ + BaZrO₃ + CaTiSiO₅ 5f CaZrTi₂O₇ + Ba₂SiO₄
-3504.38
-3422.05
-3534.47
-3517.53
-3547.62
-3511.75
-3551.66
-3617.56
-3459.87
-3542.2
-3527.1
-3510.16
-3445.10
-3498.02
-3553.76
-3702.81
-3622.05
-3734.66
-3718.29
-3750.14
-3711.04
-3750.50
-3817.90
-3656.40
-3737.16
-3726.42
-3710.05
-3637.56
-3702.43
-3754.76

AVERAGE -3516 -3715

Appendix 4: Chemical reactions for the formation of titanite from oxide reactants and associated free energy and enthalpy of formation.

Chemical reaction 44G_f - 44G_r
kJ/mol
44H_f - 44H_r
kJ/mol

CaSiO₃ + TiO₂ 5f CaTiSiO₅
CaTiO₃ + SiO₂ 5f CaTiSiO₅
Ca₂SiO₄ + TiO₂ 5f CaTiSiO₅+ CaO
(1/3) Ca₃Al₂Si₃O₁₂ + TiO₂ 5f CaTiSiO₅+ (1/3) Al₂O₃
Ca₃SiO₅ + TiO₂ 5f CaTiSiO₅ + 2 CaO
Ca₄Ti₃O₁₀ + SiO₂ 5f CaTiSiO₅ + 2 CaTiO₃ + CaO
(1/2) Ca₃Ti₂O₇ + SiO₂ 5f CaTiSiO₅ + (1/2) CaO
CaZrTi₂O₇ + CaSiO₃ 5f CaTiSiO₅ + CaZrO₃ + TiO₂
CaAl₂SiO₆ + TiO₂ 5f CaTiSiO₅+ Al₂O₃
(1/2) CaAl₂Si₂O₈ + CaTiO₃ 5f CaTiSiO₅+ (1/2) CaAl₂O₄
CaZrTi₂O₇ + Ca₂SiO₄ 5f CaTiSiO₅ + CaZrO₃+ CaTiO₃
(1/2) CaZrTi₂O₇ + CaSiO₃ 5f CaTiSiO₅ + (1/2) CaZrO₃
CaZrTi₂O₇ + SiO₂ 5f CaTiSiO₅ + TiO₂ + ZrO₂
CaO + TiO₂ + SiO₂ 5f CaTiSiO₅
Ca₂SiO₄ + 2 TiO₂ 5f CaTiSiO₅ + CaTiO₃
(1/4) Ca₄Ti₃O₁₀ + (1/4) TiO₂ + SiO₂ 5f CaTiSiO₅
(1/2) [ Ca₄Ti₃O₁₀ + ZrO₂ + TiO₂ ] + SiO₂ 5f CaTiSiO₅ + (1/2) [ CaO + CaZrTi₂O₇]
Ca₄Ti₃O₁₀ + SiO₂ + TiO₂ 5f CaTiSiO₅ + 3 CaTiO₃
(1/3) Ca₄Ti₃O₁₀ + SiO₂ 5f CaTiSiO₅ + (1/3) CaO
(1/3) Ca₄Ti₃O₁₀ + (2/3) CaO + Ca₂Al₂SiO₇ 5f CaTiSiO₅ + Ca₃Al₂O₆
(1/3) [ Ca₄Ti₃O₁₀ + Ca₃Al₂Si₃O₁₂ ] 5f CaTiSiO₅ + (1/3) [ CaO + Ca₃Al₂O₆ ]
(1/3) Ca₃Al₂Si₃O₁₂ + CaTiO₃ 5f CaTiSiO₅ + (1/3) Ca₃Al₂O₆
-2439.06
-2431.69
-2484.49
-2455.46
-2466.29
-2489.30
-2430.19
--2493.79
-2429.19
-2471.95
-2456.89
-2466.43
-2441.91
-2349.36
-2402.16
-2425.51
-2455.38
-2406.96
-2450.89
-2569.03
-2550.66
-2531.45
-2579.69
-2571.45
-2624.87
-3601.57
-2603.77
-2626.24
-2568.56
-2637.09
-2567.25
-2611.39
-2601.52
-2608.39
-2582.45
-2490.69
-2544.11
-2564.96
-2593.35
-2545.48
-2589.72
-2707.65
-2698.31
-2680.05

AVERAGE -2459 -2600

Appendix 5: Chemical reactions of formation of Ca2SiO4 from oxide reactants and associated free energy and enthalpy of formation.

Chemical reaction 44G_f - 44G_r
kJ/mol
44H_f - 44H_r
kJ/mol

CaO + CaSiO₃ 5f Ca₂SiO₄
Ca₃SiO₅ 5f Ca₂SiO₄ + CaO
2 CaSiO₃ 5f Ca₂SiO₄ + SiO₂
CaAl₂SiO₆ + CaO 5f Ca₂SiO₄+ Al₂O₃
Ca₃Al₂Si₃O₁₂ 5f Ca₂SiO₄ + CaAl₂Si₂O₈
2 CaAl₂Si₂O₈ 5f Ca₂SiO₄ + 2 Al₂SiO₅ + SiO₂
2 CaSiTiO₅ 5f Ca₂SiO₄ + SiO₂ + 2 TiO₂
2CaTiO₃ + Ba₂SiO₄ 5f Ca₂SiO₄+ 2 BaTiO₃
2 CaZrO₃ + Ba₂SiO₄ 5f Ca₂SiO₄+2 BaZrO₃
2 CaAl₂O₄ + SiO₂ 5f Ca₂SiO₄+ 2 Al₂O₃
-2153.17
-2180.39
-2242.87
-2143.30
-2278.18
-2262.22
-2288.30
-2180.76
-2147.89
-2109.57
-2270.03
-2294.11
-2359.02
-2257.59
-2418.26
-2364.31
-2406.25
-2289.40
-2262.70
-2212.07

AVERAGE -2199 -2313

Appendix 6: Chemical reactions for the formation of pyroxene from oxide reactants and associated free energy and enthalpy of formation.

Chemical reaction 44G_f - 44G_r
kJ/mol
44H_f - 44H_r
kJ/mol

CaO + Al₂O₃ + SiO₂ 5f CaAl₂SiO₆
CaSiO₃ + Al₂O₃ 5f CaAl₂SiO₆
CaAl₂Si₂O₈ 5f CaAl₂SiO₆ + SiO₂
Ca₂SiO₄ + Al₂O₃ 5f CaAl₂SiO₆+ CaO
CaAl₂O₄ + SiO₂ 5f CaAl₂SiO₆
CaO + Al₂SiO₅ 5f CaAl₂SiO₆
Ca₃Al₂Si₃O₁₂ 5f CaAl₂SiO₆+ 2 CaSiO₃
Ca₂Al₂SiO₇ 5f CaAl₂SiO₆+ CaO
CaTiSiO₅ + Al₂O₃ 5f CaAl₂SiO₆+ TiO₂
Ca₃Al₂O₆ + SiO₂ 5f CaAl₂SiO₆+ 2 CaO
Ca₃SiO₅ + Al₂O₃5f CaAl₂SiO₆+ 2 CaO
-3042.21
-3131.91
-3145.78
-3177.34
-3065.26
-3046.40
-3181.10
-3179.35
-3154.63
-3061.21
-3159.14
-3221.65
-3310.64
-3317.04
-3355.83
-3237.16
-3225.40
-3376.28
-3346.41
-3334.26
-3228.48
-3334.72

AVERAGE -3122 -3299

Appendix 8: Comparison between approximations and real values of 44Gf and 44Hf of perovskite, zirconolite, titanite, olivine and pyroxene, and relative errors. Ca₂SiO₄

44G_f est. 44G_f p.r. 44G_f est. - 44G_f p.r. % error

CaZrTi₂O₇ -3516.21 -3514.60 -1.61 0.046

CaTiO₃ -1575.24 -1575.20 -0.04 0.003

Ca₂SiO₄ -2198.66 -2198.80 0.14 -0.006

CaAl₂SiO₆ -3122.21 -3122.00 -0.21 0.007

CaTiSiO₅ -2459.00 -2461.80 2.80 -0.114

44H_f est. 44H_f p.r. 44H_f est. - 44H_f p.r. % error

CaZrTi₂O₇ -3715.48 -3713.80 -1.68 0.045

CaTiO₃ -1660.87 -1660.60 -0.27 0.016

-2313.37 -2315.20 1.83 -0.079 CaAl₂SiO₆

-3298.90 -3298.20 -0.70

44Gf est. and 44Hf est are the estimated values of 44Gf and 44Hf , 44Gf p.r. and 44Gf p.r. are the previous reported values in Appendices 3-7. Appendix 9: Chemical reactions for the formation of hollandite from oxide reactants and associated free energy and enthalpy of formation.

Chemical reaction 44G_f - 44G_r
kJ/mol
44H_f - 44H_r
kJ/mol

BaO + Al₂O₃ + 6 TiO₂ rut 5f BaAl₂Ti₆O₁₆
BaAl₂O₄ + 6 TiO₂ rut 5f BaAl₂Ti₆O₁₆
Al₂O₃ + 5 TiO₂ rut + BaTiO₃ 5f BaAl₂Ti₆O₁₆
CaAl₂O₄ + 5 TiO₂ rut + BaTiO₃ 5f BaAl₂Ti₆O₁₆ + CaO
BaO + Al₂O₃ + 6 CaTiO₃5f BaAl₂Ti₆O₁₆ + 6 CaO
BaAl₂O₄ + 6 CaTiO₃ 5f BaAl₂Ti₆O₁₆ + 6 CaO
BaSiO₃ + Al₂O₃ + 6 TiO₂ rut 5f BaAl₂Ti₆O₁₆ + SiO₂
BaSiO₃ + Al₂O₃ + 6 CaTiO₃ 5f BaAl₂Ti₆O₁₆ + 5 CaO + CaSiO₃
Al₂O₃ + 5 CaTiO₃ + BaTiO₃ 5f BaAl₂Ti₆O₁₆ + 5 CaO
BaO + Al₂O₃ + 6 CaTiSiO₅ 5f BaAl₂Ti₆O₁₆ + 6 CaSiO₃
BaAl₂O₄ + 6 CaTiSiO₅ 5f BaAl₂Ti₆O₁₆ + 6 CaSiO₃
Al₂O₃ + 5 CaTiSiO₅ + BaTiO₃ 5f BaAl₂Ti₆O₁₆ + 5 CaSiO₃
BaZrO₃ + + Al₂O₃ + 6 TiO₂ rut 5f BaAl₂Ti₆O₁₆ + ZrO₂
BaO + Al₂O₃ + 3 CaZrTi₂O₇ 5f BaAl₂Ti₆O₁₆ + 3 CaZrO₃
BaAl₂O₄ + 3 CaZrTi₂O₇ 5f BaAl₂Ti₆O₁₆ + 3 CaZrO₃
CaAl₂SiO₆ + 5 TiO₂ rut + BaTiO₃ 5f BaAl₂Ti₆O₁₆ + CaSiO₃
CaAl₂SiO₆ + 4 TiO₂ rut + BaTiO₃ + CaTiO₃ 5f BaAl₂Ti₆O₁₆ + Ca₂SiO₄
Ca₂Al₂SiO₇ + 5 TiO₂ rut + BaTiO₃ 5f BaAl₂Ti₆O₁₆ + Ca₂SiO₄
CaAl₂Si₂O₈ + 5 TiO₂ rut + BaTiO₃ + CaTiO₃ 5f BaAl₂Ti₆O₁₆ + CaSiO₃ + CaTiSiO₅
Ca₃Al₂O₆ + 5 TiO₂ rut + BaTiO₃ 5f BaAl₂Ti₆O₁₆ + 3 CaO
Ca₃Al₂O₆ + 5 TiO₂ rut + BaTiO₃ + 3 SiO₂ 5f BaAl₂Ti₆O₁₆ + 3 CaSiO₃
Ca₃Al₂O₆ + 8 TiO₂ rut + BaTiO₃ 5f BaAl₂Ti₆O₁₆ + 3 CaTiO₃
Ca₃Al₂O₆ + 5 TiO₂ rut + BaTiO₃ + 2 SiO₂ 5f BaAl₂Ti₆O₁₆ + CaSiO₃ + Ca₂SiO₄
Ca₃Al₂Si₃O₁₂ + 5 TiO₂ rut + BaTiO₃ 5f BaAl₂Ti₆O₁₆ + 3 CaSiO₃
Ca₃Al₂Si₃O₁₂ + 5 TiO₂ rut + BaTiO₃ 5f BaAl₂Ti₆O₁₆ + CaSiO₃ + Ca₂SiO₄+ SiO₂
3 Ca₃Ti₂O₇ +Al₂O₃ + BaO 5f BaAl₂Ti₆O₁₆ + 9 CaO
2Ca₃Ti₂O₇+BaTiO₃ +TiO₂ rut +CaAl₂Si₂O₈ 5f BaAl₂Ti₆O₁₆ + CaO + 2 Ca₃SiO₅
2 Ca₄Ti₃O₁₀+ BaSiO₃ + CaAl₂Si₂O₈ 5f BaAl₂Ti₆O₁₆ + 3 Ca₃SiO₅
Ca₄Ti₃O₁₀ + Ca₃Ti₂O₇ + BaTiO₃ + CaAl₂Si₂O₈ 5f BaAl₂Ti₆O₁₆ + 2 Ca₃SiO₅+ 2 CaO
2 Ca₄Ti₃O₁₀ + BaAl₂O₄+ 4 SiO₂ 5f BaAl₂Ti₆O₁₆ + 4 Ca₂SiO₄
2 Ca₄Ti₃O₁₀ + BaAl₂O₄ + 8 TiO₂ 5f BaAl₂Ti₆O₁₆ + 8 CaTiO₃
BaO + CaAl₂SiO₆ + 6 TiO₂ 5f BaAl₂Ti₆O₁₆ + CaSiO₃
BaO + CaTiO₃+ CaAl₂SiO₆ + 5 TiO₂ 5f BaAl₂Ti₆O₁₆ + Ca₂SiO₄
BaO + Ca₃Al₂Si₃O₁₂ + 6 TiO₂ 5f BaAl₂Ti₆O₁₆ + 3 CaSiO₃
BaO + Ca₃Al₂Si₃O₁₂ + 6 TiO₂ 5f BaAl₂Ti₆O₁₆ + CaSiO₃+ Ca₂SiO₄ + SiO₂
BaO + Ca₃Al₂O₆ + 6 TiO₂ + 2 SiO₂ 5f BaAl₂Ti₆O₁₆ + CaSiO₃+ Ca₂SiO₄
-7444.04
-7548.81
-7601.73
-7624.78
-7938.03
-8042.80
-7602.56
-8006.85
-8013.39
-7580.35
-7685.12
-7715.32
-7573.65
-7608.23
-7713.00
-7591.86
-7628.76
- 7603.74
- 7585.51
-7620.73
-7450.51
-7373.73
-7395.90
-7650.91
-7695.19
-7929.05
-7794.78
-7964.55
-7937.71
-7617.50
-7499.35
-7434.17
-7471.08
-7493.22
-7537.50
-7238.21
-7897.73
-7994.37
-8059.23
-8074.75
-8382.29
-8478.93
-8056.93
-8452.49
-8463.03
-8039.42
-8136.06
-8177.31
-8026.17
-8069.93
-8166.58
-8046.79
-8082.37
-8049.82
-8033.79
-8066.07
-7900.75
-7823.79
-7842.89
-8124.87
-8168.68
-8364.94
-8239.95
-8407.22
-8381.28
-8054.78
-7942.42
-7885.29
-7920.86
-7963.36
-8007.171
-7681.38

AVERAGE -7645 -8096

Appendix 7: Chemical reactions for the formation of Ti hydroxide from oxide reactants and associated free energy and enthalpy of formation.

Chemical reaction 44G_f - 44G_r
kJ/mol
44H_f - 44H_r
kJ/mol

TiO₂ (anat) + 2 H₂O 5f Ti(OH)₄
TiO₂ (rut) + 2 H₂O 5f Ti(OH)₄
TiO₂ (rut) + Zr(OH)₄ 5f Ti(OH)₄ + ZrO₂
Ti(OH)₄ aq 5f Ti(OH)₄
2 Ba(OH)₂ + TiO₂ (rut) 5f Ti(OH)₄ + 2 BaO
2 Al(OH)₃ + TiO₂ (rut) 5f Ti(OH)₄ + Al₂O₃ + H₂O
-1357.63
-1363.77
-1397.65
-1308.37
-1557.71
-1382.77
-1510.38
-1516.41
-1567.78
-1482.50
-1730.26
-1572.48

AVERAGE -1395 -1563

Chemical species	G_f° (kJ/mol)	H_f° (kJ/mol)		Reference
H₂O OH^- Al³⁺ Al(OH)²⁺ Al(OH)₂⁺ Al(OH)_3aq Al(OH)₄^- Ca²⁺ Ti⁴⁺ Ti(OH)₂²⁺ Ti(OH)₃⁺ Ti(OH)_4aq Ti(OH)₅^- ZrO²⁺	-237.14 -157.20 -488.7 -696.3 -903.7 -1109.2 -1305.6 -552.90 -391.60 -861.47 -1084.92 -1308.37 -1531.32 -840.62	-285.83 -230.03 -537.2 -769.0 -1014.2 -1251.8 -1495.8 -543.1 -449.80 -976.20 -1229.40 -1482.50 -1735.60 -933.50		Cox et al. (1989) Phillips et al. (1988) Castet et al. (1993) Castet et al. (1993) Castet et al. (1993) Castet et al. (1993) Castet et al. (1993) Phillips et al. (1988) Phillips et al. (1988) Phillips et al. (1988) Phillips et al. (1988) Phillips et al. (1988) Phillips et al. (1988) Latimer (1952)
Reaction			log K 25fbC	Reference
Zr⁴⁺ + H₂O 5f Zr(OH)³⁺ + H⁺ Zr⁴⁺ + 2H₂O 5f Zr(OH)₂²⁺ + 2H⁺ Zr⁴⁺ + 3H₂O 5f Zr(OH)₃⁺ + 3H⁺ Zr⁴⁺ + 4H₂O 5f Zr(OH)_4aq + 4H⁺ Zr⁴⁺ + 5H₂O 5f Zr(OH)₅^- + 5H⁺ ZrO₂ + 4H⁺ 5f Zr⁴⁺ + 2H₂O			0.3 -1.7 -5.1 -9.7 -16.0 -1.9	Allard et al. (1980) ; Baes and Mesmer (1986)
Chemical species	G_f° (kJ/mol)	H_f° (kJ/mol)		Reference
Zr⁴⁺ Zr(OH)³⁺ Zr(OH)₂²⁺ Zr(OH)₃⁺ Zr(OH)_4aq Zr(OH)₅^-	-554.83 -793.64 -1019.34 -1237.04 -1447.89 -1649.05	-610.71 -880.45 -1135.36 -1381.24 -1619.40 -1846.59		this study

	44G_f est.	44G_f p.r.	44G_f est. - 44G_f p.r.	% error
CaZrTi₂O₇	-3516.21	-3514.60	-1.61	0.046
CaTiO₃	-1575.24	-1575.20	-0.04	0.003
Ca₂SiO₄	-2198.66	-2198.80	0.14	-0.006
CaAl₂SiO₆	-3122.21	-3122.00	-0.21	0.007
CaTiSiO₅	-2459.00	-2461.80	2.80	-0.114
	44H_f est.	44H_f p.r.	44H_f est. - 44H_f p.r.	% error
CaZrTi₂O₇	-3715.48	-3713.80	-1.68	0.045
CaTiO₃	-1660.87	-1660.60	-0.27	0.016
-2313.37	-2315.20	1.83	-0.079	CaAl₂SiO₆
-3298.90			-3298.20	-0.70