SOLIDIONIC

Dear Colleagues!

Please consider and discuss below presented сomplete quasichemical description of some cubic oxides similar YO1.5 and double perovskites in water and oxygen atmosphere

Y₂O₃ doped by CaO                                                                                 

under water vapor and oxygen:

y²{(1+ξ)² - 4v₃}  -  3y*(1+ξ) + x*(3-x) = 0

y=[OH_O^·],  v₃ =1/w₃ ,                                           ω ₃=K₃P_water ,  ω ₄=K₄ ( P_oxygen)^1/2

ξ = (ω₄ / ω₃)^1/2 ,   x = [Ca],     [O_O^·] = [h] = yξ

Y₂O₃[V_i] with structural vacancy                                                 

under water vapor and oxygen:

y³ 4α (v₇ + α²) -16 (y*α)² +21 (y*α) – 9 = 0

y=[OH_O^·],  v₇ =1/ω_{7 ,}       ω₇  = K₇P_water,    ω ₉ = K₉ ( P_oxygen)^1/2  

ξ _9,7  = (ω₉ / ω₇)^1/2  ,    α = (1 + ξ _9,7)

[O_i^//] = 0,5*y*α,     [O_O^·] = [h] = y*ξ _9,7

The double perovskites are protonic conductors with structural disordering of oxygen subsystem            As  the example is considered  Sr_6-2xTa_2+2xO_(11+3x)[V^x]_(1-3x).

K₁P_water = [OH_o^·]*[OH_V^/] /[O_O^x]*[V^x] = ω_{1 -}-  described the equilibrium with water vapor resulted in fulfilling of structural vacancy by oxygen ion from water molecule and the formation of two hydroxide ions with different  effective charge ion “host” oxygen and on “guest” oxygen in structural vacancy corresponding.

K₂P_water = [OH_o^·]²*[O_V^//] /[O_O^x]²*[V^x] = ω₂– described              the equilibrium with water vapor resulted in fulfilling of structural vacancy by oxygen ion from water molecule and the formation of two equal hydroxide ions  on “host” oxygen,  “guest” oxygen forms the  oxide ionin structural vacancy corresponding.

K₂ ( P_oxygen)^1/2 = [O_O^·]²*[O_V^//] /[O_O^x]²*[V^x] = ω₃– described the equilibrium with molecular oxygen fullfilled the structural vacancy/.

[OH_o^·] = y_o;    [OH_V^/] = y_V,  

ῶ₁ = 1/ω₁ , α = 1 + (ω₂ /ω₃)^1/2

I have decided to show the pair of equations   linked up  y_O   and  y_V.  The final equation for the dependence of hydrogen content on factor of nonstoichiometry X  and corresponding  constant sof equilibrium of perovskite with gaseous phases could be obtaind. However, according our experience, using this pair is moe effective at the analysis of real situation .  The matter is that the formation of hydroxide ions with contrary effective charge  is very interesting effect  from fundamental point of view.

y_V = {(A – αy_o)(2B – αy_o)/[( A – αy_o) + 2ῶ₁ y_o]

y_V = {[αy_o – X(2B - αy_o)]/(1-X)}

where X = ω₂[(A- αy_o)/ y_o],   А=11+3х, В=1-3х

sub

sub/strongO strong