Correction: Ocádiz Flores et al. Thermodynamic Description of the ACl-ThCl4 (A = Li, Na, K) Systems. Thermo 2021, 1, 122–133

Jaén A. Ocádiz Flores; Bas A. S. Rooijakkers; Rudy J. M. Konings; Anna Louise Smith

doi:10.3390/thermo2040027

Corrected excess Gibbs energies of the liquid solutions in the ACl-ThCl₄ (A = Li, Na, K), as well as revised standard enthalpies of formation and standard entropies of the intermediate phases occurring in the binary systems, are presented. The phase diagrams are reproduced to a similar level of accuracy as in the original publication, and the trends in thermodynamic stability of the liquid solutions are maintained. That is, the main conclusions of the paper are not affected. The original publication has also been updated.

Text Correction

The optimized Gibbs energies for the second-nearest neighbor (SNN) exchange reactions of the liquid solutions were incorrectly reported to be polynomial expansions in terms of pair fraction expansions in Equations (7)–(9) of the original publication [1]. Rather, they were polynomial expansions in terms of coordination-equivalent fractions

Y_{A}

,

Y_{T h}

(A = Li, Na, K). Given Z

_{A B / C l}^{A}

and Z

_{A B / C l}^{B}

, the SNN coordination numbers of ions A and B in a binary chloride melt, their equivalent pair fractions are defined as [36]:

Y_{A} = Z_{A B / C l}^{A} \cdot n_{A} / (Z_{A B / C l}^{A} \cdot n_{A} + Z_{A B / C l}^{B} \cdot n_{B})

(1)

Y_{B} = 1 - Y_{A}

(2)

where

n_{i}

corresponds to the number of moles of species i. To be consistent with the notation just introduced, the aforementioned Equations (7)–(9) in [1] should have been written as:

Δ g_{L i T h / C l} = - 8000 - 4000 \cdot Y_{L i} - 2700 \cdot Y_{T h} J \cdot m o l^{- 1}

(3)

Δ g_{N a T h / C l} = - 27, 700 - 10, 000 \cdot Y_{N a}^{2} - 20, 000 \cdot Y_{T h} J \cdot m o l^{- 1}

(4)

Δ g_{K T h / C l} = - 28, 000 - 16, 000 \cdot Y_{K}^{2} - 25, 000 \cdot Y_{T h} J \cdot m o l^{- 1}

(5)

However, in order to be compatible with existing molten salt databases for nuclear applications, the excess Gibbs energies of the liquid solutions should better be expressed as polynomial expansions in the composition term

χ

:

χ_{A B / C l} = \frac{X_{A A}}{X_{A A} + X_{A B} + X_{B B}}

(6)

where X

_{A A}

, X

_{B B}

and X

_{A B}

represent cation–cation pair mole fractions. Note that in the case of binary solutions with a common anion,

χ_{A B / C l}

=

X_{A A}

, and

χ_{B A / C l}

=

X_{B B}

. Equations (7)–(9) were found to reproduce the ACl-ThCl

_{4}

(A = Li, Na, K) phase diagrams with comparable accuracy to that obtained with Equations (3)–(5).

Δ g_{L i T h / C l} = - 8000 - 3600 \cdot χ_{L i T h / C l} - 7300 \cdot χ_{T h L i / C l} J \cdot m o l^{- 1}

(7)

Δ g_{N a T h / C l} = - 27, 700 - 7500 \cdot χ_{N a T h / C l} - 14, 000 \cdot χ_{T h N a / C l} J \cdot m o l^{- 1}

(8)

Δ g_{K T h / C l} = - 40, 000 - 10, 000 \cdot χ_{T h K / C l} J \cdot m o l^{- 1}

(9)

Related to the changes in the thermodynamic model, two amendments to the original text were necessary, related to the mixing entropy of (K,Th)Cl

_{x}

solution (see Figure 4 in [1]). In Section 3.2, the sentence ‘(K,Th)Cl

_{x}

displays such a strong SRO that the entropy of mixing is negative at its minimum near X(ThCl

_{4}

) = 0.4…’ has been replaced with ‘(K,Th)Cl

_{x}

displays such strong SRO that the entropy of mixing approaches zero at its minimum near X(ThCl

_{4}

) = 0.4’. In Section 4, the sentence ‘(K,Th)Cl

_{x}

even displays negative entropy of mixing where the enthalpy of mixing is greatest in magnitude’ has been replaced with ‘(K,Th)Cl

_{x}

even displays an entropy of mixing close to zero where the enthalpy of mixing is greatest in magnitude’.

Error in Tables

Using the correct Equations (7)–(9), the Gibbs energy terms of the intermediate phases needed some adjustment also, namely the standard enthalpies of formation and, in the case of K

_{2}

ThCl

_{6}

, also the standard entropy. The re-assessed values are given in Table 2, with all other values for completeness.

Table 2. Thermodynamic data for intermediate compounds used in this work for the phase diagram assessment:

Δ_{f}

H

_{m}^{o}

(298 K)/(kJ ·mol

^{- 1}

), S

_{m}^{o}

(298 K)/(J·K

^{- 1} \cdot

mol

^{- 1}

), and heat capacity coefficients C

_{p, m}

(T/K)/(J·K

^{- 1} \cdot

mol

^{- 1}

), where C

_{p, m}

(T/K) = a + b·T + c·T

^{2}

+ d·T

^{- 2}

+ e·T

^{3}

. Optimised data are shown in bold.

The invariant equilibria as calculated with the corrected model are listed in Table 4. The corrected Tables appears below:

Table 4. Invariant equilibrium data in the ACl-ThCl

_{4}

systems.

Error in Figures

The phase diagrams as calculated with this corrected model are shown in Figure 1, Figure 2 and Figure 3. These figures replace Figures 1–3 of the original publication, while the mixing properties of the liquid solutions are shown in Figure 4a,b and Figure 5, in place of Figures 4a,b and 5 of the original publication [1]. The latter properties display the same trends (discussed in [1]) as those appearing when polynomials in coordination-equivalent sites were used.