Aging Effects in Zr(Fe0.5V0.5)2 Tritides
Abstract
:1. Introduction
2. Materials and Methods
3. Results
4. Discussion
4.1. Hydrogen and Tritum: The Virgin Alloy
4.1.1. Solubility in the Alloy
4.1.2. Conversion into the Hydride Phase
4.2. Aging Effect
4.2.1. Helium Production–Release
- (1)
- The density of the alloy is calculated by the lattice parameters and, as pointed out by Spulak [4], the critical helium concentration strongly depends on the metal atom density;
- (2)
- The density of the helium atoms in a bubble weakly depends on the initial bubble radius as (r0)3/8, but changing the material also changes r0;
- (3)
- The number density of helium bubbles changes from metal to metal;
- (4)
- The release of helium also depends on the effective surface area of the alloy;
- (5)
- Finally, the presence of a large critical value can be argued for due to the particular structure of the alloy.
4.2.2. Tritium Release
A Solution Region
B Hydride-Forming Region
- (a)
- The ionization potential for He is higher than that for hydrogen; therefore, the capture of a tritium electron entering into the metal lattice is possible;
- (b)
- The capture of an electron of the d shell of the metal by He3 would decrease the d character of the metal, increasing the heat of formation [42], and favouring the conversion to hydride, which is not what we observed;
- (c)
- Increasing the tritium concentration would make more electrons available for He3 capture, thus hampering the hydride formation, as indicated by the decrease in ∆H.
5. Consequences to the Application of the Alloy
6. Conclusions
- The alloy shows a high critical value of He3 concentration (0.48) before it enters into the accelerated helium release rate phase; the reasons for this seems to reside in the lattice structure of the alloy and in the number of defects and impurities which form an elevated number of high-density helium bubbles;
- The study of tritium dissolution after 1500 days of aging suggests that He3 is mainly present as bubbles; the lattice sites where tritium dissolves relax close to their original configuration, slightly changing the enthalpy of solution; the number of sites available for the unit cell, however, reduces and therefore the equilibrium pressures increase;
- The He3 present in the interstitial site distorts the lattice of the alloy in such a way that tritium dissolved at infinite dilution turns out to be more tightly bound than hydrogen;
- The behavior of the thermodynamic parameters in the hydride-forming region is different than that in the solution region; however, the change in the nature of the tritium bond due to the presence of He3 is not sufficient to exhaustively explain this behavior;
- To minimize the residual inventory, tritium should reside in the alloy for no longer than a week.
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
List of Symbols
(Ks)Q | temperature-dependent Sieverts’ constant Q = H, T |
∆ | enthalpy change at infinite dilution |
∆ | non-configurational entropy at infinite dilution |
∆ | non-configurational entropy |
configurational entropy | |
∆H° | enthalpy for hydride formation |
∆S° | entropy for hydride formation |
R | universal gas constant |
H/A | hydrogen over alloy ratio |
T/A | tritium over alloy ratio |
He3/A | helium over alloy ratio |
µQ | chemical potential for the Q atom Q = H or T |
θ′ | hydrogen vibrational temperature |
Appendix A
- (a)
- nonconfigurational, or excess, entropy comprising vibrational electronic and magnetic contributions;
- (b)
- configurational entropy.
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Element | % by Weight |
---|---|
Zirconium | 45.38 |
Vanadium | 27.2 |
Iron | 23.75 |
Chromium | 1.04 |
Aluminium | 0.75 |
Tin | 0.65 |
Silicon | 0.33 |
Manganese | 0.034 |
Nickel | 0.017 |
Niobium | <0.01 |
Titanium | 0.006 |
Copper | 0.0046 |
Cadmium | <0.005 |
Cobalt | 0.002 |
T (K) | Xmax | Ks (at. Ratio/Pa1/2) | |
---|---|---|---|
H2 | 298 | 0.2 | 0.9153 |
323 | 0.3 | 0.3007 | |
373 | 0.5 | 0.1260 | |
423 | 0.5 | 0.04987 | |
473 | 0.5 | 0.02385 | |
523 | 0.5 | 0.01181 | |
573 | 0.3 | 0.007921 | |
623 | 0.5 | 0.00399 | |
673 | 0.5 | 0.002699 | |
T2 | 373 | 0.97 | 0.07776 |
419 | 0.75 | 0.032507 | |
463 | 0.52 | 0.01526 | |
511 | 0.3 | 0.00796 | |
559 | 0.28 | 0.004057 | |
608 | 0.25 | 0.002396 |
Q | (kJ/molQ) | (J/K molQ) |
---|---|---|
H | −26.98 | −55.91 |
T | −27.97 | −62.61 |
Q | xQ | −A | −B | kJ/mol Q | J/K mol Q | J/K mol Q |
---|---|---|---|---|---|---|
H | 0.075 | 3.5268 | 1452.3 | 27.79 | 19.65 | 55.98 |
0.1 | 3.577 | 1408.8 | 26.97 | 20.61 | 54.53 | |
0.2 | 3.81 | 1373.9 | 26.29 | 25.073 | 53.07 | |
0.3 | 4.273 | 1469 | 28.11 | 31.912 | 56.39 | |
0.5 | 4.4027 | 1446 | 27.67 | 36.42 | 56.35 | |
Average | 27.36 ± 0.59 | 55.3 ± 1.97 | ||||
T | 0.1 | 4.0123 | 1511.6 | 28.93 | 28.95 | 62.84 |
0.3 | 4.4913 | 1503.5 | 28.76 | 38.1129 | 62.59 | |
0.5 | 4.6863 | 1451.7 | 27.79 | 41.845 | 61.782 | |
0.75 | 4.8963 | 1463.2 | 28.005 | 45.865 | 62.0437 | |
0.95 | 5.1229 | 1492 | 28.55 | 50.2016 | 64.092 | |
Average | 28.4 ± 0.41 | 62.68 ± 0.64 |
Q | xQ | kJ/mol Q2 | J/K mol Q2 |
---|---|---|---|
H | 0.8 | 56 | 88.4 |
1 | 55.6 | 90.5 | |
1.4 | 60.7 | 110.1 | |
1.6 | 55.3 | 103.3 | |
1.8 | 55.9 | 108.6 | |
2 | 56.5 | 114 | |
2.2 | 54.1 | 115.4 | |
2.6 | 54.2 | 122.9 | |
2.8 | 51.3 | 122.4 | |
Average | 55.5 ± 1.9 | 108.4 ± 5.5 | |
T | 0.9 | 64.1 | 118.3 |
1.2 | 64.9 | 125.8 | |
1.4 | 64.7 | 130.2 | |
1.6 | 65.2 | 136.5 | |
1.8 | 60.5 | 130.7 | |
2.0 | 59.6 | 133.1 | |
2.2 | 61.3 | 144.3 | |
Average | 62.9 ± 2.1 | 131.3 ± 5.7 |
(kJ/mol T) | (J/K mol T) | /R (J/K mol T) | |
---|---|---|---|
UR | 27.97 ± 0.7 | 62.61 ± 1.5 | 7.53 |
Aged1 | 27.02 ± 1.1 | 59.38 ± 2.3 | 7.14 |
Aged2 | 33.78 ± 0.6 | 66.3 ± 1.2 | 7.97 |
(kJ/mol) | (J/K mol) | |||||
---|---|---|---|---|---|---|
T/A | Unaged | Aged1 | Aged2 | Unaged | Aged1 | Aged2 |
0.7 | 63.5 | 61.2 | 64.3 | 110.6 | 104.4 | 115.2 |
0.9 | 64.1 | 61.1 | 63.2 | 118.3 | 110.6 | 119.8 |
1 | 64.9 | 60.7 | 54.8 | 125.8 | 116.6 | 108.2 |
1.2 | 64.7 | 59.9 | 57.1 | 130.2 | 121.4 | 119.5 |
1.4 | 65.2 | 57.9 | 55.1 | 136.5 | 122.8 | 120 |
1.8 | 60.5 | 57.3 | 53.1 | 130.7 | 128.4 | 121.1 |
2 | 59.6 | 57.6 | 53.7 | 133.1 | 135.9 | 130.9 |
2.2 | 61.3 | 53.7 | 49 | 144.3 | 133.9 | 126.4 |
2.4 | 58.5 | 50.9 | 142.7 | 133.7 | ||
Average | 62.9 ± 2.1 | 57.4 ± 2.6 | 55.2 ± 2.9 | 131.3 ± 5.7 | 125.4 ± 7.5 | 120.8 ± 4.5 |
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Ghezzi, F.; Shmayda, W.T. Aging Effects in Zr(Fe0.5V0.5)2 Tritides. Crystals 2024, 14, 159. https://doi.org/10.3390/cryst14020159
Ghezzi F, Shmayda WT. Aging Effects in Zr(Fe0.5V0.5)2 Tritides. Crystals. 2024; 14(2):159. https://doi.org/10.3390/cryst14020159
Chicago/Turabian StyleGhezzi, Francesco, and Walter Theodore Shmayda. 2024. "Aging Effects in Zr(Fe0.5V0.5)2 Tritides" Crystals 14, no. 2: 159. https://doi.org/10.3390/cryst14020159
APA StyleGhezzi, F., & Shmayda, W. T. (2024). Aging Effects in Zr(Fe0.5V0.5)2 Tritides. Crystals, 14(2), 159. https://doi.org/10.3390/cryst14020159