J. Mater. Sci. Technol. ›› 2021, Vol. 81: 229-235.DOI: 10.1016/j.jmst.2021.01.010
• Research Article • Previous Articles Next Articles
Chuan Moa, Wenlin Moa, Peng Zhoub, BaiXue Bianc, Yong Duc, Tao Faa,*(
), Pengguo Zhanga, Ruiwen Lia, Yanzhi Zhanga, Changsheng Zhangd, Yuanhua Xiad, Xiaolin Wange,*()
Received:2020-07-08
Revised:2020-10-13
Accepted:2020-10-31
Published:2021-01-16
Online:2021-01-16
Contact:
Tao Fa,Xiaolin Wang
About author:*E-mail addresses: taofa0917@gmail.com (T. Fa),Chuan Mo, Wenlin Mo, Peng Zhou, BaiXue Bian, Yong Du, Tao Fa, Pengguo Zhang, Ruiwen Li, Yanzhi Zhang, Changsheng Zhang, Yuanhua Xia, Xiaolin Wang. Experimental investigation and thermodynamic modeling of the U-Nb system[J]. J. Mater. Sci. Technol., 2021, 81: 229-235.
Fig. 1. Phase diagrams of U-Nb system from previous researcher: (a) Rough et al. [19], (b) Terekhov et al. [22], (c) Koike et al. [12], (d) Romig et al. [13].
| Nominal composition (Nb at.%) | 0.5 | 2 | 5 | 5.7 | 7 | 10 | 12 | 14 | 16 | 18 | 20 | 30 | 40 | 80 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Composition measured by ICP | 0.56 | 2.044 | 5.035 | 5.65 | 6.93 | 10.08 | 12.50 | 14.06 | 15.73 | 17.81 | 19.66 | 31.91 | 39.03 | 78.08 |
| 605 °C | αU | αU + γ2 | γ2 | |||||||||||
| 635 °C | αU | αU + γ1 | γ1 | γ1 + γ 2 | γ2 | |||||||||
| 655 °C | αU | αU + γ1 | γ1 | γ1 + γ 2 | γ2 | |||||||||
| 675 °C | βU | βU + γ1 | γ1 | γ1 + γ 2 | γ2 |
Table 1 Summary of the phases for the U-Nb alloys annealed at 605 °C, 635 °C, 655 °C, and 675 °C for 30 days.
| Nominal composition (Nb at.%) | 0.5 | 2 | 5 | 5.7 | 7 | 10 | 12 | 14 | 16 | 18 | 20 | 30 | 40 | 80 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Composition measured by ICP | 0.56 | 2.044 | 5.035 | 5.65 | 6.93 | 10.08 | 12.50 | 14.06 | 15.73 | 17.81 | 19.66 | 31.91 | 39.03 | 78.08 |
| 605 °C | αU | αU + γ2 | γ2 | |||||||||||
| 635 °C | αU | αU + γ1 | γ1 | γ1 + γ 2 | γ2 | |||||||||
| 655 °C | αU | αU + γ1 | γ1 | γ1 + γ 2 | γ2 | |||||||||
| 675 °C | βU | βU + γ1 | γ1 | γ1 + γ 2 | γ2 |
| Composition (Nb at.%) | 2 | 5 | 7 | 10 | Average | |
|---|---|---|---|---|---|---|
| Content (Nb at.%) | Annealed at 635 °C | 11.4 | — | 11.6 | 11.9 | 11.5 |
| Annealed at 655 °C | — | 10.3 | 10.7 | — | 10.5 |
Table 2 Content of Nb in the γ phase of the annealed U-Nb alloys (U-2Nb, U-5Nb, U-7Nb, U-10Nb) determined by EDS.
| Composition (Nb at.%) | 2 | 5 | 7 | 10 | Average | |
|---|---|---|---|---|---|---|
| Content (Nb at.%) | Annealed at 635 °C | 11.4 | — | 11.6 | 11.9 | 11.5 |
| Annealed at 655 °C | — | 10.3 | 10.7 | — | 10.5 |
| Heating rate | Pure U (This work) | Pure U Rai | 14 at.% Nb WQ | 14 at.% Nb WQ |
|---|---|---|---|---|
| α → β | α→ β | α → γ | α → β | |
| 5 K/min | 664.5 | 660.7 | —— | 669.7 |
| 10 K/min | 666 | 661.6 | 640 | 668.7 |
| 20 K/min | 666.7 | 662 | 641.3 | 668.9 |
| 30 K/min | —— | 662.7 | 643 | 668.1 |
| 0 K/min | 664.9 | 660.7 | 638.3 | 669.7 |
| Revision | 660.7 | 660.7 | 634.1 | 665.5 |
Table 3 Summary of the phase transition temperatures for the annealed U-14Nb alloy and pure uranium at different rates (5, 10, 20, and 30 K/min) by STA409, compared with the experimental data by Rai et al. [26].
| Heating rate | Pure U (This work) | Pure U Rai | 14 at.% Nb WQ | 14 at.% Nb WQ |
|---|---|---|---|---|
| α → β | α→ β | α → γ | α → β | |
| 5 K/min | 664.5 | 660.7 | —— | 669.7 |
| 10 K/min | 666 | 661.6 | 640 | 668.7 |
| 20 K/min | 666.7 | 662 | 641.3 | 668.9 |
| 30 K/min | —— | 662.7 | 643 | 668.1 |
| 0 K/min | 664.9 | 660.7 | 638.3 | 669.7 |
| Revision | 660.7 | 660.7 | 634.1 | 665.5 |
Fig. 2. Fit and extrapolation of the phase transition temperature with data from Table 3.
Fig. 3. Neutron diffraction patterns of the U-14Nb alloy (annealed at 605 °C for 30 days) during the heating process.
Fig. 4. Sections of the U-Nb phase diagram based on this work. The solid lines are phase boundaries determined from the present phase diagram data.
| Liquid: (Nb, U)1 |
|---|
| ${}^{o}G_{\text{U}}^{\text{liquid}}-H_{\text{U}}^{\text{SER}}={}^{o}G_{\text{U}}^{\text{ }\!\!\alpha\!\!\text{ U}}+12355.5-10.3239T$ |
| ${}^{o}G_{\text{U}}^{\text{liquid}}-H_{\text{Nb}}^{\text{SER}}={}^{o}G_{\text{Nb}}^{\gamma }+29781.555-10.816418T-3.06098\times {{10}^{-23}}{{T}^{7}}T<2750$ |
| $\text{=}{}^{o}G_{\text{Nb}}^{\gamma }+30169.925-10.964695T-1.528538\times {{10}^{32}}{{T}^{-9}}T>2750$ |
| ${}^{o}L_{\text{Nb},\text{U}}^{\text{liq}}=15135.9353-28.9999694{{T}^{1}}L_{\text{Nb},\text{U}}^{\text{liq}}=28372.2053-28.9993676T$ |
| $bcc\gamma :\text{ }{{\left( Nb,\text{ }U \right)}_{1}}{{\left( Va \right)}_{3}}$ |
| ${}^{o}G_{\text{U}}^{\text{ }\!\!\gamma\!\!\text{ }}-H_{\text{U}}^{\text{SER}}=-752.767+131.538T-27.5152T\ln T-0.00835595{{T}^{2}}-9.67907\times {{10}^{-7}}{{T}^{3}}+204,611{{T}^{-1}}T<1049$ |
| $=-4698.365+202.685634T-38.2836T\ln TT>1049$ |
| ${}^{o}G_{Nb}^{\text{ }\!\!\gamma\!\!\text{ }}-H_{Nb}^{\text{SER}}=-8519.353+142.045475T-26.4711T\ln T+2.03475\times {{10}^{-4}}{{T}^{2}}-3.5012\times {{10}^{-7}}{{T}^{3}}+93,399{{T}^{-1}}T<2750$ ${}^{o}L_{\text{Nb},\text{U}}^{\text{bcc}}=26613.2839-28.0313281T$ |
| ${}^{1}L_{\text{Nb},\text{U}}^{\text{bcc}}=-22540.6083$ |
| ${}^{2}L_{\text{Nb},\text{U}}^{\text{bcc}}=-25360.6090-2.02123221T$ ${}^{3}L_{\text{Nb},\text{U}}^{\text{bcc}}=-11386.2265$ |
| $tet\beta U:\text{ }{{\left( Nb,\text{ }U \right)}_{1}}$ |
| ${}^{\text{o}}G_{\text{U}}^{\text{ }\!\!\beta\!\!\text{ U}}-H_{\text{U}}^{\text{SER}}\text{=}5156.136+106.976316T-22.841T\ln T-0.01084475{{T}^{2}}+2.7889\times {{10}^{-8}}{{T}^{3}}+81,944{{T}^{-1}}T<941.5$ |
| $\text{=}-14327.309+244.16802T-42.9278T\ln TT>941.5$ |
| ${}^{\text{o}}G_{\text{Nb}}^{\text{ }\!\!\beta\!\!\text{ U}}-H_{\text{Nb}}^{\text{SER}}=={}^{\text{o}}G_{\text{Nb}}^{\text{ }\!\!\gamma\!\!\text{ }}+26107.5306$ |
| $ort\alpha U:\text{ }{{\left( Nb,\text{ }U \right)}_{1}}$ |
| ${}^{\text{o}}G_{\text{Nb}}^{\text{ }\!\!\alpha\!\!\text{ U}}-H_{\text{Nb}}^{\text{SER}}=-8407.734+130.955151T-26.9182T\ln T+0.00125156{{T}^{2}}-4.42605\times {{10}^{-6}}{{T}^{3}}+38,568{{T}^{-1}}<955$ |
| $=-22521.8+292.121093T-48.66\text{ }T\text{ }lnT\text{ }T955$ ${}^{\text{o}}G_{\text{Nb}}^{\text{ }\!\!\alpha\!\!\text{ U}}-H_{\text{Nb}}^{\text{SER}}=={}^{\text{o}}G_{\text{Nb}}^{\text{ }\!\!\gamma\!\!\text{ }}+27337.4226$ |
Table 4 Optimized thermodynamic parameters for the U-Nb system.
| Liquid: (Nb, U)1 |
|---|
| ${}^{o}G_{\text{U}}^{\text{liquid}}-H_{\text{U}}^{\text{SER}}={}^{o}G_{\text{U}}^{\text{ }\!\!\alpha\!\!\text{ U}}+12355.5-10.3239T$ |
| ${}^{o}G_{\text{U}}^{\text{liquid}}-H_{\text{Nb}}^{\text{SER}}={}^{o}G_{\text{Nb}}^{\gamma }+29781.555-10.816418T-3.06098\times {{10}^{-23}}{{T}^{7}}T<2750$ |
| $\text{=}{}^{o}G_{\text{Nb}}^{\gamma }+30169.925-10.964695T-1.528538\times {{10}^{32}}{{T}^{-9}}T>2750$ |
| ${}^{o}L_{\text{Nb},\text{U}}^{\text{liq}}=15135.9353-28.9999694{{T}^{1}}L_{\text{Nb},\text{U}}^{\text{liq}}=28372.2053-28.9993676T$ |
| $bcc\gamma :\text{ }{{\left( Nb,\text{ }U \right)}_{1}}{{\left( Va \right)}_{3}}$ |
| ${}^{o}G_{\text{U}}^{\text{ }\!\!\gamma\!\!\text{ }}-H_{\text{U}}^{\text{SER}}=-752.767+131.538T-27.5152T\ln T-0.00835595{{T}^{2}}-9.67907\times {{10}^{-7}}{{T}^{3}}+204,611{{T}^{-1}}T<1049$ |
| $=-4698.365+202.685634T-38.2836T\ln TT>1049$ |
| ${}^{o}G_{Nb}^{\text{ }\!\!\gamma\!\!\text{ }}-H_{Nb}^{\text{SER}}=-8519.353+142.045475T-26.4711T\ln T+2.03475\times {{10}^{-4}}{{T}^{2}}-3.5012\times {{10}^{-7}}{{T}^{3}}+93,399{{T}^{-1}}T<2750$ ${}^{o}L_{\text{Nb},\text{U}}^{\text{bcc}}=26613.2839-28.0313281T$ |
| ${}^{1}L_{\text{Nb},\text{U}}^{\text{bcc}}=-22540.6083$ |
| ${}^{2}L_{\text{Nb},\text{U}}^{\text{bcc}}=-25360.6090-2.02123221T$ ${}^{3}L_{\text{Nb},\text{U}}^{\text{bcc}}=-11386.2265$ |
| $tet\beta U:\text{ }{{\left( Nb,\text{ }U \right)}_{1}}$ |
| ${}^{\text{o}}G_{\text{U}}^{\text{ }\!\!\beta\!\!\text{ U}}-H_{\text{U}}^{\text{SER}}\text{=}5156.136+106.976316T-22.841T\ln T-0.01084475{{T}^{2}}+2.7889\times {{10}^{-8}}{{T}^{3}}+81,944{{T}^{-1}}T<941.5$ |
| $\text{=}-14327.309+244.16802T-42.9278T\ln TT>941.5$ |
| ${}^{\text{o}}G_{\text{Nb}}^{\text{ }\!\!\beta\!\!\text{ U}}-H_{\text{Nb}}^{\text{SER}}=={}^{\text{o}}G_{\text{Nb}}^{\text{ }\!\!\gamma\!\!\text{ }}+26107.5306$ |
| $ort\alpha U:\text{ }{{\left( Nb,\text{ }U \right)}_{1}}$ |
| ${}^{\text{o}}G_{\text{Nb}}^{\text{ }\!\!\alpha\!\!\text{ U}}-H_{\text{Nb}}^{\text{SER}}=-8407.734+130.955151T-26.9182T\ln T+0.00125156{{T}^{2}}-4.42605\times {{10}^{-6}}{{T}^{3}}+38,568{{T}^{-1}}<955$ |
| $=-22521.8+292.121093T-48.66\text{ }T\text{ }lnT\text{ }T955$ ${}^{\text{o}}G_{\text{Nb}}^{\text{ }\!\!\alpha\!\!\text{ U}}-H_{\text{Nb}}^{\text{SER}}=={}^{\text{o}}G_{\text{Nb}}^{\text{ }\!\!\gamma\!\!\text{ }}+27337.4226$ |
Fig. 5. Calculated U-Nb phase diagram, compared with the experimental data. The solid lines are according to the present calculation, while the dotted lines are calculated using the parameters from Duong et al. [6].
Fig. 6. Calculated phase diagram of U-Nb binary system in the U-rich region with the present experimental data. The dotted lines are calculated using the parameters from Duong et al. [6].
| Reaction type | Reaction | Nb (at.%) | T (°C) | References | ||
|---|---|---|---|---|---|---|
| Eutectoid | βU → α U + γ U | 1.3 | 1.1 | 10.35 | 664 | [ |
| 0.56 | 0.46 | 7.5 | 666 | Calculation | ||
| Measured | ||||||
| Monotectoid | γU → α U +γNb | 13.3 | 1.3 | 71.7 | 647 | [ |
| 12.2 | 0.7 | 70.1 | 633.8 | Calculation | ||
| 11.5 ± 0.5 | 634.1 | Measured | ||||
| Critical | (γU,Nb) → γU + γ Nb | 52.3 | 930-970 | [ | ||
| 47.3 | 981 | Calculation | ||||
| Measured |
Table 5 Comparison between the calculated and measured invariant equilibria in U-Nb system.
| Reaction type | Reaction | Nb (at.%) | T (°C) | References | ||
|---|---|---|---|---|---|---|
| Eutectoid | βU → α U + γ U | 1.3 | 1.1 | 10.35 | 664 | [ |
| 0.56 | 0.46 | 7.5 | 666 | Calculation | ||
| Measured | ||||||
| Monotectoid | γU → α U +γNb | 13.3 | 1.3 | 71.7 | 647 | [ |
| 12.2 | 0.7 | 70.1 | 633.8 | Calculation | ||
| 11.5 ± 0.5 | 634.1 | Measured | ||||
| Critical | (γU,Nb) → γU + γ Nb | 52.3 | 930-970 | [ | ||
| 47.3 | 981 | Calculation | ||||
| Measured |
Fig. 7. Heat of formation of γ-bcc U-Nb alloys as a function of composition obtained from the U-Nb CALPHAD model (at T =0 K), and compared with the current First-principles energetic calculations. Reference states are γ-bcc U and γ-bcc Nb. The solid lines are according to the present calculation, while the dotted lines are calculated using the parameters from Duong et al. [ 6].
Fig. 8. Calculated Gibbs formation energy of U-Nb at 775 °C with γ-bcc U and γ-bcc Nb as a reference state, compared with the experimental values of Vambersky et al. [ 24]. The solid lines are according to the present calculation, the dotted line is calculated using the parameters from Duong et al. [6].
Fig. 9. Calculated Gibbs formation energy of U-Nb at 900 °C with γ-bcc U and γ-bcc Nb as a reference state, compared with the experimental values of Vambersky et al. [ 24]. The solid lines are according to the present calculation, the dotted line is calculated using the parameters from Duong et al. [6].
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