J. Mater. Sci. Technol. ›› 2021, Vol. 73: 23-30.DOI: 10.1016/j.jmst.2020.09.033
• Research Article • Previous Articles Next Articles
Juanli Zhao, Yuchen Liu, Yun Fan, Wei Zhang, Chengguan Zhang, Guang Yang, Hongfei Chen, Bin Liu*(
)
Received:2020-07-04
Revised:2020-07-21
Accepted:2020-07-26
Published:2021-05-20
Online:2020-10-01
Contact:
Bin Liu
About author:*E-mail address: binliu@shu.edu.cn (B. Liu).Juanli Zhao, Yuchen Liu, Yun Fan, Wei Zhang, Chengguan Zhang, Guang Yang, Hongfei Chen, Bin Liu. Native point defects and oxygen migration of rare earth zirconate and stannate pyrochlores[J]. J. Mater. Sci. Technol., 2021, 73: 23-30.
Fig. 1. (a) Crystal structure of pyrochlore oxides A2B2O7 and (b) configuration of BO6 octahedra.
| Compounds | a (Å) | Compounds | a (Å) | ||
|---|---|---|---|---|---|
| Cal. | Exp. | Cal. | Exp. | ||
| La2Zr2O7 | 10.739 | 10.774 [ | La2Sn2O7 | 10.696 | 10.711 [ |
| Ce2Zr2O7 | 10.747 | 10.701 [ | Ce2Sn2O7 | 10.697 | 10.642 [ |
| Pr2Zr2O7 | 10.690 | 10.658 [ | Pr2Sn2O7 | 10.642 | 10.620 [ |
| Nd2Zr2O7 | 10.640 | 10.623 [ | Nd2Sn2O7 | 10.594 | 10.575 [ |
| Pm2Zr2O7 | 10.594 | - | Pm2Sn2O7 | 10.545 | - |
| Sm2Zr2O7 | 10.559 | 10.575 [ | Sm2Sn2O7 | 10.509 | 10.520 [ |
| Eu2Zr2O7 | 10.518 | 10.475 [ | Eu2Sn2O7 | 10.466 | 10.490 [ |
| Gd2Zr2O7 | 10.480 | 10.503 [ | Gd2Sn2O7 | 10.430 | 10.458 [ |
Table 1 Calculated and/or experimental lattice parameters a, of rare earth zirconate and stannate pyrochlores.
| Compounds | a (Å) | Compounds | a (Å) | ||
|---|---|---|---|---|---|
| Cal. | Exp. | Cal. | Exp. | ||
| La2Zr2O7 | 10.739 | 10.774 [ | La2Sn2O7 | 10.696 | 10.711 [ |
| Ce2Zr2O7 | 10.747 | 10.701 [ | Ce2Sn2O7 | 10.697 | 10.642 [ |
| Pr2Zr2O7 | 10.690 | 10.658 [ | Pr2Sn2O7 | 10.642 | 10.620 [ |
| Nd2Zr2O7 | 10.640 | 10.623 [ | Nd2Sn2O7 | 10.594 | 10.575 [ |
| Pm2Zr2O7 | 10.594 | - | Pm2Sn2O7 | 10.545 | - |
| Sm2Zr2O7 | 10.559 | 10.575 [ | Sm2Sn2O7 | 10.509 | 10.520 [ |
| Eu2Zr2O7 | 10.518 | 10.475 [ | Eu2Sn2O7 | 10.466 | 10.490 [ |
| Gd2Zr2O7 | 10.480 | 10.503 [ | Gd2Sn2O7 | 10.430 | 10.458 [ |
Fig. 2. Chemical potential diagram of A-B-O, where A2B2O7 is stable in the quadrangle ABCD area.
| μLa | μZr | μO | μCe | μZr | μO | μPr | μZr | μO | |
|---|---|---|---|---|---|---|---|---|---|
| A: B-&BO2-rich | -1.456 | 0 | -5.410 | -0.952 | 0 | -5.410 | -1.079 | 0 | -5.410 |
| B: O-&BO2-rich | -9.571 | -10.820 | 0 | -9.067 | -10.820 | 0 | -9.195 | -10.820 | 0 |
| C: O-&A2O3-rich | -9.186 | -11.205 | 0 | -8.712 | -11.176 | 0 | -8.887 | -11.128 | 0 |
| D: B-&A2O3-rich | -0.782 | 0 | -5.603 | -0.330 | 0 | -5.589 | -0.542 | 0 | -5.564 |
| μNd | μZr | μO | μPm | μZr | μO | μSm | μZr | μO | |
| A: B-&BO2-rich | -1.120 | 0 | -5.410 | -1.189 | 0 | -5.410 | -1.196 | 0 | -5.410 |
| B: O-&BO2-rich | -9.235 | -10.820 | 0 | -9.300 | -10.820 | 0 | -9.311 | -10.820 | 0 |
| C: O-&A2O3-rich | -8.985 | -11.071 | 0 | -9.122 | -11.003 | 0 | -9.191 | -10.941 | 0 |
| D: B-&A2O3-rich | -0.681 | 0 | -5.535 | -0.870 | 0 | -5.501 | -0.984 | 0 | -5.471 |
| μEu | μZr | μO | μGd | μZr | μO | ||||
| A: B-&BO2-rich | -1.232 | 0 | -5.410 | -1.254 | 0 | -5.410 | |||
| B: O-&BO2-rich | -9.348 | -10.820 | 0 | -9.369 | -10.820 | 0 | |||
| C: O-&A2O3-rich | -9.294 | -10.874 | 0 | -9.401 | -10.789 | 0 | |||
| D: B-&A2O3-rich | -1.139 | 0 | -5.437 | -1.309 | 0 | -5.394 | |||
| μLa | μSn | μO | μCe | μSn | μO | μPr | μSn | μO | |
| A: B-&BO2-rich | -5.367 | 0 | -2.833 | -4.930 | 0 | -2.833 | -5.092 | 0 | -2.833 |
| B: O-&BO2-rich | -9.616 | -5.665 | 0 | -9.178 | -5.665 | 0 | -9.341 | -5.665 | 0 |
| C: O-&A2O3-rich | -9.186 | -6.095 | 0 | -8.712 | -6.132 | 0 | -8.887 | -6.120 | 0 |
| D: B-&A2O3-rich | -4.615 | 0 | -3.047 | -4.113 | 0 | -3.066 | -4.300 | 0 | -3.060 |
| μNd | μSn | μO | μPm | μSn | μO | μSm | μSn | μO | |
| A: B-&BO2-rich | -5.165 | 0 | -2.833 | -5.265 | 0 | -2.833 | -5.300 | 0 | -2.833 |
| B: O-&BO2-rich | -9.414 | -5.6656 | 0 | -9.514 | -5.665 | 0 | -9.546 | -5.665 | 0 |
| C: O-&A2O3-rich | -8.985 | -6.095 | 0 | -9.122 | -6.057 | 0 | -9.191 | -6.021 | 0 |
| D: B-&A2O3-rich | -4.414 | 0 | -3.047 | -4.579 | 0 | -3.029 | -4.674 | 0 | -3.011 |
| μEu | μSn | μO | μGd | μSn | μO | ||||
| A: B-&BO2-rich | -5.361 | 0 | -2.833 | -5.405 | 0 | -2.833 | |||
| B: O-&BO2-rich | -9.610 | -5.665 | 0 | -9.655 | -5.665 | 0 | |||
| C: O-&A2O3-rich | -9.294 | -5.981 | 0 | -9.410 | -5.918 | 0 | |||
| D: B-&A2O3-rich | -4.808 | 0 | -2.991 | -4.962 | 0 | -2.959 |
Table 2 Chemical potentials (μ A, μ B and μ O) of A, B, and O at the corner points, A, B, C and D in Fig. 2.
| μLa | μZr | μO | μCe | μZr | μO | μPr | μZr | μO | |
|---|---|---|---|---|---|---|---|---|---|
| A: B-&BO2-rich | -1.456 | 0 | -5.410 | -0.952 | 0 | -5.410 | -1.079 | 0 | -5.410 |
| B: O-&BO2-rich | -9.571 | -10.820 | 0 | -9.067 | -10.820 | 0 | -9.195 | -10.820 | 0 |
| C: O-&A2O3-rich | -9.186 | -11.205 | 0 | -8.712 | -11.176 | 0 | -8.887 | -11.128 | 0 |
| D: B-&A2O3-rich | -0.782 | 0 | -5.603 | -0.330 | 0 | -5.589 | -0.542 | 0 | -5.564 |
| μNd | μZr | μO | μPm | μZr | μO | μSm | μZr | μO | |
| A: B-&BO2-rich | -1.120 | 0 | -5.410 | -1.189 | 0 | -5.410 | -1.196 | 0 | -5.410 |
| B: O-&BO2-rich | -9.235 | -10.820 | 0 | -9.300 | -10.820 | 0 | -9.311 | -10.820 | 0 |
| C: O-&A2O3-rich | -8.985 | -11.071 | 0 | -9.122 | -11.003 | 0 | -9.191 | -10.941 | 0 |
| D: B-&A2O3-rich | -0.681 | 0 | -5.535 | -0.870 | 0 | -5.501 | -0.984 | 0 | -5.471 |
| μEu | μZr | μO | μGd | μZr | μO | ||||
| A: B-&BO2-rich | -1.232 | 0 | -5.410 | -1.254 | 0 | -5.410 | |||
| B: O-&BO2-rich | -9.348 | -10.820 | 0 | -9.369 | -10.820 | 0 | |||
| C: O-&A2O3-rich | -9.294 | -10.874 | 0 | -9.401 | -10.789 | 0 | |||
| D: B-&A2O3-rich | -1.139 | 0 | -5.437 | -1.309 | 0 | -5.394 | |||
| μLa | μSn | μO | μCe | μSn | μO | μPr | μSn | μO | |
| A: B-&BO2-rich | -5.367 | 0 | -2.833 | -4.930 | 0 | -2.833 | -5.092 | 0 | -2.833 |
| B: O-&BO2-rich | -9.616 | -5.665 | 0 | -9.178 | -5.665 | 0 | -9.341 | -5.665 | 0 |
| C: O-&A2O3-rich | -9.186 | -6.095 | 0 | -8.712 | -6.132 | 0 | -8.887 | -6.120 | 0 |
| D: B-&A2O3-rich | -4.615 | 0 | -3.047 | -4.113 | 0 | -3.066 | -4.300 | 0 | -3.060 |
| μNd | μSn | μO | μPm | μSn | μO | μSm | μSn | μO | |
| A: B-&BO2-rich | -5.165 | 0 | -2.833 | -5.265 | 0 | -2.833 | -5.300 | 0 | -2.833 |
| B: O-&BO2-rich | -9.414 | -5.6656 | 0 | -9.514 | -5.665 | 0 | -9.546 | -5.665 | 0 |
| C: O-&A2O3-rich | -8.985 | -6.095 | 0 | -9.122 | -6.057 | 0 | -9.191 | -6.021 | 0 |
| D: B-&A2O3-rich | -4.414 | 0 | -3.047 | -4.579 | 0 | -3.029 | -4.674 | 0 | -3.011 |
| μEu | μSn | μO | μGd | μSn | μO | ||||
| A: B-&BO2-rich | -5.361 | 0 | -2.833 | -5.405 | 0 | -2.833 | |||
| B: O-&BO2-rich | -9.610 | -5.665 | 0 | -9.655 | -5.665 | 0 | |||
| C: O-&A2O3-rich | -9.294 | -5.981 | 0 | -9.410 | -5.918 | 0 | |||
| D: B-&A2O3-rich | -4.808 | 0 | -2.991 | -4.962 | 0 | -2.959 |
Fig. 3. Formation energies Ef of Schottky, Frenkel and cation antisite defects in (a) A2Zr2O7 and (b) A2Sn2O7.
Fig. 4. (a) Formation energy difference ΔEf of O Frenkel pairs, $\text{V}_{\text{O}}^{\cdot \cdot }$ and $\text{O}_{i}^{''}$, (b) chemical bond broken energy difference and the relaxation energy difference of $\text{V}_{\text{O}}^{\cdot \cdot }$ and $\text{O}_{i}^{''}$.
Fig. 5. Temperature dependent concentrations of the predominant native defect complexes of (a) A2Zr2O7 and (b) A2Sn2O7.
| BO2-rich (line AB in |
|---|
| $B{{\text{O}}_{2}}+\frac{1}{2}A_{A}^{\times }\leftrightarrow \frac{1}{4}{{A}_{2}}{{B}_{2}}{{\text{O}}_{7}}+\frac{1}{2}B_{A}^{\cdot }+\frac{1}{4}\text{O}_{i}^{''}$ (R1) |
| $B{{\text{O}}_{2}}+\frac{4}{7}A_{A}^{\times }\leftrightarrow \frac{2}{7}{{A}_{2}}{{B}_{2}}{{\text{O}}_{7}}+\frac{3}{7}B_{A}^{\cdot }+\frac{1}{7}\text{V}_{A}^{'''}$ (R2) |
| $B{{\text{O}}_{2}}+A_{A}^{\times }+\frac{3}{2}\text{O}_{\text{O}}^{\times }\leftrightarrow \frac{1}{2}{{A}_{2}}{{B}_{2}}{{\text{O}}_{7}}+\text{V}_{A}^{'''}+\frac{3}{2}\text{V}_{\text{O}}^{\cdot \cdot }$ (R3) |
| $B{{\text{O}}_{2}}+\frac{4}{7}A_{A}^{\times }\leftrightarrow \frac{2}{7}{{A}_{2}}{{B}_{2}}{{\text{O}}_{7}}+\frac{3}{7}B_{i}^{\cdot \cdot \cdot \cdot }+\frac{4}{7}\text{V}_{A}^{'''}$ (R4) |
| A2O3-rich (line CD in |
| $\frac{1}{2}{{A}_{2}}{{\text{O}}_{3}}+\frac{1}{2}B_{B}^{\times }+\frac{1}{4}\text{O}_{\text{O}}^{\times }\leftrightarrow \frac{1}{4}{{A}_{2}}{{B}_{2}}{{\text{O}}_{7}}+\frac{1}{4}\text{V}_{\text{O}}^{\cdot \cdot }+\frac{1}{2}A_{B}^{'}$ (R5) |
| $\frac{1}{2}{{A}_{2}}{{\text{O}}_{3}}+\frac{3}{7}B_{B}^{\times }\leftrightarrow \frac{3}{14}{{A}_{2}}{{B}_{2}}{{\text{O}}_{7}}+\frac{3}{7}A_{B}^{'}+\frac{1}{7}A_{i}^{\cdot \cdot \cdot }$ (R6) |
| $\frac{1}{2}{{A}_{2}}{{\text{O}}_{3}}+B_{B}^{\times }+2\text{O}_{\text{O}}^{\times }\leftrightarrow \frac{1}{2}{{A}_{2}}{{B}_{2}}{{\text{O}}_{7}}+\text{V}_{B}^{''''}+2\text{V}_{\text{O}}^{\cdot \cdot }$ (R7) |
| $\frac{1}{2}{{A}_{2}}{{\text{O}}_{3}}+\frac{3}{7}B_{B}^{\times }\leftrightarrow \frac{3}{14}{{A}_{2}}{{B}_{2}}{{\text{O}}_{7}}+\frac{3}{7}\text{V}_{B}^{''''}+\frac{4}{7}A_{i}^{\cdot \cdot \cdot }$ (R8) |
Table 3 Defect reactions (R: reaction) of A2B2O7 under BO2-rich and A2O3-rich conditions.
| BO2-rich (line AB in |
|---|
| $B{{\text{O}}_{2}}+\frac{1}{2}A_{A}^{\times }\leftrightarrow \frac{1}{4}{{A}_{2}}{{B}_{2}}{{\text{O}}_{7}}+\frac{1}{2}B_{A}^{\cdot }+\frac{1}{4}\text{O}_{i}^{''}$ (R1) |
| $B{{\text{O}}_{2}}+\frac{4}{7}A_{A}^{\times }\leftrightarrow \frac{2}{7}{{A}_{2}}{{B}_{2}}{{\text{O}}_{7}}+\frac{3}{7}B_{A}^{\cdot }+\frac{1}{7}\text{V}_{A}^{'''}$ (R2) |
| $B{{\text{O}}_{2}}+A_{A}^{\times }+\frac{3}{2}\text{O}_{\text{O}}^{\times }\leftrightarrow \frac{1}{2}{{A}_{2}}{{B}_{2}}{{\text{O}}_{7}}+\text{V}_{A}^{'''}+\frac{3}{2}\text{V}_{\text{O}}^{\cdot \cdot }$ (R3) |
| $B{{\text{O}}_{2}}+\frac{4}{7}A_{A}^{\times }\leftrightarrow \frac{2}{7}{{A}_{2}}{{B}_{2}}{{\text{O}}_{7}}+\frac{3}{7}B_{i}^{\cdot \cdot \cdot \cdot }+\frac{4}{7}\text{V}_{A}^{'''}$ (R4) |
| A2O3-rich (line CD in |
| $\frac{1}{2}{{A}_{2}}{{\text{O}}_{3}}+\frac{1}{2}B_{B}^{\times }+\frac{1}{4}\text{O}_{\text{O}}^{\times }\leftrightarrow \frac{1}{4}{{A}_{2}}{{B}_{2}}{{\text{O}}_{7}}+\frac{1}{4}\text{V}_{\text{O}}^{\cdot \cdot }+\frac{1}{2}A_{B}^{'}$ (R5) |
| $\frac{1}{2}{{A}_{2}}{{\text{O}}_{3}}+\frac{3}{7}B_{B}^{\times }\leftrightarrow \frac{3}{14}{{A}_{2}}{{B}_{2}}{{\text{O}}_{7}}+\frac{3}{7}A_{B}^{'}+\frac{1}{7}A_{i}^{\cdot \cdot \cdot }$ (R6) |
| $\frac{1}{2}{{A}_{2}}{{\text{O}}_{3}}+B_{B}^{\times }+2\text{O}_{\text{O}}^{\times }\leftrightarrow \frac{1}{2}{{A}_{2}}{{B}_{2}}{{\text{O}}_{7}}+\text{V}_{B}^{''''}+2\text{V}_{\text{O}}^{\cdot \cdot }$ (R7) |
| $\frac{1}{2}{{A}_{2}}{{\text{O}}_{3}}+\frac{3}{7}B_{B}^{\times }\leftrightarrow \frac{3}{14}{{A}_{2}}{{B}_{2}}{{\text{O}}_{7}}+\frac{3}{7}\text{V}_{B}^{''''}+\frac{4}{7}A_{i}^{\cdot \cdot \cdot }$ (R8) |
Fig. 6. Reaction enthalpies (ΔH) of nonstoichiometric A2B2O7 under BO2- and A2O3-rich conductions (R1-R8 are defined in Table 3).
Fig. 7. Temperature dependent concentrations of the predominant defect complexes of nonstoichiometric A2B2O7 under BO2‐ and A2O3‐rich conductions.
Fig. 8. Migration energy barriers of oxygen vacancies along adjacent 48f-48f in (a) A2Zr2O7 and (b) A2Sn2O7.
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