J. Mater. Sci. Technol. ›› 2022, Vol. 121: 154-162.DOI: 10.1016/j.jmst.2021.11.077
• Research Article • Previous Articles Next Articles
Ze Zhanga,b,c,e, Shizhen Zhua,e,c,*(
), Fu-Zhi Daib, Huimin Xiangb, Yanbo Liua,c,d, Ling Liua,c,d, Zhuang Maa,c,d, Shijiang Wuf, Fei Liuf, Kuang Sung, Yanchun Zhoub,**(
)
Received:2021-09-19
Revised:2021-11-03
Accepted:2021-11-23
Published:2022-09-10
Online:2022-03-15
Contact:
Shizhen Zhu,Yanchun Zhou
About author:** yczhou@alum.imr.ac.cn (Y. Zhou).Ze Zhang, Shizhen Zhu, Fu-Zhi Dai, Huimin Xiang, Yanbo Liu, Ling Liu, Zhuang Ma, Shijiang Wu, Fei Liu, Kuang Sun, Yanchun Zhou. Theoretical predictions and experimental verification on the phase stability of enthalpy-stabilized HE TMREB2s[J]. J. Mater. Sci. Technol., 2022, 121: 154-162.
Fig. 1. Views of the unrelaxed SQS model of (MM′)B2: (a) viewed along the a-axis, (b) viewed along the b-axis, (c) viewed along the c-axis (gray atoms represent a metal atom M, green atoms represent another metal atom M’, yellow atoms represent atom B).
| Specimen code | Composition | Molar ratio of raw materials |
|---|---|---|
| HE TM0.9Sc0.1B2 | (Hf0.225Zr0.225Ta0.225Nb0.225Sc0.1)B2 | 4.5HfO2:4.5ZrO2:2.25Ta2O5: 2.25Nb2O5:1Sc2O3:17.74B4C |
| HE TM0.8Sc0.2B2 | (Hf0.2Zr0.2Ta0.2Nb0.2Sc0.2)B2 | 4HfO2:4ZrO2:2Ta2O5: 4Nb2O5:2Sc2O3:17.48B4C |
| HE TM0.9Tm0.1B2 | (Hf0.225Zr0.225Ta0.225Nb0.225Lu0.1)B2 | 4.5HfO2:4.5ZrO2:2.25Ta2O5: 2.25Nb2O5:1Lu2O3:17.74B4C |
| HE TM0.8Tm0.2B2 | (Hf0.2Zr0.2Ta0.2Nb0.2Lu0.2)B2 | 4HfO2:4ZrO2:2Ta2O5: 4Nb2O5:2Lu2O3:17.48B4C |
| HE TM0.9Lu0.1B2 | (Hf0.225Zr0.225Ta0.225Nb0.225Tm0.1)B2 | 4.5HfO2:4.5ZrO2:2.25Ta2O5: 2.25Nb2O5:1Tm2O3:17.74B4C |
| HE TM0.8Lu0.2B2 | (Hf0.2Zr0.2Ta0.2Nb0.2Tm0.2)B2 | 4HfO2:4ZrO2:2Ta2O5: 4Nb2O5:2Tm2O3:17.48B4C |
| HE TM0.9Er0.1B2 | (Hf0.225Zr0.225Ta0.225Nb0.225Er0.1)B2 | 4.5HfO2:4.5ZrO2:2.25Ta2O5: 2.25Nb2O5:1Er2O3:17.74B4C |
| HE TM0.8Er0.2B2 | (Hf0.2Zr0.2Ta0.2Nb0.2Er0.2)B2 | 4HfO2:4ZrO2:2Ta2O5: 4Nb2O5:2Er2O3:17.48B4C |
| HE TM0.95Ho0.05B2 | (Hf0.2375Zr0.2375Ta0.2375Nb0.2375Ho0.05)B2 | 4.75HfO2:4.75ZrO2:2.375Ta2O5: 2.375Nb2O5:0.5Ho2O3:17.87B4C |
| HE TM0.9Ho0.1B2 | (Hf0.225Zr0.225Ta0.225Nb0.225Ho0.1)B2 | 4.5HfO2:4.5ZrO2:2.25Ta2O5: 2.25Nb2O5:1Ho2O3:17.74B4C |
| HE TM0.95Dy0.05B2 | (Hf0.2375Zr0.2375Ta0.2375Nb0.2375Dy0.05)B2 | 4.75HfO2:4.75ZrO2:2.375Ta2O5: 2.375Nb2O5:0.5Dy2O3:17.87B4C |
| HE TM0.9Dy0.1B2 | (Hf0.225Zr0.225Ta0.225Nb0.225Dy0.1)B2 | 4.5HfO2:4.5ZrO2:2.25Ta2O5: 2.25Nb2O5:1Dy2O3:17.74B4C |
Table 1. Composition and the corresponding molar ratio of raw materials of HE TMREB2s.
| Specimen code | Composition | Molar ratio of raw materials |
|---|---|---|
| HE TM0.9Sc0.1B2 | (Hf0.225Zr0.225Ta0.225Nb0.225Sc0.1)B2 | 4.5HfO2:4.5ZrO2:2.25Ta2O5: 2.25Nb2O5:1Sc2O3:17.74B4C |
| HE TM0.8Sc0.2B2 | (Hf0.2Zr0.2Ta0.2Nb0.2Sc0.2)B2 | 4HfO2:4ZrO2:2Ta2O5: 4Nb2O5:2Sc2O3:17.48B4C |
| HE TM0.9Tm0.1B2 | (Hf0.225Zr0.225Ta0.225Nb0.225Lu0.1)B2 | 4.5HfO2:4.5ZrO2:2.25Ta2O5: 2.25Nb2O5:1Lu2O3:17.74B4C |
| HE TM0.8Tm0.2B2 | (Hf0.2Zr0.2Ta0.2Nb0.2Lu0.2)B2 | 4HfO2:4ZrO2:2Ta2O5: 4Nb2O5:2Lu2O3:17.48B4C |
| HE TM0.9Lu0.1B2 | (Hf0.225Zr0.225Ta0.225Nb0.225Tm0.1)B2 | 4.5HfO2:4.5ZrO2:2.25Ta2O5: 2.25Nb2O5:1Tm2O3:17.74B4C |
| HE TM0.8Lu0.2B2 | (Hf0.2Zr0.2Ta0.2Nb0.2Tm0.2)B2 | 4HfO2:4ZrO2:2Ta2O5: 4Nb2O5:2Tm2O3:17.48B4C |
| HE TM0.9Er0.1B2 | (Hf0.225Zr0.225Ta0.225Nb0.225Er0.1)B2 | 4.5HfO2:4.5ZrO2:2.25Ta2O5: 2.25Nb2O5:1Er2O3:17.74B4C |
| HE TM0.8Er0.2B2 | (Hf0.2Zr0.2Ta0.2Nb0.2Er0.2)B2 | 4HfO2:4ZrO2:2Ta2O5: 4Nb2O5:2Er2O3:17.48B4C |
| HE TM0.95Ho0.05B2 | (Hf0.2375Zr0.2375Ta0.2375Nb0.2375Ho0.05)B2 | 4.75HfO2:4.75ZrO2:2.375Ta2O5: 2.375Nb2O5:0.5Ho2O3:17.87B4C |
| HE TM0.9Ho0.1B2 | (Hf0.225Zr0.225Ta0.225Nb0.225Ho0.1)B2 | 4.5HfO2:4.5ZrO2:2.25Ta2O5: 2.25Nb2O5:1Ho2O3:17.74B4C |
| HE TM0.95Dy0.05B2 | (Hf0.2375Zr0.2375Ta0.2375Nb0.2375Dy0.05)B2 | 4.75HfO2:4.75ZrO2:2.375Ta2O5: 2.375Nb2O5:0.5Dy2O3:17.87B4C |
| HE TM0.9Dy0.1B2 | (Hf0.225Zr0.225Ta0.225Nb0.225Dy0.1)B2 | 4.5HfO2:4.5ZrO2:2.25Ta2O5: 2.25Nb2O5:1Dy2O3:17.74B4C |
Fig. 2. (a) Crystal structure of metal diborides and (b) experimental lattice constant c versus a of different metal diborides: blue dashed line represents the ideal c/a axial ratio of the metal diborides.
Fig. 3. Heat maps for mixing enthalpy of (MM′)B2 with the AlB2-type structure, ΔHmix[(MM′)B2, H], calculated from first-principles using Eq. (6), the annotation ‘H’ in the figure represents the formation of the AlB2-type structure for each combination.
Fig. 4. Energy distribution of the local mixing enthalpies of all possible configurations of HE TMB2s: (a) (Hf0.2Zr0.2Nb0.2Ta0.2Ti0.2)B2, (b) (Hf0.2Zr0.2Mo0.2Nb0.2Ti0.2)B2, (c) (Hf0.2Mo0.2Ta0.2Nb0.2Ti0.2)B2, and (d) (Hf0.2Zr0.2W0.2Mo0.2Ti0.2)B2.
Fig. 5. Schematics of high-entropy diborides predictions: (a) energy distribution of the local mixing enthalpies of all possible configurations of (Hf0.2Zr0.2Ta0.2Nb0.2Sc0.2)B2, (b-f) five novel combinations obtained by replacing Sc with RE (RE = Lu, Tm, Er, Ho and Dy).
| Composition code | Composition | Lattice constant | |
|---|---|---|---|
| a (Å) | c (Å) | ||
| HE TM0.9Sc0.1B2 | (Hf0.225Zr0.225Ta0.225Nb0.225Sc0.1)B2 | 3.120 | 3.419 |
| HE TM0.8Sc0.2B2 | (Hf0.2Zr0.2Ta0.2Nb0.2Sc0.2)B2 | 3.120 | 3.430 |
| HE TM0.9Tm0.1B2 | (Hf0.225Zr0.225Ta0.225Nb0.225Tm0.1)B2 | 3.138 | 3.439 |
| HE TM0.8Tm0.2B2 | (Hf0.2Zr0.2Ta0.2Nb0.2Tm0.2)B2 | 3.140 | 3.449 |
| HE TM0.9Lu0.1B2 | (Hf0.225Zr0.225Ta0.225Nb0.225Lu0.1)B2 | 3.129 | 3.440 |
| HE TM0.8Lu0.2B2 | (Hf0.2Zr0.2Ta0.2Nb0.2Lu0.2)B2 | 3.131 | 3.449 |
| HE TM0.9Er0.1B2 | (Hf0.225Zr0.225Ta0.225Nb0.225Er0.1)B2 | 3.135 | 3.445 |
| HE TM0.8Er0.2B2 | (Hf0.2Zr0.2Ta0.2Nb0.2Er0.2)B2 | 3.137 | 3.461 |
| HE TM0.95Ho0.05B2 | (Hf0.2375Zr0.2375Ta0.2375Nb0.2375Ho0.05)B2 | 3.13 | 3.419 |
| HE TM0.9Ho0.1B2 | (Hf0.225Zr0.225Ta0.225Nb0.225Ho0.1)B2 | 3.132 | 3.434 |
| HE TM0.95Dy0.05B2 | (Hf0.2375Zr0.2375Ta0.2375Nb0.2375Dy0.05)B2 | 3.127 | 3.421 |
| HE TM0.9Dy0.1B2 | (Hf0.225Zr0.225Ta0.225Nb0.225Dy0.1)B2 | 3.13 | 3.434 |
Table 2. Lattice parameters of HE TMREB2s (TM = Hf, Zr, Ta and Nb, RE = Sc, Lu, Tm, Er, Ho and Dy).
| Composition code | Composition | Lattice constant | |
|---|---|---|---|
| a (Å) | c (Å) | ||
| HE TM0.9Sc0.1B2 | (Hf0.225Zr0.225Ta0.225Nb0.225Sc0.1)B2 | 3.120 | 3.419 |
| HE TM0.8Sc0.2B2 | (Hf0.2Zr0.2Ta0.2Nb0.2Sc0.2)B2 | 3.120 | 3.430 |
| HE TM0.9Tm0.1B2 | (Hf0.225Zr0.225Ta0.225Nb0.225Tm0.1)B2 | 3.138 | 3.439 |
| HE TM0.8Tm0.2B2 | (Hf0.2Zr0.2Ta0.2Nb0.2Tm0.2)B2 | 3.140 | 3.449 |
| HE TM0.9Lu0.1B2 | (Hf0.225Zr0.225Ta0.225Nb0.225Lu0.1)B2 | 3.129 | 3.440 |
| HE TM0.8Lu0.2B2 | (Hf0.2Zr0.2Ta0.2Nb0.2Lu0.2)B2 | 3.131 | 3.449 |
| HE TM0.9Er0.1B2 | (Hf0.225Zr0.225Ta0.225Nb0.225Er0.1)B2 | 3.135 | 3.445 |
| HE TM0.8Er0.2B2 | (Hf0.2Zr0.2Ta0.2Nb0.2Er0.2)B2 | 3.137 | 3.461 |
| HE TM0.95Ho0.05B2 | (Hf0.2375Zr0.2375Ta0.2375Nb0.2375Ho0.05)B2 | 3.13 | 3.419 |
| HE TM0.9Ho0.1B2 | (Hf0.225Zr0.225Ta0.225Nb0.225Ho0.1)B2 | 3.132 | 3.434 |
| HE TM0.95Dy0.05B2 | (Hf0.2375Zr0.2375Ta0.2375Nb0.2375Dy0.05)B2 | 3.127 | 3.421 |
| HE TM0.9Dy0.1B2 | (Hf0.225Zr0.225Ta0.225Nb0.225Dy0.1)B2 | 3.13 | 3.434 |
| Elements | Formation energy (eV/atom) | | |
|---|---|---|---|
| REB2s | REB4s | ||
| Sc | -0.839 | ||
| Lu | -0.692 | -0.557 | 0.135 |
| Tm | -0.653 | -0.578 | 0.075 |
| Er | -0.622 | -0.586 | 0.036 |
| Ho | -0.593 | -0.592 | 0.001 |
| Dy | -0.561 | -0.596 | -0.035 |
Table 3. The formation energies of rare earth diborides and rare earth tetraborides and their differences [62].
| Elements | Formation energy (eV/atom) | | |
|---|---|---|---|
| REB2s | REB4s | ||
| Sc | -0.839 | ||
| Lu | -0.692 | -0.557 | 0.135 |
| Tm | -0.653 | -0.578 | 0.075 |
| Er | -0.622 | -0.586 | 0.036 |
| Ho | -0.593 | -0.592 | 0.001 |
| Dy | -0.561 | -0.596 | -0.035 |
| Composition code | Lattice parameters | ρ (g/cm3) | ρth (g/cm3) | ρ/ρth (%) | |
|---|---|---|---|---|---|
| a (Å) | c (Å) | ||||
| HE TM0.8Sc0.2B2 | 3.118 | 3.426 | 7.76 | 8.02 | 96.7 |
| HE TM0.8Lu0.2B2 | 3.134 | 3.454 | 8.80 | 9.34 | 94.1 |
| HE TM0.8Tm0.2B2 | 3.138 | 3.474 | 8.51 | 9.19 | 92.6 |
| HE TM0.8Er0.2B2 | 3.141 | 3.478 | - | 9.15 | - |
Table 4. Lattice parameters, measured density (ρ), theoretical density (ρth) and relative density (ρ/ρth) of HE TMREB2s bulk specimens.
| Composition code | Lattice parameters | ρ (g/cm3) | ρth (g/cm3) | ρ/ρth (%) | |
|---|---|---|---|---|---|
| a (Å) | c (Å) | ||||
| HE TM0.8Sc0.2B2 | 3.118 | 3.426 | 7.76 | 8.02 | 96.7 |
| HE TM0.8Lu0.2B2 | 3.134 | 3.454 | 8.80 | 9.34 | 94.1 |
| HE TM0.8Tm0.2B2 | 3.138 | 3.474 | 8.51 | 9.19 | 92.6 |
| HE TM0.8Er0.2B2 | 3.141 | 3.478 | - | 9.15 | - |
Fig. 8. SEM images and EDS elemental mappings of four bulk samples synthesized via SPS: (a) to (c) bulk samples showing homogenous elemental distributions, (d) bulk sample exhibiting Er-rich secondary phase particles.
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