Journal of Inorganic Materials ›› 2026, Vol. 41 ›› Issue (7): 1001-1010.DOI: 10.15541/jim20260017
• DATA PAPER • Previous Articles Next Articles
ZUO Zhiping1,2(
), GUO Chun1,2, ZHOU Zhiyong1(
)
Received:2026-01-12
Revised:2026-02-27
Published:2026-07-20
Online:2026-03-02
Contact:
ZHOU Zhiyong, professor. E-mail: zyzhou@mail.sic.ac.cnAbout author:ZUO Zhiping (2001-), male, PhD candidate. E-mail: zuozhiping23@mails.ucas.ac.cn
Supported by:CLC Number:
ZUO Zhiping, GUO Chun, ZHOU Zhiyong. Machine Learning-assisted Design of High-temperature BSPT-based Piezoelectric Ceramics with Enhanced Dual Properties[J]. Journal of Inorganic Materials, 2026, 41(7): 1001-1010.
Fig. 1 (a) Results of model evaluations; (b) Performance of the XGB model on the d33 dataset; (c) Performance of the BR model on the TC dataset Colorful figures are available on website
Fig. 2 (a) Predicted results of the machine learning model; (b) XRD patterns of the BSPTGW1000x ceramics and enlarged patterns in the 2θ range of 43°-46°; (c) Room temperature Raman spectra of the BSPTGW1000x ceramics
Fig. 4 (a-d) Temperature dependence of the dielectric constant for (a) BSPTGW05, (b) BSPTGW10, (c) BSPTGW15, and (d) BSPTGW20; (e-h) Line fitted by the Curie-Weiss relationship of BSPTGW1000x ceramics Colorful figures are available on website
Fig. 5 (a) Hysteresis loops, (b) unipolar strain curves, (c) bipolar strain curves, and (d) the Pr, EC, and d33* for BSPTGW1000x ceramics Colorful figures are available on website
Fig. 6 (a) d33 and TC of BSPTGW1000x ceramics; (b) Comparison of d33 and TC between BSPTGW10 ceramic and previously reported piezoelectric ceramics; (c) Rate of change of in-situ d33 of BSPTGW10 ceramic; (d) Comparison of d33 and tanδ between BSPTGW10 ceramic and previously reported piezoelectric ceramics
Fig. 7 (a-d) PFM images of BSPTGW1000x ceramics; (e-h) “Domain writing” of BSPTGW1000x ceramics (a, e) x=0.005; (b, f) x=0.010; (c, g) x=0.015; (d, h) x=0.020. Applied voltages for the four parts in Figs. (e-h) were 3, 5, 7, and 9 V, respectively. Colorful figures are available on website
| Feature | Description |
|---|---|
| RCS12_A | Shannon's (1976) ionic radii 12 of A-site element |
| RC_A | Covalent radii of A-site element |
| RP_A | Pseudopotential core radii of A-site element |
| Rdce_A | Core electron distance of A-site element |
| Rdve_A | Valence electron distance of A-site element |
| Ven_A | Valence electron number of A-site element |
| Ne/IR_A | Ratio of electron number to ionic radii (A-site) |
| CNE_C/IR_A | Ratio of charge nuclear effective (Clementi) to ionic radii (A-site) |
| CNE_S/IR_A | Ratio of nuclear charge effective (Slater) to ionic radii (A-site) |
| VEC/Z_A | Ratio of valence electron number to nuclear charge (A-site) |
| Val/IR_A | Ratio of oxidation state to ionic radii (A-site) |
| CNE_C_A | Charge nuclear effective (Clementi) of A-site element |
| CNE_S_A | Nuclear charge effective (Slater) of A-site element |
| Valence_A | Oxidation state of A-site element |
| AN_A | Atomic number of A-site element |
| AW_A | Atomic weight of A-site element |
| AV_A | Atomic volume of A-site element |
| AR_A | Atomic radius of A-site element |
| IP_A | Ionic polarizability of A-site element |
| Electrons_A | Electron number of A-site element |
| ENA_A | Electronegativity (Alfred-Rochow) of A-site element |
| ENMB_A | Electronegativity (Martynov & Batsanov) of A-site element |
| ENP_A | Electronegativity (Pauling) of A-site element |
| EA_A | Electron affinity of A-site element |
| RVdw_A | Van der Waals radius of A-site element |
| I1_A | First ionization energy of A-site element |
| I2_A | Second ionization energy of A-site element |
| I3_A | Third ionization energy of A-site element |
| OF_A | Octahedral factor calculated by Shannon's ionic radii (A-site) |
| RCS6_B | Shannon's (1976) ionic radii 6 of B-site element |
| RC_B | Covalent radii of B-site element |
| RP_B | Pseudopotential core radii of B-site element |
| Rdce_B | Core electron distance of B-site element |
| Rdve_B | Valence electron distance of B-site element |
| Ven_B | Valence electron number of B-site element |
| Ne/IR_B | Ratio of electron number to ionic radii (B-site) |
| CNE_C/IR_B | Ratio of charge nuclear effective (Clementi) to ionic radii (B-site) |
| CNE_S/IR_B | Ratio of nuclear charge effective (Slater) to ionic radii (B-site) |
| VEC/Z_B | Ratio of valence electron number to nuclear charge (B-site) |
| Val/IR_B | Ratio of oxidation state to ionic radii (B-site) |
| CNE_C_B | Charge nuclear effective (Clementi) of B-site element |
| CNE_S_B | Nuclear charge effective (Slater) of B-site element |
| Valence_B | Oxidation state of B-site element |
| AN_B | Atomic number of B-site element |
| AW_B | Atomic weight of B-site element |
| AV_B | Atomic volume of B-site element |
| AR_B | Atomic radius of B-site element |
| IP_B | Ionic polarizability of B-site element |
| Electrons_B | Electron number of B-site element |
| ENA_B | Electronegativity (Alfred-Rochow) of B-site element |
| ENMB_B | Electronegativity (Martynov & Batsanov) of B-site element |
| ENP_B | Electronegativity (Pauling) of B-site element |
| EA_B | Electron affinity of B-site element |
| RVdw_B | Van der Waals radius of B-site element |
| I1_B | First ionization energy of B-site element |
| I2_B | Second ionization energy of B-site element |
| I3_B | Third ionization energy of B-site element |
| OF_B | Octahedral factor calculated by Shannon's ionic radii (B-site) |
| t | Tolerance_factor |
Table S1 Abbreviations and detailed meanings of all features
| Feature | Description |
|---|---|
| RCS12_A | Shannon's (1976) ionic radii 12 of A-site element |
| RC_A | Covalent radii of A-site element |
| RP_A | Pseudopotential core radii of A-site element |
| Rdce_A | Core electron distance of A-site element |
| Rdve_A | Valence electron distance of A-site element |
| Ven_A | Valence electron number of A-site element |
| Ne/IR_A | Ratio of electron number to ionic radii (A-site) |
| CNE_C/IR_A | Ratio of charge nuclear effective (Clementi) to ionic radii (A-site) |
| CNE_S/IR_A | Ratio of nuclear charge effective (Slater) to ionic radii (A-site) |
| VEC/Z_A | Ratio of valence electron number to nuclear charge (A-site) |
| Val/IR_A | Ratio of oxidation state to ionic radii (A-site) |
| CNE_C_A | Charge nuclear effective (Clementi) of A-site element |
| CNE_S_A | Nuclear charge effective (Slater) of A-site element |
| Valence_A | Oxidation state of A-site element |
| AN_A | Atomic number of A-site element |
| AW_A | Atomic weight of A-site element |
| AV_A | Atomic volume of A-site element |
| AR_A | Atomic radius of A-site element |
| IP_A | Ionic polarizability of A-site element |
| Electrons_A | Electron number of A-site element |
| ENA_A | Electronegativity (Alfred-Rochow) of A-site element |
| ENMB_A | Electronegativity (Martynov & Batsanov) of A-site element |
| ENP_A | Electronegativity (Pauling) of A-site element |
| EA_A | Electron affinity of A-site element |
| RVdw_A | Van der Waals radius of A-site element |
| I1_A | First ionization energy of A-site element |
| I2_A | Second ionization energy of A-site element |
| I3_A | Third ionization energy of A-site element |
| OF_A | Octahedral factor calculated by Shannon's ionic radii (A-site) |
| RCS6_B | Shannon's (1976) ionic radii 6 of B-site element |
| RC_B | Covalent radii of B-site element |
| RP_B | Pseudopotential core radii of B-site element |
| Rdce_B | Core electron distance of B-site element |
| Rdve_B | Valence electron distance of B-site element |
| Ven_B | Valence electron number of B-site element |
| Ne/IR_B | Ratio of electron number to ionic radii (B-site) |
| CNE_C/IR_B | Ratio of charge nuclear effective (Clementi) to ionic radii (B-site) |
| CNE_S/IR_B | Ratio of nuclear charge effective (Slater) to ionic radii (B-site) |
| VEC/Z_B | Ratio of valence electron number to nuclear charge (B-site) |
| Val/IR_B | Ratio of oxidation state to ionic radii (B-site) |
| CNE_C_B | Charge nuclear effective (Clementi) of B-site element |
| CNE_S_B | Nuclear charge effective (Slater) of B-site element |
| Valence_B | Oxidation state of B-site element |
| AN_B | Atomic number of B-site element |
| AW_B | Atomic weight of B-site element |
| AV_B | Atomic volume of B-site element |
| AR_B | Atomic radius of B-site element |
| IP_B | Ionic polarizability of B-site element |
| Electrons_B | Electron number of B-site element |
| ENA_B | Electronegativity (Alfred-Rochow) of B-site element |
| ENMB_B | Electronegativity (Martynov & Batsanov) of B-site element |
| ENP_B | Electronegativity (Pauling) of B-site element |
| EA_B | Electron affinity of B-site element |
| RVdw_B | Van der Waals radius of B-site element |
| I1_B | First ionization energy of B-site element |
| I2_B | Second ionization energy of B-site element |
| I3_B | Third ionization energy of B-site element |
| OF_B | Octahedral factor calculated by Shannon's ionic radii (B-site) |
| t | Tolerance_factor |
| Ionic size & geometric descriptors | Ionic size & geometric descriptors | ||
|---|---|---|---|
| RCS12_A | RCS12_B | Valence_A | Valence_B |
| RC_A | RC_B | CNE_C_A | CNE_C_B |
| RP_A | RP_B | CNE_S_A | CNE_S_B |
| AR_A | AR_B | Rdce_A | Rdce_B |
| RVdw_A | RVdw_B | Rdve_A | Rdve_B |
| Electronic & bonding descriptors | Derived ratios & perovskite structural factors | ||
| Ven_A | Ven_B | Ne/IR_A | |
| Electrons_A | Electrons_B | CNE_C/IR_A | |
| IP_A | IP_B | CNE_S/IR_A | |
| ENA_A | ENA_B | VEC/Z_A | |
| ENMB_A | ENMB_B | Val/IR_A | |
| ENP_A | ENP_B | Ne/IR_B | |
| EA_A | EA_B | CNE_C/IR_B | |
| I1_A | I1_B | CNE_S/IR_B | |
| I2_A | I2_B | VEC/Z_B | |
| I3_A | I3_B | Val/IR_B | |
| AN_A | AN_B | OF_A | |
| AW_A | AW_B | OF_B | |
| AV_A | AV_B | t | |
Table S2 Classification of input descriptors used in the machine learning model
| Ionic size & geometric descriptors | Ionic size & geometric descriptors | ||
|---|---|---|---|
| RCS12_A | RCS12_B | Valence_A | Valence_B |
| RC_A | RC_B | CNE_C_A | CNE_C_B |
| RP_A | RP_B | CNE_S_A | CNE_S_B |
| AR_A | AR_B | Rdce_A | Rdce_B |
| RVdw_A | RVdw_B | Rdve_A | Rdve_B |
| Electronic & bonding descriptors | Derived ratios & perovskite structural factors | ||
| Ven_A | Ven_B | Ne/IR_A | |
| Electrons_A | Electrons_B | CNE_C/IR_A | |
| IP_A | IP_B | CNE_S/IR_A | |
| ENA_A | ENA_B | VEC/Z_A | |
| ENMB_A | ENMB_B | Val/IR_A | |
| ENP_A | ENP_B | Ne/IR_B | |
| EA_A | EA_B | CNE_C/IR_B | |
| I1_A | I1_B | CNE_S/IR_B | |
| I2_A | I2_B | VEC/Z_B | |
| I3_A | I3_B | Val/IR_B | |
| AN_A | AN_B | OF_A | |
| AW_A | AW_B | OF_B | |
| AV_A | AV_B | t | |
| Material | Pr/(μC·cm-2) | S/% @5kV/mm | εr | SεrPr |
|---|---|---|---|---|
| BSPTGW05 | 38.75 | 0.255 | 1344 | 13280.40 |
| BSPTGW10 | 40.46 | 0.259 | 1386 | 14524.09 |
| BSPTGW15 | 38.72 | 0.268 | 1332 | 13822.11 |
| BSPTGW20 | 38.33 | 0.278 | 1290 | 13795.35 |
Table S3 Correlation between polarization, electrostrain and dielectric response
| Material | Pr/(μC·cm-2) | S/% @5kV/mm | εr | SεrPr |
|---|---|---|---|---|
| BSPTGW05 | 38.75 | 0.255 | 1344 | 13280.40 |
| BSPTGW10 | 40.46 | 0.259 | 1386 | 14524.09 |
| BSPTGW15 | 38.72 | 0.268 | 1332 | 13822.11 |
| BSPTGW20 | 38.33 | 0.278 | 1290 | 13795.35 |
| Material | Manufacturer | d33/(pC·N-1) | TC/℃ | tanδ/% |
|---|---|---|---|---|
| C-64 | Fuji Ceramics Corporation | 435 | 345 | 1.5 |
| C-602 | Fuji Ceramics Corporation | 310 | 360 | 1.3 |
| C-82 | Fuji Ceramics Corporation | 600 | 195 | 1.9 |
| K-350 | Piezo Technologies | 390 | 360 | 2 |
| K-500 | Piezo Technologies | 580 | 240 | 2 |
| K-600 | Piezo Technologies | 650 | 220 | 2 |
| BSPTGW10 | SICCAS | 525 | 423 | 3.2 |
Table S4 Comparison of BSPTGW10 ceramics with representative commercial piezoelectric material (data for commercial materials are taken from manufacturer datasheets)
| Material | Manufacturer | d33/(pC·N-1) | TC/℃ | tanδ/% |
|---|---|---|---|---|
| C-64 | Fuji Ceramics Corporation | 435 | 345 | 1.5 |
| C-602 | Fuji Ceramics Corporation | 310 | 360 | 1.3 |
| C-82 | Fuji Ceramics Corporation | 600 | 195 | 1.9 |
| K-350 | Piezo Technologies | 390 | 360 | 2 |
| K-500 | Piezo Technologies | 580 | 240 | 2 |
| K-600 | Piezo Technologies | 650 | 220 | 2 |
| BSPTGW10 | SICCAS | 525 | 423 | 3.2 |
| Model | Central atom | 〈λ〉 | σ2/(°)2 |
|---|---|---|---|
| Host | Sc | 1.0596 | 157.75 |
| Ti | 1.0235 | 72.34 | |
| Ga@Sc | Sc | 1.1030 | 659.40 |
| Ti | 1.0335 | 94.96 | |
| Ga | 1.1061 | 661.66 | |
| Ga@Ti | Sc | 1.1146 | 655.33 |
| Ti | 1.0446 | 121.69 | |
| Ga | 1.0849 | 672.50 | |
| W@Sc | Sc | 1.0291 | 89.55 |
| Ti | 1.0223 | 65.38 | |
| W | 1.0212 | 62.90 | |
| W@Ti | Sc | 1.0290 | 85.88 |
| Ti | 1.0172 | 55.95 | |
| W | 1.0183 | 58.70 |
Table S5 Quantitative octahedral distortion metrics for different substitution models
| Model | Central atom | 〈λ〉 | σ2/(°)2 |
|---|---|---|---|
| Host | Sc | 1.0596 | 157.75 |
| Ti | 1.0235 | 72.34 | |
| Ga@Sc | Sc | 1.1030 | 659.40 |
| Ti | 1.0335 | 94.96 | |
| Ga | 1.1061 | 661.66 | |
| Ga@Ti | Sc | 1.1146 | 655.33 |
| Ti | 1.0446 | 121.69 | |
| Ga | 1.0849 | 672.50 | |
| W@Sc | Sc | 1.0291 | 89.55 |
| Ti | 1.0223 | 65.38 | |
| W | 1.0212 | 62.90 | |
| W@Ti | Sc | 1.0290 | 85.88 |
| Ti | 1.0172 | 55.95 | |
| W | 1.0183 | 58.70 |
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