
人工晶体学报 ›› 2025, Vol. 54 ›› Issue (9): 1584-1592.DOI: 10.16553/j.cnki.issn1000-985x.2025.0068
收稿日期:2025-04-02
出版日期:2025-09-20
发布日期:2025-09-23
通信作者:
孙霄霄
作者简介:冷昊宁(1999—),男,黑龙江省人,硕士研究生。E-mail:lenghaoning1999@163.com
基金资助:
LENG Haoning(
), SUN Xiaoxiao(
), MU Baixu, NING Lina
Received:2025-04-02
Online:2025-09-20
Published:2025-09-23
Contact:
SUN Xiaoxiao
摘要: 为了深入掌握钙钛矿氧化物KNbO3在高压条件下的相变行为,并为铁电材料在极端条件下的工程应用提供关键参数,本文采用基于密度泛函理论的第一性原理方法,在绝对零度(0 K)条件下,对KNbO3高压下的结构相变、弹性性质及电子性质进行系统研究。计算结果表明,在零压下,KNbO3的最稳定结构为正交Amm2结构,材料表现为延展性,且为中心力固体。在0~50 GPa压力范围内,KNbO3经历了两次相变:7.7 GPa时,由正交Amm2结构转变为四方P4mm结构;10.1 GPa时,由四方P4mm结构转变为三方R3mR结构。两次相变均伴随着体积变化,为一级相变。弹性分析显示,KNbO3在相变过程中经历了从延展性到脆性的转变,并且具有弹性各向异性特征。能带结构分析表明,零压下Amm2结构的带隙为2.125 eV,为间接带隙半导体。随着压力的增加,带隙先减小后增大。本研究不仅丰富了对KNbO3相变行为的理解,还为设计和应用新型KNbO3材料提供了理论支持。
中图分类号:
冷昊宁, 孙霄霄, 穆柏旭, 宁丽娜. KNbO3高压下相变行为的第一性原理研究[J]. 人工晶体学报, 2025, 54(9): 1584-1592.
LENG Haoning, SUN Xiaoxiao, MU Baixu, NING Lina. First-Principles Study on the Phase Transition Behavior of KNbO3 under High Pressure[J]. Journal of Synthetic Crystals, 2025, 54(9): 1584-1592.
| Space group | a/nm | b/nm | c/nm | Fractional coordinates of atoms | H/eV | Reference |
|---|---|---|---|---|---|---|
| R3mR | 0.571 9 | 0.571 9 | 0.703 9 | K 1a(0.013 0,0.013 0,0.013 0) Nb 1a(0.500 0,0.500 0,0.500 0) O 3b(0.530 1,0.530 1,0.033 3) | -3 647.597 5 | This paper |
| R3mR | 0.565 1 | 0.565 1 | 0.694 7 | K 1a(0.000 0,0.000 0,0.000 0) Nb 1a(0.000 0,0.000 0,0.489 6) O 3b(0.175 7,0.342 1,0.354 3) | [ | |
| P4mm | 0.399 7 | 0.399 7 | 0.414 8 | K 1a(0.000 0,0.000 0,0.018 0) Nb 1b(0.500 0,0.500 0,0.500 0) O 1b(0.500 0,0.500 0,0.044 0) O 2c(0.500 0,0.000 0,0.540 0) | -3 647.588 6 | This paper |
| P4mm | 0.399 6 | 0.399 6 | 0.406 3 | K 1b(0.500 0,0.500 0, 0.556 1) Nb 1a(0.000 0,0.000 0,0.057 7) O 2c(0.500 0,0.000 0,-0.078 6) O 1a(0.000 0,0.000 0,0.558 5) | [ | |
| Amm2 | 0.398 5 | 0.576 3 | 0.579 4 | K 2a(0.000 0,0.000 0,0.013 8) Nb 2b(0.500 0,0.000 0,0.500 0) O 2a(0.000 0,0.000 0,0.536 4) O 4e(0.500 0,0.247 6,0.284 2) | -3 647.597 8 | This paper |
| Amm2 | 0.397 4 | 0.569 5 | 0.572 3 | K 2a(0.000 0,0.000 0,0.000 0) Nb 2b(0.500 0,0.000 0,0.481 1) O 2a(0.000 0,0.000 0,0.442 4) O 4e(0.500 0,0.234 5,0.183 0) | [ | |
| Pbnm | 0.568 4 | 0.568 4 | 0.803 5 | K 4b(0.000 0,0.500 0,0.000 0) Nb 4c(0.993 8,0.007 9,0.250 0) O 4c(0.054 7,0.491 7,0.250 0) O 8d(0.721 2,0.278 7,0.023 4) | -3 647.534 2 | This paper |
| Bmmb | 0.803 9 | 0.803 5 | 0.803 9 | K 4c(0.000 0,0.250 0,-0.007 0) K 4c(0.000 0,0.250 0,0.489 0) Nb 8d(0.250 0,0.000 0,0.250 0) O 8e(0.278 5,0.000 0,0.000 0) O 8f(0.000 0,0.019 1,0.226 3) O 8g(0.267 7,0.250 0,0.247 8) | -3 647.534 2 | This paper |
| Pm3m | 0.401 8 | 0.401 8 | 0.401 8 | K 1a(0.000 0,0.000 0,0.000 0) Nb 1b(0.500 0,0.500 0,0.500 0) O 3c(0.500 0,0.500 0,0.000 0) | -3 647.558 2 | This paper |
| R3cH | 0.572 2 | 0.572 2 | 1.409 9 | K 6a(0.000 0,0.000 0,0.272 3) Nb 6a(0.000 0,0.000 0,0.016 4) O 18b(0.099 9,0.336 7,0.083 3) | -3 647.590 7 | This paper |
| Cmcm | 0.803 9 | 0.803 9 | 0.803 5 | K 8d(0.750 0,0.750 0,0.000 0) Nb 4c(-0.012 0,0.000 0,0.250 0) Nb 4c(0.488 0,0.000 0,0.250 0) O 8e(0.000 0,-0.265 0,0.000 0) O 8f(-0.235 0,0.000 0,-0.012 0) O 8g(0.750 0,-0.238 6,0.250 0) | -3 647.534 2 | This paper |
| Bmm2 | 0.576 3 | 0.398 4 | 0.579 4 | K 2a(0.000 0,0.000 0,0.000 0) Nb 2b(0.000 0,0.500 0,0.517 0) O 2b(0.000 0,0.500 0,0.021 0) O 4d(0.254 0,0.000 0,0.285 0) | -3 647.597 0 | This paper |
| Ccmm | 0.803 8 | 0.803 9 | 0.803 5 | K 8d(0.750 0,0.750 0,0.000 0) K 4c(-0.012 0,0.000 0,0.250 0) Nb 4c(0.488 0,0.000 0,0.250 0) O 8e(0.000 0,-0.265 0,0.000 0) O 8f(-0.235 0,0.000 0,-0.012 0) O 8g(0.750 0,-0.238 0,0.250 0) | -3 647.534 2 | This paper |
| Pmmm | 0.401 9 | 0.401 9 | 0.401 9 | K 4c(0.000 0,0.000 0,0.000 0) Nb 8d(0.500 0,0.500 0,0.500 0) O 8e(0.500 0,0.000 0,0.500 0) O 8f(0.500 0,0.500 0,0.000 0) O 8g(0.000 0,0.500 0,0.500 0) | -3 647.558 1 | This paper |
表1 KNbO3多种结构的晶格常数、坐标值与焓值
Table 1 Lattice constants, coordinate and enthalpy values for the considered initial structures of KNbO3
| Space group | a/nm | b/nm | c/nm | Fractional coordinates of atoms | H/eV | Reference |
|---|---|---|---|---|---|---|
| R3mR | 0.571 9 | 0.571 9 | 0.703 9 | K 1a(0.013 0,0.013 0,0.013 0) Nb 1a(0.500 0,0.500 0,0.500 0) O 3b(0.530 1,0.530 1,0.033 3) | -3 647.597 5 | This paper |
| R3mR | 0.565 1 | 0.565 1 | 0.694 7 | K 1a(0.000 0,0.000 0,0.000 0) Nb 1a(0.000 0,0.000 0,0.489 6) O 3b(0.175 7,0.342 1,0.354 3) | [ | |
| P4mm | 0.399 7 | 0.399 7 | 0.414 8 | K 1a(0.000 0,0.000 0,0.018 0) Nb 1b(0.500 0,0.500 0,0.500 0) O 1b(0.500 0,0.500 0,0.044 0) O 2c(0.500 0,0.000 0,0.540 0) | -3 647.588 6 | This paper |
| P4mm | 0.399 6 | 0.399 6 | 0.406 3 | K 1b(0.500 0,0.500 0, 0.556 1) Nb 1a(0.000 0,0.000 0,0.057 7) O 2c(0.500 0,0.000 0,-0.078 6) O 1a(0.000 0,0.000 0,0.558 5) | [ | |
| Amm2 | 0.398 5 | 0.576 3 | 0.579 4 | K 2a(0.000 0,0.000 0,0.013 8) Nb 2b(0.500 0,0.000 0,0.500 0) O 2a(0.000 0,0.000 0,0.536 4) O 4e(0.500 0,0.247 6,0.284 2) | -3 647.597 8 | This paper |
| Amm2 | 0.397 4 | 0.569 5 | 0.572 3 | K 2a(0.000 0,0.000 0,0.000 0) Nb 2b(0.500 0,0.000 0,0.481 1) O 2a(0.000 0,0.000 0,0.442 4) O 4e(0.500 0,0.234 5,0.183 0) | [ | |
| Pbnm | 0.568 4 | 0.568 4 | 0.803 5 | K 4b(0.000 0,0.500 0,0.000 0) Nb 4c(0.993 8,0.007 9,0.250 0) O 4c(0.054 7,0.491 7,0.250 0) O 8d(0.721 2,0.278 7,0.023 4) | -3 647.534 2 | This paper |
| Bmmb | 0.803 9 | 0.803 5 | 0.803 9 | K 4c(0.000 0,0.250 0,-0.007 0) K 4c(0.000 0,0.250 0,0.489 0) Nb 8d(0.250 0,0.000 0,0.250 0) O 8e(0.278 5,0.000 0,0.000 0) O 8f(0.000 0,0.019 1,0.226 3) O 8g(0.267 7,0.250 0,0.247 8) | -3 647.534 2 | This paper |
| Pm3m | 0.401 8 | 0.401 8 | 0.401 8 | K 1a(0.000 0,0.000 0,0.000 0) Nb 1b(0.500 0,0.500 0,0.500 0) O 3c(0.500 0,0.500 0,0.000 0) | -3 647.558 2 | This paper |
| R3cH | 0.572 2 | 0.572 2 | 1.409 9 | K 6a(0.000 0,0.000 0,0.272 3) Nb 6a(0.000 0,0.000 0,0.016 4) O 18b(0.099 9,0.336 7,0.083 3) | -3 647.590 7 | This paper |
| Cmcm | 0.803 9 | 0.803 9 | 0.803 5 | K 8d(0.750 0,0.750 0,0.000 0) Nb 4c(-0.012 0,0.000 0,0.250 0) Nb 4c(0.488 0,0.000 0,0.250 0) O 8e(0.000 0,-0.265 0,0.000 0) O 8f(-0.235 0,0.000 0,-0.012 0) O 8g(0.750 0,-0.238 6,0.250 0) | -3 647.534 2 | This paper |
| Bmm2 | 0.576 3 | 0.398 4 | 0.579 4 | K 2a(0.000 0,0.000 0,0.000 0) Nb 2b(0.000 0,0.500 0,0.517 0) O 2b(0.000 0,0.500 0,0.021 0) O 4d(0.254 0,0.000 0,0.285 0) | -3 647.597 0 | This paper |
| Ccmm | 0.803 8 | 0.803 9 | 0.803 5 | K 8d(0.750 0,0.750 0,0.000 0) K 4c(-0.012 0,0.000 0,0.250 0) Nb 4c(0.488 0,0.000 0,0.250 0) O 8e(0.000 0,-0.265 0,0.000 0) O 8f(-0.235 0,0.000 0,-0.012 0) O 8g(0.750 0,-0.238 0,0.250 0) | -3 647.534 2 | This paper |
| Pmmm | 0.401 9 | 0.401 9 | 0.401 9 | K 4c(0.000 0,0.000 0,0.000 0) Nb 8d(0.500 0,0.500 0,0.500 0) O 8e(0.500 0,0.000 0,0.500 0) O 8f(0.500 0,0.500 0,0.000 0) O 8g(0.000 0,0.500 0,0.500 0) | -3 647.558 1 | This paper |
图3 KNbO3相变前、后三种竞争结构的体积与晶格常数随压强的变化曲线
Fig.3 Curves of volume and lattice constants of three competitive structures of KNbO3 as a function of pressure before and after phase transition
| Parameter | Amm2, 0 GPa | P4mm,0 GPa | P4mm,7.7 GPa | R3mR,0 GPa | R3mR,10.1 GPa |
|---|---|---|---|---|---|
| C11/GPa | 330.7 | 328 | 437 | 194 | 331 |
| C22/GPa | 193.6 | — | — | — | — |
| C33/GPa | 166.9 | 93 | 236 | 186 | 310 |
| C44/GPa | 20.4 | -90 | 93 | 31 | 95 |
| C55/GPa | 19.1 | — | — | — | — |
| C66/GPa | 84.1 | 89 | 93 | — | — |
| C12/GPa | 82.2 | 90 | 88 | 63 | 129 |
| C13/GPa | 79.0 | 66 | 97 | 40 | 131 |
| C14/GPa | — | — | — | -30 | 4 |
| C23/GPa | 22.7 | — | — | — | — |
| B/GPa | 88.1 | 110.63 | 179 | 75 | 145 |
| G/GPa | 47.2 | 99.39 | 94 | 61 | 145 |
| E/GPa | 120.2 | 229.45 | 240 | 144 | 328 |
| ν | 0.27 | 0.15 | 0.28 | 0.179 | 0.125 |
| B/G | 1.86 | — | 1.9 | 1.2 | 1 |
| C44/C66 | — | -1.01 | — | — | — |
表2 零压、相变压下KNbO3三种竞争结构的弹性常数Cij 、弹性模量E、剪切模量G、体积模量B与泊松比 ν
Table 2 Elastic constants Cij, elastic modulus E, shear modulus G, bulk modulus B and Poisson ratio ν of three competitive structures of KNbO3 under zero pressure and phase transition pressure
| Parameter | Amm2, 0 GPa | P4mm,0 GPa | P4mm,7.7 GPa | R3mR,0 GPa | R3mR,10.1 GPa |
|---|---|---|---|---|---|
| C11/GPa | 330.7 | 328 | 437 | 194 | 331 |
| C22/GPa | 193.6 | — | — | — | — |
| C33/GPa | 166.9 | 93 | 236 | 186 | 310 |
| C44/GPa | 20.4 | -90 | 93 | 31 | 95 |
| C55/GPa | 19.1 | — | — | — | — |
| C66/GPa | 84.1 | 89 | 93 | — | — |
| C12/GPa | 82.2 | 90 | 88 | 63 | 129 |
| C13/GPa | 79.0 | 66 | 97 | 40 | 131 |
| C14/GPa | — | — | — | -30 | 4 |
| C23/GPa | 22.7 | — | — | — | — |
| B/GPa | 88.1 | 110.63 | 179 | 75 | 145 |
| G/GPa | 47.2 | 99.39 | 94 | 61 | 145 |
| E/GPa | 120.2 | 229.45 | 240 | 144 | 328 |
| ν | 0.27 | 0.15 | 0.28 | 0.179 | 0.125 |
| B/G | 1.86 | — | 1.9 | 1.2 | 1 |
| C44/C66 | — | -1.01 | — | — | — |
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