Structural evolution and phase transition behavior of Na0.5Bi0.5TiO3 under high pressure

WANG Runji; FANG Leiming; HE Ruiqi; LENG Haojie; LIU Yongbo; CHEN Xiping; XIE Lei; FENG Qiu; SUN Anwei; XIONG Zhengwei; GAO Zhipeng

doi:10.7498/aps.75.20251220

Abstract
Relaxor ferroelectric sodium bismuth titanate (Na_0.5Bi_0.5TiO₃, NBT) exhibits outstanding ferroelectric characteristics and is widely recognized as a highly promising lead-free ferroelectric material. In order to further promote the application of this environmentally friendly ferroelectric material, it is crucial to gain a comprehensive understanding of its structural evolution and phase transition mechanism under high pressure. This study investigates the structural evolution of NBT under hydrostatic pressure up to 6.8 GPa by integrating in situ high-pressure neutron diffraction experiments with first-principles calculations. Based on high-pressure neutron diffraction experiments conducted at the China Mianyang Research Reactor (CMRR), Rietveld refinement analysis identifies a phase transition from the ambient-pressure R3c phase to the high-pressure Pnma phase in NBT, with a coexistence pressure range of 1.1–4.6 GPa. The bulk modulus of the high-pressure phase Pnma is experimentally determined to be 108.6 GPa for the first time. First-principles calculations further support the thermodynamic tendency for the pressure-induced phase transition from R3c to Pnma and produce a bulk modulus that is in close agreement with the experimental value. By correlating with the experimentally obtained trends of the internal [TiO₆] oxygen octahedral structural changes under high pressure in both phases, this study demonstrates that the difference in their macroscopic compressibility originates from the significantly higher pressure sensitivity of the oxygen octahedral distortion degree in the R3c phase than that of the Pnma phase. This relatively softer internal microstructure results in a lower bulk modulus than that of the Pnma phase. By providing a detailed analysis of the pressure-induced phase transition and microstructural evolution, this study clarifies the relationship between the microscopic structural features of the high-pressure and ambient-pressure phases of NBT and their influence on macroscopic mechanical properties, thereby establishing a fundamental connection between microscopic structural responses and bulk physical behavior under high-pressure conditions. These findings provide crucial experimental data and theoretical support for further improving the high-pressure performance and applications of lead-free ferroelectric materials.

Keywords:
sodium bismuth titanate /

high-pressure neutron diffraction /

first-principles calculation /

phase transition
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图 1 NBT的原位高压中子衍射谱　(a) NBT衍射图谱在压力下的演化; (b) 高压下对Pnma相的精修图; (c) 常压下对R3c相的精修图

Figure 1. In-situ high-pressure neutron diffraction patterns of NBT: (a) Evolution of the NBT diffraction patterns under pressure; (b) rietveld refinement plot for the Pnma phase at high pressure; (c) rietveld refinement plot for the R3c phase at ambient pressure.

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图 2 NBT的两相归一化晶胞体积和含量比随压力拟合曲线图

Figure 2. The fitted curves of normalized unit cell volume and phase content ratio versus pressure for the two-phase NBT.

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图 3 第一性原理计算获得的NBT两相归一化晶胞体积和平均原子能量随压力变化图　(a) 在设定压缩率各向同性下的计算结果; (b) 在设定压力各向同性下的计算结果

Figure 3. Normalized unit cell volume and average atomic energy versus pressure for the two-phase NBT obtained from first-principles calculations: (a) Results under the condition of isotropic compressibility; (b) results under the condition of isotropic pressure.

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图 4 NBT体积压力曲线拟合结果　(a)—(c) 中子衍射实验、Cal-1和Cal-2计算获得的R3c相体积压力曲线; (d)—(f) 中子衍射实验、Cal-1和Cal-2计算获得的Pnma相体积压力曲线图

Figure 4. Fitting results of the volume versus pressure curves for NBT: (a)–(c) Volume versus pressure curves for the R3c phase obtained from neutron diffraction experiments, Cal-1, and Cal-2 calculations, respectively; (d)–(f) volume versus pressure curves for the Pnma phase obtained from neutron diffraction experiments, Cal-1, and Cal-2 calculations, respectively.

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图 5 NBT两相在3.6 GPa压力下的结构示意图和氧八面体[TiO₆]结构示意图　(a) Pnma相; (b) R3c相; (c) 氧八面体[TiO₆]示意图

Figure 5. Schematic illustrations of the two-phase NBT structure and the [TiO₆] oxygen octahedron at 3.6 GPa: (a) Pnma phase; (b) R3c phase; (c) oxygen octahedron [TiO₆] structure diagram.

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图 6 NBT氧八面体二次伸长$ \lambda $随压力P的变化曲线(虚线对应压力值P = 1.1 GPa)

Figure 6. Pressure dependence of quadratic elongation λ for oxygen octahedra in NBT (the dashed line corresponds to P = 1.1 GPa).

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表 1 NBT晶胞参数精修结果

Table 1. Unit cell parameters of NBT from rietveld refinement.

P/GPa	Rhombohedral-R3c (Z = 6)		Orthorhobmic-Pnma (Z = 4)			R_wp/%
P/GPa	a/Å	c/Å	a/Å	b/Å	c/Å	R_wp/%
0	5.51769	13.53806	—	—	—	4.96
0.1	5.51658	13.52609	—	—	—	4.30
0.2	5.51054	13.51019	—	—	—	4.35
0.8	5.49948	13.52777	Phase appears			4.78
1.8	5.48487	13.43632	5.48603	5.48620	7.74757	6.39
2.5	5.47163	13.40546	5.47582	5.46863	7.72857	6.39
3.6	5.45653	13.36911	5.46078	5.45307	7.70844	4.95
4.2	5.44308	13.33665	5.44823	5.43878	7.6879	6.04
5.5	Phase disappears		5.43504	5.42606	7.67246	6.26
6.2	—	—	5.41434	5.41443	7.64334	5.75
6.8	—	—	5.41406	5.40337	7.63613	6.52

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表 2 NBT两相体积模量信息

Table 2. The bulk modulus information of the two phases in NBT.

	B₀/GPa	B^’
R3c	89.3	1.7	Exp, this study
	108.6	6.0	Cal-1, this study
	101.7	1.3	Cal-2, this study
	166.1	4.4	Cal, [29]
	95.2	—	Exp, [30]
Pnma	110.1	1.8	Exp, this study
	171.9	4.1	Cal-1, this study
	114.3	1.1	Cal-2, this study

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Structural evolution and phase transition behavior of Na_0.5Bi_0.5TiO₃under high pressure

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