压力对PbTiO3结构和热物性质影响的第一性原理研究

doi:10.15541/jim20210612

摘要/Abstract

摘要：

PbTiO₃是一种重要的铁电功能材料, 但压力对其结构、稳定性、力学和热力学性能的影响尚不明确, 从而限制了其在电子通讯领域的应用。本研究采用基于密度泛函理论的第一性原理方法, 研究了压力下四方铁电相钛酸铅(TP-PTO)、立方顺电相钛酸铅(CP-PTO)、四方前驱体相钛酸铅(PP-PTO)结构和热物性质。研究发现, 三种结构可压缩性由大到小依次为PP-PTO>TP-PTO>CP-PTO。能带结构和态密度均表明PTO在研究的压力范围内未发生相变。PTO带隙随着压力增大逐渐降低, TP-PTO在20 GPa由间接带隙半导体转变为直接带隙半导体, 其余两相在压力下恒为直接带隙半导体。PTO在0~30 Gpa范围力学稳定, 且具有各向异性, 其综合力学性能随着压力的增加而增强, 各向异性则是先降低后升高。通过准谐德拜近似理论研究了温度和压力对PTO德拜温度、熵、热容的影响, 结果表明德拜温度随着温度上升而下降, 随着压力增大而上升, 反映出共价键强度依次为CP-PTO>TP-PTO> PP-PTO。熵和热容随着温度上升而上升, 随着压力的增大而下降。

关键词: 钛酸铅, 电子结构, 弹性力学, 第一性原理

Abstract:

PbTiO₃ (PTO) is an important ferroelectric functional material, but its structure, stability, mechanical property, and thermodynamic property under pressure is still unknown, leading to restriction in applying in the field of electronic communication. Here, first-principles calculations based on density functional theory was performed to study the structure and thermal properties of pre-perovskite phase PbTiO₃ (PP-PTO), ferroelectric tetragonal phase PbTiO₃ (TP-PTO), and paraelectric cubic phase PbTiO₃ (CP-PTO) under pressure. It is found that their compressibility in descending order is PP-PTO>TP-PTO>CP-PTO. Under considered pressure, three PTO phases have not undergone a phase transition analyzed by band structure and density of states, and their band gap gradually decreases with increasing pressure. Among them, the TP-PTO changes from an indirect to a direct band gap semiconductor at 20 GPa, while the others remain a direct band gap semiconductor. Those PTO phases are mechanically stable and anisotropy from 0 to 30 GPa. Furthermore, their comprehensive mechanical properties increase and anisotropy firstly decreases and then increases with increasing pressure. Analysis based on quasi- harmonic Debye approximation theory was performed to study the influence of temperature and pressure on Debye temperature, entropy and heat capacity. The results illuminate that Debye temperature decreases with temperature increase, nevertheless, pressure has the opposite effect, which elucidates that the order of covalent bond from strong to weak is CP-PTO>TP-PTO>PP-PTO. Entropy and heat capacity of PTO increase with rising temperature, but decrease with the increase of pressure.

Key words: PbTiO₃, electronic structure, elastic mechanics, first-principles

中图分类号:

TQ174

文志勤, 黄彬荣, 卢涛仪, 邹正光. 压力对PbTiO₃结构和热物性质影响的第一性原理研究[J]. 无机材料学报, 2022, 37(7): 787-794.

WEN Zhiqin, HUANG Binrong, LU Taoyi, ZOU Zhengguang. Pressure on the Structure and Thermal Properties of PbTiO₃: First-principle Study[J]. Journal of Inorganic Materials, 2022, 37(7): 787-794.

图/表 12

图1 (a) CP-PTO、(b) TP-PTO和(c, d) PP-PTO的晶体结构

Fig. 1 Crystal structures of (a) CP-PTO, (b) TP-PTO and (c, d) PP-PTO

表1 不受压条件下所计算的PTO晶格常数、形成焓及可行的实验和理论计算值

Table 1 Calculated lattice constant and enthalpy of formation of PTO at 0 GPa along with feasible experimental (Exp.) and theoretical calculation (Cal.) values

Phase	Species	Present	Cal.	Exp.
TP-PTO	a=b/nm	0.389	0.389^[18]	0.39^[20]
	c/nm	0.417	0.416^[18]	0.416^[20]
	∆H_f /eV	-13.45	-13.34^[21]
CP-PTO	a=b=c/nm	0.397	0.397^[19]	0.395^[20]
	∆H_f /eV	-13.38	-13.25^[22]
PP-PTO	a=b/nm	1.244	1.216^[10]	1.237^[8]
	c/nm	0.377	0.376^[10]	0.381^[8]
	∆H_f /eV	-5.85

图2 TP-PTO、CP-PTO和PP-PTO体积比(V/V0)随压力的变化曲线

Fig. 2 Variation of TP-PTO, CP-PTO and PP-PTO volume ratios (V/V0) under different pressures

表2 计算0~30 GPa下PTO的带隙值及相关文献报道值

Table 2 Calculated band gap of PTO under 0-30 GPa pressure

	TP-PTO				CP-PTO					PP-PTO
	0 GPa	10 GPa	20 GPa	30 GPa	0 GPa	10 GPa	20 GPa	30 GPa	0 GPa	10 GPa	20 GPa	30 GPa
Present /eV	1.76 ^a	1.587	1.483	1.40	1.675 ^b	1.611	1.538	1.459	2.346 ^c	2.002	1.549	1.142

图3 不同压力下TP-PTO (a)、CP-PTO (b)和PP-PTO (c)的总态密度(TDOS)

Fig. 3 Change of total density of states (TDOS) of TP-PTO (a), CP-PTO (b) and PP-PTO (c) under different pressures

表3 PTO在压力为0的情况下的弹性常数Cij(GPa)及相关的实验和理论计算值

Table 3 Elastic constant (Cij, GPa) of PTO under 0 GPa pressure as well as available experimental (Exp.) and theoretical calculation (Cal.) data

		C₁₁	C₃₃	C₄₄	C₆₆	C₁₂	C₁₃	C₁₆
TP-PTO	Present	252.9	59.1	72.6	100.7	106.1	71.1	-
	Exp.^[34]	237	60	69	144	90	70	-
	Cal.^[18]	253.9	79.8	73.3	100.9	103.8	79	-
CP-PTO	Present	279.2	-	98.2	-	118.5	-	-
	Exp.^[35]	229	-	100	-	101	-	-
	Cal.^[18]	279.9	-	98.6	-	117.9	-	-
PP-PTO	Present	86.95	209.5	50.82	42.28	25.51	49.79	2.55
	Cal.^[9]	98.8	287.8	61.4	56.8	43.2	79.8	4.9

图4 TP-PTO、CP-PTO和PP-PTO的弹性常数(Cij)随压力变化的趋势

Fig. 4 Variation of elastic constants (Cij) of TP-PTO, CP-PTO and PP-PTO with pressure

表4 不同压力下PTO的体模量B、剪切模量G、杨氏模量E、泊松比ν和各向异性Au

Table 4 Bulk modulus (B), shear modulus (G), Young's modulus (E), Poisson's ratio (ν), and anisotropy (Au) of PTO under various pressures

	p/GPa	B/GPa	G/GPa	E/GPa	ν	A^u
TP-PTO	0	87.76	56.91	140.38	0.23	4.1150
	10	211.16	101.92	263.39	0.29	0.1345
	20	274.35	125.99	327.81	0.30	0.0413
	30	315.08	139.28	364.19	0.31	0.1059
CP-PTO	0	172.02	90.86	231.76	0.28	0.0505
	10	217.28	106.87	275.45	0.29	0.0003
	20	257.15	120.49	312.65	0.30	0.0161
	30	299.13	133.24	348.06	0.31	0.0604
PP-PTO	0	63.19	44.09	107.32	0.22	0.7114
	10	121.88	60.96	156.75	0.29	0.5906
	20	173.96	70.31	185.89	0.32	0.4811
	30	219.12	77.26	207.40	0.34	0.5568

图5 TP-PTO、CP-PTO和PP-PTO的德拜温度随压力和温度的变化曲线

Fig. 5 Variation of Debye temperature of TP-PTO, CP-PTO and PP-PTO with pressure and temperature

图6 TP-PTO、CP-PTO、PP-PTO的熵(S)随压力和温度的变化曲线

Fig. 6 Entropy (S) of TP-PTO, CP-PTO and PP-PTO as a function of pressure and temperature

图7 TP-PTO、CP-PTO、PP-PTO定容热容Cv随压力和温度的变化

Fig. 7 Pressure- and temperature-dependent heat capacity at constant volume (Cv) of TP-PTO, CP-PTO and PP-PTO

图8 TP-PTO、CP-PTO、PP-PTO定压热容(Cp)随压力和温度的变化

Fig. 8 Pressure- and temperature-dependent heat capacity at constant pressure (Cp) of TP-PTO, CP-PTO and PP-PTO

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压力对PbTiO₃结构和热物性质影响的第一性原理研究

Pressure on the Structure and Thermal Properties of PbTiO₃: First-principle Study

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