First-principles calculations of local structure and electronic properties of Er<sup>3+</sup>-doped TiO<sub>2</sub>

Chen Guang-Ping; Yang Jin-Ni; Qiao Chang-Bing; Huang Lu-Jun; Yu Jing

doi:10.7498/aps.71.20221847

Abstract

Authors and contacts

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1. 引　言
2. 理论方法
3. 结果与讨论
3.1 局域结构
3.2 电子性质
4. 结　论

References

Abstract

Trivalent rare earth erbium ion (Er³⁺) doped titanium oxide (TiO₂) can possess a very wide range of applications due to its excellent optoelectronic properties, thus standing out among many rare-earth-doped luminescent crystals. However, the issues regarding local structure and electronic properties have not been finalized. To address these problems, the CALYPSO (Crystal structure AnaLYsis by Particle Swarm Optimization) method combined with the first-principles calculations is employed, and many converged structures of Er³⁺-doped TiO₂ are successfully obtained. Further structural optimization is performed by using the VASP (Vienna ab initio simulation package) software package, and we report for the first time that the lowest energy structure of Er³⁺-doped TiO₂ has the

$P\overline 4$ m2 symmetry. It can be observed that the doped Er³⁺ ions enter into the host crystal and occupy the positions of Ti⁴⁺ ions, resulting in structural distortion, which eventually leads the local Er³⁺ coordination site symmetry to reduce from D_2d into C_2v. We speculate that there are two reasons: 1) the difference in charge between Er³⁺ ions and Ti⁴⁺ ions leads to charge compensation; 2) the difference between their electron radii is obvious: the radius is 0.0881 for Er³⁺ ion and 0.0881 for Ti⁴⁺ ion. In addition, during the structural search, we also find many metastable structures that may exist at a special temperature or pressure, which play an important role in the studying of structural evolution. When the electronic band structure of the Er³⁺-doped TiO₂ system is calculated, we adopt the method of local density approximation (LDA) combined with the on-site Coulomb repulsion parameter U to accurately describe the strongly correlated system. For the specific value of U, we adopt 3.5 eV and 7.6 eV to describe the strong correlation of 3d electrons of Ti⁴⁺ ions and 4f electrons of Er³⁺ ions, respectively. According to the calculation of electronic properties, the band gap value of Er³⁺ doped TiO₂ is about 2.27 eV, which is lower than that of the host crystal (E_g = 2.40 eV). The results show that the reduction in the band gap is mainly caused by the f state of Er³⁺ ions. The doping of Er ion does reduce the band gap value, but it does not change the conductivity of the system, which have great application prospect in diode-pumped laser. These findings not only provide the data for further exploring the properties and applications of Er³⁺:TiO₂ crystals, but also present an approach to studying other rare-earth-doped crystalline materials.

Keywords:

PACS:

61.50.Ah	(Theory of crystal structure, crystal symmetry; calculations and modeling)
31.15.es	(Applications of density-functional theory (e.g., to electronic structure and stability; defect formation; dielectric properties, susceptibilities; viscoelastic coefficients; Rydberg transition frequencies))

Authors and contacts

1.
College of Intelligent Manufacturing, Sichuan University of Arts and Science, DaZhou 635000, China
2.
Industry Technology Research Institute of Intelligent Manufacturing, Sichuan University of Arts and Science, Dazhou 635000, China
3.
Institute of Atomic and Molecular Physics, Sichuan University, Chengdu 610065, China

Corresponding author: Chen Guang-Ping, chengp205@126.com

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 12075163, 12175129, 11775253, 12175027, 11875010) and the Science Foundation of Sichuan Arts and Science University, China (Grant No. 2018SCL008Y)

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1. 引　言

稀土掺杂材料一直是研究的热点, 在X射线成像、激光显示器、闪烁体、荧光粉和生物传感器等方面都存在潜在的应用^[1-4]. 近年来, 二氧化钛(TiO₂)掺杂稀土元素受到长期关注. 二氧化钛具有半导体性质、化学稳定性高、生物相容性好、毒性低、生产简单经济等特点. 它在光致发光、生物医学、光催化等领域有着广泛的应用^[5-8]. 特别是在可见光和红外领域, TiO₂晶体被认为是一个出色的发光材料: 具有较大的折射率(2.4—2.9)^[9], 透光范围广, 带隙宽(锐钛矿为3.2 eV, 金红石为3.0 eV)^[10]. 此外, 相对较低的声子能量(<700 cm^–1)可以增加辐射跃迁的机会, 使其特别适合加入一些具有光学活性的稀土离子, 如Er³⁺离子等^[11].

铒是镧系稀土元素中的一种, 其基态电子构型为[Xe]4f¹²6s², 因此铒在失去两个6s电子和一个4f电子后成为[Xe]4f¹¹的电子构型^[12]. 由于Er³⁺离子能发出1540 nm的激光, 使得Er³⁺:TiO₂体系在平面光波导、激光器和电信光纤放大器中都能成功地应用^[13,14]. 此外, 在众多稀土离子中, 只有Er³⁺和Tm³⁺等少数离子是可以获得上转换发光^[15], 当Er³⁺离子加入到主晶体材料后, 两个近红外光子被转化为一个可见光子, 并发生上转换过程^[12,16]. 稀土Er³⁺离子所产生的绿色和红色上转换发光获得持续关注, 也诞生了诸多全新的应用, 如固态激光器、医疗诊断、显示技术和光伏电池等^[17,18].

长期以来, 掺杂Er³⁺的TiO₂晶体的结构和应用一直是热门话题. 早在2007年, Jia等^[19]通过静电纺丝法在528.1, 566.6和669.3 nm处发现了Er³⁺掺杂TiO₂的²H_11/2→⁴I_15/2, ⁴S_3/2→⁴I_15/2和⁴F_9/2→⁴I_15/2的可见光谱, 发光强度随退火温度的升高而增大. Fu等^[20]和Luo等^[21]分别于2008年和2011年报道了在TiO₂晶体中Er³⁺离子成功取代具有D_2d局部对称性的Ti⁴⁺离子. 由于Ti⁴⁺和Er³⁺的离子半径和电荷数存在差异, 晶体中的Er³⁺离子局部对称性比D_2d更低^[20,21]. 此外, Luo等^[21]也证实了Er³⁺离子的C_2v点群对称是锐钛矿材料中最合理的局部对称性. 2018年, Talane等^[15]通过溶胶-凝胶法发现, 随着掺杂浓度的增大, Er³⁺掺杂TiO₂材料的晶粒尺寸发生了明显变化, 这可能是由于掺杂离子的加入产生了内部应变. 在980 nm近红外光的激发下, 当Er³⁺离子掺杂浓度为8% (摩尔百分比)时, 上转换发光强度最高. 同年, Ren等^[22]在Er³⁺:TiO₂混合晶体相中发现了一个相结, 可以实现电荷分离, 形成电子传输层, 从而制备出高效钙钛矿太阳能电池. 由此可见, Er³⁺:TiO₂晶体是一种应用广泛的材料, 对其特性的研究仍在持续开展. 2020年, Mazierski等^[23]认为观察光催化Vis响应的关键可能是在带隙区域内有Er³⁺离子产生的新的4f态. 虽然对Er³⁺掺杂TiO₂体系的研究已经很长时间了, 但对杂质引起的微观局域结构及电子性质的变化还没有发现相关的报道. 因此, 本工作通过第一性原理计算研究了掺杂Er³⁺:TiO₂晶体的局域结构和电子性质.

本文首先采用CALYPSO (crystal structure analysis by particle swarm optimization)方法结合VASP (Vienna ab initio simulation package)软件包进行结构搜索与优化^[24-29]. 成功获得了掺Er³⁺:TiO₂的基态结构. 随后, 报道了掺杂Er³⁺:TiO₂体系的能带结构、态密度(DOS)和电子局域函数(ELF). 这些结果为Er³⁺:TiO₂晶体的后续研究和应用提供了支持.

2. 理论方法

前期研究中本课题组成功地用CALYPSO方法预测了Er³⁺:TiO₂晶体的结构^[24-26]. CALYPSO是一种预测结构的方法, 之前的学者已经成功地应用该方法预测了许多体系中的新结构^[27-29]. CALYPSO主要是通过粒子群优化(particle swarm optimization, PSO)算法进行结构搜索^[24-26], 该方法主要思想是通过个体与群体之间信息共享, 从而快速地搜索整个势能空间, 最终找到全局能量最小值. CALYPSO结构搜索开始时, 晶体结构的对称性会从230个晶体空间群中随机选取, 然后根据选取的这个空间群所属的布拉菲晶格以及体积来确定其晶格参数. 在本文的研究过程中, 首先预测了常温常压下每个模拟晶胞为48个原子的演化单元结构, 并分别预测了纯TiO₂和Er³⁺:TiO₂的40代结构, 每代产生30个结构. 然后, 筛选出能量较低的结构, 使用VASP软件包^[30-32]以确保找到最稳定的结构. 使用500 eV作为该体系的截断能, 并通过适当的k点将能量聚集到每个原子小于1 meV. 对于Ti, O和Er原子, 分别采用3s²3p⁶3d²4s², 2s²2p⁴和4f¹²5s²5p⁶6s²的电子模型进行计算. 由于Er³⁺掺杂TiO₂属于强关联体系, 特别是Ti离子的d电子和Er离子的f电子使得电子之间的库仑相互作用不可忽略, 所以在结构优化及结构稳定性判断等过程中都采用了LDA+U的方法, 在计算过程中分别将Ti⁴⁺离子和Er³⁺离子的U值取为3.5 eV^[23]和7.6 eV^[33,34]. 与此同时, 还利用PHONOPY软件计算了最低能量结构的声子谱^[35]来确定其稳定性.

3. 结果与讨论

3.1 局域结构

本文首先采用CALYPSO结构搜索方法, 当Ti与O的化学配比为 16∶32时, 在常温常压下预测TiO₂的晶体结构. 结果表明, TiO₂晶体的最低能量结构具有I4₁/amd空间群, 这与实验结果一致^[20,21], 验证了CALYPSO方法的正确性. 然后根据Ti, O, Er化学配比为15∶32∶1预测了Er³⁺掺杂TiO₂的基态晶体结构. 如图1所示, 基态Er³⁺:TiO₂晶体具有 $P\overline 4$ m2空间群. 在掺杂过程中, Er³⁺离子成功取代Ti⁴⁺离子, 并形成了[ErO₆]^9-的局域多面体结构^[36]. 在Er³⁺掺杂后, 局部对称性由C_2v降低到D_2d^[21]. 我们推测有两个原因: 1) Er³⁺离子和Ti⁴⁺离子之间的电荷差异导致了电荷补偿; 2) Er³⁺离子和Ti⁴⁺离子电子半径差异明显, 分别为0.0881和0.0605 nm^[15]. 使用的杂质Er³⁺的原子百分比为6.25%, 接近目前实验中最高效的浓度^[15]. Er—O键之间两种不同的键长分别为 2.1307 和2.2605 Å. 计算了掺杂Er³⁺离子的TiO₂晶体结构的晶格常数为a = b = 7.682 Å, c = 9.798 Å, 所有原子的坐标汇总如表1所列, 为进一步的研究提供数据参考.

$图 1 通过CALYPSO结构搜索法确定纯TiO2 (a)和Er3+掺杂TiO2 (b)的晶体结构\r\nFig. 1. Crystal structures of the pure TiO2 (a) and Er3+-doped TiO2 (b) by the CALYPSO structure search method.$

图 1 通过CALYPSO结构搜索法确定纯TiO₂ (a)和Er³⁺掺杂TiO₂ (b)的晶体结构

Fig. 1. Crystal structures of the pure TiO₂ (a) and Er³⁺-doped TiO₂ (b) by the CALYPSO structure search method.

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表 1 Er³⁺:TiO₂能量最低结构中所有原子的坐标

Table 1. Coordinates of all atoms for the low-energy structure of Er³⁺:TiO₂.

Atom	x	y	z	Wyckoff site symmetry
O(1)	0.247	0.249	0.204	4j
O(2)	0.753	0.751	0.204	4k
O(3)	0.249	0.753	0.796	2g
O(4)	0.751	0.247	0.796	8l
O(6)	0.753	0.249	0.204	2g
O(7)	0.250	0.247	0.796	4k
O(8)	0.751	0.753	0.796	4j
O(11)	0.250	0.000	0.545	2f
O(19)	0.500	0.753	0.036	2e
Ti(1)	0.000	0.250	0.251	4j
Ti(2)	0.000	0.750	0.251	4k
Ti(3)	0.250	0.000	0.749	2g
Ti(4)	0.750	0.000	0.749	4h
Ti(10)	0.500	0.000	0.495	1d
Er(1)	0.500	0.500	0.500	1c

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| 显示表格

此外, 在结构搜索过程中, 还发现了许多可能存在于特定温度或压力下的亚稳态结构, 这些亚稳态结构在基态结构演化的研究中发挥了重要作用. 图2所示为3种Er³⁺掺杂TiO₂亚稳态结构. 在表2中按照能量由低到高的顺序整理了3个亚稳态结构相对应的空间群、晶格常数和原胞体积等. 可以发现, 这些亚稳态结构中仍然是Ti⁴⁺离子被Er³⁺离子所取代, 但是具体的掺杂位置却发生了变化. 有趣的是, 亚稳态结构(a)具有与基态结构相同的空间群即 $P\overline 4m2$ , 但亚稳态结构(b)和(c)具有Cmmm对称性.

$图 2 Er3+:TiO2晶体的亚稳态结构\r\nFig. 2. Coordination structures of the metastable for Er3+:TiO2.$

图 2 Er³⁺:TiO₂晶体的亚稳态结构

Fig. 2. Coordination structures of the metastable for Er³⁺:TiO₂.

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表 2 Er³⁺:TiO₂的基态结构以及亚稳态结构的晶格参数a, b, c, 原胞体积V, 相对能量∆E

Table 2. Structural parameters a, b and c, unit-cell volume, relative energies for the optimized TiO₂ and metastable Er³⁺:TiO₂

	Space group	a/Å	b/Å	c/Å	V/Å³	∆E/eV
TiO₂	I4₁/amd	7.568	7.568	9.515	545.003	—
Er³⁺:TiO₂	$P\overline 4$ m2	7.682	7.682	9.798	578.193	0
Isomer (a)	$P\overline 4$ m2	7.681	7.681	9.799	578.213	0.051
Isomer (b)	Cmmm	13.258	13.258	6.013	1051.764	0.853
Isomer (c)	Cmmm	13.261	13.261	6.009	1051.988	0.975

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| 显示表格

接下来, 将实验结果与计算结果进行比较, 以验证本工作预测晶体结构的正确性. 首先通过使用Reflex工具模拟了纯晶体和掺杂Er³⁺晶体的X射线衍射(XRD)图, 并在图3中绘制出了20°—80°范围内衍射图案. 可以看出, X射线衍射谱中峰的位置和相对强度与Talane 等^[15]和Fu 等^[20]报道的实验结果符合良好. 为了进一步验证预测结构的动力学稳定性, 分别对纯的以及掺杂的体系进行了声子谱计算, 如图4所示, 在整个布里渊区没有出现虚频, 说明本文预测的结构稳态.

$图 3 模拟的(a) TiO2和(b) Er3+掺杂TiO2的XRD图, 并与实验值进行对比\r\nFig. 3. Simulated X-ray diffraction patterns of (a) TiO2 and (b) Er3+-doped TiO2 compared with experimental data.$

图 3 模拟的(a) TiO₂和(b) Er³⁺掺杂TiO₂的XRD图, 并与实验值进行对比

Fig. 3. Simulated X-ray diffraction patterns of (a) TiO₂ and (b) Er³⁺-doped TiO₂ compared with experimental data.

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$图 4 计算的(a) TiO2和(b) Er3+掺杂TiO2的声子谱\r\nFig. 4. Calculated phonon spectra of the (a) TiO2 and (b) Er3+-doped TiO2.$

图 4 计算的(a) TiO₂和(b) Er³⁺掺杂TiO₂的声子谱

Fig. 4. Calculated phonon spectra of the (a) TiO₂ and (b) Er³⁺-doped TiO₂.

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综上所述, 通过理论计算得到Er³⁺掺杂TiO₂晶体的基态结构是动力学稳定的, 并且模拟得到的XRD谱与实验值也符合良好, 从而证明了本文方法的可靠性. 通过上述体系理论计算, 本文首次成功给出了Er³⁺:TiO₂体系的局域结构, 为进一步探索其应用提供帮助. 由此可见, 这种研究思路为将来预测其他稀土掺杂晶体材料提供一种可靠的方法, 进而指导实验的探索和应用.

3.2 电子性质

在得到Er³⁺:TiO₂晶体的基态结构后, 计算了其能带结构和态密度(DOS), 以增加对其电子性质的了解. 如图5所示, Er³⁺掺杂TiO₂体系的带隙值约为2.27 eV, 低于基质晶体的带隙值(E_g = 2.40 eV), 由此可见, Er³⁺离子的掺杂并没有改变体系的半导体特性. 通过图5(a)可以看出, TiO₂晶体的导带底部主要是由Ti⁴⁺离子的4d电子所占据. 当三价杂质铒(Er³⁺)掺杂在TiO₂晶体中, 并取代四价钛(Ti⁴⁺)的位置, 由于铒只有3个价电子, 它和相邻的O原子构成离子键时, 缺少一个价电子, 于是就形成一个空穴. 这个空穴在铒离子的作用下, 将环绕其运动. 从图5(b)也可以看出, Er³⁺离子的f电子占据了导带底附近的位置, 形成了新的杂质能带, 最终导致体系的带隙值降低, 这与Mazierski等^[23]的结果符合良好. Er³⁺离子的掺杂不仅保持了半导体TiO₂作为光催化剂和敏化剂的特性^[37], 还提高了其可见光性能, 从而有望拓宽其从紫外光到可见光的光响应范围^[38]. 值得一提的是, 本文计算的带隙值为2.27 eV, 大约是实验值3.44 eV的2/3^[12], 这是由于第一性原理方法会普遍低估带隙值的结果^[39].

$图 5 采用LDA方法计算的(a) TiO2和(b) Er3+掺杂TiO2的能带结构和态密度\r\nFig. 5. Band structures and the DOS of (a) TiO2 and (b) Er3+-doped TiO2, all calculated by the LDA method.$

图 5 采用LDA方法计算的(a) TiO₂和(b) Er³⁺掺杂TiO₂的能带结构和态密度

Fig. 5. Band structures and the DOS of (a) TiO₂ and (b) Er³⁺-doped TiO₂, all calculated by the LDA method.

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此外, 本文计算了电子局域函数(ELF), 将Er³⁺:TiO₂晶体的化学键特性转化为直观图像^[40,41]. ELF值越大, 表示电子分布越为集中^[42]. 图6为Er³⁺:TiO₂与(010)平面的ELF图, ELF值在0—0.85之间. 在O和Er原子之间ELF的值接近0, 表明Er—O之间形成的是离子键.

$图 6 计算得到的Er3+:TiO2电子局域函数　(a)基态结构; (b) (010)平面\r\nFig. 6. Electron localized function of the Er3+:TiO2: (a) Ground-state structure; (b) (010) plane.$

图 6 计算得到的Er³⁺:TiO₂电子局域函数　(a)基态结构; (b) (010)平面

Fig. 6. Electron localized function of the Er³⁺:TiO₂: (a) Ground-state structure; (b) (010) plane.

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4. 结　论

综上所述, 结合第一性原理计算, 本工作首次采用CALYPSO方法报道了Er³⁺掺杂TiO₂的基态结构. 结果表明: Er³⁺:TiO₂的基态结构具有特殊的 $P\overline 4$ m2空间群结构, 它相对于基质晶体TiO₂的对称性I4₁/amd有所降低, 但都属于四方晶系. 通过观察局部结构的演化可以看到, 杂质Er³⁺离子取代了主晶体中的Ti⁴⁺离子, 形成了[ErO₆]^9–多面体局部结构. 随后, 通过LDA + U方法计算了Er³⁺:TiO₂晶体的能带结构和态密度, 并且计算得到掺杂体系的带隙值为2.27 eV, 它仍然保持了基质晶体的半导体性质, 从而在光伏电池以及半导体激光器等领域具有广泛地应用. 我们希望通过本计算研究为后续探索Er³⁺掺杂TiO₂的性能和应用提供帮助, 并为进一步寻找其他稀土掺杂发光晶体材料提供可靠的途径.

References

[1]	钟淑琳, 仇家豪, 罗文崴, 吴木生 2021 物理学报 70 158203 Google Scholar Zhong S L, Qiu J H, Luo W W, Wu M S 2021 Acta Phys. Sin. 70 158203 Google Scholar
[2]	孟勇军, 李洪, 唐建伟, 陈学文 2022 物理学报 71 027801 Google Scholar Meng Y J, Li H, Tang J W, Chen X W 2022 Acta Phys. Sin. 71 027801 Google Scholar
[3]	Wu B, Zhao L, Wang Y, Dong H, Yu H 2019 RSC Adv. 9 42228 Google Scholar
[4]	Menezes L D S, Araújo C B D 2015 J. Braz. Chem. Soc. 26 2405
[5]	Stengl V, Bakardjieva S, Murafa N 2009 Mater. Chem. Phys. 114 217 Google Scholar
[6]	Hassan M S, Amna T, Yang O B, Kim H C, Khil M S 2012 Ceram. Int. 38 5925 Google Scholar
[7]	Borlaf M, Colomer M T, Moreno R, Ortiz A L 2014 J. Eur. Ceram. Soc. 34 4457 Google Scholar
[8]	Bao R, Li R, Chen C, Wu H, Xia J, Long C, Li H 2019 J. Phys. Chem. Solid. 126 78 Google Scholar
[9]	Li J G, Wang X H, Kamiyama H, Ishigaki T, Sekiguchi T 2006 Thin Solid Films 506 292
[10]	Agrios A G, Pochat P 2005 J. Appl. Electrochem. 35 655 Google Scholar
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[12]	Talane T E 2018 M. S. Thesis (Gauteng Province: University of South Africa)
[13]	Pablo L I, Laeticia P, Jonathan M, Davide J, Nadia G B, Diego P, Sonia F, Chiara N, Fabrizio G, Daniel M 2017 J. Non-Cryst. Solids 460 161 Google Scholar
[14]	Mignotte C 2004 Appl. Surf. Sci. 226 355 Google Scholar
[15]	Talane T E, Mbule P S, Noto L L, Shingange K, Mhlongo G H, Mothudi B M, Dhlamini M S 2018 Mater. Res. Bull. 108 234 Google Scholar
[16]	Wild J D, Meijerink A, Rath J K, van Sark W G J H M, Schropp R E I 2011 Energy Environ. Sci. 4 4835 Google Scholar
[17]	Pablo L I, Diego P, Nadia G B, Davide J, Giovanni B, Laeticia P, Daniel M 2018 Nanomaterials 8 20 Google Scholar
[18]	van den Hoven G N, Koper R J I M, Polman A, Dam C V, Uffelen J W M V, Smit M K 1996 Appl. Phys. Lett. 68 1886 Google Scholar
[19]	Jia C W, Zhao J G, Duan H G, Xie E Q 2007 Mater. Lett. 61 4389 Google Scholar
[20]	Fu C Y, Liao J S, Luo W Q, Li R F, Chen X Y 2008 Opt. Lett. 33 953 Google Scholar
[21]	Luo W Q, Fu C Y, Li R F, Liu Y S, Zhu H M, Chen X Y 2011 Small 7 3046 Google Scholar
[22]	Ren Z, Wu J, Wang N, Li X 2018 J. Mater. Chem. A 6 15348 Google Scholar
[23]	Mazierski P, Mikolajczyk A, Grzybd T, Caicedo P N A, Wei Z, Kowalska E, Henry P P, Adriana Z M, Nadolna J 2020 Appl. Surf. Sci. 527 146815 Google Scholar
[24]	Wang Y C, Lv J, Zhu L, Ma Y M 2012 Comput. Phys. Commun. 183 2063 Google Scholar
[25]	Wang Y C, Lv J, Zhu L, Lu S H, Yin K T, Li Q, Wang H, Zhang L J, Ma Y M 2015 J. Phys. Condens. Matter. 27 203203 Google Scholar
[26]	Wang H, Wang Y C, Lv J, Li Q, Zhang L J, Ma Y M 2016 Comput. Mater. Sci. 112 406 Google Scholar
[27]	Wang Y C, Lv J, Zhu L, Ma Y M 2010 Phys. Rev. B 82 094116 Google Scholar
[28]	Gao B, Gao P, Lu S, Lv J, Wang Y, Ma Y 2019 Sci. Bull. 64 301 Google Scholar
[29]	Wang Y, Miao M, Lv J, Zhu L, Yin K, Liu H, Ma Y 2012 J. Chem. Phys. 137 224108 Google Scholar
[30]	Hafner J 2008 J. Comput. Chem. 29 2044 Google Scholar
[31]	Kresse G, Furthmüller J 1996 Phys. Rev. B 54 11169 Google Scholar
[32]	Perdew J P, Burke K, Ernzerhof M 1996 Phys. Rev. Lett. 77 3865 Google Scholar
[33]	Sanna S, Schmidt W G, Frauenheim T, Gerstmann U 2009 Phys. Rev. B 80 104120 Google Scholar
[34]	Xiao Y, Ju M, Yuan H K, Yeung Y Y 2021 J. Phys. Chem. C 125 18015 Google Scholar
[35]	Togo A, Tanaka I 2015 Scr. Mater. 108 1 Google Scholar
[36]	Phenicie C M, Stevenson P, Welinski S, Rose B C, Asfaw A T, Cava R J, Lyon S A, de Leon N P, Thompson J D 2019 Nano Lett. 19 8928 Google Scholar
[37]	Mills A, Hunte S L 1997 J. Photochem. Photobiol. A 108 1 Google Scholar
[38]	Yang J, Hu Y, Jin C, Zhuge L, Wu X 2017 Thin Solid Films 637 9 Google Scholar
[39]	Pan L, Xiao Y, Kuang X Y, Ju M 2021 Mater. Chem. Phys. 257 123824 Google Scholar
[40]	Savin A, Nesper R, Wengert S, Fässler T F 1997 Angew. Chem. Int. Ed. Engl. 36 1808 Google Scholar
[41]	Lu T, Chen F 2011 Acta Phys. Chim. Sin. 27 2786 Google Scholar
[42]	Fuentealba P, Chamorro E, Santos J C 2007 Theoretical Aspects of Chemical Reactivity 19 57

图 1 通过CALYPSO结构搜索法确定纯TiO₂ (a)和Er³⁺掺杂TiO₂ (b)的晶体结构

Figure 1. Crystal structures of the pure TiO₂ (a) and Er³⁺-doped TiO₂ (b) by the CALYPSO structure search method.

DownLoad: Full-Size Img PowerPoint

图 2 Er³⁺:TiO₂晶体的亚稳态结构

Figure 2. Coordination structures of the metastable for Er³⁺:TiO₂.

DownLoad: Full-Size Img PowerPoint

图 3 模拟的(a) TiO₂和(b) Er³⁺掺杂TiO₂的XRD图, 并与实验值进行对比

Figure 3. Simulated X-ray diffraction patterns of (a) TiO₂ and (b) Er³⁺-doped TiO₂ compared with experimental data.

DownLoad: Full-Size Img PowerPoint

图 4 计算的(a) TiO₂和(b) Er³⁺掺杂TiO₂的声子谱

Figure 4. Calculated phonon spectra of the (a) TiO₂ and (b) Er³⁺-doped TiO₂.

DownLoad: Full-Size Img PowerPoint

图 5 采用LDA方法计算的(a) TiO₂和(b) Er³⁺掺杂TiO₂的能带结构和态密度

Figure 5. Band structures and the DOS of (a) TiO₂ and (b) Er³⁺-doped TiO₂, all calculated by the LDA method.

DownLoad: Full-Size Img PowerPoint

图 6 计算得到的Er³⁺:TiO₂电子局域函数　(a)基态结构; (b) (010)平面

Figure 6. Electron localized function of the Er³⁺:TiO₂: (a) Ground-state structure; (b) (010) plane.

DownLoad: Full-Size Img PowerPoint

表 1 Er³⁺:TiO₂能量最低结构中所有原子的坐标

Table 1. Coordinates of all atoms for the low-energy structure of Er³⁺:TiO₂.

Atom	x	y	z	Wyckoff site symmetry
O(1)	0.247	0.249	0.204	4j
O(2)	0.753	0.751	0.204	4k
O(3)	0.249	0.753	0.796	2g
O(4)	0.751	0.247	0.796	8l
O(6)	0.753	0.249	0.204	2g
O(7)	0.250	0.247	0.796	4k
O(8)	0.751	0.753	0.796	4j
O(11)	0.250	0.000	0.545	2f
O(19)	0.500	0.753	0.036	2e
Ti(1)	0.000	0.250	0.251	4j
Ti(2)	0.000	0.750	0.251	4k
Ti(3)	0.250	0.000	0.749	2g
Ti(4)	0.750	0.000	0.749	4h
Ti(10)	0.500	0.000	0.495	1d
Er(1)	0.500	0.500	0.500	1c

DownLoad: CSV

表 2 Er³⁺:TiO₂的基态结构以及亚稳态结构的晶格参数a, b, c, 原胞体积V, 相对能量∆E

Table 2. Structural parameters a, b and c, unit-cell volume, relative energies for the optimized TiO₂ and metastable Er³⁺:TiO₂

	Space group	a/Å	b/Å	c/Å	V/Å³	∆E/eV
TiO₂	I4₁/amd	7.568	7.568	9.515	545.003	—
Er³⁺:TiO₂	$P\overline 4$ m2	7.682	7.682	9.798	578.193	0
Isomer (a)	$P\overline 4$ m2	7.681	7.681	9.799	578.213	0.051
Isomer (b)	Cmmm	13.258	13.258	6.013	1051.764	0.853
Isomer (c)	Cmmm	13.261	13.261	6.009	1051.988	0.975

DownLoad: CSV

[1]	钟淑琳, 仇家豪, 罗文崴, 吴木生 2021 物理学报 70 158203 Google Scholar Zhong S L, Qiu J H, Luo W W, Wu M S 2021 Acta Phys. Sin. 70 158203 Google Scholar
[2]	孟勇军, 李洪, 唐建伟, 陈学文 2022 物理学报 71 027801 Google Scholar Meng Y J, Li H, Tang J W, Chen X W 2022 Acta Phys. Sin. 71 027801 Google Scholar
[3]	Wu B, Zhao L, Wang Y, Dong H, Yu H 2019 RSC Adv. 9 42228 Google Scholar
[4]	Menezes L D S, Araújo C B D 2015 J. Braz. Chem. Soc. 26 2405
[5]	Stengl V, Bakardjieva S, Murafa N 2009 Mater. Chem. Phys. 114 217 Google Scholar
[6]	Hassan M S, Amna T, Yang O B, Kim H C, Khil M S 2012 Ceram. Int. 38 5925 Google Scholar
[7]	Borlaf M, Colomer M T, Moreno R, Ortiz A L 2014 J. Eur. Ceram. Soc. 34 4457 Google Scholar
[8]	Bao R, Li R, Chen C, Wu H, Xia J, Long C, Li H 2019 J. Phys. Chem. Solid. 126 78 Google Scholar
[9]	Li J G, Wang X H, Kamiyama H, Ishigaki T, Sekiguchi T 2006 Thin Solid Films 506 292
[10]	Agrios A G, Pochat P 2005 J. Appl. Electrochem. 35 655 Google Scholar
[11]	Camps I, Borlaf M, Toudert J, Andres A D, Colomer M T, Moreno R, Serna R 2018 J. Alloys Compd. 735 2267 Google Scholar
[12]	Talane T E 2018 M. S. Thesis (Gauteng Province: University of South Africa)
[13]	Pablo L I, Laeticia P, Jonathan M, Davide J, Nadia G B, Diego P, Sonia F, Chiara N, Fabrizio G, Daniel M 2017 J. Non-Cryst. Solids 460 161 Google Scholar
[14]	Mignotte C 2004 Appl. Surf. Sci. 226 355 Google Scholar
[15]	Talane T E, Mbule P S, Noto L L, Shingange K, Mhlongo G H, Mothudi B M, Dhlamini M S 2018 Mater. Res. Bull. 108 234 Google Scholar
[16]	Wild J D, Meijerink A, Rath J K, van Sark W G J H M, Schropp R E I 2011 Energy Environ. Sci. 4 4835 Google Scholar
[17]	Pablo L I, Diego P, Nadia G B, Davide J, Giovanni B, Laeticia P, Daniel M 2018 Nanomaterials 8 20 Google Scholar
[18]	van den Hoven G N, Koper R J I M, Polman A, Dam C V, Uffelen J W M V, Smit M K 1996 Appl. Phys. Lett. 68 1886 Google Scholar
[19]	Jia C W, Zhao J G, Duan H G, Xie E Q 2007 Mater. Lett. 61 4389 Google Scholar
[20]	Fu C Y, Liao J S, Luo W Q, Li R F, Chen X Y 2008 Opt. Lett. 33 953 Google Scholar
[21]	Luo W Q, Fu C Y, Li R F, Liu Y S, Zhu H M, Chen X Y 2011 Small 7 3046 Google Scholar
[22]	Ren Z, Wu J, Wang N, Li X 2018 J. Mater. Chem. A 6 15348 Google Scholar
[23]	Mazierski P, Mikolajczyk A, Grzybd T, Caicedo P N A, Wei Z, Kowalska E, Henry P P, Adriana Z M, Nadolna J 2020 Appl. Surf. Sci. 527 146815 Google Scholar
[24]	Wang Y C, Lv J, Zhu L, Ma Y M 2012 Comput. Phys. Commun. 183 2063 Google Scholar
[25]	Wang Y C, Lv J, Zhu L, Lu S H, Yin K T, Li Q, Wang H, Zhang L J, Ma Y M 2015 J. Phys. Condens. Matter. 27 203203 Google Scholar
[26]	Wang H, Wang Y C, Lv J, Li Q, Zhang L J, Ma Y M 2016 Comput. Mater. Sci. 112 406 Google Scholar
[27]	Wang Y C, Lv J, Zhu L, Ma Y M 2010 Phys. Rev. B 82 094116 Google Scholar
[28]	Gao B, Gao P, Lu S, Lv J, Wang Y, Ma Y 2019 Sci. Bull. 64 301 Google Scholar
[29]	Wang Y, Miao M, Lv J, Zhu L, Yin K, Liu H, Ma Y 2012 J. Chem. Phys. 137 224108 Google Scholar
[30]	Hafner J 2008 J. Comput. Chem. 29 2044 Google Scholar
[31]	Kresse G, Furthmüller J 1996 Phys. Rev. B 54 11169 Google Scholar
[32]	Perdew J P, Burke K, Ernzerhof M 1996 Phys. Rev. Lett. 77 3865 Google Scholar
[33]	Sanna S, Schmidt W G, Frauenheim T, Gerstmann U 2009 Phys. Rev. B 80 104120 Google Scholar
[34]	Xiao Y, Ju M, Yuan H K, Yeung Y Y 2021 J. Phys. Chem. C 125 18015 Google Scholar
[35]	Togo A, Tanaka I 2015 Scr. Mater. 108 1 Google Scholar
[36]	Phenicie C M, Stevenson P, Welinski S, Rose B C, Asfaw A T, Cava R J, Lyon S A, de Leon N P, Thompson J D 2019 Nano Lett. 19 8928 Google Scholar
[37]	Mills A, Hunte S L 1997 J. Photochem. Photobiol. A 108 1 Google Scholar
[38]	Yang J, Hu Y, Jin C, Zhuge L, Wu X 2017 Thin Solid Films 637 9 Google Scholar
[39]	Pan L, Xiao Y, Kuang X Y, Ju M 2021 Mater. Chem. Phys. 257 123824 Google Scholar
[40]	Savin A, Nesper R, Wengert S, Fässler T F 1997 Angew. Chem. Int. Ed. Engl. 36 1808 Google Scholar
[41]	Lu T, Chen F 2011 Acta Phys. Chim. Sin. 27 2786 Google Scholar
[42]	Fuentealba P, Chamorro E, Santos J C 2007 Theoretical Aspects of Chemical Reactivity 19 57

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