钨酸铅晶体电子结构和光学性质的研究

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目录 ............................................................................................................................. I

摘要 ..............................................................................................................................V

ABSTRACT .................................................................................................................VII

第一章引言 .................................................................................................................1

§1.1 应用背景.........................................................................................................1

§1.2 PbWO4晶体结构 .............................................................................................2

§1.2.1 完整的钨酸铅晶体结构.......................................................................2

§1.2.2 钨酸铅晶体的类白钨矿结构...............................................................4

§1.3 PbWO4晶体的基本特性 .................................................................................6

§1.3.1 PbWO4晶体的基本物理化学性质 .......................................................6

§1.3.2 PbWO4晶体的光谱特征 .......................................................................6

§1.4 PbWO4晶体的缺陷研究 .................................................................................9

§1.5 PbWO4晶体的辐照诱导光谱 .......................................................................13

§1.6 PbWO4晶体电子结构的模拟计算 ...............................................................15

§1.6.1 完整的钨酸铅晶体的电子结构计算.................................................15

§1.6.2 含缺陷的钨酸铅晶体的电子结构计算.............................................16

§1.7 光学性质的模拟计算....................................................................................17

§1.8 本章小结.......................................................................................................17

第二章密度泛函理论及其应用 .................................................................................. 20

§2.1 Thomas-Fermi 模型 .......................................................................................20

§2.2 Hohenberg-Kohn 定理 ...................................................................................21

§2.3 Kohn-Sham 方法........................................................................................... 22

§2.4 交换相关能泛函............................................................................................24

§2.4.1 交换相关能泛函简介.........................................................................24

§2.5 离散变分法基本原理...................................................................................27

§2.5.1 解Kohn-Sham 方程........................................................................... 27

§2.5.2 势函数.................................................................................................29

§2.5.3 基组.....................................................................................................31

§2.5.4 数值积分..............................................................................................33

§2.5.5 状态密度.............................................................................................35

§2.6 相对论效应...................................................................................................36

§2.7 线性缀加平面波方法...................................................................................38

§2.7.1 Mufin-tin 势...................................................................................... 38

§2.7.2 缀加平面波.........................................................................................39

§2.7.3 线性缀加平面波方法.........................................................................40

§2.7.4 FLAPW 方法 .......................................................................................42

§2.8 量子力学方法光学性质计算.......................................................................43

§2.8.1 相互作用哈密顿.................................................................................43

§2.8.2 跃迁几率.............................................................................................44

§2.8.3 直接跃迁吸收谱的量子力学处理......................................................45

第三章钨酸铅晶体诱导色心光谱实验...................................................................... 48

§3.1 钨酸铅晶体 350nm 吸收带的结构 ............................................................. 49

§3.1.1 生成态钨酸铅晶体偏振吸收谱和退火处理后的吸收谱..................49

§3.2 钨酸铅晶体辐照诱导色心转型实验...........................................................51

§3.2.1 实验和实验结果.................................................................................51

§3.3 辐照着色后的偏振吸收光谱.......................................................................52

§3.3.1 实验及实验结果.................................................................................52

第四章完整的钨酸铅晶体电子结构与光学性质的模拟计算 .................................. 54

§4.1 白钨矿结构的钨酸铅晶体电子结构的计算................................................54

§4.1.1 计算模型和计算方法.........................................................................54

§4.1.2 电子结构的计算..................................................................................56

§4.1.3 光学性质的模拟计算.........................................................................57

§4.1.4 本节小结.............................................................................................60

§4.2 斜钨矿结构的钨酸铅晶体电子结构及光学性质的模拟计算...................60

§4.2.1 电子结构的计算.................................................................................61

§4.2.2 光学性质的模拟计算.........................................................................63

§4.2.3 本节小结.............................................................................................65

第五章含缺陷的钨酸铅晶体的电子结构和光学性质研究...................................... 66

§5.1 含铅空位的钨酸铅晶体的电子结构和光学性质的模拟计算...................66

§5.1.1 晶格驰豫.............................................................................................66

§5.1.2 计算结果与讨论.................................................................................67

§5.1.3 电子结构的计算.................................................................................68

III

§5.1.4 光学性质的模拟计算.........................................................................70

§5.2 含氧空位的钨酸铅的电子结构和光学性质的模拟计算...........................74

§5.2.1 晶格驰豫.............................................................................................74

§5.2.2 电子结构的计算.................................................................................76

§5.2.3 光学性质的模拟计算.........................................................................77

§5.3 含铅氧空位对的钨酸铅晶体的电子结构和光学性质的模拟计算...........80

§5. 3.1 晶格驰豫............................................................................................80

§5. 3.2 电子结构的计算................................................................................82

§5. 3.3 光学性质的模拟计算........................................................................83

§5. 4 吸收光谱的偏振特性与实验结果的比较..................................................85

§5. 5 本章小结......................................................................................................86

第六章类白钨矿结构 Pb7.5W8O32 的钨酸铅晶体电子结构研究 ..............................88

§6.1团簇的选取及计算方法和参数的选定.......................................................88

§6. 1.1 计算所用团簇的选取........................................................................88

§6. 1.2 方法概述.............................................................................................90

§6. 2 完整的类白钨矿结构及其含铅空位结构的钨酸铅晶体的结构优化......91

§6. 2 .1 Pb7.5W8O32 结构的优化.....................................................................91

§6. 3 电子结构计算..............................................................................................92

§6. 3.1 x 射线测得的 Pb7.5W8O32 结构镶嵌到白钨矿结构中电子结构的分析

...........................................................................................................................92

§6. 3.2 中子衍射测得的 Pb7.5W8O32 结构镶嵌到白钨矿结构中电子结构的

分析...................................................................................................................95

§6. 4 本章小结......................................................................................................97

第七章钨酸铅晶体吸收带的结构起因及其缺陷模型 .............................................. 98

§7. 1 与铅空位有关的色心模型..........................................................................99

§7. 1.1 优化后的结构....................................................................................99

§7. 1.2 与铅空位相关的吸收带及电子结构..............................................100

§7. 1.3 缺陷模型..........................................................................................102

§7. 2 与氧空位有关的色心模型........................................................................105

§7. 2.1 优化后的结构..................................................................................105

§7. 2.2 与氧空位相关的吸收带及电子结构分析......................................106

§7. 2.3 缺陷模型..........................................................................................107

§7. 3 讨论............................................................................................................107

第八章结论和展望.....................................................................................................110

§8. 1 实验结果....................................................................................................110

§8. 2 模拟计算结果............................................................................................111

§8. 3 色心模型....................................................................................................112

§8. 4 存在的问题和展望....................................................................................112

参考文献 .......................................................................................................................114

在读期间公开发表的论文和承担科研项目及取得的成果...................................... 121

致谢 .........................................................................................................................124

作者简历 .......................................................................................................................125

摘要

PbWO4晶体具有高密度、辐射长度短和价格便宜等优点，而且其发光带中的

420nm 发光带衰减时间短，而被选为本世纪初在欧洲核子中心（CERN）建设的大

型强子对撞机 LHC 上CMS 谱仪的电磁能量器探测材料。由于它在室温下的发光

效率很低、发光性能和抗辐照硬度都与样品有关，因此提高钨酸铅晶体的光产额

和抗辐照硬度成为国内外研究的热点。钨酸铅晶体在高能辐照下很容易着色并出

现330nm、360nm、420nm 以及 500-700nm 吸收带，其中 420nm 吸收带与钨酸铅

晶体被选作闪烁材料的快速分支的 420nm 蓝发光部分重叠，这大大地降低了钨酸

铅晶体的光产额。因此研究钨酸铅晶体吸收带的结构起因就成为关键性问题。钨

酸铅晶体是一种典型的非化学计量晶体，存在着大量的铅空位和氧空位，仔细研

究钨酸铅晶体中这些本征缺陷可能产生的吸收带并建立对应的色心模型可为提高

钨酸铅晶体的辐照硬度提供理论依据，具有深远的指导意义。本文针对这些问题

展开研究。

本文主要工作分三部分，第一部分为与硅酸盐研究所合作完成的实验（第三

章），该部分为理论计算和缺陷模型的设计打下了良好的基础；第二部分为利用密

度泛函理论模拟计算了完整的和含缺陷的钨酸铅晶体的电子结构以及光学性质以

及类白钨矿结构的电子结构（第四，五，六章）；第三部分为钨酸铅晶体中缺陷模

型的研究（第七章）。

第一部分与硅酸盐研究所合作，通过对钨酸铅晶体不同温度条件下的退火处

理、340nm 单色光辐照、411nm 单色光的再辐照钨酸铅晶体吸收带变化情况以及

高能辐照赋色后钨酸铅晶体的偏振吸收光谱的研究得到钨酸铅晶体各个吸收带的

热稳定性和偏振特性以及它们之间相互转化的关系，并首次提出钨酸铅晶体中

350nm 吸收带是一个复合带，它由峰值位于 330nm 和360nm 两个吸收带复合而成。

这些实验结果为理论模拟计算和色心模型设计的研究提供了实验基础。

第二部分根据密度泛函理论以及光学参数与固体电子结构之间的关系模拟计

算了钨酸铅晶体的电子结构以及光学常数的色散关系，分析了电子结构与基本光

学参数之间的关系以及它们的偏振特性。通过对完整的和含空位的钨酸铅晶体计

算结果的比较得到以下结果：（1）钨酸铅晶体中 360nm 和420nm 吸收带与铅空位

的存在以及氧空位的存在都有关；（2）而 330nm 和500-700nm 吸收带与铅空位的

存在有关；（3）钨酸铅晶体中铅氧空位对的存在不会引起可见光和近紫外区域的

附加吸收。计算结果很好地解释了钨酸铅晶体吸收带的结构起因。计算结果的偏

振特性与实验结果吻合很好。用类白钨矿结构的团簇镶嵌到不同结构的微晶中来

模拟一个样品中出现不同的结构相的情形，模拟计算结果表明团簇镶嵌到不同的

环境中其电子结构发生明显的变化，预示着其物理性质可能会发生变化，这个计

算结果部分地解释了钨酸铅晶体结构敏感的原因。

第三部分根据钨酸铅晶体吸收带的实验结果以及计算得到的空位周围的晶格

结构以及电子态密度分布，建立了铅空位和氧空位周围可能存在的缺陷模型以及

它们对应的吸收带，铅空位的两价负电性是通过铅空位周围的氧共同抓获两个空

穴来维持局部电中性的，即铅空位周围形成的色心模型是[O23--VPb2--O23-]，不同的

氧离子抓获空穴方式形成不同的色心，对应不同的吸收带，根据吸收带的性质，

提出了各个吸收带对应的色心模型。氧空位抓获一个电子形成 F+心，抓获两个电

子形成 F心，氧空位周围的配位场的对称性降低可能使 F+心和 F心呈现偏振特性。

最后，根据色心模型分析了 340nm 和411nm 单色光辐照晶体引起吸收带变化的动

力学机制。

关键词：钨酸铅晶体电子结构光学性质色心密度泛函理论模拟计算

VII

ABSTRACT

Since PbWO4(PWO) crystal is of high density, short radiation length, fast decay

and cheap price, it has been chosen as a scintillator for detectors at the large collider in

CERN. However, the light output of PWO is low in room temperature and its irradiation

hardness is variable with different samples. To increase light output and radiation

hardness has attracted special interests. The PWO crystal can be easily colored by UV

irradiation. The UV irradiated crystal exhibit 4 absorption bands peaking at 350nm,

420nm, 550nm and 680nm, respectively. The 420nm absorption band overlapping with

the useful 420nm blue-luminescence band degrades the light yield significantly. Thus it

becomes urgent to study the origin of the absorption bands to enhance the scientillation

properties of the crystal. The PWO is a typical non-stoichiometric crystal. There are

lead vacancies VPb2- and oxygen vacancies VO2+ existed in the PWO crystal. It is very

important to study the physical properties of PWO with intrinsic defects and design the

color center models.

The thesis contains three parts, part I illustrates the experimental results (chapter 3), part

II illustrates the computer simulations of electronic structures and optical properties for

both the perfect PWO crystal and the PWO crystal containing intrinsic point defects

(chapter 4, 5,6), part III illustrates the origins of the absorption bands and the color

center models (chapter 7).

In part I of the thesis, I will detail the experiments performed together with the

Laboratory of Functional Inorganic Materials. (1) The absorption spectra were measured

on the sample with its crystal c-axis parallel to its surface. The measurements were

performed under the irradiation of the polarized light with its electric vector Ebeing

parallel/perpendicular to the c-axis alternatively. Subtracting the polarized light

absorption spectrum for E//c by that for Ec, the polarized light difference spectrum is

obtained. The polarized light difference spectrum indicates that the 350nm band has two

peaks and can be decomposed into two bands peaking at 330nm and 360nm. In order to

determine the detailed structure of the 350nm band, annealing experiments in air

condition of the as-grown crystal at different temperatures were performed. Difference

spectra of the annealed crystal have been obtained by subtracting the absorption spectra

VIII

of the crystal annealed at different annealing temperatures by that one of the as-grown

crystal. We found that the annealing properties of the 330nm band and the 360nm band

are obviously different. This results into the conclusion that the 350nm band is a

composed band and can be decomposed into two bands peaking at 360nm and 330nm,

respectively. (2) The 340nm monochromatic light-irradiated crystal exhibits a strong

band peaking at 420nm and a broad band in the range of 500-700nm almost in pairs

along with the reduction of the 350nm band. It is found that the 420nm and 500-700nm

bands can be reduced, with a re-irradiation of the 411nm monochromatic light, while the

350nm band is strengthened simultaneously. (3) Optical absorption spectra of polarized

light of the sample with the c-axis parallel to its surface irradiated by UV-irradiation are

measured. The spectra occur a 350nm weak band, a 400 nm strong band and a wide

band at 500-700nm. The experimental results show that the intensities of absorption

bands of polarized light with E

⊥

care larger than those with E//c in the region from

500nm to 700nm. However, the 350nm absorption band occurs weak anisotropy and the

intensity of absorption bands of polarized light with E//c. is a litte larger than that with

⊥

c, 420nm absorption band exhibits isotropy.

In part II of the thesis, the electronic structures and the optical properties for the perfect

PbWO4(PWO) crystal and the three types of PWO crystals, containing VPb2-, VO2+ and a

pair of VPb2--VO2+ have been calculated using LAPW + lo method with the lattice

structure optimized. The calculated results indicate that the optical properties of the

PWO crystal occur anisotropy, corresponding to lattice structure geometry of the PWO

crystal. The calculated absorption spectra indicate that the perfect PWO crystal does not

occur absorption band in the visible and near-ultraviolet region; The absorption spectra

of the PWO crystal containing VPb2- occur five bands peaking at 1.72eV(720nm),

2.16eV(570nm), 3.01eV(410nm), 3.36eV(365nm) and 3.70eV(335nm), respectively;

The absorption spectrum of the PWO crystal containing VO2+ occur two bands peaking

at 370nm and 420nm, respectively; The PWO crystal containing a pair of VPb2--VO2+

does not occur absorption band in the visible and near-ultraviolet region. In summary, it

reveals that the 350nm and 420nm absorption bands are related to the existence of both

VPb2- and VO2+ in the PWO crystal and the 550nm and 680nm absorption bands are

related to the existence of the VPb2- in the PWO crystal, but the existence of the pair of

VPb2--VO2+ has no visible effects on the optical properties. The scheelite like structure

clusters are embedded in different miro-crystals to simulate the case that there are two

or more structures in one sample. The electronic structures have been obtained. The

calculated results indicated that the environment embedded in has obvious effects on the

electronic structures of the cluster. It means that the properties of PWO crystal are

sensitive to its structure.

In part III of the thesis, the color center models and their corresponding absorption

spectra have been proposed, by analysing the experimental results according to the

lattice structures and the electronic structures around the vacancies. The negative

divalent VPb2- should trap two holes to maintain the local neutrality. The possible way of

the formation of the hole centers is one trapped hole shared by two O2- ions nearest to

VPb2and other one shared by another two O2- ions nearest to VPb2forming

[O23--VPb2+-O23-]. The different ways of the holes shared by different O2- ions should

form different color centers corresponding to different absorption bands. The color

center models around VPb2have been proposed. The oxygen vacancy traps an electron

forming F+color center and traps two electrons forming F color center. The F+color

center and F color centers ehxibit optical polarization. Finally, the intrinsic dynamic

process of transformation of absorption bands irradiated by 340nm and 411nm

monochromatic light re-irradiated are discussed in detail.

Key Words: PbWO4crystal, electronic structures, optical properties,

color centers, density functional theory, simulation.

第一章引言

§1.1 应用背景

为了探测构成物质的基本粒子，欧洲核子中心（CERN）将在本世纪初建成

世界上最大的强子对撞机 LHC (Large Hadron Collider)，这是一台超高能量，高流

强的质子-质子对撞机。其核心之一是建设一台高精度的电磁量能器，要求其具有

强的抗幅照能力(预计辐照剂量可达到 l0 Mrad 和1014 中子／cm2)和高的分辨率(相

互作用分辨时间<20ns)[1]。这样严酷的运行环境对用于构造其电磁量能器(ECAI)

的闪烁晶体提出了异常高的要求：(1)密度大于 6g/cm2；(2)辐照长度小于 2cm；

(3)50ns 以下的闪烁衰减成分不低于 80％：(4)光产额不低于 8pe/MeV；(5)10Mrad

的γ射线辐照下光产额的减少量在 15％以内。

通过对几种具有快速发光分量闪烁晶体的系统考察(BaF2，CeF3，CsI 和

PbWO4)，由于 PbWO4晶体具有高密度(ρ=8.2g/cm3)，成本较低及 ns 级快速发光

分量等优势，而成为新一代电磁量能器用闪烁晶体的首要候选者[2,3,4]。因此，近

几年来 PbWO4晶体成为了研究热点。

PbWO4晶体受激发射光谱主要由峰值位于 420nm 的蓝光带和峰值位于

480~510nm 的绿光带两部分组成。PbWO4闪烁晶体的快速发光部分主要源于蓝色

发射中心。然而，由于 PbWO4是一种非化学计量晶体，其生长后具有的光吸收谱

性能取决于晶体的生长条件、材料的纯度及熔体中化学计量的变化量，因此，不

同晶体之间的相差较大。典型的 PbWO4晶体生长后呈现一个比较弱的吸收带，它

的峰值位于 350nm 附近。然而 PbWO4很容易被辐照赋色，当用高能粒子甚至 UV

辐照 PbWO4晶体时，都能使 PbWO4晶体产生诱导色心。这种性质用辐照硬度来

描述。晶体越是容易辐照赋色，其辐照硬度越小。经赋色的 PbWO4晶体吸收光谱

除了具有 350nm 吸收带之外，还在 420nm 附近出现一个强吸收带和在 500－700nm

呈现一个宽带。由于 420nm 吸收带与 PbWO4晶体 420nm 发射谱交叠，严重影响

了晶体闪烁性能，并导致光产额下降。

为了提高 PbWO4晶体闪烁性能及光产额，必须搞清这些吸收带的形成，变化

及湮灭机理。经研究发现，这些吸收带多起因于 PbWO4晶体中的各类色心，在

PbWO4晶体中存在两类色心，一是空穴型色心，另一类是电子型色心。比较多的

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摘要：

I目录目录.............................................................................................................................I摘要..............................................................................................................................VABSTRACT...................................

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