Rattling效应: 一种影响微波介质陶瓷谐振频率温度系数的新机制

doi:10.15541/jim20240529

无机材料学报 ›› 2025, Vol. 40 ›› Issue (6): 656-666.DOI: 10.15541/jim20240529

Rattling效应: 一种影响微波介质陶瓷谐振频率温度系数的新机制

唐莹¹(), 李洁¹(), 相怀成¹, 方维双¹^,², 林慧兴², 杨俊峰³, 方亮¹()

1.桂林理工大学材料科学与工程学院, 有色金属及材料加工新技术教育部重点实验室, 广西光电材料与器件重点实验室, 桂林 541004
2.中国科学院上海硅酸盐研究所, 无机功能材料与器件重点实验室, 上海 200050
3.广州天极电子科技股份有限公司, 广州 510288

收稿日期:2024-12-18 修回日期:2025-02-07 出版日期:2025-06-20 网络出版日期:2025-02-13
通讯作者: 李洁, 副教授. E-mail: jielee@glut.edu.cn;
方亮, 教授. E-mail: fanglianggl001@aliyun.com
作者简介:唐莹(1988-), 女, 教授. E-mail: tangyinggl001@aliyun.com
基金资助:
广西科技计划项目(2024GXNSFFA010013);广西科技计划项目(AD24010021);国家自然科学基金(52362017)

Rattling Effect: A New Mechanism Affecting the Resonant Frequency Temperature Coefficient of Microwave Dielectric Ceramics

TANG Ying¹(), LI Jie¹(), XIANG Huaicheng¹, FANG Weishuang¹^,², LIN Huixing², YANG Junfeng³, FANG Liang¹()

1. Key Lab of New Processing Technology for Nonferrous Metals and Materials Ministry of Education, Guangxi Key Laboratory of Optical and Electronic Materials and Devices, College of Materials Science and Engineering, Guilin University of Technology, Guilin 541004, China
2. Key Laboratory of Inorganic Functional Material and Device, Shanghai Institute of Ceramics, Chinese Academy of Sciences, Shanghai 200050, China
3. Aurora Technologies Co., Ltd., Guangzhou 510288, China

Received:2024-12-18 Revised:2025-02-07 Published:2025-06-20 Online:2025-02-13
Contact: LI Jie, associate professor. E-mail: jielee@glut.edu.cn;
FANG Liang, professor. E-mail: fanglianggl001@aliyun.com
About author:TANG Ying (1988-), female, professor. E-mail: tangyinggl001@aliyun.com
Supported by:
Natural Science Funds of Guangxi Province(2024GXNSFFA010013);Natural Science Funds of Guangxi Province(AD24010021);National Natural Science Foundation of China(52362017)

摘要/Abstract

摘要：

微波介质陶瓷是5G/6G通信技术中关键的基础材料, 具有高品质因数(Q×f)、低介电常数(ε_r)以及近零谐振频率温度系数(τ_f)的材料逐渐成为研究与开发的重点。然而, 绝大多数低ε_r材料往往具有较负的τ_f。本研究首先系统概述了影响τ_f的经典机制, 包括离子极化率稀释机制、相变机制、晶胞体积机制、氧多面体畸变度、键能与键性以及键价等结构因素。随后, 详细介绍了本团队近期在无相变立方正反石榴石体系中观察到的τ_f异常变化现象, 提出“Rattling”效应是一种影响微波介质陶瓷τ_f的新机制。具有高配位数且弱化学键合的“Rattling”阳离子是影响材料整体微波介电极化和损耗的主要因素, 它不仅增大离子极化率和ε_r, 还导致τ_f正向偏移, 同时降低Q×f。该机制在不同材料体系中得到验证与应用。本研究引入了总离子极化偏差的加权函数新概念, 用于评估整个分子“Rattling”和“Compressed”效应对ε_r的影响, 并提出了离子极化率温度系数(τ_αm)新概念, 通过定量化计算从而将影响介电常数温度系数(τ_ε)正负和大小的因素简化为ε_r、τ_αm和线膨胀系数α_L之间的关系。

关键词: 微波介质陶瓷, Rattling效应, 谐振频率温度系数, 离子极化率温度系数, 影响机制, 总离子极化偏差的加权函数

Abstract:

Microwave dielectric ceramics are the key basic materials of 5G/6G communication technology, with particular emphasis on the materials that exhibit a high quality factor (Q×f), low dielectric constant (ε_r) and near-zero temperature coefficient of resonant frequency (τ_f). However, most low-ε_r materials tend to have a significantly negative τ_f value. This study provides a systematic overview of the classical ionic polarizability dilution mechanism and phase transition mechanism, along with the structural factors affecting τ_f, such as unit cell volume mechanism, oxygen polyhedron distortion, bond energy, bond ionicity, and bond valence. Subsequently, the anomalous changes in τ_f in the cubic normal and inverse garnet systems without phase transition are described in detail. The “Rattling” effect is introduced as a novel mechanism affecting the τ_f of microwave dielectric ceramics. Cations involved in “Rattling”, characterized by high coordination and weak chemical bonds, are the primary factors affecting the overall microwave dielectric polarization and loss of the material. This phenomenon results in an increase in ionic polarizability and ε_r, a forward shift in τ_f and a reduction in Q×f value, which has been verified and applied in many different material systems. Furthermore, the introduction of a weighted function for total ion polarization deviation serves to evaluate the impact of the entire molecule's “Rattling” and “Compressed” effects on ε_r. A novel concept of temperature coefficient of ionic polarizability (τ_αm) is also proposed, allowing for quantitative calculation. This simplifies the factors that affect the positive and negative of dielectric constant temperature coefficient (τ_ε), by relating it to ε_r, τ_αm and linear expansion coefficient α_L.

Key words: microwave dielectric ceramic, Rattling effect, temperature coefficient of resonance frequency, temperature coefficient of ionic polarizability, influence mechanism, weighted function for total ion polarizability deviation

中图分类号:

O484

唐莹, 李洁, 相怀成, 方维双, 林慧兴, 杨俊峰, 方亮. Rattling效应: 一种影响微波介质陶瓷谐振频率温度系数的新机制[J]. 无机材料学报, 2025, 40(6): 656-666.

TANG Ying, LI Jie, XIANG Huaicheng, FANG Weishuang, LIN Huixing, YANG Junfeng, FANG Liang. Rattling Effect: A New Mechanism Affecting the Resonant Frequency Temperature Coefficient of Microwave Dielectric Ceramics[J]. Journal of Inorganic Materials, 2025, 40(6): 656-666.

图/表 9

表1 Ca3Y2Ge3O12和Mg3Y2Ge3O12陶瓷的键长、键价和微波介电性能

Table 1 Bond lengths, bond valences and microwave dielectric properties of Ca3Y2Ge3O12 and Mg3Y2Ge3O12 ceramics

Sample	Bond type of A site	Bond valence parameter	Bond valence	Measured ε_r	Theoretical ε_th	Q×f/GHz	τ_f/(×10^-6, ℃^-1)
Ca₃Y₂Ge₃O₁₂	Ca-O	1.967	1.88	10.8	9.33	97126	-40.6
Mg₃Y₂Ge₃O₁₂	Y-O Mg-O	2.014 1.693	2.97 1.25	14.1	9.79	12600	+120.5

图1 势能随八面体中心金属离子的尺寸变化(为清晰起见, 用二维表示)[6]

Fig. 1 Variation of potential energy with displacement of a metal ion from the center of a fixed oxide octahedron (shown in two dimensions for clarity)[6] (a) Large ion; (b) Small ion; (c) Ion of intermediate size

图2 Ca3-xMgxYb2Ge3O12(0≤x≤3)陶瓷的微波介电性能[57]

Fig. 2 Microwave dielectric properties of Ca3-xMgxYb2Ge3O12 (0≤x≤3) ceramics[57] (a) Unit cell parameters and volumes; (b) Theoretical and measured permittivity; (c) Q×f; (d) τf. 1 ppm/℃=1×10-6 ℃-1

表2 Ca3-xMgxYb2Ge3O12 (0≤x≤3)陶瓷的最佳烧结温度(ST)、微波介电性能以及ταm

Table 2 Optimum sintering temperature (ST), microwave dielectric properties and ταm of Ca3-xMgxYb2Ge3O12 (0≤x≤3) ceramics

x	Ceramic	ST/℃	ε_r	Q×f/GHz	τ_f/(×10^-6, ℃^-1)	τ_αm/(×10^-6, ℃^-1)
0	Ca₃Yb₂Ge₃O₁₂	1360	10.3	98000	-48.2	+50.64
0.5	Ca_2.5Mg_0.5Yb₂Ge₃O₁₂	1380	10.6	89000	-55.6	+53.97
1.0	Ca₂MgYb₂Ge₃O₁₂	1400	11.0	87000	-56.3	+53.49
1.5	Ca_1.5Mg_1.5Yb₂Ge₃O₁₂	1400	11.2	86000	-50.4	+50.16
2.0	CaMg₂Yb₂Ge₃O₁₂	1400	11.8	78000	-40.3	+44.40
2.5	Ca_0.5Mg_2.5Yb₂Ge₃O₁₂	1420	12.4	24000	+4.7	+23.34
3.0	Mg₃Yb₂Ge₃O₁₂	1440	13.5	19800	+70.5	-3.66

图3 简谐振子模型分别在“Compressed”、平衡位置和“Rattling”状态下的回复力

Fig. 3 Restoring force of the simple harmonic oscillator model in “Compressed”, equilibrium position and “Rattling” states, respectively

图4 Ca1-x(Li0.5Eu0.5)xMoO4陶瓷的(a)热膨胀系数(50~300 ℃)和(b) τε、τf与ταm-3αL[62]

Fig. 4 (a) Thermal expansion data (50-300 ℃)and (b) τε, τf and ταm-3αL for Ca1-x(Li0.5Eu0.5)xMoO4 ceramics[62] Colorful figures are available on website; 1 ppm/℃=1×10-6 ℃-1

图5 (Ce1-xCax)(Nb1-xWx)O4陶瓷的(a)热膨胀系数(40~100 ℃)和(b) τε、τf与ταm-3αL[63]

Fig. 5 (a) Thermal expansion data (40-100 ℃) and (b) τε, τf and ταm-3αL for (Ce1-xCax)(Nb1-xWx)O4 ceramics[63] Colorful figures are available on website; 1 ppm/℃=1×10-6 ℃-1

图6 (a) SrEuAlO4和SrGdAlO4陶瓷的τf; (b) SrLnAlO4(Ln=La, Pr, Nd, Sm, Eu, Gd)陶瓷的τf和Δα[64]

Fig. 6 (a) τf of SrEuAlO4 and SrGdAlO4 ceramics; (b) τf and Δα in SrLnAlO4 (Ln= La, Pr, Nd, Sm, Eu, and Gd) ceramics[64] Colorful figures are available on website; 1 ppm/℃=1×10-6 ℃-1

图7 Ce1-xCaxO2-x(x=0~0.20)陶瓷的(a)介电常数和(b)离子极化率与x的函数关系[68]

Fig. 7 (a) Permittivity and (b) ion polarizability of Ce1-xCaxO2-x (x=0−0.20) ceramics as a function of x[68]

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Rattling效应: 一种影响微波介质陶瓷谐振频率温度系数的新机制

Rattling Effect: A New Mechanism Affecting the Resonant Frequency Temperature Coefficient of Microwave Dielectric Ceramics

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