<trans-title xml:lang="en">Rattling Effect: A New Mechanism Affecting the Resonant Frequency Temperature Coefficient of Microwave Dielectric Ceramics</trans-title>

Ying TANG; Jie LI; Huaicheng XIANG; Weishuang FANG; Huixing LIN; Junfeng YANG; Liang FANG

doi:10.15541/jim20240529

Journal of Inorganic Materials, Volume. 40, Issue 6, 656(2025)

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

Ying TANG¹, Jie LI^1、*, Huaicheng XIANG¹, Weishuang FANG^1,2, Huixing LIN², Junfeng YANG³, and Liang FANG^1、*

Author Affiliations

¹1. 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

²2. Key Laboratory of Inorganic Functional Material and Device, Shanghai Institute of Ceramics, Chinese Academy of Sciences, Shanghai 200050, China

³3. Aurora Technologies Co., Ltd., Guangzhou 510288, China

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Figures & Tables(9)

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]

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2. Microwave dielectric properties of Ca_3-_xMg_xYb₂Ge₃O₁₂ (0≤x≤3) ceramics^[57]

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

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4. (a) Thermal expansion data (50-300 ℃)and (b) τ_ε, τ_f and τ_αm-3α_L for Ca_1-_x(Li_0.5Eu_0.5)_xMoO₄ ceramics^[62] Colorful figures are available on website; 1 ppm/℃=1×10^-6 ℃^-1

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5. (a) Thermal expansion data (40-100 ℃) and (b) τ_ε, τ_f and τ_αm-3α_L for (Ce_1-_xCa_x)(Nb_1-_xW_x)O₄ ceramics^[63] Colorful figures are available on website; 1 ppm/℃=1×10^-6 ℃^-1

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6. (a) τ_f of SrEuAlO₄ and SrGdAlO₄ ceramics; (b) τ_f and Δα in SrLnAlO₄ (Ln= La, Pr, Nd, Sm, Eu, and Gd) ceramics^[64]

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7. (a) Permittivity and (b) ion polarizability of Ce_1-_xCa_xO_2-_x (x=0−0.20) ceramics as a function of x^[68]

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

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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-OMg-O	2.0141.693	2.971.25	14.1	9.79	12600	+120.5

Table 2. Optimum sintering temperature (ST), microwave dielectric properties and τ_αm of Ca_3-_xMg_xYb₂Ge₃O₁₂ (0≤x≤3) ceramics

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Table 2. Optimum sintering temperature (ST), microwave dielectric properties and τ_αm of Ca_3-_xMg_xYb₂Ge₃O₁₂ (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

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

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Paper Information

Category:

Received: Dec. 18, 2024

Accepted: --

Published Online: Sep. 2, 2025

The Author Email: Jie LI (jielee@glut.edu.cn), Liang FANG (fanglianggl001@aliyun.com)

DOI:10.15541/jim20240529

Topics

laser devices and laser physics

Lasers and Laser Optics

Laser physics

laser manufacturing

Instrumentation, Measurement and Metrology

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

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

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

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

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

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

Table 2. Optimum sintering temperature (ST), microwave dielectric properties and τ_αm of Ca_3-_xMg_xYb₂Ge₃O₁₂ (0≤x≤3) ceramics

Table 2. Optimum sintering temperature (ST), microwave dielectric properties and τ_αm of Ca_3-_xMg_xYb₂Ge₃O₁₂ (0≤x≤3) ceramics