新型毫米波器件和5G通信系统对低介微波介质陶瓷的性能提出了更高的要求，(Mg_1-xZn_x)₂SiO₄陶瓷具有低ε_r，高Q×f及成本低等特点，但烧结温度过高且τ_f值往往偏负较大，因此开发研究低温烧结高性能的(Mg_1-xZn_x)₂SiO₄微波介质陶瓷对推进毫米波通讯及基板材料的发展具有重要的科学意义和应用价值。

本文采用固相法制备了(Mg_1-xZn_x)₂SiO₄陶瓷，研究了不同配比及不同成型方式时陶瓷的介电性能，确定该实验条件下最佳的Mg/Zn比。通过溶胶凝胶法和溶胶凝胶-熔盐法合成高反应活性的纳米粉体，对比两种工艺获取最优粉体的参数，结合热压成型制备优良介电性能的(Mg_1-xZn_x)₂SiO₄陶瓷。以期通过掺杂CuO降低(Mg_1-xZn_x)₂SiO₄陶瓷的烧结温度，复合CaTiO₃调节陶瓷的谐振频率温度系数。最后基于第一性原理计算Mg₂SiO₄和(Mg_1-xZn_x)₂SiO₄的Mulliken布局分析和弹性常数等结构和物理性质，分析对比Zn取代后对Mg₂SiO₄结构的影响，并对之前的一些实验结果进行了理论验证。主要结论如下：

(1) 研究了不同组分配比对(Mg_1-xZn_x)₂SiO₄陶瓷介电性能的影响，结果表明当x = 0.2时样品的结构以Forsterite为主晶相，当x > 0.4时转变为以Willemite为主晶相。1325 ^oC下干压成型和热压成型得到的(Mg_0.4Zn_0.6)₂SiO₄陶瓷的性能参数分别为ρ = 3.53 g/cm³，ε_r = 6.74，tanδ = 8.88×10^-4和ρ = 3.96 g/cm³，ε_r = 6.36，tanδ = 1.35×10^-3。热压成型得到的(Mg_1-xZn_x)₂SiO₄陶瓷相较于干压成型的试样，其体积密度整体增大，ε_r和tanδ在论文实验条件下变化范围分别为6.16 ~ 7.57和1.10×10^-3 ~ 2.66×10^-3，展现了在不同组分和工艺条件下更稳定的性能。

(2) 通过溶胶凝胶法结合热压成型可使(Mg_0.4Zn_0.6)₂SiO₄陶瓷的烧结温度从1375 ^oC降至1225 ^oC，与固相烧结法对比，体积密度明显增大，有效降低了MZS陶瓷烧结温度，但也增大了陶瓷的介电损耗。通过溶胶凝胶-熔盐法以ZnCl₂-KCl为熔盐制备的同一组分陶瓷，在同一烧结温度下其介电常数和介电损耗均有改善。

(3) 通过CuO掺杂可有效降低干压成型(Mg_0.4Zn_0.6)₂SiO₄陶瓷的烧结温度，同时进一步提升陶瓷的介电性能，掺杂0.5 wt % CuO的陶瓷样品于1225 ^oC下烧结4 h后的ρ = 3.50 g/cm³，介电性能最优为ε_r = 6.54，tanδ = 8.85×10^-4。热压成型时1225 ^oC下1 wt % CuO掺杂的(Mg_0.4Zn_0.6)₂SiO₄陶瓷微波介电性能为ε_r = 6.49，Q×f = 2982 GHz，τ_f = -47.17  ppm/°C。研究了CaTiO₃对(Mg_0.4Zn_0.6)₂SiO₄陶瓷烧结和性能的影响，发现其不仅可以有效调制谐振频率温度系数，同时可降低烧结温度。1175 °C下烧结的90 wt % (Mg_0.4Zn_0.6)₂SiO₄-10 wt % CaTiO₃陶瓷和1200 °C下烧结的85 wt % (Mg_0.4Zn_0.6)₂SiO₄-15 wt % CaTiO₃陶瓷的谐振频率温度系数分别为-1.39 ppm/°C和1.75 ppm/°C，已平衡至0 ppm/°C左右。1175 ^oC下95 wt % (Mg_0.4Zn_0.6)₂SiO₄-5 wt % CaTiO₃陶瓷的低频介电性能和微波介电性能相对较好，其介电性能参数分别为ε_r = 7.35，tanδ = 8.97×10^-4和ε_r = 8.79，Q×f = 8959 GHz，τ_f = -17.95 ppm/°C。

(4) 通过第一性原理计算得Mg₂SiO₄和(Mg_0.4Zn_0.6)₂SiO₄的禁带宽度分别为4.588 eV和2.771 eV。(Mg_0.4Zn_0.6)₂SiO₄费米能级附近的主要贡献为O2p和Zn3d轨道，表明Zn-O键为共价键。Zn-O键贡献了晶胞中大部分的共价键，削减了结构中离子极化作用，导致(Mg_0.4Zn_0.6)₂SiO₄的介电常数相比于Mg₂SiO₄降低了约10 %。Mg₂SiO₄具有弹性稳定性，Zn原子的取代会使其失去弹性稳定性，增大体积模量、剪切模量和泊松比，从而使陶瓷的τ_f值趋近零值。

New millimeter wave devices and 5G communication systems put forward higher requirements for the performance of low dielectric microwave dielectric ceramics, (Mg_1-xZn_x)₂SiO₄ ceramics have low ε_r, high Q×f and low cost, but the sintering temperature is too high and the value of τ_f is too negative. Therefore, the development and research of low-temperature sintered high-performance (Mg_1-xZn_x)₂SiO₄ microwave dielectric ceramics has important scientific significance and application value for promoting the development of millimeter wave communication and substrate materials.

In this paper, (Mg_1-xZn_x)₂SiO₄ ceramics were prepared by the solid-phase sintering method. The dielectric properties of ceramics with different ratios and different molding methods were studied, and the optimal Mg/Zn ratio was determined under the experimental conditions. High reactive nano powders were synthesized by sol-gel method and sol-gel molten salt method. Comparing the two processes to obtain the optimal powder parameters, combined with hot pressing to prepare (Mg_1-xZn_x)₂SiO₄ ceramics with excellent dielectric properties. It is expected that the sintering temperature of (Mg_1-xZn_x)₂SiO₄ ceramics can be reduced by doping CuO, and the resonant frequency temperature coefficient of ceramics can be adjusted by composite CaTiO₃. Finally, the Mulliken layout analysis, elastic constant and other electronic structures and physical properties of Mg₂SiO₄ and (Mg_1-xZn_x)₂SiO₄ are calculated based on the first principle. The effects of Zn substitution on the structure of Mg₂SiO₄ are analyzed and compared, and some previous experimental results are verified theoretically. The main conclusions are as follows:

(1) The effect of different composition ratios on the dielectric properties of (Mg_1-xZn_x)₂SiO₄ ceramics was studied. The results showed that Forsterite is the main crystal phase when x = 0.2, and Willemite is the main crystal phase when x > 0.4. The performance parameters of (Mg_0.4Zn_0.6)₂SiO₄ ceramics formed by dry pressing and hot pressing at 1325 ^oC are ρ = 3.53 g/cm³, ε_r = 6.74, tanδ = 8.88×10^-4 and ρ = 3.96 g/cm³, ε_r = 6.36, tanδ = 1.35×10^-3. The bulk density of (Mg_1-xZn_x)₂SiO₄ ceramics obtained by hot pressing is higher than that of dry pressing, ε_r and tanδ under the experimental conditions, the variation range are 6.16 ~ 7.57 and 1.10×10^-3~ 2.66×10^-3, showing more stable performance under different components and process conditions.

(2) The sintering temperature of (Mg_0.4Zn_0.6)₂SiO₄ ceramics decreased from 1375 ^oC to 1225 ^oC by sol-gel method combined with hot pressing. Compared with the solid-phase sintering method, bulk density increased significantly, and the sintering temperature of MZS ceramics was effectively reduced, but the dielectric loss of ceramics was also increased. The same component ceramics prepared by sol-gel molten salt method using ZnCl₂-KCl as molten salt, the dielectric constant and dielectric loss of ceramics were optimized at the same sintering temperature.

(3) CuO doping can effectively reduce the sintering temperature of dry pressed (Mg_0.4Zn_0.6)₂SiO₄ ceramics and further improve the dielectric properties of ceramics. The ceramic samples doped with 0.5 wt % CuO were sintered at 1225 ^oC for 4 h ρ = 3.50 g/cm³, the best dielectric properties are ε_r = 6.54, tanδ = 8.85×10^-4. The microwave dielectric properties of 1 wt % CuO doped (Mg_0.4Zn_0.6)₂SiO₄ ceramics at 1225 ^oC during hot pressing are ε_r = 6.49, Q×f = 2982 GHz, τ_f = -47.17 ppm/°C. The effect of CaTiO₃ on the sintering and properties of (Mg_0.4Zn_0.6)₂SiO₄ ceramics was studied. It was found that CaTiO₃ can not only effectively modulate the temperature coefficient of resonant frequency, but also reduce the sintering temperature. The resonant frequency temperature coefficients of 90 wt % (Mg_0.4Zn_0.6)₂SiO₄-10 wt % CaTiO₃ ceramics sintered at 1175 °C and 85 wt % (Mg_0.4Zn_0.6)₂SiO₄-15 wt % CaTiO₃ ceramics sintered at 1200 ^oC are -1.39 ppm/°C and 1.75 ppm/°C respectively, which have been balanced to about 0 ppm/°C. The low-frequency dielectric properties and microwave dielectric properties of 95 wt % (Mg_0.4Zn_0.6)₂SiO₄-5 wt % CaTiO₃ ceramics at 1175 °C are relatively good, and their performance parameters are ρ = 3.70 g/cm³, ε_r = 7.35, tanδ = 8.97×10^-4 and ε_r = 8.79, Q×f = 8959 GHz, τ_f = -17.95 ppm/°C.

(4) The band gap widths of Mg₂SiO₄ and (Mg_0.4Zn_0.6)₂SiO₄ calculated by the first principle are 4.588 eV and 2.771 eV respectively. The main contributions near the Fermi level of (Mg_0.4Zn_0.6)₂SiO₄ are O2p and Zn3d orbitals, indicating that the Zn-O bond is covalent. The Zn-O bond contributes most of the covalent bonds in the crystal cell and reduces the ion polarization in the structure, resulting in a decrease of about 10 % in the dielectric constant of (Mg_0.4Zn_0.6)₂SiO₄ compared with Mg₂SiO₄. Mg₂SiO₄ has elastic stability. The substitution of Zn atoms make it lose its elastic stability, increase the bulk modulus, shear modulus and Poisson ratio, and make the τ_f value of ceramics approaches zero.

[1] Lee Y C, Chiang C S, Huang Y L. Microwave dielectric properties and microstructures of Nb2O5-Zn0.95Mg0.05TiO3+0.25TiO2 ceramics with Bi2O3 addition[J]. J Eur Ceram Soc, 2010, 30: 963-970.

[2] Liu F, Qu J J, Yan H G, et al. Study on phase structures and compositions, microstructures, and dielectric characteristics of (1-x) NdGaO3-xBi0.5Na0.5TiO3 microwave ceramic systems[J]. Ceram Int, 2020, 46(10): 16185-16195.

[3] Gui L, Yang H C, Qian Z, et al. Synthesis of low temperature firing scheelite-type BaWO4 microwave dielectric ceramics with high performances[J]. Ceram Int, 2022, 48: 1360-1365.

[4] Zhang P, Xie H, Zhao Y G, et al. Synthesis and microwave dielectric characteristics of high-Q Li2MgxO3+x ceramics system[J]. Materials Research Bulletin, 2018, 98: 160-165.

[5] 唐莹. 石榴石型低介电常数微波介质陶瓷制备与性能[D]. 北京: 北京科技大学, 2021.

[6] 马调调. 微波介质陶瓷材料应用现状及其研究方向[J]. 陶瓷, 2019, 04: 13-23.

[7] Ding G A, Liu F, Qu J J, et al. Microwave dielectric polymer-ceramics sintered at near room-temperature with moisture-proof ability[J]. Ceram. Int, 2021, 47: 26400-26409.

[8] Guo H H, Zhou D, Pang L X, et al. Microwave dielectric properties of low firing temperature stable scheelite structured (Ca, Bi)(Mo,V)O4 solid solution ceramics for LTCC applications[J]. J Eur Ceram Soc, 2019, 39:2365-2373.

[9] Hameed I, Wu S Y, Li L, et al. Structure and microwave dielectric characteristics of Sr2[Ti1-x(Al0.5Nb0.5)x]O4(x ≤ 0.50) ceramics[J]. J Am Ceram Soc, 2019, 102(10): 6137-6146.

[10] Kamutzki F, Schneider S, Barowski J, et al. Silicate dielectric ceramics for millimetre wave applications[J]. J Eur Ceram Soc, 2021, 41(7): 3879-3894.

[11] Raveendran A, Sebastian M T, Raman S. Applications of microwave materials: a review[J]. J Electron Mater, 2019, 48(5): 2601-2634.

[12] Zhou M, Bin T, Zhang S R. Effects of adding TEOS on sintering process, morphology and microwave dielectric properties of Y3Al5O12 ceramics[J]. Ceram Int, 2021, 47: 12826-12832.

[13] Liu L T, Chen Y G, Feng Z B, et al. Crystal structure, infrared spectra, and microwave dielectric properties of the EuNbO4 ceramic[J]. Ceram Int, 2021, 47: 4321-4326.

[14] 李皓. MgO-TiO2体系微波介质陶瓷材料结构与性能优化研究[D]. 成都: 电子科技大学, 2016.

[15] Reaney I M, Iddles D. Microwave dielectric ceramics for resonator and filters in mobile phone networks[J]. J Am Ceram Soc, 2006, 89: 2063-2072.

[16] Ohsato H. Functional advances of microwave dielectrics for next generatian[J]. Ceram Int, 2012, 38(supp-S1): S141-S146.

[17] Tummala R R. Cheminform Abstract: Ceramic and glass-ceramic packaging in the 1990s[J]. J Am Ceram Soc, 1991, 74(5): 895-908.

[18] Freer R, Azough F. Microstructural engineering of microwave dielectric ceramics[J]. J Eur Ceram Soc, 2008, 28(7): 1433-1441.

[19] Seabra M P, Ferreira V M, Zheng H, et al. Structure property relations in La(Mg0.5Ti0.5)O3-based solid solution[J]. J Appl Phys, 2005, 97(3): 33525-33525.

[20] Ohsato H, Tsunooka T, Sugiyama T, et al. Forsterite ceramics for millimeterwave dielectrics[J]. J Electroceram, 2006, 17(2-4): 445-450.

[21] Lv Y, Zhou W F, Dong Z W, et al. Influence of CaO-B2O3-SiO2 crystallizable glass on microstructure and microwave dielectric of LiMg0.9Zn0.1PO4 ceramics for LTCC substrate applications[J]. J Alloy Compd, 2020, 844(5): 156212.

[22] Sasikala T S, Suma M N, Mohanan P, et al. Forsterite-based ceramic-glass composites for substrate applications in microwave and millimeter wave communications[J]. J Alloy Compd, 2008, 461: 555-559.

[23] Sebastian M T, Jantunen H. Low loss dielectric materials for LTCC applications: a review[J]. International Materials Reviews, 2008, 53(2): 57-90.

[24] Dernovsek O, Eberstein M, Schiller W A. LTCC glass-ceramic composites for microwave application[J]. J Eur Ceram Soc, 2001, 21(10): 1693-1697.

[25] 黄新杰. ZnO-Al2O3-SiO2基微波介质陶瓷的制备及圆极化微带天线的设计[D]. 广州: 华南理工大学, 2019.

[26] 方梓烜. 高介Ti基与低介Li基微波陶瓷的制备及性能机理研究[D]. 成都: 电子科技大学, 2019.

[27] 李亚菲. 低烧低介Li2(Mg1-xZnx)SiO4陶瓷材料及其性能[D]. 成都: 电子科技大学, 2018.

[28] 胡杰, 吕学鹏, 张天宇, 等. 低介电常数微波介质陶瓷研究进展[J]. 材料导报, 2017, 31(A02): 107-114.

[29] Tsunooka T, Androu M, Higashida Y, et al. Effects of TiO2 on sinterability and dielectric properties of high-Q forsterite ceramics[J]. J Eur Ceram Soc, 2003, 23(14):2573-2578.

[30] Guo Y P, Ohsato H, Kakimoto K I. Characterization and dielectric behavior of willemite and TiO2-doped willemite ceramics at millimeter-wave frequency[J]. J Eur Ceram Soc, 2006, 26: 1827-1830.

[31] Cheng L, Liu P, Qu S X, et al. Microwave dielectric properties of AWO4 (A=Ca, Ba, Sr) ceramics synthesized via high energy ball milling method[J]. J Alloys Compd, 2013, 581: 553-557.

[32] Surendran K P, Bijumon P V, Mohanan P, et al. (1-x) MgAl2O4-x TiO2 dielectrics for microwave and millimeter wave applications[J]. Appl Phys, A 2005, 81: 823-826.

[33] Sasikala T S, Pavithran C, Sebastian M T. Effect of lithium magnesium zinc borosilicate glass addition on densification temperature and dielectric properties of Mg2SiO4 ceramics[J]. J Mater Sci: Mater Electron, 2010, 21: 141-144.

[34] Dou G, Zhou D X, Guo M, et. al. Low-temperature sintered Mg2SiO4-CaTiO3 ceramics with near-zero temperature coeffificient of resonant frequency[J]. J Mater Sci: Mater Electron, 2013, 24: 1431-1438.

[35] Dou G, Zhou D X, Guo M, et. al. Low-temperature sintered Zn2SiO4-CaTiO3 ceramics with near-zero temperature coeffificient of resonant frequency[J]. J Alloy Compd, 2012, 513: 466-473.

[36] 李冉. Li2MgSiO4基微波介质陶瓷的低温烧结及微波介电性能[D]. 南京: 南京航空航天大学, 2011.

[37] Tamada O, Fujino K, Sasaki S. Structures and electron didtributions of α-Co2SiO4 and α-NiSiO4[J]. Acta Cryst., 1983, B39: 692-697.

[38] Andou M, Tsunooka T, Higashida Y. Development of high Q forsterite ceramics for high-frequency applications[C]. York: MMA 2002 Conference, 2002: 10-20.

[39] Kosanovic C, Stubicar N, Tomasic N, et al. Synthesis of a forsterite powder by combined ball milling and thermal treatment[J]. J Alloys Compd, 2005, 389: 306-309.

[40] Lai Y, Tang X, Huang X, et al. Phase composition, crystal structure and microwave dielectric properties of Mg2-xCuxSiO4 ceramics[J]. J Eur Ceram Soc, 2018, 38(4): 1508-1516.

[41] Masoumeh K, Touradj E, Sara B. Preparation of forsterite/MBS (MgO-B2O3-SiO2) glass-ceramic composites via conventional and microwave assisted sintering routes for LTCC application[J]. Ceram Int, 2017, 43: 9259-9266.

[42] Chang H J, Park H D, Sohn K S, et al. Electronic structure of Zn2SiO4 and Zn2SiO4: Mn[J]. J Korean Physi Soc, 1999, 34(6): 545-548.

[43] Tang K, Wu Q, Xiang X Y. Low temperature sintering and microwave dielectric properties of zinc silicate ceramics[J]. J Mater Sci: Mater Electron, 2012, 23(5): 1099-1102.

[44] 郑昌伟. (Mg1-xZnx)Al2O4低介电常数微波介质陶瓷[D]. 杭州: 浙江大学, 2007.

[45] 王莹莹. 低温烧结(Zn1-xMgx)2SiO4基陶瓷的微波介电性能研究[D]. 南京: 南京航空航天大学, 2012.

[46] Ohsato H, Tsunooka, T Ando. Millimeter-wave dielectric ceramics of alumina and forsterite with high quality factor and low dielectric constant[J]. J Korean Ceram Soc, 2003, 40(4): 350-353.

[47] Segnit E R, Holland A E. The System MgO-ZnO-SiO2[J]. J Am Ceram Soc, 1965, 48(8): 409-413.

[48] Song K X, Chen X M, Zheng C W. Microwave dielectric characteristics of ceramics in Mg2SiO4-Zn2SiO4 system[J]. Ceram Int, 2008, 34(4): 917-920.

[49] Lei W, Lu W Z, Wang X H, et al. Phase composition and microwave dielectric properties of ZnAl2O4-Co2TiO4 low-permittivity ceramics with high quality factor[J]. J Am Ceram Soc, 2011, 94(1): 20-23.

[50] Anjana P S, Sebastian M T. Microwave dielectric properties and low-temperature sintering of cerium oxide for LTCC applications[J]. J Am Ceram Soc, 2009, 92(1): 96-104.

[51] 宋开新. 低介电常数微波介质陶瓷[D]. 杭州市: 浙江大学, 2007.

[52] 王雯, 樊嘉杰, 王中俭, 等. (Mg1-xZnx)2SiO4系列微波介质陶瓷材料[J]. 华东理工大学学报(自然科学版), 2010, 3: 384-388.

[53] 姜红梅, 张树人, 周晓华. (Zn1-xMgx)2SiO4基微波陶瓷的介电性能研究[J]. 压电与声光, 2008, 30(5): 615-617.

[54] 杨东海, 姚林侠. Zn2SiO4-Mg2SiO4复相陶瓷的合成与性能研究[J]. 中国电子科学研究院学报, 2014, 9(2): 130-135.

[55] Li L X, Ji L J, He X W, et al. Sintering behaviour and microwave dielectric properties of sol‐gel synthesised (Zn0.4Mg0.6)2SiO4 ceramics[J]. Materials Research Innovations, 2012, 16(5): 316-320.

[56] Li L X, Wang Y C, Xia W S, et al. Effects of Zn/Mg ratio on the microstructure and microwave dielectric properties of (Zn1-xMgx)2SiO4 ceramics[J]. J Electron Mater, 2012, 41(4): 684-688.

[57] Zhang Q L, Yang H, Zou J L. Low-temperature sintering of (Zn0.8Mg0.2)2SiO4-TiO2 ceramics[J]. Materials Letters, 2008, 62(23): 3872-3874.

[58] Keshavarz M, Ebadzadeh T, Banijamali S. Preparation of forsterite/MBS (MgO-B2O3-SiO2) glass-ceramic composites via conventional and microwave assisted sintering routes for LTCC application[J]. Ceram Int, 2017, 43: 9259-9266.

[59] Li B, Tang B, Zhang S R, et al. Low-temperature sintered (ZnMg)2SiO4 microwave ceramics with TiO2 addition and calcium borosilicate glass[J]. Ceramics-Silikáty, 2011, 55(1): 14-19.

[60] Wang W, Tang L J, Bai W F, et al. Microwave dielectric properties of (1-x) (Mg0.4Zn0.6)2SiO4-x CaTiO3 composite ceramics[J]. J Mater Sci: Mater Electron, 2014, 25(8): 3601-3607.

[61] 黄琦, 郑勇, 吕学鹏, 等. 微波介质陶瓷介电机理研究进展[J]. 电子元件与材料, 2016, 35(1): 6.

[62] Payne M C, Teter M P, Allan D C, et al. Iterative minimization techniques for ab initio total energy calculations molecular-dynamics and conjugate gradients[J]. Rev Mod Phys, 1992, 64(4): 1045-1097.

[63] Diao C L, Wang C H, Luo N N, et al. First-principle calculation and assignment for vibrational spectra of Ba(Mg1/3Nb2/3)O3 microwave dielectric ceramic[J]. J Appl Phys, 2014, 115(11): 787-791.

[64] 何开华. 典型半导体材料第一性原理研究[D]. 成都: 四川师范大学, 2005.

[65] 程琳. 陶瓷介质微波性能的第一性原理研究[D]. 西安: 陕西师范大学, 2015.

[66] Ogawa H, Kan A, Ishihara S, et al. Crystal structure of corundum type Mg4(Nb2-x Tax)O9 microwave dielectric ceramics with low dielectric loss[J]. J Eur Ceram Soc, 2003, 23(14): 2485-2488.

[67] Karazhanov S Z, Ravindran P, Vajeeston P, et al. Phase stability and pressure-induced structural transitions at zero temperature in ZnSiO3 and Zn2SiO4[J]. Journal of Physics Condensed Matter, 2009, 21: 485801.

[68] Núñez-Valdez M, Umemoto K, Wentzcovitch R M. Fundamentals of elasticity of (Mg1-x, Fex)2SiO4 olivine[J]. Geophysical Research Letters, 2010, 37: L14308.

[69] Dosler U, Krzmanc M M, Suvorov D. Phase evolution and microwave dielectric properties of MgO-B2O3-SiO2-based glass-ceramics[J]. Ceram Int, 2012, 38: 1019-1025.

[70] Wang H P, He Z P, Li D H, et al. Low temperature sintering and microwave dielectric properties of CaSiO3-Al2O3 ceramics for LTCC applications[J]. Ceram Int, 2014, 40: 3895-3902.

[71] Chen H W, Su H, Zhang H W, et al. Low temperature sintering and microwave dielectric properties of (Zn1-xCox)2SiO4 ceramics[J]. Ceram Int, 2014, 40: 14655-14659.

[72] Gong J, Zhou H, He F, et al. Structural evolution, low-firing characteristic and microwave dielectric properties of magnesium and sodium vanadate ceramic[J]. Ceram Int, 2015, 41(9): 11125-11131.

[73] 董树义. 近代微波测量技术[M]. 北京: 电子工业出版社, 1995, 153.

[74] Hakki B W, Coleman P D. A dielectric resonator method of measuring inductive capacities in the millimeter range[J]. IEEE Trans Microwave Theory Tech, 1960, 402-410.

[75] 闫文. (Zr0.8Sn0.2)TiO4中介微波介质陶瓷的制备、低温烧结及改性[D]. 西安: 西安科技大学, 2019.

[76] 叶泽君. 低温共烧Zn2SiO4低损耗微波材料及天线阵列设计研究[D]. 成都: 电子科技大学, 2020.

[77] 雷文. ZnAl2O4基低介电常数微波介质陶瓷的结构与性能[D]. 武汉: 华中科技大学, 2008.

[78] Fukami Y, Wada K, Kakimoto K, et al. Microstructure and microwave dielectric properties of BaLa4Ti4O15 ceramics with template particles[J]. J Eur Ceram Soc, 2006, 26(10-11): 2055-2058.

[79] 邹佳丽, 张启龙, 杨辉, 等. Zn2SiO4微波陶瓷溶胶-凝胶法制备及性能研究[J]. 稀有金属材料与工程, 2008, 37(S2): 575-578.

[80] Kim J S, Song M E, Joung M R, et al. Effect of B2O3 addition on the sintering temperature and microwave dielectric properties of Zn2SiO4 ceramics[J]. J Eur Ceram Soc, 2010, 30: 375-379.

[81] Kan A, Ogawa H, Ohsato H, et al. Influence of M (M = Zn and Ni) substitution for Cu on microwave dielectric characteristics of Yb2Ba(Cu1−xMx)O5 solid solutions[J]. Jpn J Appl Phys, 2001, 40: 5774-5778.

[82] Fang L, Liu Q, Tang Y, et al. Adjustable dielectric properties of Li2CuxZn1−xTi3O8 (x = 0 to 1) ceramics with low sintering temperature[J]. Ceram Int, 2012, 38: 6431-6434.

[83] 赖元明. 低介低损耗LTCC微波介质材料及应用研究[D]. 成都: 电子科技大学, 2019.

[84] Cheng H, Chung P, Shen S. Liquid phase sintering of CaTiO3-MgTiO3 microwave dielectric ceramics[J]. Materials Chemistry and Physics, 2002, 78: 111-115.

[85] 王浩. 改性CaTiO3基微波介质陶瓷结构与介电性能的研究[D]. 武汉: 武汉理工大学, 2004.

[86] Tseng C F. Microwave dielectric properties of a new Cu0.5Ti0.5NbO4 ceramics[J]. J Eur Ceram Soc, 2015, 35: 383-387.

[87] R D Shannon. Dielectric polarizabilities of ions in oxides and fluorides[J]. J Appl Phys, 1993, 73(1): 348-366.

[88] Kim E S, Chun BS, Freer R, et al. Effects of packing fraction and bond valance on microwave dielectric properties of A2+B6+O4 (A2+: Ca, Pb, Ba; B6+: Mo, W) ceramics[J]. J Eur Ceram Soc, 2010, 30: 1731-1736.

[89] Su H, Wu S. Studies on the (Mg, Zn)TiO3-CaTiO3 microwave dielectric ceramics[J]. Mater. Lett., 2005, 59(18): 2337-2341.

[90] 方俊鑫, 殷之文. 电解质物理学[M]. 科学出版社出版社, 2000: 25-38.

[91] 方丹华. CaTiO3-LaAlO3微波介质陶瓷的制备与介电性能研究[D]. 武汉: 湖北大学, 2015.

[92] 江娟. CaTiO3-LaAlO3陶瓷的结构与微波介电性能研究[D]. 武汉: 湖北大学, 2016.

[93] 罗至利. Zr-Al-C体系层状陶瓷结构与性质的第一性原理研究[D]. 西安: 长安大学, 2019.

[94] 李素. 电化学法制备镁盐晶须及第一性原理研究[D]. 太原: 太原理工大学, 2011.

[95] Peng R, Su H, Di A, et al. The sintering and dielectric properties modification of Li2MgSiO4 ceramic with Ni2+ ion doping based on calculation and experiment[J]. Journal of Materials Research and Technology, 2020, 9(2): 1344-1356.

[96] 田晶鑫. BiFeO3基陶瓷的结构调控和电学行为及第一性原理计算[D]. 哈尔滨: 哈尔滨工业大学, 2020.

[97] 刘哲. Ti-Al-C三元层状陶瓷结构,弹性和电子性质的第一性原理研究[D]. 西安: 长安大学, 2019.

[98] 丁超, 李卫, 刘菊燕, 等. Sb, S共掺杂SnO2电子结构的第一性原理分析[J]. 物理学报, 2018, 67(21) :141-147.

[99] 高洁. 纤锌矿型MgxZn1-xO的第一性原理研究[D]. 呼和浩特: 内蒙古大学, 2014.

[100]齐欣欣. 基于第一性原理的三元层状Cr-Al-B陶瓷性能预测[D]. 哈尔滨: 哈尔滨工业大学, 2018.

[101]蒋瑞娇. 第一性原理研究ZrN2, HfN2和BC6N的高压性质[D]. 西安: 西安建筑科技大学, 2020.

[102]Pugh S F. XCII. Relations between the elastic moduli and the plastic properties of polycrystalline pure metals[J]. The London, Edinburgh, and Dublin philosophical magazine and Journal of Science, 1954, 45(367): 823-843.

[103]Mo Y, Rulis P, Ching W Y. Electronic structure and optical conductivities of 20 MAX-phase compounds[J]. Physical Review B, 2012, 86(16): 2733-2737.

[104]代礼彬. 硅酸镁系陶瓷基板材料的制备与性能研究[D]. 成都: 电子科技大学, 2010.