Nonlinear impedance of 50Bi2VO5.5-50SrB4O7 partially crystallized glass at 613 K measured with impedance spectroscopy method at high temperature region

The nonlinear electrcial properties of 50Bi2VO5.5-50SrB4O7 partially crystallized glass was measured by impedance spectroscopy method. In order to prepare glasses two compounds: Bi2VO5.5 and SrB4O7 were synthesized via a solid state reaction route. The Bi2VO5.5 was synthesized from the stoichiometric mixture of initial powders of Bi2O3 and V2O5 which were ball-milled in pure acetone for 6 h at room temperature. The milling was performed in steps of 1 h with rest intervals of 10min. The mixture was heated up to 1020K in air and kept at this temperature for 24 h. The heating and cooling rate was of 50K h-1. The obtained powder was checked by X-ray diffraction method. The SrB4O7 was synthesized from the stoichiometric mixture of analytical grade SrCO3 and H3BO3 which were mashed in a mortar. Next the mixture was heated up to 1073K and kept at this temperature for 12 h. Samples of a composition of 50Bi2VO5.5–50SrB4O7 (in mol%) were prepared by the conventional melt quenching technique. The melting was conducted in alumina crucibles at 1373K for 2 h. The melts were poured onto a preheated (573 K) brass plate and pressed by another plate to obtain flat circular disks of 1–2mm thickness and 20–30mm diameter. Glass was partially crystallized due to heat treatment at 613 K. For the electrical measurements gold electrodes were evaporated at the preheated samples. Impedance measurements were carried out in the temperature range from 373 K to 813 K, with the ac voltage of 1 Vrms with Concept 40 broadband dielectric spectrometer. The higher harmonic components (harmonic 0, harmonic 1 and harmonic 2) were measured up to frequency of 1000 Hz. Measurements were conducted during heating and cooling. Here the impedance for harmonic components was defined as the ratio of the voltage base wave to the n-th harmonic current component: Zn∗= U0∗/In∗, where Zn⁎ including the base wave generally depend on the sample voltage U1⁎ base wave amplitude. From Zn⁎ allother independent variables are calculated. The dependence of current density on the cosinusoidal electric field E(t)= E0cos(ωt) leads to the following expression: j´ = σ´0hE0 cos (ωt) + σ´1hE0 cos (2ωt) + σ´2hE0 cos (3ωt) + …Where σ´0h denotes base conductivity, while σ´1h, σ´2h etc. are higher harmonics conductivity. The admittivity for harmonic components with n ≥1, is calculated from relation σ⁎n = i2πfε0ε⁎n.

采用阻抗谱法（impedance spectroscopy）测试了50Bi₂VO₅.₅-50SrB₄O₇部分微晶玻璃的非线性电学性质。为制备目标玻璃，先通过固相反应法（solid state reaction route）合成了Bi₂VO₅.₅与SrB₄O₇两种前驱体化合物。Bi₂VO₅.₅的合成：将Bi₂O₃与V₂O₅初始粉体按化学计量比混合，以纯丙酮为球磨介质，于室温下球磨6 h，球磨采用1 h研磨、10 min间歇的分步循环方式。将所得混合粉体置于空气中升温至1020 K，保温24 h，升降温速率均为50 K·h⁻¹。采用X射线衍射法（X-ray diffraction）对合成所得粉体进行物相表征。SrB₄O₇的合成：将分析纯级SrCO₃与H₃BO₃按化学计量比在研钵中充分研磨混合，随后将混合粉体升温至1073 K，保温12 h。采用传统熔融淬火法（melt quenching technique）制备摩尔组成为50Bi₂VO₅.₅-50SrB₄O₇的玻璃样品。熔融过程于氧化铝坩埚（alumina crucibles）中进行，保温温度为1373 K，保温时长2 h。将熔融液浇至预热至573 K的黄铜板上，随后用另一块平板压制成厚度1~2 mm、直径20~30 mm的扁平圆形玻璃薄片。经613 K热处理后，玻璃发生部分晶化。电学测试前，先在预热后的样品表面蒸镀金电极作为测试电极。采用Concept 40宽频介电光谱仪（broadband dielectric spectrometer），于373 K至813 K的温度区间内开展阻抗测试，测试所用交流电压幅值为1 Vrms。测试频率范围覆盖至1000 Hz，同时采集高次谐波分量（谐波0、谐波1与谐波2）。测试在升温和降温两个过程中均进行了数据采集。本研究中，高次谐波分量的阻抗定义为电压基波与n次谐波电流分量的比值：Zₙ∗ = U₀∗/Iₙ∗，其中包含基波在内的Zₙ∗通常与样品电压基波U₁∗的幅值相关。基于Zₙ∗可计算得到其余所有独立变量。当电流密度随余弦电场E(t)=E₀cos(ωt)变化时，可推导出如下表达式：j′ = σ′₀ₕE₀cos(ωt) + σ′₁ₕE₀cos(2ωt) + σ′₂ₕE₀cos(3ωt) + …。式中σ′₀ₕ代表基波电导率，σ′₁ₕ、σ′₂ₕ等则为对应高次谐波的电导率。对于n≥1的谐波分量，其导纳率可通过如下关系式计算：σₙ∗ = i2πfε₀εₙ∗。