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Substrate dependence of the self-heating in lead zirconate titanate (PZT) MEMS actuators 锆钛酸铅(PZT)微机电致动器的自热与基底的关系
Pub Date : 2024-04-23 DOI: 10.1063/5.0204385
Yiwen Song, Kyuhwe Kang, P. Tipsawat, Christopher Y. Cheng, Wanlin Zhu, Michael LaBella, Sukwon Choi, Susan E. Trolier-McKinstry
Lead zirconate titanate (PZT) thin films offer advantages in microelectromechanical systems (MEMSs) including large motion, lower drive voltage, and high energy densities. Depending on the application, different substrates are sometimes required. Self-heating occurs in the PZT MEMS due to the energy loss from domain wall motion, which can degrade the device performance and reliability. In this work, the self-heating of PZT thin films on Si and glass and a film released from a substrate were investigated to understand the effect of substrates on the device temperature rise. Nano-particle assisted Raman thermometry was employed to quantify the operational temperature rise of these PZT actuators. The results were validated using a finite element thermal model, where the volumetric heat generation was experimentally determined from the hysteresis loss. While the volumetric heat generation of the PZT films on different substrates was similar, the PZT films on the Si substrate showed a minimal temperature rise due to the effective heat dissipation through the high thermal conductivity substrate. The temperature rise on the released structure is 6.8× higher than that on the glass substrates due to the absence of vertical heat dissipation. The experimental and modeling results show that the thin layer of residual Si remaining after etching plays a crucial role in mitigating the effect of device self-heating. The outcomes of this study suggest that high thermal conductivity passive elastic layers can be used as an effective thermal management solution for PZT-based MEMS actuators.
锆钛酸铅(PZT)薄膜在微机电系统(MEMS)中具有运动幅度大、驱动电压低和能量密度高等优点。根据不同的应用,有时需要使用不同的基底。由于畴壁运动的能量损失,PZT 微机电系统中会出现自热现象,这会降低设备的性能和可靠性。在这项工作中,研究了硅和玻璃上的 PZT 薄膜以及从基底上释放的薄膜的自加热情况,以了解基底对器件温升的影响。纳米粒子辅助拉曼测温法被用来量化这些 PZT 激励器的工作温升。使用有限元热模型对结果进行了验证,其中体积发热量是通过滞后损失实验确定的。不同基底上的 PZT 薄膜的体积发热量相似,而硅基底上的 PZT 薄膜由于通过高导热基底有效散热,温升最小。由于没有垂直散热,释放结构上的温升比玻璃基板上的温升高 6.8 倍。实验和建模结果表明,蚀刻后残留的一薄层硅在减轻器件自热效应方面起着至关重要的作用。这项研究的结果表明,高导热被动弹性层可作为一种有效的热管理解决方案,用于基于 PZT 的微机电致动器。
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引用次数: 0
Rapid subsurface analysis of frequency-domain thermoreflectance images with K-means clustering 利用 K-means 聚类对频域热反射图像进行快速地表下分析
Pub Date : 2024-04-22 DOI: 10.1063/5.0201473
Amun Jarzembski, Zachary T. Piontkowski, Wyatt Hodges, Matthew Bahr, Anthony McDonald, William Delmas, Gregory Pickrell, L. Yates
K-means clustering analysis is applied to frequency-domain thermoreflectance (FDTR) hyperspectral image data to rapidly screen the spatial distribution of thermophysical properties at material interfaces. Performing FDTR while raster scanning a sample consisting of 8.6 μm of doped-silicon (Si) bonded to a doped-Si substrate identifies spatial variation in the subsurface bond quality. Routine thermal analysis at select pixels quantifies this variation in bond quality and allows assignment of bonded, partially bonded, and unbonded regions. Performing this same routine thermal analysis across the entire map, however, becomes too computationally demanding for rapid screening of bond quality. To address this, K-means clustering was used to reduce the dimensionality of the dataset from more than 20 000 pixel spectra to just K=3 component spectra. The three component spectra were then used to express every pixel in the image through a least-squares minimized linear combination providing continuous interpolation between the components across spatially varying features, e.g., bonded to unbonded transition regions. Fitting the component spectra to the thermal model, thermal properties for each K cluster are extracted and then distributed according to the weighting established by the regressed linear combination. Thermophysical property maps are then constructed and capture significant variation in bond quality over 25 μm length scales. The use of K-means clustering to achieve these thermal property maps results in a 74-fold speed improvement over explicit fitting of every pixel.
K-means 聚类分析应用于频域热反射(FDTR)高光谱图像数据,以快速筛选材料界面热物理特性的空间分布。在对由 8.6 μm 的掺杂硅(Si)与掺杂硅基板结合而成的样品进行光栅扫描时执行 FDTR,可识别次表层结合质量的空间变化。对选定像素进行常规热分析,可量化键合质量的这种变化,并确定键合、部分键合和未键合区域。然而,在整个地图上执行相同的常规热分析,对快速筛选粘接质量的计算要求太高。为了解决这个问题,我们使用 K 均值聚类将数据集的维度从 20,000 多个像素光谱降低到 K=3 分量光谱。然后,通过最小二乘最小化线性组合,利用这三个分量光谱来表达图像中的每个像素,从而在空间变化特征(如粘合到非粘合的过渡区域)上提供分量之间的连续插值。根据热模型拟合分量光谱,提取每个 K 簇的热属性,然后根据回归线性组合确定的权重进行分布。然后构建热物理性质图,并捕捉 25 μm 长度尺度上键合质量的显著变化。与明确拟合每个像素相比,使用 K 均值聚类来绘制这些热物理性质图的速度提高了 74 倍。
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引用次数: 0
Conduction-band engineering of polar nitride semiconductors with wurtzite ScAlN for near-infrared photonic devices 极性氮化物半导体的传导带工程与用于近红外光子器件的晶格ScAlN
Pub Date : 2024-04-22 DOI: 10.1063/5.0195021
Govardan Gopakumar, Z. Abdin, Rajendra Kumar, Brandon Dzuba, Trang Nguyen, M. J. Manfra, O. Malis
Wurtzite ScxAl1−xN/GaN (x = 0.13–0.18) multi-quantum wells grown by molecular beam epitaxy on c-plane GaN are found to exhibit remarkably strong and narrow near-infrared intersubband absorption in the technologically important 1.8–2.4 μm range. Band structure simulations reveal that, for GaN wells wider than 3 nm, the quantized energies are set by the steep triangular profile of the conduction band caused by intrinsic polarization fields. As a result, the intersubband transition energies provide unique and direct access to essential ScAlN polarization parameters. Measured infrared absorption indicates that the spontaneous polarization difference of the presumed lattice-matched Sc0.18Al0.82N/GaN heterostructure is smaller than the theoretically calculated value. The intersubband transition energies are relatively insensitive to the barrier alloy composition indicating negligible variation of the net polarization field in the probed 0.13–0.18 Sc composition range.
通过分子束外延在 c 平面氮化镓上生长出的沃特兹ScxAl1-xN/GaN (x = 0.13-0.18)多量子阱在具有重要技术意义的 1.8-2.4 μm 范围内表现出明显的强而窄的近红外带间吸收。带状结构模拟显示,对于宽于 3 nm 的氮化镓阱,量子化能量是由本征极化场导致的导带陡峭三角剖面设定的。因此,带间跃迁能量提供了独特而直接的 ScAlN 基本极化参数。测量到的红外吸收表明,假定晶格匹配的 Sc0.18Al0.82N/GaN 异质结构的自发极化差小于理论计算值。带间跃迁能对势垒合金成分相对不敏感,这表明在所探究的 0.13-0.18 Sc 成分范围内,净极化场的变化可以忽略不计。
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引用次数: 0
Nickel–silicon interfacial adhesion strength measured by laser spallation 通过激光溅射测量镍硅界面粘附强度
Pub Date : 2024-04-22 DOI: 10.1063/5.0198331
Xiao Yan, Jacob M. Diamond, Nathan J. Fritz, Satoshi Matsuo, K. F. Rabbi, Ishrat Zarin, Nenad Miljkovic, P. V. Braun, N. Sottos
Thin films of amorphous silicon (a-Si) coated on metals such as nickel (Ni) are one of the most promising anode architectures for high-energy-density lithium-ion (Li-ion) batteries. The performance and longevity of batteries with this type of electrode depend on the integrity of the Ni/a–Si interface. The integrity of the a-Si /Ni bonded interface during cycling is critical, but the experimental characterization of interfacial failure of this material system is highly challenging and there is a sparsity of interface strength data in the literature. Here, we describe a laser spallation (LS) technique to characterize the interfacial adhesion strength of Ni/a–Si multilayer films created by chemical vapor deposition (CVD). The LS technique enables the non-contact measurement of the tensile interfacial strength with high precision when compared to conventional methods for characterizing adhesion. Interferometric measurement combined with finite element analysis shows that the Ni/a–Si interface, created via the CVD of a-Si on Ni surfaces can withstand ≈46–72 MPa in tension before failure initiation. To ensure successful and precise characterization of interfacial adhesion strength using LS, we further develop a design criterion for multi-layer samples by analyzing the thin-film mechanics. Our study provides insights into the strength of the Ni/a–Si interface that governs the performance and durability of high-energy-density anodes and offers design guidelines for improving thin-film electrode integrity.
涂覆在镍(Ni)等金属上的非晶硅(a-Si)薄膜是高能量密度锂离子(Li-ion)电池最有前途的阳极结构之一。采用这种电极的电池的性能和寿命取决于镍/非晶硅界面的完整性。硅/镍结合界面在循环过程中的完整性至关重要,但这种材料系统界面失效的实验表征极具挑战性,而且文献中的界面强度数据非常稀少。在此,我们介绍了一种激光剥落(LS)技术,用于表征通过化学气相沉积(CVD)形成的镍/a-硅多层薄膜的界面粘附强度。与表征附着力的传统方法相比,LS 技术能够以高精度非接触式测量拉伸界面强度。干涉测量结合有限元分析表明,通过 CVD 在镍表面形成的非晶硅镍/非晶硅界面在失效前可承受 ≈46-72 兆帕的拉力。为确保使用 LS 成功、精确地表征界面粘附强度,我们通过分析薄膜力学进一步制定了多层样品的设计标准。我们的研究深入揭示了影响高能量密度阳极性能和耐用性的镍/a-硅界面强度,并为改善薄膜电极完整性提供了设计指南。
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引用次数: 0
Interaction between water and point defects inside volume-constrained α-quartz: An ab initio molecular dynamics study at 300 K 体积受限的α-石英内部水与点缺陷之间的相互作用:300 K条件下的ab initio分子动力学研究
Pub Date : 2024-04-22 DOI: 10.1063/5.0190356
D. Choudhuri, Alex J. Rinehart
Quartz-based minerals in earth’s crust are well-known to contain water-related defects within their volume-constrained lattice, and they are responsible for strength-loss. Experimental observations of natural α-quartz indicate that such defects appear as hydroxyl groups attached to Si atoms, called Griggs defect (Si-OH), and molecular water (H2O) located at the interstitial sites. However, factors contributing to the formation of Griggs and interstitial H2O defects remain unclear. For example, the role of point defects like vacancy sites (O2− and Si4+), and substitutional (Al3+) and interstitial (Li+, K+, Ca2+, Mg2+, etc.) ions has remained largely unexplored. Here, we performed ab initio molecular dynamics at 300 K to examine the energetics and structure of water-related defects in volume-constrained α-quartz. Several configurations were systematically interrogated by incorporating interstitial H2O, O2− and Si4+ vacancies, substitutional Al3+, and interstitial Li+, Ca2+ and Mg2+ ions within α-quartz. Interstitial H2O defect was found to be energetically favorable in the presence of Substitutional Al3+, and interstitial Ca2+, Mg2+, and Li1+. In the presence of O2− and Si4+ vacancies, H2O showed a strong tendency to dissociate into OH—to form Griggs defect—and a proton; even in the presence of substitutional and interstitial ions. These ions distorted the α-quartz lattice and, in the extreme case, disrupted long-range order to form local amorphous domains; consistent with experimental reports. Our study provides an initial framework for understanding the impact of water within the crystal lattice of an anhydrous silicate mineral such as quartz. We provide not only thermodynamic and process-related information on observed defects, but also provides guidelines for future studies of water’s impact on the behavior of silicate minerals.
众所周知,地壳中的石英基矿物在其体积受限的晶格中含有与水有关的缺陷,它们是造成强度损失的原因。对天然α-石英的实验观察表明,这些缺陷表现为硅原子上附着的羟基(称为格里格缺陷(Si-OH))和位于间隙位点的分子水(H2O)。然而,导致格里格斯缺陷和间隙 H2O 缺陷形成的因素仍不清楚。例如,空位(O2- 和 Si4+)、置换离子(Al3+)和间隙离子(Li+、K+、Ca2+、Mg2+ 等)等点缺陷的作用在很大程度上仍未得到探讨。在此,我们在 300 K 温度下进行了 ab initio 分子动力学研究,考察了受体积约束的 α-quartz 中与水有关的缺陷的能量和结构。通过在α-石英中加入间隙 H2O、O2- 和 Si4+ 空位、置换 Al3+ 以及间隙 Li+、Ca2+ 和 Mg2+ 离子,系统地研究了几种构型。研究发现,在存在Al3+、Ca2+、Mg2+和Li1+的情况下,间隙H2O缺陷在能量上是有利的。在 O2- 和 Si4+ 空位存在的情况下,H2O 显示出解离成 OH(形成格里格斯缺陷)和质子的强烈倾向;即使在存在取代离子和间隙离子的情况下也是如此。这些离子扭曲了 α-石英晶格,在极端情况下,破坏了长程有序性,形成局部无定形域;这与实验报告一致。我们的研究为理解水在石英等无水硅酸盐矿物晶格中的影响提供了一个初步框架。我们不仅提供了观察到的缺陷的热力学和过程相关信息,还为今后研究水对硅酸盐矿物行为的影响提供了指导。
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引用次数: 0
Effect of phase transition on the piezoelectric properties of scandium-alloyed gallium nitride 相变对钪合金氮化镓压电特性的影响
Pub Date : 2024-04-22 DOI: 10.1063/5.0191816
K. Hirata, Yu Ikemoto, Masato Uehara, Hiroshi Yamada, S. A. Anggraini, M. Akiyama
In this study, the piezoelectric properties of scandium-alloyed gallium nitride (ScGaN), which is expected to be applied to microelectromechanical systems devices, are evaluated by first-principles calculations. The piezoelectric constant (d33) of GaN is found to increase by up to approximately 30 times upon the addition of 62.5 mol. % of Sc. The piezoelectric stress constant (e33) increases and the elastic constant (C33) decreases with increasing Sc content of ScGaN, driving the rise of d33. The improved piezoelectric properties of ScGaN compared with those of GaN are largely attributed to elastic softening, which is thought to be related to the transition from a wurtzite to hexagonal boron nitride (h-BN) structure driven by the change in bonding states between atoms caused by the addition of Sc to GaN. The crystal orbital Hamilton population analysis suggests that addition of Sc to GaN results in the combination of weaker Sc–N and Ga–N bonding, which makes the crystal structure unstable. This weakened bonding is thought to be the main cause of the destabilization of the wurtzite structure and transition to the h-BN structure of ScGaN. The elastic softening associated with this structural transition leads to the dramatic improvement in piezoelectric properties.
本研究通过第一原理计算评估了钪合金氮化镓(ScGaN)的压电特性,该材料有望应用于微机电系统设备。研究发现,加入 62.5 摩尔% 的钪后,氮化镓的压电常数(d33)最多可增加约 30 倍。随着 ScGaN 中 Sc 含量的增加,压电应力常数(e33)增大,弹性常数(C33)减小,从而推动了 d33 的增大。与氮化镓相比,ScGaN 的压电特性得到改善主要归因于弹性软化,而弹性软化被认为与氮化镓中添加 Sc 引起的原子间键合状态变化所驱动的从渥兹态到六方氮化硼(h-BN)结构的转变有关。晶体轨道汉密尔顿群分析表明,在氮化镓中加入 Sc 会导致 Sc-N 和 Ga-N 结合力减弱,从而使晶体结构变得不稳定。这种键合的减弱被认为是ScGaN的沃特兹结构失稳并过渡到h-BN结构的主要原因。与这种结构转变相关的弹性软化导致了压电特性的显著改善。
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引用次数: 0
Measurement and modeling of strain waves in germanium induced by ultrafast laser pulses 超快激光脉冲诱导的锗应变波的测量与建模
Pub Date : 2024-04-22 DOI: 10.1063/5.0197957
Martin Aagaard, Brian Julsgaard
Transient reflectivity measurements are used to probe the strain waves induced by ultrashort laser pulses in bulk [100] germanium. The measurement signals are compared to purely analytical model functions based on the known material parameters for germanium. The modeling includes (i) a derivation of analytical solutions to the wave equation for strain waves coupled to the diffusion equation for heat and charge carriers and (ii) an expression for the impact on reflection coefficients that are caused by perturbations to the dielectric function but extended to cover a non-isotropic, uniaxial dielectric tensorial form. The model is held up against transient reflectivity measurements with an s- and a p-polarized probe and with a probe wavelength in the range of 502–710 nm. Excellent agreement is found when comparing the oscillatory shape of the measurement signals to the models. As for the magnitude of the oscillations, the models reproduce the overall trends of the experiment when using the previously published values for the elasto-optical tensor measured under static strain.
瞬态反射率测量用于探测超短激光脉冲在块状[100]锗中引起的应变波。测量信号与基于已知锗材料参数的纯分析模型函数进行了比较。建模包括:(i) 应变波波形方程与热量和电荷载流子扩散方程耦合的分析解的推导;(ii) 介电函数扰动对反射系数影响的表达式,但已扩展到非各向同性的单轴介质张量形式。该模型与使用 s 偏振和 p 偏振探针以及探针波长在 502-710 纳米范围内进行的瞬态反射率测量结果进行了对比。在将测量信号的振荡形状与模型进行比较时,发现两者非常一致。至于振荡的幅度,当使用以前公布的在静态应变下测量的弹性光学张量值时,模型再现了实验的总体趋势。
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引用次数: 0
Noncollinear electro-optic detection of terahertz waves: Advantages and limitations 太赫兹波的非共轭电光探测:优势和局限性
Pub Date : 2024-04-22 DOI: 10.1063/5.0206493
M. Kurnikov, M. Bakunov
Electro-optic sampling of terahertz waves by noncollinearly propagating femtosecond laser pulses in electro-optic crystals can provide high efficiency and high spectral resolution of terahertz detection with various types of crystals and laser wavelengths, unlike the conventional collinear scheme. We develop an analytical theory of noncollinear electro-optic sampling detection technique that describes the modulation of the probe laser beam polarization as a result of nonlinear interaction between the optical and terahertz fields. The theory accounts for finite widths of the terahertz and probe beams. It is found that noncollinear scheme operates as a low-pass terahertz filter with the frequency cut-off determined by the width of the probe beam and the crossing angle of the terahertz and probe beams. We apply the theory to two practical situations: sampling of terahertz waves by fiber laser pulses (1.55 μm wavelength) in a GaAs crystal and sampling by Ti:sapphire laser pulses (800 nm wavelength) in a LiNbO3 crystal.
通过在电光晶体中以非共线方式传播飞秒激光脉冲,对太赫兹波进行电光采样,与传统的共线方案不同,这种方法可以在各种类型的晶体和激光波长下实现高效率和高光谱分辨率的太赫兹探测。我们提出了非共轭电光采样探测技术的分析理论,该理论描述了光场和太赫兹场之间的非线性相互作用对探测激光束偏振的调制。该理论考虑了太赫兹光束和探测光束的有限宽度。研究发现,非共轭方案可用作低通太赫兹滤波器,其频率截止由探测光束的宽度以及太赫兹光束和探测光束的交叉角决定。我们将该理论应用于两种实际情况:在砷化镓晶体中利用光纤激光脉冲(波长 1.55 μm)对太赫兹波进行采样,以及在氧化铌锂晶体中利用钛:蓝宝石激光脉冲(波长 800 nm)进行采样。
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引用次数: 0
Predicted thermophysical properties of UN, PuN, and (U,Pu)N UN、PuN 和 (U,Pu)N 的预测热物理性质
Pub Date : 2024-04-22 DOI: 10.1063/5.0177315
C. Galvin, N. Kuganathan, N. J. Barron, R. W. Grimes
Molecular dynamics and density functional theory simulations are used to predict the lattice and electronic contributions of thermophysical properties for UN, PuN, and mixed (U,Pu)N systems. The properties predicted include the lattice parameter, linear thermal expansion, enthalpy, and specific heat capacity, as a function of temperature. The simulation predictions for high temperature specific heat capacity are compared against experimental measurements to understand the behavior, and why differences in the experimental measurements are observed. The influence of adding U vacancies, N interstitials, and Pu to UN is also examined. For this, a new PuN potential parameter set is developed and used with the Kocevski UN potential, enabling the dynamics of mixed (U,Pu)N systems to be studied. How defects impact the thermophysical properties is important for understanding fuel behavior under different reactor conditions, and these mechanistic predictions can be used to support fuel performance codes where data is scarce.
分子动力学和密度泛函理论模拟用于预测 UN、PuN 和混合 (U,Pu)N 系统热物理性质的晶格和电子贡献。预测的特性包括晶格参数、线性热膨胀、焓和比热容与温度的函数关系。将模拟预测的高温比热容与实验测量结果进行比较,以了解其行为以及实验测量结果出现差异的原因。此外,还研究了在 UN 中添加 U 空位、N 间隙和 Pu 的影响。为此,我们开发了一套新的 PuN 电位参数,并与 Kocevski UN 电位一起使用,从而能够研究混合(U,Pu)N 系统的动力学。缺陷如何影响热物理性质对于理解不同反应堆条件下的燃料行为非常重要,这些机理预测可用于支持数据稀缺的燃料性能代码。
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引用次数: 0
Thermal cycle stability and microstructure of Pb(Mg1/3Nb2/3)O3-PbTiO3 single crystals Pb(Mg1/3Nb2/3)O3-PbTiO3 单晶的热循环稳定性和微观结构
Pub Date : 2024-04-22 DOI: 10.1063/5.0197826
Min Liang, Ruibin Xiong, Shuli Chen, Zujian Wang, B. Su, Rongbin Su, Ying Liu, Chao He
The Pb(Mg1/3Nb2/3)O3-PbTiO3 (PMN-PT) ferroelectric single crystals have been commercially available as important components in medical ultrasound transducers due to their excellent piezoelectric and electromechanical coupling performance. The variation in piezoelectric and dielectric properties of PMN-PT single crystals with ambient temperature is an important application indicator. In this work, the PMN-PT single crystals after direct current poling (DCP) and alternating current poling (ACP) were subjected to the cyclic thermal treatment process. The thermal cycling stability and microstructural changes in PMN-PT single crystals were investigated. The ACP single crystals exhibit a higher dielectric constant ε33T/ε0 (6500–7600) and piezoelectric coefficient d33 (2100–2500 pC N−1) compared to the DCP single crystals (ε33T/ε0 of 4100–5000, d33 of 1200–1300 pC N−1). Under thermal cycling at 60 °C, the DCP and ACP single crystals exhibit good thermal cycling stability after 150 cycles. Microstructural observations show that the domain structure of the DCP single crystals exhibits “staggered domain walls, inhomogeneous domain size, variety of domain structure,” while the relatively homogeneous stripe-like domains were observed in the ACP single crystals. After thermal cycling, new fine striped domains appear in both the DCP and ACP single crystals due to the instability of rotated polarization, but the piezoelectric and dielectric properties are not greatly affected. This work provides an intensive understanding of the effects of thermal cycling on the domain structure, which is useful for applications.
Pb(Mg1/3Nb2/3)O3-PbTiO3(PMN-PT)铁电单晶体具有优异的压电和机电耦合性能,已作为医用超声换能器的重要元件投入商用。PMN-PT 单晶的压电和介电特性随环境温度的变化是一项重要的应用指标。在这项工作中,对经过直流极化(DCP)和交流极化(ACP)的 PMN-PT 单晶进行了循环热处理。研究了 PMN-PT 单晶的热循环稳定性和微观结构变化。与 DCP 单晶(ε33T/ε0 为 4100-5000,d33 为 1200-1300 pC N-1)相比,ACP 单晶表现出更高的介电常数 ε33T/ε0 (6500-7600) 和压电系数 d33 (2100-2500 pC N-1)。在 60 °C 的热循环条件下,DCP 和 ACP 单晶在 150 次循环后表现出良好的热循环稳定性。微观结构观察结果表明,DCP 单晶的畴结构表现出 "畴壁交错、畴尺寸不均匀、畴结构多样",而 ACP 单晶则观察到相对均匀的条纹状畴。经过热循环后,由于旋转极化的不稳定性,DCP 和 ACP 单晶中都出现了新的细条纹畴,但压电和介电性质并未受到很大影响。这项研究深入了解了热循环对畴极结构的影响,这对应用很有帮助。
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引用次数: 0
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Journal of Applied Physics
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