In this work, ferroelastic domain walls inside BaTiO${}_3$ (BTO) tetragonal nanocrystals are distinguished by Bragg peak position and studied with Bragg coherent X-ray diffraction imaging (BCDI). Convergence-related features of the BCDI method for strongly phased objects are reported. A ferroelastic domain wall inside a BTO crystal has been tracked and imaged across the tetragonal-cubic phase transition and proves to be reversible. The linear relationship of relative displacement between two twin domains with temperature is measured and shows a different slope for heating and cooling, while the tetragonality reproduces well over temperature changes in both directions. An edge dislocation is also observed and found to annihilate when heating the crystal close to the phase transition temperature. {I. Introduction} Perovskite transition-metal oxides have been studied for decades because of both their broad applications and fundamental scientific questions. The displacement of Ti and Ba ions relative to the oxygen in unit cell leads to local polarization, which gives rise to exotic electrical properties such as elevated dielectric susceptibility, ferroelectricity and piezoelectricity [1-4] By analogy with well-studied magnetic systems, it is believed that it is not the local polarization in unit cell level that directly links with these macroscopic electrical properties, but rather via the formation and rearrangement of polarized nanodomains. Therefore, the study of domain structures, preferably in three dimensions (3D), is important for understanding and improving these properties. BaTiO${}_3$ (BTO), for example, is frequently chosen as a lead-free functional material for both actuator and sensor applications [5-6] It goes through a series of crystal lattice systems: cubic, tetragonal, orthorhombic and rhombohedral upon cooling [7]. The corresponding transitions are first-order with critical temperatures of 393K, 278K and 183K, respectively, which can be adjusted by varying strain and sample size. The cubic-tetragonal phase transition temperature, for example, can be increased from 393K to 813K with 1.7{%} compressive strain [8] and can decrease to room temperature when the particle size is reduced to 3nm [9]. Recently, it was reported that the local structure remains locally rhombohedral throughout all phases [1011] The phase transition is also complex, demonstrating both order-disorder and displacive character [1213] From the high symmetry cubic phase to the lower symmetry tetragonal phase, the paraelectric ensemble breaks into ferroelectric domains of uniform electric polarization, driven by the minimization of the sum of electrostatic and elastic energy [1-4]. To accommodate local energy landscape and strain different types of domains could be formed by rotation or translation of crystal regions or domains into different locations with welldefined domain-wall interfaces. For example, there are 71, 109and 180domain walls in rhombohedral BTO [14]. In tetragonal BTO, the flipping of one region of a crystal along a face-diagonal leads to a ferroelectric and ferroelastic 90domain wall (twin boundary). While flipping along the long side of the tetragonal unit cell creates a ferroelectriconly 180domain wall instead, in which the a-domain and c-domain are …

中文翻译：

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钛酸钡纳米粒子相变过程中铁弹性畴壁的演变

在这项工作中，BaTiO内的铁弹性畴壁${}_3$（BTO）四方纳米晶体通过布拉格峰位置进行区分，并通过布拉格相干X射线衍射成像（BCDI）研究。报告了强相控对象的BCDI方法的收敛相关特征。在BTO晶体内的铁弹性畴壁已被跟踪并在四方立方相变中成像，并证明是可逆的。测量了两个孪晶畴之间相对位移与温度的线性关系，并显示出不同的加热和冷却斜率，而四边形在两个方向的温度变化中都能很好地再现。当将晶体加热到接近相变温度时，还观察到边缘位错并且发现其消失。{一世。引言}由于钙钛矿过渡金属氧化物的广泛应用和基础科学问题，人们对其进行了数十年的研究。Ti和Ba离子相对于晶胞中的氧的位移会导致局部极化，从而产生奇异的电性能，例如介电常数，铁电性和压电性提高[1-4]类似于经过深入研究的磁系统，它据认为，不是晶胞水平上的局部极化与这些宏观电学性质直接相关，而是通过极化纳米域的形成和重排。因此，对域结构的研究，最好是在三维（3D）方面，对于理解和改善这些特性很重要。钛酸钡 Ti和Ba离子相对于晶胞中的氧的位移导致局部极化，从而引起奇异的电性能，例如介电常数，铁电性和压电性提高[1-4]类似于经过深入研究的磁系统，它据认为，不是晶胞水平上的局部极化与这些宏观电学性质直接相关，而是通过极化纳米域的形成和重排。因此，对域结构的研究，最好是在三维（3D）中，对于理解和改善这些特性很重要。钛酸钡 Ti和Ba离子相对于晶胞中的氧的位移导致局部极化，从而引起奇异的电性能，例如介电常数，铁电性和压电性提高[1-4]类似于经过深入研究的磁系统，它据认为，不是晶胞水平上的局部极化与这些宏观电学性质直接相关，而是通过极化纳米域的形成和重排。因此，对域结构的研究，最好是在三维（3D）中，对于理解和改善这些特性很重要。钛酸钡 铁电性和压电性[1-4]通过与经过深入研究的磁系统类似，人们认为与这些宏观电学性质直接相关的不是晶胞水平的局部极化，而是通过极化纳米域的形成和重排。因此，对域结构的研究，最好是在三维（3D）方面，对于理解和改善这些特性很重要。钛酸钡 铁电性和压电性[1-4]通过与经过深入研究的磁系统类似，人们认为与这些宏观电学性质直接相关的不是晶胞水平的局部极化，而是通过极化纳米域的形成和重排。因此，对域结构的研究，最好是在三维（3D）中，对于理解和改善这些特性很重要。钛酸钡 对于理解和改善这些特性很重要。钛酸钡 对于理解和改善这些特性很重要。钛酸钡${}_3$例如，（BTO）经常被选作致动器和传感器应用的无铅功能材料[5-6]冷却时会经历一系列晶格系统：立方，四方，正交和菱面体[7] 。相应的转变是一阶的，临界温度分别为393K，278K和183K，可以通过改变应变和样品大小进行调整。例如，立方-四方相变温度可以在1.7 {％}的压缩应变下从393K增加到813K [8]，并且当粒径减小到3nm时可以降低到室温[9]。最近，据报道，局部结构在所有阶段都保持局部菱形[1011]相变也很复杂，展示有序和无序特征[1213]从高对称立方相到低对称四方相，顺电系团在静电能和弹性能之和最小的驱动下，分裂为均匀极化的铁电区。 -4]。为了适应局部能量景观和应变，可以通过将晶体区域或畴旋转或平移到具有明确定义的畴壁界面的不同位置来形成不同类型的畴。例如，菱形BTO中有71、109和180个畴壁[14]。在四边形BTO中，晶体的一个区域沿面对角线的翻转会导致铁电和铁弹性90畴壁（双边界）。