Dynamic reconstruction for atom probe tomography

Progress in the reconstruction for atom probe tomography has been limited since the first implementation of the protocol proposed by Bas et al. in 1995. This approach and those subsequently developed assume that the geometric parameters used to build the three-dimensional atom map are constant over the course of an analysis. Here, we test this assumption within the analyses of low-alloyed materials. By building upon methods recently proposed to measure the tomographic reconstruction parameters, we demonstrate that this assumption can introduce significant limitations in the accuracy of the analysis. Moreover, we propose a strategy to alleviate this problem through the implementation of a new reconstruction algorithm that dynamically accommodates variations in the tomographic reconstruction parameters.     

A method to determine the local surface profile from reconstructed exit waves

Reconstructed exit waves are useful to quantify unknown structure parameters such as the position and composition of the atom columns at atomic scale. Existing techniques provide a complex wave in a flat plane which is close to the plane where the electrons leave the atom columns. However, due to local deviation in the flatness of the exit surface, there will be an offset between the plane of reconstruction and the actual exit of a specific atom column. Using the channelling theory, it has been shown that this defocus offset can in principle be determined atom column-by-atom column. As such, the surface roughness could be quantified at atomic scale. However, the outcome strongly depends on the initial plane of reconstruction especially in a crystalline structure. If this plane is further away from the true exit, the waves of the atom columns become delocalized and interfere mutually which strongly complicates the interpretation of the exit wave in terms of the local structure. In this paper, we will study the delocalization with defocus using the channelling theory in a more systematic way.     

Impact of laser pulsing on the reconstruction in an atom probe tomography

The implementation of fast pulsed laser has significantly improved the performance of the atom probe technique by enabling near-atomic-scale three-dimensional analysis of poorly conducting materials. This has broadened the range of applications for the atom probe, addressing a major limitation of the technique. Despite this, the implications of lasing on the tomographic reconstruction of atom probe data have yet to be fully characterised. Here, we demonstrate how changes in the shape of the specimen surface, induced by laser pulsing, affect the ion trajectories, and hence the projection parameters used to build the three-dimensional map.     

Pragmatic reconstruction methods in atom probe tomography

Data collected in atom probe tomography have to be carefully analysed in order to give reliable composition data accurately and precisely positioned in the probed volume. Indeed, the large analysed surfaces of recent instruments require reconstruction methods taking into account not only the tip geometry but also accurate knowledge of geometrical projection parameters. This is particularly crucial in the analysis of multilayers materials or planar interfaces. The current work presents a simulation model that enables extraction of the two main projection features as a function of the tip and atom probe instrumentation geometries. Conversely to standard assumptions, the image compression factor and the field factor vary significantly during the analysis. An improved reconstruction method taking into account the intrinsic shape of a sample containing planar features is proposed to overcome this shortcoming.     

Atom probe trajectory mapping using experimental tip shape measurements

Atom probe tomography is an accurate analytical and imaging technique which can reconstruct the complex structure and composition of a specimen in three dimensions. Despite providing locally high spatial resolution, atom probe tomography suffers from global distortions due to a complex projection function between the specimen and detector which is different for each experiment and can change during a single run. To aid characterization of this projection function, this work demonstrates a method for the reverse projection of ions from an arbitrary projection surface in 3D space back to an atom probe tomography specimen surface. Experimental data from transmission electron microscopy tilt tomography are combined with point cloud surface reconstruction algorithms and finite element modelling to generate a mapping back to the original tip surface in a physically and experimentally motivated manner. As a case study, aluminium tips are imaged using transmission electron microscopy before and after atom probe tomography, and the specimen profiles used as input in surface reconstruction methods. This reconstruction method is a general procedure that can be used to generate mappings between a selected surface and a known tip shape using numerical solutions to the electrostatic equation, with quantitative solutions to the projection problem readily achievable in tens of minutes on a contemporary workstation.     

Crystallographic structural analysis in atom probe microscopy via 3D Hough transformation

Whereas the atom probe is regarded almost exclusively as a technique for 3D chemical microanalysis of solids with the highest chemical and spatial resolution, we demonstrate that the technique can be used for detailed crystallographic determinations. We present a new method for the quantitative determination of crystal structure (plane spacings and angles) using a Hough transformation of the reconstructed atom probe data. The resolving power is shown to be high enough to identify poorly established, discontinuous planes that are typical in semiconducting materials. We demonstrate the determination of crystal geometry around a grain boundary and the use of the technique for the optimisation of tomographic reconstruction. We propose that this method will enable automatic spatial analysis and, ultimately, automated tomographic reconstruction in atom probe microscopy.     

Applications of scanning optical microscopy in materials science to detect bulk microdefects in semiconductors

A three-dimensional atom probe permits the elemental reconstruction of a small volume of a specimen by determining the x , y and z positions and mass-to-charge ratio of the atoms in that volume. The historical development of this new type of atom probe is described. Several variants of these instruments including the position-sensitive atom probe, the optical atom probe and the tomographic atom probe are reviewed. The various methods of data visualization and analysis are summarized. The performance of the three-dimensional atom probe is compared with the energy-compensated atom probe.     

Exploring the next neighbourhood relationship in amorphous alloys utilizing atom probe tomography

A new algorithm is developed to explore the next neighbourhood atomic vicinity from the analysed data obtained using the tomographic atom probe (TAP) technique. The presented algorithm allows to calculate the atomic distances among different next neighbours of different elements as applied to bulk amorphous alloys. The results obtained for Pd55 Cu23 P22 bulk amorphous alloys show reasonable consistency to already available data from different diffraction techniques. The Pd-Pd atoms have highest probability to be a next neighbour than others. The established view that P is not a direct next neighbour to each other is also manifested from these results. Normalizing the distances of the next neighbours to the first neighbour distance in this particular amorphous system possesses a definite order for all elemental correlations. Furthermore, the algorithm was processed for different critical reconstruction parameters to explore the corresponding effect on the distance distribution of next neighbouring atoms. The minor changes in the product of the geometric factor and the evaporation field of the sample does not make any egregious difference on the next neighbourhood evaluation (NNE).     

Improvements in planar feature reconstructions in atom probe tomography

Standard atom probe tomography spatial reconstruction techniques have been reasonably successful in reproducing single crystal datasets. However, artefacts persist in the reconstructions that can be attributed to the incorrect assumption of a spherical evaporation surface. Using simulated and experimental field evaporation, we examine the expected shape of the evaporating surface and propose the use of a variable point projection position to mitigate to some degree these reconstruction artefacts. We show initial results from an implementation of a variable projection position, illustrating the effect on simulated and experimental data, while still maintaining a spherical projection surface. Specimen shapes during evaporation of model structures with interfaces between regions of low- and high-evaporation-field material are presented. Use of two-and three-dimensional projection-point maps in the reconstruction of more complicated datasets is discussed.     

Field ion microscopy and 3-D atom probe analysis of Al3Zr particles in 7050 Al alloy

Field ion microscope images have been used to measure the local evaporation field of a Al3Zr particle in 7050 Al alloy. Using the matrix Al evaporation field (19 V/nm) as a reference, the evaporation field of Al3Zr has been estimated to be 36 V/nm, similar to the theoretical value for the field evaporation of Al2+ or Zr3+ ions. A strong local magnification effect from the large difference in evaporation fields between the particle and matrix has been found to cause a severe distortion of the apparent particle morphology in a three-dimensional atom probe reconstruction when using parameters based on the Al matrix. Use of the measured evaporation field for Al3Zr has allowed accurate reconstruction of the morphology of the particle. A simple worst-case analysis predicts that trajectory overlaps increase with increasing cross-section of particle, and the calculated overlaps agree well with experimental estimates of approximately 1.4-2.0 nm for variations in the particle cross-section from 7 to 12 nm. The chemical composition of Al3Zr in a 7050 Al alloy has been measured to be 64.8-67.7 at% Al, 23.6-24.8 at% Zr, 6.9-9.1 at% Zn, 0.4-0.7 at% Cu, 0.5-1.2 at% Mg, with a (Al+Zn)/Zr ratio close to 3. Specimen analysis temperatures of either 25 or 80 K show little effect on the measured chemical compositions of the particle.     

High precision measurements of atom column positions using model-based exit wave reconstruction

In this paper, it has been investigated how to measure atom column positions as accurately and precisely as possible using a focal series of images. In theory, it is expected that the precision would considerably improve using a maximum likelihood estimator based on the full series of focal images. As such, the theoretical lower bound on the variances of the unknown atom column positions can be attained. However, this approach is numerically demanding. Therefore, maximum likelihood estimation has been compared with the results obtained by fitting a model to a reconstructed exit wave rather than to the full series of focal images. Hence, a real space model-based exit wave reconstruction technique based on the channelling theory is introduced. Simulations show that the reconstructed complex exit wave contains the same amount of information concerning the atom column positions as the full series of focal images. Only for thin samples, which act as weak phase objects, this information can be retrieved from the phase of the reconstructed complex exit wave.     

Field evaporation behavior in [0 0 1] FePt thin films

Though the atom probe has provided unprecedented atomic identification and spatial imaging capability, the basic reconstruction assumption of a smooth hemispherical tip shape creates significant challenges in yielding high fidelity chemical information for atomic species with extreme differences in fields required for field evaporation. In the present study, the evaporation behavior and accompanying artifacts are examined for the super-cell lattice structure of L1₀ FePt, where alternating Fe and Pt planes exist in the [0 0 1] orientation. Elemental Fe and Pt have significant differences in field strengths providing a candidate system to quantify these issues. Though alloys can result in changes in the elemental field strength, the intrinsic nature of elemental planes in [0 0 1] L1₀ provides a system to determine to what extent basic assumptions of elemental field strengths can break down in understanding reconstruction artifacts in this intermetallic alloy. The reconstruction of field evaporation experiments has shown depletion of Fe at the (0 0 2) pole and zone axes. Compositional profiles revealed an increase in Fe and atom count moving outward from the pole. The depletion at the low indexed pole and zone axes was determined to be the result of local magnification and electrostatic effects. The experimental results are compared to an electrostatic simulation model.     

Reverse Monte Carlo reconstruction algorithm for discrete electron tomography based on HAADF‐STEM atom counting

In this paper, we propose an algorithm to obtain a three‐dimensional reconstruction of a single nanoparticle based on the method of atom counting. The location of atoms in three dimensions has been successfully performed using simulations of high‐angle‐annular‐dark‐field images from only three zone‐axis projections, [110], [310] and [211], for a face‐centred cubic particle. These three orientations are typically accessible by low‐tilt holders often used in high‐performance scanning transmission electron microscopes.     

基于单目摄像机的光学立体标定技术

为了构建一种基于单摄像机的三维视觉系统,提出了重构光学标定点三维坐标、计算重构误差和优化标定参数的方法。通过移动高精度位移平台,构建三维视觉系统,计算左右摄像机位的初始参数,引入质心坐标法计算两摄像机位间的旋转平移矩阵,利用最优三角剖分法重构光学标定点的三维坐标,计算并最小化重构误差,对标定参数进行优化。实验表明：重构误差直接反映了三维重建的效率,该方法的精度和鲁棒性得到了显著的提高;实物外形测量的误差从0.1123 mm减小到0.0191 mm,标准差从0.1838减小到0.1275。该方法适合应用于三维视觉系统标定质量的评估。     

A model based reconstruction technique for depth sectioning with scanning transmission electron microscopy

Depth sectioning in high angular annular dark field scanning transmission electron microscopy is considered a candidate for three-dimensional characterization on the atomic scale. However at present the depth resolution is still far from the atomic level, due to strong limitations in the opening angle of the beam. In this paper we introduce a new, parameter based tomographic reconstruction algorithm that allows to make maximal use of the prior knowledge about the constituent atom types and the microscope settings, so as to retrieve the atomic positions and push the resolution to the atomic level in all three dimensions.     

Qualification of the tomographic reconstruction in atom probe by advanced spatial distribution map techniques

New and improved spatial distribution map (SDM) methods are developed to identify and extract crystallographic information within atom probe tomography three-dimensional (3D) reconstructions. Detailed structural information is retrieved by combining z-SDM offset distribution analyses computed in multiple crystallographic directions, accurately determining inter-planar spacings and crystallographic angles. The advantages of this technique in comparison to applying the complete z-SDM and complementary xy-SDM analysis to a single crystallographic direction are investigated. Further, in determining these multidirectional z-SDM and xy-SDM profiles, background noise reduction and automatic peak identification algorithms are adapted to attain increased accuracy and is shown to be particularly effective in cases where crystal structure is present but poorly resolved. These techniques may be used to calibrate the reconstruction parameters and investigate their dependence on the design of individual atom probe experiments.     

Optimisation of specimen temperature and pulse fraction in atom probe microscopy experiments on a microalloyed steel

This paper details the effects of systematic changes to the experimental parameters for atom probe microscopy of microalloyed steels. We have used assessments of the signal-to-noise ratio (SNR), compositional measurements and field desorption images to establish the optimal instrumental parameters. These corresponded to probing at the lowest possible temperature (down to 20 K) with the highest possible pulse fraction (up to 30%). A steel containing a fine dispersion of solute atom clusters was used as an archetype to demonstrate the importance of running the atom probe at optimum conditions.     

基于U曲线法的油气润滑ECT系统图像重建病态优化

采用U曲线法确定油气润滑ECT系统图像重建中的正则化参数,分析正则化处理后灵敏度矩阵的病态性;通过LBP算法和Tikhonov正则化算法分别对油气润滑ECT系统管道截面进行第一次图像重建;对第一次重建图像的灰度分布矩阵进行门限滤波阈值的优化,并对管道截面进行二次图像重建。结果表明:相较于L曲线法,U曲线法选取的正则化参数在削弱灵敏度矩阵病态程度方面的作用显著;第一次图像重建中,图像重建质量有较大改善;门限滤波阈值优化后的二次图像重建中,图像重建质量进一步提高。研究表明U曲线法确定的正则化参数和门限滤波阈值优化有助于提高油气润滑ECT系统的图像重建质量。     

GPS双目摄像机标定及空间坐标重建

为减轻双目摄像机标定过程中对高精度靶标的依赖,实现摄像机参数的精确标定,并对空间坐标进行高精度重建,提出一种GPS双目摄像机标定及空间坐标重建方法,采用GPS代替2D或3D靶标进行双目摄像机标定。将GPS的位置在视场中任意移动,由被标摄像机拍摄多组含有GPS的图像,利用空间三维坐标与图像二维坐标间的映射关系,结合摄像机成像模型和双目摄像机标定原理,标定出双目摄像机参数,并对空间坐标进行精确重建。通过空间重建坐标与GPS实际测量值之间的相对距离误差,对重建精度进行检验。实验证明,该方法能够克服双目摄像机标定过程中对高精度靶标的依赖,空间重建坐标具有较高的精度,相对距离误差从1.56%减小到0.52%。     

ECT图像重建正则化参数选取新方法

电容层析成像图像重建是一不适定反问题。此种情况下，仅使用最小二乘法不能保证获得满意的介质分布图像重建结果，因此广泛使用TIkhonov正则化算法来产生适当的解。正则化参数的合适选取对图像重建至关重要，其对重建质量和计算时间都有影响。本文提出了一种基于最平坦斜率的Tikhonov正则化参数选择方法，并针对2种典型介质分布，将基于此方法计算的正则化参数同L-曲线法在电容测量数据无噪声和施加噪声情况下的图像重建结果进行了比较。