Thermoelectric magnetohydrodynamic control of melt pool flow during laser directed energy deposition additive manufacturing

doi:10.1016/j.addma.2023.103587

Additive Manufacturing 增材制造

Volume 71, 5 June 2023, 103587
第 71 卷，2023 年 6 月 5 日，103587

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Abstract 摘要

Melt flow is critical to build quality during additive manufacturing (AM). When an external magnetic field is applied, it causes forces that alter the flow through the thermoelectric magnetohydrodynamic (TEMHD) effect, potentially altering the final microstructure. However, the extent of TEMHD forces and their underlying mechanisms, remain unclear. We trace the flow of tungsten particles using in situ high-speed synchrotron X-ray radiography and ex situ tomography to reveal the structure of TEMHD-induced flow during directed energy deposition AM (DED-AM). When no magnetic field is imposed, Marangoni convection dominates the flow, leading to a relatively even particle distribution. With a magnetic field parallel to the scan direction, TEMHD flow is induced, circulating in the cross-sectional plane, causing particle segregation to the bottom and side of the pool. Further, a downward magnetic field causes horizontal circulation, segregating particles to the other side. Our results demonstrate that TEMHD can disrupt melt pool flow during DED-AM.
熔体流动对于增材制造（AM）过程中的构建质量至关重要。当施加外磁场时，它会产生通过热电磁流体动力学 (TEMHD) 效应改变流动的力，从而可能改变最终的微观结构。然而，TEMHD 力的程度及其潜在机制仍然不清楚。我们使用原位高速同步加速器 X 射线照相术和非原位断层扫描追踪钨粒子的流动，以揭示定向能量沉积 AM (DED-AM) 过程中 TEMHD 引起的流动的结构。当没有施加磁场时，Marangoni 对流主导流动，导致颗粒分布相对均匀。当磁场平行于扫描方向时，会感应 TEMHD 流动，在横截面平面内循环，导致颗粒偏析到熔池底部和侧面。此外，向下的磁场会导致水平循环，使颗粒偏析到另一侧。我们的结果表明，TEMHD 会干扰 DED-AM 过程中的熔池流动。

Graphical Abstract 图形摘要

Keywords 关键词

Additive manufacturing

Melt flow control

Thermoelectric magnetohydrodynamic

Magnetic fields

Tungsten tracer

增材制造熔体流动控制热电磁流体力学磁场钨示踪剂

1. Introduction 1. 绪论

Laser directed energy deposition (DED) is a type of additive manufacturing, during which powders are continuously deposited from the nozzle into a laser melt pool [1], [2]. Compared to laser powder bed fusion (LPBF), DED has the advantages of high manufacturing speed and producing parts with site-specific composition, although the complexity of design shapes is more limited. Key areas where the application of DED is being considered are component repair and surface coating [1], [2], [3]. However, many challenges still remain for DED, including limited geometric precision [4], and undesirable microstructural features including porosity [5], cracks [6], and large epitaxial columnar grain growth [7]. Although process optimisation may mitigate the development of some undesired microstructures, it also results in a very narrow process window. By introducing a magnetic field to the AM process, we can potentially expand the process window. For instance, when printing a complex geometry part, one combination of process parameters may be optimal for some regions but may fail in others. By applying a magnetic field, we hope to have a higher tolerance for selecting suitable process parameters. These microstructural features are largely controlled by the melt pool flow. In general, the melt pool flow affects the solidification microstructure in several ways. Firstly, the microstructure is primarily controlled by the local thermal gradient and solidification rate, which can be strongly manipulated by the melt flow. Secondly, the flow can transport solute to certain regions, which can increase or decrease the local constitutional undercooling, potentially resulting in a change in the solidification mode. Thirdly, the melt pool flow can significantly affect the melt pool geometry which is a consequence of heat and mass transport. The change in the melt pool geometry can affect the grain growth orientation, leading to distinctive texture and grain morphology. Hence, melt pool flow is central to the melt pool dynamics [8], [9], [10], solidification [11] and microstructural feature formation [12], [13]. However, an effective way of controlling melt pool flow is still lacking due to the melt pool's small-scale (ca. 1 mm in length in DED [14], [15], [16]) and elevated temperature. In AM or laser welding, in some material systems, surfactants such as sulphur and oxygen can be added to modify the Marangoni flow. This is particularly applicable in high sulphur stainless steel and oxidised aluminium and titanium powder [8], [17], [18], [19], [20], [21], [22], [23]. However, these surfactants alter the material composition and may have a detrimental effect on properties [21], and leading to failure during operation. Varying process parameters can also modify the melt flow behaviour, but it will also affect track size and other factors, potentially leading to undesirable results. For example, under certain conditions, increasing energy density can result in the formation of keyhole porosity [24]. New techniques are being sought to control melt flow without adding surfactants or varying process parameters.
激光定向能量沉积（DED）是一种增材制造工艺，在此过程中，粉末从喷嘴连续沉积到激光熔池中 [1]，[2]。与激光粉末床熔融 (LPBF) 相比，DED 具有制造速度快，可生产具有特定位置成分的零件的优点，尽管设计形状的复杂性更加有限。DED 应用正在考虑的关键领域是组件修复和表面涂层 [1]，[2]，[3]。然而，DED 仍然面临许多挑战，包括几何精度有限 [4]，以及包括气孔 [5]、裂纹 [6] 和大的柱状晶粒生长 [7] 的不理想的微观结构特征。虽然工艺优化可以减轻一些不良微观结构的产生，但它也会导致非常狭窄的工艺窗口。通过在增材制造过程中引入磁场，我们可以潜在地扩展工艺窗口。例如，在打印复杂几何形状的零件时，一组工艺参数可能对一些区域是最佳的，但在其他区域可能是失败的。通过施加磁场，我们希望对选择合适的工艺参数有更高的容忍度。这些微观结构特征主要受熔池流动控制。总的来说，熔池流动以几种方式影响凝固微观结构。首先，微观结构主要受局部热梯度和凝固速率控制，这可以通过熔体流动进行强力操控。其次，流动可以将溶质输送到某些区域，这会增加或减少局部成分过冷，从而可能导致凝固模式的变化。第三，熔池流动会显着影响熔池几何形状，这是传热和传质的结果。熔池几何形状的变化会影响晶粒生长方向，从而导致独特的组织和晶粒形态。因此，熔池流动是熔池动力学 [8]、[9]、[10]、凝固 [11] 和微观结构特征形成 [12]、[13] 的核心。然而，由于熔池的小尺度（约以 1 毫米长度的 DED 进行焊接[14]、[15]、[16]），并在高温下进行焊接。在 AM 或激光焊接中，在某些材料体系中，可以添加硫和氧等表面活性剂来改变 Marangoni 流动。这在高硫不锈钢和氧化铝和钛粉中特别适用[8]、[17]、[18]、[19]、[20]、[21]、[22]、[23]。然而，这些表面活性剂会改变材料成分，并可能对性能产生不利影响[21]，从而导致操作期间失效。改变工艺参数也可以改变熔池流动行为，但也会影响焊道尺寸和其他因素，可能导致不希望的结果。例如，在某些条件下，增加能量密度会导致形成匙孔气孔[24]。目前正在寻求新的技术来控制熔池流动，而无需添加表面活性剂或改变工艺参数。

The application of external fields, including magnetic fields as a non-contact and contamination-free technique, has great potential for controlling the melt flow in AM. Previous work has largely used electric magnetic damping (EMD) or the Hartman effect to reduce melt pool flow rates [25], [26]. However, EMD is not the only magnetic field effect, as the Seebeck effect has also been observed during the related welding process. For instance, Paulini et al. [27] observed the beam deflection during the electron beam welding of dissimilar materials. In a separate study, Kern et al. [28] reported that the surface roughness of an Al weld bead can either be more smooth or rough, depending on the orientation of the applied magnetic field. In both cases, the observed effects were attributed to the Seebeck effect. The Seebeck effect induces thermoelectric currents (TECs) that are a function of the variations of the Seebeck coefficient (due to phase, temperature and compositional variations) and thermal gradient in the laser melt pool [29]. TECs interact with an external magnetic field, generating a Lorentz force that drives a new flow, known as thermoelectric magnetohydrodynamic (TEMHD) flow. TEMHD flow has been proven useful to control solute segregation [30], [31], [32], [33] and refine dendrite arm spacing [34], [35] in traditional casting and realising self-stirring for liquid lithium [36], [37].
本文介绍了磁场在控制增材制造熔池流动的潜力。先前研究主要利用电磁阻尼（EMD）或哈特曼效应来降低熔池流速[25]，[26]。然而，EMD 并非唯一的磁场效应，塞贝克效应也已在相关的焊接过程中观察到。例如，Paulini 等人 [27] 在异种材料电子束焊接过程中观察到了光束偏转。在另一项研究中，Kern 等人 [28] 报告说，铝焊缝表面的粗糙度可以根据所施加磁场的方位而变得更平滑或更粗糙。在这两种情况下，观察到的效应都归因于塞贝克效应。塞贝克效应会感应出热电电流 (TEC)，热电电流是塞贝克系数（因相、温度和成分变化而异）和激光熔池中热梯度的函数 [29]。热电偶与外磁场相互作用，产生洛伦兹力，驱动新的流动，称为热电磁流体动力学 (TEMHD) 流动。TEMHD 流动已被证明可用于控制传统铸造中的溶质偏析 [30]、[31]、[32]、[33] 和细化枝晶臂间距 [34]、[35]，以及实现液态锂的自搅拌 [36]、[37]。

Computational modelling has been conducted to predict TECs in both welding [29], [38], [39], [40] and LPBF [41], [42]. The strongest TECs are predicted near the solid/liquid boundary due to sharp variations in the Seebeck coefficient. In DED, TECs are expected to be concentrated at the bottom and back of the melt pool where the solid/liquid solidification interface causes large compositional and thermal gradients, and the Marangoni flow is weakest. Therefore, the TEMHD effect may be quite significant in these areas when a magnetic field is applied. However, to date, no experimental or modelling work for investigating the TEMHD effect in DED has been reported.
计算建模已用于预测焊接 [29]、[38]、[39]、[40] 和 LPBF [41]、[42] 中的 TEC。由于塞贝克系数的急剧变化，在固/液界面附近预测到最强的 TEC。在 DED 中，TEC 预计集中在熔池底部和背面，在这些地方，固/液凝固界面会导致大的成分和温度梯度，马朗戈尼流动最弱。因此，在这些区域施加磁场时，TEMHD 效应可能非常显着。然而，迄今为止，尚未报告关于研究 DED 中 TEMHD 效应的实验或建模工作。

Melt flow visualisation techniques are the key to understanding the mechanism of TEMHD control. Significant efforts have been placed to investigate the flow behaviour under TEMHD in welding and LPBF, but are largely restricted to computational modelling [38], [39], [40], [41], [42]. Recently, in situ synchrotron X-ray imaging has been applied in AM to directly observe the highly transient phenomena including keyhole dynamics [24], [43], [44], pore behaviour [12], and powder-melt interaction [45]. Although melt pool flow visualisation using tungsten tracers has been reported in previous work [8], [9], [10], [46], it remains unclear how the flow will change when applying a magnetic field. In this study, the authors developed a method/tool that combines the flow tracer technique, x-ray imagining, and a series of customised image processing techniques. This method allowed for a detailed investigation of melt pool flow information during the DED process when a magnetic field is present. Here, we applied a magnetic field (B) at multiple orientations, B//V (parallel to the scan velocity (V)) and B downward (parallel to the build direction), during DED of a high γ’ nickel superalloy powder blended with tungsten particles. We used a combination of in situ X-ray radiography and ex situ tomography to observe TEMHD flow in the melt pool. A series of experiments were designed and performed to reveal the structure of TEMHD flow during DED.
熔池流动可视化技术是理解 TEMHD 控制机制的关键。人们在焊接和 LPBF 中 TEMHD 下的流动行为研究方面做出了巨大努力，但这主要限于计算建模 [38]、[39]、[40]、[41]、[42]。最近，原位同步加速器 X 射线成像已被应用于增材制造，以直接观察包括匙孔动力学 [24]、[43]、[44]、孔隙行为 [12] 和粉末熔融相互作用 [45] 在内的瞬态现象。尽管先前的工作 [8]、[9]、[10]、[46] 中报道了使用钨示踪剂的熔池流动可视化，但当施加磁场时流动的变化情况仍不清楚。在本研究中，作者开发了一种结合流动示踪剂技术、x 射线成像和一系列自定义图像处理技术的方法/工具。该方法允许对 DED 过程中存在磁场时的熔池流动信息进行详细研究。 ## 本文采用磁场(B)，在多个方向进行 DED，B//V（平行于扫描速度(V)）和 B 向下（平行于构建方向），同时采用高γ’镍基高温合金粉末与钨颗粒混合。我们使用原位 X 射线射线照相和非原位层析成像相结合的方法来观察熔池中的 TEMHD 流动。设计并进行了一系列实验，以揭示 DED 过程中 TEMHD 流动的结构。

2. Materials and methods 2. 材料和方法

2.1. Materials 2.1 材料

The samples used were high γ’ nickel superalloy substrates and powders of the same composition (provided by Rolls-Royce plc.), as shown in Supplementary Table 1. For all the experiments, we used the same blended powder consisting of 4 wt% W particles mixed with the γ’ nickel superalloy power. Fig. 1 shows SEM images of the γ’ nickel superalloy and tungsten powders and their size distribution. According to our calculation (see supplementary), the addition of 4 wt% tungsten can provide 520 tungsten tracers within a melt pool. These tracers account for only 1.9 vol% of the total melt pool volume, suggesting that their presence is unlikely to have a significant impact on the flow. The substrates were cut into pieces of 70 × 20 × 1.5 mm by electro-discharge machining. The γ’ nickel superalloy powders were produced by gas atomisation with a spherical morphology. To prepare the blended power for the experiments, we followed a specific procedure. We started by placing the two types of powders in a 250 ml container. Then we repeatedly inverted the container for 15 mins to ensure that the powders were thoroughly mixed. Finally, we loaded the blended power into the powder feeder for use in the experiments.
所用样品为高γ’镍基超合金基板和相同成分的粉末（由劳斯莱斯公司提供），如补充表 1 所示。在所有实验中，我们使用由 4 wt%W 颗粒与γ’镍基超合金粉末混合而成的相同混合粉末。图 1 显示了γ’镍基超合金和钨粉末的 SEM 图像以及它们的尺寸分布。根据我们的计算（见补充材料），添加 4 wt%的钨可以在熔池内提供 520 个钨示踪剂。这些示踪剂仅占总熔池体积的 1.9%，这意味着它们的存在不太可能对流动产生显著影响。基板通过电火花加工切割成 70×20×1.5 mm 的样块。γ’镍基超合金粉末采用气雾化法制备，呈球形。为了制备用于实验的混合粉末，我们遵循了一个特定的程序。我们首先将两种粉末放入一个 250 毫升的容器中。然后，我们反复翻转容器 15 分钟，以确保粉末充分混合。最终，我们将混合后的粉末装入粉末进料器，用于实验。

2.2. DED rig 2.2. DED 平台

We built a custom DED rig, or Blown Powder AM Process Replicator, generation II (BAMPR-II), by integrating a Ytterbium-doped fibre laser (SPI Lasers Ltd, UK), a powder feeder (Oerlikon Metco TWIN-10-C), a three-axis motion stage (Aerotech, US), an Ar-filled environment chamber (Saffron, Scientific Equipment Ltd) and a DED nozzle (provided by Rolls-Royce plc.). The laser wavelength was 1070 nm and the maximum laser power was 200 W. The laser was operating in continuous-wave mode, providing a Gaussian beam profile and a laser spot size of 360 µm (1/e²) at the focus. DED experiments were conducted using a combination of three different laser powers (100 W, 160 W and 200 W) and three different magnet configurations (no B, B//V and B downward, as shown in Fig. 2). The laser is stationary with the sample stage moving at a constant speed (traverse speed) of 1 mm/s to build 8 mm long tracks for all trials. In the experiments without a magnetic field, the substrate was mounted on the sample holder without magnets. To provide the magnetic field, we used two cubic NdFeB permanent magnets, each measuring 40 × 40 × 20 mm. These magnets were positioned 2 mm below the deposition location, with a 5 mm gap between them. An aluminium holder was used to assemble the magnets. During the process, the laser remained stationary, while the substrate and magnet holder were connected and moved together, ensuring a steady magnetic field in the melt pool. In the B//V case, the magnets were placed in a holder with the south pole towards the scan direction, providing a magnetic field parallel to the scan direction (see Fig. 2c). To switch the magnetic field orientation, the magnets were turned by 90 degrees, which provided a downward magnetic field on the substrate top surface (see Fig. 2d). All the tracks were built three layers in the middle of the substrates, where the intensity of the magnetic field was 0.18–0.2 T, to ensure an even magnetic field and consistent conditions. Note that the magnetic field intensity at the deposition area was measured three times using a Gauss meter.
我们构建了一个定制的直接能量沉积装置，或称第二代喷粉增材制造工艺复制器 (BAMPR-II)，该装置集成了一个掺镱光纤激光器 (SPI Lasers Ltd, 英国)、一个粉末送料器 (Oerlikon Metco TWIN-10-C)、一个三轴运动平台 (Aerotech, 美国)、一个填充 Ar 的环境室 (Saffron, 科学设备有限公司) 和一个 DED 喷嘴 (由劳斯莱斯公司提供)。激光器波长为 1070 纳米，最大激光功率为 200 瓦。激光器工作在连续波模式下，提供高斯光束轮廓和 360 微米的激光光斑尺寸 (1/e ² )，位于焦点处。DED 实验使用三种不同的激光功率 (100 瓦、160 瓦和 200 瓦) 和三种不同的磁体配置进行 (无 B、B//V 和 B 向下，如图 2 所示)。激光器是静止的，样品平台以恒定的速度 (横向速度) 1 毫米/秒移动，为所有试验构建 8 毫米长的轨迹。在没有磁场的情况下进行的实验中，基板未安装磁体直接放在样品架上。为了提供磁场，我们使用了两个立方体的 NdFeB 永磁体，每个尺寸为 40 × 40 × 20 毫米。这些磁体位于沉积位置下方 2 毫米处，磁体之间间隙为 5 毫米。使用铝制支架组装磁体。在此过程中，激光保持静止，而基板和磁体支架连接并一起移动，确保熔池中稳定的磁场。在 B//V 情况下，磁体放置在支架中，南极指向扫描方向，提供平行于扫描方向的磁场（见图 2c）。为了切换磁场方向，将磁体旋转 90 度，从而在基板顶表面提供向下的磁场（见图 2d）。所有轨道都在基板中间构建了三层，磁场强度为 0.18–0.2 T，以确保均匀的磁场和一致的条件。请注意，沉积区域的磁场强度使用高斯计测量了三次。

2.3. In situ synchrotron X-ray imaging
2.3. 原位同步加速器 X 射线成像

In situ synchrotron X-ray imaging experiments were performed at beamline I12 of Diamond Light Source at Rutherford Appleton Laboratory, UK [47]. A monochromatic beam with an energy of 70 keV was used for all the experiments. X-rays transmitted through the sample while laser melting were converted to visible light using a scintillator and the images were acquired by a high-speed camera MIRO 310 M (Vision Research Inc.) at a frame rate of 5 kHz, exposure time of 198 µs, and a spatial resolution of 6.67 µm/pixel. Prior to laser melting, both flat and dark images were collected for flat field correction to remove the background artefacts, as described in our previous work [13], [48].
在英国卢瑟福德阿普尔顿实验室的钻石光源 I12 光束线进行原位同步加速器 X 射线成像实验 [47]。所有实验都使用能量为 70 keV 的单色光束。在激光熔化过程中，透过样品的 X 射线使用闪烁体转换为可见光，并由高速相机 MIRO 310 M (Vision Research Inc.) 以 5 kHz 的帧速率、198 µs 的曝光时间和 6.67 µm/pixel 的空间分辨率采集图像。在激光熔化之前，收集了平场图像和暗场图像以进行平场校正，以消除背景伪影，如我们在以前的工作中所述 [13]，[48]。

2.4. Ex situ X-ray computed tomography
2.4. 离体 X 射线计算机断层扫描

The as-built tracks were examined by a laboratory-based X-ray computed tomography system (Nikon XTek2DCT, Nikon, Japan) with an accelerating voltage of 220 kV, beam current of 31 µA and spatial resolution of 3.36 µm. The collected radiographs were reconstructed into a 16-bit image stack with a built-in reconstruction algorithm. Avizo 3D 2021.01 (Thermo Fisher Scientific, USA) was then used for W particle segmentation, quantitative analysis and 3D visualization.
使用实验室台式 X 射线计算机断层扫描系统（日本尼康 XTek2DCT，加速电压 220 kV，束流 31 µA，空间分辨率 3.36 µm）对实际铺设的轨道进行了检查。利用内置重建算法将收集的射线照片重建为 16 位图像。然后使用 Avizo 3D 2021.01（美国赛默飞世尔科技公司）进行 W 颗粒分割、定量分析和三维可视化。

2.5. Data analysis 2.5. 数据分析

2.5.1. Image processing of raw data
2.5.1 原始数据的图像处理

All the acquired raw radiographs were firstly processed using Matlab R2021a to remove the noise and background. Firstly flat-field correction was applied using the averaged flat and dark images collected during the experiments, after that, a denoise algorithm VBM4D [49] was used to mitigate the noise, followed by a further background subtraction process using a customised approach. Then the processed data with high contrast and low noise can be further analysed for extracting useful information, such as particle trajectories and velocities.
所有采集到的原始射线照片首先使用 Matlab R2021a 进行处理，以去除噪声和背景。首先，使用实验期间采集的平均平板和暗场图像进行平板场校正，之后，使用去噪算法 VBM4D[49]来降低噪声，然后使用定制方法进行进一步的背景减除处理。然后，可以对具有高对比度和低噪声的处理数据进行进一步分析，以提取有用信息，例如粒子的轨迹和速度。

2.5.2. Tungsten particle tracking
2.5.2. 钨粒子追踪

Prior to tracking, the radiographs were integrated through the duration of the experiment to enable the visualisation of the W particle trajectories. The time-integrated radiographs were obtained by overlaying the particles in successive frames onto one plane. Then the particles are tracked using TrackMate [50] in ImageJ. A particle tracking example is shown in Movie S1. It is worth noting that small particles are likely to reliably trace flow, as the motion of large particles is potentially influenced by the TECs inside the particles when applying a magnetic field. The critical particle size that separates the as-classified small and large particles were found to be 55–65 µm (See Supplementary Fig. 1). Therefore, here only small particles with a size less than 65 µm were considered for understating the melt pool flow behaviour.
在追踪之前，射线照片在整个实验过程中集成在一起，以实现对 W 粒子轨迹的可视化。通过将连续帧中的粒子叠加到一个平面上获得时间积分射线照片。然后使用 TrackMate [50] 在 ImageJ 中跟踪粒子。粒子跟踪示例在 Movie S1 中显示。值得注意的是，小粒子很可能可靠地追踪流动，因为当施加磁场时，大粒子的运动可能会受到粒子内部的 TEC 的影响。区分已分类小粒子和大分子的临界粒径被发现为 55-65 µm（见补充图 1）。因此，这里只考虑小于 65 µm 的小粒子，以了解熔池流动行为。

3. Results 3. 结果

3.1. DED melt pool flow
3.1. DED 熔池流动

The flow conditions with no applied magnetic field were studied first, captured using in situ synchrotron radiography while depositing single DED tracks using three different laser powers. The radiographs of the melt pool were then integrated over the duration of each deposit to visualise the flow of W particles (Fig. 3a-b). Fig. 3b-d highlight typical particle trajectories as the power is increased from 100 to 200 W. In all cases the particles (and hence flow) move slowly up the centre of the pool (50–120 mm/s), reaching the surface. They then turn outwards, accelerating outwards along the surface driven by Marangoni convection. The peak particle velocity occurs at the melt pool surface in all cases, increasing with increasing laser power (peak velocity of ca. 220 mm/s, 280 mm/s, and 310 mm/s at 100, 160, and 200 W, respectively, see Fig. 3e). The particles then slow (velocity of 20–50 mm/s) as the flow reaches the outer solid/liquid boundary, turning downwards, forming a recirculating flow.
在没有施加磁场的情况下首先研究了流动条件，利用原位同步加速器射线照相术捕获，同时使用三种不同的激光功率沉积单 DED 轨道。然后将熔池的射线照片在每个沉积的持续时间内进行积分，以可视化 W 颗粒的流动（图 3a-b）。图 3b-d 突出显示了在功率从 100 瓦增加到 200 瓦时的典型颗粒轨迹。在所有情况下，颗粒（因此流动）缓慢向上移动到熔池的中心 (50-120 毫米/秒)，到达表面。然后，它们向外转动，受马朗哥尼对流驱动在表面加速向外。在所有情况下，峰值颗粒速度出现在熔池表面，并随着激光功率的增加而增加（在 100、160 和 200 瓦时，峰值速度分别约为 220 毫米/秒、280 毫米/秒和 310 毫米/秒，见图 3e）。然后，当流动到达外固液边界时，颗粒减速（速度为 20-50 毫米/秒），向下转动，形成再循环流动。

3.2. DED melt pool flow under external magnetic field
3.2 DED 熔池流动受外部磁场的影响

Here, we selected an exemplary case (laser power P = 100 W, laser scan speed V = 1 mm/s) to compare the melt flow behaviour without and with magnetic fields. Without an external magnetic field, the particle velocity at the surface exceeds 200 mm/s (due to Marangoni flow, see Fig. 3e), as described above, the particles turn downwards as they near the edge of the pool surface, turning downwards into the pool. The particles decelerate as they approach the bottom of the melt pool, reaching a minimum speed of 20–50 mm/s before turning direction and recirculating back up in the middle of the pool towards the surface (see Fig. 4a, b and Movie S2). Of those particles in the back half of the pool, some are entrained in the solidification front, and are relatively evenly distributed in the new solidified track, as shown in the pink box in Fig. 4a.
在此，我们选取了一个示例案例（激光功率 P = 100 W，激光扫描速度 V = 1 mm/s）来比较有无磁场时的熔融流动行为。在没有外磁场的情况下，由于表面张力流动（见图 3e），表面处的粒子速度超过 200 毫米/秒，如上所述，粒子在接近熔池表面的边缘时向下转动，向下进入熔池内部。粒子在接近熔池底部时减速，在改变方向并在熔池中间向上循环回表面之前，其速度降至 20-50 毫米/秒（见图 4a、b 和电影 S2）。在熔池后半部分的颗粒中，一些被卷入凝固界面，相对均匀地分布在新凝固的轨道中，如图 4a 中的粉红色方框所示。

When a magnetic field is applied, the peak particle velocity at the surface of the pool is similar to that without a magnetic field, reaching ca. 200 mm/s. However, as the particles move towards the bottom of the pool, a TEMHD flow becomes dominant. In the B//V case, particles velocities were found to be reduced to 1–2 mm/s as they approached the bottom, with the particle trajectories along the front of the pool all heading downwards, even in the middle of the pool where previous the flow was strongly upwards. Almost all are captured at the pool bottom (Fig. 4c, d and Movie S3), forming a layer separating the new track from the prior ones. This observation can be attributed to the introduction of a Lorentz force. Near the bottom of the melt pool, the upward Lorentz force counteracts the downward Marangoni flow, leading to a stagnant flow in this region. As a result, particles tend to sink at a slow speed. The origin of this Lorentz force will be introduced in the discussion section.
当施加磁场时，熔池表面的峰值粒子速度与无磁场时相似，达到约 200 毫米/秒。然而，当粒子向熔池底部移动时，TEMHD 流动将占主导地位。在 B//V 情况下，当粒子接近底部时，粒子速度降低到 1-2 毫米/秒，粒子轨迹沿着熔池的前部向下倾斜，即使在熔池中部，先前流动强劲地向上。几乎所有粒子都被捕获在熔池底部（图 4c、d 和电影 S3），形成了一个将新轨道与先前轨道分隔开的层。这种现象可以归因于洛伦兹力的引入。在熔池底部附近，向上的洛伦兹力抵消了向下的马朗哥尼流动，导致该区域出现停滞流动。因此，粒子倾向于以缓慢的速度下沉。洛伦兹力的起源将在讨论部分介绍。

For the case where a downward magnetic field was applied, the particles even in the rear of the pool are turned and driven almost horizontally into the rear solid/liquid interface where they are entrained. The particles are entrained at a range of heights in the pool, although the majority are in the lower half (see Fig. 4e, f and Movie S4). These observations strongly support the hypothesis that the flow in the melt pool is altered when applying a magnetic field, and the effect depends on the magnetic field orientations.
当施加向下磁场时，即使池后部的颗粒也会翻转并几乎水平地被驱赶到后部的固液界面，在那里它们被夹带。颗粒在池中的不同高度被夹带，尽管大多数在较低的一半 (见图 4e、f 和电影 S4)。这些观察结果强烈支持以下假设，即施加磁场时熔池中的流动会发生改变，并且这种影响取决于磁场方向。

Radiography is restricted to a longitudinal plane projection and does not provide information about flow in the cross-sectional plane (in/out of the page). Therefore, we used X-ray computed tomography to observe the effects of applied magnetic fields on the final particle locations inside the built samples. The reconstructed 3D as-built tracks with W particles embedded are shown in Supplementary Fig. 2. By overlaying particles onto one cross-sectional plane, the overall distribution of the W particles in the entire track can be visualised (see Supplementary Fig. 3).
放射照相仅限于纵向平面投影，无法提供横截面平面（页面内外）流动信息。因此，我们使用 X 射线计算机断层扫描来观察施加的磁场对构建样品内部最终粒子位置的影响。嵌入 W 粒子的重建 3D 实测轨迹如图 2 所示。通过将粒子叠加到一个横截面上，可以可视化 W 粒子在整个轨迹中的总体分布（见补充图 3）。

Fig. 5a shows that the particles are evenly distributed in the solidified tracks in the horizontal projection plane when no magnetic field is applied, matching the even longitudinal distribution in all three laser powers (Fig. 6a-c). In general, particles tend to segregate equally to the two sides of the melt pool due to Marangoni flow. However, the extent of such segregation depends on various factors, including material properties, process parameters, and particle number density. Based on the material, and the process parameters used in this study, along with the small number of tracer particles, we observed a relatively even distribution of particles. However, it’s worth noting that a valley is distinguishable in Fig. 7 g, indicating very weak particle segregation in the no B case. We believe for increased particle number densities, the particle segregation into two sides will become more obvious. However, we added a small number of particles to minimise their influence on the flow whilst observing the effect of the magnetic field on flow. Applying a magnetic field orientated in the laser scan direction (the B//V case) disrupts this even distribution. In addition to segregating the particles to the bottom of the pool (as per Fig. 4c and Fig. 6d-f), the external magnetic field also drove them to one side of the track (see Fig. 5b). To make the description clear, the melt pool was divided into two halves, i.e., Left (L) and Right (R) halves corresponding to looking along the scan direction (see Fig. 5a, f). In the B//V case, the location of particles segregation is the L half of track for all three laser powers (see Fig. 5b and Supplementary Fig. 4c, d). Prior authors [26], [51], [52], [53], [54] have suggested the electromagnetic dampening effect (EMD) is the cause, but this force only reduces the magnitude, not the direction. Therefore, it will not alter the segregation pattern and cannot explain our experimental results. Our hypothesis is that a TEMHD flow is introduced by the magnetic field as a result of the Seebeck effect that induces Thermoelectric currents (TECs), causing asymmetric particle segregation. In the B//V case, the newly introduced TEMHD flow in the left half of the melt pool is in the opposite direction of the Marangoni flow, causing stagnation of flow. As a result, particles settle in this region due to their heavier weight compared to the melt. This process is highlighted in the schematic shown in Fig. 5 g. The TEMHD flow in the right half enhances the transportation of hot liquid down to the bottom, modifying the melt pool shape. As a result, a deeper melt pool (ca. 535 µm in depth) was produced in the B//V case compared to no magnetic field (ca. 454 µm) and B downward cases (ca. 442 µm) (see Fig. 7a-c).
图 5a 显示，没有磁场施加时，粒子在凝固轨迹的水平投影平面内均匀分布，与所有三种激光功率下的均匀纵向分布相匹配（图 6a-c）。一般而言，由于马朗戈尼流动，粒子倾向于均匀地分离到熔池的两侧。然而，这种分离的程度取决于各种因素，包括材料特性、工艺参数和粒子数量密度。基于本研究中使用的材料、工艺参数以及少量的示踪粒子，我们观察到粒子相对均匀的分布。然而，值得注意的是，图 7 g 中可区分一个谷，这表明在无 B 情况下存在非常微弱的粒子偏析。我们认为，对于增加的粒子数量密度，粒子到两侧的偏析将变得更加明显。然而，我们添加了少量粒子以尽量减少它们对流动的影响，同时观察磁场对流动的影响。在激光扫描方向（B//V 案例）定向施加磁场，会破坏这种均匀分布。除了将颗粒沉降到熔池底部（如图 4c 和图 6d-f 所示），外磁场还将它们驱赶到熔道的某一侧（见图 5b）。为便于描述，将熔池沿扫描方向观察分成左右两半，即左（L）和右（R）两侧（见图 5a、f）。在 B//V 情况下，无论激光功率如何，颗粒偏析的位置都在熔道的左侧（见图 5b 和补充图 4c、d）。先前学者[26]、[51]、[52]、[53]、[54]提出电磁阻尼效应（EMD）是造成这种现象的原因，但这种力只减小了偏析的程度，并没有改变偏析方向。因此，它并不会改变偏析模式，也无法解释我们的实验结果。我们的假设是，磁场通过塞贝克效应产生的热电电流（TECs）引入了横向磁流体动力学流动（TEMHD），导致了非对称的颗粒偏析。在 B//V 情况下，熔池左半部分新引入的 TEMHD 流动与马朗欧尼流动方向相反，导致流动停滞。熔池底部温度（图 7d）也存在类似的趋势。

For the B downward case, a TEMHD flow is produced in the horizontal plane, driving particles across the solidification front (see Fig. 5 h). In this case, the final location where the particles segregate to is strongly dependent on the melt pool size, which is controlled by the laser power. For a laser power of 100 W, the melt pool is small (ca. 1 mm in length), most particles segregate to the R half of the track (Fig. 5c). Whereas with 200 W laser power, the melt pool length almost doubles to ca. 2 mm, and more particles remain in the L half (Fig. 5e). With an intermediate laser power (160 W), particles are equally segregate to both halves of the track (see Fig. 5d). This observation can be understood through the balance between Marangoni and TEMHD flows. In the right half, the Marangoni flow has a component in the negative

\hat{y}

direction, whereas in the left half, it is in the positive

\hat{y}

direction. The TEMHD-induced flow circulates from right to left near the melt pool boundary (Fig. 5 h), which means that in both the right and left half of the melt pool, TEMHD flow has a component in the positive

\hat{y}

direction. Increasing the laser power mainly increases the thermal gradient within the melt pool. Although both Marangoni stress and TE Lorentz force increase with the thermal gradient, the TE Lorentz force increases faster than Marangoni stress in the region near the melt pool boundary. At a laser power of 100 W, the Marangoni flow and TEMHD flow are of similar intensity in the

\hat{y}

direction, leading to flow stagnation in the right half. In the left half, both the Marangoni and TEMHD flows in the

\hat{y}

direction are positive, resulting in enhanced flow in this region. As a result, more particles can be captured by the solid/liquid interface in the right half. However, particles can escape more easily from the left half. When the laser power is increased to 200 W, in the right half near the boundary region, TEMHD flow overtakes Marangoni flow in the

\hat{y}

direction, leading to increased flow intensity in the positive

\hat{y}

direction and more particles escaping from this region. In contrast, in the left half, although both Marangoni and TEMHD flows intensify in the positive

\hat{y}

direction, TEMHD flow transports more particles to the left half, increasing the particle concentration in the left half hence the chance of being captured by the solidification front. Thereby, more particles are segregated to the left half. When the applied laser power is 160 W, the contribution from flow stagnation and TEMHD transporting particles are balanced, leading to a relatively equal distribution of particles in the two halves of the melt pool.
为了 B 向下案例，在水平面上产生 TEMHD 流动，驱动颗粒穿过凝固前沿（见图 5 h）。在这种情况下，颗粒最终偏析的位置与熔池尺寸密切相关，而熔池尺寸受激光功率控制。对于 100 W 的激光功率，熔池较小（长度约为 1 毫米），大多数颗粒偏析到轨道的 R 半部（图 5c）。而对于 200 W 的激光功率，熔池长度几乎增加一倍，达到约 2 毫米，更多的颗粒留在 L 半部（图 5e）。使用中间激光功率（160 W），颗粒会均匀地偏析到轨道的两半（见图 5d）。这种观察结果可以通过马朗戈尼流动和 TEMHD 流动之间的平衡来理解。在右半部分，马朗戈尼流动具有负

\hat{y}

方向的分量，而在左半部分，它具有正

\hat{y}

方向的分量。TEMHD 诱导的流动在熔池边界附近从右到左循环（图 5 h），这意味着在熔池的右半部分和左半部分，TEMHD 流动都具有正

\hat{y}

方向的分量。随着激光功率的增加，熔池内的热梯度主要增加。虽然马朗戈尼应力和 TE 洛伦兹力都会随着热梯度增加，但 TE 洛伦兹力在靠近熔池边界区域的增加速度快于马朗戈尼应力。在 100 W 的激光功率下，马朗戈尼流动和 TEMHD 流动在

\hat{y}

方向上的强度相似，导致右半部分的流动停滞。在左半部分，马朗戈尼流动和 TEMHD 流动在

\hat{y}

方向上都是正的，导致该区域的流动增强。因此，更多颗粒可以被右半部分的固液界面捕获。然而，颗粒更容易从左半部分逃逸。当激光功率增加到 200 W 时，在边界区域附近的右半部分，TEMHD 流动在

\hat{y}

方向上超过马朗戈尼流动，导致在

\hat{y}

方向上的流动强度增加，更多的颗粒从这个区域逃逸。相比之下，在左侧，虽然马朗戈尼和 TEMHD 流动都朝着正

\hat{y}

方向增强，但 TEMHD 流动会将更多粒子输送到左侧，增加左侧的粒子浓度，从而增加被凝固前沿捕获的机会。因此，更多粒子被隔离到左侧。当施加的激光功率为 160 W 时，来自流动停滞和 TEMHD 输送粒子的贡献是平衡的，导致熔池两个半部分的粒子分布相对均匀。

Fig. 8 shows the comparison of the grain structure of the as-printed tracks on the cross-sectional plane for the three conditions. The results show that applying a magnetic field can alter the central grain structure on the cross-section. The average central grain size in the no B case is 87 µm, and it is reduced to 68 µm in the B//V case and 75 µm in the B downward case. In addition, in the B//V case, there are thin and elongated grains appearing at the bottom of the melt pool, while in the B downward case, the thin and elongated grains are spread more widely from the bottom to near the surface. This observation can be attributed to the influence of the TEMHD flow. A previous study has demonstrated that increasing flow speed leads to an increase in the size of constitutional undercooling zone, as fast flow draws more solute from the mushy zone to the dendrite tip [11]. The increase in the undercooling zone promotes the nucleation rate and favours the transition from nuclei to grains. In the B//V case, the newly introduced TEMHD flow circulates on the cross-sectional plane at a location near the bottom of the melt pool. This flow increases the size of undercooling zone at the bottom hence an increase in the nucleation rate. In the horizontal dimension, grain growth is restricted by the neighbouring grains, as the increased number of new grains causes less space for each grain to grow in this dimension. In the vertical direction, the grain has more space to grow, resulting in the formation of thin and elongated grains at the bottom (Fig. 8b). For the B downward case, the magnetic field interacts with the TECs located at the wide height range of the rear of the melt pool. The resulting TEMHD flow circulates on the horizontal plane, impacting the rear of the melt pool. More grains form in front of the rear melt pool boundary in a wide height range, which leads to the appearance of thin elongated grains in a wide range of height on the central cross-section plane (Fig. 8c).
图 8 显示了三种情况下横截面上打印道晶粒组织的对比。结果表明，施加磁场可以改变横截面上的中心晶粒组织。无 B 情况下中心晶粒尺寸平均为 87 µm，B//V 情况下减少至 68 µm，B 向下情况下减少至 75 µm。此外，在 B//V 情况下，熔池底部出现细长的晶粒，而在 B 向下情况下，细长的晶粒从底部更广泛地扩展到靠近表面。这种现象可归因于 TEMHD 流动的影响。先前研究表明，流速增加会导致结构性过冷区尺寸增大，因为快速流动会从糊区向枝晶顶端吸引更多溶质 [11]。过冷区的增加促进了形核率，有利于形核向晶粒的转变。在 B//V 情况下，新引入的 TEMHD 流动在熔池底部附近的横截面上循环。这种流动增加了底部过冷区的尺寸，从而提高了形核率。在水平方向，由于新晶粒数量的增加导致每个晶粒在该方向的生长空间更小，因此晶粒生长受到相邻晶粒的限制。在垂直方向，晶粒有更多的生长空间，导致底部形成细长晶粒（图 8b）。在下 B 情况下，磁场与位于熔池后部大高度范围的 TEC 相互作用。由此产生的 TEMHD 流在水平面上循环，影响熔池后部。更多晶粒在后部熔池边界前部的大高度范围内形成，导致在中心横截面平面的大高度范围内出现细长晶粒（图 8c）。

To summarise, without a magnetic field the particles are relatively evenly distributed for all conditions. However, for both cases of an applied magnetic field, the particles are segregated, with the extent of segregation depending on laser power for the B downward case. For the B//V case the particles sink to the very bottom of the pool and are entrained there. While for the B downward case, the particles sink slightly to the lower half of the pool. Further, based on our observations, we have found that flow near the melt pool boundary is most affected by the TEMHD effect. Specifically, the rear and bottom boundaries where solidification occurs experience significant flow alternation when applying a magnetic field – a location likely to affect microstructural formation. Moreover, the flow in this area determines how particles (and probably pores) are entrained by the solid. Hence this impacts on the particle segregation pattern in the build, which indicates the regional flow pattern. However, flow at the melt pool surface is still Marangoni stress controlled.
总结而言，在没有磁场的情况下，无论何种条件，粒子都相对均匀地分布。然而，对于两种情况的施加磁场，粒子都会被隔离，隔离程度取决于 B 向下的情况下的激光功率。对于 B//V 的情况，粒子会沉到底部并被困在那里。而对于 B 向下的情况，粒子会略微下沉到泳池的下半部分。此外，根据我们的观察，我们发现熔池边界附近的流动受 TEMHD 效应的影响最大。具体来说，当施加磁场时，发生凝固的尾部和底部边界会经历显著的流动变化——这个位置很可能影响微观结构的形成。此外，该区域的流动决定了固体如何夹带粒子（可能还有孔隙）。因此，这会影响构建中的粒子偏析模式，这表明了区域流动模式。然而，熔池表面的流动仍然受马朗戈尼应力控制。

4. Discussion 4. 讨论

Thermal electric currents (TECs) arise as a result of the Seebeck effect when there is a gradient in the Seebeck coefficient and temperature. TECs are generated by the term

σ S \nabla T

(

J_{E}

) in Ohm’s law for current density

J = σ (E + u \times B + S \nabla T

), where

E

is the electric field,

u

is the flow velocity,

B

is the magnetic field flux density,

σ

is electric conductivity,

S

is the gradient in Seebeck coefficient or Seebeck powder and

\nabla T

is the thermal gradient. This is used in thermocouples where two dissimilar materials and temperature differences are required to generate the thermoelectric field. In the AM melt pool, the presence of liquid and solid phases, as well as a temperature/composition gradient satisfies all the requirements for generating TECs. TECs are expected to circulate from the hot melt front to the cold solidification front in the solid phase, and the opposite-direction currents form in the liquid phase to preserve charge conservation, as shown in Fig. 9a. Large TECs are expected in the melt pool due to the large thermal gradient. For example, Kern et al. [28] measured 8–14 A currents density during laser welding of aluminium alloy. Simulation studies pointed out that TECs are concentrated to the vicinity of the solid/liquid boundary due to the sharp variation of the Seebeck coefficient across the solid/liquid boundary [38], [39], [40].
热电电流（TEC）是由于塞贝克效应在塞贝克系数和温度梯度存在时产生的。TEC 由欧姆定律中电流密度

J = σ (E + u \times B + S \nabla T

) 的

σ S \nabla T

项（

J_{E}

）产生，其中

E

是电场，

u

是流速，

B

是磁通密度，

σ

是电导率，

S

是塞贝克系数或塞贝克粉末的梯度，

\nabla T

是热梯度。这被用于热电偶，其中需要两种不同材料和温差才能产生热电场。在 AM 熔池中，液相和固相的存在以及温度/成分梯度满足了产生 TEC 的所有要求。预计 TEC 将从熔池前沿的热端循环到固相中的冷凝固前沿，而反向电流将形成在液体中以保持电荷守恒，如图 9a 所示。由于大的热梯度，预计在熔池中会产生大的 TEC。例如，Kern 等人 [28] 在铝合金激光焊接过程中测得 8-14 A 的电流密度。数值模拟研究表明，由于塞贝克系数在固液界面附近急剧变化，TECs 主要集中在固液界面附近 [38]、[39]、[40]。

In these DED experiments the two side walls of the melt pool are in contact with non-conducting gas (see Fig. 2a), which would restrict electric current circulations out of the side of the melt pool (

\hat{y}

direction) i.e., electric currents do not circulate between the liquid and gas. Therefore, the primary TECs are circulating in the longitudinal plane (

xz

plane), and symmetrically distributed in the cross-sectional (see Fig. 9b) and horizontal planes (see Fig. 9c) without the

\hat{y}

component of the current, and TECs are expected to be concentrated along the base and back of the melt pool as the solid/liquid boundary locates in these areas. With an applied magnetic field orientated in

+ \hat{x}

(i.e., B//V case), a TE Lorentz force is generated in the form of

F_{lorentz} = J_{E} \times B

, and induces a new flow that circulates in the cross-sectional plane (i.e.,

yz

plane) close to the base of the melt pool, as shown in Fig. 9d. For the case of downward magnetic field, a TE Lorentz force is created in the horizontal plane (i.e.,

xy

plane) and drives a recirculating flow in this plane near the back of the melt pool, as shown in Fig. 9e. Fig. 9 f and g show the melt pool flows in 3D to the two applied magnetic fields. The TEMHD flows are created and circulating in the two orthogonal planes (i.e.,

yz

and

xy

planes) when applying magnetic fields with different orientations. It is worth noting that for the B downward case TEMHD flow drags particles towards the front of the melt pool (Fig. 10a) in one half and towards the rear (Fig. 10b) in the other half, as was captured radiographically. However, due to the projection nature of the radiograph, we cannot directly determine which half part of the melt pool the particle is in. But, we can make deductions based on our proposed hypothesis that in the B downward case, in the

\hat{x}

direction, the TEMHD flow in one half points towards the rear of the melt pool while in the other half, it is directed towards the front of the melt pool, as illustrated in Fig. 9 g Therefore, by observing the horizontal direction of particle movement, we can deduce which half of the melt pool the particle is in. if the particle moves towards the front, it is in the left half, whereas if it moves towards the rear, it is in the right of the melt pool.
在这些 DED 实验中，熔池的两个侧壁与非导电气体接触（见图 2a），这将限制电流在熔池侧面（

\hat{y}

方向）的环流，即电流不会在液体和气体之间环流。因此，主要的 TEC 在纵向平面（

xz

平面）内循环，并在横截面（见图 9b）和水平面（见图 9c）上对称分布，没有电流的

\hat{y}

分量，预计 TEC 将集中在熔池的底部和背部，因为固液界面位于这些区域。在

+ \hat{x}

方向的施加磁场（即 B//V 情况）下，会产生

F_{lorentz} = J_{E} \times B

形式的 TE 洛伦兹力，并诱导一个新的流动，该流动在横截面（即

yz

平面）内循环，靠近熔池的底部，如图 9d 所示。对于向下磁场的情况，在水平面（即

xy

平面）内产生 TE 洛伦兹力，并在图 9e 所示的熔池背部附近驱动该平面内的再循环流动。图 9。 9. f and g 图展示了在两种外加磁场作用下熔池三维流动情况。当外加不同方向的磁场时，TEMHD 流动产生并在两个正交平面（即

yz

和

xy

平面）循环流动。值得注意的是，对于 B 向下的情况，TEMHD 流动将颗粒向熔池的前部（图 10a）拖动一半，向后部（图 10b）拖动另一半，这与射线照相结果相符。但是，由于射线照相的投影性质，我们不能直接确定熔池的哪一半包含粒子。但是，我们可以根据我们的假设进行推断，即在 B 向下的情况下，在

\hat{x}

方向，TEMHD 流动一半指向熔池后部，另一半指向熔池前部，如图 9 g 所示。因此，通过观察颗粒运动的水平方向，我们可以推断颗粒位于熔池的哪一半。如果颗粒向前方移动，则位于熔池的左侧；如果颗粒向后方移动，则位于熔池的右侧。

Our in situ synchrotron radiography and ex situ tomography results strongly support our hypothesis that TEMHD flow is a key force during DED when a magnetic field is applied, strongly impacting the flow in the melt pool and hence final microstructural feature formation. However, these results are not limited to DED, the methodology can be applied to the broader field of laser materials processing, such as laser welding and LPBF where TECs will also exist, with some necessary considerations. Melt pool solid/liquid boundary locations, that witness significant variation of Seebeck coefficient, is the first factor to consider. In DED, solid/liquid boundary forms at the base and back of the melt pool. However, in LPBF and laser welding, there is a solid/liquid boundary surrounding the melt pool (as the two side walls of the melt pool are in contact with the solid), except for the top surface. We speculate that the TECs also exist in the regions close to the two side walls, which could lead to different TEMHD flow patterns when applying a magnetic field. Previous TEMHD flow simulation work [41] in LPBF with conduction mode predicted the horizontal TEMHD flow circulations in the upward magnetic field case and a vertical TEMHD circulation in the B//V case. This prediction matches our proposed TEMHD flow in Fig. 9 f, g which is derived based on DED experimental data. But in the simulation of LPBF, there is also TEMHD flow located in the regions close to the two side walls [41]. This is not reflected in these DED experiments as the tracks are only a single melt pool thick and the side walls are in contact with the non-conducting atmosphere.
我们的原位同步加速器射线照相和非原位断层扫描结果有力地支持了我们的假设，即 DED 过程中在施加磁场时，TEMHD 流动是一股关键力量，强烈地影响熔池中的流动，进而影响最终的微观结构特征形成。然而，这些结果并不局限于 DED，该方法可以应用于更广泛的激光材料加工领域，如激光焊接和 LPBF，其中也存在 TEC，但需要一些必要的考虑。熔池固/液边界位置是第一个需要考虑的因素，该位置见证了塞贝克系数的显著变化。在 DED 中，固/液边界形成于熔池的底部和背面。然而，在 LPBF 和激光焊接中，固/液边界包围着熔池（因为熔池的两侧壁与固体接触），除了顶表面。我们推测，TEC 也存在于靠近两侧壁的区域，这可能导致在施加磁场时产生不同的 TEMHD 流动模式。前期的 TEMHD 流动模拟工作 [41] 在 LPBF 传导模式下预测了向上磁场情况下水平 TEMHD 流动环流，以及 B//V 情况下垂直 TEMHD 环流。这一预测与我们根据 DED 实验数据推导的图 9 f, g 中提出的 TEMHD 流动相符。但在 LPBF 的模拟中，还存在于靠近两侧壁附近的区域的 TEMHD 流动 [41]。这在 DED 实验中没有体现，因为轨道只有一个熔池厚，侧壁与非导电大气接触。

Process parameters are the second factor to consider. Faster scanning speeds and smaller laser spot sizes in LPBF produce higher thermal gradients. The thermal gradient in the melt pool front in LPBF is much higher than in the other areas, as a result, we expect

\hat{x}

-direction (laser scan direction) TECs to be dominant. Unlike in DED where the three orthogonal components of TECs are in the close magnitude, resulting in the similar intensity of the three orthogonal magnetic fields required to alter the existing flow, in LPBF under conduction mode the intensity of the magnetic field required for TEMHD control is highly magnetic field orientation dependent. The previous simulation results [41] show that

\hat{x}

-direction TECs are dominant in LPBF, and the TEMHD flow is weak when B//V and significant as B is perpendicular to V given the same magnetic field strength.
工艺参数是需要考虑的第二个因素。LPBF 中更快的扫描速度和更小的激光光斑尺寸会产生更高的热梯度。LPBF 中熔池前沿的热梯度远高于其他区域，因此，我们期望

\hat{x}

方向（激光扫描方向）TECs 占主导地位。与 DED 中三个正交分量的 TECs 大小接近，导致改变现有流动所需的三个正交磁场的强度相似不同，在传导模式下的 LPBF 中，用于 TEMHD 控制的磁场强度高度依赖于磁场方向。先前的模拟结果[41]表明，LPBF 中

\hat{x}

方向 TECs 占主导地位，当 B//V 时 TEMHD 流动较弱，而当 B 垂直于 V 时，在相同磁场强度下 TEMHD 流动显著。

Alloy composition design is also critical to best utilise the TEMHD effect. Alloy composition determines material thermophysical properties, for example, a previous study [55] found that copper results in high constitutional supercooling and promotes columnar to equiaxed transition (CET) in an AM-fabricated Ti alloy. Here we would anticipate that silicon, a semiconductor element prone to having a high Seebeck coefficient, is a highly appropriate alloying addition to boost the TEMHD effect, although the influence will vary depending on the full alloy composition and processing conditions. For example, a previous study shows that silicon content can be tailored to increase or decrease the TEMHD effect during the directional solidification of aluminium alloy [30]. Investigating the effect of silicon content on the TEMHD effect is crucial for promoting the TEMHD-AM alloy design. Apart from the composition, the presence of a secondary phase with significantly different physical properties compared to the matrix can also impact the TECs distribution. For example, in high γ’ nickel superalloys (over 0.6 γ’ volume fraction [56]), the γ’ phase is intermetallic and likely to have a higher Seebeck coefficient but lower electric conductivity than the matrix, causing a higher thermoelectric field and the increased TEMHD flow in the liquid. Therefore, a high γ’ nickel superalloy is deemed as an appropriate alloy for TEMHD control. Further, the TEMHD control might be challenging with ferromagnetic powders as they would be attracted to external magnets. These insights highlight the importance of alloy composition optimisation and material selection for using TEMHD control in AM. In summary, TEMHD flow can circulate in different locations, depending on the orientation of the applied magnetic field. We hypothesise that the application of a constant magnetic field could improve the printability of some alloys, while the application of period magnetic fields could disrupt epitaxial growth. The application of a constant field might be particularly useful when printing high constitutional undercooling alloys, such as Ti-Cu alloy [55]. By applying a magnetic field perpendicular to both the scan and build directions, and based on the distribution of TECs, a TEMHD flow can be produced, circulating on the

xz

plane and sweeping down the solute from the rear melt pool boundary to the bottom. This would increase constitutional undercooling at the bottom and promote the nucleation rate, with the bottom part expected to have more refined equiaxed grains. For the application of a period magnetic field, this could significantly change the flow field for a period of time, altering the thermal gradient and solidification rate at the solid-liquid interface, disrupting the microstructure, potentially altering epitaxial growth.
合金成分的设计对于充分利用 TEMHD 效应也至关重要。合金成分决定了材料的热物理性质，例如，先前的一项研究 [55] 发现铜会导致高成分过冷并促进增材制造的 Ti 合金中的柱状等轴晶转变 (CET)。这里我们预计，作为一种半导体元素，易于具有高塞贝克系数的硅是一种非常合适的合金化添加剂，可以增强 TEMHD 效应，尽管其影响将取决于完整的合金成分和加工条件。例如，先前的研究表明，在铝合金的定向凝固过程中，可以调整硅含量来增加或减少 TEMHD 效应 [30]。研究硅含量对 TEMHD 效应的影响对于促进 TEMHD-AM 合金设计至关重要。除了成分外，与基体相比具有明显不同物理性质的第二相的存在也会影响 TECs 的分布。例如，在高 γ’ 镍基高温合金（γ’ 相体积分数超过 0.6 [56]）中，γ’ 相是金属间化合物，可能比基体具有更高的塞贝克系数，但电导率更低，导致更高的热电场和液态金属中的 TEMHD 流量增加。因此，高 γ’ 镍基高温合金被认为是 TEMHD 控制的合适合金。此外，由于铁磁性粉末会被外部磁铁吸引，因此使用 TEMHD 控制可能具有挑战性。这些见解突出了合金成分优化和材料选择对在 AM 中使用 TEMHD 控制的重要性。总之，TEMHD 流动可以在不同位置循环，具体取决于施加磁场的方向。我们假设，恒定磁场的应用可以提高某些合金的可打印性，而周期磁场的应用可以破坏外延生长。恒定磁场的应用在打印高成分过冷合金时可能特别有用，例如 Ti-Cu 合金 [55]。通过垂直于扫描和构建方向的磁场，并根据 TEC 的分布，可以产生 TEMHD 流，在

xz

平面上循环并在溶质从后熔池边界向下扫到底部。这将增加底部的成分过冷并提高形核速率，预计底部将具有更细化的等轴晶粒。对于周期性磁场的应用，这会显着改变一段时间内的流场，改变固液界面处的温度梯度和凝固速率，破坏微观结构，可能改变外延生长。

5. Conclusions 5. 结论

In summary, by combing in situ synchrotron X-ray imaging and ex situ tomography characterisation, we revealed the melt pool flow pattern under the influence of TEMHD during DED process, and investigated the role of magnetic field orientation in disrupting the melt pool flow. The major conclusions are drawn below:
总之，通过结合原位同步加速 X 射线成像和非原位断层扫描表征，我们揭示了定向磁流体动力学（TEMHD）作用下 DED 过程中的熔池流动模式，并研究了磁场方向在破坏熔池流动中的作用。主要结论总结如下：

1.
TEMHD flow is found to circulate in the cross-sectional plane under the B//V condition, however with B downward, TEMHD flow circulates in the horizontal plane.
TEMHD 流在 B//V 条件下被发现以横截面平面环流，然而 B 向下时，TEMHD 流在水平面环流。
2.
That the key force is thermoelectric magnetohydrodynamics (TEMHD), rather than just magnetic damping as previously hypothesised. In particular, TEMHD-induced flow dominates close to the liquid/solid boundary where solidification microstructures form.
关键力是热电磁流体动力学 (TEMHD)，而不是仅仅如先前假设的磁阻尼。特别是，TEMHD 诱导的流动在液/固边界附近占主导地位，在那里形成凝固微观结构。
3.
TEMHD effect alters melt pool flow, leading to the change in melt pool geometry and the resulting grain structure.
TEMHD 效应改变熔池流动，导致熔池形貌和最终晶粒组织发生变化。

Our findings demonstrate that applying a magnetic field can significantly alter the melt pool flow, opening the way to influence and perhaps control the formation of microstructural features during AM, and also being critical for the development of a reliable numerical model for the magnetic field-assisted AM process.
我们的研究结果表明，施加磁场可以显著改变熔池流动，为控制增材制造过程中微观结构特征的形成开辟了途径，同时也为建立可靠的磁场辅助增材制造过程数值模型至关重要。

CRediT authorship contribution statement
CRediT 署名贡献声明

Xianqiang Fan: Conceptualization, Formal analysis, Investigation, Writing – original draft. Tristan G. Fleming: Investigation, Writing – review & editing. David T. Rees: Investigation, Writing – review & editing. Yuze Huang: Investigation, Writing – review & editing. Sebastian Marussi: Methodology, Writing – review & editing. Chu Lun Alex Leung: Methodology, Writing – review & editing. Robert C. Atwood: Methodology, Resources, Writing – review & editing. Andrew Kao: Conceptualization, Supervision, Writing – review & editing. Peter D. Lee: Conceptualization, Project administration, Supervision, Funding acquisition, Writing – review & editing.
仙强樊：概念化、形式分析、调查、撰写 - 初稿。特里斯坦·G·弗莱明：调查、撰写 - 审阅和编辑。大卫·T·里斯：调查、撰写 - 审阅和编辑。黄宇泽：调查、撰写 - 审阅和编辑。塞巴斯蒂安·马鲁西：方法论、撰写 - 审阅和编辑。梁卓伦亚历克斯：方法论、撰写 - 审阅和编辑。罗伯特·C·阿特伍德：方法论、资源、撰写 - 审阅和编辑。Andrew Kao：概念化、指导、撰写 - 审阅和编辑。Peter D. Lee：概念化、项目管理、指导、资金获取、撰写 - 审阅和编辑。

Declaration of Competing Interest
利益声明

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
本论文作者声明，他们没有任何已知的竞争性财务利益或个人关系可能影响本文所述工作。

Acknowledgements 致谢

This research was supported under MAPP: UK-EPSRC Future Manufacturing Hub in Manufacture using Advanced Powder Processes (EP/P006566/1) and a Royal Academy of Engineering Chair in Emerging Technologies (CiET1819/10). The authors acknowledge UK-EPSRC support (grants EP/W031167/1, EP/W032147/1, EP/W037483/1, EP/W006774/1, EP/W003333/1, EP/V061798/1). XF acknowledges the China Scholarship Council. DTR acknowledges a Rolls-Royce plc. and EPSRC-iCASE. All authors are grateful for the use of the facilities provided by Research Complex at Harwell and thank Diamond Light Source for providing the beamtime (MG28804) and staff in beamline JEEP-I12 for the technical assistance. Thanks to Saurabh Shah for the tomography help. The provision of materials from Rolls-Royce plc. is gratefully acknowledged.
本研究受以下项目资助：MAPP：英国工程与自然科学研究理事会未来制造中心，先进粉末工艺制造 (EP/P006566/1) 和英国皇家工程院新兴技术教授席位 (CiET1819/10)。作者感谢英国工程与自然科学研究理事会的支持（项目编号 EP/W031167/1、EP/W032147/1、EP/W037483/1、EP/W006774/1、EP/W003333/1、EP/V061798/1）。XF 感谢中国国家留学基金管理委员会。DTR 感谢劳斯莱斯公司和 EPSRC-iCASE 的支持。所有作者感谢牛津哈威尔校区提供的研究设施，并感谢英国钻石同步加速器提供的光束时间 (MG28804) 和 JEEP-I12 束线的技术人员提供的技术帮助。感谢 Saurabh Shah 对计算机断层扫描的帮助。感谢劳斯莱斯公司提供材料支持。

Appendix A. Supplementary material
附录 A. 补充材料

What’s this? 这是什么？

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Supplementary Table 1. Supplementary material.

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Supplementary Table 2. Supplementary material.

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Supplementary Table 3. Supplementary material.

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Supplementary Table 4. Supplementary material.

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Supplementary Table 5. Supplementary material.

Data Availability 数据可用性

Data will be made available on request.
根据要求提供数据。

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Cited by (17)

Solidification in metal additive manufacturing: challenges, solutions, and opportunities
2025, Progress in Materials Science
The physics of alloy solidification during additive manufacturing (AM) in methods such as laser powder bed fusion (LPBF), electron beam powder bed fusion (EPBF), and laser directed energy deposition (LDED) is distinct due to the combination of (a) the rapid solidification conditions that often prevail in AM, (b) adjoining scan tracks that result in the overlap of the adjacent melt pools, and (c) layer-wise fabrication that causes the pre-deposited layer to influence the subsequent layer’s microstructural evolution. The complex interplay between these and each alloy’s distinct solidification characteristics results in a wide spectrum of hierarchical microstructures that span multiple length scales, with diverse grain morphologies and non-equilibrium phases. Consequently, a detailed understanding of the solidification phenomena that occur during LPBF, EPBF, and LDED is necessary for controlling the microstructural evolution, which ensures repeatable and predictable mechanical response of the built part and, hence, structural reliability of it in service. Keeping this in view, substantial efforts have been made to develop a detailed understanding of the solidification during AM of alloys, which are summarised in this review. From the local interfacial equilibrium applicable to a range of rapid solidification conditions to non-equilibrium conditions that prevail during ultra-fast solidification are reviewed. Numerical efforts ranging from the atomic scale to the macro-scale have been reviewed to highlight the phenomena of dislocation evolution, grain growth, and phase formation during solidification. Specific challenges, such as solidification cracking in non-weldable alloys and porosity-cracking dilemmas, are discussed. Unique opportunities for tailoring microstructures, such as in-situ alloying, are presented.
Laser powder bed fusion for the fabrication of triply periodic minimal surface lattice structures: Synergistic macroscopic and microscopic optimization
2024, Journal of Manufacturing Processes
Citation Excerpt :
Influenced by the Marangoni flow in the molten pool, two opposite thermoelectric currents are generated on both sides of the grains due to the thermoelectric effect. As a result of the interaction between the TE current and the MF, thermoelectric magnetic force (TEMF) are generated at the top and bottom of the grains [51]. TEMF can influence the flow of the molten pool, thereby affecting the grain growth direction.
The lightweight nature and superior mechanical properties of the triply periodic minimal surface (TPMS) structure have attracted considerable attention across various fields, including aerospace, automotive, and medicine. Currently, research on TPMS structures primarily focuses on optimizing macro-scale mechanical properties, with the limited investigation into macro/micro dual-scale optimization. This study introduces a novel nonlinear gradient TPMS structural design method, regulating the porosity of the TPMS structure through trigonometric functions, and designs Gyroid sin and Gyroid sin square structures. To fully tune the mechanical properties of the samples on both macro and micro scales, laser powder bed fusion (PBF-LB) and magnetic field (MF) were used to produce the structures. The effects of MF-assisted machining and annealing on the mechanical properties of Gyroid gradient structures were investigated by compression tests. The results show that the gradient specimens along the build direction have high energy absorption capacity and the gradient specimens perpendicular to the build direction have high elastic modulus. Annealing reduces the residual stresses and the MF refines the grains, which improve the mechanical properties of the structure. Additionally, after the addition of MF and subsequent annealing treatment, all structures show higher plateau stresses, and the energy absorption capacity of the structures along the gradient of the build direction is also improved.
Influence of compound field-assisted on the mechanical properties of 316L stainless steel fabricated by laser powder bed fusion
2024, Journal of Materials Research and Technology
The advantages of field-assisted laser additive manufacturing in optimizing microstructure and performance are increasingly recognized. Recently, we investigated the effects of acoustic field (AF) assisted laser powder bed fusion (LPBF) on the mechanical properties of 316L stainless steel (SS) and 316L SS/WC composite materials. Due to the effects of acoustic streaming and cavitation, acoustic field-assisted LPBF achieved optimized mechanical properties. Building on our previous research on AF-assisted LPBF, we introduced magnetic field (MF) and compound field (MF+AF) to study their effects on the microstructure and mechanical properties of 316L SS, 1 wt% and 3 wt% WC/316L SS. Application of the MF induces induced currents in the melt pool due to the Thomson-Seebek effect. The interaction between the MF and induced currents generates thermoelectric magnetic force (TEMF) and thermoelectric magnetic convection (TEMC), which inhibit the growth of columnar grains and enhance mass and heat transfer in the melt pool. Compound field-assisted LPBF reduced the dislocation density of 316L SS, refined grain size, alleviated the concentration distribution of grain orientation, and the ultimate tensile strength of the samples reached 777 MPa and the elongation at break reached 57.5%. Interestingly, for WC/316L SS, both MF and compound field resulted in a decrease in tensile performance, with ultimate tensile strengths as low as 677 MPa and elongations at break as low as 25.1%. This is because the MF affects the uniform distribution of WC particles, causing significant agglomeration and severe unmelted defects in the composite material, leading to a decrease in tensile performance.
Transient and steady models for blue laser directed energy deposition
2024, Journal of Materials Processing Technology
Citation Excerpt :
Tang et al. (Tang et al., 2023) revealed the relationships among the molten pool characteristics, depositing states, and appearance defects by molten pool surface high-speed photography in blue laser DED, and proposed the molten pool surface dynamic mechanism. Fan et al. (Fan et al., 2023) traced the flow of tungsten particles using synchrotron X-ray in-situ photography and ex-situ tomography to reveal the structure of thermoelectric magnetohydrodynamic-induced flow during DED. The multiphysics simulation based on the computational fluid dynamics(CFD) platform has been used more and more widely to explain molten pool flow mechanisms in the AM process.
Laser Directed Energy Deposition (DED) is an important process for additive manufacturing because of the advantage of high manufacturing speed. 450 nm blue laser has a higher absorption rate than traditional infrared laser for highly reflective materials such as Al and Cu. However, it is still unclear how the blue laser affects the particles and the molten pool flow in the DED process. In this work, we first designed two models to reveal the mechanism of the molten pool behaviors in the blue laser DED process: the transient model and the steady deposition model. The models are validated by in-situ and ex-situ experiments respectively. It is found that the three stages can be concluded for a particle impacting the molten pool: particle impacts, surface oscillates and the molten pool recovers. The particles whose diameter is less than 100 µm are necessary for steady deposition. The influence of process parameters on DED is investigated, and a suitable process parameters window is found. we also verified the superiority of the blue laser for DED of highly reflective materials through the simulation models. The current study provides new insights into the mechanism from the interaction in the molten pool scale to single-track forming in the blue laser DED, and can provide theoretical guidance on the application of blue laser DED of highly reflective materials.
Experimental quantification of inward Marangoni convection and its impact on keyhole threshold in laser powder bed fusion of stainless steel
2024, Additive Manufacturing
Citation Excerpt :
By automatically tracing hundreds of moving particles in the melt pool from thousands of consecutive frames, the fluid flow is visualized and quantified with an exceptional lateral resolution of approximately 10 µm. The findings reveal the presence of a prevalent inward fluid flow (from cold area to hot area on the melt pool surface) in the melt pool, which differs from the previously reported outward flow with other commercial LPBF materials [16,23–25], along with the coexistence of outward and inward convections in the keyhole mode. This study primarily centers on gaining a deep understanding of the mechanisms underlying inward Marangoni convection and its dual impact on the behavior of the melt pool and the conduction-keyhole threshold within laser-based AM.
Laser metal additive manufacturing has the potential to revolutionize the production of complex geometries with high precision across various industrial applications. To optimize the reliability of the process, a detailed understanding of the melt pool dynamics during the process is essential, particularly in the nearly pore-free regimes. In this study, the melt pool dynamics across conduction mode to keyhole mode in laser powder bed fusion processing of stainless steel 316 L have been investigated by means of in-situ synchrotron X-ray imaging utilizing tungsten particles as tracers. The spatial distribution of the fluid flow in the melt pool has been quantified with a resolution of ∼10 µm through automatic tracing all moving particles in the melt pool. The results identified the influence of the interplay between laser power and scanning speed on melt flow velocities. The measurements also revealed a pronounced impact of the inward Marangoni convection on the conduction-keyhole threshold, offering a new degree of freedom to broaden the pore-free process window of laser-based additive manufacturing. These findings contribute to a more comprehensive understanding of the melt pool dynamics during laser metal additive manufacturing and provide a valuable reference for calibrating high-fidelity computational fluid dynamics models.
A review on in-situ process sensing and monitoring systems for fusion-based additive manufacturing
2023, International Journal of Mechatronics and Manufacturing Systems

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Outline 大纲 Note: * The "Outline" will not be translated because it is a proper noun in English * The punctuation mark "." will be retained in the translated text

Cited by (17) (被 17 篇文献引用)

Figures (11) 图（11）

Extras (5)

Additive Manufacturing 增材制造

Abstract 摘要

Graphical Abstract 图形摘要

Keywords 关键词

1. Introduction 1. 绪论

2. Materials and methods 2. 材料和方法

2.1. Materials 2.1 材料

2.2. DED rig 2.2. DED 平台

2.3. In situ synchrotron X-ray imaging
2.3. 原位同步加速器 X 射线成像

2.4. Ex situ X-ray computed tomography
2.4. 离体 X 射线计算机断层扫描

2.5. Data analysis 2.5. 数据分析

2.5.1. Image processing of raw data
2.5.1 原始数据的图像处理

2.5.2. Tungsten particle tracking
2.5.2. 钨粒子追踪

3. Results 3. 结果

3.1. DED melt pool flow
3.1. DED 熔池流动

3.2. DED melt pool flow under external magnetic field
3.2 DED 熔池流动受外部磁场的影响

4. Discussion 4. 讨论

5. Conclusions 5. 结论

CRediT authorship contribution statement
CRediT 署名贡献声明

Declaration of Competing Interest
利益声明

Acknowledgements 致谢

Appendix A. Supplementary material
附录 A. 补充材料

Data Availability 数据可用性

References

Cited by (17)

Solidification in metal additive manufacturing: challenges, solutions, and opportunities

Laser powder bed fusion for the fabrication of triply periodic minimal surface lattice structures: Synergistic macroscopic and microscopic optimization

Influence of compound field-assisted on the mechanical properties of 316L stainless steel fabricated by laser powder bed fusion

Transient and steady models for blue laser directed energy deposition

Experimental quantification of inward Marangoni convection and its impact on keyhole threshold in laser powder bed fusion of stainless steel

A review on in-situ process sensing and monitoring systems for fusion-based additive manufacturing

Thermoelectric magnetohydrodynamic control of melt pool flow during laser directed energy deposition additive manufacturing激光定向能量沉积增材制造过程中的熔池流动热电磁流体控制

Abstract 摘要

Graphical Abstract 图形摘要

Keywords 关键词

1. Introduction 1. 绪论

2. Materials and methods 2. 材料和方法

2.1. Materials 2.1 材料

2.2. DED rig 2.2. DED 平台

2.3. In situ synchrotron X-ray imaging2.3. 原位同步加速器 X 射线成像

2.4. Ex situ X-ray computed tomography2.4. 离体 X 射线计算机断层扫描

2.5. Data analysis 2.5. 数据分析

2.5.1. Image processing of raw data2.5.1 原始数据的图像处理

2.5.2. Tungsten particle tracking2.5.2. 钨粒子追踪

3. Results 3. 结果

3.1. DED melt pool flow3.1. DED 熔池流动

3.2. DED melt pool flow under external magnetic field3.2 DED 熔池流动受外部磁场的影响

4. Discussion 4. 讨论

5. Conclusions 5. 结论

CRediT authorship contribution statementCRediT 署名贡献声明

Declaration of Competing Interest利益声明

Acknowledgements 致谢

Appendix A. Supplementary material附录 A. 补充材料

Data Availability 数据可用性

References

Thermoelectric magnetohydrodynamic control of melt pool flow during laser directed energy deposition additive manufacturing
激光定向能量沉积增材制造过程中的熔池流动热电磁流体控制

2.3. In situ synchrotron X-ray imaging
2.3. 原位同步加速器 X 射线成像

2.4. Ex situ X-ray computed tomography
2.4. 离体 X 射线计算机断层扫描

2.5.1. Image processing of raw data
2.5.1 原始数据的图像处理

2.5.2. Tungsten particle tracking
2.5.2. 钨粒子追踪

3.1. DED melt pool flow
3.1. DED 熔池流动

3.2. DED melt pool flow under external magnetic field
3.2 DED 熔池流动受外部磁场的影响

CRediT authorship contribution statement
CRediT 署名贡献声明

Declaration of Competing Interest
利益声明

Appendix A. Supplementary material
附录 A. 补充材料