# Synchrotron µ-CT-based morphological characterization of additively manufactured open porous structures

Robert Otto, Knut Sørby, Bernhard Hesse, Javier Gerber, Emely Bortel, Christoph Kiener

► To cite this version:

Robert Otto, Knut Sørby, Bernhard Hesse, Javier Gerber, Emely Bortel, et al. Synchrotron µ-CT-based morphological characterization of additively manufactured open porous structures. Additive Manufacturing, 2022, 55, pp.102874. 10.1016/j.addma.2022.102874. hal-05075980

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Research Paper

# Synchrotron µ-CT-based morphological characterization of additively manufactured open porous structures

Robert Otto<sup>a, b, *, 1, 2</sup>, Knut Sørby<sup>b</sup>, Bernhard Hesse<sup>c, d, 1</sup>, Javier Gerber<sup>c</sup>, Emely Bortel<sup>c, 1</sup>, Christoph Kiener<sup>a</sup>

<figure><img src="image_3.png" /></figure>

## ARTICLE INFO

### Keywords:

Additive Manufacturing (AM)

Laser-based powder bed fusion of metals (PBF-LB/M)

X-ray tomography

Synchrotron imaging

µ-CT

Open porosities

## ABSTRACT

Additive Manufacturing of open porous metallic structures has a high potential for advanced applications such as for cooling or catalysis on small length-scales. For such applications the 3D morphology, and in particular the surface geometry, will strongly determine the performance. Attached spherical particles on the surface of functional structures made by Laser-based Powder Bed Fusion (PBF-LB) have been observed in various studies. This study applies a novel approach to characterize such complex structures made by Additive Manufacturing. In this study, synchrotron µ-CT was applied to analyze the surface morphology of six different open porous PBF-LB-samples at ~ 1.5 µm voxel size. Due to the high level of detail, the reconstructed 3D images allow an impression very close to the original physical sample. In contrast to classic functional design for AM, the open porosities considered in this study are the result of the manufacturing parameters (e.g. hatch spacing) and not of a CAD-design. The work shows that scan strategy and process parameters have a major impact on the resulting surface area and the volume of the open porous structures. In particular, the surface area is driven by the attached particles, while their impact on the volume is considerably lower. This difference between material distribution and material property could be used to determine specific application properties. The presented findings may thus pave the path for adding an additional level of functionality to Additive Manufacturing of porous metallic samples.

## 1. Introduction

Over the past years, Additive Manufacturing (AM) has become a well-integrated complement to conventional means of manufacturing. Especially laser-based powder bed fusion of metals (PBF-LB/M) has evolved to be the most important additive manufacturing technology for metals. Design freedom of AM does not only allow complex shape designs but also the manufacturing of functionality driven structures [1]. Such structures could be open porosities, to be understood as an interconnected pore network of void volumes. As those volumes are open to ambient media, they allow mass flow passing through as media exchange with their surrounding environment [2]. As the use of open porosities in general is advantageous in heat transfer and flow

applications, recent studies have demonstrated the potential for industrial use of additively manufactured open porosities.

One common observation of previous studies on PBF-LB/M is the unintended attachment of semi-molten powder particles to the part surface. Attached particles are mentioned in studies on lattice structures [3–8], single laser tracks [9–13] and related open porosities [1]. Structures based on single laser tracks and unsupported structures seem to be susceptible for semi-molten particles. Fig. 1 shows attached powder particles on an open porous structure. Even though several studies observe the presence of such remnants, no comprehensive study to characterize their distribution and influence on volume and surface area has been conducted so far at this high resolution in 3D.

During the past decades, X-ray tomography has become a popular

<footnote><sup>a</sup> Siemens AG, Technology, Germany</footnote>

<footnote><sup>b</sup> Norwegian University of Science and Technology, Norway</footnote>

<footnote><sup>c</sup> Xploraytion GmbH, Germany</footnote>

<footnote><sup>d</sup> ESRF, The European Synchrotron, France</footnote>

<footnote>* Corresponding author at: Siemens AG, Technology, Germany.
E-mail addresses: robert-otto@siemens.com, robert.otto@ntnu.no (R. Otto).</footnote>

<footnote n="1">1 All three authors contributed equally to this work.</footnote>

<footnote n="2">2 Otto-Hahn-Ring 6, 81739 Munich, Germany.</footnote>
method for the characterization of additively manufactured parts including their pores and porosity [14]. In a series of publications since 2018, du Plessis et al. analyzed the general implementation of X-ray tomography for inspection of AM parts, proposing an interlaboratory round robin test [15] and focussing on evaluation of image quality [16]. X-ray tomography has been used for in-situ analyses of the PBF-LB/M process. Lhuissier et al. [17] used X-ray tomography to study the melt pool and remelting of underlaying material on supported single laser tracks. Leung et al. [18] studied defects and melt pool dynamics on an unsupported single laser track, e.g. the formation of melt pools on loose powder. X-ray tomography-based 3D images of manufactured parts are also used for geometrical deviation analysis [19,20] in which the resulting shape of a part is compared to its digital CAD representation. Synchrotron-based µCT is drastically reducing scan times and at the same time improving image quality as compared to laboratory-based µCT tools. This is because of the high photon flux and the high coherence of X-rays generated by synchrotrons [13].

This paper presents a novel synchrotron-based 3D imaging approach to characterize the remaining powder particles on structures made by PBF-LB/M. As an example, open porosities have been chosen, with a morphology that is mainly determined by the manufacturing parameters and notably differs from CAD-based designs, as presented by Otto et al. [1]. This means that the resulting morphology is not a reproduction of a prior designed CAD-model. Instead, this structure will be the result of applied manufacturing parameters which either result in a solid or open porous material in a designated area. Further, the present study aims to develop an awareness of the influence of manufacturing parameters on the formation of attached particles and loose, trapped particles. Increased understanding will help to either reduce the impact of remaining particles for future applications or enable applications which make use of their features.

## 2. Material and methods

### 2.1. Open porous samples

The samples used for this study have been produced by Laser-based powder bed fusion (PBF-LB/M) technology. For this process, layer-wise applied metal powder material is selectively fused by a laser beam. After one layer is fused the build area is lowered, controlling the lead thickness of the next applied powder layer. Here, an EOS M290 equipped with a 1070 nm wavelength Yb:YAG fiber laser was used. All samples are made of Inconel 625 with a powder particle size of 15–45 µm. Argon was used as shielding gas and a brush powder recoater was equipped. Generally, the resulting open porosity is affected by at least four process parameters: laser power (P), velocity of the laser (v), layer thickness (t) and the hatch spacing (h). In this study the process parameters are summarized as volumetric energy density, which is defined as: $E_{vol} = P/(v \cdot t \cdot h)$. Furthermore, two different scan strategies were realized.

For the “ROT” strategy the laser tracks were aligned parallel and rotated 67° every layer, while for the “GRID” strategy perpendicular tracks were added, resulting in an equidistant square grid pattern in every layer. Six cuboid samples with a 5 × 5 mm footprint were manufactured. All samples have been carefully de-powdered and washed in an isopropyl alcohol filled tumbler, placed in a water ultrasonic bath. No further heat treatment was applied. Cleaned samples will be called raw samples in the following analysis. An overview of the applied scan strategies, process parameters and resulting volumetric energy densities is given in Table 1. The samples can be divided into two groups: samples made by the GRID or ROT strategy. For each of these groups three sets of parameters were defined to focus on different manufacturing aspects. Particularly the second set of each group (Sample 2 and 4) focusses on the impact of hatch spacing by increasing it from 420 µm up to 540 µm. For the third set (Sample 3 and 6) the layer thickness was doubled from 40 µm to 80 µm and to stabilize the process the laser power was increased to 210 W.

Fig. 2 shows 2D computer tomography slices of all characterized samples, representing a view parallel to the build plate. The samples are numbered according to Table 1. The gray areas indicate solid material, whereas the black areas represent the void volume, i. e. the pores. The impact of different manufacturing sets can clearly be distinguished. For samples produced by the GRID-scan strategy (top row) the spatial density appears to be higher than for ROT-scan strategy samples, although applying the identical volumetric energy density input.

### 2.2. Tomography

Synchrotron radiation µ-CT data were acquired at the beamline ID 19 of the European Synchrotron Radiation Facility (ESRF; Grenoble, France) using a beam energy of 71 keV. The sample to detector distance was 1 m. A total of 5000 radiographs over an angle of 360° were captured with an isotropic pixel size of 1.44 µm. Each image was exposed for 30 ms (camera: pco.edge 4.2, PCO AG, Kelheim, Germany). To increase the field of view the rotation axis was offset, resulting in datasets with dimensions of 5.2 × 5.2 × 2.9 mm. Reconstruction was performed using Paganin’s method in combination with the conventional filtered back projection algorithm [21]. The reconstructed grey value volumes were stored in units of 16-bit integers.

<table><caption>**Table 1**

Overview of the manufacturing sets.</caption><thead><tr><th>Sample</th><th>1</th><th>2</th><th>3</th><th>4</th><th>5</th><th>6</th></tr></thead><tbody><tr><td>Scan strategy</td><td>GRID</td><td>GRID</td><td>GRID</td><td>ROT</td><td>ROT</td><td>ROT</td></tr><tr><td>Laser power, P [W]</td><td>180</td><td>180</td><td>210</td><td>180</td><td>180</td><td>210</td></tr><tr><td>Laser speed, v [mm/s]</td><td>800</td><td>800</td><td>800</td><td>800</td><td>800</td><td>800</td></tr><tr><td>Hatch spacing, h [µm]</td><td>420</td><td>540</td><td>420</td><td>420</td><td>540</td><td>420</td></tr><tr><td>Layer thickness, t [µm]</td><td>40</td><td>40</td><td>80</td><td>40</td><td>40</td><td>80</td></tr><tr><td>E<sub>vol</sub> [J/mm<sup>3</sup>]</td><td>13.4</td><td>10.4</td><td>7.8</td><td>13.4</td><td>10.4</td><td>7.8</td></tr></tbody></table>

<figure><img src="image_4.png" /><figcaption>**Fig. 1.** 3D representation (rendering) of one sample with notable remaining powder particles at the surface.</figcaption></figure>
<figure><img src="image_5.png" /><figcaption>**Fig. 2.** 2D computer tomography slices of the six analyzed samples. The top row shows results of the GRID-scan strategy, the bottom row shows resulting structures of the ROT-scan strategy.</figcaption></figure>

## 2.3. Characterization properties and data handling

Data processing was performed using ImageJ (distribution FIJI [22]), Avizo (v. 2019.3; Thermo Fisher Scientific Inc.) and MATLAB (R2018b; The MathWorks, Inc.).

The 16-bit datasets were converted to binary masks with an automated histogram-based thresholding approach [23]. Spatial density was calculated as the ratio of all material voxels to the sum of all voxels. The porosity is the opposite of the spatial density. To differentiate between open and closed pores, a connected component labeling was performed on the pore mask. All pixels that have no connection to the background (which is the porosity) are defined as closed porosity. To determine the surface, a 1 pixel dilation and a 1 pixel erosion was performed on the initial mask. The surface is here defined as half the number of the non-zero voxels of subtracting the eroded from the dilated mask.

Local thickness was evaluated by a sphere-fitting algorithm implemented in ImageJ. The diameter of the maximum sphere that fits inside the structure is extracted as the structural thickness. A Euclidean distance transform (EDT) was applied to the binary masks, assigning its shortest distance to the next border to all pixels. To normalize the local thickness and account for the volumes of larger spheres an ImageJ analysis “regional maxima 3D” [24] was performed on the result, and multiplied with the result of the local thickness. This calculation was performed on the material mask to obtain the thickness of the structures but also on the filtered pore mask to obtain the thickness of the pores.

To exclude sample boundary effects all analyzes were performed on a cropped dataset with 2500 × 2500 × 1500 pixel.

MATLAB was used to fit the obtained distributions and to extract the maximum thicknesses.

The data sets were digitally processed (“filtered”) to eliminate attached particles, and both the surface area and the material volume were extracted. Then, the effect of remaining spherical powder particles

that are attached to the material surfaces could be analyzed. Filtering was performed through a morphological opening with a spherical structuring element with a diameter of 20 voxels to maintain the original structure without particles smaller than about 60 µm. Some of the particles, especially in the GRID strategy samples might not be attached to the surface, but trapped within small open pores. To give an estimate of these particles, the filtered surface was dilated by the mean size of the attached particles of each sample as shown in Fig. 3. The inverted result was multiplied with the corresponding particle mask. The remaining particles are defined as trapped particles that are not attached to the surface of the bulk.

The number of particles was calculated by dividing the total particle volume by the volume of a sphere using the mean particle diameter of the corresponding sample.

# 3. Results and discussion

## 3.1. *Description of the raw samples*

Based on the µ-CT images, various features of the open porous structures could be distinguished. Examples are given in Fig. 4. In the open pore regions in some samples with high spatial density, various spherical particles (white arrowhead with black outline) can be found. These particles are usually attached to the surface (often seen in “cleaner regions”, marked with a white star). There are also “crowded regions” (white arrowhead) where many small particles might be trapped in open pores with small canals preventing a proper cleaning. Besides reminiscent material in the form of the spherical particles, also closed pores are found in the samples. These can further be categorized into pores within the unfused powder (the raw material for the process, white transparent arrowhead) and pores within already fused powder (black arrowhead with white outline). In contrast to open pores, gases and particles in
<figure><img src="image_6.png" /><figcaption>Fig. 3. Visualization on how attached and trapped particles are estimated.</figcaption></figure>

<figure><img src="image_7.png" /><figcaption>Fig. 4. Overview of different features identified in the samples.</figcaption></figure>

closed pores are surrounded by solid material and therefore cannot interact with ambient media. Recent studies indicate that closed pores can have various reasons [25,26]. Generally two kinds of pores are distinguished: spherical gas pores and irregular pores. Gas pores can be due to already existing pores in the powder raw material, key-hole effects or an overheating of the material and resulting evaporation. Irregular pores are normally the consequence of insufficient fusing of the powder material. They might then be shaped according to the not liquefied parts of the powder.

In Fig. 5 the results of the sphere-fitting algorithm for the local thickness of the solid material (A), the spherical particles (B) and the open pore network (C) are visualized for sample 4.

An example of the local size distribution is given in Fig. 6. The counts of pixels are plotted against its assigned size. For spherical structures such as the remaining particles, each count represents one particle. For non-spherical structures, like the pores and non-particle-structures, several spheres of different size will fill this structure giving an impression about the size of the structure at that point. The structure is not discrete and thus is represented by multiple pixels (counts). In the graph, two peaks can be identified for the structure thickness at 15 µm and 140 µm. Following the applied structuring elements, with a size of 20 voxels, these peaks represent the mean thickness of the particles and structures respectively. It can be observed that the first peak has a rather steep gradient compared to the second peak, indicating that the size
<figure><img src="image_8.png" /><figcaption>Fig. 5. Visualization of the local thickness of sample 4 with its fused powder material structure (A), remaining particles (B) and pore network (C).</figcaption></figure>

<figure><img src="image_9.png" /><figcaption>Fig. 6. Size distribution graph of sample 4 showing the structural thickness and pore sizes based on the sphere-fitting algorithm.</figcaption></figure>

<table><caption>**Table 2**

Properties of the raw samples.</caption><thead><tr><th rowspan="2">Dimensions (pixel)</th><th rowspan="2">2500 × 2500 × 1500</th><th colspan="6">Sample code</th></tr><tr><th>1</th><th>2</th><th>3</th><th>4</th><th>5</th><th>6</th></tr></thead><tbody><tr><td>V<sub>total</sub></td><td>28 mm<sup>3</sup></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Scan strategy</td><td></td><td>GRID</td><td>GRID</td><td>GRID</td><td>ROT</td><td>ROT</td><td>ROT</td></tr><tr><td>E<sub>vol</sub></td><td>[J/mm<sup>3</sup>]</td><td>13.4</td><td>10.4</td><td>7.8</td><td>13.4</td><td>10.4</td><td>7.8</td></tr><tr><td>spatial density</td><td>%</td><td>86.8</td><td>79.9</td><td>69.7</td><td>64.0</td><td>52.6</td><td>46.2</td></tr><tr><td>porosity</td><td>%</td><td>13.2</td><td>20.1</td><td>30.3</td><td>36.0</td><td>47.4</td><td>53.8</td></tr><tr><td>open porosity</td><td>as % from porosity</td><td>99.42</td><td>99.80</td><td>99.88</td><td>99.94</td><td>99.96</td><td>99.97</td></tr><tr><td>closed porosity</td><td>as % from porosity</td><td>0.58</td><td>0.20</td><td>0.12</td><td>0.06</td><td>0.04</td><td>0.03</td></tr><tr><td>SA<sub>raw</sub></td><td>mm<sup>2</sup></td><td>494</td><td>445</td><td>404</td><td>370</td><td>335</td><td>326</td></tr><tr><td>V<sub>raw</sub></td><td>mm<sup>3</sup></td><td>24.3</td><td>22.4</td><td>19.5</td><td>17.9</td><td>14.7</td><td>12.9</td></tr><tr><td>SA<sub>raw</sub>/V<sub>raw</sub></td><td>mm<sup>-1</sup></td><td>20.3</td><td>19.9</td><td>20.7</td><td>20.6</td><td>22.8</td><td>25.2</td></tr><tr><td>SA<sub>raw</sub>/V<sub>total</sub></td><td>mm<sup>-1</sup></td><td>17.6</td><td>15.9</td><td>14.4</td><td>13.2</td><td>12</td><td>11.6</td></tr><tr><td>mean thickness</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>- structures</td><td>μm</td><td>150</td><td>151</td><td>143</td><td>141</td><td>140</td><td>131</td></tr><tr><td>- spherical particles</td><td>μm</td><td>16.8</td><td>25</td><td>19.3</td><td>14.6</td><td>22.2</td><td>16.7</td></tr><tr><td>mean pore size</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>- filtered</td><td>μm</td><td>61</td><td>71</td><td>94</td><td>106</td><td>149</td><td>180</td></tr></tbody></table>
distribution of remaining particles is considerably smaller than the thickness of the structure. These observations correlate well to the analyzed structures. As the powder material is 15–45 µm in diameter, the possible size of remaining particles is limited to this size. In contrast to that, the thickness of the structure is mainly driven by the melt pool size, which is determined by the process parameters. The melt pool size mainly depends on the spot diameter of the laser and effects like balling and necking. Balling is an effect in which the molten liquid material of a fused scan track is interrupted, and the material tends to form a sphere (ball) due to surface tension. Necking usually occurs when the liquid scan track contracts (neck) and solidifies before the fused laser track gets interrupted. The spot diameter of the laser is considerably larger than the powder size. All these effects result in an overall larger variation of structural thickness. The pore sizes have a rather equal size distribution up to around 175 µm. The number of larger pores is steadily descending.

A summary of the raw sample evaluation is given in Table 2. The calculated porosity, including open and closed pores, ranges from around 13% up to 54%. The predominant part herein (at least 99.4%) is open porosity. The share of closed porosity decreased with increasing total porosity. Both surface area and material volume decrease towards higher porosities. These observations for the volume are quite rational and correlate to the measured spatial densities, as they are mainly driven by geometrical considerations. Decreasing porosity towards higher sample number can be explained by decreasing energy input, based on increased hatch spacing and layer thickness. Consequently, less fused powder is contributing to the spatial solid structure. Further, as samples 1–3 are produced by the “GRID” strategy, the double amount of laser tracks has been fused in comparison to samples 4–6, which were made with the “ROT” strategy.

The ratio of the raw surface area $SA_{raw}$ to raw volume $V_{raw}$ and the ratio of $SA_{raw}$ to the total volume $V_{total}$ are calculated. In this experiment, the ratio $SA_{raw}/V_{raw}$ stays relatively stable around 20–21 for the GRID samples. The ratio increases clearly towards higher porosities for the ROT samples from 21 to 25, indicating a higher surface per raw volume than for the GRID samples. Yet, the ratio $SA_{raw}/V_{total}$ of the samples indicates that GRID samples generally have a higher surface area per spatial volume of the structure than the ROT samples, while the ratio increases towards higher volumetric energy density, $E_{vol}$.

The normalized mean structural thickness is generally of similar size for all analyzed samples and ranges from 130 µm to 150 µm. Especially for samples 1 and 2 as well as samples 3 and 4, which have been manufactured with the same scan strategy and the same line energy, which is defined as $E_{line} = P/v$, respectively, the mean thickness is almost identical. GRID samples generally have about 10 µm larger structural thickness than ROT samples. As this applies for all samples of the same $E_{line}$, this observation can be explained by the applied scan strategy. The difference in hatch spacing has no noticeable impact on the mean structural thickness. More fused material in samples made by the GRID strategy will result in more support for following layers. Thereby melt pool effects like balling and necking do not become predominant. In ROT samples, where the fused tracks are less supported, these effects might result in lower structural thickness. The mean structural thickness of samples 3 and 4 are 7–10 µm smaller than samples produced with the same scan strategy. Those samples are manufactured with the lowest $E_{vol}$ each, mainly due to the doubled layer thickness. Although the laser power was increased to stabilize the process this increase might not have resulted in similar melt pool sizes like for samples produced with 40 µm layer thickness. This will result in smaller mean structural thicknesses. Thereby, the subsequently fused tracks are even less supported as well, which might lead to necking of the tracks rather than track interruption and balling. The tendency of slightly increasing mean thickness towards lower $E_{vol}$, observed in a previous study [1], could be explained by an unfavorably mix of hatch spacing, rotation of the laser tracks and $E_{vol}$ which might lead to balling of the material.

The obtained mean size of the spherical particles is in a range of 15–25 µm for nearly all samples. As the powder raw material for the

process is sized at 15–45 µm it can be concluded that especially the powder particles at the lower size range are susceptible to remain attached to the bulk material.

The pore size increases with increasing porosity of the structures from 61 µm up to 180 µm. This increased range of 120 µm compared to the range of observed mean structural thicknesses can be explained by geometrical considerations of the scan strategies. As twice the tracks are fused in GRID samples than in ROT samples, resulting pore sizes will be reduced considerably. This behavior is amplified by the rotation of the scan strategy for every layer, which might interrupt pores in the build direction. An increase of pore sizes within the same scan strategy can be explained by less fused powder. An increase of hatch spacing will result in a larger pore size each layer, as it increases the space between two fused laser tracks. A larger area between those tracks will stay unmolten. Due to the decreased $E_{vol}$ for the doubled layer thickness additional effects like balling and necking can become predominant if fused tracks are not sufficiently supported.

## 3.2. Characterization of virtually rendered structures and spherical particles with digitally filtering

Although the trend of the surface area of the raw samples appears to be predictable, like increasing with higher volumetric energy density $E_{vol}$ and with more fused tracks for the GRID strategy, attached particles need to be considered to explain this behavior. Therefore, the particles were removed by means of volumetric image processing (filtering) from the grid structures by morphologically opening of the raw structures. Datasets of the isolated spherical particles and a filtered structure were obtained which could then be analyzed individually. Fig. 7 displays the results of such a morphologically opening of the raw structures. The section view shown in Fig. 7 is the same as in Fig. 5. Volumes smaller than the structuring element are defined as separate particles (highlighted in pink on the right-hand side). The particles are uniformly distributed in the shown cross-section.

The effect of removing particles is visualized in a 3D rendering of sample 4 in Fig. 8.

The characterization of the remaining particles is summarized in Table 3. The surface area and volumes of the raw sample are given as a reference.

It can be observed that the filtered surface area $SA_{filtered}$ of the ROT samples is decreasing with decreasing $E_{vol}$. This trend could be seen for the raw structures as well. The GRID samples however show an opposite trend with increasing $SA_{filtered}$ with decreasing $E_{vol}$. As for the ROT samples the trend can be explained by the fact that more material is fused for lower hatch spacings thus higher $E_{vol}$. Since this strategy does only consist of parallel laser tracks, fused tracks will result in new free surfaces that do not overlap to other tracks. Only their overlap to underlaying tracks reduces their surface but is necessary to ensure a connected open porous structure. For the GRID strategy, additional perpendicular tracks may reduce the total surface area, due to the reduced surface at the crossing points of the tracks. This “lost” surface area at the crossing points can be made up for by the surface of the extra perpendicular tracks. Yet, even if more material is fused for lower hatch spacings thus higher $E_{vol}$ this new free surface gets smaller. The “lost” surface of the crossings stay constant per crossing due to the steady thickness of the fused tracks.

Despite different trends for the surface area, the filtered surface area of the structures $SA_{filtered}$ stays within the same size and has a range of 40 mm². However, the range of the surface area of the raw samples $SA_{raw}$ is 170 mm².

With a surface area ranging from 120 mm² up to 280 mm², the spherical particles are a major factor driving the surface area of the raw samples, as visualized on the left plot in Fig. 9. Especially for GRID samples the range of the particles’ surface area is large while the surface area is relatively constant for ROT samples. With increasing $E_{vol}$ the surface area of the particles $SA_{particles}$ increases from 170 mm² up to
<figure><img src="image_10.png" /><figcaption>**Fig. 7.** 2D comparison of the sample 4 before (left) and after (right) a morphological opening with a spherical structuring element with a diameter of 20 pixels. The small spherical particles on the surfaces can clearly be separated from the structure.</figcaption></figure>

<figure><img src="image_11.png" /><figcaption>**Fig. 8.** 3D rendering of the original “raw” dataset (left) with highlighted powder particles (center) and the filtered structure's surface (right) of sample 4. The bottom row shows a magnification of a cubic cut of the volume renderings seen in the upper row.</figcaption></figure>

280 mm² for the GRID strategy. This can be explained by the fact that a reduced hatch spacing and layer thickness will lead to more fused material and thereby to an increased energy input. This leads to higher process temperature and to more semi-molten powder, thus also to more attached particles. This effect is further increased by the many surfaces

which are close to each other for the GRID samples, as explained above. The relatively constant values for ROT samples of 120–130 mm² might be explainable again by the orientation of the parallel laser tracks. The ratio of particles surface to the raw surface area is around 36–40% for ROT samples and around 42–57% for the GRID samples.
<table><caption>**Table 3**

Morphological description of the remaining particles.</caption><thead><tr><th>Dimensions (pixel)</th><th>2500 × 2500 × 1500</th><th colspan="6">Sample code</th></tr><tr><th>V<sub>total</sub></th><th>28 mm<sup>3</sup></th><th>1</th><th>2</th><th>3</th><th>4</th><th>5</th><th>6</th></tr></thead><tbody><tr><td><strong>Scan strategy</strong></td><td></td><td>GRID</td><td>GRID</td><td>GRID</td><td>ROT</td><td>ROT</td><td>ROT</td></tr><tr><td><strong>E<sub>vol</sub></strong></td><td>[J/mm<sup>3</sup>]</td><td>13.4</td><td>10.4</td><td>7.8</td><td>13.4</td><td>10.4</td><td>7.8</td></tr><tr><td><strong>S<sub>raw</sub></strong></td><td>mm<sup>2</sup></td><td>494</td><td>445</td><td>404</td><td>370</td><td>335</td><td>326</td></tr><tr><td><strong>V<sub>raw</sub></strong></td><td>mm<sup>3</sup></td><td>24.3</td><td>22.4</td><td>19.5</td><td>17.9</td><td>14.7</td><td>12.9</td></tr><tr><td><strong>Virtually filtered structures</strong></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td><strong>SA<sub>filtered</sub></strong></td><td>mm<sup>2</sup></td><td>211</td><td>219</td><td>234</td><td>236</td><td>213</td><td>197.</td></tr><tr><td>- as % from SA<sub>raw</sub></td><td>%</td><td>42.7</td><td>49.2</td><td>57.9</td><td>63.8</td><td>63.6</td><td>60.4</td></tr><tr><td><strong>V<sub>filtered</sub></strong></td><td>mm<sup>3</sup></td><td>22.04</td><td>20.7</td><td>17.95</td><td>16.95</td><td>13.77</td><td>11.92</td></tr><tr><td>- as % from V<sub>raw</sub></td><td>%</td><td>90.7</td><td>92.3</td><td>92.0</td><td>94.6</td><td>93.5</td><td>92.2</td></tr><tr><td><strong>SA<sub>filtered</sub>/V<sub>filtered</sub></strong></td><td>mm<sup>-1</sup></td><td>9.56</td><td>10.61</td><td>13.07</td><td>13.92</td><td>15.46</td><td>16.52</td></tr><tr><td><strong>Virtual spherical particles</strong></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td><strong>SA<sub>particles</sub></strong></td><td>mm<sup>2</sup></td><td>283</td><td>226</td><td>170</td><td>134</td><td>122</td><td>129</td></tr><tr><td>- as % from SA<sub>raw</sub></td><td>%</td><td>57.3</td><td>50.8</td><td>42.1</td><td>36.2</td><td>36.4</td><td>39.6</td></tr><tr><td><strong>V<sub>particles</sub></strong></td><td>mm<sup>3</sup></td><td>2.26</td><td>1.7</td><td>1.56</td><td>0.96</td><td>0.96</td><td>1.01</td></tr><tr><td>- as % from V<sub>raw</sub></td><td>%</td><td>9.3</td><td>7.7</td><td>8.0</td><td>5.4</td><td>6.5</td><td>7.8</td></tr><tr><td><strong>SA<sub>particles</sub>/V<sub>particles</sub></strong></td><td>mm<sup>-1</sup></td><td>125.3</td><td>131.8</td><td>108.8</td><td>139.6</td><td>127.3</td><td>128.2</td></tr><tr><td><strong>No. of particles per volume</strong></td><td>mm<sup>-3</sup></td><td>33,715</td><td>7741</td><td>15,349</td><td>21,820</td><td>6207</td><td>15,188</td></tr><tr><td><strong>No. of trapped particles per volume</strong></td><td>mm<sup>-3</sup></td><td>1917</td><td>281</td><td>497</td><td>99</td><td>28</td><td>79</td></tr><tr><td>- as % from all particles</td><td>%</td><td>5.90</td><td>3.76</td><td>3.36</td><td>0.47</td><td>0.48</td><td>0.54</td></tr></tbody></table>

<figure><img src="image_12.png" /><figcaption>**Fig. 9.** Composition of the surface area (left) and volume (right) of the raw structures.</figcaption></figure>

The volumes of the filtered structure and particles have been analyzed. Like the spatial densities of the samples, the volume of the structures increases with increasing $E_{vol}$ and is generally higher for the GRID strategy. This trend follows above given arguments, as the amount of fused material depends on the hatch spacing, the layer thickness and the scan strategy. The volumes of the filtered structures $V_{filtered}$ ranges from 12 to 22 mm³.

The volume of the particles $V_{particles}$ stays relatively stable around 1 mm³ for the ROT samples. For GRID samples $V_{particles}$ increases with higher $E_{vol}$ from around 1.5–2.3 mm³. The ratio $V_{particle} / V_{raw}$ is higher for the GRID strategy than for the ROT strategy. This ratio increases with lower $E_{vol}$ for ROT samples as the volume of the particles stays stable, while the volume of the filtered structure decreases. The composition of the volume of the raw structures is visualized in the right plot of Fig. 9.

The ratio of surface area to volume allows a relative comparison on how efficient a new surface is generated by volume elements. The filtered structures and the particles are such volume elements. The higher the ratio, the more suitable is the combination of process parameters and scan strategy to create new surfaces while keeping the volume at a lower size.

The surface-to-volume ratio of the filtered structures, $SA_{filtered}/V_{filtered}$, is higher for the ROT strategy than for the GRID strategy. The ratio increases with decreasing volumetric energy density, so with increasing hatch spacing and layer thickness. This observation might be explained by the increased rate of laser track deformations and interruption. With decreasing $E_{vol}$ and less laser tracks, less powder is fused that can support following layers. This can lead to balling and necking effects. Necking increases the surface area, while the volume is reduced. If tracks are interrupted, balling effects might reduce the surface-to-volume ratio locally. As balling is the consequence of surface tension, the melt pool might get a spherical shape which has lowest surface-area-to-volume ratio compared to other shapes. Nevertheless, as balling might occur on various points in the volume the creation of new surfaces becomes predominant and the ratio $SA_{filtered}/V_{filtered}$ increases.

The ratio of $SA_{particles}/V_{particles}$ for the remaining particles is around 125–140 for most samples. Yet, sample 3 has a reduced ratio of around 108 which might be explained by a more spherically shape of the particles.

The number of remaining particles per mm³ ranges from over 6,000 up to nearly 34,000. For both the GRID and ROT strategy the samples
with highest hatch spacing show the lowest number of particles. Samples with the lower hatch spacing and layer thickness have the highest number of remaining particles. The results indicate that the number of remaining particles increases crucially with higher energy input for the same layer thickness. This might be explained by higher process temperatures leading to more semi-molten powder. Higher line energies for the higher layer thickness cause the same effect.

As “crowded regions” could be observed in various samples it was further analyzed which number of particles is attached to the surfaces or loose and trapped. For the GRID strategy samples 3.4–5.9% of the particles are trapped and not attached to the solid structures. For the ROT strategy samples only ~ 0.5% of the particles are trapped. Since in these samples the open porosities are larger, minor amounts of particles are expected to be trapped. Whereas GRID samples generally have a smaller pore size than ROT samples, particles in open pores can not be cleaned sufficiently. The impact of remaining trapped powder on functional properties can vary. While they are expected to have little impact on heat transmission due to their small contact points, their impact on permeability might be more significant.

## 4. Conclusion

This study focuses on the µ-CT characterization of open porous structures made by PBF-LB/M. The main scope is the analysis of powder particles attached to the structure. The surface area and volume of the particles have been analyzed and compared to the surface area and volume of the raw and digitally filtered porous structure.

Attached powder particles have been reported in various PBF-LB/M studies, especially for single laser tracks and lattice structures. Yet, there has been no comprehensive overview on their characterization and quantification throughout the parts' volume. With µ-CT-based 3D-imaging their distribution across the volume could be analyzed in a non-destructive way. The following can be concluded:

- µ-CT-based 3D-imaging has been proven to be an advantageous tool for characterizing AM made structures, especially for remaining powder particles.

- Remaining powder particles account for about 5–10% of the structural volume.

- The predominant part of the remaining particles is attached to the structures. For GRID samples up to 6% of the particles can be trapped in open pores.

- The remaining particles contribute to around 36–57% of the total surface area.

- The surface area of the structures varies considerably with applied scan strategy and process parameters. In general, the fraction of the surface area caused by powder particles increases towards higher $E_{vol}$ and for samples made by GRID scan strategy.

- This knowledge enables the possibility to create structures with high surface-to-volume ratio.

The presented results indicate the complexity of characterizing additively manufactured functional structures. Especially, attached powder particles have been found to be a major factor for the resulting surface area. Potential applications could lie for example in the field of thermal management, such as combustion or hot gas systems [27,28, 34], or chemical applications, like catalysts [29,30], where a larger surface can be advantageous. Also for AM made orthopedical or dental implants [31] the finding about surface modulations induced by powder remnants is important as it will influence the contact area between tissue and implant but at the same time a larger surface may potentially emit larger amount of material-derived ions and particles [32,33].

To customize open porous structures and their application related properties it is necessary to understand the relation between the manufacturing parameters and the resulting structural features. The present study shows how this understanding can be achieved and how it

can benefit future application design.

## CRediT authorship contribution statement

**Gerber Javier:** Data curation, Visualization. **Hesse Bernhard:** Conceptualization, Investigation, Validation, Writing – review & editing. **Kiener Christoph:** Writing – review & editing, Supervision, Funding acquisition. **Bortel Emely:** Conceptualization, Investigation, Methodology, Validation, Writing – original draft. **Sørby Knut:** Writing – original draft, Supervision, Conceptualization. **Otto Robert:** Investigation, Conceptualization, Writing – original draft, Supervision, Project administration.

## Declaration of Competing Interest

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.

## Acknowledgement

We acknowledge the kind support of Mrs. Elodie Boller with the preparation of the Synchrotron µ-CT setup and data collection at beamline ID19 of the ESRF.

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