Exploring crystallographic texture manipulation in stainless steels via laser powder bed fusion: insights from neutron diffraction and machine learning

Laser powder bed fusion of metals (PBF-LB/M) is a pivotal additive manufacturing technique that enables the production of intricate components. In addition to enabling the production of complex shapes, it allows for a high degree of freedom in manipulating the microstructure. The present investigation explores the manipulation of the crystallographic texture in AISI 304L stainless steels via PBF-LB/M, due to the possibility of tailoring the secondary hardening phenomena. Neutron diffraction provides efficient texture assessment, while decision tree regression reveals the complex interplay between processing parameters and the resulting crystallographic textures. Our investigation identifies the optimal PBF-LB/M processing parameters for obtaining strong texture along the build and laser scan directions. Additionally, microstructural characterisation of selected samples reveals the complex solidification structures. By employing advanced characterisation techniques and machine learning, this work provides insights into achieving or avoiding specific crystallographic textures during PBF-LB/M processing of stainless steels or other materials.


Introduction
Powder bed fusion-laser beam (PBF-LB/M) is an additive manufacturing process that allows the fabrication of near-net-shape components with complex geometries [1].A laser source is used for melting and consolidating metallic powders, in a layer-by-layer fashion, until the desired geometry is achieved.By employing appropriate process parameters, nearly defect-free metallic components can be produced -a primary goal that surpasses any further efforts to produce advanced materials.
Pioneering studies in the direction of texture manipulation with PBF-LB/M have pointed out the importance of the thermal gradient and the heat flow within the melt pool.Based on these observations, many studies have showcased the control of the crystallographic texture in various alloy systems [11][12][13][14][15][16][17][18][19][20][21][22][23].The case of austenitic stainless steels is of particular interest, since it has been shown that specific crystallographic textures can enhance or suppress the secondary hardening phenomena upon deformation (i.e. the Transformation Induced Plasticity-TRIP and Twinning Induced Plasticity-TWIP effects).Sun et al. managed to produce single crystal-like crystallographic texture in AISI 316L by keeping a constant <101> crystallographic orientation along the Building Direction (BD).Additionally, a bidirectional scanning pattern without any rotation between the successive layers is necessary for achieving a strong <001> crystallographic texture along the Scanning Direction (SD) [18,19,22].Taking these observations one step further, Sofinowski et al. [18] produced blocks of AISI 316L with different crystallographic textures along the in-plane direction by simply changing the laser scan angle with respect to one of the in-plane directions.
Although there are studies where strongly textured AISI 316L parts are obtained by PBF-LB/M, the required processing windows for the formation of each texture component are not yet clear [11,12,18,19,22].Thus, typically trial and error studies are undertaken to optimise the sensitive interplay between the most impactful process parameters, i.e. laser power, scanning speed, hatch distance and layer thickness.As such, a large number of samples are manufactured and characterised using time-consuming techniques, like Electron Backscattered Diffraction (EBSD).
The motivation of this work is to employ a high throughput characterisation method, like neutron diffraction, for optimising the process parameters and to assess the experimental data with state-of-the-art data science methods to achieve tailored process optimisation.To this end, Time of Flight (ToF) neutron diffraction is a very efficient characterisation method which enables the quantitative assessment of the crystallographic texture along the BD and the SD.Neutrons can deeply penetrate into the samples, giving nondestructive bulk information about, amongst other things, the crystallographic texture.The use of a wide neutron spectrum, enabled by the ToF, ensures that various crystallographic planes satisfy Bragg's law for diffraction in the course of a measurement; as such, a diffraction pattern containing several Bragg peaks renders this method ideal for efficient texture characterisation.
In the field of additive manufacturing and materials science, machine learning (ML) techniques have gained significant importance as they can help accelerate the process optimisation and material design in terms of relative density and mechanical strength [27][28][29][30][31][32][33][34].Some state of the art application of ML in metallurgy for instance include: Ueji et al. [29] employed a sparse mixed regression method to optimise the chemical composition and processing conditions of TRIP steels in order to develop compositions with superior tensile strength and elongation.Yao et al. [31] defined the processing routes that lead to a good balance between strength and ductility in Ti-6Al-4 V alloys processed by PBF-LB/M by applying a random forest regression model.Most recently, Minkowitz et.al [35] applied a combination of decision tree regression and extra tree regression in order to optimise the PBF-LB/M process parameters of an AlSi10Mg alloy in terms of density, ultimate tensile strength and hardness.
The primary goal of this investigation is to optimise the PBF-LB/M process parameters for manipulating the crystallographic texture of AISI 304L stainless steel.Additionally, the study seeks to reveal processing windows that should be adopted during PBF-LB/M.These findings will enable achievement or avoidance of strongly textured microstructures, both along the BD and SD.ToF neutron diffraction allows for a high throughput, quantitative assessment of the crystallographic texture, while decision tree regression enables a rapid identification of the complex relationships between the large number of process parameter combinations and the resulting crystallographic textures investigated in the present study.The trained decision tree model provides excellent predictive capabilities, as the process parameters proposed by the model lead to the fabrication of strongly textured samples.The microstructure of selected samples is analyzed with EBSD, in terms of crystallographic texture and melt pool morphology both along the BD and SD.This study unequivocally demonstrates the effect that each process parameter has on the crystallographic texture, narrows down the processing windows where each texture component is achievable, and provides a comprehensive guide for future studies that explore crystallographic texture formation in stainless steels by PBF-LB/M.

Sample fabrication
For the PBF-LB/M process, nitrogen atomised AISI 304L powder with maximum particle size of 45 μm, was purchased from Carpenter, UK.The PBF-LB/M fabrication was performed using a Sisma MySint 100 with a spot size of 55 μm, under an argon atmosphere (less than 100 ppm oxygen in circulation).A range of different process parameters were used for building test cubes of 5 × 5 × 5 mm 3 .Table 1 lists the different values of process parameters that were combined to produce the samples which were used to create the decision tree regression model.Supports were not used for the fabrication of the samples.Table S1, in the Supplementary material section, shows the label of each sample along with the processing parameters used to fabricate the sample, its volumetric energy density, its density and the r 220 and r 200 (both are explained in the next section of the manuscript).In order to investigate how the process parameters affect the crystallographic texture along the in-plane direction, a bi-directional scanning pattern without any rotation between the successive layers was adopted.
For each set of process parameters, the volumetric energy density (VED) was calculated for all samples, by using the following equation [20]: where P is the laser power in W, v is the laser scan speed in mm/s, h is the hatch distance in μm and l is the layer thickness in μm.

Neutron diffraction
The samples were mounted on the ToF neutron diffractometer POLDI at the SINQ neutron source of the Paul Scherrer Institute, in Switzerland [36].ToF diffraction provides a high throughput method for assessing the crystallographic texture along the BD and SD, as several diffraction patterns can be measured simultaneously, in particular for POLDI, the diffraction peaks in the q-range of 3-9 Å −1 .A series of neutron diffraction measurements were undertaken with a 3.8 × 3.8 × 3.8 mm 3 gauge volume.Two measuring positions were employed.For the first, the scattering vector was parallel to the BD while for the second, the samples were rotated so that the scattering vector was parallel to the SD.Each sample was measured for 10 minutes, at each position.The neutron data were reduced and fitted using the open-source software Mantid [37] and the POLDI-specific functions.For the assessment of the crystallographic textures, at either BD or SD, the integrated diffraction intensity of the diffraction peaks was used.In particular, the following diffraction intensity ratios were calculated for every sample at every direction: where or {200} planes, respectively, aligned perpendicular to the scattering vector, Q, (i.e. the [220] and [200] crystallographic directions parallel to Q).In contrast, in a powder sample that was measured as a reference, the values of r220 or r200 are 0.28 and 0.32, respectively.

Regression trees
Decision tree regression (DTR), or regression trees, is a commonly used supervised machine learning technique, which aims at training a model using well-labelled data.
Based on that data, the model can make predictions [38,39].In more simple terms, the labelled data act as 'supervisors' to the model, so that it predicts the output correctly.DTR can be used for all sizes of datasets, and most importantly, they are not sensitive to outliers.DTR provides a very balanced tradeoff between the result accuracy and time efficiency, as well as to the programming and result interpretation difficulty, when compared to other techniques.The resulting trees from the DTR have a hierarchical structure, which to the most part resembles an actual tree [35,[40][41][42][43][44].Based on the input data, DTR creates a single tree that can predict a specified outcome.When it comes to growing the tree, the first priority is the preparation of the dataset.The dataset needs to be split into two categories, the dependent variables or responses that are the ones to be predicted, and the independent variables or predictors used for the task [35,40,42].With the entire dataset at the first node of the tree or root node, the algorithm evaluates different split points for each one of the predictors and it selects the one that provides the minimum summary of squared residuals [28,35,40,42].As a result, for that node this split is the optimal one.This process goes on until a pre-specified criterion has been met.The maximum tree depth, the minimum number of observations per leaf, or the minimisation of the sum of squared residuals can be used as stopping criteria for the tree growth.One can realise that a deep tree, with few observations per leaf, may have excellent predictive performance on the data that were used to train the model, however it may fail to make accurate predictions when using new data.On the other hand, a very small tree may not capture important information about the data.Consequently, the tree size is one of the most important properties that can prevent overfitting and lead to a good balance between predictive accuracy and model complexity; it needs to be optimised before any predictions are made.
The most common technique that is used for optimising the size of the regression tree is called pruning.In general, pruning involves removing nodes or branches that do not significantly contribute to the predictive accuracy of the entire regression tree.For the present investigation, the so-called cost complexity pruning technique was employed, in order to find the optimal tree size for the studied datasets [45,46].By starting from the full-sized regression tree, cost complexity pruning aims at creating a sequence of subtrees by removing nodes and at finding the optimal subtree by minimising a cost complexity metre, R α (T), that is dependent on the prediction accuracy and the size of the tree.More specifically, R α (T) is defined as: where R(T) is the sum of squared residuals of the tree, α is the cost complexity parameter and T is the number of leaves of the tree.The degree of pruning can be controlled by the value of the cost complexity parameter.
For small values of α, larger trees are favoured, since they typically exhibit a smaller sum of squared residuals, while for larger values of α, smaller trees are favoured.One can realise that the value that is selected for the cost complexity parameter is of high importance.To compute the optimal value of α and to ultimately find the optimal size of the regression tree, the algorithm starts with a full-size regression tree and calculates the R a (T) for α equal to zero.Then it proceeds to the first subtree and it calculates the R a (T) by iterating different, increasing values of α, until the subtree has a better R a (T) than the previous tree.This process continues until a subtree with only one node is reached.The optimal subtree is the one with a value of α that leads to the smallest cross-validation error.This process is repeated 10 times to ensure a 10-fold cross validation and thus to avoid overfitting.After the 10 iterations are carried out, the value of α that results in the smallest cross-validation error on average, is selected as the optimum.In the end, the optimal regression tree is the subtree with the minimum computed R α (T) using the previously identified optimal value of α.For the present study, the DTR algorithm was built in MATLAB.Figure S1 of the supplementary materials section shows the performance of the DTR model for both BD and SD.

Density and microstructural characterisation
The density of the samples was determined by the Archimedes principle, using a Mettler-Toledo XSR204DR scale equipped with the dedicated density measurement kit.
In order to ensure statistical accuracy, each sample was measured 3 times and the reported results are the mean density value of each sample.
For the microstructural characterisation, the samples were ground with a 1200 grit SiC paper and then electropolished for 10 s with a 16:3:1 (by volume) ethanol, glycerol and perchloric acid solution at 48 V to obtain appropriate surface quality.A selection of samples was also electrochemically etched by using a 10% aqueous oxalic acid solution for 60 s at 15 V to reveal the melt pool boundaries.A field emission gun scanning electron microscope (FEG SEM) Zeiss ULTRA 55 equipped with EDAX Hikari Camera operated at 20 kV in high current mode with 120 µm aperture was used.For each of the IPFs shown later, several EBSD maps were stitched together (covering an area of ∼3.2 mm 2 ) to improve the grain statistics and the reliability of the texture analysis.The EBSD raw data was post-processed using the EDAX OIM Analysis 8 software.

Effect of density on the resulting crystallographic texture
Before conducting any assessment and model prediction on the crystallographic textures, achievable by PBF-LB/M on AISI 304L stainless steels, it is important to assess the density of the printed parts.Apart from the profound reason of mechanical and structural integrity, it has been observed that formation of pores during PBF-LB/M can interfere with the heat flow within the melt pool [20].As presented in the introduction, the heat flow is crucial for the manipulation of the crystallographic texture.Figure 1 shows EBSD orientation maps of two AISI 304L stainless steels that have been processed with different process parameters.Both low and high magnification EBSD orientation maps of Figure 1(a), show that the employed process parameters led to the formation of keyhole porosity at the tips of the melt pools, despite the high degree of melt pool overlap, compared to Figure 1(b).It should be noted that the melt pool overlap depends on the melt pool size, which is a consequence of the combined effect of laser power and laser scan speed.
The pores disturb the heat flow within the melt pool, negatively influencing the solidification of the grains within the melt pool and thus hinder the epitaxial growth of the grains between adjacent melt pools.As a result of the combined process parameters and the defect formation, the resulting crystallographic texture is nearly random.In contrast, in the low and high magnification EBSD orientation maps of Figure 1(b), the chosen process parameters lead to a sample that is almost free of porosity.Additionally, the melt pools of that sample are wide and deep, resulting in an almost single crystal like <101> crystallographic texture along the BD, with the occasional occurrence of strongly <001>//BD textured grains along the centerline of the melt pools.
It is apparent, therefore, that in order to facilitate the DTR predictions of the crystallographic texture, the processing window needs to be defined wherein the formation of pores is avoided.This is crucial since DTR model is not capable of taking the porosity into account for predicting the desired textures.
The VED is often used as a metric to compare components manufactured with different sets of PBF-LB/M process parameters and relate them to porosity formation [47,48]. Figure 2(a) shows the relationship between VED and porosity for the samples that were also probed with neutron diffraction and are used to create the DTR model.As also known from the literature and observed in Figure 2(a), low VED values are associated with the formation of lack of fusion porosity and high VED with the formation of keyhole porosity [49].shows a micrograph of a sample that was produced with very low VED and as a result lack of fusion pores are evident across the sample.Figure 2(c) shows a micrograph of a sample that has been produced with high VED, where keyhole pores are present.As discussed in section 3.3., porosity strongly affects the formation of crystallographic texture and therefore, when evaluating the results of the DTR model, the predicted process parameters need to yield a VED value that lies in the range where dense material is produced, i.e. the so-called conduction/stable keyhole mode regimes.Despite the fact that VED appears to correlate well with the formation of porosity, it has been shown that it does not predict well other properties like the melt pool characteristics [47], which is essential for texture formation during PBF-LB/M.

Crystallographic texture prediction using DTR
Figure 3 shows the results of the previously described, optimised DTR model for the prediction of the <101>-texture along the BD, i.e. using the r220 value of the neutron diffraction results.The table of Figure 3 shows both the training error of the model and the 10fold cross validation error.Both errors are very low, showing that DTR fits satisfactorily the dataset.The model predicts that there are three pathways or processing routes that lead to the formation of a strong <101>-texture along the BD, i.e. high values of r220.Among the used scanning speed values (listed in Table 1) the DTR reveals that in order to achieve a strong <101> along the BD, the scanning speed must have a maximum value of 900 mm/s.Hence strong <101>texture along the BD can be obtained for scanning speeds ranging between 400 and 900 mm/s.On the other hand, the laser power can vary greatly, however, in accordance with keeping the VED in the appropriate range of values, i.e. achieving dense parts which is typically achieved at VEDs in the range of 60-110 J/mm 3 .In our analysis, the DTR model reveals that the laser power on its own appears to be a poor indicator of the <101>texture strength along the BD, as the pathways where strong <101>-texture is obtained contain almost all values of laser power that were used for manufacturing the control samples.The hatch distance has to be restricted in a relatively narrower range, as compared to the laser power.The DTR model recommends that the hatch distance has to be set towards the upper limit of the process parameter range, specifically larger than 75 μm, to achieve a strong <101>-texture along the BD.The DTR model identifies the laser scan speed as the process parameter with the largest influence on the intensity of <101>-texture along the BD, and strong crystallographic texture is obtained in samples with scanning speeds of up to 900 mm/s.The importance of the scanning speed is also depicted in the bar chart of Figure 3.This chart shows the importance that each predictor (i.e.laser power, scanning speed, hatch distance) has on the model prediction, where the scanning speed has the highest importance, while the laser power has the least.In order to achieve a strong <101>-texture along the BD, the laser power can vary a lot, taking values that range from 120 W to 175 W. Lastly, in terms of importance, the hatch distance lies somewhere in the middle between the scanning speed and the hatch distance, and strong <101>-texture along the BD can be achieved for values of hatch distance ranging from 75 μm to 100 μm.Taking the above observation into consideration, it appears that a strong <101>-texture along the BD can be achieved by adapting scanning speeds in the middle of the used range, by keeping the hatch distance to relatively high values, and by adjusting the laser power appropriately to ensure a VED that produces dense samples.
Figure 4 shows the results of the previously described, optimised DTR model for the <001>-texture along the SD.The table of Figure 4 presents both the training error of the model and the 10-fold cross validation error.As it is the case for the dataset of the <101>-texture along the BD, here both errors have also very low levels, showing that the DTR fits the dataset very well.The DTR predicts that there are five pathways or processing routes that lead to the formation of a strong <001>texture along the SD.Contrary to the prediction of the model for the BD, where all the processing routes for the strong <101>-texture along the BD are located in one branch of the tree, here the processing routes that lead to a strong <001>-texture along the SD are spread in different branches of the tree.The DTR reveals that the formation of <001>-texture along the SD is favoured in general by relatively low hatch distances.More specifically, for low values of laser power and medium values of scanning speed, the hatch distance must remain below 75 μm.For medium values of power, the hatch distance must be limited to 65 μm.In this case, the scanning speed needs to be adjusted accordingly, to avoid the formation of keyhole porosity, as discussed above, in association with a reasonable value of the VED.Additionally, a strong <001>-texture along the SD can be obtained for hatch distance values between 75 and 85 μm and for high values of laser power (above 142.5 W).It is thus seen that, in contrast to the formation of <101>-texture along the BD, the formation of a strong <001>-texture along the SD is not heavily dependent on only one process parameter.This is also verified by the bar chart of Figure 4 that shows the importance of each process parameter for the <001>-texture along the SD.It is observed that the hatch distance has the strongest effect on the <001> texture along the SD.However, even for medium values of hatch, strong <001>-texture along the SD can be achieved, with the appropriate combination of laser power and scanning speed.
To evaluate the accuracy of the prediction of the DTR model regarding the crystallographic texture along the building and the scanning directions respectively, additional control samples were produced with process parameters other than that of the training dataset, and their r220 and r200 values were obtained by neutron diffraction.Table 2 shows the processing parameters used for each control sample, their VED and Table 3 and Table 4 report the measured r220 and r200 and the DTR predicted r220 and r200 respectively, along with their corresponding errors.The error values of the measured r220 and r200 have been calculated by applying the error propagation rule, originating by the fitting error of the integrated intensity of each diffraction peak.The error of the DTR-predicted values has been calculated from the mean squared error of the DTR model.It is observed that the DTR model predicts both texture ratios, r220 and r200, very well.Additionally, the processing routes and the trends that the DTR model reveals for the manipulation of the crystallographic texture along both the BD and SD are also verified by the control samples.More specifically, considering the crystallographic texture along the BD, the samples that are processed with the lowest scanning speed (see e.g.sample Nr4 with 450 mm/s laser scan speed) are the ones with the strongest <101>-texture along the BD.As the scanning speed increases, the intensity of the crystallographic texture decreases, as illustrated by sample Nr6 that has a scanning speed of 900 mm/s and the weakest <101>-texture along the BD.On the other hand, considering the crystallographic texture along the SD, the samples with the lowest hatch distance tend to have the strongest <001>-texture along the SD.It is also observed that a combination of high laser power with low scanning speed and a medium hatch distance can also lead to a strong <001>-texture along the SD.Lastly, sample Nr4, which has a hatch distance of 110 μm, shows the weakest <001>-texture along the SD.It is also noted that all control samples listed in Table 2 are dense.

Microstructural characterisation
To understand the effect of different process parameters on the resulting microstructure and crystallographic texture, samples 4 and 6 (hereafter denoted as V4 and V6 accordingly) from the validation set were investigated with EBSD. Figure 5(a,b) show EBSD maps with IPF colouring parallel to the BD where the plane of observation is perpendicular to the SD (cf. the schematic in Figure 5).Figure 5(c,d) show EBSD maps with IPF colouring parallel to the SD where the plane of observation is perpendicular to the BD (cf. the schematic in Figure 5).Figure 5(e,f) show the corresponding pole Figures for samples V4 and V6.As it has been predicted by the DTR model and validated by neutron diffraction, both samples exhibit strong <101> and <001> textures both along the BD and SD respectively.Specifically, sample V4 exhibits stronger <101> texture along the BD, compared to V6.On the other hand, sample V6 exhibits a stronger <001> along the SD compared to V4.These observations corroborate well to the neutron diffraction data.
Figure 6(a,d) shows SEM micrographs of samples V4 and V6 respectively.For these micrographs, the samples are etched in order to reveal the melt pool boundaries along with the fine details of the rapid solidification structure of the samples.Sample V4 exhibits wider and shallower melt pools compared to sample V6.In addition, it is observed that for sample V6 the melt pools have a larger degree of overlap than they do for sample V4.This is a direct consequence of the vastly different hatch distance that was used for the fabrication of each sample, thus corresponding to significantly more track overlap during the bidirectional scanning.During PBF-LB/M, the crystallographic texture formation is closely associated with the geometric and morphological characteristics of the melt pool, as the melt pool shape determines to a large degree the thermal gradient within the melt pool.It is established in literature [22,23] that for deeper and wider melt pools, the heat flow along the melt pool centerline is vertical, while at either side of the melt pool the heat flow is perpendicular to the inclined melt pool boundaries and directed towards the centerline.The grains solidify with their easy growth direction, the <001> direction, aligned with the heat flow.As a result, the grains have an orientation with their <001> aligned with the BD along the centerline, while on the sides of the melt pool grain growth occurs at a ± 45 o angle with respect to the BD.Such typical grain morphology is seen in Figure 6. Figure 6(b) and e show the growth of the solidification cells for samples V4 and V6 respectively.As observed in literature [14,15,18] and despite the differences in the melt pool shape, for both samples along the centerline of the melt pool, the solidification cells are parallel to the BD (shown with red arrows in Figure 6(b,e)), while on the sides of the melt pool the cells solidify at angles approximately at ±45 o with respect to the BD (shown with green arrows in Figure 6(b,e)).This can be validated by EBSD of the same or similar areas, where it is observed that the centerline of the melt pool has a strong <001>texture along the BD while the sides of the melt pool have strong <101>-texture along the BD (Figure 6(c,d) for samples V4 and V6 respectively).Crucial for the texture formation is the role of epitaxial growth between adjacent melt pools, whether sideways or along the BD.It is well known that the nucleation of new grains is energetically less favourable than grain growth [18].As a result, new solidification cells tend to grow epitaxially along the <001> directions of the already solidified cells.In Figure 6(b,e) the epitaxial growth of the solidification cells both along the centerline and the sides of the melt pools can be seen, and thus large grains extend along multiple PBF-LB/M layers.
For the crystallographic texture along the scanning direction, existing literature suggests that as long as a strong <101>-texture is obtained along the BD, with the application of a bi-directional scanning pattern without any rotation between the subsequent layers, a strong <001>-texture develops along the SD [15,18,22].However, in our investigation, as predicted by the DTR model and confirmed by the neutron diffraction and the EBSD data, despite the fact that sample V4 exhibits a stronger <101>-texture along the BD, it exhibits a weaker texture in the SD direction, compared to sample V6.Sample V4 was produced with two times larger hatch distance compared to sample V6 (110 μm versus 55 μm).In contrast to the well-understood mechanism of texture development along the BD, there have been several different theories on the texture development along the SD [15,18].One mechanism suggests that the development of the strong <001>-texture along the SD is a result of the intra-layer epitaxial growth that is promoted by the bi-directional scanning strategy [18].It has been observed that the melt pool centerlines also solidify with an angle of 10-15 o and thus the heat flow is also inclined towards the SD.As the laser rotates 180 o during the bi-directional scan, grains with <001> orientation grow further as the only means to maintain the epitaxial growth between adjacent laser scans.However, the inclined heat flow with respect to the SD often leads to the solidification of grains with orientations different from the desired <001> along the SD [18].These grains are mainly found to be located along the tail of the melt tracks.Such grains are typically seen as stripes of relatively random crystallographic texture, as shown in Figure 5  (a,c).Additionally, grains with orientation far from the ideal, can also solidify along the sides of the melt pools due to stochastic events.In our investigation, we observe that despite the fact that sample V4 exhibits stronger texture along the BD than sample V6, this does not apply for the SD, as sample V6 has much stronger crystallographic texture along the SD.The aforementioned angle of the heat flow towards the SD that has been observed in literature can be the reason behind the texture difference between the two samples with respect to SD.For the case of sample V4, the relatively low scanning speed results in short melt tracks that do not promote epitaxial growth between adjacent scanning tracks and give rise to the solidification of grains with undesired orientations.As such, sample V4 exhibits a larger fraction of grains that have escaped the epitaxial growth, as seen in Figure 5(c).Additionally, the large hatch distance leads to limited remelting between the adjacent melt tracks.This is evident by the smaller overlap that the melt pools have for sample V4 compared to V6 (see Figure 6).Since the extent of remelting is relatively low, the likelihood that grains with undesired orientation are remelted and solidified again with the desired orientation is small.Additionally, combined with shorter lengths of the scanning track, the larger hatch distance is another factor that can hinder the intra-layer epitaxial growth between adjacent melt tracks.The mechanism of the intralayer epitaxial growth for the development of strong <001>-texture along the SD aligns well with the DTR model.It underscores the primary importance of the hatch distance, with the scanning speed being the second most important parameter.
Typically the building size can affect the microstructure [50][51][52], specifically when employing short scanning in the mm range [53].The 5 mm specimen size employed in the present study is considered representative of the behaviour of larger samples and the obtained results were applied to full-scale sample fabrication, obtaining equivalent crystallographic textures in [54].The influence of each process parameter and the trends identified by the decision tree regression model, for both BD and SD, can be utilised for replicating similar microstructures using different machines and materials.However, it is recommended that the identified process parameters are taken into account as ranges (i.e.low -medium -high) rather than as absolute values.This is because it is well known that different laser powder bed fusion setups yield different results [55] for the same processing parameters, due to variations in beam spot size, energy distribution, beam shaping, gas flow, base plate size or other parameters that influence the heat flow and thus can potentially affect the texture control.

Conclusions
In the present investigation we identify the optimal processing windows of the PBF-LB/M process to achieve or avoid the fabrication of strongly textured AISI stainless steel samples, by combining neutron diffraction with a decision tree approach.Below we summarise the main findings: The combination of neutron diffraction with a decision tree regression represents a high throughput and easily interpretable synergy between experimental techniques and data analysis.This approach has low computational cost and it provides accurate predictions of the resulting crystallographic texture, both along the BD and SD, for AISI 304L stainless steel samples.According to the decision tree regression model, strong <101> crystallographic texture along the BD is influenced by the combination of scanning speed and hatch distance, with the scanning speed being the most important parameter.On the other hand, strong <001>-texture along the SD is not predominantly influenced by any single parameter, but rather by a combination of parameters.Amongst these, the hatch distance exhibits marginally higher importance, compared to the scanning speed and laser power.Microstructural analysis of the validation samples confirms that the strong texture along the BD derives from the inclined solidification of the grains within the melt pool, and the epitaxial growth between melt pools of adjacent layers.Along the SD, it is revealed that the dominant mechanism for the formation of a strong <001>-texture is the intralayer epitaxial growth induced by the bi-directional scanning strategy between adjacent melt tracks.In this process, the hatch distance appears as the most influential parameter.
220 and I 200 are the integrated intensities of the 220 and the 200 diffraction peaks accordingly, and I total is the sum of the integrated intensities of the 111, 200, 220 and 311 fcc diffraction peaks.Thus, values of r220 or r200 close to 1 indicate single crystals with the {220}

Figure 2 .
Figure 2. (a) Relationship between the VED and porosity for the samples that were used as the input for the DTR model.(b) Lack of fusion pores for a sample that has been produced with low VED.(c) Keyhole porosity for a sample that has been produced with high VED.

Figure 2 (
Figure 2(b)  shows a micrograph of a sample that was produced with very low VED and as a result lack of fusion pores are evident across the sample.Figure2(c)shows a micrograph of a sample that has been produced with high VED, where keyhole pores are present.As discussed in section 3.3., porosity strongly affects the formation of crystallographic texture and therefore, when evaluating the results of the DTR model, the predicted process parameters need to yield a VED value that lies in the range where dense material is produced, i.e. the so-called conduction/stable keyhole mode regimes.Despite the fact that VED appears to correlate well with the formation of porosity, it has been shown that it does not predict well other properties like the melt pool characteristics[47], which is essential for texture formation during PBF-LB/M.

Figure 3 .
Figure 3. Results of the DTR model for the prediction of the crystallographic texture along the BD.

Figure 4 .
Figure 4. Results of the DTR model for the prediction of the crystallographic texture along the SD.

Figure 5 .
Figure 5. EBSD maps of (a) sample V4, (b) sample V6 along the BD, (c) sample V4, (d) sample V6 along the SD and the corresponding pole Figures for (e) sample V4 and (f) sample V6.The schematic depicts the areas of observation for (a) and (b) or (c) and (d) with respect to the sample coordinate system.

Figure 6 .
Figure 6.Low magnification SEM micrographs showing the melt pool characteristics of (a) sample V4 and (d) sample V6.High magnification SEM micrographs showing the solidification structure within the melt pools for (b) sample V4 and (e) sample V6.High magnification EBSD maps showing the crystallographic orientation of the solidification structure within the melt pool for (c) sample V4 and (f) sample V6.

Table 1 .
Ranges of process parameters utilised to produce the samples that were used for creating the decision tree regression model.

Table 2 .
Process parameters and VED for a small batch of samples that were produced in order to validate the predictive ability of the DTR model.

Table 3 .
Measured and predicted r220 for a small batch of samples that were produced in order to validate the predictive ability of the DTR model.

Table 4 .
Measured and predicted r200 for a small batch of samples that were produced in order to validate the predictive ability of the DTR model.