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Scientic Reports | (2021) 11:10393 |
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Non‑oxide precipitates in additively
manufactured austenitic stainless
steel
Manas Vijay Upadhyay1*, Meriem Ben Haj Slama1,2, Steve Gaudez1,3, Nikhil Mohanan1,
Lluis Yedra2,4,5, Simon Hallais1, Eva Héripré2 & Alexandre Tanguy1
Precipitates in an austenitic stainless steel fabricated via any Additive Manufacturing (AM), or 3D
printing, technique have been widely reported to be only Mn‑Si‑rich oxides. However, via Transmission
Electron Microscopy (TEM) studies on a 316L stainless steel, we show that non‑oxide precipitates
(intermetallics, suldes, phosphides and carbides) can also form when the steel is fabricated via
Laser Metal Deposition (LMD)—a directed energy deposition‑type AM technique. An investigation
into their origin is conducted with support from precipitation kinetics and nite element heat
transfer simulations. It reveals that non‑oxide precipitates form during solidication/cooling at
temperatures ≥ 0.75Tm (melting point) and temperature rates ≤ 105 K/s, which is the upper end of the
maximum rates encountered during LMD but lower than those encountered during Selective Laser
Melting (SLM)—a powder‑bed type AM technique. Consequently, non‑oxide precipitates should form
during LMD, as reported in this work, but not during SLM, in consistency with existing literature.
Additive Manufacturing (AM), or 3D printing, of alloys is a revolutionary technology that simultaneously manu-
factures a part with a desired geometry and creates the material microstructure without the need for tooling.
is unique ability has generated a widespread industrial interest to adopt AM not only to manufacture entire
alloy parts but also to repair broken/damaged parts. However, manufacturing entire parts or repairing portions
of a broken part via AM to obtain microstructures that exhibit desired material properties is a great challenge,
and it has been a subject of intensive research in recent years.
An AM process involves reading a 3D part geometry from a computer-aided design le and building it in a
layer-by-layer manner by locally melting a feedstock (powder/wire) using a moving heat-source (laser/electron
beam). Based on the manner in which heat-source and feedstock interactions occur, alloy AM processes can be
classied1 into (i) Directed Energy Deposition (DED), where the feedstock material is directly fed into the moving
heat-source, and (ii) Powder Bed Fusion (PBF), a two-step repetitive process involving powder deposition on a
powder-bed followed by scanning via a heat-source. AM of austenitic stainless steel parts is typically done via
Laser Metal Deposition (LMD: a laser-based DED approach) and Selective Laser Melting (SLM: a laser-based
PBF approach). In both approaches, the heat-matter interactions subject the material to a sequence of highly
non-equilibrium processes, viz. melt-pool dynamics, rapid solidication and solid-state cooling-heating cycles,
which result in the formation of hierarchical microstructures exhibiting physical and chemical heterogeneities
at multiple length scales1.
In the case of 316L Stainless Steel (316LSS) fabricated via SLM or LMD, the hierarchical microstructures are
composed1–8 of (i) precipitates, micro-segregations, porosities and dislocation structures at the intragranular level
and (ii) heterogeneous grain morphologies and sizes, texture and voids at the polycrystalline level. Amongst all
these features, precipitates are one of the smallest in size and they play a crucial role in determining the material
response3,4. During plastic deformation, precipitates can impede dislocation motion resulting in hardening via
mechanisms such as Orowan bypass, cross-slip, etc.9 Furthermore, the presence/absence of some precipitates
OPEN
Laboratoire de Mécanique des Sols, Structures et Matériaux (MSSMat), CNRS
*
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can aect the corrosion, wear, fatigue and fracture resistance of a steel2,10. It is therefore important to understand
their origin in order to control their formation in the microstructure and optimize material properties.
Conventionally processed/post-processed 316LSS is known to contain a plethora of dierent kind of pre-
cipitates including oxides of transition metals (Fe, Cr, Ni, Mn, Mo) and silicon11–13 as well as non-oxides such
as transition-metal carbides10, suldes14–17, phosphides18 and intermetallics19,20. In contrast, however, a series of
recent Transmission Electron Microscopy (TEM) studies2–7 report the sole presence of Mn-Si–O precipitates in
SLM and LMD 316LSS. is signicant dierence in the type of precipitates between conventionally processed/
post-processed and additively manufactured (LMD or SLM) 316LSS can be attributed to the dierences in the
temperature rates encountered during these processes. In addition, oxidation of Mn and Si precipitates results
in the highest reduction in the Gibbs free energy in comparison to other transition-metal (Fe, Cr, Ni and Mo)
oxides21, which favors the formation of Mn-Si-O over other oxide precipitates.
It is well known that precipitate sizes in steels decrease with increasing solidication/cooling temperature
rates15,16. For conventionally processed/post-processed 316LSS, where temperature rates much less than 102K/s
are encountered, oxide and non-oxide precipitate sizes typically range from 1μm to several tens of microns15,16.
Meanwhile, during LMD and SLM processes, the maximum temperature rates encountered fall in the range
102–105K/s22 and 106–107K/s23, respectively. ese magnitudes are consistent with the average size of Mn-Si-O
precipitates reported in LMD 316LSS (> 100nm) and SLM 316LSS (< 100nm)3,7, respectively. However, none
of these works report the presence of non-oxide precipitates. Based on these studies, one could deduce that the
temperature rates at which non-oxide precipitates stop forming in 316LSS should be below 102K/s, which is the
lower end of the maximum rate encountered during any AM process.
Recent TEM studies on 316LSS powders fabricated via inert gas atomization1,7,24 have revealed the presence
of a signicant amount of non-oxide precipitates (rich in Mo, Cr, P and S) together with Mn-Si–O precipitates.
Interestingly, the maximum cooling rates encountered during inert gas atomization25–27 are in the same range
as those occurring during LMD i.e., 102–105K/s, which suggests that there should be a signicant presence of
non-oxide precipitates in LMD 316LSS. However, none of the existing studies on precipitates in LMD 316LSS
conclusively report the presence of non-oxides. In a very recent study, Barkia etal.28 reported the presence of
an Mo-Cr-rich zone and an Mn–Mo–Cr-rich zone (around an Mn–Si–O precipitate) within the walls of an
intragranular cellular solidication structure in their LMD 316LSS. However, these cell walls are known to be
sites of preferential segregation of Mo and Cr1, and the reported presence of Mo–Cr and Mn–Mo–Cr zones can
be considered only as circumstantial evidence of the presence of non-oxide precipitates.
In light of the above, the main aim of this paper is to answer the following questions: Can non-oxide pre-
cipitates form during LMD of 316LSS? What is the threshold temperature and temperature rate above which
non-oxide precipitates stop forming in 316LSS? To answer the rst question, we have performed a series of
Scanning-TEM (STEM) studies together with Electron-Dispersive X-ray Spectroscopy (EDS). To answer the
second question, we have performed Finite Element (FE) heat transfer simulations to better understand the
temperature rates encountered during LMD and used this information together with the results of precipitation
kinetics simulations to understand the role of temperature and temperature rates on nucleation and growth of
non-oxide precipitates. is analysis is also applied to understand the absence of non-oxides in SLM 316LSS.
e 316LSS powder used in this work had been produced via the inert gas atomization process by Höganäs
AB. e wrought alloy used to manufacture this powder had the chemical composition in weight percent (wt.
%): Cr—16.9, Ni—12.7, Mo—2.5, Mn—1.5, Si—0.7, P—0.015, C—0.011, S—0.005 and Fe-balance. Presence of
trace amounts of oxygen in the inert gas atomization chamber can introduce oxygen into the 316LSS powder
obtained at the end of this process; according to the documentation of Höganäs AB29, a 316LSS powder particle
produced via their inert gas atomization process can contain up to 0.05 wt. % of O.
e 316LSS powder had been fed into the LMD machine to print a single-track (one linear laser pass per
layer) 3-layer wall on a hot-rolled 316LSS substrate via a bidirectional (forth–back–forth) scanning strategy
as illustrated in Fig.1a. Following the building of the 3-layer wall and aer the substrate had cooled down, a
60-layer wall was built on the same substrate as shown in Fig.1a. e Electron Back-Scattered Diraction (EBSD)
orientation map of a cross-section in the middle part of the 3-layer wall (Fig.1b) and the 60-layer wall (Fig.S1)
reveal a weakly-textured microstructure with columnar grains in the bulk surrounded by a thin layer of smaller
equiaxed grains, which is typical for an LMD process.
ree TEM lamellae (L1, L2 and L3), each thinner than 100nm, had been extracted from three dierent
columnar grains of cross-section A-A of the 3-layer wall (Fig.1b). Two lamellae (L4 and L5) were extracted from
two columnar grains, one near the top and one near the bottom of the 60-layer wall (Fig.S1). All lamellae were
studied via (i) High-Angle Annular Dark-Field (HAADF) STEM imaging to identify the location of precipitates
and (ii) EDS chemical mapping to understand their chemical composition (Fig.2 and Fig.S2). HAADF images
and EDS chemical maps help identify intragranular chemical heterogeneities; in LMD 316LSS, these heteroge-
neities are cellular solidication structures and precipitates.
Intragranular cellular solidication structures in any AM 316LSS typically have cell walls with lower concen-
tration of Fe and higher concentration of Cr and Mo than the surrounding matrix1,4; these cellular structures can
be discerned from the EDS maps in Fig.2 and Fig.S2. ese structures also have their long-axes aligned with the
crystal growth direction during solidication1. Since L1 and L2 had been extracted in directions nearly parallel
and perpendicular to the growth direction of their respective grains (Fig.1), the long-axis of cellular structures in
L1 and the grid-like cross-section of the cellular structures in L2 can be discerned. L3 forms a random angle with
the grain growth direction, which makes it dicult to discern the cellular structures. Nevertheless, a Y-shaped
band can be observed in its Fe, Cr and Mo maps. L4 also shows a complex intragranular cellular structure whose
precise orientation is hard to discern from the Fe, Cr and Mo maps (Fig.S2). L5 has the long-axes of its cellular
solidication structures aligned in-plane at a small angle with the horizontal direction. Similar to Barkia etal.28,
Mo-Cr and Mo-Cr-Mn rich zones are observed in the cellular solidication structures in L1 and L4, however,
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at the magnication level shown in Fig.2 and Fig.S2, it is not possible to discern whether or not these zones
are forming precipitates.
e chemical composition of the lamellae L1–L5 obtained from the EDS maps shows that all lamellae have
a lower wt. % of Fe and Cr and higher wt. % of Mn, O, P, S and C than the wrought alloy (TableS1). Ni is higher
for L1, L2, L4 and L5 but lower for L3. Mo is higher for L3 and L5 but lower for the rest. Si is higher for L1, L2
and L3 but lower for the rest.
55 precipitates have been identied in these lamellae: 16 in L1, 5 in L2, 2 in L3, 17 in L4 and 15 in L5. Most
of them could be discerned from the HAADF images in Fig.2 and Fig.S2, however, some of them were discov-
ered aer performing high-resolution HAADF imaging (Fig.3 and Fig.S3). In order to facilitate identifying the
precipitates and dierentiating between them, a classication scheme and a nomenclature system is proposed
in Table1. Based on this classication scheme, out of the 55 precipitates, 16 are oxides (29.1%), 3 are non-oxides
(5.4%) and 36 (65.5%) are mixed.
Figure3 shows the HAADF images and EDS chemical maps for all non-oxide and mixed precipitates together
with at most one oxide precipitate (if any) in L1–L3; Fig.S3 shows the HAADF images and EDS maps for non-
oxide and mixed precipitates in L4 and L5. EDS line prole analysis (Methods) has been performed for each
precipitate; Fig.4 shows the EDS line proles for two of the most complex mixed precipitates. Following this
analysis, the chemical composition of all precipitates had been compared with the nominal composition of the
316LSS wrought alloy. Based on this comparison the elements in each oxide and non-oxide precipitate, and
all the inclusions in each mixed precipitate, have been classied into two categories: (i) higher and (ii) lower
composition than wrought alloy. is classication is used to tabulate each element in all precipitates of L1, L2
and L3 in TableS1.
All precipitates consistently show a decrease in Fe with respect to the wrought alloy and the lamella to which
they belong. Most precipitates show a decrease in Ni, however, these concentrations never become zero. TEM
lamella preparation can lead to partial slicing of precipitates and in most cases include some proportion of the
surrounding matrix along the thickness direction; this is also evidenced via the distortions caused by dislocation
lines in the HAADF images of oxides (Fig.3). Hence, non-zero compositions of Fe in all precipitates should
mainly arise from the matrix above or below the precipitate.
All oxides are amorphous in nature, which has been conrmed from high-resolution STEM imaging and
convergent beam diraction (not shown) and it is consistent with existing literature7. ey are richer in Mn–Si–O
with respect to the wrought alloy, however, in some cases, Si and O are lower in wt. % than their respective com-
positions in the associated lamellae (TableS1). Furthermore, proportions of Mn, Si and O vary (drastically in
some cases) from one oxide to another. ese results indicate the presence of dierent combinations of MnxSiyOz
(x,y ≥ 0, z > 0) in these precipitates. Along with Mn-Si-O, oxides have higher concentrations of P, S and C than
the wrought alloy but oen lower C concentration than their corresponding lamella (TableS1); furthermore, in
most cases, the P, S and C concentrations increase from the oxide center to the oxide-matrix interface.
Figure1. Design and crystallographic orientation map of the LMD 316LSS walls from which TEM lamellae
are extracted. (a) An illustration (not-to-scale) of the single-track bidirectionally-printed 3-layer and 60-layer
LMD 316LSS walls on a hot-rolled 316LSS substrate. Directions
x
,
y
and
z
respectively represent the printing,
thickness and building directions. e top view and the front view of a cross-section A–A are shown. e red
arrows in the front-view show the direction of printing of each layer. (b) An EBSD orientation map color-
coded according to IPF along building direction at a cross-section B–B approximately at the mid-section of the
3-layer wall. Dotted lines in (b) represent the approximate position of interlayer boundaries. e black solid
circles in (b) indicate the points X, Y and Z that correspond to the locations in the FE simulations from where
the temperature vs time data has been extracted and plotted in Fig.7. Subgures in (b) show zoomed-in EBSD
maps. Yellow-colored lines demark zones underneath which lamellae L1, L2 and L3 are extracted (in the out-of-
plane direction). ese lines correspond to the top side of L1, L2 and L3 in the HAADF images in Fig.2. Aztec
v4.2 (Oxford Instruments https:// nano. oxinst. com/ produ cts/ aztec/) and Microso PowerPoint have been used
to prepare this gure.
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Amongst the 3 non-oxide precipitates, (i) P161 is richer in Cr–Mo–Mn–Si–O–P–S–C in comparison to the
wrought alloy and L1, (ii) P154 is richer in Ni–Mo–Mn–O–P–S–C in comparison to the wrought alloy but only
Mo-Mn-P-S are higher than those in L4, and (iii) P75 is richer in Ni–Mo–Mn–O–P–S in comparison to the
wrought alloy but only Mo-Mn-P are higher than those in L5. All non-oxide precipitates are embedded either
above, below or in between the matrix. Whenever a non-oxide precipitate contains a higher wt. % of Cr than its
surroundings, it results in a brighter contrast with respect to its surrounding in the HAADF image, as evidenced
from P161.
Similar to non-oxide precipitates, all mixed precipitates also exhibit a non-zero oxygen composition with
respect to the wrought alloy, and all non-oxide inclusions in mixed precipitates that have a higher wt. % of Cr
than the surrounding matrix show a brighter contrast in the HAADF images. Out of the 36 mixed precipitates,
34 (94.44%) contain both oxide and non-oxide inclusions; P151 and P144 contain only non-oxide inclusions.
Amongst these 34 mixed precipitates, 26 (72.22% out of 36) clearly show oxide inclusions at their core and non-
oxide inclusions around the oxides. However, it is harder to arrive at this conclusion for the remaining 8 (22.22%
out of 36): P11, P91, P34, P84, P124, P15, P25 and P45.
Figure2. STEM HAADF images and EDS chemical maps of L1, L2 and L3 extracted from the 3-layer wall of
Fig.1. EDS maps have been generated from within the black outlined region in each HAADF image. e dotted
green lines in each HAADF image represents the zone where the lamella composition has been computed
and presented in TableS1 (Supplementary Data). Precipitates that are easily visible in the HAADF images are
numbered in yellow font. Precipitates that have been detected aer high resolution imaging are numbered in red
font. Scale for EDS maps of each lamella are shown in their C map. HAADF images and EDS maps have been
acquired using the TIA v4.2 (FEI https:// www. fei. com) and the Esprit v1.9 (Brucker https:// www. bruker. com)
soware, respectively. Fiji v2.1.0/1.53c (https:// ji. sc/) and Microso Powerpoint have been used to prepare this
gure.
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Out of the 36 mixed precipitates, 30 are composed of two inclusions each that manifest either next to each
other or one surrounds the other; they are P121–P151, P12, P22, P42, P52, P24, P44–P64, P84–P104, P134, P144,
P164, P174, P15–P65, P95–P135. e remaining 6 i.e., P11, P91, P23, P34, P74 and P124 are composed of more than
2 inclusions.
Figure3. STEM HAADF images and EDS maps of all non-oxide and mixed precipitates, and at maximum
one oxide precipitate, in L1–L3. To facilitate visualization, picture corrections have been made for all the EDS
maps. ImageJ and Microso PowerPoint have been used to prepare this image. HAADF images and EDS maps
have been acquired using the TIA v4.2 (FEI https:// www. fei. com) and the Esprit v1.9 (Brucker https:// www.
bruker. com) soware, respectively. Fiji v2.1.0/1.53c (https:// ji. sc/) and Microso PowerPoint have been used to
prepare this gure.
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P11 is a complex combination of 3 zones and 5 small inclusions. Based on the morphology, brightness evolu-
tion and composition of these zones, we can deduce that (i) zone 1 was part of a larger oxide inclusion before the
lamella was prepared, (ii) zone 2 is made up of two inclusions: one is the same oxide as in zone 1 and the other
is a Cr–Mo–P–S non-oxide that overlaps the rst, (iii) the brightness changes across zone 2 as the amount of
the oxide inclusion along L1’s thickness direction decreases and that of the non-oxide inclusion increases. (iv)
e oxide terminates at the interface between zone 2 and zone 3 such that (v) zone 3 is rich only in Cr–Mo–P–S
(Figs.3 and 4). Due to the high O-content of the ve elliptical inclusions, they are classied as oxides. ey are
also rich in Cr–Mo–Mn–P–S–C with respect to the wrought alloy but these contributions could arise due the
overlap of these inclusions with zones 2 and 3 along L1’s thickness.
P91 also has three zones. Similar to P11, the morphology of these zones and of the surrounding matrix sug-
gests that prior to L1’s preparation, zone 1 was part of a larger oxide inclusion and zone 2 includes a portion from
the same oxide inclusion embedded underneath or above the surrounding matrix. e portion of this oxide in
L1 terminates at the outer boundary of zone 2. Zone 3 is a non-oxide inclusion richer in Cr–Mo–P–S–C with
respect to the wrought alloy and Cr–Mo–P–S with respect to L1.
e presence of dierent zones in P23 can be explained in a manner similar to P11 and P91. However, the mor-
phology of dierent inclusions, their composition and dierence between their contrast in the HAADF image,
clearly shows that the oxide inclusion in P23 is not circular and it is highly unlikely that it would have been spheri-
cal prior to the extraction of L3. Distorted oxide inclusions are also observed in other mixed precipitates such as
P121. Meanwhile, pure oxide precipitates always manifest as circles. erefore, these results strongly suggest that
the presence of non-oxides can deviate the morphology of oxide inclusions away from a perfect spherical shape.
Similar to P11, P34 and P124 also contain multiple small oxide inclusions embedded in non-oxide inclusions
(Fig.S3); their sizes and distributions make it hard to separate them into clear zones. e oxide inclusions in
P124 are rich only in Mn–O; the composition of Si is lower than that in the wrought alloy and the surround-
ing matrix. P74 contains a single large oxide inclusion at the core and it is surrounded by multiple non-oxide
inclusions richer in Mo–Cr–P and Mo–Cr–S than the surrounding matrix. Meanwhile, contrary to other mixed
precipitates containing oxide inclusions in the core, P84, P15, P25 and P45 contain a large non-oxide inclusion at
their core surrounded by a smaller oxide inclusion.
P151 and P144 are the only mixed precipitates that are composed of only non-oxide inclusions. P151 is made
up of two inclusions next to each other. e darker one is richer in Ni–Mo–Mn–Si–O–P–S–C than the wrought
alloy but only Mo–Mn–S–C are higher than in L1. e brighter one is also richer in Ni–Mo–Mn–Si–O–P–S–C
than the wrought alloy but only Mo–Mn–P–C are higher than in L1. P144 is made up of two nearly concentric
non-oxide inclusions (Fig.S3). e larger one is richer in Ni-Mo-Mn–O–P–S than the wrought alloy but only
Mo–P are higher than in L4. Interestingly, in comparison to the surrounding matrix, this inclusion is richer
in Cr–Mo–P; the presence of Cr results in a brighter contrast with respect to the surrounding matrix in the
HAADF image. e smaller darker one is richer in Mo–Mn–O–P–S than the wrought alloy but it is richer in
Cr–Mo–Mn–P than L4. Interestingly, P144 is the only precipitate that has negligibly small C composition with
respect to the wrought alloy.
e TEM analysis has clearly shown that a plethora of dierent kinds of non-oxide inclusions are present in
L1–L5. Furthermore, out of the 55 precipitates, 39 (70.9%) are either non-oxide precipitates or mixed precipitates
containing only non-oxide inclusions. Bearing this fact in mind together with the fact that the TEM lamellae
have been extracted from dierent locations of our LMD 316LSS walls and they occupy a very small volume in
these walls, we can claim with high condence that non-oxide inclusions are abundantly present in the 3-layer
and the 60-layer LMD 316LSS walls.
In order to check whether similar kind of precipitates occur or not in the 316LSS powder, a TEM lamella “LP”
had been prepared from a 316LSS powder particle (Fig.5). e composition of LP is similar to L1–L5 (TableS1).
It has lower Fe and Cr, slightly higher Ni, and the remaining alloying elements higher than the wrought alloy
along with a high proportion of O. HAADF image of LP reveals 5 mixed precipitates containing both oxide and
non-oxide inclusions with sizes similar to their counterparts in the 3-layer and 60-layer LMD 316LSS walls.
Table 1. Classication and nomenclature of precipitates in lamellae L1–L5. Precipitates are classied into
oxides, non-oxides and mixed based on the oxygen content (in EDS maps) and brightness (in HAADF image)
with respect to the surrounding (austenite) matrix. Each precipitate is numbered according the sequence
shown in the HAADF images in Fig.2 and the lamella number is added as a subscript.
Precipitate classication Description
Nomenclature
L1 L2 L3 L4 L5
Oxide
Single inclusion with nearly uniform
composition. Contains higher O than the
matrix and appears darker than matrix in
the HAADF image
P21–P81, P101, P111P32P13P14, P114P85, P145, P155
Non-oxide
Single inclusion with nearly uniform
composition. Contains lesser oxygen than
the matrix and appears brighter than oxide
precipitates in HAADF images
P161– – P154P75
Mixed Two or more inclusions with dierent
elemental compositions P11, P91, P121–P151P12, P22, P42, P52P23P24–P104, P124–P144, P164, P174P15–P65, P95–P135
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Now, the only common factor between inert gas atomization and LMD is the maximum temperature rate
encountered during these processes, which is expected to be in the range 102–105K/s22,25–27. Furthermore, it
is well-known that the precipitate sizes in steels decrease with increasing temperature rate15–17. Based on this
knowledge and the TEM results of this work, we hypothesize that the temperature rate encountered during AM
of 316LSS is the main factor that determines the size of dierent kinds of precipitates. In order to verify this
hypothesis, we have performed thermodynamics computations to study the precipitation kinetics of a non-
oxide at dierent temperature rates. However, in order to perform these computations, we need (i) to assess the
oxide and non-oxide inclusion/precipitate size distribution in our LMD 316LSS walls, and (ii) to estimate the
temperature rates encountered during LMD of our 316LSS wall.
Figure6 shows the size distribution of oxide and non-oxide precipitates and inclusions in L1–L5. In general,
a wide scatter is observed in the size distribution of all precipitates and inclusions; the largest scatter occurs for
oxide inclusions in mixed precipitates. e size distributions could be either (i) an apparent scatter caused by
the 2D nature of a TEM analysis, or (ii) it could be due to dierences in inclusion nucleation and growth rates
arising from variations in local temperature rates. In order to diminish the inuence of these eects, only the
average sizes of the precipitates and inclusions are analyzed.
Figure4. HAADF images and EDS line proles for precipitates P11 and P91 along dierent paths. e points
in the curves have been tted using c-splines. e key for both HAADF images is presented below the HAADF
image of P11. HAADF images have been acquired using the TIA v4.2 (FEI https:// www. fei. com) soware. Fiji
v2.1.0/1.53c (https:// ji. sc), gnuplot v5.4 (http:// www. gnupl ot. info) and Microso PowerPoint have been used to
prepare this image.
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e average size of non-oxide precipitates/inclusions (72.69nm/85.67nm) is smaller than the average size of
oxide precipitates/inclusions (148.65nm/116.19nm). A similar trend in the size dierences between oxide and
non-oxide inclusions is also found in the 316LSS powder. Furthermore, a similar trend has also been reported
during solidication of a cast steel15–17. From here one can deduce that for the same temperature rate and starting
temperature during processing of 316LSS, the average size of oxide inclusions/precipitates should be larger than
the average size of their non-oxide counterparts irrespective of the processing technique used.
In order to obtain an order of magnitude of the temperature rates that are encountered during the LMD
of our samples, solid-state heat transfer FE simulations (see Methods for simulation setup) were performed
for the 3-layer wall using the geometry shown in Fig.1a. e temperature v/s time history was extracted from
the mid-section of the 3-layer wall, approximately at the location of points X, Y and Z shown in Fig.1b. ese
temperature v/s time curves are plotted in Fig.7. Since points X and Y belong to the mid-layer of the 3-layer
wall, they experience a cooling-heating-cooling sequence. Since Z belongs to the top layer of the 3-layer wall, it
only experiences a cooling sequence. Just aer deposition, the three points experience a temperature above the
equilibrium solidus (1673K) of 316LSS. However, since the FE simulations do not account for uid dynamics
or solidication, we shall restrict the discussion to cooling rates at temperatures below the equilibrium solidus.
Between 1273K (typically the lowest annealing temperature for 316LSS) and equilibrium solidus, the three points
experience cooling rates between 1.15 × 104K/s and 2.91 × 104K/s; the latter rate is the highest rate encountered
by any point. e lowest cooling rate experienced by any point is 1K/s at 305K. Meanwhile, the highest heating
rate, 1.8 × 105K/s, is experienced by Y at 1074K. e lowest heating rate between 1273 K and 1673K experienced
by Y is 2.08 × 103K/s at 1517K.
e temperature v/s time curves shown in Fig.7 are relevant for lamellae L1, L2 and L3. Meanwhile, lamella
L4 should experience an initial cooling-heating-cooling similar to point X followed by 58 heating–cooling cycles
at decreasing temperature rates. L5 should experience a single cooling cycle at a temperature rate lower than
the maximum one shown in Fig.7. erefore, in the range of 300K to 1673K, any material point in the 3-layer
Figure5. SEM micrograph of (a) polished 316LSS powder particles and (b) a powder particle at higher
magnication. e TEM lamella LP in (c) is extracted from underneath the red zone in (b), which is embedded
within a grain whose outline is shown in blue. (c) STEM HAADF image of the lamella LP extracted from
the 316LSS powder particle in (b). (d) STEM HAADF images and EDS maps of all the precipitates of LP.
Precipitates are named by adding a prex “P” to their corresponding number in (c). SEM micrographs have
been captured using the XT v10 (ermoFisher https:// www. therm osh er. com/) soware. HAADF images and
EDS maps have been acquired using the TIA v4.2 (FEI http:// www. fei. com) and the Esprit v1.9 (Brucker https://
www. bruker. com) soware, respectively. Fiji v2.1.0/1.53c (https:// ji. sc/) and Microso PowerPoint were used to
prepare this gure.
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and the 60-layer walls should experience cooling and heating rates from 1K/s to 105K/s, which is typical for
an LMD process22.
Now, we perform a thermodynamic analysis to understand why non-oxide precipitates are present in our
LMD 316LSS walls. e rst step involves analyzing the most stable (i.e., lowest Gibbs free energy) equilibrium
phases that could exist in the liquid and solid states of 316LSS. is analysis is performed using the ermoCalc
soware and the results are presented in sectionS4 of the supplementary material for several dierent tempera-
tures in both the solid and liquid states. It reveals that the main phase in the solid 316LSS is γ-austenite and the
main phase in the liquid is molten 316LSS, henceforth called Liquid A (LA). Amongst all the possible oxides,
MnSiO3 is the most stable equilibrium phase in both the liquid and solid states; in the liquid state it exists in the
form of Liquid B (LB), which is an Mn–Si–O rich liquid with composition close to MnSiO3 having trace amounts
of Fe and S. Non-oxide (carbide, sulde and phosphide) phases do not exist above the equilibrium liquidus
temperature i.e., above 1703K (1430°C). Below the equilibrium solidus i.e., 1673K (1400°C), M–S (M = Mn,
Cr and Fe in descending wt.%) is the most stable equilibrium non-oxide phase.
Figure6. Comparison of equivalent diameters, also called size, of oxide precipitates (Oxides), non-oxide
precipitates (Non-oxides), and the oxide (Mixed oxides) and non-oxide (Mixed non-oxides) inclusions in
mixed precipitates in L1–L5. Equivalent diameter is the diameter of a circle whose area is equivalent to the
corresponding area of the precipitate/inclusion in its HAADF image. Values in black font represent maximum
and minimum equivalent diameters. Values in colored font represent average equivalent diameters, which
are the diameters of a circle whose area is equivalent to the average of the areas of all precipitate/inclusions
belonging to a category. e colored dashes represent the individual sizes of a precipitate/inclusion. Gnuplot
v5.4 (http:// www. gnupl ot. info) was used to prepare this gure.
Figure7. Temperature v/s time curves obtained from the heat transfer FE simulation of LMD of the 3-layer
wall of Fig.1b at the locations X, Y and Z. e temperature rates shown inside the plot have units K/s.
Superscript ‘c’ implies cooling and ‘h’ implies heating. e rates in red, blue and green font correspond to
the rates encountered by points X, Y and Z, respectively, during LMD. e subscripts ‘min’ and ‘max’ to the
temperature rates correspond to minimum and maximum, respectively, rates for a given curve. EQ solidus
stands for the equilibrium solidus temperature.
TM
−
S
min
is the minimum temperature below which M–S (M = Mn,
Cr and Fe) does not precipitate for any temperature rate in the range 1–107K/s (see discussion related to Figs.9
and 10). While the simulation begins at 0s, however, X and Y are deposited at 5.7s and Z is deposited at 9.9s
aer the start. Gnuplot v5.4 (http:// www. gnupl ot. info) was used to prepare this gure.
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Next, element solubility analysis is performed in order to understand the temperature dependent equilib-
rium composition and volume fraction of the most stable phases that coexist in the solid (γ-austenite, M-S and
MnSiO3) and liquid (LA and LB) 316LSS.
Figure8a shows the equilibrium atomic composition and stoichiometry of M–S as a function of temperature.
Starting as purely MnS below 473K, the composition of M-S evolves between 473K and equilibrium solidus as
Mn is increasingly substituted mainly by Cr and in much lesser proportion by Fe from the γ-austenite. Mean-
while, the equilibrium atomic composition and stoichiometry of MnSiO3 (not shown) does not change with
temperature until equilibrium solidus is reached.
Figure8b shows the equilibrium volume fraction as a function of temperature for γ-austenite, M-S, MnSiO3,
LA and LB. In the solid-state, γ-austenite is the dominant phase with some non-zero volume fraction of MnS
and MnSiO3. Between equilibrium solidus (1673K) and liquidus (1703K), the phase fraction of γ-austenite
decreases and that of LA correspondingly increases. At liquidus and beyond, all γ-austenite is replaced by LA.
e volume fraction of MnSiO3 also decreases above 1673K; however, up to 1703K, the decrease in MnSiO3 is a
combination of dissolution as well as the fact that the density of LA is lower than that of γ-austenite. At ~ 1743K,
MnSiO3 begins to transform into LB and the transformation is complete at ~ 1783K. Meanwhile, just above
equilibrium solidus, M-S dissolves into LA faster than γ-austenite transforms into LA; at 1683K, all M-S has
dissolved into LA.
e data used to plot the elemental solubility curves is then used to perform the precipitation kinetics simula-
tions for nucleation and growth of M–S inclusions on MnSiO3. Recalling that TEM observations show 72.22% of
the 36 mixed precipitates have oxide inclusions at their core and non-oxide inclusions surrounding the oxides,
the most important assumption made during the precipitation kinetics simulations is that M-S inclusions can
nucleate only on existing MnSiO3 inclusions (see Methods). e precipitation kinetics simulations are performed
during solidication/cooling from the liquid phase and heating from the room temperature.
Figure9a,b show the M–S diameter and volume fraction, respectively, as a function of temperature for dif-
ferent cooling rates, including 2 × 104K/s, which is approximately the average of the cooling rates encountered
between 1273 K and 1673K (Fig.7). e non-equilibrium solidus 1643K (1370°C) reported by Dépinoy etal.30
is considered as the reference solidus temperature for these simulations. e model parameters have been chosen
such that the predicted average diameter of M-S inclusions matches the measured average size of the non-oxide
inclusions in the mixed precipitates in Fig.6 for 2 × 104K/s at the non-equilibrium solidus. is tting results in
an excellent match between the predicted average diameters at cooling rates 1K/s and 8.33K/s and the experi-
mental measurements of Kim etal.16; thus, validating not only the precipitation kinetics predictions but also FE
predicted temperature rates.
For cooling rates 1K/s, 10K/s, 102K/s and 103K/s, precipitate growth saturates prior to reaching equilib-
rium solidus. For 104K/s, it saturates at the non-equilibrium solidus. For cooling rates 105–107K/s, precipitates
continue to grow below the non-equilibrium solidus, however, the increase in their diameter is overestimated
below this temperature because the simulations have been performed using the diusion coecient of M–S in
liquid (Methods). When the simulations are reperformed (not shown) using the diusion coecient of M–S in
γ-austenite, which is approximately 5 orders of magnitude lower than that in liquid, the changes in diameters
below the non-equilibrium solidus for all temperature rates are much smaller. Furthermore, at any cooling rate,
M–S does not nucleate/grow below 1273K i.e., below 0.76Tm (Tm = equilibrium melting point), which is also
the lowest annealing temperature for 316LSS. e predicted average diameters of M–S at the non-equilibrium
solidus are (in nm) 3395.1, 1131, 375.5, 144.5, 107.8, 29.1, 8.5 and 3.6, respectively, for cooling rates (in K/s) 1,
10, 102, 103, 104, 105, 106 and 107.
Figure8. Equilibrium atomic composition and volume fraction curves. (a) Equilibrium atomic composition of
only M–S (M = Mn, Cr and Fe), and (b) equilibrium volume fraction of γ-austenite, LA, LB, MnSiO3 and M–S,
as a function of temperature. ‘EQ solidus’ stands for equilibrium solidus. Gnuplot v5.4 (http:// www. gnupl ot.
info) was used to prepare this gure.
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Figure9b shows that the M–S volume fraction for cooling rates from 1 to 103K/s is ~ 0.021%. At cooling rates
higher than 103K/s, the volume fraction begins to decrease faster than the increase in cooling rate. At 2 × 104K/s,
the volume fraction is ~ 0.0145% at non-equilibrium solidus, which is still comparable to the one obtained at
1K/s. At 105K/s, the M–S volume fraction is less than 0.002%, and it is negligibly small at 106 and 107K/s. A
signicant change in M–S volume fraction is not expected for temperatures lower than non-equilibrium solidus
at any cooling rate.
Figure10 shows the M–S volume fraction as a function of temperature for dierent heating rates, includ-
ing 2.08 × 103K/s, which is the lowest predicted temperature rate encountered by point Y between 1273 K and
1673K. For these simulations, the diusion coecient of M–S in γ-austenite has been used and, for simplicity,
equilibrium solidus is considered as the reference solidus. Note that during rapid heating, the non-equilibrium
solidus should be higher than the equilibrium solidus, however, this is not considered here because the precipi-
tation kinetics simulations use the equilibrium solubility curve of M–S (Fig.8) and this curve shows that M–S
has already completely dissolved at only 10K above the equilibrium solidus.
Similar to the solidication/cooling case, the volume fraction of M–S does not change below 1273K at any
heating rate. e volume fraction of M–S for heating rates 1K/s and 10K/s rapidly increases to 0.025% but only
above 1273K, and then decreases with increasing temperature until equilibrium solidus is reached. A similar
trend occurs at 102K/s but starting from 1373K and reaches a slightly lower maximum volume fraction than
at 1K/s. At 103K/s, the volume fraction starts to increase from 1473K and reaches to ~ 0.008% at equilibrium
solidus. At 2.08 × 103K/s, the volume fraction starts to increase from ~ 1573K and reaches a maximum of
0.0025%, which is an order of magnitude lower than that occurring during cooling at 2 × 104K/s. For heating
rates ≥ 104K/s, the change in M–S volume fraction is negligible at any temperature.
e most important results of the precipitation kinetics simulations are as follows: (i) there is no change to
the M–S average diameter or volume fraction below 1273K for any temperature rate, (ii) during solidication/
cooling, the M–S volume fraction only increases at cooling rates lower than 105K/s in magnitude, and (iii) dur-
ing heating, the maximum M–S volume fraction increases at rates lower than 104K/s.
Combining the results obtained from the FE simulations (Fig.7) and the precipitation kinetics simulations,
it can be seen that the M–S volume fraction increase during solidication/cooling at 1.15 × 104 – 2.91 × 104K/s
is higher by an order of magnitude than that during heating at the lowest rate 2.08 × 103K/s. erefore, the
nucleation and growth of M–S on oxide inclusions should be signicant only during solidication/cooling at
temperatures above 1273K; the heating should play a negligible role. is explains why M-S inclusions have
been observed in TEM lamellae L1–L5.
Since the inert gas atomization of 316LSS is expected to have similar maximum solidication/cooling rates as
the LMD process, the precipitation kinetics simulations also explain why M–S inclusions in LMD 316LSS have
a similar size to those observed in TEM lamella LP taken from the inert gas atomized 316LSS powder (Fig.5).
Furthermore, the analysis also explains why M–S inclusions have not been observed in TEM studies of SLM
316LSS2–4,7. During SLM, the maximum temperature rates of 106–107K/s can be encountered at temperatures
above 1273 K23. At these rates, the predicted average diameters of M–S precipitates are very small and their
volume fraction is negligible (Fig.9), which makes it very dicult to detect them even with high-resolution
STEM imaging.
Figure9. M–S precipitation kinetics simulation predicted (a) average diameter (log scale) and (b) volume
fraction as a function of temperature during solidication/cooling at dierent temperature rates. ‘EQ solidus’
and ‘NEQ solidus’ respectively stand for the equilibrium and non-equilibrium solidus temperatures; the latter
(1643K) is obtained from Dépinoy etal.30 e black curves in (a,b) correspond to approximately the average
cooling rate obtained from Fig.7 between 1273 and 1673K. e red and green empty circles in (a) represent the
M–S precipitate diameters reported by Kim etal.16 for cooling rates 1K/s and 8.33K/s, respectively. e black
empty circle represents the non-oxide inclusion diameter in mixed precipitates obtained from Fig.6. Gnuplot
v5.4 (http:// www. gnupl ot. info) was used to prepare this gure.
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Finally, although precipitation kinetics of non-oxide inclusions other than M–S have not been performed,
nevertheless, similar thermodynamic arguments can also be used to explain their presence in LMD 316LSS
and inert gas atomized 316LSS studied in this work, as well as their absence in SLM 316LSS in other works2–4,7.
In conclusion, the TEM studies performed in this work have revealed a plethora of dierent kinds of non-
oxide inclusions (carbides, suldes, phosphides and intermetallics) in the LMD 316LSS samples studied in this
work. Furthermore, 70.9% of all the precipitates found in the TEM lamellae extracted from the LMD 316LSS
samples are either purely non-oxide inclusions or mixed precipitates containing non-oxide inclusions together
with oxide inclusions. ese results prove that non-oxide inclusions can indeed form during DED-type AM
processes such as LMD.
e presence/absence of non-oxide inclusions is dependent on the temperature rates experienced during
processing as well as a minimum temperature below which they do not form. e precipitation kinetics simula-
tions performed in this work show that new non-oxide inclusions form only during solidication/cooling (and
not heating) at temperatures above 1273K (1000°C) i.e., 0.76Tm, and at temperatures rates less than or equal to
105K/s. e FE simulations performed in this work, supported by existing literature22, reveal that the highest
temperature rate magnitudes encountered during the LMD of 316LSS samples are less than 105K/s at tempera-
tures above 1273K; these thermal conditions occur only during the initial stages of the heating–cooling cycles in
a material just aer its deposition. Furthermore, similar rates must be experienced during inert gas atomization
because the size of inclusions in gas atomized 316LSS are similar to the ones obtained in LMD 316LSS. ese
predictions explain the presence of non-oxide inclusions in both inert gas atomized 316LSS powder and LMD
316LSS samples. Meanwhile, the highest temperature rates typically encountered during powder-bed based tech-
niques such as SLM at temperatures above 1273K are in the range 106–107K/s23. erefore, non-oxide inclusions
should not form during SLM 316LSS, which is fully supported by existing TEM studies2–4,7.
Methods
316LSS powder properties and LMD process parameters. e 316LSS powder has been produced
via the inert gas atomization process. is process involves slowly melting a wrought alloy and pouring it into
an atomization chamber from the top. While being poured, the molten alloy is acted upon by high-speed inert
gas (Ar) jets that disperse it into smaller droplets. ese droplets rapidly solidify and cool during their descent
and they are collected into a crucible at the bottom of the chamber. e solidication/cooling temperature rates
attained during this process depend on several factors such as desired powder particle sizes, gas used, gas jet
speed, etc. A sieve analysis has revealed the particle sizes range from 45 to 90μm. Following the gas atomization
process, the powder is typically stored in a sealed container, transported to the location where it is used for AM,
and stored in a powder feeding chamber for the AM process.
e powder-based LMD process, also known as Direct Metal Deposition (DMD) or Laser Engineered Net
Shaping (LENS), had been carried out inside the “Mobile” machine from BeAM. More details on the material,
powder characteristics and specications of the LMD machine can be found in 31,32.
A single-track bidirectionally-printed 3-layer wall had been built on a hot-rolled 316LSS substrate using this
machine (Fig.1a). A 3-layer wall ensures that (i) precipitates formed in the top layer are not aected by chemical
heterogeneities on the substrate surface, and (ii) solidication/cooling rates are similar to those experienced by
the rst deposited layer during its deposition and comparable to those occurring during gas atomization. e
LMD process parameters used to print the samples are summarized in Table2. e nal dimensions of the as-
built wall are 100mm × 0.8mm × 0.6mm.
During the LMD process, the 316LSS powder particles are mixed with an inert gas (Ar in our case) and then
transported to the focusing head, which contains laser ber optic cable, gas and powder inlet, focusing lenses
and a nozzle to direct the powder enveloped in inert gas. e laser melts the powder and the molten powder gets
Figure10. M–S precipitation kinetics simulation predicted volume fraction as a function of temperature
during heating at dierent temperature rates. ‘EQ solidus’ stands for the equilibrium solidus temperature.
e black curve corresponds to the minimum heating rate obtained from Fig.7 between 1273 K and 1673K.
Gnuplot v5.4 (http:// www. gnupl ot. info) was used to prepare this gure.
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deposited on the substrate or the part being built. While the focusing head continues its trajectory to deposit the
layer, the molten powder solidies, typically in a few milliseconds, and then cools down, until the subsequent
laser passage either on the same layer but adjacent to the material that is just deposited or on the layer above the
deposited material. Subsequent deposition results in thermal cycling of the material in the solid-state and the
number of cycles, their amplitudes and temperature rates depend on the number of laser passages and layers
that remain to be built.
Scanning Electron Microscopy (SEM): equipment and TEM lamellae preparation tech‑
nique. e as-built wall and substrate had been mechanically cut near the mid-section and along the direc-
tion normal to the build and print directions (section B-B in Fig.1a). is cross-section had been polished rst
using SiC papers with dierent grits (from 800-grit to 4000-grit), followed by diamond paste polishing with grit
sizes 3μm and 1μm, and nally ion polishing. en, this cross-section has been analyzed via SEM using a FEI
Quanta 650 FEG Environmental-SEM microscope equipped with the symmetry detector (Oxford Instruments)
for EBSD measurements.
e EBSD map shown in Fig.1b for the 3-layer wall is a single map with a resolution of 2000 (height) × 1750
(width) pixels (1 × 0.88 mm2) of step size 0.5μm. e acceleration voltage of the electron beam was 20kV. e
indexing success rate was 99%. e EBSD map shown in Fig.S1 for the 60-layer wall was stitched from 80 images
of 1005 (width) × 692 (height) pixels (0.51 × 0.35 mm2) each with step size 0.5μm. e acceleration voltage of
the electron beam was 30kV. e indexing success rate was 97.4%.
e 316LSS powder has also been analyzed via SEM. Some powder particles had been embedded inside a
diluted conductive carbon cement and polished using the same approach as above.
Following the preliminary EBSD analysis, the sample had been transported to a FEI Helios Nanolab 660
dualbeam SEM microscope, which is equipped with a dual beam Focused Ion Beam (FIB). Using the standard
li-out process, the FIB-SEM is used to extract 4 TEM lamellae: 3 lamellae (L1, L2 and L3) from the 3-layer wall,
2 lamellae (L4 and L5) from the 60-layer wall, and 1 lamella (LP) from the powder sample.
TEM: equipment and analysis
e six lamellae had been studied in an aberration-corrected FEI Titan3 G2 60–300 TEM microscope operating
at 300kV. is TEM is equipped with a Cs probe corrector, and a series of detectors including a High-Angle
Annular Dark Field (HAADF) detector. It is also equipped with 4 EDS detectors, which allow generating chemi-
cal maps.
EDS takes advantage of the X-ray uorescence to analyze the composition of the sample.
Working in STEM mode, it is possible to scan the sample and store the local X-ray spectrum at each pixel
in the scanned zone. However, characteristic X-ray peaks from each element are convoluted with background
contributions as well as any overlap with peaks of other elements; for example, the
Kα
peak of S has an overlap
with the
Lα
peak of Mo. It is necessary to deconvolute these peaks in order to generate images separating the
composition of each element in the scanned zone. e deconvolution procedure ts the experimental peaks using
a linear combination of theoretical peaks of all the alloying elements in 316LSS. is method also removes the
background contributions (e.g. Cu from the TEM grid). Following deconvolution, images are quantied using
the standardless Cli-Lorimer method33 to link experimental intensities to the relative amount of each element.
All EDS images shown in this work are deconvoluted and quantied such that they are devoid of any thickness,
density or peak overlap. EDS images of elements with lower concentration require brightness adjustment to
facilitate visualization.
EDS line prole plots have been generated from the quantied EDS spectra for multiple precipitates in order
to study the variation in elemental composition across dierent line paths through the precipitates. e plots
have been generated by averaging over a width of 10 pixels.
Precipitate size (equivalent diameter) determination has been performed from the TEM images using the
Fiji soware.
Heat transfer FE simulation setup
Solid-state heat transfer FE simulations have been performed to simulate LMD of the 3-layer wall in Fig.1 in
order to generate the temperature v/s time curves shown in Fig.7.
Governing equations and variational formulation. e heat transfer model used in this work is a
continuum-based initial boundary value problem that accounts for heat conduction, convection and radiation
based on the work of Weisz-Patrault34. Let
�(t)⊂
R
3
be a temporally evolving domain with boundary
∂�(t)
. Let
T=[0, tmax]
be the time interval of interest, where
tmax
is known. e governing equations for the heat transfer
problem at a material point
x∈�(t)
are:
(1)
ρcv˙
T
=−∇·
q
in �(t)×T
Table 2. LMD process parameters used to build the 316LSS wall in Fig.1.
Laser power Powder ow rate Deposition speed Initial vertical position / vertical displacement of focusing head
225W 0.1083g/s 33.33mm/s 3.5 mm above substrate / 0.2mm aer deposition of one layer
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e initial conditions are:
e boundary conditions are:
where
T
is the absolute temperature,
K
is the second order thermal conductivity tensor,
cv
is the specic heat at
constant volume,
∇
is the dierential operator vector,
q
is the heat ux vector,
∇θ
is the temperature gradient,
Tini
is the initial temperature
∂�base
is the bottom surface of the baseplate that does not evolve with time and it
is applied a Dirichlet boundary condition.
∂�laser(t)
,
∂�Ar(t)
,
∂�air(t)
and
∂�rad(t)
are dened as those sur-
faces that have been respectively subjected to surface heat ux from the laser beam
qlaser
, forced convective heat
transfer
qAr
due to the Ar-gas owing from the nozzle of the focusing head, natural air convective heat transfer
qair
and radiative heat ux
qrad
, respectively; note that these surfaces evolve with time.
hAr
and
hair
are the con-
vective heat transfer coecients for Ar-gas and air, respectively.
σ
and
ǫ
are the Stefan-Boltzmann constant and
emissivity of the deposited material, respectively.
Tinf
is the innitive temperature. e laser beam interaction
with the material is modeled as a surface heat ux condition having a 2D Gaussian distribution with maximum
power
Plaser
and absorptivity
ηlaser
acting on a circular area with radius
Rlaser
centered at
xlaser
. e Ar-gas heat
ux is also modeled as a Gaussian with its peak at the center of the laser beam
xlaser
and a radius
RAr >Rlaser
that is large enough to cover some area around the build.
At a given time step, the following variational (weak) form of the governing equations with the boundary
conditions is solved:
where a Euler backward time integration scheme has been used,
T
is the temperature test function,
Th
is the
approximate solution sought,
q
h=−
K
· ∇
Th
and the subscript
n
is the current time step.
e weak form has been implemented in the FEniCS35 open-source (LGPLv3) FE computational platform
for solving partial dierential equations and the non-linear Newton iterative solver is used.
Mesh. e simulated geometry shown is created based on the experimental setup (Fig.1). It consists of a
baseplate (not shown in Fig.1 but present during the experiment), the hot-rolled 316LSS substrate, and the
3-layer LMD 316LSS wall. e baseplate, substrate and wall are created as independent volumes and merged to
form a single material volume for the simulations. e geometry is then decomposed into subdomains as shown
in Fig.S5 and meshed using the open-source gmsh36 soware.
e structured regions of the substrate and baseplate were meshed using 6mm seeds and the structured region
of wall was meshed using 0.1mm seeds. An unstructured region was necessary to transition from the 0.1mm
seeds of the wall to the 6mm seeds of the substrate and baseplate. is unstructured region starts around the wall
and goes to a distance of 15mm in all directions to ensure a uniform increase in mesh element size. All elements
are chosen to be tetrahedral with quadratic interpolation (P2). A conformal mesh is obtained aer recombining
using “transnite” mesh options in gmsh (Fig.S6).
For simplicity, mass addition is simulated via a mesh element addition procedure. e initial mesh only
contains the substrate and the baseplate. When the laser passes over the region where the rst mass is added, a
new element is generated at the location where the laser passes. However, this element is not added to the exist-
ing mesh. Instead, a new geometry and mesh is generated. is new mesh is an augmentation of the geometry
and mesh of the previous time step with one additional geometric element to mimic the deposition of some
material on a layer. At the beginning of the deposition of each layer, a cuboid element of size 0.6mm (along
x
) × 0.6mm (along
y
) × 0.2667mm (along
z
) is generated. Each of the subsequent elements added to that layer
are of size 0.1mm × 0.6mm × 0.2667mm. Finally, for the 3-layer simulation, the initial and nal FE meshes are
composed of 170056 and 457948 elements, respectively, with approximately 100 mesh elements added for the
additional geometry element.
(2)
q
=−
K
· ∇
T
in �(t)×T
(3)
T(x,0
)=Tini ∀x∈�(0)
(4)
T(x,t)=T0on ∂�base ×T
(5)
q
laser (x,t)=2ηlaser
Plaser
πR2
laser
exp
−2�x−xlaser �
2
R2
laser
on ∂�laser(t
)
(6)
q
Ar (x,t)=hAr
T−Tinf
exp
−2�x−xlaser �
2
R2
Ar
on ∂�Ar(t
)
(7)
qair
(
x
,
t
)=
hair T
−
Tinf
on ∂�
air
(
t)
(8)
q
rad(x,t)=σε
T4−T4
inf
on ∂�(t
)
(9)
ρcε
T
h
n−T
h
n−1
t
TdV=
qh·∇
TdV−
∂laser
qlaser
TdS−
∂Ar
qAr
TdS−
∂air
qair
TdS−
∂rad
qrad
TdS
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Simulation setup. e FE simulation parameters are presented in Table3. e baseplate has the same
length and breadth as the substrate but its thickness is 40mm (5 times the thickness of the substrate in Fig.1).
At the rst timestep, a cuboidal element of 0.6mm × 0.6mm × 0.2667mm is generated and initialized to 1885K.
e laser beam and the Ar-gas jet are centered on the top surface of this element and although the element
is initialized to 1885K, the action of the Ar-gas almost instantaneously reduces the temperature to ~ 1773K
(1500°C), which is similar to the melt temperature at deposition. All the remaining surfaces are provided with
natural air ow
qair
boundary condition. In addition, radiation heat loss condition
qrad
is imposed over all sur-
faces
(∂�rad =∂�
).
e simulation starts with the rst deposition at
t=0
s. e simulation time step is 3ms. Deposition of
each layer takes 994 steps i.e., 2.982s; this value corresponds to a deposition speed of 33.53mm/s, which is very
close to LMD deposition speed of 33.33mm/s. Between successive layer depositions, a dwell time of 1.221s
(407 steps) is provided to account for focusing head deceleration and reverse acceleration. Aer the deposition
of the nal layer, a dwell time of 0.609s (204 steps) is provided. erefore, the total simulation steps are 4000,
which correspond to a total simulated time of 12s. e simulation was performed on a single CPU thread and
it took 22h 26min 12s to complete.
Thermodynamic calculations
e phase stability and elemental solubility analysis is performed using the ermo-Calc soware version 2019b
with the TCFE9 database.
A mean eld precipitate kinetics model based on the classical nucleation and growth theories37–41 is used
to predict the nucleation, growth and coarsening kinetics of M–S precipitates on MnSiO3 precipitates already
present in γ-austenite/LA. M–S precipitates are assumed to be spherical and their growth is assumed to be con-
trolled by the diusion in γ-austenite/LA. eir growth rate is calculated following Zener’s approximate solution
for spherical precipitates42. e Gibbs–omson eect43 is also taken into account. γ-austenite/LA is assumed
to be an ideal supersaturated solid/liquid solution containing both interstitial and substitutional elements. e
solubility of each element in γ-austenite, MnSiO3, M-S, LA and LB is taken from the ermoCalc soware
generated data used to plot Fig.8.
An important step in the precipitation kinetics simulations is to estimate the number of potential nucleation
sites for M-S. In order to understand how these sites are chosen, the TEM results for L1 – L5 are reconsulted
(Fig.3, S3 and S6). ese results show that 72.22% of all the mixed precipitates contain oxide inclusions at
their core and non-oxide inclusions surround them. ese numbers strongly suggest that non-oxide inclusions
mainly nucleate on oxide inclusions, a phenomenon that has already been observed in other studies performed
at slower cooling rates15,16. Meanwhile, Fig.6 shows that (i) the average size of oxide precipitates is larger than the
average size of oxide inclusions in mixed precipitates and (ii) with the exception of 2 oxide inclusions in mixed
precipitates, the remaining oxide inclusions are either in the size range of oxide precipitates or smaller than the
smallest oxide precipitate. ese results show that the growth of non-oxide inclusions could stunt further growth
of oxide inclusions. erefore, when computing the number of potential nucleation sites for M–S, the following
assumptions have been made: (i) only one M–S inclusion grows on one oxide inclusion, and (ii) the diameter
of an oxide inclusion is the average size of the oxide inclusions in mixed precipitates from Fig.6 i.e., 116.19nm.
Oxide inclusions are assumed to be only MnSiO3 and to have a spherical shape. We also assume that the
maximum possible equilibrium phase fraction of MnSiO3 (Fig.8) is present in γ-austenite/LA. e composition
of γ-austenite/LA is assumed to be such that all oxygen is used up to form MnSiO3; it is as follows (in at. %):
Cr—18.063, Ni—12.027, Mo—1.448, Mn—1.464, Si—1.331, P—0.025, S—0.009, C—0.05 and Fe—balance. In
the following, a maximum volume fraction of
fo
max =0.3%
(rounded up from the equilibrium calculation below
solidus in Fig.8) is considered for MnSiO3.
e diameter of MnSiO3 precipitates is taken as the average diameter of oxide inclusions in mixed precipitates
from Fig.6. From the average mixed oxide volume (
Vo
r
=
4
3
πr
3
with
r=58.095 ×10−9
m from Fig.6) and
fo
max
,
the MnSiO3 number density (
No
m-3) can be estimated as:
Table 3. Parameters for the FE simulations appearing in Eqs.(1)–(9).
σ
(W m−2 K−4)5.67 × 10–8
ε
0.65
cε
(J kg−1 K−1) 500
η
0.9
hAr
(W m−2 K) 12,500 × 106
hair
(W m−2 K) 15 × 106
Tini
=
T0
=
Tsub
(K) 300
RAr
(mm) 20
Rlaser
(mm) 0.6
K11
=
K22
=
K33
(W mm−1 K−1) 16.3
ρ
(kg m−3) 8000
Plaser
(W) 225
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We have assumed that only one M–S precipitate nucleates on one MnSiO3. erefore,
No
is the potential
number of nucleation sites for M–S nucleation on MnSiO3. Finally, the diusion coecient is given as:
where
D0
(m2/s) is the pre-exponent factor,
Q0
(J/mol) is the activation energy,
R
is the universal gas constant,
T
is the temperature, and
α
is a tting parameter.
e parameters used for the precipitate kinetics simulations are reported in Table4; some were either obtained
from the literature41,44 or tted to reproduce the measured non-oxide inclusion size reported in Fig.6. For further
information about this well documented model see38,40,45. e model calculates a particle size distribution fol-
lowing the Euler-type multi-class approach38 and only the average diameter of the particle is plotted in Fig.9a.
Received: 6 February 2021; Accepted: 4 May 2021
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N
o=
fo
max
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o
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0.003
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−22 =3.65 ×1018/m
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Interfacial energy (J/m2) 0.25
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Mn in γ-austenite D0 = 0.178 × 10–4, Q0 = 2.64 × 105, α = 1
Mn in LA D0 = 1.8 × 10–7, Q0 = 1.3 × 104, α = 1
Cr in γ-austenite D0 = 0.169 × 10–4, Q0 = 2.639 × 105, α = 1
Cr in LA: D (m2/s) D = 4.9 × 10–9
S in γ-austenite D0 = 7.52 × 10–4, Q0 = 2.364 × 105, α = 1
S in LA D0 = 4.33 × 10–8, Q0 = 3.5 × 104, α = 1.45
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Acknowledgements
M.V.U., M.B.H.S. and E.H. are grateful to the Fédération Francielliene de Mécanique (F2M) for their support
through the Coup de Pouce 2019 grant. M.V.U. and S.G. are grateful to the European Research Council (ERC) for
their support through the European Union’s Horizon 2020 research and innovation programme (Grant agreement
No. 946959). N. M. is grateful to the doctoral school of Ecole Polytechnique for their support through the PhD
scholarship program. FIB-SEM and TEM work was carried out using the facilities available at the MSSMat labo-
ratory within the MATMECA consortium, which is supported by the Agence National de la Recherche (ANR)
under the contract number ANR-10-EQPX-37. Finally, the authors would like to thank Y. Balit for performing
the 3D printing of the LMD sample used in this work.
Author contributions
M.V.U. conceived the main idea, designed and led this study. M.V.U. and M.B.H.S. are the main contributors
to the writing of this manuscript, designing of the gures and tables. S.G. developed the precipitation kinetics
model and performed the ermoCalc and precipitation kinetics simulations. N.M. developed the FE imple-
mentation of the heat transfer model and performed the FE simulations of the LMD process. L.Y. performed the
TEM studies while being assisted by M.V.U and M.B.H.S. M.B.H.S. and L.Y. performed the post-processing of
the TEM data. E.H. prepared the TEM lamellae. S.H. performed the EBSD studies. A.T. helped with the sample
preparation for EBSD analysis and assisted with the EBSD studies. All authors contributed to the discussions
related to the results and their analysis.
Competing interests
e authors declare no competing interests.
Additional information
Supplementary Information e online version contains supplementary material available at https:// doi. org/
10. 1038/ s41598- 021- 89873-2.
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