Our study showed a negative correlation between changes in soil organic C stocks in the 0–100 cm soil layer and mean annual precipitation (MAP). The most humid site (1500 mm MAP) had less C in shrub-encroached sites while the drier sites (300–350 mm MAP) had more C than their paired open grasslands. This study generally showed soil organic C gains in low precipitation areas, with a threshold value between 750 mm and 900 mm. Our threshold value was higher than that found in North America, suggesting that one cannot extrapolate across continents.Grasslands and savannas are experiencing intensive land-cover change due to woody plant encroachment. This change in land cover is thought to alter soil carbon (C) and nitrogen (N) storage in these ecosystems. Some studies have reported a negative correlation between soil C and N and mean annual precipitation while others have indicated that there is no relationship with mean annual precipitation. We quantified the changes in C and N pools and δ A small change in soil organic C (SOC) may have a great impact on atmospheric C and subsequently on the earth’s climate4. Land-cover change is one of the main factors that can alter SOC content6. One of the major sources of land-cover change, especially in tropical and subtropical regions, is encroachment by native woody plant species. In South Africa, this problem is particularly acute; encroachment affects about 10–20 million ha, seriously reducing the productivity for a country where >70% of its agricultural area is largely grazing lands7.Soils are a major reservoir of terrestrial carbon (C), storing more C  than terrestrial biomass (560 Gt C) and atmospheric pools (750 Gt C)et al.8 examined the effects of vegetation change on SOC at six paired grassland and invaded woody sites along a precipitation gradient in the south-western USA, testing relationships between biomass C gains and SOC losses for common native woody invaders, such as Prosopis (mesquite), Larrea (creosote) and Juniperus (juniper) species. In that study, they found that there was a greater increase in SOC stored in the encroached sites than in the open grasslands in drier locations ). However, Jackson et al.8 also observed lower values of SOC in encroached sites than in open grasslands in the more humid locations. Other data show that generally organic C and total N pools in soils beneath shrub canopies increase linearly with time since shrub establishment9. Findings from several studies11 indicated that woody plant encroachment is a potentially, but highly uncertain, carbon sink. A subsequent meta-analysis of SOC data on woody plant encroachment found that the change in soil organic C in response to woody plant encroachment was highly variable and unrelated to MAP12.Jackson 12 while SOC accumulated with increasing clay content14. Barger et al.12 reported that SOC accumulated linearly with increasing clay content (r2 = 0.76), presumably reflecting greater occlusion and protection of organic matter afforded by clay micelles14. They also found that soil C accumulation decreased as soil bulk density increased, with C gains (r2 = 0.52) being confined to soil densities less than 1.6 g cm−3.Soil bulk density and clay content mediate the magnitude and direction of change in SOC with woody encroachment. In encroached grasslands SOC decreased as soil bulk density increased4 plants (African grasses use this photosynthetic pathway) to C3-dominated woody vegetation14. The change in the dominant photosynthetic pathway offers a unique opportunity to use the natural abundance of 13C to evaluate changes in C cycles due to woody plant encroachment of grasslands. Variations in 13C/12C ratios of plants utilising the C3 and C4 photosynthetic pathways provides a natural tracer when a C4 community type (δ13C ≈ −14‰) is replaced by a C3 community (δ13C ≈ −27‰) or vice versa16, allowing for the differentiation of the C derived from C4 vegetation from C derived from C318.Woody plant encroachment in tropical grasslands usually alters the ecosystem from C19. The frequent increase of N2-fixing woody species in grasslands21 has strong potential for altering the N-cycle, primary production, and other key ecosystem processes22. Plant species are likely to influence ecosystem N cycling via alterations in N-use efficiency and by changing N inputs and losses23. Changes to the soil total N pool via the shift in the balance of N inputs versus losses should be apparent in the natural abundance of 15N in the plant-soil system21.SOC in encroached grasslands can also be enhanced by an increase in available soil nitrogen. Change in nitrogen availability in ecosystems is likely to drive net primary productivity and thus C sequestration2-fixing shrubs . We focused on responses in C sequestration, and in particular its relationship with MAP, as a key continental scale driver of ecosystem function24. We recorded SOC, N, δ13C and δ15N at depth intervals of 0–10, 10–30, 30–60 and 60–100 cm and determined the δ13C and δ15N isotopic ratio in plant leaves and plant litter. We also determined the contribution of C4 plants to SOC in the encroached grasslands. Our study sites contained mostly warm-season C4 grasses (Table −1), Stanger (900 mm yr−1), Bergville (750 mm yr−1), Bloemfontein (500 mm yr−1), Pniel (350 mm yr−1) and Middelburg (300 mm yr−1). At each site, we examined six encroached and six open grasslands. We predicted that in encroached grasslands there would be a negative correlation between changes in SOC and MAP8. We also predicted a negative correlation between C change due to woody plant encroachment and soil bulk density and a positive correlation between C change due to woody encroachment and silt and clay content10. We predicted similar relationships for soil N because of the tight relationship between soil C and N8. We also predicted that δ13C will become less enriched in shrub-encroached grasslands compared to open grasslands because of transition from C4 grasses to C3 woody-shrubs and trees16.In this study, we quantified and compared C and N pools (measured as concentrations and mass stocks) between adjacent woody- encroached and open-grassland plots along a precipitation gradient (300 mm to 1500 mm per annum) in South Africa. The major encroaching species in our sites (except at the 300 mm MAP site in Middelburg) were potentially N1, 10 = 83.70, P < 0.0001 and F1, 10 = 103.9, P < 0.0001) in the open grasslands than in shrub-encroached grasslands  in encroached grassland than in open grasslands  in the encroached grasslands compared to open grasslands in the upper soil layer.At the most humid site (1500 mm MAP), in the 0–10 cm layer, SOC concentration and SOC stocks were significantly greater  . In con.68 Fig. ) and bet.77 Fig. ).Figure 2 = 0.62, P = 0.064; data not shown). There was no significant relationship between total N change between encroached and open grasslands and soil bulk density  or between total N change and silt and clay content .Nitrogen was significantly higher in shrub-encroached grasslands than in the open grasslands in the 0–10 cm soil layer in the 900, 500, 350 and 300 mm MAP sites  . There was no significant enrichment of δ15N with increasing depth in both the encroached and open grasslands  in the 0–10 cm soil layer . Although there was a positive relationship between δ15N change and silt and clay content, the relationship was marginally significant . However, we found a significant and negative correlation between δ15N change and soil bulk density .At 0–10 cm depth, the δnds Fig.  across ayer Fig. . δ15N ch26, the isotopic-mixing model indicated that the percentage contribution of C3 plants (i.e. woody species) to SOC in the encroached grassland increased from 24.7% in the 0–10 cm soil layer to 31.6% in the 60–100 cm soil layer at the 1500 mm MAP site. From the 900 to the 300 mm MAP sites, the contribution of C3 plants to SOC generally decreased with increasing depth in the encroached grasslands  having more C than our 500 mm MAP site.Our study lacked a direct test of SOC change independent of other covarying factors, such as fire, grazing intensity and microbial activities. Nonetheless, our findings agree with several studies31. This increase in SOC agrees with the well-described island of fertility32. Shrubs and trees develop extensive root systems that extract nutrients from the horizontal and vertical planes30, leading to local nutrient recycling and greater biomass production associated with organic matter accumulation30. The accumulation of SOC in the drier shrub-encroached grasslands can also be due to greater rates of primary productivity in the more arid sites because the encroached grasslands had greater biomass than open grasslands. Greater primary productivity increases soil organic matter input in the soil beneath deep-rooted shrubs through increased surface litter and accumulation of complex organic compounds, which are resistant to decomposition24. The humid site (MAP = 1500 mm) had more C in the open grassland compared to the encroached grassland. This finding for our most humid site was contrary to that of Chiti et al. (2016)33 who found that woody plant encroachment resulted in the increase in SOC. However, our results were consistent with the findings of Jackson et al.8. In high-precipitation areas, grasslands are highly productive and allocate a large proportion of SOC belowground with greater root turnover rates8.The increase of SOC in the drier sites due to shrub encroachment is in accordance with the findings from several studies13C values of the plant foliage was generally lower than those of soil organic carbon across all sites. In the shrub-encroached grasslands, δ13C values of organic inputs were characteristic of C3 plants (−32 to −28‰) while δ13C values of the associated SOC was −25 to −14‰. These contrasting values suggest that our shrub-encroached grasslands dominated by C3 plants were once occupied by C4 grasses.Based on the carbon isotopes, this study also indicated that the current organic matter inputs are not in isotopic equilibrium with soil organic matter in shrub-encroached grasslands. The δ13C soil values in our open grasslands (−18 to −12‰) where generally comparable to other C4 grasslands and savannas across the world (−16 ± 2.2‰)34. Thus, the δ13C values across all our six study sites showed that SOC in open grasslands came from a C4 dominated ecosystem. The discrepancy between δ13C values of vegetation and soils in open grasslands of our drier study sites may reflect lateral intrusion of C3 plant roots from the shrub-encroached grasslands. Shrubs in semi-arid region have been shown to have extensive roots that can extend to several meters35.δ4 plants that once dominated these sites was shown by SOC δ13C values at depths deeper than 30 cm, while the humid sites (1500 and 900 mm MAP) showed a significant δ13C change across the whole range of depth studied. This may indicate a quick SOC turnover in humid sites compared to semi-arid sites. It may also suggest that shrub-encroachment is more recent in semi-arid sites relative to the humid sites. Recent changes in C4 to C3 productivity might be evident in the δ13C of SOC near the surface were SOC turnover is most rapid and current organic input are concentrated.In our drier sites , a strong memory of C4 plants that occupied the shrub-encroached grassland was very evident in δ13C values for our 750 mm MAP sites, which ranged from −14 to −12‰ across the soil depth. This finding indicates that organic carbon at this shrub-encroached site was exclusively from C4 plants and that little SOC was derived from the present C3 vegetation. This very strong C4 memory can be attributed to the high clay content of the soil at the site34. The finding is consistent with other studies which showed slow turnover of clay associated organic carbon34. Organic carbon associated with clay soils contains aliphatic hydrocarbons which are inert from carbon turnover36.A particularly strong memory of C13C signature in encroached grasslands indicated that new SOC from woody plants has been incorporated into the soil. However, the finding that this humid site had low SOC may indicate that the rate at which SOC is being lost is higher than that being added by the C3 plants. The woody plants have added approximately 24.7% of SOC compared to 50.5% lost due to encroachment. This humid site had also the lowest SOC and SN compared to our other humid sites. The isotopic mixing model also shows that C3 SOC contribution for this site increased with depth from 24.3% in the 0–10 cm depth to 31.6% in the 60–100 cm depth. These findings may indicate high nutrient leaching accelerated by the sandy soil type and high MAP.In the 1500 mm MAP site the δ3 plants, the bulk of the SOC likely comes from the C4 plants according to the mixed-isotopic model we used. The higher SOC δ13C deeper in the soil may be interpreted as supporting this conclusion, although this depends on there being limited discrimination against 13C during respiration/decomposition26. We have shown elsewhere, using aerial and fixed-point photography, that several of the sites  were open grasslands 20 to 50 years ago34. Although 1500 mm MAP site possibly indicated a decrease in the contribution of the C4 plants in SOC with increasing depth, the bulk of the SOC is still potentially derived from the C4 plants. This decrease could also mean that the 1500 mm MAP site has been encroached for a much longer period than in the other sites.Although the encroached grasslands are dominated by CVachellia erioloba, Vachelliakarroo and Senegalia mellifera. N2-fixing plants ameliorate and increase N in the soil35. However, at the 1500 mm MAP site, soil nitrogen was significantly higher in the open compared to the encroached grasslands, which is consistent with the SOC trends at this site. This finding is consistent with results from other African savanna ecosystems where sites encroached by woody species have been compared with open grasslands39.Soil N was higher in the encroached grasslands compared to open grasslands at the 900, 500, 350 and 300 mm MAP sites over the 0–10 cm soil depth probably because most of the encroaching woody species at these sites are leguminous N-fixing plants such as 15N values with MAP. This finding is consistent with many other studies that showed a negative correlation between δ15N and MAP42. A plausible explanation for this decrease in δ15N with increasing MAP is that photosynthetic activity become more water-than nutrient- limited41. Arid environments have high nutrient availability therefore have a more open N cycle resulting in a less negative δ15N compared to humid ecosystems.There was a general decrease of plant material δ15N values between shrub-encroached and open grasslands across all depths as would be expected if the source of the increase in soil N pools was N fixation37. This might suggest other processes affecting 15N concentration, such as N pumping from deeper soil layers and isotope fractionation during litter decomposition43 and denitrification39, to be contributing to soil nitrogen levels in the shrub-encroached grasslands.There were no significant differences in δ4 plants that previously occupied the area. The significant difference between our study and the North American study of Jackson et al.8 which showed a threshold of 400 mm indicates that extrapolation across continents is problematic, as has been indicated for savannas elsewhere44.This study generally showed shrub encroachment may result in SOC gains in areas with a threshold value between 750 mm and 900 mm MAP. Most of the SOC in the shrub-encroached grasslands came from the C45. Each site was divided into encroached and unencroached sections, using adjacent sections to minimize differences in topography. In three of our sites  there is documented evidence49, while for the other three sites we have strong oral evidence, suggesting that our sites were once open grasslands 20–50 years ago. Encroached sites were defined as those areas with >40% shrub cover. Six 1 m-deep and 1 m-wide pits were dug at random at each site in each section. Within each pit, two soil cores of 100 cm3 each were sampled  at centre of each of the four different depth intervals . One core was used to quantify soil bulk density (BD) and soil texture, and the other core was used to determine soil organic carbon (SOC), total nitrogen (TN), δ13C and δ15N values. Bulk density and soil texture were quantified using the core method and pipette method, respectively51. The soil cores designated for SOC, TN, δ13C and δ15N were air-dried and passed through a 2 mm sieve. Soil samples for SOC and δ13C were treated to remove soil carbonates. To remove soil carbonates, soil samples were treated with 1N H2SO4/5% FeSO4 and double-checked for complete inorganic C removal51. Soil samples were air-dried at 40 °C and then sieved (2-mm mesh). Generally, our soil samples were free of rocks. Total SOC and N were measured using a Europar elemental analyser (Germany) at BemLabs . The SOC and N stocks were calculated using the following equation:s is the SOC or nitrogen stocks (Mg C ha−1); x1 is the C or N concentration in the soil material (%); x2 is the soil bulk density (Mg m−3); x3 is the thickness of the soil layer (cm).Soil samples were collected between October 2013 and March 2014 at six different sites. The site are described in Table 13C and δ15N signatures.We collected plant foliage from the five most abundant species at each site in each landcover area (encroached and open grassland). We sampled litter layer composed of plant debris in different stages of decomposition using a 15 cm × 15 cm wooden frame around each station. Both the plant material and the litter layer were air dried for 3–4 days and then oven dried at 60 °C. The plant foliage and the litter-layer material were then ground before the determination of their δ13C and δ15N values, c. 40 mg of soil, 2 mg of plant foliage and 5 mg of litter- layer material was weighed into tin capsules  and combusted in a Thermo Flash EA 1112 series elemental analyser; the gases were fed into a Delta Plus XP isotope ratio mass spectrometer . The C isotopic ratio of a sample were expressed relative to the Pee Dee Belemnite standard52 and the N isotopic ratios was expressed relative to atmospheric nitrogen53.For δ13C values of soils  and C4 (grass) species  of C4 sources, and δ13CC3 is the mean δ13C (‰) of C3 sources37. The isotopic mixing model used here does not consider δ13C fractionation with depth due to decomposition. Several studies have shown no indication of isotopic fractionation during decomposition26, while several other studies have shown various 13C fractionations due to decomposition27.Assuming complete and unbiased mixing in the soil, we used the δils Fig.  and our 15N and δ13C values attributable to the effects of shrub encroachment and soil depth were analysed using a multivariate ANOVA analysis (MANOVA) to reduce problems with Type I error because we examined several dependent variables simultaneously. The datasets used in this study are available from the corresponding author on request.The data on SOC and N concentration, and SOC stocks, δ


Semiconductor pn junctions are elementary building blocks of many electronic devices such as transistors, solar cells, photodetectors, and integrated circuits. Due to the absence of an energy bandgap and massless Dirac-like behaviour of charge carriers, graphene pn junction with electrical current rectification characteristics is hardly achieved. Here we show a graphene pn junction diode can be made exclusively from carbon materials by laminating two layers of positively and negatively charged graphene oxides. As the interdiffusion of oppositely charged mobile counterions, a built-in potential is created to rectify the current by changing the tunnelling probability of electrons across the junction. This graphene diode is semi-transparent, can perform simple logic operations, and since it has carbon nanotubes electrodes, we demonstrate an all carbon materials pn diode. We expect this graphene diode will expand material choices and provide functionalities (e.g. grafting recognition units on graphene oxides) beyond that of traditional semiconductor pn junctions. Chemically functionalized graphene oxide-based pn junction diodes have potential for future electronic device applications. Here, the authors report an all carbon pn diode with graphene oxide and carbon nanotubes electrodes showing excellent current rectification and efficient logic gates. In contrast to conventional semiconductors, its conduction and valence bands meet at Brillouin zone corners and, therefore, fabricating electronic components from this zero-gap semiconductor should find an unusual way11. Techniques such as cutting graphene into nanoribbons12, placing bias on bilayer graphenes13, and applying mechanical strains14 were developed to open a bandgap and turn off the current of graphene field-effect transistors. In addition, graphene diodes have received particular attention because diodes are the basic building blocks in a wide variety of electronic/photonic systems. Since graphene is metallic at a sufficiently large Fermi energy, Schottky diodes were fabricated by bringing metallic graphenes and semiconductor materials into contact16. With a gate modulation of localized energy levels, tunable light-emitting diode was demonstrated by using a semi-reduced graphene oxide17. Although pn junctions with a planar geometry could be realized by multiple electrostatic gating18, local chemical doping19, and engineering of substrates20, no current rectifying effect was observed owing to the Klein tunnelling of relativistic Dirac fermions21. In the vertical structure pn junctions, current rectifying was achieved by inserting/forming a thin layer of insulating or semiconducting barrier material between p and n graphene layers, showing behaviours of a typical resonant tunnelling diode23. So far, there is still lack of robust technique in making graphene diodes especially the diode as a similar structure to semiconductor pn junction. On the other hand, graphene oxide (GO) contains various reactive oxygen groups , which provide possibility for chemical modification and produce functional materials for a variety of applications25.Graphene, an atomically-thin hexagonal lattice, has currently attracted enormous research interest because of its great promising use for a wide range including electronic devicesHere, the graphene pn junction diode was fabricated by laminating two layers of such chemically functionalized positively (p) and negatively (n) charged graphene oxides on the transparent substrates. As the contact of two layers, mobile counterions diffused across the interface while the anchored charges on graphene oxides frame were immobile. An equilibrium condition was reached in which an internal electric field was established to tune the electron tunnelling probability through the junction. The coupled movement of ions and electrons as well as the current rectification were modelled by using a combination of Nernst–Planck diffusion and Poisson’s equations. Since carbon nanotubes were used as conductive electrodes, we demonstrated an all carbon materials pn diode. To evaluate the utility of these graphene diodes to build the processing units needed for simple computation, in combination with graphene resistors, all carbon materials AND and OR logic gates were constructed.3)4N+OH−, TMAH, pH = 10), while the positively charged GO was synthesized via a two-step procedure27  and O–H (3415 cm−1) stretching peak were greatly suppressed while amide-I band, amide-II band, and amide-III band appeared at 1631 cm−1, 1460 cm−1, and 1384 cm−1, respectively, which were attributed to C=O stretching vibrations in RNH–CO and the coupling of C–N stretching vibration to N–H bending vibration  were seen while these peaks were not observed prior to positive modification  and charged GOs solutions were successively filtered through a mixed cellulose ester membrane . (Note: 1) the CNT electrodes were also chemically functionalized by the similar procedures to the GOs (see Methods) to eliminate possible dipole formation at the interface between CNT and GO layers; (2) the conductivity of charged 20 nm-thick CNT electrodes was over 10 the CNT I–V) characteristics of the graphene pn junction diode was shown in Fig. A typical current–voltage 4N+, see Fig. In the GO layers, the charges anchored onto the GO frames are jammed and restricted to migration, but the counterions (Cl29). This model combined Nernst–Planck diffusion and Poisson’s equations, in which both counterions and electrons could diffuse in response to concentration gradients and migrate due to local electric fields. The interdiffusion of counterions  characteristics cs Figs. .Fig. 3MoTo demonstrate the utility of the graphene pn junction diode to build the processing units needed for simple computation, AND and OR logic gates were constructed Fig. . For theIt must be noted that the cutting-off capability of the AND gate  the interdiffusion happened at the mixing zone rather than the depletion region in semiconductor pn diode, (2) the formation of internal electric field was entropically driven, unlike in semiconductor pn junctions where the voltage arose from equilibration of the electron chemical potential, (3) the internal electric field of graphene diode increased the probability of electron tunnelling/hopping from n to p layer, in contrast to a semiconductor pn diode where the band alignment allowed electrons to flow from n type region to p type region, but not in the reverse direction, and (4) the interdiffusion-created electric field was pointing from p to n layer while in the depletion region of a semiconductor pn diode, this field was reversed from n to p region. On the other hand, diodes based on pure ionic charge transport32 are often labelled as P or N based on the sign of conducting charge carriers: mobile cations are given as P while conducting anions are denoted by N. If positive biases are applied to the P (GO(−) with positive counterions) side of the device—i.e., forward bias—high currents are ordinarily expected. In fact, this bias corresponds to low current in the present diode. Moreover, either the device structure or rectifying principle of the graphene pn junction diode is distinct from other graphene diodes such as Schottky diodes16, light-emitting diode17, and resonant tunnelling diodes23. These differences strongly suggest the use of charged GOs as the electron-carrying phase leads to a different mechanism for diode behaviour than those that have been reported previously. Based on Zeta potential measurements  diffuse/drift across the interface and at the equilibrium condition, a depletion region was created and an internal electric field is established pointing from n region to p region in the absence of an external applied biashowever,  the inteFinally, we wish to emphasize on the relatively low rectification ratio Fig.  of the g33, systems for recording and manipulating tissue behaviours34, and even smart self-powered devices with multi-functionalities35. Also, we wish to integrate functions of GOs  25 into our graphene circuit which is hard to achieve in semiconductor electronics.In summary, we have demonstrated a semi-transparent all carbon materials pn junction diode by laminating two layers of oppositely charged GO layers. This diode is distinct from previous devices where the current rectification happens because an internal field controls the tunnelling and/or hopping probability of conduction electrons. The observation of current rectification in graphene pn junctions greatly expands the class of materials and physical phenomena that can be used to build electronic components. Looking forward, we envision our graphene pn diode being inkjet-printed from aqueous carbon inks on flexible, transparent, and even stretchable substrates in a wide range of applications. These applications could be skin-like electronics to monitor the physiological conditions−1, Graphenea Inc.) under constant stirring. 5 min later, the mixture solution was heated to 35 °C and kept reacting for 3 h36. 63 mL DI water was then poured into the mixture. 15 min later, additional 200 mL DI water and 3.5 mL hydrogen peroxide (30 wt%) were added to stop the reaction. The yellowish product was thoroughly washed with 200 mL dilute hydrochloric acid (3.5 wt%) for 5 times and then re-dispersed in DI water . This further oxidization procedure produces GOs with more –COOH groups .In a typical synthesis, 35 mL sulphuric acid (98 wt%) and 2.60 g potassium permanganate were carefully added into an ice-bath-cooled flask with 50 mL commercially available GO solution , and 60 mg HATU (O–(7-Aza-1H-benzotriazol-1-yl)–N,N,N’,N’-tetramethyluronium hexafluorophosphate) were firstly mixed and reacted at 65 °C for 6 h in 60 mL N,N-Dimethylformamide (DMF). This step was repeated for three times to ensure the majority of –COOH groups were amidated. Next, 500 μL hydrochloric acid (36.5%) and 5.5 g 3-Chloro-1,2-propandiol (98 wt%) were added into an aqueous solution of above amidated GOs . The mixture was heated to 85 °C and kept reacting for 7 h under constantly stirring and refluxing. The grayish products were washed with DI water for 4 times and finally dispersed into DI water (0.25 mg mL−1).A two-step procedure was employed to synthesize positively charged GOs2SO4 and 3 M HNO3 with 3 to 1 volume ratio) and refluxed for 2 h at 80 °C under stirring. This step produces CNTs with more –COOH groups. The products were collected and washed with DI water for 5 times and then re-dispersed into DI water by the assistance of Sodium deoxycholate and sonication . To produce negatively charged CNTs, Tetramethylammonium hydroxide was only used (pH = 10). For the synthesis of positively charged CNTs, the same procedure with GO(+) was employed, while Hexadecyltrimethylammonium bromide (CTAB) was added to improve their dispersity.100 mg carboxyl functionalized CNTs powder  was added into 100 mL mixed acid solution (3 M H−1. 15 mL CNT(−) was firstly vacuum filtered through a mixed cellulose membrane  and thoroughly washed with 20 mL DI water to remove surfactants. 10 mL GO(−) was subsequently added. The MCE-carbons film was peeled off and cut into desired pieces (15 mm × 10 mm) when all the carbons were dried. The MCE was then removed by floating the film onto DMF solvent for approximately 120 min and the negatively charged GO layer was transferred onto the transparent glass slide (20 mm × 14 mm). The layer was finally dried by using nitrogen gas. This produces a layer of approximately 20 nm CNTs and approximately 40 nm GOs  for 1 h. Gradient centrifugation was then used to collect highly dispersed carbon solutions. The concentration of all carbon materials is approximately 0.03 mg mLThe structure of carbon materials was characterized by using scanning electron microscopy  and transmission electron microscopy . The composition of GOs was evaluated by using X-ray photoelectron spectroscopy  and Fourier-transform infra-red spectroscopy . Ultraviolet-visible spectroscopy  was used to evaluate the light transmission capability. Zeta potential is tested on Zetasizer Nano ZS. The surface roughness and thickness of carbon layers were measured by using Dektak XT Stylus Profiling System. The conductivity of carbon layers was characterized by a four-probe technique (MST 4145-B). The measurement of graphene pn diode was conducted under ambient condition with a computer-interfaced high precision electrometer (Keithley 6517). To drive logic circuits, an additional 6517 electrometer was applied.29. For simplicity, we considered one dimensional domain which contain four regions: CNT(−), GO(−), GO(+), and CNT(+). We assumed that the CNT electrode layer (either CNT(−) or CNT(+)) is equipotential37 and the electrons are free to move out or into the layers. The accumulation of mobile counterions in CNT layers was neglected. The flow of electrons as well as the rearrangement of ionic charges throughout the layers produced the electric current J. The dimensionless electric current density (L represents the thickness of GO(+) and GO(−) layers and ni and ne are the number density of mobile ions and conduction electrons respectively, Di and De are the ion and electron diffusivities, Zi is the valence of the mobile ions, e is the elementary charge, kB is the Boltzmann constant, T is the absolute temperature, u is the electrostatic potential, ε0 is the vacuum dielectric constant, and the ε is relative dielectric constant; Di = De = 1.0 × 10−9 cm2 s−1, ε = 4.5. The coupling Eqs.29 were then solved by using a commercial finite element solver (COMSOL 5.1).The graphene pn junction diode was simulated by using a continuum charge-transport model, which combined Nernst-Planck diffusion and Poisson’s equations. The details of this model was presented in referencesmentclass2pt{minimSupplementary Information


Replying to Wei et al. Nature Communications 10.1038/s41467-019-13492-9 (2019)1 raises a question on the conclusion reached in our published work, particularly regarding the docking calculations of PET substrate into the PETase from Ideonella sakaiensis (IsPETase)2. The authors showed the ethylene glycol torsion angle Ψ in an amorphous PET material of 0.25 mm thickness (Goodfellow Cambridge Ltd.) using solid-state nuclear magnetic resonance experiments and determined trans/gauche ratio of 9:91 at 30 °C in good agreement with the previous report on amorphous PET (14 ± 5%)3. Based on the result, they suggested that the conformation of the docked 2-HE(MHET)4 in our published work that showed a trans content of ethylene glycol higher than 25% is rarely present in amorphous PET polymer chains, and claimed that the residues in subsite IIb and IIc we suggested are unlikely to interact with the two MHET moieties of 2-HE(MHET)4. To support the latter statement, they further demonstrated that the transition from gauche to trans conformation is highly restricted in amorphous PET at 30 °C by magic-angle-spinning nuclear magnetic resonance method. They also suggested that, instead of the perfect accommodation, the key factor facilitating the substrate binding seems to be the fragile contact between the phenylene moieties and the surrounding hydrophobic residues. In general, we agree that the comments by Wei et al. provide concrete experimental results showing that ethylene glycol units of amorphous PET polymer do not have the free rotational properties to fit into its substrate binding site as the form of 2-HE(MHET)4 at 30 °C. Thus, the study provides the scientific community with useful information on PET degradation by IsPETase.The manuscript entitled “Conformational fitting of a flexible oligomeric substrate does not explain the enzymatic PET degradation” by Wei et al.2 were independent of temperature setting and not restricted to the temperature of 30 °C. Although IsPETase cannot maintain its activity at high temperature due to its low thermal stability, efforts to increase thermal stability of the enzyme have already been reported4. Thus, an engineered IsPETase with high thermal stability might be able to accommodate the PET substrate in the manner we presented at temperatures higher than 30 °C as the trans content of the material was increased to 56% at 70 °C1.However, our previous docking calculationsGoodfellow amorphous PET in our published works4, which counters the comment that IsPETase showed almost “no” activity against crystalline PET polymer1. It was also previously shown that the semi-crystalline PET material exhibits much higher trans conformation of ethylene glycol than amorphous one at ambient temperature3. Thus, we believe that the authors’ claims regarding the residues in subsite IIb and IIc may not apply under all conditions. In sum, while we agree that Wei et al. provide useful evidences that the used docking calculation is not suitable in amorphous PET at low temperature such as 30 °C, their observations are not necessarily incompatible with the general findings of our previous work2. We anticipate that Wei et al.’s work and our own will inspire future studies aimed at unraveling the exact mechanisms of PET degradation.Moreover, we did not use the


A mechanistic model of photosynthetic protein turnover explains leaf acclimation to light and nitrogen availabilities and suggests that suboptimal photosynthetic nitrogen partitioning is due to daily light fluctuations. Nph) at the canopy level. To investigate the complex interplay between external signals during the acclimation processes, a mechanistic model based on the concept of protein turnover (synthesis and degradation) was proposed and parameterized using cucumber grown under nine combinations of nitrogen and light in growth chambers. Integrating this dynamic model into a multi-layer canopy model provided accurate predictions of photosynthetic acclimation of greenhouse cucumber canopies grown under high and low nitrogen supply in combination with day-to-day fluctuations in light at two different levels. This allowed us to quantify the degree of optimality in canopy nitrogen use for maximizing canopy carbon assimilation, which was influenced by Nph distribution along canopy depth or Nph partitioning between functional pools. Our analyses suggest that Nph distribution is close to optimum and Nph reallocation is more important under low nitrogen. Nph partitioning is only optimal under a light level similar to the average light intensity during acclimation, meaning that day-to-day light fluctuations inevitably result in suboptimal Nph partitioning. Our results provide insights into photoacclimation and can be applied to crop model improvement.Plants continually adjust the photosynthetic functions in their leaves to fluctuating light, thereby optimizing the use of photosynthetic nitrogen ( Acclimation of leaf traits to fluctuating environments is a key mechanism to maximize fitness .Vertical nitrogen distribution in response to light has been intensively studied . This diOptimizing functional partitioning within the leaf is of great importance because it improves carbon gain by enhancing photosynthetic nitrogen use efficiency  is defined as biologically active nitrogen in the proteins involved in photosynthetic functions, i.e. carboxylation, electron transport and light harvesting. Leaf Nph is calculated as the sum of nitrogen in the carboxylation pool (NV), electron transport pool (NJ) and light harvesting pool , maximum electron transport  and leaf chlorophyll , respectively (where V (μmol CO2 mmol−1 N s−1) is the carboxylation capacity per unit Rubisco nitrogen, and χJ (μmol e− mmol−1 N s−1) is the electron transport capacity per unit electron transport nitrogen. χCJ (mmol Chl mmol−1 N) and χC (mmol Chl mmol−1 N) are the conversion coefficients for chlorophyll per electron transport nitrogen and per light harvesting component nitrogen, respectively. Photosynthetic nitrogen partitioning fraction of a pool X (pX) is determined as the ratio of nitrogen in the pool X  to Nph:where χNX is determined by the instantaneous protein synthesis rate  and degradation rate  of the corresponding enzymes and protein complexes at a given leaf age :The rate of change of NX state:Protein synthesis as an age-dependent and zero-order process  is the maximum protein synthesis rate of NX that occurs at the early stage of leaf development (Supplementary JXB online). The constant tXd, (°Cd−1) describes the relative decreasing rate of the protein synthesis over time :The degradation rate SXmax, in Eq. (5) is a function of daily light interception :The variable SXmm, (mmol N m−2 °Cd−1) is the potential maximum protein synthesis rate and kXI, is the rate constant describing the increase of SXmax, with ILd. The factor rXN, increases with nitrogen level in the nutrient solution  by a Michaelis–Menten constant, kXN, (mM):where Vcmax, Jmax, and Chl were estimated from functional nitrogen pools NV, NJ, and NC, using Eq. (2a–c). The net photosynthetic rate  is defined as the minimum of RuBP carboxylation-limited  and RuBP regeneration-limited  net photosynthetic rate (Photosynthetic parameters Cc (μmol CO2 mol−1) is the chloroplastic CO2 concentration, Γ* (μmol CO2 mol−1) is the CO2 compensation point in the absence of dark respiration, Kc (μmol CO2 mol−1) and Ko (mmol O2 mol−1) are Michaelis–Menten constants of Rubisco for CO2 and O2, respectively, O (mmol O2 mol−1) is the O2 concentration at the site of carboxylation, Vc (μmol CO2 m−2 s−1) is carboxylation rate, and J (μmol e− m−2 s−1) is electron transport rate. Daytime respiration rate Rd (μmol CO2 m−2 s−1) is assumed to vary with t and the mean ILd during the previous 4 d (ILd4d):where Rmax (μmol CO2 d mol−1 photons s−1) relates ILd4d to the maximum Rd, Rg (m2 d °Cd−1 mol−1 photons) influences the decrease in the growth respiration, and Rm (μmol CO2 d °Cd−1 mol−1 photons s−1) affects the increase in the maintenance respiration with t.where Vc and J are calculated from Vcmax and Jmax, respectively, depending on the photosynthetic photon flux density (PPFD) incident on the leaf  according to – µmol photons−1) is the conversion efficiency of photons to J, and θ (unitless) is a constant convexity factor describing the response of J to ILc. Leaf absorptance  is related to Chl  and mesophyll conductance  to CO2:Chloroplastic COCa (μmol CO2 mol−1) is atmospheric CO2 concentration, and gsc is calculated with species-specific constants of stomatal conductance, g0 and g1  occurs and vgm is the standard deviation of the curve; gmmax is linearly related to Nph, since a similar relationship has been reported for C3 plants (e.g. where rgm (mol CO2 mmol−1 N s−1) describes the rate of increase of gmmax in relation to Nph, and rgm0 (mol CO2 m−2 s−1) is the minimum gmmax.where Ac was solved analytically with Eqs (9b), (14), and (15), and Aj with Eqs (9c), (14), and (15), following The steady-state Cucumis sativus ‘Aramon’, Rijk Zwaan, De Lier, The Netherlands) plants were grown in two experiments at the Institute of Horticultural Production Systems, Leibniz Universität Hannover, Germany (latitude 52.4°N).Cucumber (3)2 and Ferty Basisdünger 1 . Nutrient solution was replaced weekly and adjusted to pH 6.0–6.5 two times a week. Three constant light conditions with daily photosynthetic photon integrals (DPI) of 28.9, 14.2, and 4.4 mol photons m−2 d−1 were provided using metal halide lamps. Four plants were grown under each treatment combination. Three leaves per plant  were maintained horizontally and well exposed to incoming light using custom-made leaf holders, while the rest of the shoot was trained downward to avoid mutual shading. Gas exchange (see below) and relative chlorophyll content  were measured at different thermal ages of the leaves, ranging from 45 °Cd to 558 °Cd, calculated by subtracting a base temperature of 10 °C . Cucumber seeds were sown in rock-wool cubes (36 × 36 × 40 mm) on 5 October. Eight days later, seedlings were transplanted to larger rock-wool cubes (10 × 10 × 6.2 cm) for another 8 d until the second true leaves appeared (leaf length ≥3 cm). Plants were transferred into 25 litre plastic containers (one plant per container) on 21 October and cultivated hydroponically with a 12 h light period and 24 °C day/20 °C night air temperature. Three nitrogen levels, 9.6, 4.6 and 2.3 mM, were supplied using Ca and 2.5 mM , by drip irrigation using the same fertilizers as described in the growth chamber experiment. During the experimental period, average nitrogen supply was calculated from the nitrogen concentration in the nutrient supply and rock-wool slabs, which was 8.2 and 2.0 mM for HN and LN, respectively. Plants were grown under either high light (HL) or low light (LL) regimes. The southern half of the greenhouse was unshaded as the HL regime. The LL regime was created in the northern half of the greenhouse by shading nets to reduce incoming light from top and sides, where PPFD was reduced on average to ca. 40% of that under HL (38 ± 1.3% under sunny and 42 ± 0.2% under cloudy condition). Average DPI above the canopy was 21.4 and 8.5 mol photons m−2 d−1 for HL and LL, respectively, during the experimental period. DPI during the experimental period was recorded by the weather station located above the greenhouse. An average light transmittance of 49.8% through the greenhouse structure was applied (39.2% on a sunny day and 60.4% on a cloudy day). Air temperature in the middle canopy was recorded continuously using data loggers and was significantly higher under HL (0.5 °Cd per day). Gas exchange measurements and harvests were conducted at four time points on 21 April, 28 April, 5 May, and 12 May at two different canopy layers with two replications. Leaf age at measurement ranged from 77 to 414 °Cd. Leaf elevation angle was obtained by a 3D digitizer  according to 2 m−2).One greenhouse experiment was carried out from 4 April to 12 May 2017 under two light regimes and two nitrogen supply levels to evaluate the model performance and to collect input data for optimality analyses. Seeds were sown on 14 March and transplanted to larger rock-wool cubes on 22 March. After the third true leaves had appeared, plants were transferred onto rock-wool slabs on 4 April with plant density of 1.33 plants m−2 s−1  and light response curves were measured using a portable photosynthesis system . All measurements were carried out under sample CO2 400 µmol mol−1, leaf temperature 25 °C and relative humidity 55–65%. Rd was estimated from the linear portion of the light response curve .Light-saturated net photosynthetic rate under PPFD of 1300 µmol photons mse curve . Vcmax wyperbola . MesophyChl were determined  and (8)] by least squares fitting in SigmaPlot  as well as the influences of t and ILd on Rd [Eq. (10)] and gm [Eqs (16) and (17)].The differential equations (4)–(6) were solved and the coefficients were quantified using R  by using the packages ‘deSolve’ and ‘DEoptim’, which minimizes the sums of squares of the residuals between observations and simulations. The data obtained in the growth chamber experiment were used for the parameterization. Nph, mmol N m−2), photosynthetic nitrogen per leaf  and total leaf photosynthetic nitrogen content of the canopy . First, leaf elevation angle of each leaf and LAI were simulated empirically depending on t  to simulate protein turnover. Light interception was calculated by the Beer–Lambert law  was simulated using greenhouse canopy characteristics obtained at the last harvest as input (D) 1.2 kPa and Ca 400 μmol CO2 mol−1 were used in all simulations, similar to the environmental conditions during the gas exchange measurements. Scenarios with different DPI levels were defined for simulating DCA. Up to six DPI levels were taken as relative to the average DPI during acclimation (aDPI) to simulate the influence of day-to-day DPI fluctuation on DCA. To simulate DCA, diurnal PPFD above the canopy was simulated for a given DPI level with a time step of 0.1 h by a simple cosine bell function  to create variations in the rate of protein synthesis, and a partitioning factor fXp, was introduced into Eq. (7) to create variations in the maximum protein synthesis rate of different functional pools:To evaluate the effects of between-leaf distribution and within-leaf partitioning of fd=1 and fXp,=1, when all coefficients in the synthesis process  to the DCA increase were calculated along the canopy depth.A control condition was defined with  process  remainedSmm, coefficient td, and protein degradation constant, Dr. The coefficient td affects the decrease in the rate of synthesis, and Dr contributes to the degradation rate, which together influence the developmental effect on protein turnover dynamics. The low value of td  and the electron transport pool (NJ), while the light harvesting pool (NC) had a lower Dr . When light was increased 2.5-fold (from LL to HL), Smax increased by 50% in NV and NJ, and by 10% in NC, while nitrogen level had less influence on Smax (<10%), which only occurred under low nitrogen concentration (<3.5 mM) and the higher light intensity  and two nitrogen levels (HN and LN) were measured in two canopy layers weekly for four consecutive weeks. The model predicted leaf photosynthetic characteristics with high accuracy 70–91%,  and a trNph  was evaluated by introducing a distribution factor fd to create variations in the rate of protein synthesis. In our model, protein synthesis and degradation rates determined simultaneously (i) total leaf photosynthetic nitrogen content of the canopy , (ii) Nph distribution in the canopy, and (iii) Nph partitioning fractions of pools X (pX) in the leaf. Thus, it was impossible to modify single elements while maintaining the other two constant. Increasing fd led to a faster reduction of Nph during leaf ageing and more acropetal Nph reallocation. However, it also reduced Ncanopy and tended to increase pC (data not shown). Therefore, to obtain the leaf photosynthetic nitrogen content  with comparable Ncanopy, simulated Nileaf, with fd=n  was adjusted proportionally to the ratio between Ncanopy calculated with fd=1 and with fd=n:The influence of pX,i was set equal to the control value:Ncanopy among the distribution patterns. The factor fd was varied between 0.5 and 5.0 at intervals of 0.5 in the simulation, which gave values of Nph comparable to those measured in cucumber leaves , 100% (aDPI100) and 50% (aDPI50) of average DPI during acclimation (aDPI) were used in the DCA simulation. Under aDPI100 and aDPI50, enhancing acropetal Nph reallocation did not significantly increase DCA (<5%), suggesting that Nph distribution was optimal under constant and decreasing DPI  were identified as optimal and the maximal DCA was compared with control DCA  to light and to nitrogen by their effects on the maximum protein synthesis rate  doubled Smax of the carboxylation pool (NV) and electron transport pool  or qualitative ] in the DCA simulation resulted in a 4-fold above-optimum investment in NV even under aDPI (data not shown). Since Rubisco is not an especially inefficient catalyst in comparison with other chemically related enzymes  and using top-lighting, possibly in combination with inter-lighting, during the low-light season (ca. 25% increase in DCA; ca. 6% increase in DCA; In greenhouse cultivation, it is possible to achieve a more stable light environment using supplemental lighting. This can be a plausible solution to improve the vertical light distribution  and to mNph and pX in the older leaves (NJ over NC under LN with increasing leaf age (Light fluctuations occur particularly in the lower canopy layer, where sunflecks cause strong and frequent variations in light, thereby increasing variations of r leaves . Interesleaf age , which mleaf age . Since wleaf age . This caWe propose a mechanistic model to quantify the effects of leaf age, nitrogen and light availabilities on photosynthetic acclimation. The model predicts the observed photosynthetic acclimation under different combinations of nitrogen supply and light availability in the greenhouse. Model simulation indicates that photosynthetic nitrogen distribution is close to optimum and photosynthetic nitrogen partitioning can be optimal under constant light conditions. However, large fluctuation in light between days under natural conditions inevitably leads to suboptimal nitrogen partitioning. Our study provides insights into photosynthetic acclimation and the model can be used for crop model improvement and provides guidelines for greenhouse management.JXB online.Supplementary data are available at Fig. S1. Schematic diagram of photosynthetic nitrogen turnover.Fig. S2. Relationship between relative chlorophyll content and leaf chlorophyll concentration.Fig. S3. Environmental input for the model evaluation and simulation.Fig. S4. Relationships between leaf angle, LAI, and age.Fig. S5. Leaf area distribution used as input in the daily canopy assimilation simulation.Fig. S6. Comparisons of simulated photosynthetic nitrogen traits between nitrogen supply levels and between light conditions.Fig. S7. Leaf photosynthetic nitrogen distributions with the vertical light distribution.Table S1. Canopy characteristics used in the daily canopy assimilation simulation.Supplementary Figures S1-S7 and Table S1Click here for additional data file.


Paracartia grani can actively modify the size-spectrum of oil droplets. Direct manipulation through the movement of the feeding appendages and egestion work in concert, splitting larger droplets (Ø = 16 µm) into smaller ones (Ø = 4–8 µm). The copepod-driven change in droplet size distribution can increase the availability of oil droplets to organisms feeding on smaller particles, sustaining the transfer of petrochemical compounds among different compartments. These results raise the curtain on complex small-scale interactions which can promote the understanding of oil spills fate in aquatic ecosystems.Oil spills are one of the most dangerous sources of pollution in aquatic ecosystems. Owing to their pivotal position in the food web, pelagic copepods can provide crucial intermediary transferring oil between trophic levels. In this study we show that the calanoid  Oil spills can either occur at the sea surface, as in the case of petroleum tankers shipwrecks , or underwater, typically owing to deepwater oil well blowouts . Recent work in environmental science and marine pollution has focused on both experimental determination and theoretical prediction of the oil droplet size distribution following an underwater well blowout2. By turbulent mixing, subsurface spills create oil droplets (ODs): those larger than 5 mm can reach the surface within hours, while rising times for smaller droplets can extend up to 24 h or more2. In such a case, OD distribution is additionally influenced by hydrostatic pressure and presence of dissolved gases3. In the case of surface spills, the activity of breaking waves breaks up oil slicks into ODs with diameter ranging 10–100 µm4.Recent years have seen increased public awareness about the consequences of oil spills in marine ecosystems. The release of petroleum represents a critical source of environmental risk, with heavy consequences on the life of aquatic organisms6 and enhancing natural degradation by bacteria8. Dispersants allow the creation of ODs with Ø < 70 μm, which remain suspended in the water for weeks to months owing to colloidal stability5. It has been estimated that, in the framework of the Deepwater Horizon blowout, 1.84 Mgal of chemical dispersant were applied9, and that 16% of spilled oil remained suspended in the form of ODs10 upon the application of COREXIT® EC9500A, currently the dispersant of choice5.Chemical dispersants are operationally adopted to facilitate the breaking of surface slicks, limiting the oiling of beaches and coastal areas13. The dimensional and rheological properties of ODs are similar to those of phytoplankton cells, making them eligible “fake prey” for many planktonic organisms19. Pelagic copepods, in particular, are crucial intermediaries between trophic levels, providing the link between primary producers and secondary consumers, but also sustaining the microbial loop and the recycled production through egestion and excretion20. Copepods can uptake oil by ingestion as well as by diffusion over the body surface, accumulating petrochemical compounds in egg lipids, egesting them in fecal pellets or even metabolising them21. Evidences also demonstrate that ODs can additionally adhere to copepods’ body and limbs22. Exposure to oil compounds may lead to long-term bioaccumulation23, with acute toxicity effects more intense in temperate species compared to Arctic ones24, as well as to the death of the individuals16. Furthermore, recent studies have demonstrated that long-term bioaccumulation can also result from short-term exposures23.As a mixture of hydrocarbon and non-hydrocarbon compounds, crude oil and its products can exert strong toxic, carcinogenic, teratogenic and mutagenic effects on aquatic organismsCalanus finmarchicus can accumulate more than 10 mL oil kg−1 biomass25, whereas model simulations predicted that the same species can reprocess up to 40% of a spilled oil mass, with higher rates in case of subsurface blowouts creating a larger amount of turbulent-mixing driven ODs22. Considering that copepods are staple food for other organisms, such as chaetognaths26 and fish larvae27, the accumulation of ODs within their body may critically contribute to the transfer of oil compounds among trophic levels.Calculations based on ingestion experiments reported that 29; in addition, they have evolved surprising handling techniques to effectively detect and manipulate prey items31. To address the main goal of the research, an almost monodispersed distribution of ODs (peak Ø = 16 µm) was created using a tailored microfluidic platform. The modifications in the droplet size distribution after 24 h incubation under controlled conditions in presence of 2, 4 and 6 adult female individuals of the calanoid copepod Paracartia grani were studied. The results indicate that the mechanical action of copepods  modifies the size spectrum of ODs, shifting it towards smaller Ø. The feasibility of a direct manipulation through feeding limbs is confirmed by numerical calculations evidencing that the energy necessary to split an OD into two daughter droplets can be covered by the actual energy of copepod appendages movement. These novel observations promote our understanding of the biological processes affecting the weathering of spilled oil, and pave the way to further experimentation at microscale level.In this study we delved into the role of copepod feeding behaviour in reshaping the size spectrum of dispersed ODs, evidencing the role of potential biological-driven microscale processes in modifying the dimension of droplets in the aftermath of an oil spill. Notwithstanding their reduced body dimensions, pelagic copepods are capable of active movement in the fluidg = 1.021) to very large (4–8 µm Ø: g > 1.300) size effect (Table SI3). The presence of Paracartia grani females in ETs (see “Methods”) manifestly emphasised such distributional shift relative to CT . The mean OD Ø decreased linearly as a function of copepod abundance , although the Kruskal-Wallis H test indicated a statistical similarity of the values . Remarkably, the 10–14 µm diameter range remained scarcely populated.In comparison to the mother suspension, the OD size distribution in CT (see “Methods”) evidenced a reduction in the 16 µm class in favour of an increase in the 4–8 µm range Figs  and SI3, CT Fig. . As the  CT Fig. . Such an16 33 and Cyclops scutifer (120 × 10−12 J)34. Using CFD simulations for Diaptomus minutus, a suspension-feeding species with a body length comparable to P. grani, the mechanical power cost can be estimated in the range of 2–6 × 10−9 W35. Assuming a copepod-OD interaction time <1 s31, the energy output of the feeding current would be on the order of 10−9 J (O pJ). The curve shown in Fig. If the copepods were able to split an OD with Ø = 16 μm into two daughter ODs of equal volume, these would have Ø ≃ 12.7 μm Fig. . LookingODs, µL) demonstrated that the oil volume was conserved among treatments . The Kruskal-Wallis H test returned p = 0.22, indicating no difference in VOD between CT and ETs. This result was backed up by the post hoc pairwise analysis. The conservation of VOD suggests that only a negligible part of the oil was retained by copepods’ guts, and supports the effectiveness of the manipulation process leading to a change in OD size distribution. It is worth noting that, upon visual inspection after the completion of the experiments, no trace of ODs was evident on vials walls.The calculation of OD volumes . Physically-driven size shift can be accompanied by biologically-driven processes. In this framework, this study demonstrates that P. grani appendage movement. In particular, the biased shift observed can be justified considering that the energy required to detach a small parcel from a bigger OD is lower than that required to split a droplet in two symmetric halves. Furthermore, considering P. grani clearance rate at high food concentration39, the recursive manipulation of increasingly smaller ODs supports the observed shift in OD size distribution. The resizing operated by P. grani closely recalls the disaggregation of marine snow aggregates operated by Euphasia superba through small-scale shear generated by its swimming activity40. Such commonality supports the ability of zooplankters to actively modify the size spectrum of material suspended in the water column.The OD size distributions observed in ETs clearly show that, as the number of incubated copepods increases, the OD dimensional spectrum is progressively shifted towards smaller Ø, in particular in the 4–8 µm window. The calculated energy required to actively cut an OD could be realistically covered by 16. In this second case, their Ø would likely be <10 µm16, in line with the dimensional range scored in the present investigation. The egestion of ODs as such might have been emphasized by the absence of food during the incubation period. Notwithstanding this, the increase in ODs with Ø = 4–8 µm scored in the present investigation provides an experimental support to previous observations16, and validate the feasibility of such a resizing process operated by copepods. It is worth underlining that the 24 h incubation period used in the experiments is fully compatible with the gut passage and evacuation time of congeneric Acartia species, ranging from 11 to 97 min .Swallowed ODs can instead be resized in the gut, being encapsulated in fecal pellets and/or defecated as such44. This setup represents a crucial step forward compared to other OD forming systems such as magnetic stirring, which creates an oil emulsion without an accurate definition of droplet size16.The creation of a monodispersed suspension of ODs is fundamental to investigate the interaction of copepods with prey-like droplets. The microfluidic device implemented in the present work efficiently built a well-peaked distribution of ODs, equalling the efficiency of a similar experimental device46. The present investigation provides new evidence on the interactions between copepods and ODs, which may affect the availability of petrochemical compounds to organisms feeding on smaller particles. Copepod manipulation produces smaller droplets falling in a range accessible to protozoans17, copepod nauplii15, meroplankton larvae38 and pelagic tunicates18. As many of these organisms may be preyed upon by copepods, OD manipulation can determine a negative feedback on copepods themselves, as they may re-ingest oil they had already manipulated. Furthermore, oil dispersion may affect copepod vertical distribution, as demonstrated for Calanus finmarchicus copepodites47. Smaller ODs can additionally be colonized by hydrocarbon-degrading bacteria8; in particular, droplets with Ø ≃ 5 µm are degraded at a faster pace compared to larger ones (Ø = 100 µm)48. The encapsulation of ODs inside copepod fecal pellets sustains the transfer of oil to microbes and benthic organisms16, while bacteria indigenous to copepod guts are responsible for the degradation of oil entrapped in fecal pellets49.Over the last years, mounting evidence has gathered about the role of copepods as stepping stones in the transfer of plastic debris across the food web14, and can also result in significant higher mortality15. Toxic effects are further aggravated by the presence of UVB radiation15, as well as by the presence of oil dispersants15. The adoption of a non-toxic paraffin oil excluded lethal effects or behavioural/physiological impairments on tested individuals. Such experimental procedure allowed testing the potential ability of copepods to manipulate ODs. The overall impact in the field may however be less pronounced, as copepod activity might be lowered owing to toxic effects of crude oils. The manipulation ability of copepods may additionally be dependent on the specific physical properties  of the spilled oil.The exposure to sublethal concentrations of crude oil can reduce the reproduction and egestion rates in different copepod species53. The unanticipated results of the present research elucidate key mechanisms by which copepods can contribute to the creation of ODs in the lower end of the dimensional spectrum. This process sheds new light on the physical-biological interactions occurring at the microscale, and fosters research on the direct and indirect interactions between ODs and planktonic organisms.Based on modelling and laboratory studies, the mean Ø of droplets created upon massive release of oil after spills or shipwrecks spans several order of magnitude, from μm to mmParacartia grani, a calanoid copepod frequent in neritic marine environments, were used for the experiments. These suspension-feeding copepods are routinely maintained under culture by the Zooplankton Ecology Group at the Institute of Marine Sciences of Barcelona (CSIC), where the experiments were performed. The species was chosen due to the existing broad information about its ecological role in marine ecosystems, from the interaction between zooplankton and physical variables, to its feeding role and mechanisms and the effects of food on growth, production, survival rates, and even ageing54. Individuals were cultured in the laboratory at 19.0 ± 0.1 °C and fed on Rhodomonas salina.Adult females of 5. Crude oils have demonstrably lethal effects on copepods when massively present in the environmental fluid, but even at sublethal concentrations they may exert negative impacts, for example lowering feeding rates55, reducing egg production, egg hatching and egestion rates14, and impairing mating success56. For the experiments discussed in this work, the use of the non-toxic Hodernal® allowed focusing on the capacity of copepods to modify OD size distribution without introducing potential elements of variability due to the intrinsic toxicity of crude oils.A custom microfluidic platform generated size-controlled droplet distributions. ODs were created using Hodernal® , an inert, non-toxic paraffin oil, and 2% Tween 80 , a non-ionic saccharide-based surfactant included in COREXIT® EC9500Aoil = 0.850 g mL−1 at 20 °C the API gravity (°) for Hodernal® can be calculated as57:Crude oils have a wide range of densities and viscosities, depending on several factors including geographic origin and chemical composition. Based on manufacturer’s data sheet, considering a relative density ρwater). Since Eq. oil between 20 °C and 15 °C (O 10−3) and considering ρwater = 0.999 g mL−1, Hodernal® API gravity equalled 34.8° (SG = 0.851), a value typical of light crude oils58. As a reference, for Macondo crude oil spilled from Deepwater Horizon rig typical values score ρMacondo = 0.820–0.860 g mL−1 resulting in API gravity ranging 32.8°–40.8°61. Based on these values, Hodernal® could be used as non-toxic substitute for light crude oils58. At the end of the incubation period, the vitality and health of P. grani were visually checked to verify the absence of stress-induced behaviour.being mentclass2pt{minim−1, corresponding (as ppm) to that of the saturating ingestion for P. grani feeding on R. salina. The OD concentration fell within the range of Ø tested for ingestion experiments in doliolids18. The selected Ø (16 µm) was also representative of the typical major axis (length) of the ovoidal R. salina (10–14 µm)62, allowing the creation of ODs mimicking a typical P. grani prey item. More technical details on the setup are provided as Supplementary Information.A mother suspension of ODs  at 12:12 light:dark photoperiod. To view and count droplets before and after incubation, three aliquots (1 mL) of the suspensions were pipetted from each vial into a glass Sedgewick counting chamber. 50 random pictures were taken for each aliquot, equalling 150 pictures for each vial (450 pictures for each treatment), and ODs were automatically counted and measured using ImageJ64. As the resolution of the CCD microscopy camera used in the experiments approached ~1–2 µm, and considering the necessity of using specific dyes to identify microscopic artefacts , ODs with Ø < 4 µm could not be safely quantified. As a consequence, 4 µm was used as lower threshold for ODs analysis.All incubation experiments were performed at the same OD concentration using filtered seawater without food. 30 mL OD-containing vials were filled with 2, 4, or 6 copepods per triplicate . Two vials without copepods were used as control (CT). The experimental volumes were equivalent to those tested in previous 66 were used to compare the percent contribution of the most predominant OD Ø classes among the different experimental conditions tested. This was complemented by the measurement of the effect size67 by which quantifying the difference between the groups. In particular, owing to the small sample size, the measure of the effect size was calculated using Hedges’ g68. Depending on g values, differences between means were ranked from small to very large, following the criteria established in the literature69. More details are provided in the Supplementary Information.OD counts from the three aliquots of each single vial were grouped together and binned into 2 µm wide Ø classes, which were subsequently pooled among replicates. BoxplotsW (pJ) needed to increase the surface area 70:γ represents the surface tension (mN m−1) and γ values for n-alkanes with 5–16 C-atoms range between 50 and 55 mN m−132.When a spherical oil droplet of volume OD) was calculated starting from the associated OD size distribution and pooled among treatments. Owing to the small sample size , normality tests could not be reliably used to reject the null hypothesis. In such conditions, a nonparametric ranking test should thus be used71. Basing on the threshold values for k and N73, the statistical comparison of the VODs calculated for CT and ET treatments was carried out using a Kruskal-Wallis H test74 returning a p value for the rejection of the null hypothesis that none of the k groups statistically dominated over the others. However, since the Kruskal-Wallis is an omnibus test, a post hoc test was mandatory to control the inflation of type I errors. Since samples were independent and with unknown distribution, a multiple pairwise comparison procedure using Dunn-Šidák’s correction76 was employed. The same statistical approach was used to compare the mean OD Ø among the different treatments.As a proxy for mass balance, for each 1 mL aliquot the total OD volume (VSupplementary InformationVideo S1Video S2Video S3


Additively manufactured (AM) metallic materials commonly possess substantial microscale internal stresses that manifest as intergranular and intragranular residual stresses. However, the impact of these residual stresses on the mechanical behaviour of AM materials remains unexplored. Here we combine in situ synchrotron X-ray diffraction experiments and computational modelling to quantify the lattice strains in different families of grains with specific orientations and associated intergranular residual stresses in an AM 316L stainless steel under uniaxial tension. We measure pronounced tension–compression asymmetries in yield strength and work hardening for as-printed stainless steel, and show they are associated with back stresses originating from heterogeneous dislocation distributions and resultant intragranular residual stresses. We further report that heat treatment relieves microscale residual stresses, thereby reducing the tension–compression asymmetries and altering work-hardening behaviour. This work establishes the mechanistic connections between the microscale residual stresses and mechanical behaviour of AM stainless steel. The impact of grain-scale residual stresses on the mechanical behaviour of 3D-printed metals and alloys remains unexplored. Here, the authors combine in situ synchrotron X-ray diffraction and computer simulations to link residual stresses in steel to its tensile behaviour. Its presence can influence the mechanical behaviour of AM parts. This issue is especially significant for AM materials processed by selective laser melting (SLM), which inevitably results in substantial residual stresses. The buildup of high residual stresses during SLM processing can induce the damage and eventual failure of AM parts in service. Hence, mitigation of residual stresses is considered as one of the most outstanding challenges in the AM field. To palliate the deleterious effects of residual stresses, a fundamental understanding of their impact on the mechanical behaviour of AM materials is needed.Residual stress is one of the most critical issues for additively manufactured (AM) metallic materials7 macroscale and microscale residual stresses. The so-called Type I macroscale residual stresses are distributed across the overall dimension of a part and contribute to its distortion. For example, they arise due to long-range gradients of plastic deformation in the part. By contrast, the microscale residual stresses manifest at the scale of microstructure and are categorized into two types: Type II intergranular residual stresses and Type III intragranular residual stresses. Type II self-equilibrates over a length scale of grains and results from strain incompatibility between grains. Type III is associated with the heterogeneous microstructure such as dislocation cells inside grains and also satisfies the self-equilibrium condition. In general, microscale residual stresses develop after material processing and subsequently evolve under applied loading. Following the literature8, we use the terms ‘residual stress’ and ‘internal stress’ interchangeably with regard to these microscale residual stresses. To understand and control the microscale residual stresses, it is necessary to track their spatiotemporal evolution in real time at high resolution. This has been often pursued by means of in situ X-ray or neutron diffraction methods17.The residual stresses in polycrystalline materials can be categorized according to two major classes:4. These microstructural characteristics can result in mechanical properties that significantly differ from materials produced by the conventional methods such as wrought and cast19. During L-PBF processing, the highly localized heating and rapid cooling of a melt pool, in conjunction with the layer-by-layer repetition of such a thermomechanical process, give rise to large thermal gradients and heterogeneous residual stresses within a non-equilibrium microstructure23. The thermal gradients are affected by many processing parameters24, including powder-bed temperature, laser power, powder thermophysical characteristics, melt pool size, etc. The convolution of these parameters often leads to a complex residual stress field. Although studies of the macroscale residual stresses in AM materials have revealed various deleterious effects such as loss of net shape, detachment from support structures or failure of the build parts25, the ways in which microscale residual stresses influence the mechanical performance of AM materials remain elusive. This is due to the difficulty in measurement and understanding of the spatiotemporal evolution of residual stresses at the scale of individual grains or phases6.The additive manufacturing of metallic materials via laser powder-bed-fusion (L-PBF) results in highly non-equilibrium microstructures with a high density of dislocations, irregular and tortuous grain morphologies, cellular structures and chemical segregationHere we present a combined experimental and modelling study of the microscale residual stresses in AM 316L austenitic stainless steel. We perform in situ synchrotron X-ray diffraction (SXRD) measurements of lattice strains in AM stainless steel under uniaxial tension. Micromechanics and crystal plasticity finite element (CPFE) models are developed to understand the impact of elastic anisotropy, progressive yielding and hardening on the extent and evolution of lattice strains and associated Type II intergranular residual stresses. We measure pronounced tension–compression asymmetries in yield strength and strain hardening for AM stainless steel. Combining the experimental and CPFE modelling results, we show that the tension–compression asymmetries are associated with back stresses originating from heterogeneous dislocation distributions and resultant Type III intragranular residual stresses. Our work not only demonstrates an effective approach to quantitatively evaluate the microscale residual stresses of both intergranular and intragranular characters, but also conveys practical ramification that the microscale residual stress effects should be carefully considered when using additive manufacturing to design and build complex components for structural applications.5, as the latter possessed a relatively strong texture as well as significant chemical segregation in the solidification cell walls.We used an open architecture Fraunhofer L37 L-PBF machine to build 316L stainless steel plates with the face-centred cubic structure. The detailed laser conditions are given in the Methods section and Supplementary Table σ – ε) curves up to the onset of necking, respectively. The 0.2% offset yield strength σY is 541 ± 11 MPa, which is consistent with the earlier results18. Such high strength is two to three times those of coarse-grained counterparts and has been attributed to the printing-induced sub-grain microstructures such as dislocation cells5. Figure σY results in significant strain hardening, which is due to the deformation-induced evolution of heterogeneous microstructures5. For polycrystalline materials, the {hkl} grain family refers to a set of grains having the normal vector of {hkl} planes in a common direction. The lattice strain for the {hkl} grain family is defined as ɛhkl = /σ, is appreciably higher under compression than tension . As shown in Fig. ion Fig. . For comion Fig.  for sampεhkl from the linear response along LD, σa is the applied tensile stress. Δεhkl has often been used to examine the progressive yielding and hardening behaviour of different grain families. Figure ε200 and Δε200 are used for further analysis of the lattice strain9 in the nonlinear regime against applied stress. Figure εhkl prior to loading of the as-printed sample shows a marked initial value of compressive lattice strain, particularly for the {200} family, and thus suggests the high magnitude of Type II residual stresses in the as-printed sample. After annealing, such compressive shift reduces substantially but is not completely removed  develop with forward stresses in the hard regions of cell walls and back stresses in the soft regions of cell interiors32. As a result, back stresses resist the forward motion of dislocations and assist their reverse glide in the cell interiors, leading to a lower yield stress during reverse loading. This is known as the Bauschinger effect that gives rise to kinematic hardening30. The back stresses are expected to prevail in AM materials with heterogeneous microstructures. Using Dickson’s method33, we measured the effective back stress of σb ≈ 229 MPa at 3% strain under compressive loading–unloading and σb ≈ 180 MPa at 3% strain under tensile loading–unloading, respectively ( and strain εr).The micromechanics model illustrated in Fig. σa and use the above micromechanics solution to derive the corresponding lattice strain εhkl and stress σhkl along LD in the {hkl} grain family in the linear elastic regime (Methods). It follows that the diffraction elastic constant is given by Ehkl, αhkl and βhkl for the four grain families are listed in Table Ehkl from the micromechanics model confirm that the {200} and {111} families are the softest and stiffest along LD, respectively, which are consistent with the SXRD results and closely match the modelling results by Clausen et al.8. The relative magnitudes of the tensile stress along LD (given by αhkl) follow monotonically those of the diffraction elastic constant. More interestingly, the relative magnitudes of the maximum resolved shear stress (given by βhkl) and thus the maximum Schmid factor do not follow monotonically those of the diffraction elastic constant and tensile stress along LD. Due to the favoured orientation between the most stressed βhkl values of both the {311} and {111} families are lower than that of the {220} family, indicating that yielding for these two families occurs at higher applied stresses than the {220} family. The {200} family still has the minimum resolved shear stress and thus the minimum Schmid factor, which indicates the latest onset of plastic yielding among the four grain families. Finally, we note that although the diffraction elastic constants are independent of the printing-induced residual stresses that exist prior to loading, the stress and yielding responses in each grain family can be affected by these residual stresses, which will be further analysed by CPFE modelling.To understand the lattice strain and stress responses during in situ SXRD experiments, we consider an applied uniaxial tensile stress mentclass2pt{minim35. To account for the effects of Type II and Type III residual stresses, we introduce the eigen-strain tensor E* and the back-stress tensor B in the crystal plasticity model, respectively. More specifically, E* represents the printing-induced residual lattice strains and thus reflects the impact of Type II residual stresses. The components of E* for different grain families were estimated based on in situ SXRD measurements before loading. On the other hand, the back-stress tensor B represents the effective internal stresses within grains arising from heterogeneous dislocation distributions, thus reflecting the impact of Type III residual stresses14. As such, the so-called intergranular and intragranular back stresses in previous studies28 are collectively considered as the Type III residual stresses in this work. The back-stress tensor B is assumed to be deviatoric within the present pressure-independent crystal plasticity model. The initial values of the back-stress tensor, denoted as B0, were assigned to represent the internal stresses arising from printing-induced heterogeneous dislocation structures. These initial values are responsible for the tension–compression asymmetry of yield strength of the as-printed samples. Furthermore, the back-stress tensor B in individual grains evolves with the local plastic shear on different 36 by writing a user material subroutine VUMAT. The finite element simulations generated the macroscopic stress–strain curves and lattice strain responses in different grain families (Methods).We develop a CPFE model (Methods) to study the nonlinear lattice strain behaviour as well as the impact of Type II and Type III residual stresses on the mechanical behaviour of AM stainless steel. The crystal plasticity constitutive equations are formulated within the rate-dependent, finite-strain framework of elastic–plastic deformation for individual grain crystalsEhkl from CPFE simulations  in these two grain families. These results reinforce the notion that a stress-relief heat treatment of AM samples can alter their microscale residual stresses.For comparison, Fig. In summary, our work demonstrates that microscale residual stresses have profound impacts on the yielding and strain-hardening behaviour of AM stainless steel. The in situ SXRD experiments provide a powerful approach to unravel the residual lattice strains and associated Type II intergranular residual stresses for individual grain families in as-printed stainless steel as well as their evolution under applied loads. The combined SXRD and modelling results elucidate the effects of elastic anisotropy, progressive yielding and strain hardening on the extent and evolution of lattice strains and associated Type II intergranular residual stresses in different grain families. A pronounced tension–compression asymmetry of yield strength is observed, together with an asymmetric work-hardening behaviour. Such tension–compression asymmetries are shown to be governed by Type III intragranular residual stresses and associated back stresses, which arise from heterogeneous dislocation distributions that can be strongly influenced by both L-PBF processing and mechanical loading. Hence, it is important to distinguish the printing and loading-induced back stresses. Our CPFE simulations show that the former dictates the tension–compression asymmetry of yield strength in as-printed samples, whereas the latter can quickly build up during loading and thereby affect both the yield strength and strain-hardening responses. Both L-PBF processing and subsequent mechanical loading can contribute substantially to the back-stress evolution as measured from the loading–unloading experiment on as-printed samples, leading to the strong Bauschinger effect of AM stainless steel. Moreover, we show that thermal annealing of as-printed samples could mitigate both Type II and Type III residual stresses but is difficult to erase completely these microscale residual stresses. Altogether, our results demonstrate the quantitative and mechanistic connections between the microscale residual stresses and mechanical behaviour of AM stainless steel. Future studies on linking the printing parameters with the resultant microstructural heterogeneities and associated microscale residual stresses are necessary to enable the control and mitigation of these residual stresses. We expect that our work has general implications to AM metallic materials, as multiscale residual stress is a critical issue for this rapidly developing technology.5. Samples with an overall dimension of 40 mm × 40 mm × 3 mm were built on a 304 stainless steel substrate under the processing conditions listed in Supplementary Table 37.The 316L stainless-steel samples used in this study were fabricated by an open architecture Fraunhofer L37 laser powder-bed fusion machine equipped with a fibre laser of 400 W with a laser spot size of 207 μm (ellipse beam). The plasma atomized 316L powder was used . The powder has particle sizes ranging from ~20–80 μm with the mean value of ~ 30 μm, as described in our prior workθ was 2–10° and high-angle grain boundary when θ > 10°.To examine the microstructure of as-printed 316L stainless steel, EBSD tests were performed in an FEI Quanta 200 environmental scanning electron microscope equipped with a Hikary backscatter electron detector from EDAX at an accelerating voltage of 30 KeV. A step size of 0.1–2 μm was used depending on the magnification selected. EBSD samples were hand polished with abrasive papers of grits up to 5 µm, followed by polishing with diamond suspensions up to 1 µm and a final vibratory polishing for several hours. EBSD data were analysed with the Orientation Imaging Microscopy Analysis™ software provided by EDAX. To calculate the grain size, each grain was considered as a sphere from which the diameter (grain size) was deducted. Interfaces between grains were considered as low-angle grain boundary when the misorientation angle TEM was conducted with an FEI Titan at 300 KeV. Bright-field and dark-field images were obtained in the TEM mode, and HAADF images were obtained in the scanning mode (STEM). TEM samples were mechanically polished down to a thickness near 100 µm with abrasive papers of grits up to 5 µm and with diamond suspensions up to 1 µm, and then electropolished with a 10% perchloric acid and 90% acetic acid solution at 5 °C. A twinjet Fischione polisher was used with the electrical voltage/current maintained at 30 V/50 mA.λ = 0.123984 Å) was used. The X-ray beam size was 0.4 × 0.8 mm2 (height × width). Diffraction patterns were collected in transmission, every 2 s upon testing, on a GE amorphous silicon detector with 200 μm × 200 μm pixel size positioned 115.663 cm behind the sample. The samples were loaded with a Zwick-Roell Z2.5 tester equipped with a non-contact laser extensometer to measure the strain at a nominal strain rate of 5 × 10–4 s−1. The diffraction patterns were integrated in 10° azimuthal bins using XRDUA to obtain one-dimensional (1-D) diffraction patterns as a function of the azimuthal angle. To quantify the lattice strain, inhomogeneous strain (peak broadening) and texture changes during loading, the 1-D patterns were fit using a pseudo-Voigt function by a custom Matlab programme. To determine the stress-free lattice spacing d-spacing d is the variation in d-spacing (mm), λ the X-ray wavelength (1.24 × 10−8 mm), θ is the scattering angle (°), D is the radial distance of the scattering angle on the detector (mm), L is the sample-to-detector distance (1155.56 mm), and ΔL is the estimated variation in sample-to-detector distance (<0.2 mm). The position of all samples in our experiments is determined by the tensile machine grips, which is fixed against camera. The major error bar comes from the sample thickness variation. Standard deviations for the experimental elastic moduli for each grain family shown in Table SXRD experiment was conducted in situ during tensile testing with the Advanced Photon Source of Argonne National Laboratory at the beamline 6-ID-D. A high X-ray energy of 100 keV  with a displacement resolution of 1 μm. Before tests, all samples were polished down to metallurgical grit of 1200. Apiezon grease was applied at the two specimen/platen interfaces to reduce interfacial friction during loading. To study the influence of residual stresses on the yield asymmetry, both as-printed and annealed samples were tested. The samples were annealed at 500 °C for 4 h in a tube furnace at a heating rate of 25 °C/min under protective argon atmosphere and subsequently furnace cooled. The temperature was selected based on a series of hardness measurements by which the original microstructure was almost retained, while residual stresses could be significantly reduced . Dog-bone-shaped uniaxial tension samples with gauge dimension of 6.5 mm (length) × 1.4 mm (width) × 1.4 mm (thickness) and compression pillars of 1.5 mm × 1.5 mm × 3 mm (height) were cut from the centre of the plate by EDM, respectively. To ensure the similar thermal history and microstructure, tension and compression samples were cut from neighbouring area along the same direction. Mechanical tests were carried out via an Instron  3345 universal test machine at a nominal strain rate of 5 × 1034. Kröner has previously derived a self-consistent solution of the diffraction elastic constant38. However, his solution was published in German and not easily accessible. Here we adopted the modern micromechanics notation to derive the analytic solution of diffraction elastic constant under uniaxial loading. As illustrated in Fig. Lr)( and strain tensor εr) in Table To predict the diffraction elastic constant, we developed a micromechanics model of a polycrystalline aggregate based on the self-consistent model and Eshelby inclusion solutionmentclass2pt{minimmentclass2pt{minim35. Here we present the major constitutive equations and highlight the new development that accounts for Type II and Type III residual stresses in AM stainless steel. Within each single-crystal grain, the deformation gradient tensor F is given in terms of the elastic deformation gradient tensor Fe and plastic deformation gradient tensor Fp using the multiplicative decomposition, F = FeFp. The second Piola–Kirchhoff stress T* is given byLr) for individual grains in the four grain families. Then we performed a CPFE simulation to relax the entire polycrystalline aggregate of 8000 grains without loading, so as to obtain the eigen-strain tensor E* for all grains in the simulated polycrystalline aggregate. More specifically, let us consider, as an example, one grain that belongs to both the {220} family along the LD (within a deviation of ±5°) and the {200} grain family along the TD (within a deviation of ±5°). The corresponding E* for this grain is given byn220 and n002 denote the unit vector along the [220] and [002] direction, respectively. Suppose the LD is along the x axis and the TD along the y axis. The corresponding matrix components of E* can be written asE* were chosen to be twice the corresponding residual lattice strains measured from the SXRD experiment. After the CPFE relaxation without loading, the residual lattice strains in the {220}, {111}, {200} and {311} grain families were changed from their initially assigned values to closely match the SXRD measurements; meanwhile, the residual lattice strains in other grain families were also obtained. The E* values were not changed during subsequent deformation simulations.We stress that B0 for all grains in the simulated polycrystalline assembly, which approximately represent the average type III intragranular internal stresses in these grains. To match the asymmetry of tensile and compressive yield strengths between experiment and simulation, the initial back-stress components along LD and TD within the build plane are both chosen to be 30 MPa. As such, compared with the annealed sample without the initial back stresses, the compressive yield strength is elevated approximately by 30 MPa, as the initial back stress is directional and effectively increases the resistance to plastic yielding. On the other hand, the tensile yield strength is lowered approximately by 30 MPa, because the initial back stress effectively reduces the resistance to plastic yielding. In addition, the initial back stress component along BD is chosen to be −60 MPa and the shear components of B0 are zero, so as to make B0 deviatoric. As a result, such initial back stresses lead to the asymmetry of tensile and compressive yield strengths by ~60 MPa in CPFE simulations. The standard deviation for Ehkl (CPFE) in Table Due to the lack of direct experimental characterization of type III intragranular internal stresses in individual grains, we assigned identical values to Supplementary Information