Simultaneous strength and ductility enhancements of high thermal conductive Ag7.5Cu alloy by selective laser melting

High electrical and thermal conductive metals (HETCM) play a key role in smart electronics, green energy, modern communications and healthcare, however, typical HETCM (e.g., Ag, Au, Cu) usually have relatively low mechanical strength, hindering further applications. Selective laser melting (SLM) is a potentially transformative manufacturing technology that is expected to address the issue. Ag is the metal with the highest thermal conductivity, which induces microscale grain refinement, but also leads to high internal stresses by SLM. Here, we select Ag7.5Cu alloy as an example to demonstrate that multi-scale (micro/meso/macro) synergies can take advantage of high thermal conductivity and internal stresses to effectively strengthen Ag alloy. The mimicry of metal-hardened structures (e.g., large-angle boundary) is extended to the mesoscale by controlling the laser energy density and laser scanning strategy to manipulate the macroscale internal stress intensity and mesoscale internal stress direction, respectively, to form mesoscale large-angle "grains", resulting in multiple mutual perpendicular shear bands during fracture. The presented approach achieved a significant enhancement of yield strength (+ 145%) and ductility (+ 28%) without post-treatment. The results not only break the strength-ductility trade-off of conventional SLM alloys, but also demonstrate a multi-scale synergistic enhancement strategy that exploits high thermal conductivity and internal stresses.

High electrical and thermal conductive metal (HETCM), such as, Ag, Au, Cu etc., has been widely used in key fields of medical science, smart electronics, modern communication (5G) and green energy (photovoltaic) due to its multi-functions in biomedical (antibacterial effect), electricity, thermology, optics and chemistry [1][2][3][4][5] . However, the expanding applications in high-tech fields of typical HETCM (such as Ag, Au) is hindered by its relatively low hardness, yield strength and high cost 6 .
As a common additive manufacturing (AM), selective laser melting (SLM) is well-known for its advantages in mechanical strengthening, precision manufacturing, and multi-scale precision control, which is expected to address the issue 7,8 . Many studies have reported that laser rapid solidification in SLM process facilitates grain refinement and thus improves metal strength [9][10][11][12] . The high thermal conductivity metal is expected to further increase the solidification rate, offering the possibility to improve the HETCM's strength. Currently, multi-scale synergistic enhancement of mechanical properties of AM metals is a hot research topic in recent years [13][14][15] . The unique laser process used in metal AM results in complex hierarchical micro-macro structure 13,16 . Wang et al. 17 have found that metallic materials produced by additive manufacturing experience complex stress and thermal gyrations along the build direction. This has the potential to produce complicated heterogeneous microstructures that may exhibit a wide variety of mechanical properties 17 . The results reveal a remarkable hierarchy of microstructures clarifies the relationships amongst different features and provides guidance for future structural manipulation of materials produced by additive manufacturing 17 . Wang et al. 13 reported that austenitic 316L stainless steels via a SLM technique exhibit a combination of yield strength and ductility that surpasses that of conventional 316L steels. High strength is attributed to solidification-enabled cellular structures, low-angle grain boundaries, and dislocations formed during manufacturing, while high uniform elongation correlates to a steady www.nature.com/scientificreports/ solid alloys. Similarly to the mimicry of structures within biological systems (or organic materials) in order to design bio-inspired materials 15,[37][38][39] , in this approach, mimicking of the micro-scale metal hardening structure (e.g. large-angle boundary) is extended to the meso-scale, forming meso-scale "grains" with desired properties. Based on the high thermal conductivity of silver and the rapid solidification of laser leading to microscale grain refinement, the macroscale internal stress intensity and mesoscale internal stress direction in different domains (analogous to high-angle boundaries) are manipulated by controlling the laser energy density (LED) and designing laser scanning strategies, respectively, to form large-angle mesoscale "grains" with desirable properties, which promotes the formation of multiple shear bands perpendicular to each other at fracture, resulting in high-performance AM alloy parts (high strength, density and ductility).

Results and discussion
Effect of the composition of SLM Ag-Cu at the microscale. Effect of Ag alloying on microstructure. At the micro-scale, grain refinement, grain equiaxed and solid solution strengthening can be achieved by selecting a suitable solute of silver alloy. Research on using alloys to improve silver's properties has a long history 6,40 . A silver alloy containing 7.5 wt.% non-silver solute is specified as the standard for sterling-silver, which is widely used as a conductor of heat and electricity, and standard coins and high-end crafts 41 . Ag and Cu have the same atomic packing properties and, similar lattice constants (Ag: 0.40 nm, Cu: 0.36 nm), providing an appropriate concentration of low-energy barrier heterogeneous nucleation sites ahead of the solidification front 34 . The rapid solidification by SLM lead to a significant non-equilibrium solute-trapping effect in supersaturated Ag alloy, which relieves the solubility limitations and facilitates solid solution strengthening in supersaturation 20,21,42 . During the solidification of alloys, segregation of solutes facilitates the formation of a constitutional undercooling zone ahead of the solid/liquid interface. "Secondary" nucleation within the constitutional undercooling zone can restrict the growth of the "primary" grains, resulting in grain refinement 29,30 . The grain-refining efficiency of solutes can be quantitatively expressed by its Q value 30,31,43 . Through the simulation of a Scheil-Gulliver solidification curve (Fig. 3a), Ag7.5Cu alloy is found to have a high Q value (32 K). According to interdependence theory 43 , Ag alloy with high Q value promote grain refinement and equiaxed. The grainrefining efficiency of AM Ag7.5Cu alloys stems from the capability of the Cu solute to establish a sufficiently large constitutional supercooling zone in front of the solid-liquid interface when the solute copper segregates 44 .  www.nature.com/scientificreports/ Forming equiaxed grains can help reduce stress cracking and improve its suitability for metal AM 44 . Refined and equiaxed grains lead to short channels of fluid that can easily be backfilled compared to columnar grains, thereby reducing stress cracking and increasing strength 29,31,34 .
Effect of high thermal conductivity of Ag on microstructure. The high thermal conductivity of silver alloy and its small freezing range further promotes grain refinement. The laser process offers extremely high solidification rates compared to the casting process. Experiments have shown that the average grain diameter of cast silver alloys is 166.18 μm for the same alloy composition (Fig. S2a), while laser silver alloys can achieve an average grain diameter of as little as 0.70 μm (Fig. 3d-e). Generally, larger Q values mean a higher grain-refining efficiency 30 . According to the interdependence model (Eq. 1), in addition to high Q value, high solidification rates (v) also play an important role in grain refinement 43 .
where d gs is the grain size and v is the solidification rate. The high thermal conductivity of silver increases the solidification rate ( v ). The high solidification rate ( v ) increases and the grain size decreases through a reductions in the first two terms of Eq. (1) 28 . According to physical property simulation, during the solidification process, Ag7.5Cu has six-fold greater thermal conductivity than that of Ti8.5Cu (Fig. 3b), and 78% narrower freezing range between its liquidus and solidus temperatures (Fig. 3b). Even at the same cooling rate, the solidification time of Ag7.5Cu is two-thirds of that of Ti8.5Cu (Fig. 3c). Therefore, in high Q alloy systems, the high thermal conductivity of Ag and narrow freezing range can induce further grain refinement and ultra-fine grains. In addition, the Scheil-Gulliver model can be used to determine the solidification path and freezing range and is often used to predict the likelihood of cracking during solidification 44 . Reducing the temperatures difference between the solidus and liquidus (freezing range) will also improve resistance to high internal stress tearing 34 . Zhang et al. 44 showed that ultrafine equiaxed grains (9.6 μm) can be produced in Ti8.5Cu alloys (high Q value, without nucleants) and successfully realized high-strength titanium alloys 45 . Although, the Q value of Ag7.5Cu (32 K) is lower than that of Ti8.5Cu (62 K), Ag7.5Cu has a higher thermal conductivity and forms finer equiaxed grains (0.70 μm, Fig. 3d) at (LED) of 37.5 J/mm 3 , which is 1/14 as that of Ti8.5Cu (9.6 μm) reported by Zhang et al. 44 , regarded as the finest grain in existing SLM literature [46][47][48][49][50][51][52][53] . www.nature.com/scientificreports/

Effect of LED on internal stress intensity at the macroscale.
To achieve multi-scale synergistic strengthening, the effect of LED on macroscale internal stress is analyzed. At the macro-scale, LED affects not only the volume density, but also the internal stress intensity of the entire AM component (optimization process of high-volume density process parameters; refer to Methods and, Fig. S3, Supplementary Information). Generally, LED is proportional to the volume density and is a basic parameter setting 8,21,42,[55][56][57][58][59] . Through the cube test, two groups of parameters that produced the high-volume densities are selected as optimum, while one group of parameters that produced a lower volume density is used as reference. These three groups of parameters are mentioned repeatedly, so the samples prepared are named α, β, and γ, respectively ( Fig. 4, 7, 9, 10; Detailed parameters for the three samples are given in the supplementary information, Fig. S3f.). In this study, sample-β had the highest volume density (10.08 g/cm 3 ; Fig. 4a), but it is not the sample with the highest LED. The effect of parameters on the forming performance is not merely a summary of the LED. Excessive LED causes stress cracks and pores, thereby reducing volume density and mechanical strength ( Fig. 4d-e). Similar to metal welding process induces melting and conducts, local expansion and shrinkage during laser AM result in deformation and internal stresses 60 . High internal stresses in AM processes lead to stress cracking when the LED is extremely high (120 W, 400 mm/s; Fig. 4d). At less than maximum volume density, a higher LED helps to reduce internal stresses, since a reduced thermal expansion mismatch between solidified melt track and surrounding material 61 . However, when the volume density reaches its maximum, a further increase in the LED results in increased internal stresses between melt pools of local expansion. The same direction of the laser scanning track during the forming process leads to the accumulation of internal stresses in the same direction and increases the macroscopic internal stress intensity. According to finite element analysis (FEA) of AM process simulation, a higher LED also leads to higher deformations of fully dense alloys due to internal stresses (Fig. 4c). The XRD patterns of samples-α, -β, -γ shift towards the higher diffraction angles compared with that of Ag alloy powder, also indicating higher internal stresses 21,62,63 . The internal stress acts on the grain boundaries, which may influence the lattice parameters, causing the 2θ angles shift to high values 63 .Apart from the unprocessed silver powder, sample-β (with the highest volume density) had the smallest 2θ angles. Therefore, sample with the highest volume density (sample-β) tended to develop relatively low internal stresses, while further increases (sample-α) or decreases (sample-γ) in the LED all increased internal stress.

Effect of laser scanning strategy on internal stress direction at the meso-scale. The mimicry
of metal-hardened structures (e.g., large-angle boundary) is extended to the mesoscale by designing a bi-offset scanning strategy to manipulate the differences in internal stress directions of different domains, to form "grains" with large-angle boundaries at the meso-scale, so the meso-scale "grains" also refer to the domains scanned by the same type. Notably, past research on large-angle boundary effects has focused on the micro-scale. A single grain consists of a unit cell of the same type and orientation, but most alloys consist of multiple grains, each of which contains different lattice orientations with its neighbors. The orientation of neighboring lattices is important in forming a large-angle boundary, which prevents the propagation of cracks and strengthens the alloy 15 . Related literature 18 also indicates that mechanical property differences between grains can enhance large- www.nature.com/scientificreports/ angle boundary effects. Pham et al. 15 use the hardening mechanisms found in crystalline materials to develop architected materials that are robust and damage-tolerant, by mimicking the micro-scale structure of crystalline materials-such as grain boundaries. Here we achieved different directional internal stresses (Fig. 5) between adjoining mesoscale domains by creating a boundary, similar to the boundary between the two adjoining microscale grains. The laser scanning strategy is a unique molding method in metal AM. The design method of a bi-offset scanning strategy is detailed in the Methods. Figure 5a shows the single layer morphology after metallographic polishing and etching. At the same time, FEA of the AM process according to the bi-offset scanning strategy clearly shows the peak temperature distributions of the three scanning types (A, B, C), which are in lined with the OM image ( Fig. 5d-e). Different metallographic morphology of aforementioned types (same LED) reflects variations in mechanical properties among domains (analogous to different "grains"; Fig. 5e) 21,62,63 . It is also observed that the direction of deformation at the boundary between mesoscale "grains" changes significantly ( Fig. 5f) which stands for the direction differences of internal stress concentrations. Therefore, by designing bi-offset scanning strategy, the difference in internal stress direction of different domains is successfully achieved, extending the mimicry of metal-hardened structures (e.g., large-angle boundaries) to the meso-scale.
Multi-scale synergistic mechanical enhancement. The formation of multi-scale synergistic enhancement effects, at the macroscale, is due to the increase in LED increasing internal stress intensity (Fig. 6a). At the meso-scale, due to the bi-offset scanning strategy, mechanical properties (especially internal stress direction) in each domain are different from each other (Fig. 6b). Although the macro-and meso-scale synergies increase the large-angle boundary effect, they also increase the tendency for internal stress cracking. Therefore, at the microscale, grain refinement and equiaxing are indispensable in preventing stress induced defects caused by the introduction of high internal stresses during the manufacturing process ( Fig. 6c) 29,31,34 . If an alloy retains a large volume of cracks caused by internal stresses it will have a detrimental effect on its strength.
The fracture surface of sample-α had an obvious perpendicular shear band in the SEM image (Fig. 7a). The morphology of the shear band is consistent with the mesoscale "grain" boundaries mentioned above, caused by different scanning types. Cracks did stop at incoherent large-angle boundaries, preventing fast brittle fracture by impeding the dislocations move across the "grain" 15,65 . It was also observed that the fracture surface morphology of sample-β (Fig. 7b), -γ (Fig. 7c) and casting (Fig. 7d) do not form mutually perpendicular shear bands and their tensile strength and ductility are lower than that of sample-α.
As an extension of this method, tailoring the scanning strategy can produce not only the large angle boundary (Fig. 8a), but also other types of metal hardening structures (e.g. meso-scale equiaxed "grain" (Fig. 8b) and precipitation hardening (Fig. 8c)) inspired by micro-structure of crystalline materials. Pham et al. 15 have shown that the designing meso-scale structure can strengthen materials by mimicking the micro-structure of crystalline materials-such as grain boundaries, precipitates and phases. The study 15 suggests that these crystal-inspired meso-scale structures are as important for their mechanical properties as are crystallographic micro-structures in metallic alloys. In our study, FEA have shown the predictability of scanning strategy on its thermal and mechanical effects (Fig. 5d,e). On this basis, FEA can be used to further verify and optimize the meso-scale control strategy to achieve the desired "grain" structure and performance and reduce the number of precious metal AM experiments. The bi-offset scanning strategy designed in this experiment forms columnar "grains" along a < 001 > direction (Z-axis; Fig. 8a), which are more inclined to introduce anisotropy. Therefore, FEA is used to demonstrate the scanning strategy of further offset at equidistant layer thickness can achieve an equiaxed "grain" (Fig. 8b, Video S1, Supplementary Information). By comparing the plastic strain distribution of columnar and equiaxed "grains", it is shown that the latter alleviates the residual stress usually occurs in single-direction scanning (Fig. 8: points d, e). Furthermore, we demonstrated the possibility to produce precipitation hardening by adjusting the laser parameters at "grain" boundaries (Fig. 8c). In precipitate-hardened alloys, precipitates act as obstacles to the movement of dislocations thereby enhancing mechanical properties 15 . Laser parameters (such as laser power and scanning speed) can control the mechanical properties (such as hardness) of AM silver alloy 21 . We introduced precipitation strengthening into a mesoscale "grain" structure by producing embedded "precipitate domains" using different laser parameters from equiaxed "grains" (Fig. 8c). In FEA, the thermal and mechanical characteristics of "precipitate domains" (Fig. 8c: point f) are significantly different from the adjacent "grains". The introduction of precipitate domains creates dislocation obstacles, which are expected to prevent similar problems of a rapid reduction in stress induced by slip activity in single crystals 65 . For FEA simulations of the AM process related to different scanning strategies, see Video S1, Supplementary Information. However, although some reports suggested that these studies of crystal-inspired meso-scale structures are no less important than microstructures in mechanical strengthening 15 , we realize that the two scales cannot be simply equated and that future studies are needed to explain their strengthening mechanisms more fully.
Further analysis shows that multi-scale synergistic enhancement of ductility requires the interaction of three length-scale effects (Fig. 6) and designing a bi-offset scanning strategy at the meso-scale only is not sufficient to form large-angle "grains" (Fig. 9a). By comparing samples α and β, the syngenetic strengthening mechanism can be better illustrated (Fig. 9a,b). The two samples have the same alloy composition, bi-offset scanning strategy and both with high volume density. However, their morphological and mechanical properties (Fig. 5, 7) are significantly different. In Fig. 9a,d, "density & homogeneous morphology" and "'columnar grain' morphology" www.nature.com/scientificreports/ are the melt pool morphologies formed by two different process parameters or thermal field. The "columnar grain" also refers to the domains scanned by the same type of island strips. By observing the region of "density & homogeneous morphology", there is very little porosity in this region and the morphology tends to be the same in different regions. Whereas, the "'columnar grain' morphology", are affected by the bi-offset scanning strategy and the morphology varies significantly from region to region, which is longitudinally banded and has a slight increase in porosity. According to the two sample parameters, two cubes are polished and etched in the ZY-plane. Sample-α has a full mesoscale "columnar grain" morphology matching the bi-offset scanning strategy (Fig. 9d), and it only break in the "columnar grain" area. This indicates that the "columnar grain" morphology region, which can induce multiple shear bands, results in a greater yield strength and ductility. While sample-β has a "columnar grain" morphology in the upper half, but a dense and homogeneous morphology in the lower half (Fig. 9a), where then become a weakness point in tensile test. The fracture surface is flat and homogeneous accounting for low ductility (Fig. 7b,e). The gradient change of sample-β in the Z-axis directions is mainly because the layer-by-layer fabrication leads to multiple thermal cycles, while the heat dissipation of the lower part is sever than the upper part 44 . The increase in the gradient of the thermal field causes sample-β's morphology to change from dense and homogeneous to meso-scale columnar "grains" (Fig. 9a). The LED of sample-α is higher than that of sample-β, which is equivalent to providing a higher thermal field, hence a full "columnar grain" morphology is formed (Fig. 9d). Further increasing the LED (thermal field) in the highest volume density parameter range also promotes an increase in internal thermal stresses (Fig. 4b,c). Therefore, the formation of meso-scale "grains" is accompanied by an increase in internal stress intensity by increasing the LED at the macro-scale and a difference in internal stress direction by designing a bi-offset scanning strategy at the meso-scale (Fig. 5). At the microscale, combined with the high Q value, the small freezing range can help reduce thermally induced stress cracking resulted from high LED and different internal stress direction of different domains. Meanwhile, www.nature.com/scientificreports/ ultra-fine equiaxed grains (0.30 μm) and solid solution strengthening of Ag7.5Cu cause yield strength enhancement and substantial hardening during plastic deformation (Fig. 7e). This capacity to constrain deformation at the micro-scale and prevent the rapid propagation of slip minimizes the decreases in stress 71 and strengthens the meso-scale "grain". Finer equiaxed micro-structures allow easier grain rotation and deformation, providing a method to accommodate strain, thus preventing crack initiation and growth 34 . Consequently, yield strength and ductility are both affected to achieve a multi-scale synergistic enhancement effect (Fig. 2). Furthermore, by observation of the OM images and EBSD-IPF maps (Fig. 9a,d; Fig. 10a-c), the heterogeneity of the melt pool morphology and grain structures are evident on the meso-scale scanned domain, which indicates that the setting of the laser parameters can control different domains with different types of grain structures, thus forming different types of domains at the meso-scale. For example, many columnar grains are observed in the scanned domain of type B while a large number of fine equiaxed grains are observed in the scanned domain of type C (Fig. 10b,c). There is a more distinct boundary between the scanned domains of type B and type C (Fig. 10b,c). Also, elements such as silver, copper and oxygen were detected by EDS. Of these, elemental oxygen may have been introduced into the as-built sample during the printing process (Fig. 9f). However, local chemical inhomogeneities at the meso-scale were not evident when elemental mapping was carried out (Fig. 9b,c,e). By EDS line scan, no significant compositional changes were observed at the outer boundaries of island strips (Fig. 10d). This suggests that the elemental distribution tends to be homogeneous on the mesoscale, although heterogeneity in melt pool morphology and grain structures can be observed on the meso-scale scanned domain (Fig. 10b,c). This may be due to four reasons. (1) The extremely high solidification rate within the very small local laser melt pool is not conducive to the separation of the different elemental components due to the extremely high thermal conductivity of silver. Several studies 6,72 have shown that high cooling rates can be used to effectively prevent segregation and increase the solubility of the alloying elements, resulting in supersaturated silver alloys with high strength. (2) The small melt pool formed by partial melting prevents extensive composition segregation. (3) The study material, Ag7.5Cu, is only a binary alloy with a relatively simple composition. Therefore, the possibility of many different elements segregating in different regions is lacking. (4) Trace elements may not be readily detectable.  www.nature.com/scientificreports/

Conclusions
We proposed multi-scale synergistic reinforcement strategies to make good use of high thermal conductivity of silver and internal stress during SLM processes to simultaneously improve the strength and ductility, thus breaking the strength-ductility trade-off of conventional SLM alloys. The study on nature and the formation mechanisms of the meso-scale structural heterogeneity, such as heterogeneity of melt pool morphology, are also explored. Through controlling the internal stress intensity at the macro-scale, internal stress direction of different domains at the meso-scale, mimicking of the metal hardening structure (e.g., large-angle boundary) is extended to the meso-scale, forming meso-scale "grains" with desired properties. Without the need to post-treatments, the presented approach revealed the highest yield-strength (+ 145%) and ductility (+ 28%) compared to that of casting. Meanwhile, the high thermal conductivity of Ag and high growth restriction factor (Q) solute of Cu are induced to further refine the grains, thus strengthening the meso-scale "grains". By the synergistic multi-scale control, the silver alloy forms multiple shear bands perpendicular to each other during fracture, which effectively improves the mechanical properties and achieves higher yield strength (+ 145%) and higher ductility (+ 28%) than conventional silver alloy castings. In this case, Au7.5Cu parts achieved significant mechanical enhancement without complex AM equipment or post-processing. Besides, the FEA also demonstrate the feasibility to control the mechanical properties by mimicking various micro hardening mechanisms and designing different "grain" structures, even bionic structures. The proposed multi-scale synergistic reinforcement method described here can also be extended to other alloys with high thermal conductivity requiring high mechanical performances.

Methods
Powder materials. Ag7.5Cu alloy powder prepared by the gas atomization method was purchased from the Legor Group. (Table 1; Fig. 11a, S1, Supplementary Information). 92.5 wt.% silver alloy, also known as sterlingsilver, is the standard for sterling products and industrial components, while the other 7.5 wt.% is reserved for alloying elements 6 .
Parameter settings and preparation of sample by AM and casting. A Mysint100 SLM device was equipped with an active fiber laser (wavelength: 1070 nm, laser beam size: 0.030 mm, tuneable laser power: 0-200 W). The metal powder was layered with a rubber scraper. The distance between the bottom of the scraper  www.nature.com/scientificreports/ and the previous layer was defined as the layer thickness (h). By spreading a thin layer over the previous layer, the laser selectively melted each layer of powder in the set area and welded it with the previous layer to build metallic parts. As shown in Fig. 11a, the main parameters included the laser power (P), scan speed (v l ), layer thickness (h), hatch distance (d) and scan strategy (s), of which d refers to the distance between two adjacent scanning traces in the XY-plane. Meanwhile, the LED (Eq. (2)) was also introduced as a reference factor 8 .
The process parameters were adjusted to determine the LED range needed to achieve a high-volume density. Previous studies 21,73 have shown that laser power plays a critical role in the influence of LED on material properties. The values of > 80 W and < 80 W are defined as high and low LED, respectively.
The hatch distance is calculated according to the overlap ratio (Hr) of the melt pool width (w) under different parameters, according to Eq. (3).
According to Eq. (3), a higher overlap ratio (Hr) is associated with a smaller hatch distance (Fig. 11a). In this experiment, the overlap ratio (Hr) ranged from 30 to 70%.
Three types of models were prepared: a single-wall, cube and tensile rod. Their microstructures, morphologies, densities, phases, and mechanical properties were then characterized. The detailed parameters are listed in Fig.  S3, Supplementary Information. As shown in Fig. 11b, the single-wall sample was formed by scanning a singletrack layer-by-layer in the Z-axis, so the single-wall width was that of the melt pool. The cube samples can be considered as a parallel arrangement of single walls in the XY-direction (Fig. 11c). Analysis of single-wall samples served as a basis for analysis of the parameters and performance of the cube samples 21 . Compared to single-wall tests, which only involved three parameters (P, v and h), the cube and tensile tests required further consideration of parameters d and s. The scanning strategy (s) was designed by Materialise Magics software. The bi-offset scanning strategy included an angular-offset in the XY plane and a positional-offset on the next layer ( Fig. 11d-h). Finally, the bi-offset scanning strategy forms meso-scale columnar "grains" along a < 001 > direction (Fig. 11h).
The parameter optimization process used to obtain high density was firstly based on analysis of the singlewall morphology, which obtained suitable parameters for laser power, scan speed and layer thickness. Through the cube test, two groups of parameters that produced the high-volume densities were selected as optimum, while one group of parameters that produced a lower volume density was used as reference. These three groups of parameters were mentioned repeatedly, so the samples prepared were named α, β, and γ, respectively (Fig. 4 , 7, 9, 10). They were used to manufacture cube samples for the analysis of morphology, microstructure and density, as well as tensile rod samples for testing of mechanical properties. According to the ISO 6892-1-2009 standard, building directions of 90° were used to fabricate the tensile rods. A control group consisting of tensile rod samples of the same sizes and raw materials but prepared by casting were manufactured for comparison. Cast samples made of wax were place in a container of liquid plaster. Once the plaster set, the wax was molten in a furnace, and the remaining plaster became the mould. Then, molten Ag alloy (950 °C) was poured into this mould through a sprue gate and allowed to set. Finally, the mould was opened after 12 h using water injection 5 . Sectioning and sample preparation for characterization. Representative samples were prepared for characterization of morphology and defects by slicing them along the XY-and ZY-planes. Sections were ground and polished for SEM-EDS and XRD, using standard metallographic method up to 0.3 μm silica 21 . Then, 50 ml ammonia water, 50 ml H 2 O 2 (3 vol.%) and 50 ml distilled water were used as an etchant to reveal the morphology and microstructure 21 . Representative sample preparation using argon ion polishing for EBSD.

Materials characterization.
Morphological and microstructural images were obtained by an optical microscope (LeicaM205; OM) and a scanning electron microscope equipped with an energy dispersive spectroscope (Hitachi-Su8010; SEM-EDS), respectively. The average grain size was measured from optical micrographs of each alloy using the linear intercept technique 44 . The IPF maps and pole figures were obtained by OXFORD C-Nano EBSD at 20 kV.
The Archimedes method was used to calculate the volume density 21 . The relative density was obtained by dividing the measured density by the theoretical density 21 . ImageJ 1.52 software was used to analyse the morphology and porosity based on colour thresholds 54 . It should be noted here that since different methods were used for volume density and porosity testing, led to the existence of incomplete agreement in the test results. This is due to the non-homogeneous of sample defects leading to errors in the porosity tested based on the cross-sectional area method. Therefore, on a macro-scale, the volume density tested based on Archimedes' principle is more representative of the densifications of a sample.
Elemental analysis of the samples was carried out using an energy dispersive spectroscope (EDS). Representative samples (orientation: Y-axis) were subjected to XRD diffraction (Bruker AXS D8-Focus diffractometer) to determine the phases and possible preferential crystallographic orientations induced by the process. The analyses were carried out with Cu-Kα radiation at 40 kV and 40 mA in the range 2θ = 20°-90°, using a step size of 0.02 74 .
Mechanical testing. Tensile specimen dimension was determined according to GB6397-86 standard (Fig. 12a). Tensile properties of the samples were obtained in accordance with ISO 6892-1-2009 standard, using a servo-electric CMT4304 frame equipped with a 30-kN load cell. Samples were clamped by the ends of the dog-