Deformation-free geometric recrystallisation in a metastable β-Ti alloy produced by selective laser melting

ABSTRACT Super-transus heat treatments conducted on an additively manufactured body-centred-cubic β-Ti alloy led to the formation of equiaxed β grains from an initially columnar structure. The grain structure was transformed thanks to a combination of Plateau-Rayleigh instability and grain growth driven by reduction in grain boundary surface area. This is a new type of geometric recrystallisation with no deformation involved. Other mechanisms proposed based on either deformation-induced recrystallisation or martensitic decomposition are dismissed owing to low dislocation density and absence of martensitic transformation in the alloy studied. IMPACT STATEMENT Columnar to equiaxed transformation of β by super-tranus heat treatment of SLM-fabricated Ti is due to Rayleigh instability and grain growth, dismissing the belief that usual deformation-driven recrystallisation is responsible. GRAPHICAL ABSTRACT


Introduction
The epitaxial growth of crystals during additive manufacturing (AM) of Ti creates columns of bcc-structured prior β grains along < 100 > [1,2], leading to a significant anisotropy in mechanical properties [3][4][5]. It is desirable to replace the as-AM grain structure by an equiaxed one, achievable by heat treatment (HT) above the β transus temperature (T β ) [6] or deposition on a pre-heated substrate using proper parameters, as in the case of electron beam melting (EBM) [7]. This morphological change was first observed in an SLM-fabricated α-β Ti-6Al-4V heat treated at 1200°C for 5 min [6]. No mechanism was suggested, although recrystallisation was ruled out since the equiaxed grains obtained were larger than those after recrystallisation in the counterpart wrought alloys. On the other hand, the transformation into equiaxed grains during wire and arc AM of Ti-6Al-4V [8] was attributed to recrystallisation, based on the argument that the ultrahigh cooling rates induced large thermal stresses leading to increased dislocation density high enough to cause recrystallisation, although no evidence was provided. A recent study [9] on Ti-6Al-4V by EBM plus hot isostatic pressing (HIP) at super-transus temperatures proposed that decomposition of martensitic α' during EBM created β grains with different orientations from that of the prior β and they grew during HIP to produce randomly oriented, equiaxed grains. These studies, however, hypothetically proposed mechanisms based on the final microstructure after HTs without investigating the early stages of the transformation. Further, they all focused on the α-β Ti-6Al-4V alloy which experienced martensitic transformation, raising the question whether equiaxed β grains can also form in additively manufactured β-Ti alloys with no martensitic transformation upon quenching, and if so, what mechanism is responsible.
To close this gap, here we produced a β Ti-5Al-5V-5Mo-3Cr-0.5Fe (Ti-5553) using selective laser melting (SLM), and performed HTs at super-transus temperatures for short times to observe early stages of the morphological transformation. Equiaxed β formed without involving martensite decomposition or dislocationbased recrystallisation. Instead, the high surface area of β columns was the driving force. A new mechanism was proposed based on Plateau-Rayleigh instability and grain growth driven by reduction in the grain boundary area.

Experimental materials and procedures
A plasma atomised Ti-5Al-5V-5Mo-3Cr-0.5 Fe (wt.%) powder (15−45 μm) supplied by AP&C was used (the chemical composition in Table S1 in the Supplementary Materials). Renishaw AM250 was employed for printing rods of φ 8×20 mm using stripe scanning strategy on a titanium substrate at room temperature in an atmosphere containing < < 100 ppm oxygen. Other printing parameters are listed in Table 1. Density of 99.7% relative to 4.65 g/cm 3 for Ti-5553 [10] was achieved. Heat treatments were conducted at 1000°C ( > T β of ∼ 845°C [11]) for 0.5-10 min followed by iced-water quenching.
Microstructures were characterised by SEM (FEI Quanta FEG200 and Teneo Volume Scope), and TEM (FEI Tecnai F20). TEM samples were cut using focused ion beam (FEI Nova 200 Nanolab DualBeam). AZtec HKL Standard with Symmetry 51N2033 was employed to acquire EBSD maps using 20 kV, 9.5 nA and step sizes of 1-5 μm. When needed, samples were etched using Kroll's Reagent.   ∼ 400-500 μm in length. The grain boundary density (ρ GB ) in Figure 1(a) was estimated to be 95 mm/mm 2 . {100} pole figure in Figure 1(b) indicates that < 100 > with the intensity of ∼ 22 multiples of uniform distribution (MUD) are aligned with build and crystal growth directions (complete sets of data for all alloys in Supplementary Material). SEM showed straight grain boundaries and melt pool and layer boundaries (Figure 1(c)). A closeup in Figure 1(d) reveals internal cells of < 1 μm thick, and etch pits (yellow arrows) in the melt pool and layer boundaries, later identified as dislocations using TEM. Figure 1(e-f) shows the EBSD IPF-Y map and {100} pole figure, respectively, of the SLM Ti-5553 after HT at 1000°C for 10 min. The morphology of β grains was changed into equiaxed with ρ GB of 12 mm/mm 2 , 8 times smaller than that before HT. However, the {100} pole figure (Figure 1(f)) revealed that the general texture remained the same as that before HT (i.e. < 100 > were mostly oriented along the build direction) although its intensity ( ∼ 14 MUD) was lower. For comparison, EBSD was conducted on SLM Ti-5553 after tensile deformation and HT at 1000°C for 10 min (IPF-Y and {100} pole figure in Figure 1(g,h)), revealing much finer grains and weaker texture along < 100 > with significantly lower intensity of < 5 MUD. Figure 1(i-l) quantitatively shows the distributions of grain sizes and aspect ratios in the as-SLM (Figure 1(i-j)) and SLM + HT (Figure 1(k,l)) Ti-5553, respectively. HT coarsened the grains from ∼ 10-40 μm (Figure 1(i)) to ∼ 50-200 μm with a few even larger (Figure 1(k)). It is also obvious that HT significantly reduced the aspect ratios from mostly > 5 (up to 25) to ∼ 1-3, indicating morphological change form columnar to equiaxed. Figure 2(a-c) shows SEM of the SLM Ti-5553 after HT at 1000°C for 30-120 s, revealing the early stages of the formation of the equiaxed grains. Thanks to homogenisation, most internal cells disappeared after 30 s, although there were still some in isolated areas (Figure 2(a)). The melt pool and layer boundaries were recognisable, but the etch pits in the boundaries (inset in Figure 2(a)) were not as clear as those before HT (Figure 1(d)). By counting the etch pits (selectively yellow arrowed), the dislocation density was estimated to be ∼ 10 6 -10 7 cm -2 , too low to cause recrystallisation. The number of dislocations decreased drastically after HT for 60-120 s ( Figure  2(b,c)), indicating recovery. There was no recrystallisation even after 120 s which would be long enough for significant recrystallisation if there were enough dislocations [12]. Instead, longer HT caused first the melt pool and layer boundaries to become less well defined (after 60 s, Figure 2(b)), and ultimately their complete disappearance after 120 s (Figure 2(c)). The residual internal cells also vanished in both cases. The grain boundaries turned wavy after 60 s and serrated substantially after 120 s, creating thin necks in the β columns.

Results
Dislocation configurations were investigated using TEM ( Figure 3). Dislocations arrayed with spacing of < 15 nm in the melt pool and layer boundaries ( Figure  3(a,b)), confirming that the etch pits in Figure 1(d) are dislocations. A much smaller number of individual dislocations were found inside the grains and in grain boundaries (arrowed in Figure 3(c,d)). Since the formation of dislocations during SLM stems from thermal stresses [13], it is reasonable to assume that the Burgers vectors (b) are of < 111 > type. In the particular example of Figure 3(d), BF TEM with the diffraction vector (g) of 002 makes all < 111 > dislocations visible since g·b = 0. Figure 3(e-g) shows TEM after HT at 1000°C for 60 s. Dislocation arrays in the melt pool boundaries became less dense with larger dislocation spacing of > 30 nm (Figure 3(e,f)), indicating dislocation annihilation. This, together with compositional homogenisation, could explain the diffuse melt pool boundaries in Figure  2

Discussion
In contrast to the current knowledge, the results here suggest that neither martensitic α' decomposition [9] nor recrystallisation [8,9] is responsible for the formation of the equiaxed β grains after HT of the SLM Ti-5553. The former is not applicable since no martensite forms in Ti-5553 owing to high contents of β stabilising elements. Recrystallisation is also ruled out considering the dislocation configurations observed. Deformationdriven recrystallisation requires a high number of dislocations being entangled so that they do not undergo annihilation during HT [14]. Only individual dislocations are identified here which tend to disappear after HT at 1000°C (Figure 3). In fact, the dislocation density of ∼ 10 6 -10 7 cm -2 before HT (Figure 2(a)) is too low (at the lower end of 10 7 -10 8 cm -2 for annealed metals [15] and well below that, i.e. > 10 9 cm -2 in cold worked metals, required for recrystallisation) and there is no recrystallisation even after longer times of HT ( Figure  2(b,c)). Higher dislocation density in the arrays shown in Figure 3(a,b) is also incapable of initiating recrystallisation as dislocations annihilate during HT to produce larger spacing (Figure 3(e,f)), indicating recovery. This argument is reinforced by the unchanged texture after HT (Figure 1(f)). If recrystallisation were responsible for the formation of the equiaxed grains, their sizes would have been much smaller and orientations much more random, as in Figure 1(g,h) (SLM + tensile deformation + HT).
The formation of the equiaxed grains during HT, however, significantly reduces the grain boundary area (i.e. ρ GB reduced by 8 times). SolidWorks was used to model the microstructure of the as-SLM alloy and that after HT for 10 min, as shown in Figure 4(a,b). The β columns are modelled as hexagonal prisms of ∼ 400 μm long with base edge of < 40 μm based on Figure 1(a,i,j), while the equiaxed grains as Weaire-Phelan structures with the edge size of ∼ 100 μm based on Figure 1(e,k,l). For a cube of ∼ 7 mm used in the modelling, enough to include a large number of grains, the surface area of the columnar structure is calculated to be > ∼ 320 mm 2 , much larger than that of ∼ 220 mm 2 of the equiaxed structure. Therefore, the morphological change can be explained using a combination of Plateau-Rayleigh instability and grain growth driven by the reduction in the surface area. Plateau-Rayleigh instability [16,17], often called Rayleigh instability, explains the breakup of rodlike (high-aspect-ratio) structures into spherical shapes. The initially smooth rod surface becomes wavy due to axial perturbations. Perturbations with λ/D > π, where λ is the wavelength and D rod diameter, are amplified owing to the local direction of the surface tension, leading eventually to the breakage [16,17]. Although Rayleigh instability was first used to explain the breakage in liquid jets (e.g. tap water) [18] and balling during laser deposition [19], it has been observed in solids, as in the examples of spheroidisation of lamellar structures at high temperatures in Al-10Si [20], steels [21,22] and TiAl/Ti 3 Al [23].
Such mechanism appears to be operating during HT at 1000°C of the as-SLM Ti5553, as illustrated in Figure 4(c-e). At the early stage, thermal fluctuation of atoms, particularly solute ones, in grain boundaries and absorption of dislocations into the boundaries lead to grain boundary roughening [24,25] and ultimately wavy shapes (Figures 2(b) and 4(c)). The Rayleigh instability criterion of λ/D > π is fulfilled since λ/D > 4 ( Figure 2). The surface tension (arrowed) forces the convex boundaries to bulge and the concave ones to shrink, creating thin necks and grain boundary nodes (Figures 2(b,c) and 4(d)). Additionally, inner grain boundaries in the columns can contribute to the formation of nodes through grain grooving [26]. In the case of balling, liquid jets, or spheroidisation of high-aspectratio lamellae, spherical particles are formed since the surrounding phase (e.g. air in falling water beads and ferrite in cementite spheroids) can fill the spacing between them. However, in SLM Ti-5553, spherical grains cannot form because there is no surrounding phase to fill the gap. Instead, the bulging and pinching sections would meet, respectively, to form nodes, causing redistribution of surface tension (γ ) and forces in new directions (black arrows in Figure 4(d)). The balances between these forces would drive grain growth, eventually creating the equiaxed but coarsened grain structure shown in Figure 4(e) (observed in Figure 1(e)). The final grain size after HT at 1000°C for 10 min can be estimated using D n -D n 0 = Kt, where t (s) is time and the constants n and K for Ti-5553 at 900°C (close to the temperature used here) are ∼ 2 and 49 μm 2 /s, respectively [12]. Taking D 0 = ∼40 μm (the initial β columnar width, Figure  1(a)) results in D = 176 μm, in good agreement with the observation (Figure 1(k)). In conclusion, the equiaxed β grains form by the breakup of high-aspect-ratio β columns without nucleation of new crystals with different orientations, maintaining the general texture of the as-SLM alloy ( Figure 1). Such formation of equiaxed grains is similar to geometric dynamic recrystallisation (GDRX) in Al alloys during hot rolling [27]. Deformation elongates the grains, increasing their aspect ratios to > 2-4. At the early stages, grain boundaries are serrated owing to the formation of subgrains. Further straining pinches off grain boundaries, breaking elongated grains into equiaxed ones. GDRX is geometrically equivalent to recrystallisation, but without nucleation and significant change in the existing texture. Comparing GDRX and the mechanism illustrated in Figure 4(c-e), the formation of the equiaxed grains during HT of SLM Ti-5553 can be considered as a deformation-free geometric recrystallisation. High-aspect-ratio grains are produced thanks to epitaxial growth (instead of rolling), grain boundaries are serrated by thermal fluctuations and moving of dislocations to the boundaries (not subgrains), and finally, long grains are broken into equiaxed ones by surface tension (rather than external forces from rolling).
In summary, transformation of β columns to equiaxed grains during super-transus HT of SLM Ti-5553 was attributed to Rayleigh instability and grain growth driven by reduction in the grain boundary area. The equiaxed grains formed by breaking up the existing high-aspectratio columnar grains without nucleation and significant changes in orientation, similar to GDRX but with no deformation involved. This dismisses the belief that conventional recrystallisation is responsible, since the dislocation density was too low and the as-SLM texture was maintained after HT.