Superior room-temperature ductility of typically brittle quasicrystals at small sizes

The discovery of quasicrystals three decades ago unveiled a class of matter that exhibits long-range order but lacks translational periodicity. Owing to their unique structures, quasicrystals possess many unusual properties. However, a well-known bottleneck that impedes their widespread application is their intrinsic brittleness: plastic deformation has been found to only be possible at high temperatures or under hydrostatic pressures, and their deformation mechanism at low temperatures is still unclear. Here, we report that typically brittle quasicrystals can exhibit remarkable ductility of over 50% strains and high strengths of ∼4.5 GPa at room temperature and sub-micrometer scales. In contrast to the generally accepted dominant deformation mechanism in quasicrystals—dislocation climb, our observation suggests that dislocation glide may govern plasticity under high-stress and low-temperature conditions. The ability to plastically deform quasicrystals at room temperature should lead to an improved understanding of their deformation mechanism and application in small-scale devices.

I n materials science, plasticity describes the non-reversible deformation of a solid in response to applied forces and determines the ability of a material to change its shape permanently without breaking. Regular crystalline materials, including most metals and ceramics, are generally plastically deformed through dislocation motion 1 or twinning 2 . The plasticity of amorphous solids, such as metallic glasses, is based on the formation and propagation of shear bands 3 . In quasicrystals 4 , despite their lack of periodicity, plastic deformation can also be achieved by dislocation activities 5 . In contrast to the situation in periodic crystals, every movement of a dislocation in a quasicrystal creates a cloud behind, which is called phason fault 6 . As a consequence, the dislocation motion gets hindered and the material appears brittle. Although a great variety of quasicrystals have been synthesized 7,8 , and some have even been discovered in nature 9 , and found to be technologically interesting [10][11][12][13] and useful 14 , only few of them can be found in applications so far, mainly limited by their poor ductility and formability at room temperature. Hence, improving the room-temperature ductility of quasicrystals is not only of academic interest but also essential for technological applications.
Early studies of the plastic deformation of quasicrystals focused on an easily grown icosahedral quasicrystal, i-Al-Pd-Mn, in the high-temperature regime above B600°C (B70% of its melting temperature). These studies demonstrated that the plastic deformation of i-Al-Pd-Mn was dominated by dislocation climb-with the Burgers vector out of the plane of dislocation motion, rather than dislocation glide-with the Burgers vector restricted in the plane of dislocation motion 15 . It is generally believed that dislocation climb is a much easier deformation mode in quasicrystals than dislocation glide 16 . Although there are some hints that the glide motion may be possible in lowtemperature conditions as suggested by numerical simulations 17 or under high hydrostatic pressures 18 , the required stress to activate glide is extremely high, on the order of 1/10 of its shear modulus-a stress level generally leading to fracture without showing any ductility. It has been a long-standing question concerning the deformation mechanism in quasicrystals at room temperature. Despite several investigators have sought to explore the plastic deformation of quasicrystals at or near room temperature using indentation or by confining gas or solid pressures [19][20][21][22] , so far there has been no common conclusion: the explanations include shear banding similar to metallic glasses 23 , phase transformation 24,25 , grain-boundary glide 21 , pure dislocation climb 22 , dislocation climb dominant 26 and crystallization 27 . Therefore, one has to conclude that the plastic deformation of quasicrystals under a wide range of temperatures and pressures has been poorly understood-much in contrast to crystalline and amorphous solids. Two fundamental questions are still open: can steady-state plastic deformation be achieved at room temperature? If so, what is the underlying deformation mechanism?
Unveiling room-temperature plasticity in quasicrystals hence relies on a new method to suppress fracture before plastic yielding in a simple loading experiment. Our strategy is to increase the fracture strength over the yield strength in a quasicrystal by reducing the sample size. Although similar methods have been explored for other brittle materials such as ceramics 28 and metallic glasses 29,30 , it has, to our knowledge, not previously been reported for quasicrystals-a large family of unusual solids. In this study, we demonstrate a brittle-to-ductile transition in quasicrystals at room temperature due to a sample size reduction-a submicron-sized quasicrystal pillar exhibits superior ductility at room temperature. Furthermore, we suggest that dislocation glide may control the plastic deformation of quasicrystals at room temperature and attempt to shed light on the underlying deformation mechanism in the low-temperature regime.

Results
A model to predict brittle-to-ductile transition. To estimate at what size range a typically brittle quasicrystal may become ductile, we compared the different deformation mechanisms as a function of the sample size: dislocation activities, crack propagation 31 and mass transport by diffusion 32 . We identified three deformation regimes: cracking-controlled, displacivedeformation-controlled (dislocations or shear bands) and diffusion-controlled, as illustrated in Fig. 1. We estimated the critical size, r p , for the brittle-to-ductile transition to be B500 nm, and the size of the diffusion-controlled zone, r d , to be around 10 nm (see the detailed analysis in Methods section at the end of the article). Our targeted sample size to attain steady-state plasticity thus falls in a range from B100 to B500 nm.
Micro-compression of small-sized quasicrystal pillars. In our experiments, we compressed single-quasicrystalline i-Al-Pd-Mn pillars with diameters ranging from B1.8 mm to B150 nm. We observed a brittle-to-ductile transition with the critical pillar diameter between 510 and 350 nm (Fig. 2a): the 1.8-mm pillar exhibits a catastrophic failure at B3% compressive strain; the 870-and 510-nm pillars show cracks at about 45°along the loading direction, failing at B6% strain; when the pillar diameter is below 500 nm, the pillars present significantly improved ductility with compressive strains over 50% and without any cracking. The 400-and 200-nm pillars clearly show 1,000 10,000 Semi-quantitative predictions for room temperature deformation. If D4r p , defined as the intersection of the fracture strength, s f (the blue dashed lines), and the yield strength, s y (the black solid line), the material fails by cracking without notable plasticity, following the Griffith's criterion 37 , s f ¼ K Ic /[a(pa) À 1/2 ] with K Ic the fracture toughness of the material, a a geometrical parameter on the order of unity and a the size of pre-existing cracks or flaws. The s f shows a smaller-is-stronger trend. If Dor d , defined as the intersection of s y and s d , the diffusion governs the strength, following s d / K_ eTD 3 with K, surface diffusivity, _ e, strain rate, and T, temperature. The s d shows a smaller-is-weaker phenomenon. In between r p and r d , the curves of s f , s d and s y are crossed and define a zone controlled by displacive deformation. The size range of this zone may vary by flaw sizes and strain rates, as illustrated.
deformation bands, while the 140-nm pillar reveals the deformation localized at the upper part of the pillar. All the corresponding stress-strain curves exhibit a displacement-burst phenomenon (Fig. 2a), which is generally observed in metals 33,34 and metallic glasses 29,30 . The 140-and 240-nm pillars exhibit earlier plastic yielding than the other pillars, which could be due to localized deformation on the pillar top region or the lateral friction between the indenter tip and the top surface of the pillar. nm. An initial crack occurs near the pillar base at the bending angle of B20-30°and eventual fracture happens at the bending angle of B40°. (b) TEM snapshots during bending tests on a pillar in the diameter of B100 nm, showing a homogenous deformation without any fracture, and the maximum tensile strain at the pillar centre estimated to be over 50%. Scale bars, 300 nm (a) and 100 nm (b). NATURE COMMUNICATIONS | DOI: 10.1038/ncomms12261 ARTICLE Here, the flow stresses after the first displacement bursts were used to give a best estimation of their yield strengths. How the fracture strain or maximum plastic strain changes by decreasing the sample size also demonstrates the brittle-to-ductile transition between 510 and 350 nm (Fig. 2b). When the pillar diameter is smaller than 350 nm, no cracking is observed in our experiments. Regarding the size dependence of strength, the fracture strength increases from B3.5 to B4.5 GPa with decreasing pillar diameters in the brittle regime, while the yield strength (the flow stress at the first displacement burst) is about 4.5 GPa in the ductile regime (Fig. 2c).
In situ bending tests of small-sized quasicrystal pillars. Brittle materials usually show higher ductility in compression than tension. To examine the tensile ductility of the quasicrystal pillars but avoid the complex experimental setup of the tensile test for sub-micrometer-sized samples, we employed micro-bending tests to induce an asymmetrical stress distribution and compare the bending ductility of the pillars in different sizes. The in situ scanning electron microscopy (SEM) bending of a 300-nm pillar shows that the deformation localizes near the pillar base by necking. We detected that the crack forms at the bending angle of B20-30°, and eventually fails in a catastrophic feature at the bending angle of B40° (Fig. 3a). The in situ transmission electron microscopy (TEM) bending of a 100-nm pillar shows in a rather homogenous deformation without any cracking and fracture (Fig. 3b). The longitudinal tensile strain near the pillar centre is estimated to be over 50%. The strain bands' motion during the tests implies dislocation activity during the deformation (Supplementary Fig. 1).
TEM characterization and diffraction simulations. A representative bright-field TEM image reveals the upper part of a deformed pillar along a threefold axis (Fig. 4a). We find a slip line through the pillar and a step at the pillar edge. The loading direction is along a twofold axis and the slip plane contains another twofold axis. The high-resolution TEM image shows a very narrow band of B2-5 nm in thickness. Along the band, there are strain-contrast modulations with a nearly equal distance of B2-5 nm and the area surrounding deformation band is nearly defect-free. (Fig. 4b; Supplementary Fig. 2). We do not observe any evidence of melting, crystallization, phase transformation or cracking that was used to explain room-temperature deformation in quasicrystals. Different from the deformation bands formed in i-Al-Pd-Mn under hydrostatic pressures and at room temperature 18 , the bands observed here are much narrower and contain a much lower defect density. Using the inverse Fourier transformed images (Fig. 4c,d from the boxed areas in Fig. 4b), we identify a few inserted fringes along the deformation band. These inserted fringes indicate the distortions caused by dislocations. Together with the sharp deformation band and the step at the pillar edge (Fig. 4a), the fringes suggest that their Burgers vectors may contain the components along the slip or shear direction-dislocation glide might have occurred. Our atomic model of i-Al-Pd-Mn quasicrystal matches the orientation of the sample before and after deformation, respectively (Fig. 4e,f). Along the slip line shown in Fig. 4f, we can identify the mismatch region generated by the dislocation glide due to the local shear between the quasi-lattice planes (Fig. 4g,h). Such discontinuous quasi-lattice planes could be interpreted as dislocations with Burgers vector along the slip direction, which compares to the fringe patterns in Fig. 4c,d. The strain contrast shown in Fig. 4b could be attributed to strain fields of the dislocations or related phason faults left behind. This is a strong indication that the plasticity of quasicrystals at room temperature can be dominated by dislocation glide.

Discussion
The results shown in Figs 2 and 3 confirm that i-Al-Pd-Mn pillars are capable of both excellent ductility (compressive and tensile) and maintaining high strength when the pillar diameter is below about 500 nm. To our knowledge, this result has never been reported for quasicrystals before. The quasicrystal fine-scale pillars exhibit minor size dependence of strength and a deformation morphology with wavy features (see high-resolution SEM images in Supplementary Fig. 3), which is more similar to metallic glasses 29,30 than to metals 35 . Nevertheless, we show that the quasicrystal plasticity at room temperature is still controlled by dislocation mechanisms. Although in quasicrystals climb leads to the removal or insertion of so-called 'worms' without overlaps or open spaces 15 , this process requires thermal activation. At room temperature, the atomic diffusion in quasicrystals is generally believed to be inhibited. Dislocation glide, however, may be active and even dominate under high-stress and low-temperature conditions, generating a high density of heavily distorted zones in the wake of the dislocation glide. The approach of reducing sample size to enhance the ductility of otherwise brittle quasicrystals may pave way to fundamentally understand the deformation mechanism of quasicrystals at room temperature, possibly at even lower temperatures and for all the other types of quasicrystals 36 .
Towards technological applications, fine-scale quasicrystals are attractive not only due to combining high strength with ductility but also because they offer extraordinary specific strength (strength divided by density or elastic energy density, B1 MJ kg À 1 ) among metallic micro/nano-pillars reported to date (Fig. 5), which might be used to store elastic energy. Small dimensional quasicrystals having superior strength and ductility, together with their interesting functional properties, may also enable components that are both structurally and functionally useful in micro-or nano-electromechanical systems. While much work remains to optimize their properties, our observation of superior room-temperature ductility in quasicrystals motivates further fundamental and technological exploration. Methods Sample preparation and characterization. An initial compact of composition Al 70 Pd 21.5 Mn 8.5 was prepared from pure metals (Al 99.9999%, Pd 99.9%, Mn 99.95%). The sample was pre-alloyed in an arc furnace, and subsequently placed in an Al 2 O 3 crucible and sealed in a quartz glass ampoule under an Ar atmosphere. The heat treatment consisted of the following steps: heating to 1323 K (above its melting temperature), slow cooling to 1083 K at the rate of 30 K h À 1 , annealing at 1,083 K for 150 h, and subsequent quenching in water. The composition of the resulting sample was confirmed using energy dispersive X-ray spectroscopy. The X-ray powder diffraction pattern (Supplementary Fig. 4) and TEM diffraction patterns ( Supplementary  Fig. 5) indicate that the resulting sample is a single-phase icosahedral quasicrystal, which is comparable to that in literature 60 .
The prepared i-Al-Pd-Mn was thermodynamically stable with an average grain size of about 300 mm and was also highly isotropic. We fabricated single-quasicrystalline pillars, in cylindrical shapes, from a coarse grain in a well-polished i-Al-Pd-Mn sample using a FIB system (Helios Nanolab 600i, FEI): a coarse milling condition of 30 kV and 80 pA and a final milling condition of 5 kV and 7 pA. The diameters of the FIB-milled pillars are in the range of B150 nm to B2 mm and the aspect ratios are B3.0-4.5. A taper of 2-3°was generally observed and the top diameter of the pillar was chosen to calculate stress.
Micro-mechanical testing. We used the nanoindenter (Hysitron Inc., USA) with a diamond flat-punch tip (5 mm in diameter, Synton-MDP, Switzerland) to compress the pillars in a displacement control mode and the strain rate of 2 Â 10 À 3 s À 1 by feedback mechanism. At least four pillars for each size were compressed. The deformed pillars were imaged using a high-resolution SEM (Magellan, FEI). For the post-mortem TEM characterization, the deformed pillars were thinned down to a lamella by ion milling, lift-out, thinning and polishing in the FIB system. Their cross-sections were then examined using a TEM (Tecnai F30, FEI, operated at 300 kV). In situ SEM and TEM bending tests were carried out using a nano-manipulator (Kleindiek, Germany) fitted to a SEM (Hitachi SU 8200) and an indenter holder (Nanofactory Instruments AB, SA2000N) fitted to a TEM (JEOL JEM-2100), respectively, with a displacement rate of B5 nm s À 1 .
Prediction of the brittle-to-ductile transition. In a brittle material, the fracture strength, s f , follows the Griffith's criterion 37 , as s f ¼ K Ic /[a(pa) 1/2 ] with K Ic the fracture toughness of the material, a a geometrical parameter on the order of unit and a the size of pre-existing cracks or flaws. Statistically, larger samples are more likely to contain larger flaws, or weaker links, and consequently, smaller samples usually exhibit higher fracture strengths than the large ones-the size effect due to the Weibull statistics 38 . Because the fracture strength, s f , cannot rise above the yield strength, s y , below a certain length scale plastic flow may determine the strength. The intersection between the curves for s f and s y provides a critical size, r p , for a brittle-to-ductile transition, as illustrated in Fig. 1a. Assuming that the largest pre-existing cracks or flaws is one order of magnitude smaller than the sample dimension, we can obtain r p of B500 nm for i-Al-Pd-Mn, using a, B1, K Ic , B1.25 MPa Â m 1/2 (ref. 39) and the hardness, H, B8.5 GPa (ref. 39). However, further reduction of the sample size down to the nanometre scale leads to a significant increase of the surface-to-volume ratio, and surface diffusion may control the plastic flow, resulting in a reduced strength. In a relation similar to the Coble creep 40 , the diffusion strength, s d , reflects a 'smaller-is-weaker' phenomenon. The crossover between s d and s y defines a diffusion-controlled zone with the length scale of r d (Fig. 1a). Although it is difficult to calculate the exact value of r d due to the lack of available literature data, recent studies on Al 90 Fe 5 Ce 5 metallic glass 41 and pure Sn 42 demonstrate that diffusion controls plasticity below the sample sizes of 20 nm and 130 nm, respectively, at a strain rate of B10 À 3 s À 1 and room temperature. Hence, we estimate the r d for i-Al-Pd-Mn as a few tens of nanometres (definitely smaller than 100 nm), under similar experimental conditions. On the basis of this analysis, our targeted sample size to attain steady-state plasticity falls in a range from B100 to B500 nm.
Diffraction simulations. We used the Quiquandon-Gratias atomic model (B70 Å in diameter) of icosahedral Al-Pd-Mn 43 . We oriented the model along the threefold axis (high-magnification image in Supplementary Fig. 6), and calculated the diffraction pattern and compared with the experimental electron diffraction pattern. This agreement indicates that the orientation of our model matches the orientation of the sample.
Data availability. The data that support the findings of this study are available from the corresponding author upon request.