nanoporous gold

Transcript

1. Atomic-scale Analysis of the Mechanical Behavior of Gold Nanofoams K. Kolluri1 and M. J. Demkowicz Materials Science and Engineering, MIT, Cambridge, MA 1Present address, MST-8, Los Alamos National Lab, NM Acknowledgments: Amit Misra, Antonia Antoniou, A. S. Argon, W. C. Carter, L. J. Gibson, K. J. Van Vliet, M. Kabir, R. E. Baumer Acknowledgments: User Project at Center for Integrated Nanotechnologies (CINT) at Los Alamos National Lab (LANL)
2. Nanoporous gold Single crystal nanoporous gold with voids H. Rosner et al., Adv. Mat., 9, 535, (2007) using the program MAVI. MAVI affords a rization of 3-D structures by analysis of their repre- ns as binary and spatially discrete images, using the ms described in reference [22]. Electron Microscopy entional TEM micrographs, such as the bright-field aphs of Figure 1, are 2-D projections which reveal ion about the average density along the beam direc- re, the micrographs illustrate the typical microstruc- nanoporous gold, which is composed of nanometer ments and pores. Energy dispersive analysis of X-ray ence of the sample volume shown in Figure 1(a) indi- t the average composition is Au96 Ag4 . Details of indi- old ligaments are shown in Figure 1(b). ected area electron diffraction (SAED) pattern (the corresponds to a circular area of about 800 nm in ) from the same volume as shown in Figure 1(a) (see veals a preferred <100> out-of-plane orientation, con- (b) connected network structure composed of single-crystalline gold ligaments nsity of gold ligaments due to the overlap in the 2-D projection. The corre- t indicates a preferred <100> out-of-plane orientation with considerable Single crystal nanoporous gold J. Erlebacher et al., Nature, 410, 450, (2001) FIG. 1. SEM micrograph obtained from (a) synthesized Au porous samples and (b) dark-field and bright-field TEM micro showing four distinct grains <50 nm. The corresponding selected area diffraction pattern is shown in the inset. J. Mater. Res., Vol. 20, No. 3, Mar 2005 Polycrstalline crystal nanoporous gold A. M. Hodge et al., J. Mater. Res., 20, 3, (2005) • Dealloyed nanofoams come in a wide variety • They are all open cell with ligaments and pores
3. Nanoporous gold: promising but controllable? as prepared Annealed for 2h at 400C Annealed for 6h at 400C • High surface area per unit volume promising for applications • However, high surface area driving force for coarsening A. M. Hodge et al., Acta Mater., 55, 1343, (2007)
4. Nanoporous gold Single crystal nanoporous gold with voids H. Rosner et al., Adv. Mat., 9, 535, (2007) using the program MAVI. MAVI affords a rization of 3-D structures by analysis of their repre- ns as binary and spatially discrete images, using the ms described in reference [22]. Electron Microscopy entional TEM micrographs, such as the bright-field aphs of Figure 1, are 2-D projections which reveal ion about the average density along the beam direc- re, the micrographs illustrate the typical microstruc- nanoporous gold, which is composed of nanometer ments and pores. Energy dispersive analysis of X-ray ence of the sample volume shown in Figure 1(a) indi- t the average composition is Au96 Ag4 . Details of indi- old ligaments are shown in Figure 1(b). ected area electron diffraction (SAED) pattern (the corresponds to a circular area of about 800 nm in ) from the same volume as shown in Figure 1(a) (see veals a preferred <100> out-of-plane orientation, con- (b) connected network structure composed of single-crystalline gold ligaments nsity of gold ligaments due to the overlap in the 2-D projection. The corre- t indicates a preferred <100> out-of-plane orientation with considerable Single crystal nanoporous gold J. Erlebacher et al., Nature, 410, 450, (2001) FIG. 1. SEM micrograph obtained from (a) synthesized Au porous samples and (b) dark-field and bright-field TEM micro showing four distinct grains <50 nm. The corresponding selected area diffraction pattern is shown in the inset. J. Mater. Res., Vol. 20, No. 3, Mar 2005 Polycrstalline crystal nanoporous gold A. M. Hodge et al., J. Mater. Res., 20, 3, (2005) • Dealloyed nanofoams come in a wide variety • They are all open cell with ligaments and pores • Their formation, coarsening, and deformation mechanisms are of interest
5. bons (A) before , 40, and 50 at Figure 2. SEM images showing the microstructure of NPC by dealloying of (a) Al 33 at % Cu, (b and c) Al 35 at % Cu, (d and e) Al 40 at % Cu, and (f) Al 50 at % Cu alloys in the 5 wt % HCl solution Nanoporous metals not limited to gold Pt J. C. Thorp et al., Appl. Phys. Lett., 88, 033110 (2006) Cu Z. Qi et al., J. Phys. Chem. C, 113, 6694 (2009) M. Hakamada et al., Appl. Phys. Lett., 94, 153105 (2009) Ni
6. Model for formation of nanoporous metal during dealloying s e n - r - e z g d s f n a g. w m - nt al at Figure 6. Schematic illustrating porosity evolution during selective dissolu- tion: ͑a͒ lateral stripping of LN species ͑uncolored͒ from the alloy surface exposed to electrolyte; concentration of noble atoms species ͑shaded͒ in regions of positive step curvature ͑e.g., kink sites͒; ͑b͒ formation and coars- ening of islands comprised of noble species atoms remaining from dissolu- J. Erlebacher, J. Electrochem. Soc. 151 (10), C614-C626 (2004) J. Erlebacher et al., Nature, 410, 450, (2001) Surface diffusion of atoms from high-curvature regions to low- curvature regions leads to formation of nanoporous metal assuming no role of vacancies
7. Deficiencies of the model series alignment was made by iterative cross-correlations to sub-pixel accuracy. The aligned tilt series was reconstructed diameter) from the same volume as shown in Figure 1(a) (see inset) reveals a preferred <100> out-of-plane orientation, con- 536 http://www.aem-journal.com © 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ADVANCED ENGINEERING MATERIALS 2007, 9, No. 7 (a) (b) Fig. 1. a) Bright-Field micrograph showing a fully connected network structure composed of single-crystalline gold ligaments and pores. Darker regions are related to a higher density of gold ligaments due to the overlap in the 2-D projection. The corre- sponding diffraction pattern (SAED) in the inset indicates a preferred <100> out-of-plane orientation with considerable mosaic spread. b) Bright-Field micrograph: detail revealing individual gold ligaments. Examples of encased voids are marked by arrow heads. ying rate are seen to be correlated, with more faster dealloying at higher ED . This is con- e apparent density differences seen in TEM d 1(b)]. In view of the higher Au fraction in eaf, it is not unexpected that its amount of ig. 3(c) is less than for the bulk material. Yet, gnificant here. t, our observation of a reduction in the outer transport of Au atoms from that surface into of the porous layer. In view of the unusually l diffusion coefficient of Au at the metal-elect face (see references in Ref. [10]), this might the most obvious shrinkage mechanism in t stages of dealloying, when the dissolution occ macroscopic sample surface. However, as the front propagates into the bulk, the diffusion di Photographs of Ag-Au samples. 6 carat leaf sample (a) before and (b) after dealloying, showing an area e leaf is floating on an electrolyte; a ring-shaped counter electrode is located outside the image area. ut 1 mm3 volume, master alloy and NPG. 04 (2006) P H Y S I C A L R E V I E W L E T T E R S 23% reduction in volume after dealloying S. Parida et al., Phys. Rev. Lett., 97, 035504, (2005) Voids inside the ligaments H. Rosner et al., Adv. Mat., 9, 535, (2007) In the surface-diffusion dominated model • lattice sites conserved: volume shrinkage can not be explained • voids inside the ligament can not form with only surface diffusion
8. Methods: Molecular dynamics • An initial random atomic structure was constructed from an FCC lattice corresponding to 20% - 42% density of Au • The resulting structure relaxed using conjugate gradient minimization followed by annealing at 300K and constant volume • EAM potential to model interatomic interactions [SM Foiles et al, Phys. Rev. B, 33, 7983 (1986)] • Simulations conducted using LAMMPS, an open source MD software
9. Talk outline Is there a different mechanism of coarsening of np-metals? • Creating a model np-Au atomic structure • Coarsening during annealing of np-Au • Coarsening during deformation of np-Au • Critical ligament radius below which coarsening is spontaneous
10. Spontaneous np-Au-like from Au gas t = 0.812ns! Initial! ρ = 0.19ρAu! Many previous investigation of similar phenomena F. F. Abraham et al., Phys. Rev. Lett. 261 (1976)
11. Microstructure of Model Au Nanofoam 0 1 2 3 4 5 2 4 6 8 10 12 r (Å) g(r) ʪ110ʫ ʪ100ʫ ʪ112ʫ ʪ110ʫ Surface atoms All atoms Microstructure of the annealed np-Au: • Annealed structure is crystalline and FCC • Surfaces normal to crystallographicʪ111ʫ • Annealed structure is polycrystalline ʪ123ʫ ρ = 0.19ρAu Atoms colored according to local deviation from crystallographic [100] orientation
12. Microstructure of Model Au Nanofoam Five-fold twins where several ligaments meet Twinned ligament hcp fcc unknown ρ = 0.19ρAu Surface atoms not shown for clarity Atoms classified using CNA • Twin boundaries in ligaments and nodes are common • Total twin boundary area greater than stacking fault area
13. Talk outline Is there a different mechanism of coarsening of np-metals? • Creating a model np-Au atomic structure • Coarsening during annealing of np-Au • Coarsening during deformation of np-Au • Critical ligament radius below which coarsening is spontaneous
14. Spontaneous formation of model nanoporous gold Annealing % of atoms at the surface time (ns) 0.2 0.22 0.24 0.26 0.28 0.3 0.32 0.34 0.36 0.38 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 Ligament radius (nm) No diffusion
15. Coarsening of np-Au during annealing Annealing % of atoms at the surface time (ns) 0.2 0.22 0.24 0.26 0.28 0.3 0.32 0.34 0.36 0.38 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 Ligament radius (nm) No diffusion
16. Coarsening during annealing by collapse of ligaments 3 nm • Shear at the bases of adjacent ligaments due to dislocation motion • Subsequently, shear at the ligaments themselves • Shear leads to “displacive” motion of ligaments towards each other and eventual collapse ρ = 0.19ρAu
17. 5 nm • Ligament pinch-off assisted by plastic deformation • collapse of other nearby ligaments • Pinch-off of a ligament creates additional surface • Surface area lost by ligament collapse more than compensates the surface area created by pinchoff Coarsening during annealing by collapse of ligaments
18. Void formation during ligament collapse 4 nm If ligament collapse is not contiguous, voids form
19. Talk outline Is there a different mechanism of coarsening of np-metals? Network restructuring enabled by localized plasticity • Creating a model np-Au atomic structure • Coarsening during annealing of np-Au • Coarsening during deformation of np-Au • Critical ligament radius below which coarsening is spontaneous
20. Talk outline Is there a different mechanism of coarsening of np-metals? Network restructuring enabled by localized plasticity • Creating a model np-Au atomic structure • Coarsening during annealing of np-Au • Coarsening during deformation of np-Au • Critical ligament radius below which coarsening is spontaneous
21. Volume conserving uniaxial compression • Volume-conserving strain increments (εzz < 0, εxx = εyy > 0) • Strain increments of 0.0099 (0.99%) up to a deviatoric strain of ~0.65 • Each Strain increment is followed by conjugated gradient minimization (0 K)
22. Mechanical response to volume conserving uniaxial compression σeq (MPa) εdev 19% 30% 42% 0 50 100 150 200 250 300 350 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 compare stress 0 50 100 150 200 250 300 350 0.2 0.25 0.3 0.35 0.4 0.45 0 50 100 150 200 250 300 350 ρ/ρAu σeq (MPa) σ σs = Cρrel 3/2 • Elastic-perfect plastic stress-strain response reminiscent of the compaction plateau of conventional foams • Critical yield strength backed out from Gibson-Ashby equation is in excellent agreement with those obtained directly for the model Au used. • When deformed under zero pressure the foams would densify; under constant volume, however, they begin to break up after εdev ~ 0.3
23. Coarsening during deformation 0.19 0.195 0.2 0.205 0.21 0.215 0.22 0.225 0.23 0.235 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 1.65 1.7 1.75 1.8 1.85 1.9 1.95 Ligament radius (nm) εdev % of atoms at the surface
24. 6 nm Coarsening during deformation by collapse of ligaments • Ligament pinch-off assisted by plastic deformation • Pinched-off ligaments collapse onto each other, leading to coarsening
25. Talk outline Is there a different mechanism of coarsening of np-metals? Network restructuring enabled by localized plasticity • Creating a model np-Au atomic structure • Coarsening during annealing of np-Au • Coarsening during deformation of np-Au • Critical ligament radius below which coarsening is spontaneous
26. Surface area change for one pinchoff/collapse event Change in energy per ligament during pinch-off/collapse given by dEsurface = [C0p12⇡L p24⇡R] dR surface energy surface area created surface area destroyed Fraction of ligaments that collapse extent of collapse of ligaments If two ligaments collapse to form just one ligament, then this value is 0.74. Fraction of pinched-off ligaments that do no collapse
27. Change in energy per ligament during pinch-off/collapse given by dEsurface = [C0p12⇡L p24⇡R] dR ⇢rel = C2 ⇣ rl rp ⌘2 h 1 D2 ⇣ rl rp ⌘i rl = R rp = L dEsurface = 2⇡p1 K1 C0 2 p ⇢ rel RdR K1 ⇡ (C0 2p2 p1 C0 2 p ⇢ rel ) where L ⇡ R C0 2 p ⇢rel Scaling expression After substitution Surface area change for one pinchoff/collapse event
28. Plastic work required for the ligament pinch-off/collapse may be estimated as dWplastic = p1[⌧b(2⇡RdR)]( 1 K0 L b ) Work required to glide a dislocation of Burgers vector b across a ligament of radius R in a material with flow stress Number of dislocations that need to glide across the ligaments to move them by a distance that is comparable to that of the pore size O(1) Plastic work done per pinchoff/collapse event
29. Critical radius for spontaneous coarsening by network reconstruction dEsurface = 2⇡p1 K1 C0 2 p ⇢ rel RdR K1 ⇡ (C0 2p2 p1 C0 2 p ⇢ rel ) dWplastic = p1[⌧b(2⇡RdR)]( 1 K0 L b ) Coarsening is spontaneous if dWplastic dR < dEsurface dR dW(R⇤)plastic dR = dE(R⇤)surface dR R⇤ = K ⌧ where K = K0(C0 2 p2 p1 C0 2 p ⇢ rel ) Network topology
30. Spontaneous coarsening regime (by plastic deformation) R⇤ = K ⌧ where K = K0(C0 2 p2 p1 C0 2 p ⇢ rel ) For Au, we get Average ligament radii of real np-Au reported in the literature are all above this critical value R⇤ ⇡ 1 5 nm ⌧ ⇡ 800 MPa 2.5 GPa {111} = 1.25 Jm 2 Assuming K0 = 2, C0 = 0.74 and P2/P1 <<1
31. Conclusions • Our simulations suggest that coarsening of np-Au may occur by network restructuring by collapse of neighboring ligaments – caused by localized plasticity • Indirect evidence – densification of np-metals upon annealing – voids enclosed in ligaments – critical ligament radius below which restructuring is spontaneous • Direct evidence required – high spatio-temporal resolution of x-ray tomography perhaps?