Diffraction from nanocrystalline materials

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1 Diffraction from nanocrystalline materials Paolo Scardi Department of Civil, Environmental & Mechanical Engineering University of Trento

2 PRESENTATION OUTLINE 2 PART I Diffraction from nanocrystalline materials: reciprocal space vs direct space methods PART II Selected case studies: nanocrystalline catalysts and highly deformed metals Chapter VIII X-ray diffraction by crystalline materials Davide Viterboe Giuseppe Zanotti Chapter X Powder diffraction and synchrotron radiation Gilberto Artioli Chapter XVIII Diffraction from nanocrystallinematerials Paolo Scardi and Luca Gelisio

3 DIFFRACTION PATTERN FROM A POLYCRYSTALLINE 3 {22} {12} {2} {11} {1} powder (bulk polycrystalline) nanocrystalline powder 1 nm

4 SCATTERING FROM NANOCRYSTALS Scattering from a small fcc crystal 4 s λ S s λ One scattering centre (electron, atom, unit cell) 2 * I A = AA r m O r n I A A * sc m n m n ( ) πisr ( ) 2πiSrm 2 = fme fe n m n n

5 SCATTERING FROM NANOCRYSTALS 5 Scattering from a small fcc crystal s λ S s λ S s s 2sinθ = = λ λ S r m s λ r mn O r mn s λ r n 2θ ( ) πisr ( ) 2πiSr 2 m I f e fe sc m n m n n = f fe π m n m n ( ) 2 isrmn

6 SCATTERING FROM NANOCRYSTALS Scattering from a small fcc crystal 6 ( ) πisr ( ) 2πiSr 2 m I f e fe sc m n m n n = f fe π m n m n ( ) 2 isrmn Q=2πS

7 SCATTERING FROM NANOCRYSTALS Scattering from a small fcc crystal 7 ( ) πisr ( ) 2πiSr 2 m I f e fe sc m n m n n = f fe π m n m n ( ) 2 isrmn Q=2πS

8 FROM SINGLE CRYSTAL TO POWDER DIFFRACTION 1. Reciprocal space approach (Laue Wilson) sum+average Two possible approaches 2. Direct (real) space approach (Debye) average+sum 8 ( ) πisr ( ) 2πiSr 2 m I f e fe sc m n m n n = f fe π m n m n ( ) 2 isrmn

9 FROM SINGLE CRYSTAL TO POWDER DIFFRACTION Two possible approaches -#1 reciprocal space 9 1. Factorize the contribution from a unit cell ( F 2 F, structure factor ) s λ S s λ

10 FROM SINGLE CRYSTAL TO POWDER DIFFRACTION Two possible approaches -#1 reciprocal space 1. Factorize the contribution from a unit cell ( F 2 F, structure factor ) (u n,v n,w n ) 1 (,,1) (1,,1) (½,½,1) (,1,1) (1,1,1) (,½,½) (½,,½) (½,1,½) (1,½,½) r = ua+ v b+ wc n n n n (,,) (1,,) (½,½,) (,1,) (1,1,) ( ) πisr ( ) 2πiSr 2 m I f e fe uc m n m n n

11 FROM SINGLE CRYSTAL TO POWDER DIFFRACTION Two possible approaches -#1 reciprocal space 1. Factorize the contribution from a unit cell ( F 2 F, structure factor ) S 11 s λ s s 2sinθ S = = λ λ r = ua+ v b+ wc n n n n 2θ s λ ( ) πisr ( ) 2πiSr 2 m I f e fe uc m n m n n N = n= 1 ( wl) 2 iuh vk fe π + + n n n n 2 = F 2

12 Two possible approaches -#1 reciprocal space 1. Factorize the contribution from a unit cell ( F 2 F, structure factor ) I FROM SINGLE CRYSTAL TO POWDER DIFFRACTION Then build the diffraction signal for a small crystal (unit cell volume, V uc ) (Interference function) sc N 2 2 iuh vk Iuc F = fe π + + n n= 1 see ZANOTTI s lecture ( π ) ( π ) ( π ) F sin Nh sin Nk sin Nl V sin ( πh) sin ( πk) sin ( πl) uc D=Na ( wl) n n n 12 2 a I sc ( π ) ( π ) ( π ) F sin Nh sin Nk sin Nl V π ( h h') π ( k k') π ( l l') uc h' = k' = l' =

13 SCATTERING FROM A POWDER Two possible approaches -#1 reciprocal space 1. Factorize the contribution from a unit cell ( F 2 F, structure factor ) 13 I Then build the diffraction signal for a small crystal (unit cell volume, V uc ) sc (Interference function) ( π ) ( π ) ( π ) F sin Nh sin Nk sin Nl V sin ( πh) sin ( πk) sin ( πl) uc I sc ( π ) ( π ) ( π ) F sin Nh sin Nk sin Nl V π ( h h') π ( k k') π ( l l') uc h' = k' = l' =

14 SCATTERING FROM A POWDER Two possible approaches -#1 reciprocal space 1. Factorize the contribution from a unit cell ( F 2 F, structure factor ) 14 Then build the diffraction signal for a small crystal (unit cell volume, V uc ) (Interference function) I sc ( π ) ( π ) ( π ) F sin Nh sin Nk sin Nl V π ( h h') π ( k k') π ( l l') uc h' = k' = l' = Intensity h = 1 h = 2 1 s λ Example: (1) point Powder Integration Tangent Plane Approximation, TPA (Laue) 1 2 2θ s λ

15 POWDER INTEGRATION: TANGENT PLANE APPROX. Two possibleapproaches -#1 reciprocal space Powder Integration (TPA): (1) peak, powder of cubic crystallites (edge D=Na) sin ( πnh)sin ( πnk)sin ( πnl) 2 sin ( πnl) IPD F dh dk F π h π k π l π l ( 1) ( 1) 15 Integral breadth 2 sin ( π Nl) dl 2 ( l 1) 2 π = = I() 1 N l 2 l -[1] D=Na l tangent plane 1 =1 k -[1] h -[1] a I(l) s θ S 1 s θ

16 SCATTERING FROM A POWDER 16 Two possible approaches -#1 reciprocal space 1. Factorize the contribution from a unit cell ( F 2 F, structure factor ) Then build the diffraction signal for a small crystal, ( πnh) ( πnk) ( πnl ) sin sin sin sin ( πh) sin ( πk) sin ( πl) and integrate over the powder diffraction sphere for calculating the signal from all domains in the powder {22} {12} {2} {11} {1} D traditional Powder Diffraction approach I S F Φ SD, PD 2 ( ) ( )

17 DIRECT SPACE APPROACH TO POWDER DIFFRACTION Two possible approaches -#2 real space 2. Average over all possible orientations of r mn in space 17 S s s 2sinθ = = λ λ s λ S f S r mn = Sr mn cosφ r mn 2θ s λ ( ) πisr ( ) 2πiSr 2 m I f e fe sc m n m n n = f fe π m n m n ( ) 2 isrmn

18 DIRECT SPACE APPROACH TO POWDER DIFFRACTION Two possible approaches -#2 real space Average over all possible cosφ values: r mn isallowed to take all possible orientationsin space s λ S f S r mn = Sr mn cosφ r mn s λ ( ) PD m n m n XII SILS School -Grado, ( ) 2 isrmn I S f f e π = Debye equation f f sin 2π Sr ( ) mn m n m n 2π Srmn

19 DIRECT SPACE APPROACH TO POWDER DIFFRACTION Debye equation for one fcc unit cell 19 ( ) I S f f = sin2π Sr mn PD m n m n 2π Srmn a r mn = a 2 a a 32 a 2 a 3 I PD ( Qa ) 3sin Qa ( Qa ) ( Qa ) ( Qa ) = 72sin 2 48sin 32 24sin 2 8sin Qa 2 + Qa + Qa 32 + Qa 2 + Qa 3

20 DIRECT SPACE APPROACH TO POWDER DIFFRACTION 2 I PD Powder of (random oriented) Cu unit cells. Mo Kα (.793 nm) ( Qa ) 3sin Qa ( Qa ) ( Qa ) ( Qa ) = 72sin 2 48sin 32 24sin 2 8sin Qa 2 + Qa + Qa 32 + Qa 2 + Qa 3 35 Intensity (a.u.) θ (degrees) Cu bars: multiplicity

21 DIRECT SPACE APPROACH TO POWDER DIFFRACTION Powder of (random oriented) Cu unit cells. Mo Kα (.793 nm) 21 IPD LP e Q 2 2 u S Intensity (a.u.) θ (degrees) , Cu bars: ICSD #46699

22 DIRECT SPACE APPROACH TO POWDER DIFFRACTION Powder of α-fe (bcc) cubic crystals. Cu Kα (.1546 nm) 22 2 (11) 1x1x1 4 (11) 3x3x Intensity 1 5 (211) (311) (2) (22) (222) Intensity 2 1 (211) (311) (2) (22) (222) Intensity (11) 2θ (degrees) (211) (311) (2) (22) (222) θ (degrees) 5x5x5 XII SILS School -Grado, Intensity 12k (11) 1k 8k 6k 4k 2k θ (degrees) (211) (311) (2) (22) (222) θ (degrees) 15x15x15

23 DIRECT SPACE APPROACH TO POWDER DIFFRACTION Powder of α-fe (bcc) cubic crystals. Cu Kα (.1546 nm) 12k 1k (11) 15x15x atoms 23 Intensity 8k 6k 4k 2k (211) (311) (2) (22) (222) θ (degrees)

24 DIRECT SPACE APPROACH TO POWDER DIFFRACTION Powder of α-fe (bcc) cubic crystals. Cu Kα (.1546 nm) 24 5k 15x15x atoms 4k Intensity 3k 2k 1k θ (degrees)

25 DIRECT SPACE APPROACH TO POWDER DIFFRACTION Powder of α-fe (bcc) cubic crystals. Cu Kα (.1546 nm) 25 1M 1M 1M 15x15x atoms I() = = Intensity 1k 1k 1k θ (degrees)

26 DEBYE EQUATION: APPLICATIONS 26 nanocrystals and non-crystalllographic nanoparticles effect of multiple twins real nanoparticles: fi effect of energy minimization GEOMETRICAL RELAXED (ENERGY MINIMIZED)

27 DEBYE EQUATION: APPLICATIONS "perfect" sphere twinned sphere K. Beyerlein, PhD Thesis, Univ. of Trento (211) 1 1 Intensity Intensity SAXS "perfect" sphere twinned sphere q (degrees) SAXS WAXS q (degrees) Twinned spherical domains (fcc, Au atoms, nominal size 9.8 nm)

28 DEBYE EQUATION: APPLICATIONS 28 L. Gelisio, PhD Thesis, Univ. of Trento, 214 Carbon nanotubes

29 DEBYE EQUATION: APPLICATIONS Molecular dynamics of a cluster of nanocrystalline metal grains 4x1 6 A. Leonardi, PhD Thesis, Univ. of Trento, Intensity (a.u.) 3x1 6 2x1 6 1x q (degrees) XII SILS School -Grado, Normalized unit cell parameter Average grain diameter Grain diameter of equivalent-volume sphere [ A. Leonardi, M. Leoni & P. Scardi, J. Appl. Cryst. 46 (213) 63 ]

30 3 QUESTIONS??

31 RECIPROCAL SPACE APPROACH 31 Intensity a.u. 2 ( ) Φ(, ) I S F SD PD 2 = ( ) cos( 2π ) max S F A L LS dl L S = 2sinθ/λ [Å -1 ] s Å 1 V(L) s hkl 1. D AJC Wilson, X-ray Optics, Methuen, 1962 L A S (L) = V(L)/V L L Distance (Angstrom) max

32 RECIPROCAL SPACE APPROACH 32 2 ( ) Φ(, ) I S F SD PD 2 = ( ) cos( 2π ) max S F A L LS dl L L S ( ) ( ) I S A L FF e dl max * 2πiLS L L P L * FF L F 2 2 i hkl e πψ ( L) e π 2 isl ε L S hkl

33 RECIPROCAL SPACE APPROACH 33 2 ( ) Φ(, ) I S F SD PD 2 = ( ) cos( 2π ) max S F A L LS dl L L S ( ) ( ) I S A L FF e dl max * 2πiLS L L P L * FF L F 2 2 i hkl e πψ ( L) e 2πiSLεL ( D A ) S hkl max S D 2πiLS I S AA e dl ( ) L

34 RECIPROCAL SPACE APPROACH 34 2 ( ) Φ(, ) I S F SD PD 2 = ( ) cos( 2π ) max S F A L LS dl L L S ( ) ( ) I S A L FF e dl max * 2πiLS L L L ( F F + ) P A ib * FF L F 2 2 i hkl e πψ ( L) e 2πiSLεL ( D A ) S hkl max S D F F 2πiLS I S AA ( A ib ) e dl ( ) L +

35 WHOLE POWDER PATTERN MODELLING - WPPM 35 2 ( ) Φ(, ) I S F SD PD 2 = ( ) cos( 2π ) max S F A L LS dl L L S ( ) ( ) I S A L FF e dl max * 2πiLS L L 2 2 hkl ( ) FF i L * L F e πψ L ( F F + ) P A ib e 2πiSLεL ( D A ) S hkl max IP S D F F APB 2πiLS I S T AA ( A + ib ) A... e dl ( ) L

36 WHOLE POWDER PATTERN MODELLING - WPPM ( ) ( 1 ) exp( π σ ln2) exp( 2πσ ) T L = k L + k L Instrumental profile IP pv s s Domain size effect: m, s c 2 ( ) µ σ A L H ln Erfc LK (3 n) M L 3 S c l,3 n n ( ) = n n= σ 2 2Ml,3 Dislocation (strain) effect: r, Re,(C hkl ) D 1 2 * 2 * A{ hkl} ( L) = exp b Chkl π ρd Lf LR 2 Faulting: α (def.), β (twin) A B F hkl F hkl 2 ( α β α ) () L = Ld 2 * { hkl} o 2 o 2 { hkl} ( e) L Lo ( L) = σl β 3 6β 12α β + 12α o L L Anti-Phase Domains: g A ( L) = exp o L σ h L o 2 2 ( ) ( h k ) L ( + + ) 2γ + APB { hkl} dhkl 2 h 2 k 2 l 12 A BC Frequency hk + kl + lh Chkl = A+ B = A+ B H ( h + k + l ) Grain diameter (nm) * d hkl ABC * A B d hkl * d hkl * d hkl TEM WPPM 5 nm

37 37 QUESTIONS??

38 WPPM APPLICATIONS: NANOCRYSTALLINE CERIA 38 Nanocrystalline cerium oxide from sol-gel method: thermally treated 1 h at 4 C is the dried xerogel crystalline? O Ce O O O Ce Ce Ce O Ce O O O O O Ce Ce Ce Ce O O O O O Ce Ce Ce Ce O O O O O Ce Ce Ce Ce O O O O O Ce Ce Ce Ce O O O O Ce O O O = chelating ligand model: lognormal distribution of spherical domains

39 WPPM APPLICATIONS: NANOCRYSTALLINE CERIA 39 Xerogel obtained by vacuum-drying: broad diffraction lines of nanocrystalline fcc phase 8 ESRF ID31 -glass capillary, λ=.6325 nm 8 Intensity (counts) Intensity (counts) θ (degrees) θ (degrees)

40 WPPM APPLICATIONS: NANOCRYSTALLINE CERIA 4 Xerogel obtained by vacuum-drying: broad diffraction lines of nanocrystalline fcc phase Intensity (counts) ESRF ID31 -glass capillary, λ=.6325 nm Intensity p(d) (a.u.) (counts) θ (degrees) D (nm) θ (degrees) <D>=2.25(1) nm O O O Ce Ce Ce Ce O O O O O Ce Ce Ce Ce O O O O O O Ce Ce Ce Ce Ce Ce O O O O O O O O Ce Ce C Ce O O O O Oe Ce Ce C Ce O O O e

41 WPPM APPLICATIONS: ZIRCONIA-CERIA CATALYSTS 41 nanocrystalline ZrO 2-9%CeO 2 catalyst

42 WPPM APPLICATIONS: ZIRCONIA-CERIA CATALYSTS XRD data collected at Campinas Synchrotron (Brasil) nanocrystalline ZrO 2-9%CeO 2 catalyst Intensity (counts) Intensity (counts) θ (degrees) θ (degrees)

43 WPPM APPLICATIONS: ZIRCONIA-CERIA CATALYSTS XRD data collected at Campinas Synchrotron (Brasil) nanocrystalline ZrO 2-9%CeO 2 catalyst 43 3 Intensity (counts) θ (degrees)

44 WPPM APPLICATIONS: ZIRCONIA-CERIA CATALYSTS XRD data collected at Campinas Synchrotron (Brasil) ZrO 2-9%CeO 2 catalyst: comparison between WPPM and TEM 4 35 WPPM) HRTEM (nm) 44 Frequency Mean sd N HRTEM nm 8.61 nm 564 XRD-WPPMH 9.75 nm 5.72 nm P. Scardi et al., Powder Diffraction, 2 (25) D (nm)

45 WPPM APPLICATIONS: NANOCRYSTALLINE Fe-1.5%Mo 45 Planetary ball milling w W Courtesy of R Ciancio (TASC, Trieste)

46 WPPM APPLICATIONS: NANOCRYSTALLINE Fe-1.5%Mo 46 Ball milled Fe1.5Mo (Fritsch P4) data collected at ESRF ID31 λ=.632 nm hours Intensity (x1 3 counts) Intensity (x1 3 counts) θ (degrees) θ (degrees)

47 WPPM APPLICATIONS: NANOCRYSTALLINE Fe-1.5%Mo 47 Ball milled Fe1.5Mo (Fritsch P4) data collected at ESRF ID31 λ=.632 nm Intensity (x1 3 counts) (b) Intensity (x1 3 counts) hours θ (degrees)

48 WPPM APPLICATIONS: NANOCRYSTALLINE Fe-1.5%Mo 48 Ball milled Fe1.5Mo (Fritsch P4) data collected at ESRF ID31 λ=.632 nm Intensity (x1 3 counts) (b) Dislocation density, ρ (x1 16 m -2 ) 3,5 3, 2,5 2, 1,5 1,,5, Ball milling time (h) Mean domain size, D (nm) θ (degrees)

49 WPPM APPLICATIONS: NANOCRYSTALLINE Fe-1.5%Mo 49 Ball milled Fe1.5Mo (Fritsch P4) data collected at ESRF ID31 λ=.632 nm In addition to mean values, WPPM provides the size distribution Domain size distribution, g(d) Dislocation density, ρ (x1 16 m -2 ) Courtesy of R Ciancio (TASC, Trieste) Ball milling time (h) Mean domain size, D (nm) h 2 h 16 h 32 h 64 h 128 h 128h D (nm) M. D Incau. Univ. of Trento, PhD Thesis. 26. In press.

50 5 QUESTIONS??

51 DIFFRACTION FROM NANOCRYSTALLINE MATERIALS neglected facts in powder diffraction: TDS 51 λ max 2D VDOS D TDS ω min = 2 πc s ( ω) λ max

52 TEMPERATURE DIFFUSE SCATTERING - TDS 52 MD simulation of dynamical properties of nanocrystals Still 1 1 no Thermal Vibration Thermalized 3K (MD) TDS Thermalized Intensity θ /degrees)

53 DIFFRACTION FROM NANOCRYSTALLINE MATERIALS Challenges in nanotechnology: controlling size and shape of nanoparticles 53 1 nm 1 nm Ag nanoparticles from AgNO3 reduction: increasing growth time (Sun & Xia, Science, 298 (22) 2177)

54 DIFFRACTION FROM NANOCRYSTALLINE MATERIALS Challenges in nanotechnology: controlling size and shape of nanoparticles 54 Pt nanoparticles from H2 reduction of H2PtCl6 (Beyerlein et al., MS&E A, 528 (21) 83) (111) (111) (1) (1) (111) Wulff polyhedra j / macm Cu UPD on single crystals E vs Pd/H / V Pd(11) Pd(1) Pd(111)

55 DIFFRACTION FROM NANOCRYSTALLINE MATERIALS Wulff polyhedra 55 CO CO25 CO θ (degrees)

56 DIFFRACTION FROM NANOCRYSTALLINE MATERIALS Wulff polyhedra 56 (111) CO CO25 CO1 (2) θ (degrees)

57 DIFFRACTION FROM NANOCRYSTALLINE MATERIALS nanocrystal shape control and self-assembling 57 2 nm 2 nm St Peter square, Rome 2 nm 2 nm 2 nm 2 nm

58 DIFFRACTION FROM NANOCRYSTALLINE MATERIALS Challenges in nanotechnology: controlling size and shape of Pd nanoparticles 58 Pd nanoparticles from H2PdCl4 reduction (Scardi et al., 213)

59 DIFFRACTION FROM NANOCRYSTALLINE MATERIALS Challenges in nanotechnology: controlling size and shape of Pd nanoparticles 59 [111]

60 DIFFRACTION FROM NANOCRYSTALLINE MATERIALS Edge length distribution three batches, total 768 nanoparticles 6 frequency #1 #2 #3 Total (768 np) edge length (nm)

61 DIFFRACTION FROM NANOCRYSTALLINE MATERIALS MCX beamline (Italian Synchrotron ELETTRA, Trieste) Debye-Scherrer geometry, 15 kev, Ø.5 mm kapton capillary Intensity (counts) Intensity (counts) kapton θ (degrees) θ (degrees)

62 DIFFRACTION FROM NANOCRYSTALLINE MATERIALS MCX beamline (Italian Synchrotron ELETTRA, Trieste) Debye-Scherrer geometry, 15 kev, Ø.5 mm kapton capillary Experimentally measured absorption coefficient: m=2.71 cm -1, mr» A(θ,R,µ) θ (degrees) R 2π { } ( ) A( θ, R, µ ) = exp µ R r sin 2 ( θ + ϕ) + R r sin ( θ ϕ ) cosh 2µ rsinθsinϕ rdrdϕ π R

63 DIFFRACTION FROM NANOCRYSTALLINE MATERIALS MCX beamline (Italian Synchrotron ELETTRA, Trieste) Debye-Scherrer geometry, 15 kev, Ø.5 mm kapton capillary Experimentally measured absorption coefficient: m=2.71 cm -1, mr» Intensity Intensity θ (degrees) θ (degrees)

64 DIFFRACTION FROM NANOCRYSTALLINE MATERIALS Whole Powder Pattern Modelling (WPPM) PM2K software 64 5x1 5 Intensity (counts) 4x1 5 3x1 5 2x1 5 1x1 5 Intensity (counts) θ (degrees) θ (degrees)

65 DIFFRACTION FROM NANOCRYSTALLINE MATERIALS WPPM lognormal distribution of cubes vs spheres: shape matters! 65 Intensity (counts) 5x1 5 4x1 5 3x1 5 2x1 5 1x1 5 CUBES WSS = 218, GoF=2.89 Intensity (counts) 5x1 5 4x1 5 3x1 5 2x1 5 1x1 5 Intensity (counts) 5x1 5 4x1 5 3x1 5 2x1 5 1x θ (degrees) SPHERES WSS = 593, GoF=4.75 Intensity (counts) 5x1 5 4x1 5 3x1 5 2x1 5 1x θ (degrees) θ (degrees) XII SILS School -Grado, θ (degrees)

66 DIFFRACTION FROM NANOCRYSTALLINE MATERIALS WPPM Temperature Diffuse Scattering (TDS) from nanocrystals 5x Intensity (counts) 4x1 5 3x1 5 2x1 5 1x1 5 Intensity (counts) 2x1 4 1x θ (degrees) TDS θ (degrees)

67 DIFFRACTION FROM NANOCRYSTALLINE MATERIALS XRD WPPM results vs TEM histogram frequency Total (768 np) XRD-WPPM edge length (nm)

68 DIFFRACTION FROM NANOCRYSTALLINE MATERIALS Challenges in nanotechnology: controlling size and shape of Pd nanoparticles 68

69 DIFFRACTION FROM NANOCRYSTALLINE MATERIALS Challenges in nanotechnology: controlling size and shape of Pd nanoparticles 69 Y. Xiong, Y. Xia, Adv. Mater. 27, 19, 3385

70 DIFFRACTION FROM NANOCRYSTALLINE MATERIALS Challenges in nanotechnology: controlling size and shape of Pd nanoparticles 7 [11] [11]

71 DIFFRACTION FROM NANOCRYSTALLINE MATERIALS XRD WPPM results vs TEM histogram 71 some nanoparticles sit on a (11) edge (ridge): use the shortest edge in the histogram instead of both edges ( 5% of nanocrystals with apparent rectangular shape in TEM pictures) [11] [1] Pd nanocrystals are not perfect (sharp-edge) cubes: use the Common Volume approach (Leonardi et al, JAC, 212) to calculate the line profile

72 DIFFRACTION FROM NANOCRYSTALLINE MATERIALS XRD WPPM results: size distribution of cubic and non-cubic nanoparticles 72 3 nanocrystalline Pd coarse grained Pd coarse grained Pd nanocrystalline Pd 25 Eastman JA (1992), 1st conference on nanostructuredmaterials, Cancun frequency cubic np non-cubic np 92% (vol. fraction) β =.27(1) % (twins) ρ 1 14 m -2 (dislocations) 8% (vol. fraction) β = 13(1) % (twins) ρ ~ 1 16 m -2 (dislocations) edge length (nm)

73 DIFFRACTION FROM NANOCRYSTALLINE MATERIALS XRD WPPM results vs TEM histogram frequency TEM histogram XRD-WPPM edge length (nm)

74 DIFFRACTION FROM NANOCRYSTALLINE MATERIALS % of exposed surfaces: Cu UPD vs XRD WPPM 74 Cu Under Potential Deposition (UPD) WPPM : truncated cubic Pd nanocrystal 8.x1-5 6.x1-5 4.x1-5 Chi^2/DoF E-13 R^ Peak Area Center Width Height E E E E E E E E Intensity (counts) 5x1 5 4x1 5 3x1 5 2x1 5 1x1 5 frequency TEM histogram XRD-WPPM edge length (nm) 2.x1-5 Cu UPD on a polyoriented Pd crystal. Baseline substraction -2.x x (1) area: 63.9 % Surface area fraction θ (degrees) truncation (1) area: 64 % (11) area: 28% (111) area: 8% 8% 92%

75 75

76 76 Diffraction Analysis of Materials Microstructure E.J. Mittemeijer & P. Scardi, editors. Berlin: Springer-Verlag, 24. Powder Diffraction: Theory and Practice R.E. Dinnebier & S.J.L. Billinge, editors. Cambridge: RSC Publishing, 28. Cap. XIII, p.376

77 Diffraction from nanocrystalline materials Paolo Scardi Department of Civil, Environmental & Mechanical Engineering University of Trento

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