PCT & PMN-PT Ferroelectrics

Transcription

1 Combined Analysis: texture, structure, microstructure, phase, stress, reflectivity (multiphase bulks and thin films, x-rays and neutron diffraction): some case studies Daniel Chateigner CRISMAT-ENSICAEN (Caen-France) Bi2223 Superconductors PCT & PMN-PT Ferroelectrics Irradiated FAp ceramics Ca 3 Co 4 O 9 Thermoelectrics nano-si thin films IMN Jean Rouxel 2006

2 Implemented codes Extracted Intensities Specular Reflectivity WIMV, E-WIMV Harmonics Orientation Distribution Function Rietveld Roughness, electron Density & EDP, Thickness pole figures inverse pole figures Fresnel, Matrix (Parrat), DWBA Geometric mean Structure + Microstructure + phase % Popa-Balzar, sin 2 ψ Le Bail Structural parameters atomic positions, substitutions, vibrations cell parameters Multiphased, layered samples: Thickness, Anisotropic Sizes and µ-strains (Popa), Stacking faults (Warren), Distributions Residual stresses Strain Distribution Function Phase ratio (amorphous + crystalline) Le Bail Rietveld

3 Texture from Spectra Orientation Distribution Function (ODF) From pole figures From spectra

4 Residual Stresses and Rietveld Macro elastic strain tensor (I kind) Crystal anisotropic strains (II kind) Fe Cu C Macro and micro stresses Applied macro stresses Textured samples: Reuss, Voigt, Hill, Bulk geometric mean approaches

5 Texture How it works (Combined) Nphases I calc 2 i (χ,φ) = S n L k F k;n S ( 2θi 2θ k;n )P k;n (χ,φ)a + bkg i n=1 from Generalized Spherical Harmonics: k P k (χ,φ) = ϕ f (g,ϕ)dϕ P k (χ,φ) = l l 1 k n l ( χ,φ) C mn l k *m n Θ k φ k 2l +1 l= 0 n= l m= l ( ) f (g) = l l= 0 m,n= l C l mn T l mn (g) from the WIMV (left) iterative process or entropy maximisation (right): ( g) f ( g) n 0 n+ 1 f ( g) = Nn 1 I M h IM n Ph h= 1 m= 1 f ( y) h f n+ 1 ( g) = f n ( g) M h m= 1 P P h n h ( y) y ( ) rn M h

6 Layering ( 1 exp( µ Tg / cosχ) )/( 1 exp( 2µ T /sin ωcosχ) ) topfilm Cχ = g1 2 C cov.layer χ ( ( ' ' ) ( ( ' ' exp g µ T / cosχ / exp 2 µ T /sin ωcosχ ) topfilm = C χ 2 i i i i Popa anisotropic shapes & microstrains... <R h > = R 0 + R 1 P 2 0 (x) + R 2 P 2 1 (x)cos ϕ + R 3 P 2 1 (x)sin ϕ + R 4 P 2 2 (x)cos2 ϕ + R 5 P 2 2 (x)sin2 ϕ + < ε h 2 >E h 4 = E 1 h 4 + E 2 k 4 + E 3l 4 + 2E 4 h 2 k 2 + 2E 5l 2 k 2 + 2E 6 h 2 l 2 + 4E 7 h 3 k + 4E 8 h 3 l + 4E 9 k 3 h + 4E 10 k 3 l + 4E 11l 3 h + 4E 12l 3 k + 4E 13 h 2 kl + 4E 14 k 2 hl + 4E 15l 2 kh Roughness and/or microabsorption R S R rough 2 ( q ) = R( q ) exp( q q ) z = 1 p exp q z z, 0 z,1σ - q sinθ ( ) + p exp Low-angles (reflectivity) high-angle (Suortti)

7 Fresnel: matrix: Born approximation: Specular reflectivity: q=(0,0,z) ( ) q q i q q q i q q q R x c z z c z z δ δ λ β π λ β π = q h k r r r r h k r r r r R Z Z flat,1 1,2 0,1 2 1,2 2 0,1,1 1,2 0,1 2 1,2 2 0,1 cos cos = 2 * ) ( 1 ) (. ) ( dz e dz z d q R r r q R z iq s z F z z + = = ρ ρ

8 Phase Strain-Stress W S Φ Φ = N Φ i= 1 Z S Φ i M Z i Φ M V i Φ V I II III ε( X) = ε + ε ( X) + ε ( X) i ε ( y) h E( g) V d V d 1 = V I = ( ε I ( ε = d = V = V d I ( ε cos ε I cosφ + ε d( hkl, φ, ψ ) d V d V d E E 0 II 33 φ + ε 23 + ε I 12 III 33 ) dv I sin 2φ + ε sin 1 sinφ )sin 2ψ + V V d d ( hkl) SC SC 0 22 d ( hkl) ( g) f ( g) dg ( g) f ( g) dg d 1 V d 2 φ ε V d ( ε I 33 IIe 33 )sin + ε 2 IIti 33 ψ + ε + ε C C IIpi 33 M ijkl M ijkl I 33 + ) dv = M ( S ) ijkl M ( S ) 1 ijkl Isotropic samples: Tri-, bi-, uni-axial stress states Textured samples: Tri-, bi-, uni- stress states + ODF + SDF + model 1 Reuss, Voigt, Hill Geometric mean, VPSC

9 Minimum experimental requirements 1D or 2D Detector + 4-circle diffractometer (X-rays and neutrons) CRISMAT, ILL + ~1000 experiments (2θ diagrams) in as many sample orientations + Instrument calibration (peaks widths and shapes, misalignments, defocusing )

10 Calibration 60 ω = ω = 40 χ χ 0 0 KCl, LaB 6 FWHM (ω, χ, 2θ ) 2θ shift gaussianity asymmetry misalignments...

11 Methodology implementation L. Lutterotti, Trento User friendly interface Java codes Java web start updates

12 Bi2223 compounds E. Guilmeau, CRISMAT Pressure Eléments chauffants circulaires resistances σ Sinter-Forging Ag Feuilles sheaths Τ, σ c d Ag Pastille Bi2223 Bi2223 pellet Disques Alumina Alumine Cylinder Grain alignment Jc

13 (00l) Texture 2300 (0010)-Bi2223 (0012)-2223 (0010) Intensity (a. u) (OO8)-Bi2212 (0014)-2223 (0012) Theta Angle ( )

14 Bi Secondary phases Bi2223

15 Combined Analysis (119) 220-(2212) 220-(2223) 0212/2012-(2223) 1111-(2212) 1111-(2223) 020/200-(2212) 020/200-(2223) χ=90 χ= (2223) 008-(2212) 14 : (2212) 0012-(2223) 0012-(2212) 0014-(2223) 2θ -Neutrons -Sample: 70 mm 3-2θ patterns for χ=0 to 90 -No ϕ rotation (fibre texture).

16 χ=90 Δχ=5 χ=0 Bi Bi2212 Rw=9.12 RP=16.24

17 a) Recalculated (WIMV) b) Extracted (Le Bail) Logarithmic density scale, equal area projection Stacking faults and/or intergrowth on the c-axis New periodicities and peaks characterized with intermediate c parameters. However, no algorithm is included to solve intergrowths in the combined approach. Logarithmic density scale, equal area projection

18 Effect of the sinter-forging treatment on the texture development, crystal growth, transport properties Sinterforging dwell time (h) Orientation Distribution Max (m.r.d.) % Bi2223 Cell parameters (Å) Bi2212 Bi2223 Bi2223 Bi2212 Crystallite size Bi2223 (nm) Rb (%) Rw (%) Rexp (%) RP0 (%) RP1 (%) J c (A/cm 2 ) ±1.3 a=5.419(3) b=5.391(3) c=37.168(3) a=5.414(3) b=5.393(3) c=30.800(3) 205± ±2.9 a=5.419(3) b=5.408(3) c=37.192(3) a=5.416(3) b=5.396(3) c=30.806(3) 273± ±4.6 a=5.410(3) b=5.405(3) c=37.144(3) a=5.412(3) b=5.403(3) c=30.752(3) 303± ±4.1 a=5.417(3) b=5.403(3) c=37.199(3) a=5.413(3) b=5.407(3) c=30.792(3) 383± Sinter-forging Time Texture strength % Bi2223 Crystallite Size J c E. Guilmeau et al., JAC

19 Ca3Co4O9 thermoelectrics M. Prevel, CRISMAT Ca3Co409: Misfit lamellar and modulated Structure, with high thermopower Two monoclinic sub-systems: S1 with a 4.8Å, b1 4.5Å, c 10.8Å et β 98 (NaCl-type) S2 with a 4.8Å, b2 2.8Å, c 10.8Å et β 98 (CdI2-type) Γ=σab/σc 10 Texture

20 powder Textured bulk Magnetic alignment and Templated Growth method 10 µm 10 µm Analysis: - neutrons - 3D Supercell: a=4.8309å, b 8b1 13b Å, c= å, β= atoms/cell -Sample : 0.6 cm3

21 χ=90 Δχ=5 χ=0 Supercell RP=19.7%, Rw=11.9%

22 9.8 MPa for 2 h 19.6 MPa for 6 h 19.6 MPa for 20 h Electrical conductivity σ ab (10 4 S/m) Power Factor PF ab (mw/mk 2 ) Templated Growth Method 1.8 2h 6h 20h 0.4 Uniaxial Pressing duration time (h)

23 Logarithmic density scale, equal area projection (b) Neutrons 27.4 m.r.d 1 m.r.d 0.01 m.r.d Magnetic Alignment - magnetic alignment really efficient to obtain strong textures - combined analysis of modulated structures possible

24 Ferroelectric PCT films J. Ricote, DMF-Madrid thin films: (Ca 0.24 Pb 0.76 )TiO 3 sol-gel synthesised solutions deposited by spin coating on a substrate of Pt/TiO 2 /Si, with and without a treatment at 650ºC for 30 min. All films are crystallised at 700ºC for 50 s by Rapid Thermal Processing (RTP; 30ºC/s). A series is also recrystallised at 650ºC for 1 to 3 h. 60 ω = 20 (111) ϕ χ m.r.d. 0 χ 0 Refinement of individual spectra

25 Limitations of the simple Quantitative Texture Analysis Structural parameters are difficult to obtain due to: Substrate influence: overlapping of reflections from the film and the substrate Pt PCT thin film 20 TEXTURE effects: peaks that do not appear at low χ angles Intensity (a.u.) Pt reflections 5 101, , Pt θ (º)

26 PCT Pt a = (1) Å T = 457(3) Å t iso = 458(3) Å ε' = (1) rms a = (1) Å c = (3) Å T = 2525(13) Å t iso = 390(7) Å ε = (1) rms R W = 13%; R B = 12%; R exp = 22%.(Rietveld) R W = 5%; R B = 6% (E-WIMV)

27 Atom Pb Ca Ti O1 O2 Occupancy x y z (2) 0.060(2) 0.631(1)

28 Structural parameters Pt layer a (Å) thickness (nm) R factors (%) non-treated substrate Pt (1) 45.7(3) R W =13, R B =12, R exp =22 annealed substrate Pt (4) 46.4(3) R W =8, R B =14, R exp =21 Pt (Recryst. 1h) (2) 47.8(3) R W =9, R B =20, R exp =21 Pt (Recryst. 2h) (1) 46.9(3) R W =9, R B =14, R exp =22 Pt (Recryst. 3h) (4) 47.5(9) R W =27, R B =12, R exp =21 Annealing of the substrate does not introduce significant variations on the structure of the Pt layer PTC film a (Å) c (Å) thickness (nm) on non-treated substrate PCT (1) (6) 272.5(13) on annealed substrate PCT (6) (8) 279.0(9) PCT (Recryst. 1h) (2) (4) 266.1(11) PCT (Recryst. 2h) (2) (4) 258.4(9) PCT (Recryst. 3h) (4) (11) 253.6(29) Recrystallisation reduces the stress on the film, and, increases the lattice parameters

29 Structural, microstructural and texture quantitative characterisation of ferroelectric thin films by the combined method Analysis of the X-ray diffraction diagrams of a PCT film on Pt/TiO 2 /Si 001, , , 111-Pt 002, Pt , , , Pt 311-Si R W = 13%; R B = 12%; R exp = 22%.(Rietveld) R W = 5%; R B = 6% (E-WIMV)

30 Substrate influence on Residual Stress and Texture Tensile stress Texture Pyroelectric Index Coefficient (m.r.d. 2 ) (10-8 C cm -2 K -1 ) PCT on Pt/TiO 2 /(100)Si mrd PCT on Pt/(100)MgO PCT on Pt/(100)SrTiO Compressive stress Enhancement of <001> texture

31 Compliance coefficients [10-3 GPa -1 ] PbTiO 3 single crystal (data set A) Film random orientation PCT-Si <001> contrib 17% PLT <001> contrib. 49% PCT-Mg <001> contrib. 68% s s s s s s s s s s s s s 33 /s s 13 /s Geometric mean average + biaxial stress state

32 Ferroelectric PMN-PT films J. Ricote, DMF-Madrid Pt a = (1) Å T = 583(5) Å t iso = 960(1) Å ε = (1) rms σ 11 = 0.639(1) GPa σ 22 = 0.651(1) GPa σ 12 = (1) GPa Pb 0.7 (Mg 1/3 Nb 2/3 )O 3 -Pb 0.3 TiO 3 /Ti0 2 /Pt/Si-(100) PMN-Pt a = (9) Å b = (9) Å c = (4) Å β = (1) Å T = 1322(9) Å t iso = 1338(2) Å ε = (1) rms

33 Si nanocrystalline thin films M. Morales, SIFCOM-Caen Silicon thin films deposition by reactive magnetron sputtering: Ä power density 2W/cm 2 Ä total pressure: p total = 10-1 Torr Ä plasma mixture: H 2 / Ar, ph 2 / p total = 80 % Ä temperature: 200 C Ä substrates: amorphous SiO 2 (a-sio 2 ) (100)-Si single-crystals Ä target-substrate distance (d) a-sio 2 substrates: d = 4, 6, 7, 8, 10, 12 cm films A, B, C, D, E, F (100)-Si: d = 6, 12 cm films G, H Aim: quantum confinement, photoluminescence properties

34 Isotropic (111) (111) X-rays ω Textured <111> (111) (111) X-rays ω

35 Typical refinement Intensity (a.u.) χ = χ( ) χ = 0 broad, anisotropic diffracted lines, textured samples

36 Refinement Results RX Anisotropic sizes (Å) Texture parameters Reliability factors (%) Sample d (cm) a (Å) thickness Maximum minimum Texture index RP 0 R w R B R exp (nm) <111> <220> <311> (m.r.d.) (m.r.d.) F 2 (m.r.d 2 ) A (3) B (2) 711 (50) C (4) 519 (60) D (2) 1447 (66) E (2) 1360 (80) F (3) 1110 (57) G (3) 1307 (50) H (2) 1214 (18)

37 Mean anisotropic shape <111> 10 nm 4 nm Schematic of the mean crystallite shape for Sample D represented in a cubic cell, as refined using the Popa approach and exhibiting a strong elongation along <111>, and TEM image

38 001 Inverse Pole Figures A B C a-sio 2 D E F (100)-Si G H min 0 max

39 10 0 Sample B (d = 6 cm) reflectivity XRR: Roughness governed experimental refined 1/q q z (Å -1 ) AFM: homogeneous roughness

40 Refractive index n n E g Tauc gap E g (ev) inter-electrode d spacing (cm)

41 Irradiated FluorApatite (FAp) ceramics S. Miro, PhD CRISMAT Self-recrystallisation under irradiation, depending on SiO 4 / PO 4 ratio (FAp / Nd-Britholite) and on irradiating species TEM of FAp irradiated with 70 MeV, Kr cm -2 ions

42 texture corrected, Kr cm -2 Virgin, with texture correction Virgin, no texture correction

43 Fluence (ions.cm -2 ) Vc/V (%) A (Å) c (Å) <t> (nm) Δ a/a0 (%) Δ c/c0 (%) R w (%) R B (%) (3) 6,8560(5) 294(22) Kr (1) (9) (8) 294(20) (1) (5) (5) 291(20) (1) (4) (5) 294(22) I (2) (3) (5) 90(10) (2) (3) (5) 91(6) (5) (5) (6) 77(11) (2) (4) (6) 82(9) Single impact model associated to crystal size reduction Cell parameters and volume increase, then relax Amorphisation / recrystallisation competition: single or double impact

44 Amorphous/crystalline volume fraction (damaged fraction Fd = Va / V) as determined by x-ray diffraction 1 0,8 B 0,6 0,4 0,2 70 MeV Krypton ,8 0,6 Krypton Iodine Single impact Double impact Single impact Fitting parameters Fd = B(1- exp(-a φ t)) Fd = B(1 (1+ A φ t) Fd = B(1- exp(-a φ t)) exp(-a φ t)) A = π R 2 (cm 2 ) 1.85 ± ± ± Radius R (nm) 2.4 ± B ± ± 0.2 (Max.damage rate) χ ,4 0,2 127 MeV Iodine ,

45 Conclusions a) Texture affects phase ratio and structure determination b) Microstructure (crystallite size) affects texture (go to a) c) Stresses shift peaks then affects structure and texture determination d) Combined analysis may be a solution, unless you can destroy your sample or are not interested in macroscopic anisotropy... e) If you think you can destroy it, perhaps think twice f) more information is always needed: local probes g)