Preparation and characterisation Julia Lyubina Institute for - PowerPoint PPT Presentation

Preparation and characterisation Julia Lyubina Institute for Metallic Materials, IFW Dresden, Germany Characterisation x-ray diffraction imaging techniques (SEM, AFM, MFM) differential scanning calorimetry Preparation (included in Nanostructured Hard Magnets ) sintering hydrogen-assisted methods (HD, HDDR) melt spinning mechanical alloying hot deformation

Characterisation methods

Characterisation methods X-ray diffraction (XRD)

X-ray diffraction (XRD) Bragg‘s law (elastic scttering) θ 2d hkl sin θ = n λ θ θ Lattice planes d hkl sin θ (hkl) d hkl Constructive interference → the path length difference = whole number of λ Properties: min = λ /2 � sin θ = 1 ⇒ 2d hkl = n λ ⇒ d hkl � Diffraction pattern is obtained for θ θ = var, λ θ θ λ λ λ = const (powder diffraction, Debye-Scherrer, rotation, Kossel methods) θ θ θ = const, λ θ λ λ λ = var (Laue method) � Positions of reflections are determined by the respective set of cell dimensions

X-ray diffraction (XRD) → Diffraction a crystal placed in an incident beam of hard x-rays reflects this beam in many directions http://itl.chem.ufl.edu/2041_f97/matter/FG11_039.GIF

X-ray diffraction (XRD) r j f j e 2 π i( h x j + k y j + l z j ) ] 2 N |F hkl | 2 = [ ∑ Structure factor = j 1 Integrated intensity I hkl = C 0 ·|F hkl | 2 ·LP·m hkl ·e -2M ·P k (kinematic theory) Dynamic theory: Kinematic theory: - no interaction between the incident intensity is weakened due to and scattered waves; extinction - single scattering event; - no absorption valid for small crystals (< 0.5 µm) and low scattering power http://cristallo.epfl.ch/flash/crystal_web_6_english.swf

Structure factor: chemical ordering FePt (A1 ≡ fcc) FePt (L1 0 ) c c z z y x y x b b a a r j f j e 2 π i( h x j + k y j + l z j ) ] 2 N |F hkl | 2 = [ ∑ Structure factor = j 1 A1 [ [000; ½½0; 0½½; ½0½]] L1 0 [ [ Pt 000; ½½0; Fe 0½½; ½0½]] Basis all F ss = 2 S (f Pt – f Fe ) F f = 4(c Pt f Pt + c Fe f Fe ) even h+k hkl even or odd The existence of SS reflections is the evidence for ordering!

Phase identification Qualitative → comparison of the observed data with interplanar spacings d and relative intensities I of known phases Quantitative → Integrated intensity I hkl ~ vol. % of the phase Problem: overlapping diffraction lines! 2000 � several phases Nearly stoichiometric 1500 possible Intensity (counts) nanocrystalline Nd-Fe-B � low symmetry 1000 � large cell 500 Independent determination of 0 peak position and I 30 50 70 90 110 2 θ (degrees) not possible

Rietveld refinement → Rietveld refinement a whole-pattern fitting with parameters of a model function depending on the crystallographic structure, instrument features and numerical parameters = + φ θ − θ ( 2 2 ) y y ∑ s ∑ I Calculated intensity ci bi p hkl i k p k background profile function scale factor ~ vol. % approximates the effects produced by instrument and sample-related ξ ξ ξ ξ Aim → find a set of parameters ( ) features (<D> and <e>) describing the observed pattern as good as possible ξ : vol. %, lattice and profile parameters, ξ ξ ξ ∂ U ξ = − = y y U 1 site occupation, preferred orientation… 2 ∑ i ci ∂ ξ ( ) ( ) y 0 i i H. M. Rietveld, J. Appl. Cryst. 2 (1969) 65.

Phase identification Even overlapping peaks contribute information about the structure! Nanocrystalline Nd 2 Fe 14 B + 3 vol. % α -Fe 2000 observed calculated 1500 Intensity (counts) 1000 500 0 30 50 70 90 110 2 θ (degrees) Refined (obtained) parameters global: background, sample shift structural : phase fraction, lattice constants, profile parameters ( → grain size/strain)

Phase identification: minority phases Fe 55 Pt 45 powder Qualitative analysis → L1 0 phase only ) . u . a ( Rietveld refinement → y t i s n e t additional phases n I A1 FePt, Fe 3 Pt and FePt 3 20 30 40 50 60 70 80 90 100 20 30 40 50 60 70 80 90 100 2 θ (degrees) 2 θ (degrees) Severe overlap of lines → close cell dimensions line broadening due to nanocrystallinity Lyubina et al., JAP 95 (2004) 7474.

Line broadening: grain size and lattice strain 2 θ 2 Observed diffraction profile h (2 θ ) is θ = θ − h ( ) f ( y ) g ( y ) d y a convolution of the physical f (2 θ ) → ∫ 2 2 and instrumental g (2 θ ) profiles 2 θ 1 f max Integral breadth φ θ θ ( ) d(2 ) ∫ β = 2 φ max Separate f (2 θ ) and g (2 θ ) using e.g. integral breadth method

Line broadening: grain size and lattice strain Separation of f (2 θ ) and g (2 θ ) using integral breadth method I) Measurement of a a Standard Reference Material SRM (e.g. LaB 6 ) s t n u o c 2 θ II) Select the shape of the peak (e.g. pseudo-Voigt) IIIa) Interpolate the FWHM of the SRM IIIb) Decompose it into Lorenzian and Γ = θ + θ + Gaussian and correct the integral 2 tan 2 U V tan W β = β − β f h g breadths as IRF L L L IVa) Correct β = β − β f h g Γ = Γ − Γ ( ) ( ) ( ) 2 2 2 2 2 G G G sample measured IRF

„Average size-strain“ method /modified Williamson-Hall analysis/ * = β β θ λ cos / Integral breadths in the reciprocal units Lorenzian Gaussian − θ − θ θ − θ 1 2 2 = γ + + − γ −         4 2 2 4 ln 2 2 2 i k i k βπ β β β π V 1 4   ( 1 ) exp 4 ln 2                       size effects strain effects β = η β L = ε * * d / 2 * 1 / G β = β β + β − β = ε β + η 2 2 * * 2 1 * * 2 2 ( / d ) /( d ) ( / 2 ) ⇒ L G J.I. Langford, in Proc. Int. Conf.: Accuracy in powder diffraction II (NIST, Washington, DC, 1992), p. 110.

„Average size-strain“ method β = ε − β + η * * 2 1 * * 2 2 ( / d ) /( d ) ( / 2 ) -4 1.5x10 111 Spherical particle Pt <D> = 1.333 ε 200 -4 1.0x10 2 < e > = η π rms strain ( β */d*) / 2 2 α -Fe 220 311 222 110 -5 400 5.0x10 α -Fe Pt 220 112 200 <D> , nm 43 29 <e> , % 0.21 0.16 0.0 -3 -2 -2 -2 -2 -2 5.0x10 1.0x10 1.5x10 2.0x10 2.5x10 3.0x10 Scherrer eq.: 2 β */d* <D> = 0.9 λ / β cos θ ⇒ for α - Fe <D> = 15 nm! <D> XRD ≈ ≈ 5…200 nm ≈ ≈

Diffraction from amorphous materials Amorphous materials → the atoms has permanent neighbours, but there is no repeating structure (short range order). Ball-milled Nd-Fe-B 1000 α -Fe <D> ≈ 10 nm, <e> ≈ 0.6 % Intensity (counts) amorphous crystall I hkl phase 500 I halo 0 30 50 70 90 110 2 θ (degrees)

Diffraction from amorphous materials Scattering intensity I Scattering intensity I Radial distribution function 4 π R 2 ρ (R) (structure factor) for liquid Fe (structure factor) Statistical scattering 1550 °C 1750 °C Radial distribution function 4 π R 2 ρ (R) coord. sphere radius radial function of atomic density bcc fcc Suzuki et al., 1987 Umansky et al., 1982

Properties of neutrons • Behave either as particels or as waves • Wavelength varies depending on the source temp.: hot (0.2-1 Å), thermal (1-4 Å), cold (3-30 Å) Nuclear scattering interaction with the nucleus via strong nuclear force → crystal structure determination from diffraction experiments Magnetic scattering The neutron possesses a spin → can be scattered from variations in magnetic field via the electromagnetic interaction → magn. structure probe http://www.ill.fr/index_ill.html

X-rays or neutrons? f j e 2 π i( h x j + k y j + l z j ) ] 2 ~ I int N |F hkl | 2 = [ ∑ Structure factor = j 1 X-rays Neutrons f j - atomic form factor f j (b j ) - neutron coherent scattering length Neutrons interact with the nucleus ⇒ b j = ∀ ∀ ∀ ∀ X-rays interact with e - cloud ⇒ f j ~ z � Weak absorption ⇒ large penetration depth � Possibility to locate light atoms or distinguish neighbouring atoms in the periodic table � Magnetic structure probe Example: L1 0 FePt F ss = 2 S (f Pt – f Fe ) z Pt (= 78) >> z Fe (= 26) h+k even ⇒ f Pt >> f Fe BUT b Pt ≈ ≈ ≈ ≈ b Fe Site occupation (and order parameter S) determination is possible with x-rays, not with neutrons

Magnetic structure by neutron diffraction L1 0 Fe 50 Pt 50 Neutron coherent scattering length b Pt ≈ b Fe • Magnetic reflections evolve on cooling around 725 K • Int. intensity ~ (magnetic structure factor) 2 ~ (projection of m ⊥ k ) 2 APL 89 (2006) 032506

Characterisation methods Scanning electron microscopy (SEM)

Electron microscopy: interaction of e - with matter incident Back reflection electron beam (SEM) backscattered electrons (atomic contrast, imaging, EBSD) secondary electrons (surface imaging) X-rays (chemical analysis, Auger electrons Kossel diffraction) (surface analysis) Sample absorbed electrons X-rays Transmission (chemical analysis, (TEM) Kossel diffraction) elastically scattered electrons inelastically scattered electrons (SAD-point diagrams, dark field imaging) (Kikuchi-diagrams) transmitted electrons (bright field imaging)