Title: Nano- and microstructures charaterized by transmission electron microscopy
1Nano- and microstructures charaterized by
transmission electron microscopy
- Dominique (Nick) Schryvers
- Electron Microscopy for Materials Science (EMAT)
- University of Antwerp, Antwerp, Belgium
- nick.schryvers_at_ua.ac.be
2How it all started ... etc.
- 1989 Winterschool on Mathematics and
Microstructures, Edinburgh, UK
- 1992 Workshop on "Mathematical Problems in
Materials Science", Edinburgh, UK - 1994 Microstructures and Phase Transitions,
Udine, Italy - 1995 IMA meeting on Phase Transformations, Nov.,
Minneapolis, USA - 1998 2002 TMR project "Phase Transformations in
Crystalline Solids". - 1999 MPI meeting From Atomic to Continuum
Scales, 21 25 June, Ringberg Castle, München,
Germany - 1999 Phase Transformations and Microstructure, 13
17 Sep., Newton Institute for Mathematical
Sciences, Cambridge, UK - 2000 Autumn School on Pattern Formation, 3 6
Oct., Padova, Italy - 2004 2008 FP6 MC RTN MULTIMAT Multi-scale
modeling and characterization for phase
transformations in advanced materials - 2006 Third International conference on Multiscale
Materials Modeling, 18 22 Sep., Freiburg,
Germany - ...
3one-way shape memory
(paperclip from Ch. Somsen, Bochum, Ge.)
4Structural background
- Crystalline materials
- atoms on regular lattice
- Structurale change upon cooling (or under stress)
- high to low symmetry
- e.g., cubic to tetragonal
martensitic transformation
Martenite Phase (low temperature)
Austenite Phase (high temperature)
shape change, ordering remains unchanged !
5Cubic to orthorhombic example
6 variants
A/M interfaces with twinned martensite to
minimize strain
6HT
RT
RT
(K. Bhattacharya Microstructure of Martensite,
OUP, 2003)
7Instrument
illumination system
electron gun
sample
imaging system
image (up to 2 106)
diffraction (reciprocal space)
energy loss spectrometer (inelastic scattering)
8Typical TEM results
9Pre-martensite and adaptive phase L. Tanner
...
10Phonen dispersion
inelastic
Ni62.5Al37.5 B2 cubic parent phase
- dip at 1/6 in 110 transverse acoustic branche
of phonon mode - deepens upon cooling
- austenite lattice softening prior to the
martensitic transformation
elastic
11Ni-Al pre-martensitic modulations
- 6(110) modulations superposed onto cubic basic
latice image and with same wavelength as
ensuing martensitic stacking sequence - imaging strain fields around point defects
microtweed - sometimes extra modulation inside single strain
field R
12Long period martensite
- Pre-martensitic modulation locks in as 52
stacking (7R structure) upon cooling below Ms - Competition with 43 stacking as adaptive phase
(A. Khatchaturyan) - Nanotwins
13Microcrack
- different stackings in stress field around
microcrack
3R 52
- constant composition, different stress
distribution (direction, strength)
14Microtwinning P. Boullay ...
15Normally internal twins are used to accommodate
habit plane strain (LIS)
hard to find a still habit plane due to the speed
of the transformation, thus information often
found from final RT observations
1690 (fork) examples in Ni65Al35
a
- difference between crossing and step still a
bit unclear
17complex microstructures
austenite
fork
spear
120
Self-accommodating group can only exist or grow
with 3 variants and a 120, interface 110b
(Bhattacharya AMM 39, 2431 (1991))
18in-situ nucleation of spear
- in-situ cooling of melt-spun Ni62.5Al37.5
- all 3 deformation variants involved (from
diffraction) - (-101)b midrib
1990 (fork) examples in Ni65Al35
20atomic resolution at step
U1
U2
U2
U1
- local bending, tapering and splitting
- of smallest variant and only on one side
- some dislocations
212D linear elasticity fit from continuum theory
- measurement and prediction of bending
(Boullay, Schryvers, Kohn, Physical Review B 64,
144105 (2001))
2290 (fork) examples in Ni65Al35
- zooming in on crossing case
23atomic detail crossing a lt 90
3nm
a
The macrotwin boundary corresponds to a
(010)? plane
U1
U1
- - angle between crossing microtwin families lt 90
- - large variant U1 on both sides, elongation //
macroplane
24extra lattice rotation
- 0 - 50 nm region lattice rotation central
region, severe deformation in small tips
25features without lattice rotations
(Boullay, Schryvers and Ball, Acta materialia 51,
1421 - 1436 (2002) )
- atomic ledges for continuous bending of
microtwins, without measurable reorientation of
the lattice
26macrotwin fork formation
(100)
U1
(010)
100
vol. U1 gt vol. U2
U2
- formation of the gt 90 and lt 90 cases
27Non-linear elasticity theory
- The macrotwin plane is of the 100B2 type
- The angle between the microtwin planes for the
(100)B2 case is given by 90g-f1, with (l
microtwin volume fraction)
a gt 90 theory 93.8
exp. 92-97
a gt 90 theory 86.2 exp. 83-86
28SMA with special parameters R. Delville
29Crystal structures in Ni-Ti
High temperature phase Austenite
Cubic B2 (CsCl, bcc)
High crystal symmetry
b 97 ,12 variants, multiple twinning
possibilities
30Ni-Ti-XX Au, Pt, Pd
Ms gt RT Type I, II
l1,2,3 are eigenvalues of austenite martensite
transformation matrix U
Ms lt RT compound
(J. Cui, R. James et al., Nature Materials, Vol
5, April 2006)
- l2 1 implies small hysteresis and no
twinning in martensite
31n1
Twinning modes and twin ratios for Ti50Ni50-xPdx,
x 9, 11, 20, calculated from the GNLTM K1 is
the twinning plane and n1 the shear
direction The twin ratio ? is defined as the
width ratio between two martensite variants
accommodating a habit plane with the austenite.
Samples from Minneapolis
32Ti50Ni50-xPdx Evolution of microstructure
33Ni27Ti50Pd23 l2 gt 1
- Ms 175C
- few expected Type I twins
- large spacings between twin planes
34 Ti50Ni30Pd20
Some martensite plates have a very small twin
ratio
35Ti50Ni30Pd20
Inside a martensite plate no twin detected but.
131 B2
121 B19
retained austenite as fine parallel lines
36Inhomogeneous twinning
- Pd11
- l2 1.0001
- nearby Ti2Ni precipitates
37Pd11 l2 1.0001
local lattice parameters composition to be
checked
38Ni40Ti50Pd10 l2 1
NO accommodating twins in occasional martensite
plate !
39Ti50Ni40Pd10
Sample frozen before observation
010 B19
011 B2
40Ni40Ti50Pd10 l2 1
In-situ cooling TEM
41Triangular self-accommodation pattern
inTi50Ni41Pd9
111 type I twin plane
111 type I twin plane in the 21-1 zone axis
42Ni43Ti50Pd7 l2 lt 1
- Ms -150C
- in-situ transformation
- no twins observed so far
43- In-situ straining
- W. Tirry
44Straining sample
Top view
2.5mm
Stress direction
Side view
45Results
- First formation of martensite
- at crack tips
- around carbide/oxide particles
- Secondly martensite starts growing in plain matrix
- Thin platelets
- Discontinuous
- Reversible upon relaxing
- Different growing directions (variants in
different areas)
400nm
46Observation in Diffraction Mode
11-1B2?1-10B19
(101)B2
(00-1)B19
Orientation relationship 1-1 0B19 1
1-1B2 (0 0-1)B19 rot 4.2 (101)B2
47Twinning ?
1) Typical twinning contrast is not visible in BF
or DF images. 2) Diffraction patterns compared to
simulations
Microtwinning not observed
48Absence of twinningproposed explanation with CTM
X
X
QU
B2
B19
... towards analytical numerical solution ....
J. Ball B. Muite
493D distribution of precipitates FIB
slice-and-view S. Cao
50Sketch of the FIB/SEM DualBeam System
52
FIB Focused Ion (Ga) Beam
51Cross-sectioning
- Pt layer protection
- Cross mark for drift and ion beam shift control
- U-cutting avoid reflection of sputtered ions
- Milling step 50nm
- Number of images 98
52Material and treatment
Ms
- Material Ni51Ti49
- Solution 950oC, 1h
- Aging 500oC, 4h yields Ni4Ti3 disc shaped
precipitates
8 variant families
532D thresholding segmentation
- small edges mostly retained
- max. effect on volume of 4
54No missing variants
- 4 variant families visible
- angle between 1, 2 and 3 close to 60 so zone
nearly lt111gt - variant 4 close but not exactly circle
553D reconstruction
6.69 x 4.4 x 4.85mm3
56Results 3D distribution
- Real 3D distribution
- Overall volume of precipitates is 5.60.2
- Overall change in composition due to formation of
precipitates 50.62 0.02at Ni (Ms ? 68)
(fits EDX measurements 50.4 ? 0.6) - Average distance between precipitates of same
variant 0.986 0.076 µm - Measured angle between central disc of
precipitates 109.5 1.0 (theoretical value
109.5 111)
57Last but not least W. Tirry, S. Van den broeck
58Last but not least
Ni65Al35
59SEM
60FIB lithography
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62(No Transcript)
63Thanks to
- Philippe BOULLAY (post-doc) (Ni-Al)
- Wim TIRRY (Ph.D., post-doc.) (Ni4Ti3)
- Rémi DELVILLE (M.Sc., pre-doc.) (Ni-Ti-Pd)
- Shanshan CAO (M.Sc., pre-doc.) (3D
slice-and-view) - Lee TANNER (Dr., Lawrence Livermore National
Laboratory, USA) - Jan VAN HUMBEECK (Prof. Materials Science, Kath.
Univ. Leuven, Belgium) - Robert KOHN (Prof. Mathematics, Courant
Institute, New York, USA) - Sir John BALL (Sedleian Prof. Mathematics, Oxford
University, UK) - Richard JAMES (Russell J. Penrose Prof. Aerospace
Engineering, University of Minnesota, USA)
64Acknowledgments
National Science Foundation Flanders GOA
project on EELS from University of Antwerp
Marie Curie Research Training Network MULTIMAT
from the European Commission (FP6)
65(No Transcript)
66Conclusions
- Advanced but also conventional EM is extremely
valuable in resolving and supporting modern day
materials science problems
67Electron Microscopy for Materials Science
68Elastic constant measurement by energy loss
plasmon Z. Yang
69Elastic modulus of precipitates
Free electron approximation electrostatic
attraction and repulsion, kinetic energy.
Oleshko and Howe et al., J. Electr. Microsc.,
53, 339, 2004 Microsc. Microanal., 8, 350, 2004.
70Elastic moduli of B2 and Ni4Ti3
YB2 118 4 GPa BB2 106 3 GPa
Low loss
Y43 163 4 GPa B43 141 3 GPa
calculated values Bulk modulus B2 165
GPa Ni4Ti3 172 GPa
Ni4Ti3 precipitates are harder than B2 matrix
71Eshelby model
exx strain component for a precipitate with a
diameter of 50 nm
Calculated maximum strain value much lower (at
least a factor of 10) than measured values and
extension of field much larger Possibly due to
use of same elasticity moduli for both matrix and
precipitate, anisotropy, concentration,
(code by K. Gall)
72High Resolution of Ni4Ti3
- 001H zone (111B2)
- internal structure of the precipitate
- structure confirmation by image simulation
73Other example Ni4Ti3 precipitates
- Lattice deformation
- aB2 0.30121 nm
- 111B2 0.5217 nm
- ahex 1.124 nm (lt112gtB2)
- chex 0.508 nm (lt111gtB2)
- coherent 300 nm
- Composition change
- original matrix Ni/Ti 1.04
- precipitate Ni/Ti 1.33
lt111gtB2
Ni Ti
Ni4Ti3
Tadaki et al. model (Trans. JIM 27, 731 (1986))
Wim Tirry
74NiTi SMA
- Austenite-martensite phase transformation Ni4Ti3
- Strain field
- Bataillard et al., Philos Mag 1998 in situ
observations - Quantified by Wim Tirry et al., Acta Mater 2005.
(ii) Composition
752D picture of (101)B2 deformations
?d lt 2 at the tip, i.e. compression
-111B2 zone
76Concentration gradient balance of Ni upon
precipitation
- Assumption symmetry c(x)c(-x)
77Concentration gradient EFTEM
pre-edge 1
pre-edge 2
post-edge
depleted region down to 0.96 ratio
78Summary EDX EELS - EFTEM
- Ni concentration next to precipitate drops to Ni
values below 50 at (compared with nominal
composition of Ni51Ti49), which implies that Ms
locally increases from 150K to RT !
Z. Yang, Scr. Mater. (2005)
79Summary micro-wire
- Naturally formed surface layer contains TiO as
well as rutile TiO2, with the latter more stable
phase probably being formed after the former one
(protection against toxic Ni) - Some Ni-rich particles are formed at the
interface of the alloy and the oxide - Concentration gradient with increasing Ni
concentration towards surface (related with
Ti-depletion due to oxidation) fits with
observation of B2 B19 boundary
80Tadaki model
Ni Ti
Ni4Ti3
Tadaki et al. model (Trans. JIM 27, 731 (1986))
100
100R//-120B2
81Multi Slice Least Squares
J. Jansen
- DP with parallel beam and small probe size
Recorded on CCD - Measure Intensities of the (hkl) reflections
- Im
- Input model of the structure
- Calculate intensities of (hkl) reflections with
Multi-Slice - Ical
82Input structure
Tadaki
Atom X Y Z Occ
Ni 0 0 0 1
Ni 0.5 0.5 0.5 1
Ni 0.78571429 0.07142857 0.64285714 1
Ti 0.28571428 0.57142857 0.14285714 1
R-factor 12.5
83Refinement of the positions
DFT structure used as starting structure
R-factor 8.2
MSLS
Atom X Y Z Occ
Ni 0 0 0 1
Ni 0.5 0.5 0.5 1
Ni 0.7574 0.0605 0.5931 1
Ti 0.2513 0.4989 0.1125 1
no improvement when refining composition or
space group
84111R orientation
Ni and Ti not centred at one column anymore
Ti moves 0.35Å Ni moves 0.27Å
Tadaki
Refined structure
lt111gtB2
851-10B2 projection
00143 111B2
Ni4Ti3
NiTi
Explains contraction along normal to disc
86Small precipitates (Ø 50 nm)
87unexpected compound twin
? deformation twin ? local composition difference
88two-way shape memory
89Medical applications
orthodontics
www.endovasc.com/images/graphics/stent.jpg
90martensite in local stress field
U1
U2
- changing habit plane with changing microstructure
- different habit planes for given stacking in one
wing - habit planes nearly // with microtwins
- only small difference between similar habit
planes in different wings
91(No Transcript)
92other examples of spears
Ni-Mn
splat-cooled Ni65Al35
- little or no deformations
- 110b midrib
93measures from processed images
94complex microstructures
austenite
fork
spear
90
120
What happens when two separate plates meet ?
95single plate characteristics
- Per choice of variants, resp. volumes and
microtwin plane - one particular microtwin orientation (q, rotation
axis) - one volume ratio l between microtwin variants
- two possible habit plane orientations m
96- Fair to good match between discrete measures from
experimental atomic lattice images and a
functional relation from continuum theory
97bending microtwins
a lt 90
a gt 90
- 50 - 500 nm region continuous bending of
microtwins
98- how well can we measure the volume fractions to
compare with theoretical predictions ? - no information from X-ray studies
99- possible definition l d1/(d1 d2)
100- changing volume fraction related to grain
boundary - hairpins or needles for changing variant
- facetted boundary
101- volume fraction close to constant
- microtwin width increases from A over B to C
- grain size also increases
- elastic ? surface energy
102Cubic to orthorhombic example
6 variants
A/M interfaces with twinned martensite to
minimize strain
103Sample preparation Focused Ion Beam
Company label (Memory Metalle) 49.48 at. Ni,
50.52 at. Ti
in-situ lift-out
Ø 50 micron, 30 cold-worked, no annealing
104Structural data
B2 B19 boundary
Pt
105Ni3Ti layer
106Co38Ni33Al29
- Fresnel images of the magnetic domain structure
observed during an in-situ cooling experiment.
107domain walls // (111) twinning
108SMA with special parameters R. Delville
109 Ti50Ni25Cu25 (melt-spun ribbons)
- Addition of Cu substituting Ni promotes the
stability of the transformation temperatures with
composition and yields a smaller hysteresis. - Crystallography of the transformation
- cubic B2 austenite to monoclinic B19 martensite
below 10 at. Cu - B2 ? B19 ? B19 between 10-15 at Cu.
- cubic B2 austenite to orthorhombic B19 martensite
above 15 at. Cu - Fast solidification (5 x 105 K/s) yields
amorphous ribbons
110Crystallization 10 min. at 693 K
- large amorphous regions containing some micron
sized spherical particles of B2 (bcc) austenite - mostly single crystal particles
- often with "hole" in the center
- some multi-grain particles (no fixed number of
grains 2 - 6)
111Quantitative EDX measurements
- No chemical differences (within 0.5 at. ) have
been detected by EDX, thus nucleation is not
promoted by long range diffusion.
112Typical example 4 grains
inclined and irregular interfaces several
common directions
113Other particle
- again lt111gt en lt115gt zones with changing
interface planes
114First particle lt110gt
X 7º Y -28.6º
- 1/2 twinning over -2-111
- 1/4 twinning over -21-11
- 3 4-1-1 zone fits well with 0-1-1 of 1
grain interfaces not // to twin planes
115Stereographic analysis
- shows that in all particles the same type of
crystallographic relations exist between
different grains - simuntaneously observed zones (lt111gt lt115gt)
- common directions and planes
- often, but not always 112 twinning
- interfaces not parallel to twin planes ((110),
(114), (115), (123), )
116Ideal multiply twinned bcc
- lt110gt zones
- 112 interfaces (111 fcc)
- 5 grains
- remaining gap 7.35 ( fcc)
- surface planes less close packed, thus less
energy gain than in case of fcc - thus, many possible faulty particles
7.35
Maybe single crystal microparticles started as
perfect multiply twinned 5-fold bcc nanoparticles
117- Strain field surrounding Ni4Ti3 precipitates
- W. Tirry
118Strain field around precipitate
g 120B2
Conventional two-beam TEM
- due to lattice mismatch - affects any
subsequent transformation (R-phase, B19, ...)
119High resolution of precipitate and -111B2
surrounding matrix
5 nm window
- similar structure
- expected difference in interplanar spacings of
a few
distance d between the maxima of the spots yields
average lattice spacing for total window area
120 Calculating strain
111B2
121Strain contour plot
most of the strain is concentrated alongside the
precipitate (as expected)
122Intermediate R-phase
measured deformation of matrix
123- Confirmation of the fact that the 90 case is NOT
a self-accommodating microstructure - Direction and amount of bending correspond with
current continuum theory predictions
124Evolution of Materials Research
- Macro- ? micro- ? nanostructures ? atomic scale
- Describing ? understanding ? predicting
- Materials science ? materials design
- Nice images ? accurate and precise numbers
- required precision 0.001 nm ? 0.025 eV
- required resolution 0.1 nm ? 1 eV
125Atomic scale
- lattice defects affect mobility and location of
twin and habit planes - opens possibility of training and shape memory
126fit with (non-)linear thermoelasticity
- volume preservation h1 0.93, h3 1.15
(65Ni)
(later a)
127What in case of deformed austenite ?
a0
- First attempt
- Change in lattice parameter a0
- Compression
- Tensile
- ?2 1 only in case of 3.5 compression in all
directions. - In-situ neutron diffraction shows compressed
matrix in coexistence with martensite 1 - However, 3.5 full compression is not realistic
- Tensile strain? (current experiment)
1 P. Sittner et al. Mat. Sc. Eng. A
200437897-104
128 deformation of B2 and B19
Determination of D and G by a computer
optimization ? ?2 1
D
G
further optimization for volume preservation and
4.2 angle
129Concentration Energy Dispersive X-ray (EDX)
50 nm probe
Z. Yang, Scr. Mater. (2005)