Nano- and microstructures charaterized by transmission electron microscopy

1
Nano- 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

2
How 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
• ...

3
one-way shape memory
(paperclip from Ch. Somsen, Bochum, Ge.)
4
Structural 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 !
5
Cubic to orthorhombic example
6 variants

• X 2 for monoclinic

A/M interfaces with twinned martensite to
minimize strain
6
HT
RT
RT
(K. Bhattacharya Microstructure of Martensite,
OUP, 2003)
7
Instrument
illumination system
electron gun
sample
imaging system
image (up to 2 106)
diffraction (reciprocal space)
energy loss spectrometer (inelastic scattering)
8
Typical TEM results
9
Pre-martensite and adaptive phase L. Tanner
...
10
Phonen 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
11
Ni-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

12
Long 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

13
Microcrack

• different stackings in stress field around
  microcrack

3R 52

• constant composition, different stress
  distribution (direction, strength)

14
Microtwinning P. Boullay ...
15
Normally 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
16
90 (fork) examples in Ni65Al35
a

• difference between crossing and step still a
  bit unclear

17
complex 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))
18
in-situ nucleation of spear

• in-situ cooling of melt-spun Ni62.5Al37.5
• all 3 deformation variants involved (from
  diffraction)
• (-101)b midrib

19
90 (fork) examples in Ni65Al35

• zooming in on step case

20
atomic resolution at step
U1
U2
U2
U1

• local bending, tapering and splitting
• of smallest variant and only on one side
• some dislocations

21
2D linear elasticity fit from continuum theory

• measurement and prediction of bending

(Boullay, Schryvers, Kohn, Physical Review B 64,
144105 (2001))
22
90 (fork) examples in Ni65Al35

• zooming in on crossing case

23
atomic 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

24
extra lattice rotation

• 0 - 50 nm region lattice rotation central
  region, severe deformation in small tips

25
features 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

26
macrotwin fork formation
(100)
U1
(010)
100
vol. U1 gt vol. U2
U2

• formation of the gt 90 and lt 90 cases

27
Non-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
28
SMA with special parameters R. Delville
29
Crystal structures in Ni-Ti
High temperature phase Austenite
Cubic B2 (CsCl, bcc)
High crystal symmetry
b 97 ,12 variants, multiple twinning
possibilities
30
Ni-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

31
n1
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
32
Ti50Ni50-xPdx Evolution of microstructure
33
Ni27Ti50Pd23 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
35
Ti50Ni30Pd20

Inside a martensite plate no twin detected but.
131 B2
121 B19
retained austenite as fine parallel lines
36
Inhomogeneous twinning

• Pd11
• l2 1.0001
• nearby Ti2Ni precipitates

37
Pd11 l2 1.0001
local lattice parameters composition to be
checked

• unexpected compound twin

38
Ni40Ti50Pd10 l2 1
NO accommodating twins in occasional martensite
plate !

• Ms RT

39
Ti50Ni40Pd10
Sample frozen before observation

010 B19
011 B2
40
Ni40Ti50Pd10 l2 1
In-situ cooling TEM

• Twinless martensite

41
Triangular self-accommodation pattern
inTi50Ni41Pd9
111 type I twin plane
111 type I twin plane in the 21-1 zone axis
42
Ni43Ti50Pd7 l2 lt 1

• Ms -150C
• in-situ transformation
• no twins observed so far

43

• In-situ straining
• W. Tirry

44
Straining sample
Top view
2.5mm
Stress direction
Side view
45
Results

• 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
46
Observation 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
47
Twinning ?
1) Typical twinning contrast is not visible in BF
or DF images. 2) Diffraction patterns compared to
simulations
Microtwinning not observed
48
Absence of twinningproposed explanation with CTM
X
X
QU
B2
B19
... towards analytical numerical solution ....
J. Ball B. Muite
49
3D distribution of precipitates FIB
slice-and-view S. Cao
50
Sketch of the FIB/SEM DualBeam System
52
FIB Focused Ion (Ga) Beam
51
Cross-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

52
Material and treatment
Ms

• Material Ni51Ti49
• Solution 950oC, 1h
• Aging 500oC, 4h yields Ni4Ti3 disc shaped
  precipitates

8 variant families
53
2D thresholding segmentation

• small edges mostly retained
• max. effect on volume of 4

54
No 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

55
3D reconstruction
6.69 x 4.4 x 4.85mm3
56
Results 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)

57
Last but not least W. Tirry, S. Van den broeck
58
Last but not least
Ni65Al35

• Polarized OM

59
SEM
60
FIB lithography
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Thanks 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)

64
Acknowledgments
National Science Foundation Flanders GOA
project on EELS from University of Antwerp
Marie Curie Research Training Network MULTIMAT
from the European Commission (FP6)
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Conclusions

• Advanced but also conventional EM is extremely
  valuable in resolving and supporting modern day
  materials science problems

67
Electron Microscopy for Materials Science
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Elastic constant measurement by energy loss
plasmon Z. Yang
69
Elastic 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.
70
Elastic 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
71
Eshelby 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)
72
High Resolution of Ni4Ti3

• 001H zone (111B2)
• internal structure of the precipitate
• structure confirmation by image simulation

73
Other 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
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NiTi 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
75
2D picture of (101)B2 deformations
?d lt 2 at the tip, i.e. compression
-111B2 zone
76
Concentration gradient balance of Ni upon
precipitation

• Assumption symmetry c(x)c(-x)

77
Concentration gradient EFTEM

• Standard 3-window method

pre-edge 1
pre-edge 2
post-edge
depleted region down to 0.96 ratio
78
Summary 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)
79
Summary 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

80
Tadaki model
Ni Ti
Ni4Ti3
Tadaki et al. model (Trans. JIM 27, 731 (1986))
100
100R//-120B2
81
Multi 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

82
Input 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
83
Refinement 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
84
111R orientation
Ni and Ti not centred at one column anymore
Ti moves 0.35Å Ni moves 0.27Å
Tadaki
Refined structure
lt111gtB2
85
1-10B2 projection
00143 111B2
Ni4Ti3
NiTi
Explains contraction along normal to disc
86
Small precipitates (Ø 50 nm)
87
unexpected compound twin
? deformation twin ? local composition difference
88
two-way shape memory
89
Medical applications
orthodontics

• stents

www.endovasc.com/images/graphics/stent.jpg
90
martensite 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

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other examples of spears
Ni-Mn
splat-cooled Ni65Al35

• little or no deformations
• 110b midrib

93
measures from processed images
94
complex microstructures
austenite
fork
spear
90
120
What happens when two separate plates meet ?
95
single 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

97
bending 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

102
Cubic to orthorhombic example
6 variants

• X 2 for monoclinic

A/M interfaces with twinned martensite to
minimize strain
103
Sample 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
104
Structural data
B2 B19 boundary
Pt
105
Ni3Ti layer

• Intermediate layer

106
Co38Ni33Al29

• Fresnel images of the magnetic domain structure
  observed during an in-situ cooling experiment.

107

• domain walls // (001)

domain walls // (111) twinning
108
SMA 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

110
Crystallization 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)

111
Quantitative EDX measurements

• No chemical differences (within 0.5 at. ) have
  been detected by EDX, thus nucleation is not
  promoted by long range diffusion.

112
Typical example 4 grains

• X -2º
• Y 3.4º

inclined and irregular interfaces several
common directions
113
Other particle

• again lt111gt en lt115gt zones with changing
  interface planes

114
First 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
115
Stereographic 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), )

116
Ideal 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

118
Strain field around precipitate
g 120B2
Conventional two-beam TEM
- due to lattice mismatch - affects any
subsequent transformation (R-phase, B19, ...)
119
High 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
121
Strain contour plot
most of the strain is concentrated alongside the
precipitate (as expected)
122
Intermediate 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

124
Evolution 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

125
Atomic scale

• lattice defects affect mobility and location of
  twin and habit planes
• opens possibility of training and shape memory

126
fit with (non-)linear thermoelasticity

• volume preservation h1 0.93, h3 1.15

(65Ni)
(later a)
127
What 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
129
Concentration Energy Dispersive X-ray (EDX)
50 nm probe
Z. Yang, Scr. Mater. (2005)