Time resolved Laue diffraction of deforming micropillars
Auxiliary Material
Robert Maaß1, Steven Van Petegem1, Helena Van Swygenhoven1*, Peter M. Derlet1,
Cynthia A. Volkert2, Daniel Grolimund1
A1: Methods
A1.1: In-Situ Micro Compression Set-Up:
The experiments were conducted with a micro compression device (MCD), designed to
be mounted on the rotational stage of the six-axis sample manipulator at the microXAS
beamline at the Swiss Light Source. Figure A-1 shows a schematic of the MCD-set-up
and (inset at sample stage) an optical image of a row of Au-pillars, the corresponding
fluorescent map and the approaching indentation tip. The MCD consists of several
independent piezo stages that are used to allow correct positioning and alignment of the
compression head relative to the sample. For the compression head, a truncated conical
diamond indentation tip with 60° opening angle and end tip radius of 11 μm was used.
Several setscrews combined with a high resolution optical microscope served for control
of tilt between the sample and the compression head. All manipulations of the
compression head and the sample as well as the touch down procedure and compression
can be monitored in a high resolution optical microscope.
Figure A-1. Schematic of the experimental set-up, showing the micro compression
device (MCD) in the synchrotron beam line environment and as inset an optical image of
a row of Au pillars with diameters ranging from 10 to 2 μm from right to left. Also
visible in the inset is the approaching flat-punch indenter and the X-ray fluorescence map
of the pillar row.
The MCD is equipped with a Hysitron TriboScope© single axis transducer, which
generates both load and displacement via the applied voltage on the three-plate capacitive
transducer. The displacement range is limited to 5 μm. The force range is limited to 9 mN
and can be measured with sub-μN resolution. All data presented here were measured
under load control with loading rates of 1 μN/sec (2, 4 μm samples) or 0.5 μN/sec (10
μm sample).
Once the indentation tip has been positioned, the pillar to be compressed is mapped using
X-ray fluorescence for sub-micron precision positioning within the X-ray beam. Prior to
white beam Laue diffraction, the touch down of the tip was controlled by the transducer
force feedback output. The tip was driven towards the sample with a velocity of 5 nm/sec
and once a set force threshold was exceeded the tip was considered to be in contact with
the sample.
A1.2 Laue Diffraction:
Polychromatic diffraction patterns were performed using conventional Laue transmission
geometry with photon energies ranging from 2 keV to 24 keV. Kirkpatrick-Baez mirror
focusing optics was used to obtain a beam FWHM of 1.5 to 2.5 μm2 in the focal plane
with a maximum angular divergence of 0.2 x 0.3 mrads. A large area charged-coupleddevice (CCD) detector (Photonic Science, FDI-VHR 150) with 3862 x 2526 pixel
resolution and a pixel size of 31 μm was placed perpendicular to the incident beam
direction. During in-situ measurements Laue patterns were continuously measured, with
CCD exposure times of the order of 10-20 sec. To increase the dynamical range of the
CCD detector a special 16-bit fusion driver was used. This driver automatically takes
accurate sub-range intensity information for the camera images scaled to different
intensity saturation levels in the CCD sensor during the acquisition of one final outputted
image. For further information on the Photonic Science 16-bit Fusion Driver the authors
refer to www.photonic-science.co.uk.
A1.3: Materials:
For the transmission Laue diffraction a special sample holder was designed to minimize
possible interaction with the diffracted beam and the underlying bulk material. For this a
large grained Au foil has been placed on a sample holder with its surface-normal oriented
horizontally. This foil was then locally thinned to a final thickness of ~20 μm. Grains
were detected by electron backscattered diffraction and by a multi-step procedure, larger
cylindrical base structures were cut. The final step included the FIB-machining of the
pillar, which was cut out from the top part of the base structure, resulting in a row of free
standing samples all having the same top level, equally distanced from each other, and
with a geometry giving ~40 degrees of spatial freedom for the diffracted beam. For the
diffraction experiments this row was placed normal to the incoming beam.
A2: Auxiliary Results:
A2.1: Compression of a 2 micron Au Pillar:
As the crystal rotates, the critical resolved shear stress changes and accordingly the
Schmid factors also change. For the 2 micron pillar the five highest Schmid factors are
displayed in Figure A-2 as a function of number of the Laue pattern taken. The 2 micron
pillar initially exhibits dislocation activity on the (1-1-1)[01-1] slip system, which has a
low Schmid factor, corresponding with the observed Laue streaking due to the initial
strain gradient, as is presented for the (02-2) reflection in the movie Movie A-2. The first
crystal rotation is detected when emitting the satellite peak (pattern 25) as is shown in 3D
in Movie A-1, where the (-22-2) reflection first streaks and after reduction emits a
satellite peak. During further deformation (pattern 28-32) the (-1-11)[1-10] slip system
becomes increasingly active, however the strain bursts between pattern 29-30 and 32-33
evidence intermittent activity with the (1-1-1)[01-1]-system which has the second highest
Schmid factor.
Figure A-2. The evolution of the five highest Schmid factors as a function of Laue
diffraction pattern recorded during deformation of the 2μm pillar. The Schmid factors
have been determined from the evolution of the compression axis in the reciprocal space
of the pillar shown in Fig. 3a.
A2.2: Compression of a 10 micron Au Pillar:
As for the 2 micron pillar, the evolution of the vertical axis of the 10 micron pillar in the
reciprocal space is shown in the inverse pole figure (Figure A-3a) demonstrating that the
pillar deforms on the geometrically predicted (1-1-1)[01-1] slip system resulting in
crystal rotation where the vertical axis rotates towards the line [0-10]-[1-10]. Figure A-3b
shows the (-22-2) Laue reflection with the streaking (in white) and rotation (in black)
directions indicated (b) prior to deformation, (c) at 12MPa (Laue pattern 40), (d) at 30
MPa (Laue pattern 90) and (e) at 35 MPa (Laue pattern 105). The anisotropy of the peak
shape before loading evidences a strain gradient, however compared to the 2 micron
pillar the gradient seems to be less pronounced. Despite the initial anisotropic peak shape,
first isotropic peak broadening is observed till 12 MPa (number 40), followed by a
directional streaking reaching a maximum at 30 MPa (number 105). Note that a nonnegligible amount of strain is observed during directional streaking (number 40 and 105)
which was not the case for the 2-micron pillar. This behaviour is well illustrated in the
online movies (Movie A-3, Movie A-4) of the (-22-2) and (02-2) Laue spots. Despite the
presence of the initial strain gradient, the Laue spot splits into a sub-peak moving away
along the classically predicted (1-1-1) rotation direction, with a remaining low intensity
part along the (1-11) rotation direction, conform with the slip lines visible on the SEM
surface of the pillar. Note that the (1-11)[0-1-1] system is the next favoured slip system
predicted classically when the compression axis approaches the borders of the primary
triangle.
Figure A-3. Results obtained from the Laue patterns taken during deformation of the 10
μm pillar. a, Inverse pole figure showing that the 10 μm pillar deforms as geometrically
predicted towards the [0-10]-[1-10] line. The orientation before deformation is indicated
in red. The arrow indicates the sequential evolution of the compression axis. Intensity
distribution of the (-22-2) reflection for the unloaded state (b), at 12 MPa (c), at 30 MPa
(d) and at 35 MPa (e). White lines represent the streaking directions and black lines the
peak path associated with crystal rotation.
A2.3 Supplementary Information Movie Captions
Movie A-1. The movie shows the evolution of the (-22-2) reflection as a 3D surface plot
for the 2 micron sample. The frame numbers correspond to those displayed in the stressstrain curve (Fig. 1). Initially increasing peak streaking during loading is observed
followed by a reduction and the emission of a satellite peak.
Movie A-2. The movie shows the evolution of the (02-2) reflection in an intensity plot
for the 2 micron sample. The frame numbers correspond to those displayed in the stressstrain curve (Fig. 1). Initially increasing peak streaking during loading is observed
followed by a reduction and the emission of a satellite peak. The dotted black lines
indicate the peak movement direction associated with classical crystal rotation and the
dotted white line indicates the streaking directions for the (1-11)[0-1-1] slip system.
Movie A-3. The (-22-2) reflection for the 10 micron sample is shown in an intensity plot.
The peak evolution is shown up to the 150th Laue pattern taken, as indicated on the stressstrain curve (Fig. 1). The dotted black lines indicate the peak movement direction
associated with classical crystal rotation for the (1-11) and (1-1-1) slip planes.
Movie A-4. The (02-2) reflection for the 10 micron sample is shown in an intensity plot.
The peak evolution is shown up to the 150th Laue pattern taken, as indicated on the stressstrain curve (Fig. 1). The dotted black lines indicate the peak movement direction
associated with classical crystal rotation for the (1-11) and (1-1-1) slip planes.