strength and texture of pt compressed to...
TRANSCRIPT
Strength and texture of Pt compressed to 63 GPa
Susannah M. Dorfman,1,a) Sean R. Shieh,2 and Thomas S. Duffy3
1Earth and Planetary Science Laboratory, Ecole Polytechnique F�ed�erale de Lausanne, Station 3, CH-1015Lausanne, Switzerland2Department of Earth Sciences, University of Western Ontario, London, Ontario N6A 5B7, Canada3Department of Geosciences, Princeton University, Princeton, New Jersey 08544, USA
(Received 18 September 2014; accepted 28 January 2015; published online 10 February 2015)
Angle- and energy-dispersive X-ray diffraction experiments in a radial geometry were performed
in the diamond anvil cell on polycrystalline platinum samples at pressures up to 63 GPa. Observed
yield strength and texture depend on grain size. For samples with 70–300-nm particle size, the yield
strength is 5–6 GPa at �60 GPa. Coarse-grained (�2-lm particles) Pt has a much lower yield
strength of 1–1.5 GPa at �60 GPa. Face-centered cubic metals Pt and Au have lower strength to
shear modulus ratio than body-centered cubic or hexagonal close-packed metals. While a 300-nm
particle sample exhibits the h110i texture expected of face-centered-cubic metals under
compression, smaller and larger particles show a weak mixed h110i and h100i texture under
compression. Differences in texture development may also occur due to deviations from uniaxial
stress under compression in the diamond anvil cell. VC 2015 AIP Publishing LLC.
[http://dx.doi.org/10.1063/1.4907866]
I. INTRODUCTION
The deformation behavior of materials is fundamental to
physics, engineering, and geoscience and is determined by
both elastic and plastic properties.1 While a variety of meth-
ods can be employed to independently measure elasticity
and plasticity at ambient conditions, X-ray diffraction is one
of the only established techniques that can be used to explore
these properties in situ at extreme pressures.2–4 Existing
diffraction-based methods use diffraction line shifts2–4 and
widths5,6 to constrain material deformation but typically suf-
fer from uncertainties due to confounding of multiple varia-
bles and limited control and measurement of experimental
conditions such as the applied stress.5,7 The uncertainties in
high-pressure measurements of strength and anisotropy can
be evaluated by systematic study of simple materials such as
platinum metal.
Platinum (Pt) is a face-centered cubic (FCC) metal and
does not undergo phase transitions up to multi-megabar pres-
sures.7,8 Due in part to its simple structure, Pt is widely used
in high-pressure experiments as a pressure calibrant and laser
absorber.9 Nanoparticles of Pt10 and other metals11 have also
been observed to have anomalously low compressibility, and
this has possible implications for pressure calibration using
metal powders. Recently, Pt has also been used as a devia-
toric strain marker: the success of laser annealing or pressure
media in minimizing deviatoric stresses has been judged by
comparison to the strength of Pt as a function of pres-
sure.8,12–15 The sensitivity of Pt to deviatoric stress due to its
strength and elastic properties is also a source of systematic
uncertainty in pressure calibration.8,14
In previous high-pressure experimental studies, Kavner
and Duffy concluded that Pt is one of the hardest FCC
metals16 and unusually strong for its shear modulus,1 while
Singh et al. found that Pt is weak.7 The key difference
between these studies may be grain size. In the former study,
sample grain size was not characterized, but in the latter,
much higher strength was observed for 20-nm Pt grains rela-
tive to 300-nm grains.7 The Hall-Petch effect, i.e., higher
strength at nm-scale grain size, is consistent with this differ-
ence. However, these two previous studies of Pt reached
their different conclusions using different X-ray diffraction
geometries (radial16 vs. axial7) and diagnostic techniques
(diffraction line shifts16 vs. line broadening7).
Diffraction-based measurements of deformation in a
diamond anvil cell (DAC) can be performed in either an
axial geometry (with incident X-rays along the loading axis)
or in a radial geometry (with incident X-rays perpendicular
to the loading axis). The radial geometry provides the most
detailed measurement of strain at high pressures in the dia-
mond anvil cell. Unlike the axial geometry used in the study
by Singh et al.,7 this technique samples a wide range of
crystallite orientations and is sensitive to elastic constants
and texture as well as stress. Radial X-ray diffraction of plat-
inum has been limited to pressures below 24 GPa so far. In
this work, we re-examine the effect of grain size on the
strength of platinum. We also extend measurements of the
strength and deformation texture of Pt by X-ray diffraction
in a radial geometry to 63 GPa.
II. THEORETICAL BACKGROUND
Compression of polycrystalline materials in the diamond
anvil cell produces non-hydrostatic stresses due to the effects
of both uniaxial loading (macro-stress) and of stress hetero-
geneities at grain boundaries (micro-stress).2,3 In the dia-
mond anvil cell, the maximum stress, r3, is approximately
aligned with the compression axis and the minimum stress,
r1, is in the plane of the gasket. The differential stress, t, is
a)Author to whom correspondence should be addressed. Electronic mail:
0021-8979/2015/117(6)/065901/9/$30.00 VC 2015 AIP Publishing LLC117, 065901-1
JOURNAL OF APPLIED PHYSICS 117, 065901 (2015)
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defined as the difference between these stresses, r3 � r1.
Differential stress reflects the non-hydrostatic stress compo-
nents that result in deviatoric strain. For a given lattice plane
in a crystallite, the deviatoric strain depends on its orienta-
tion relative to the compression axis and the elastic anisot-
ropy of the crystal. Microscopic deviatoric stresses also
produce micro-strains in the polycrystalline aggregate. Both
macro-strain and micro-strain are limited by the yield
strength of the material, which may vary with pressure, grain
size, and deformation rate.1 After yielding, the total strain is
a combination of elastic and plastic deformation.17–21
Lattice strain analysis of radial X-ray diffraction data
has been described in detail elsewhere;2–4 here we summa-
rize the major relations used to calculate strain and stress in
energy- and angle-dispersive diffraction modes. The varia-
tion of measured lattice spacings, dm(hkl), can be described
by a d-spacing resulting from the hydrostatic component of
stress, dp(hkl), plus a non-hydrostatic component:
dmðhklÞ ¼ dpðhklÞ½1þ ð1� 3 cos2wÞQðhklÞ�: (1)
The angle, w, is defined between the lattice plane normal
and the direction of maximum stress. w is related to the dif-
fraction angle, h, and the azimuthal orientation of the dia-
mond anvil cell relative to the detector, d, (defined as 0� at
the diamond anvil cell compression axis) as cos w¼ cos dcos h (Figure 1). Q(hkl) is a function of t and the shear modu-
lus G, where GR(hkl) is the modulus under iso-stress (Reuss
bound) conditions and GV under iso-strain (Voigt bound):
Q hklð Þ ¼ t
3
a
2GR hklð Þ þ1� a2GV
� �: (2)
The parameter a is a measure of the degree of stress/
strain continuity across crystallite boundaries. Under iso-
stress conditions, a¼ 1; measured values of a typically range
from 0.5 to 1, although it has been suggested that values
greater than 1 may occur depending on the elastic anisotropy
of the material.22,23 For materials of cubic symmetry, the fol-
lowing equations relate GR(hkl) and GV to the elastic compli-
ances, Sij, and the Miller indices of the lattice plane:
1
2GR¼ S11 � S12 � 3SC hklð Þ; (3)
S ¼ S11 � S12 �S44
2; (4)
1
2GV¼ 5
2
S11 � S12ð ÞS44
3 S11 � S12ð Þ þ S44½ � ; (5)
C hklð Þ ¼ h2k2 þ k2l2 þ l2h2
h2 þ k2 þ l2ð Þ2: (6)
In Eqs. (3) and (4), S is a measure of the elastic anisotropy of
a cubic crystal.
As a complement to lattice strain analysis, diffraction
line widths can be used to constrain micro-strain, g, and
grain size, D.5,7 For diffraction using monochromatic
X-rays,24,25
whkl cos hhklð Þ2 ¼ kD
� �2
þ g2hkl sin2hhkl: (7)
In this equation, whkl is the full width at half maximum
of the diffraction peak and k is the X-ray wavelength. The
slope of the linear relationship between (whklcos hhkl)2 and
FIG. 1. Schematic of radial-geometry
X-ray diffraction experiments in
energy-dispersive and angle-dispersive
modes.
065901-2 Dorfman, Shieh, and Duffy J. Appl. Phys. 117, 065901 (2015)
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sin2 hhkl terms is used to determine average micro-strain,
while the intercept provides the grain size. An additional cor-
rection is needed to account for instrumental broadening.
Lattice strain theory has been successfully applied to the
high-pressure deformation of metals, ceramics, and miner-
als.1 Both stress and elastic constants have been derived for
materials undergoing purely elastic deformation.16,23,26–29
However, on compression beyond the yield strength, elastic
constants were observed to deviate from values derived from
other techniques such as ultrasonic interferometry or
Brillouin spectroscopy.17,27 For this case, more complex
models have been developed to account for plastic deforma-
tion.30 When the elastic moduli are known independently,
the lattice strain technique has been demonstrated to provide
accurate estimates of non-hydrostatic stress.31
III. METHOD
Polycrystalline Pt samples were obtained with three dif-
ferent particle sizes. Particle shapes and sizes were charac-
terized by scanning electron microscopy. The bulk sample
(designated B) is made up of irregular platelets with median
Feret diameter �2 lm and minimum dimension �450 nm
(supplementary Figure 1).32 Nano-grained samples N1 and
N2 are sub-spherical particles with median diameters 300
and 70 nm and minimum diameters 70 and 40 nm, respec-
tively (supplementary Figures 2 and 3).32 We note that parti-
cle sizes measured by microscopy represent upper bounds on
grain size of these samples.
Each powdered sample was packed in a 100-lm sample
chamber drilled in an X-ray transparent beryllium (Be) gas-
ket. X-ray diffraction of the gasket material shows doublets
for each Be peak, suggesting the presence of both Be and an
exsolved Be-rich alloy phase due to impurities in the gasket.
We also observed hexagonal BeO, most likely resulting from
oxidation of Be grain surfaces. All samples were loaded in
symmetric or panoramic diamond anvil cells with 300-lm
diameter diamond culets. A 10–20-lm diameter piece of Mo
was loaded at the center of the diamond culet on one side as
position marker. Upon compression, sample chamber diame-
ters typically shrank to 50–80 lm.
Both energy-dispersive (EDXD) and angle-dispersive
(ADXD) X-ray diffraction experiments were performed at
beamline X17C of the National Synchrotron Light Source.
Both methods were used for experiments with samples B and
N1. Sample N2 was examined only with the ADXD method.
Diamond anvil cells were mounted such that incident X-rays
entered and exited the sample radially through the Be gasket
(Figure 1).
In energy-dispersive X-ray diffraction experiments in a
radial geometry (Figure 1),33 the symmetric DAC was
rotated around the beam axis to angles d¼ 0�, 24�, 35�, 45�,55�, 66�, and 90�. The incident X-ray beam size was �50
� 50 lm. Diffracted X-rays were collected using a solid-
state Ge detector positioned at diffraction angle
2h¼ 10�–12�. Detector energy calibration was performed
using fluorescent standards, and detector angle was cali-
brated with an Au standard.
In radial angle-dispersive X-ray diffraction experiments
(Figure 1),34 the panoramic DAC was mounted at a fixed
angle and the diffracted X-rays were collected on a charge-
coupled device (MarCCD). Due to space limitations in the
X17C experimental station, the detector was laterally
displaced relative to the beam center. As a result, diffraction
Inte
nsity
(ar
bitr
ary
units
)
2.42.22.01.81.61.41.21.0
d-spacing (Angstroms)
111
200
220
222
311
400
Be
Be
Be
Be
Be
Mo
Mo M
o
Be
0
24
35
45
55
66
48 GPa
δ=90º
FIG. 2. Energy-dispersive diffraction patterns for bulk Pt (sample B) at
48 GPa.
FIG. 3. Angle-dispersive diffraction pattern for nano-grained Pt sample N1
at 52 GPa. X and Y axes describe the locations of pixels on the CCD detec-
tor. Each pixel is 79.6 � 79.6 lm.
065901-3 Dorfman, Shieh, and Duffy J. Appl. Phys. 117, 065901 (2015)
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was observed at 2h values of more than 25�, but over only a
limited azimuthal range of 80�–190�. Detector distance and
orientation were calibrated with CeO2 and Au standards. The
wavelength of the monochromatic X-rays was 0.4066 A, and
beam size was �20 � 30 lm.
IV. RESULTS
Samples were compressed to maximum pressures of
48–63 GPa. After each pressure increase, samples were
allowed to relax for 30–120 min, or until the measured pres-
sure stabilized. Example diffraction patterns from an EDXD
measurement of sample B at 48 GPa are shown in Figure 2.
An example two-dimensional ADXD pattern of sample N1
at 52 GPa is shown in Figure 3. All diffraction lines corre-
spond to the Pt sample, Mo marker, and Be and BeO in the
gasket. Gasket diffraction peaks are highly textured and
invariant with pressure. Lattice d-spacings of Pt and the
weak Mo marker change with azimuth d from the loading
axis due to differences in stress. Texture development in Pt
can also be observed as intensity variations along the azi-
muthal angle, d, with different maxima for different lattice
orientations.
EDXD patterns were analyzed by fitting peaks to Voigt
lineshapes. ADXD patterns were integrated using FIT2D35 at
azimuthal intervals of 4�–5� over a range from d¼ 45�–145�,the maximum azimuthal range at which the (222) line is
observed at all pressures. Full-profile strain and texture anal-
ysis were performed with MAUD software36 (details are
given in supplementary material).32 Pressure was determined
from the lattice parameter of Pt as measured at d¼ 55�, the
angle at which the measured d-spacing corresponds to the
hydrostatic d-spacing under uniaxial conditions.3 As in
the previous studies of strength and deformation of Pt,7,16 we
calibrate pressure with the equation of state of Holmes et al.9
A. Line shift analysis
For each diffraction line, a linear relationship between
lattice spacing and the orientation function 1–3cos2w is
observed (Figure 4 and supplementary Figure 4).32
Curvature in this relationship may be due either to stress var-
iations in the diffraction volume or non-uniaxial stress. For
EDXD data, Q(hkl) was determined from the slope and inter-
cept of this linear relationship as in Eq. (1). For ADXD data,
Q(hkl) in Pt was refined from full-profiles in MAUD (Figure
5). Pt diffraction peak widths were fit by refining grain size
and micro-strain. We fit each Q(hkl) and the orientation of
the maximum strain. The angle between the maximum strain
and the compression axis, b, was 6��27� at maximum
FIG. 4. Lattice parameter and d-spac-
ings for Pt from EDXD for nano-
grained sample N1 at 61 GPa.
Spacings for (111) planes are shown in
red dots, (200)¼ blue squares,
(220)¼ yellow up-pointing triangles,
(311)¼ green down-pointing triangles,
and (222)¼ pink diamonds. Ranges of
d-spacings on plots are scaled to a con-
stant percentage of the value at
w¼ 55�.
065901-4 Dorfman, Shieh, and Duffy J. Appl. Phys. 117, 065901 (2015)
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pressures reached for both ADXD and EDXD measurements
(supplementary Figure 4).32 This deviation from uniaxial
stress has been observed in other studies37 and may be due to
deformation of the gasket hole at low pressures and bending
of diamond anvils at higher pressures. The relative impor-
tance of these two mechanisms changes from run to run. In
one sample, the angle b was observed to increase to 20�–30�
by �10 GPa (gasket deformation), while other samples
exhibited more continuous increase at higher pressures (dia-
mond bending). By correcting the orientation of the ADXD
data, the curvature of lattice spacing vs. 1–3cos2w can be
almost entirely removed (supplementary Figure 4),32 sug-
gesting that the stress orientation is the dominant cause of
observed non-linearity.
The observed lattice strain increases strongly with pres-
sure until the sample yields, above which pressure the lattice
strain increases at a weaker rate (Figure 6(a)). Difference
between EDXD and ADXD measurements represents run-to-
run differences in the magnitude and orientation of devia-
toric stress. Higher strain was observed for the nano-grained
samples N1 and N2 at all pressures relative to the bulk sam-
ple. For the bulk sample, we could not resolve the pressure
at which yielding occurred due to the low strain exhibited
and the size of the pressure steps. For samples N1 and N2,
yielding occurred at �9 GPa, similar to previous observa-
tions of sub-micron Pt.7,16
According to purely elastic models, the strain function
Q(hkl) is linearly related to the crystal orientation function
C(hkl) as in Eqs. (2)–(6). The slope of this linear relationship
is related to the elastic anisotropy, S, of Pt as well as the
magnitude of the differential stress. Due to the high elastic
anisotropy of Pt,8 the observed Q(hkl) depends strongly on
lattice plane (Figure 6(b)). The linear relationship between
Q(hkl) and C(hkl) can be used to determine the change in
elastic anisotropy with pressure. The measured elastic anisot-
ropy is lower than that predicted for Pt by ab initio density
functional theory.38 This discrepancy is due to effects of
plastic deformation on Q(hkl). Plastic deformation can be
neglected if elastic compliances Sij are fixed for analysis of
stress conditions.
While the elastic constants of Pt are well-constrained at
1 bar and high temperature, their evolution with pressure has
not been determined by experiment. Only the elastic modu-
lus C44 was measured by ultrasonic interferometry (and only
to pressures <0.3 GPa).39 The elastic constants of Pt were
computed by ab initio density functional theory up to
660 GPa.38 As the authors noted, the predicted ambient pres-
sure derivative of the C44 modulus, C440 ¼ dC44/P, is signifi-
cantly larger than the ultrasonic value.39 In this study (as in
the previous study by Singh et al.7), we use the ultrasonic
value for C440 and other zero-pressure elastic moduli and
FIG. 5. Full-profile refinement of Pt sample N1 at 52 GPa from MAUD pro-
gram (above¼fit, below¼ binned data). Pt diffraction lines are curved and
smoothly textured due to non-hydrostatic stress state and plastic deforma-
tion. The diffraction pattern from the gasket is composed of Be doublets
with large, randomly oriented grains and BeO with finer grains.
FIG. 6. a) For sample N1 (300 nm particles), the strain function Q(hkl) in
the (111) diffraction peak for ADXD (dots) and EDXD (squares) runs. The
change in slope at �9 GPa indicates yielding.1 (b) Variation of Q(hkl) for
different diffraction peaks at 61 GPa.
065901-5 Dorfman, Shieh, and Duffy J. Appl. Phys. 117, 065901 (2015)
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pressure derivatives from density functional theory.38,39 The
computed and ultrasonic values for zero-pressure elastic con-
stants and their pressure derivatives were extrapolated using
the finite strain equations.40 One additional parameter is
required to solve Eqs. (2)–(6): the stress-strain continuity pa-
rameter, a. Previous analysis of both peak width and line
shifts data for Pt suggested that the best value for a is 0.6.7
We calculate differential stress assuming a to be either 0.6 or
1 and observe a difference in t of �1.5%, much lower than
other uncertainties. Differential stress assuming a¼ 0.6 is
plotted in Figure 7.
Differential stress in the bulk Pt sample reaches a maxi-
mum of 1–1.5 GPa at 60 GPa (Figure 7). This is consistent
with axial diffraction measurements of linewidths that are
used to constrain the strength of Pt with 300-nm grain size7
but considerably lower than previous radial diffraction meas-
urements of line shifts.16 We concur with Singh et al.7 that
the difference between these studies is likely due to grain
size differences. The nano-scale samples, N1 and N2, exam-
ined in this study exhibited much higher yield strengths of
5–6 GPa at 60 GPa. These stresses are comparable to those
observed in Ref. 16 and slightly lower than those observed in
Ref. 7 for 20-nm grains, consistent with the particle size of
70–300 nm.
B. Peak width analysis
Diffraction peak widths typically increase with pressure
due to increasing micro-strain and stress gradient across the
sample. Grain size reduction may also increase peak widths
for nanocrystalline samples. Peak broadening in these
experiments was analyzed by peak fitting as well as analysis
using MAUD.
Observed peak widths were consistent with grain sizes
similar to particle sizes observed by SEM and remained
approximately constant with pressure (Figure 8 and supple-
mentary Figure 5).32 For �300-nm N1 sample particles,
grain size determined by peak widths was 200–400-nm.
Diffraction peak widths of the bulk-grained sample were
within error of the instrument resolution at loading. Fits to
the bulk sample peak widths at 20–60 GPa yield a grain size
of �1 lm, consistent with the particle size observed by
SEM. For the two finer-grained samples, the width of dif-
fraction peaks increased below the yield stress, decreased
immediately after yielding, and remained constant above
�10–20 GPa (Figure 8). Changes in peak widths are most
likely due to buildup of micro-strain before yielding and
release of micro-strain through plastic flow after yielding.
Other possible mechanisms for peak sharpening are grain
growth, which is unlikely at 300 K, or collapse of the gasket
hole, reducing the pressure gradient over the measured sam-
ple.41 No significant peak broadening is observed above the
12
10
8
6
4
2
0
Diff
eren
tial S
tres
s (G
Pa)
706050403020100
Pressure (GPa)
Nano-grains
Bulk grains
Method:Axial diffraction
20-nm grains (Ref. 7) 300-nm grains (Ref. 7)
Radial diffraction (Energy-dispersive) 300-nm particles (This study) Size unknown (Ref. 16) 2-μm particles (This study)
Radial diffraction (Angle-dispersive) 70-nm particles (This study) 300-nm particles (This study) 2-μm particles (This study)
FIG. 7. Maximum differential stress, or yield strength, measured for Pt sam-
ples of different grain size. Data from this work are shown with filled sym-
bols, with squares for EDXD and circles for ADXD (red¼ sample B,
green¼ sample N1, and cyan¼ sample N2). Data from previous work are
20-nm (open diamonds) and 300-nm (filled diamonds) grain sizes studied by
axial diffraction peak width analysis in Ref. 7 and unknown-size grains
(open squares) studied by EDXD in Ref. 16. Stress was calculated with
a¼ 0.6.
0.5
0.4
0.3
0.2
0.1
0.0
Diff
ract
ion
peak
wid
th a
t ψ=
90°
(deg
rees
)
50403020100
Apparent Pressure at ψ=90° (GPa)
111200
70 nm
300 nm
2 μm
FIG. 8. Diffraction peak widths measured for each particle size
(red¼ sample B, green¼ sample N1, and cyan¼ sample N2) in ADXD pat-
terns at w¼ 90�, corresponding to the axial geometry. Apparent pressure is
computed from d-spacings observed at w¼ 90�. Due to lattice strain, d-spac-
ings are larger and apparent pressure lower than those determined at
w¼ 54.7�, the orientation of approximately hydrostatic stress, by up to 8,
12, and 17 GPa for samples B, N1, and N2, respectively.
065901-6 Dorfman, Shieh, and Duffy J. Appl. Phys. 117, 065901 (2015)
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yield stress indicating no significant decrease in grain size
due to yielding.
C. Texture analysis
Nano-particle samples initially exhibited continuous,
untextured diffraction rings. For the bulk sample, diffraction
rings are randomly textured due to large grain size relative to
the X-ray beam. Upon compression to comparable pressures
of 49–52 GPa (Figures 9(a)–9(c)), stronger textures were
observed for the �300-nm particle size than for smaller or
larger particles. In addition, the nature of the texture devel-
opment differs with particle size. In sample N1 (300-nm
size), the grains are oriented to exhibit a maximum in (111)
at minimum stress (Figure 9(b)). However, a different
texture was observed in the other two samples, with a mini-
mum in the (111) planes at the minimum stress orientation
(Figures 9(a) and 9(c)).
These textures were evaluated from ADXD experiments
by refinement in MAUD software (Figures 9(d)–9(f)). For
sample N1, the texture index is observed to increase strongly
from 13 GPa, just above the yield pressure, to 34 GPa, above
which pressure it is saturated at �3 maximum of a random
distribution (m.r.d.). The deformation texture in this sample
is a h110i fiber texture typical of FCC metals under compres-
sion.42 The other two samples are weakly textured, with
texture index �1.1 at maximum pressures. The maximum
intensity is found in the h100i direction, more typical of
tension in FCC metals at ambient pressure.42
Different textures observed for different particle sizes
indicate changes in deformation mechanisms. The main
deformation mechanisms in cold-compressed powders are dis-
location creep and grain boundary processes. Which of these
mechanisms dominates depends on multiple factors including
grain size, pressure, temperature, and strain rate. Dislocation
creep is thought to dominate deformation in coarse (>100-nm
grain size) metals and produces strong lattice-preferred orien-
tation under compression. With decreasing grain size, disloca-
tions become increasingly unfavorable, and grain boundary
sliding and rotation dominate deformation in metals with
grain size smaller than �20-nm.43–46 Increasing pressure may
support formation of dislocations even in 3-nm particles.44
Unlike dislocation creep, grain rotation was reported to ran-
domize texture.15,44,47,48 In addition, this change in deforma-
tion mechanism at small grain sizes was suggested to cause a
decrease in strength.45,46
The bulk Pt sample in this study surprisingly does not
develop a strong compression texture, yet grain-boundary-
mediated processes are not expected to be dominant. The
differential stress supported by the sample is low, however,
and confirms that the bulk grains are relatively weak. In
addition, the irregular particles in this sample should inhibit
grain boundary sliding and rotation. The weak tension
texture in this sample may reflect low statistics due to large
grain size. Random texture from loading of the bulk sample
persists at the maximum pressures examined.
The elastic strain observed in the two Pt nano-powders
in this study is similar, but texture development differs. The
FIG. 9. a)–(c) Strain and texture in Pt 111 line at 49–52 GPa for samples with different particle sizes. The red horizontal line marks the orientation of the gasket
plane (90� from the DAC axis), which is the minimum stress direction for uniaxial compression. (d)–(f) Inverse pole figures showing texture development
along the compression axis at 49–52 GPa in each sample. Texture was fit in MAUD with the E-WIMV model and fixed cylindrical geometry (see supplemen-
tary material).32
065901-7 Dorfman, Shieh, and Duffy J. Appl. Phys. 117, 065901 (2015)
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70-nm and 300-nm particles are both stronger than previ-
ously measured 300-nm grain size Pt but weaker than 20-nm
grain size Pt.7 Since only the particle size is known, each
sample may be composed of clumps of smaller grains. The
weaker texture in the 70-nm particles may indicate that grain
sizes in this sample are small enough to promote grain
boundary sliding and rotation as a primary mechanism of
plastic deformation. Alternatively, the stronger texture in the
300-nm-particle sample may be due to the large deviation
from uniaxial stress in this experimental run (supplementary
Figure 4(a)). The h100i texture in the 70-nm and bulk Pt
samples would then be more representative for Pt under pure
uniaxial stress.
V. IMPLICATIONS
While earlier radial diffraction experiments16 reported
that platinum could be unusually strong for an FCC metal
with low shear modulus, consideration of grain size effects7
brings the behavior of this metal into agreement with the
general trends at high pressure displayed by other metals.
Our radial diffraction results for multiple grain sizes of Pt
confirm the low strength of bulk Pt observed by the axial dif-
fraction method by Singh et al.7 Like Au, another FCC
metal, Pt exhibits a differential stress/shear modulus ratio
lower than that of metals with body-centered cubic (BCC) or
hexagonal close-packed (HCP) structures (Figure 10).
The strong dependence of strength on grain size
increases the importance of careful characterization of grain
sizes of materials used as differential stress markers and cali-
brants. The sub-micron Pt samples examined in this work
were also used as differential stress markers in previous stud-
ies of the equation of state of various materials including
MgGeO3, CaF2, and Gd3Ga5O12.12,49,50 Lattice strain analy-
sis of Pt was performed using the axial geometry in these
cases. The effectiveness of Ne or He pressure media8 and
laser annealing12,49,50 for reducing deviatoric stresses at
Mbar pressures was evaluated by comparison to the yield
strength of the Pt marker. The high strength of sub-micron
Pt confirms that the observed differential stress in these pre-
vious studies was low relative to the yield strength, and
quasi-hydrostatic conditions were achieved. For all similar
measurements, the yield strength and grain size of the
marker are critical for this evaluation of deviatoric stress.
However, knowledge of the initial grain size of the
strain marker may not be sufficient to fully constrain the
strength at high pressures and temperatures. Grain size
changes with pressure and/or temperature may occur and be
difficult to detect. For example, reversible pressure-induced
grain size reduction has been reported previously but is not
yet understood;7,51 this may be due to the difficulty in sepa-
rating the effects of grain size, micro-strain, and plastic de-
formation on diffraction peak widths. In laser heating
studies, both reduced strength and grain growth are expected.
This uncertainty in grain size is thus a limitation to the use
of differential stress markers in diamond anvil cell
experiments.
This study provides an important test of different techni-
ques for characterizing deformation at high pressure. Our
results using multiple techniques demonstrate the consis-
tency of measurements of the strength of bulk and nano-
grained Pt by analysis of diffraction peak widths7 and both
energy-dispersive16 and angle-dispersive X-ray diffraction in
a radial geometry. The major sources of uncertainty in these
measurements are the poorly constrained high-pressure
elastic properties, stress-strain continuity factor, and non-
uniaxial stress in the diamond anvil cell. By measuring
diffraction across a wide and continuous range of orienta-
tions and stress conditions, radial ADXD provides the most
complete information for reducing these uncertainties.
VI. SUMMARY
Strength and deformation of Pt powder samples with
various grain sizes were examined at pressures up to 63 GPa
by radial diffraction experiments in both energy- and angle-
dispersive modes. For micron-scale grain size samples,
the yield strength of Pt reaches 1–1.5 GPa at �60 GPa.
For nanometer-scale grain sizes, the yield strength is much
larger: differential stress of 5–6 GPa is observed at
�60 GPa. These observations confirm that contrasting val-
ues of the strength of Pt in previous axial-geometry studies7
are the result of differences in grain size. Analysis of dif-
fraction peak widths suggests no significant grain size
reduction due to yielding or compression. Texture develop-
ment in the sample with �300-nm particles is strong and
typical of FCC metals under compression. For both larger
and smaller particle sizes, observed texture is weaker and
more typical of mixed compression and tension in FCC met-
als. Texture style may also depend on non-uniaxial stress.
Platinum, like FCC gold, exhibits a lower strength to shear
modulus ratio at high pressure than metals with BCC or
HCP structures including Mo, Re, and W. Smaller grain
sizes exhibit higher yield strength; characterization of the
grain size is thus critical to analysis of strain and stress in
high-pressure experiments.
3.0x10-2
2.5
2.0
1.5
1.0
0.5
0.0
Diff
eren
tial s
tres
s/S
hear
mod
ulus
706050403020100
Pressure (GPa)
Mo
Re
Au
W
Pt (this study)
FIG. 10. Strength to shear modulus ratio for metals at high pressures. Data
shown from this study are from the bulk sample. FCC Au26,52 and Pt are
weaker than BCC and HCP metals26,52,53 studied to date.
065901-8 Dorfman, Shieh, and Duffy J. Appl. Phys. 117, 065901 (2015)
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ACKNOWLEDGMENTS
Z. Chen, X. Hong, and S. Ghose supported beamline
operations at X17C. L. Miyagi provided helpful advice in
data analysis with MAUD. We thank A. K. Singh and two
anonymous reviewers for comments that improved this
manuscript. Electron microscopy was performed at the at the
Centre Interdisciplinaire de Microscopie Electronique at the
Ecole polytechnique f�ed�erale de Lausanne. This research
was partially supported by COMPRES, the Consortium for
Materials Properties Research in Earth Sciences under NSF
Cooperative Agreement No. EAR 10-43050. Use of the
National Synchrotron Light Source, Brookhaven National
Laboratory was supported by the U.S. Department of
Energy, Office of Science, Office of Basic Energy Sciences
under Contract No. DE-AC02-98CH10886.
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