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Journal of
Applied
Crystallography
ISSN 0021-8898
Powder diffraction beyond the Bragg law: study of palladium
nanocrystals
Zbigniew Kaszkur
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J. Appl. Cryst. (2000). 33, 1262–1270
Zbigniew Kaszkur
Palladium nanocrystals
research papers
Powder diffraction beyond the Bragg law: study of
palladium nanocrystals
Journal of
Applied
Crystallography
ISSN 0021-8898
Zbigniew Kaszkur
Received 24 February 2000
Accepted 13 July 2000
Institute of Physical Chemistry, Polish Academy of Sciences, Kasprzaka 44/52, 01-224, Warszawa,
Poland. Correspondence e-mail: [email protected]
# 2000 International Union of Crystallography
Printed in Great Britain ± all rights reserved
An experimental method of measurement of the subtle changes of structure of
metal nanocrystals occurring on chemisorption of oxygen, interaction with inert
gas and hydrogen, etc., is proposed. The measured patterns and their evolution
are interpreted via atomistic simulations. Described are quantitative observations of the changes in peak position, intensity and half width of the 111
diffraction peak of a palladium catalyst caused by modifying the gaseous
environment. The results of the measurements are in line with an atomistic
model proposed earlier and prove that the measured average lattice constant of
palladium clusters evolves according to their surface relaxation. The evolution
of the measured peak intensity suggests surface ordering effects and was used to
propose a detailed structural model of nanocrystalline metal particles. The
transition of palladium into -Pd-H in hydrogen under normal conditions was
used as a structure probe and provided evidence for the presence of icosahedral
clusters in a highly dispersed catalyst. The icosahedral phase is not signi®cantly
modi®ed under hydrogen atmosphere and does not transform into the hydride.
1. Introduction
Metallic nanoparticles of size 2.0±6.0 nm are known to
demonstrate properties that are different from those speci®c
to the bulk material. For various metals, it has been shown that
the nanoparticles are characterized by a much lower melting
point (Buffat & Borel, 1976; Peters et al., 1998), a noticeable
decrease in the interlayer spacing next to the surface (Lamber
et al., 1995; Barnes et al., 1985) and possible signi®cant
modi®cations of their magnetic and quantum properties
(Schaaff et al., 1997; Apsel et al., 1996). It has also been shown
that during thermal and simple chemical treatment, the
change in the interatomic spacing next to the surface may be
experimentally observed through the change in the average
lattice constant, using standard powder diffraction techniques
(Kaszkur, 1998). For such small clusters, one faces, however, a
new fundamental dif®culty in understanding their diffraction
patterns. Although the peaks resemble those of a polycrystalline pattern, with decreasing cluster size the peaks give
different values of the lattice parameter when they are
indexed as for polycrystals; thus indexing makes limited sense
(Kaszkur, 2000). To interpret these patterns, one needs a tool
that makes no use of structural periodicity and reaches beyond
the Bragg law.
The structural evolution of nanocrystals during mild
physical and surface chemical processes expresses itself in the
diffraction pattern through peak shifts and changes in the
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Zbigniew Kaszkur
Palladium nanocrystals
peak shape, width and intensity. The latter point concerning
evolution of the intensity has already been exploited for
platinum nanoparticles (Gnutzmann & Vogel, 1989). For small
clusters, the scattered peak intensity is approximately
proportional to the number of atoms (Kaszkur, 2000) and the
maximum change of the peak intensity on the reordering of
the cluster surface is roughly equal to the particle dispersion
(i.e. to the ratio of the number of surface atoms to the total
number of atoms). For the cluster sizes considered here, the
surface rearrangement may result in a 20±50% change in the
peak intensity. This suggests that much smaller changes
corresponding to more subtle surface processes may be
recorded in a properly designed experiment. Additionally,
monitoring of the peak width and position, which are sensitive
to surface-relaxation effects, provides more information,
interpretable via modelling.
The aim of the present work is to report the experimental
realisation of a powder diffraction technique able to monitor
subtle changes in a diffraction pattern of a metal nanopowder
occurring on changes of the gas atmosphere, and to interpret
these changes on the basis of molecular modelling. The
presented experimental data are for a palladium nanocrystalline catalyst supported on silica. The basis for the understanding of the experimental data has been developed by
atomistic modelling and published separately (Kaszkur, 2000).
Nevertheless, for the sake of a coherent line of reasoning,
throughout this paper the experimental observations are
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J. Appl. Cryst. (2000). 33, 1262±1270
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discussed with reference to arguments originating from
atomistic modelling, including arguments not covered in the
earlier work (Kaszkur, 2000).
All diffraction patterns presented in this article are for the
Ê ).
wavelength of Cu K ( = 1.5418 A
2. Experimental procedure
Diffraction patterns of palladium nanoparticles supported on
amorphous SiO2 were collected with a Siemens 5000 generator
using an INEL CPS120 position-sensitive detector (PSD), a
¯at graphite monochromator and a homemade camera for in
situ studies. The camera (Fig. 1) was covered with a stainlesssteel cap, equipped with a beryllium X-ray window, and sealed
to the base with a Viton gasket. Its design is based on a device
described in the literature (ZielinÂski & BorodzinÂski, 1985),
adapted to work with the PSD. The camera allowed collection
of powder data in the angular range 10±100 (2) using ¯atsample non-focusing geometry, enabled controlled ¯ow of
reaction gases and heating of the sample to 873 K, and was
vacuum proof. The latter point appeared to be crucial for
maintaining an oxygen-free atmosphere and achieving relatively quick full exchange of the gases. Special care has been
taken to supply oxygen-free inert gas (Ar) and to monitor the
oxygen content in the outlet gases. This was achieved using
columns ®lled with MnO/SiO2. One of them, specially calibrated, allowed the detection of traces of oxygen in the outlet
gases with an accuracy of up to 10 8 mol O2. The procedure,
referred to as `¯ushing with argon', consisted of pumping out
the camera ®lled with air and ¯ushing it with a ¯ow of
10 ml min 1 of argon, and resulted in no measurable traces of
oxygen in the outlet stream during 30 min after the ¯ush. The
amount of oxygen suf®cient for monolayer coverage of the
surface of a measured palladium nanocrystalline sample was
estimated to be about 10 5 mol.
The sample studied was 10% (weight) palladium supported
on silica, freshly obtained by precipitation from a solution of
PdCl2, calcined for 4 h in dried air at 653 K, and then reduced
Figure 1
Schematic view of the in situ camera used. The operating temperature is
from room temperature to 873 K, with gas pressure from 10 4 torr to
1 atm (10 2±105 Pa). The camera is made of stainless steel.
J. Appl. Cryst. (2000). 33, 1262±1270
in hydrogen. Catalysts prepared in the same way from the
same starting components had been investigated before
(Juszczyk et al., 1993; èomot et al., 1995). The existence of a
dry atmosphere during the calcination stage was found to be
crucial for obtaining a well dispersed metal phase. To this end,
the feeding gas line was equipped with a cold trap (solid CO2)
to capture traces of water vapour. The sample was spread over
the surface of a ¯at porous glass plate (1 2 cm) and ®xed
to the stainless-steel block containing the heater (Fig. 1). The
cross section of the surface of the material under study and of
the primary beam lay along the symmetry axis of the curvilinear detector. Two samples were investigated: (1) an undried
sample calcined at 733 K (3 K min 1), and (2) a well dried
sample calcined in dry air at 733 K (heating rate 3 K min 1).
The average crystallite size in argon atmosphere as charÊ for the ®rst
acterized by the Scherrer method was 53 A
Ê
sample and 20 A for the second.
Powder diffraction patterns of the samples were collected in
situ, every 3 min (sample 1) and every 5 min (sample 2) over
considerable periods of time, under changing gas-atmosphere
cycles: exposure to argon, followed by exposure to dried air,
¯ushing with argon and ®nally reduction in hydrogen at room
temperature.
A set of X-ray powder diffraction patterns obtained in this
way was reviewed and analysed by ®tting a Gaussian or
Lorentzian pro®le to each pattern in the desired angular
range. Determination of the accuracy of the peak position was
performed in a test using the standard 111 re¯ection of
polycrystalline palladium measured every 3 min over 10 h. It
showed a Gaussian-like distribution of the peak positions,
spread over less than 0.01 (2), provided that the PSD electronics were kept at constant temperature (Fig. 2). Air
conditioning of the laboratory (1 K) proved to be a suf®cient
arrangement.
Besides systematic error (uncertainty), the other, dominating kind of error involved in the measurements arose from
poor counting statistics speci®c to the supported nanocrystals.
In the analysis of the diffraction patterns of such weakly
scattering nanocrystalline samples, the spread of the peak
positions was broadened to about 0.02 (0.01 ) for sample 1
and 0.1 (0.05 ) for sample 2, with the statistical error being
the dominant broadening factor. These values indicate the
signi®cance of analysing a long series of patterns measured
under the same gas atmosphere to arrive at a statistical error
of the average position of below 0.01 . The error of intensity
measurement was estimated from the statistics of many data
sets, assuming no systematic errors. It was in most cases at the
level of 1%.
The statistical error of the measurement is transformed
onto the error of the peak position, width and intensity via a
nonlinear ®tting routine. To test the effect of the data analysis
method on the statistics of the measured evolution of a peak
position, peak intensity and peak width, the measured
diffraction patterns have been subjected to the following
procedure. A whole set of patterns was created by adding
randomly generated statistical noise to the measured diffraction pattern, with Gaussian distribution and a standard
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Figure 2
An experimental test of the stability of the position-sensitive detector
(PSD). Results are presented for the 111 peak analysis for a polycrystalline palladium standard sample measured every 3 min over 10 h. Upper
curve: the statistics of the peak intensity. Middle curve: full width at halfmaximum (FWHM) of the Gaussian ®t to the peak for every member of
the series. Lower curve: peak position of the Gaussian ®t for every
pattern.
Figure 3
A numerical test of the data analysis method used and of its sensitivity to
experimental counting statistics. Addition of random noise of Gaussian
distribution to the experimental pattern collected for sample 2 in argon
produced 100 patterns, which were subjected to the analysis. The
intensity, FWHM and position of the Lorentzian ®t to the 111 diffraction
peak are presented.
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deviation equal to the square root of the measured intensity.
This collection of data was analysed routinely by ®tting a
Lorentzian pro®le to the main maximum. Fig. 3 shows the
statistics of the pro®le width, intensity and position. The
statistical error of a peak position is approximately equal to
0.05 and the estimated error of the average position is
0.005 .
The angular calibration of a PSD is generally not a trivial
problem and needs some comment. A routine calibration in
this work involved 40 re¯ections using three standards: quartz, annealed polycrystalline palladium and barium behanate, covering a small diffraction angle region. Setting up of
the camera involved, however, positioning of the sample
surface on the PSD axis, which could cause some peak position
error. To put the peak positions on an absolute scale, the
internal-standard method was thus used, which involved
mixing up the sample with a minute amount of -quartz of
precisely determined lattice parameters. The accuracy of the
method was estimated to be better than 0.01 (2). This
technique was applied at the ®nal stage of the collection of
every set of diffraction patterns, following the sample treatment.
Palladium crystals under normal conditions in hydrogen
undergo transition to the palladium hydride phase and
subsequently in argon decompose to palladium metal. The
hydride phase is also face-centred cubic (f.c.c.), with the lattice
parameter increased by 4.9% (Villars & Calvert, 1991) or
3.6% (Benedetti et al., 1981) with respect to that of pure bulk
palladium. If the palladium phase is contaminated by an
element that is soluble within the palladium lattice, the lattice
constant in argon may not change visibly, but the palladium
hydride may not form under hydrogen, indicating contamination. This is why the hydride transition under hydrogen was
used extensively in our laboratory as an additional structure
probe. Literature data suggest that palladium nanocrystals
undergo hydride transition with decreasing hydrogen intake
for decreasing nanocrystal size (Benedetti et al., 1981; Pinna
et al., 1997). Below a certain particle size, the hydride may not
form, although the question is still under debate.
In this work, the evolution of the patterns was analysed in
terms of the variation of the 111 peak position, intensity and
half width. The palladium f.c.c. 111 re¯ection was chosen as it
has the maximum intensity, therefore providing the best
counting statistics, and also for direct comparison with the
molecular-modelling predictions computed for that peak
(Kaszkur, 2000).
The theoretical argument exploited in further data analysis
is the proportionality of the peak intensity to the number of
atoms of a scattering cluster. It is illustrated in Fig. 4, showing
the intensity of the 111 peak per atom for the range of relaxed
palladium cubooctahedra. It is clear that in the small size
Ê ) the intensity versus number-ofrange (diameter D < 30 A
atoms relation departs signi®cantly from proportionality. For
larger clusters the linearity is conserved within 3%,
converging with size to the strict proportionality. The details of
the calculations of the data for Fig. 4 are the same as presented
earlier (Kaszkur, 2000).
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J. Appl. Cryst. (2000). 33, 1262±1270
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Figure 4
Intensity of the 111 powder diffraction peak per atom calculated for
energy-relaxed cubooctahedra. The calculations were via the Debye
formula with results in absolute units.
Another question, closely related to the previous one, is
how much the peak intensity depends on the actual
morphology of the cluster. The comparison of interest here
concerns nanocluster models with no texture, no qualitative
differences in their diffraction patterns (which in an experiment could suggest a phase transition), with no striking change
in the preferred shape, and with conservation of the number of
constituent atoms. Amorphization or surface reconstruction
may change the peak intensity, but the magnitude of this
change is never greater than that between the perfect structure and the amorphous one corresponding e.g. to a fully
melted and subsequently quenched cluster. Computer simulations for palladium show that this maximum loss of intensity
Figure 5
The absorption-corrected in situ X-ray diffraction patterns for sample 1 in
hydrogen (full line) and in argon (dotted line). The observed diffraction
peaks correspond to polycrystalline 111, 200, 220, 311 and 222 re¯ections.
J. Appl. Cryst. (2000). 33, 1262±1270
Ê cluster to
on amorphization ranges from 10% for an 18 A
Ê.
22% for 37 A
In the reported measurements, the peak intensity was
corrected for absorption in a varying gas atmosphere. It was
assumed that the total measured intensity should be conserved
if no scattering atoms were added to the sample and no major
intensity redistribution occurred. As scattering from oxygen
and hydrogen may be neglected because of the small scattering power of these elements and the low concentration of
the sorbed atoms, the method consisted of mere normalization
of the total intensity. In every measured case, one can test the
necessity for an angle-dependent absorption correction by
calculating the quotient of the actual pattern and that
recorded in hydrogen. Any systematic de¯ection of the
background line of the quotient from the constant value
suggests that the angle-dependent absorption correction has
to be applied. In the cases discussed below, the angle-dependent absorption correction was not necessary.
3. Data analysis and discussion
3.1. Sample 1
The absorption-corrected patterns for sample 1 in argon
and in hydrogen, showing the shapes of the re¯ections of
palladium and -Pd-H, are displayed in Fig. 5. A noticeable
feature is a slight narrowing and rise in height of the observed
re¯ections of -Pd-H with respect to those of pure palladium.
The change in 111 peak height is more than 40%. This
observation is reproducible in consecutive cycles of the
hydride formation and its decomposition in argon, which
supports the conclusion that no considerable interparticle
palladium transport occurs during -Pd-H formation. The
peak narrowing and its growth in height may be attributed to
the rise of the average length of an ordered row of atoms in a
given crystallographic direction. This may be caused by the
perfection of the whole structure of the nanocrystal, as well as
by ordering of its surface. The observed 111 peak narrowing
implies an increase of the size of coherent blocks in the [111]
Ê . This is roughly the thickness of one atomic
direction by 3 A
layer.
Both the rise of the peak height and the peak narrowing
result in an increase of 31% in the peak intensity. The 111
peak of the hydride phase is shifted towards smaller scattering
angles, at which the square of the scattering factor is larger by
3%. This means that for the same structure, an increase of
the lattice constant caused by the transition to -Pd-H would
produce a 111 peak of intensity 1.03 times larger than that of
the original structure. One can conclude that during transition
of sample 1 to -Pd-H, the increase of the 111 peak intensity
attributed to the change of structure itself is thus only 27%
(corresponding to 1.31/1.03 = 1.27).
The ordering of the surface layer of cubooctahedra for the
Ê may be responsible for the
estimated size of cluster of 53 A
111 intensity rise that cannot exceed the gain of 23% on
adding the outermost shell of atoms. This was estimated in the
following way. The intensity for the ordered cubooctahedra is
roughly proportional to the number of scattering atoms
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(Kaszkur, 2000). The considered effect corresponds then to
the ratio of the number of surface atoms to the total number of
Ê
atoms (i.e. to dispersion) of the cluster. Clusters of 53 A
diameter correspond to 11±12 shell cubooctahedra with a
dispersion of 23%. The observed structure-dependent
increase in the peak intensity on transition to the hydride
exceeds the estimated maximum allowed for the surface
ordering. Such an observation is a common one in the author's
Ê . This
studies of metallic clusters of size greater than 40 A
means that the palladium clusters of the catalyst in argon
suffer deeper structure rearrangement, not restricted to their
surface.
Attempting to model the palladium clusters in argon, one
has to bear in mind that even a rough surface (described as
below) contributes to the intensity quite signi®cantly. Simulations show that imposing maximum disorder onto the
surface layer of a cluster, e.g. by a high-temperature molecular-dynamics approach with constraints ®xing the core
atoms, causes only a minor loss of the diffracted 111 intensity.
Ê) a
For example, for a 923 atom cubooctahedron (D ' 27 A
rough surface generated in this way results in an 11±12%
intensity loss compared to the perfect 923 atom cubooctahedron, whereas the removal of the surface atoms leads to a 44%
loss. The dispersion for this cluster is 39%; the 5% difference
between the two numbers comes from the nonlinearity of the
intensity versus number-of-atoms dependence (Fig. 4). On the
other hand, the experimental diffraction patterns in argon and
in hydrogen do not look much different, so the overall
perfection of the structure has to be similar in both cases. The
experimentally observed intensity change may be realised
only by assuming serious destruction of the surface layer
connected with a displacement of the surface atoms by at least
Ê from the cluster. The intensity corresponding to distances
5A
between the atoms of this layer forms only a higher background for the 111 peak and an amorphous halo at 25 (2)
(Fig. 6).
The observed evolution of the 111 peak position, intensity
and half width for sample 1 is shown in Fig. 7. Inspection
thereof reveals that after reduction of the sample in hydrogen,
and ¯ushing with argon, the 111 re¯ection of the diffraction
pattern moves gradually towards lower angles on exposing the
sample to dried air. The ®nal shift is 0.05 (2). At the same
time, the absorption-corrected peak height rises by 25% and
the peak width slightly decreases, suggesting an increase of the
Ê only. The change in
apparent mean column length by 2.5 A
the peak intensity is 19%. All these changes agree well with
the following scenario. Freshly reduced clusters kept in argon,
similar to clusters in vacuum, demonstrate a surface contraction effect consisting of the shortening of the bonds with the
surface atoms. Chemisorption of oxygen on the surface of the
clusters relaxes this contraction, leading to extension of
surface bonds and overall increase of the observed lattice
parameter. The shift in the lattice parameter is only slightly
greater than the value estimated earlier (Kaszkur, 2000) via
molecular simulation, assuming complete extension of the
Figure 6
The diffraction intensity calculated via the Debye formula as scattered by
a model of a hemishell. The hemishell was half of a shell cut off the
Ê , and consisted of
palladium f.c.c. lattice by spheres of radii 20 and 12 A
910 atoms. The convex part of the surface (305 atoms) was subsequently
expanded and disordered, using energy-minimization and molecularÊ from the crystalline core of
dynamics routines, to sites displaced by 5 A
the model. The intensity distribution before the surface expansion (full
line), the total intensity for the expanded model (small circles), the
contribution from the distances between the atoms of the expanded
surface (squares), and the contribution from the distances between the
crystalline core and the surface (thick line) are presented.
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Palladium nanocrystals
Figure 7
The experimental evolution of the 111 diffraction peak for sample 1.
From top to bottom: measured peak intensity, absorption-corrected
intensity, FWHM, peak position. The columns separated by the vertical
lines correspond to the gas atmosphere: (A) argon, (B) dry air, (C)
reduction in hydrogen (data not shown).
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surface bonds like in a cluster covered with the next palladium
Ê , as results
shell. This estimate assumes a cluster size of 53 A
from the interpretation of the peak width via the Scherrer
equation. This cluster size value was accepted as the real size
because the value of the I(111)/I(311) ratio for sample 1 was
about 3, indicating the lack of signi®cant disorder and of peak
broadening linked to it (Kaszkur, 2000). The observed
increase of the peak intensity on exposure to dry air, and of
the apparent cluster size, strongly suggest ordering of the
outermost cluster layer. This notion assumes that the outer
layer in argon is disordered or otherwise does not contribute
to the intensity. The relative contribution to the intensity from
the surface ordering does not exceed dispersion of the mean
cluster. For the clusters of the observed size it is 23%.
Comparing this value with the 19% experimentally observed
rise in intensity, one may conclude that the ordering of the
surface layer is now less perfect than for -Pd-H.
3.2. Sample 2
The background-subtracted and absorption-corrected
diffraction patterns of sample 2 in argon and in hydrogen are
displayed in Fig. 8(a). As the background, a pattern belonging
to the same set of measurements but before the reduction of
metal particles was used. The transition to -Pd-H alters
visibly the 111±200 peak pro®les. These changes evolve to a
slight degree after a few cycles of exposure to argon±dry-air±
hydrogen. This evolution mainly involves the slight development of the 200 peak and narrowing of the right-hand slope of
111 (Fig. 9).
Some features of the experimental patterns are striking.
The peaks in argon have Lorentzian-like shape, the 111 peak is
asymmetric with an expanded left-hand slope and the 200
peak has reduced intensity. The latter, together with the
change of the pro®le on transition to -Pd-H, suggests that the
pattern is composed of at least two patterns from different
phases. Both have to be of the palladium phase, as heating of
the sample in argon at 673 K leads gradually to the regular
palladium f.c.c. pattern (Fig. 9). The pattern in argon (Fig. 8a)
displays a 111 peak that is about three times larger than the
200 peak. Their intensity ratio for polycrystalline material is
2.1; much larger values were found only for models of
icosahedral and semi-amorphous structure. The calculated
diffraction patterns of these two models were considered in
detail. For both models, the main maximum is shifted towards
higher angles in comparison to that of the palladium f.c.c. 111
peak and there is no, or a very reduced, higher-angle
companion peak at angles close to the position of palladium
f.c.c. 200. It will be shown below that the maximum observed
in argon moves by 0.15 (2) towards lower angles on
exposure to dry air. The peak shape is not affected during this
process. This behaviour is interpreted as the moderation of
surface contraction by chemisorbing oxygen. Simulation
shows that this shift should be signi®cantly lower for amorphous clusters. The angular shift was calculated following the
Ê palladium cluster
method of Kaszkur (2000) for an 19 A
melted via molecular dynamics and subsequently quenched,
and was less than 0.01 (2). On the other hand, model
icosahedra, being ordered structures, give the main peak shift
on full surface relaxation, comparable to that of cuboocta-
Figure 8
(a) The background-subtracted and absorption-corrected X-ray diffraction patterns of sample 2 in hydrogen (small circles) and in argon (full
line). (b) Powder diffraction patterns representing the weighted sum of
the patterns calculated for models 1a and 1b (small circles), and the
weighted sum of models 2a and 2b (full thick line). The decomposition of
the weighted sums into constituent models is presented below: 1a, 1b
(dotted line); 2a, 2b (dashed line). In the weighting, the same in both
cases, it is assumed that the mass of palladium icosahedral particles (1b,
2b) is 1.7 times greater than the mass of f.c.c. particles (1a, 2a).
J. Appl. Cryst. (2000). 33, 1262±1270
Figure 9
Diffraction pattern evolution of sample 2 as measured in argon: the initial
pattern after calcination and reduction at room temperature (bottom
curve), after a cycle of exposure to argon±dry-air±hydrogen (middle
curve), after heating at 673 K in argon (top curve).
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hedra. For a 147-atom icosahedron the calculated shift is 0.19
(2). The conclusion drawn from the experimentally observed
peak shift is that the non-f.c.c. palladium phase, observed
experimentally together with f.c.c.-like nanocrystals, corresponds to the icosahedral phase. Fig. 10 shows the diffraction
pattern of the ®rst-magic-number relaxed icosahedra. Fig. 8(b)
shows a model interpretation of the experimental patterns of
Fig. 8(a). The ®gure does not attempt to describe the full
complexity of the real structure as such an interpretation
would involve better estimation of the background and
accounting for the distribution of cluster size, especially the
small contribution to the pattern from larger clusters
responsible for sharp peak tops.
The model interpretation considered in Fig. 8(b) assumes
two kinds of clusters in hydrogen. The ®rst one (1a) is half of
Ê , off
the spherical shell, cut by spheres, of radii 20.7 and 12.4 A
Ê
the f.c.c. lattice of palladium with a lattice constant of 4.025 A
(i.e. the hydride phase). This hemishell consists of 910 atoms.
The distribution of column lengths for this model cluster ®ts
the observed peak shape better than that for the cubooctahedron model, but the same peak shape may be reconstructed
assuming a certain distribution of cubooctahedron size. The
hemishell model was used for its simplicity. The hydrogen
atoms, as practically not contributing to the intensity, were
neglected. The second model cluster (1b) is the 147-atom
icosahedron relaxed with Sutton±Chen palladium potentials
Ê ) (Kaszkur, 2000).
(a = 3.89 A
To model the experimental system in argon, both clusters
were modi®ed. The convex surface of the 910-atom hemishell
Ê (cut off
of palladium lattice with a lattice constant of 3.89 A
Ê
with spheres of radii 20 and 12 A) was `evaporated' into the
nearby vicinity by a combination of energy-minimization and
molecular-dynamics techniques (with constrains) (model 2a).
The average distance between the `evaporated atoms' and the
Ê . Model 1b was evolved
solid part of the cluster was 5±5.5 A
by evaporation of the surface atoms into the nearby vicinity,
Ê,
with an average distance to the 55-atom core of 5±5.5 A
forming model 2b.
The diffraction patterns calculated for the above models
were summed, employing a weighting scheme in which it was
assumed that the mass of the icosahedron was about 1.7 times
greater than the mass of palladium in the f.c.c. form. The
resulting diffraction pro®les re¯ect most of the characteristics
of the experimental patterns.
The observed peak pro®le change agrees well with the
concept that the icosahedral palladium phase does not
undergo the transition to -Pd-H. The overall increase of the
pro®le intensity on exposing the sample to hydrogen, after
correction for absorption of the gas in the camera, is about
23%. This relative intensity rise in comparison to the average
dispersion is lower than that for the ®rst sample, but it can be
understood if the icosahedral phase does not form -Pd-H.
The evolution of the 111 peak position, intensity and half
width for sample 2 is represented in Fig. 11. As for sample 1,
the 111 re¯ection position after reduction of the sample in
hydrogen and ¯ushing with argon moves towards lower angles
Figure 10
Figure 11
Calculated diffraction patterns of the ®rst-magic-number icosahedra.
From the bottom to the top: 13 atom (full line), 55 atom (open circles),
147 atom (open squares), 309 atom (®lled squares), 561 atom (open
triangles). Intensity is given in absolute values as calculated via the Debye
formula.
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Palladium nanocrystals
The experimental evolution of the 111 diffraction peak for sample 2.
From top to bottom: measured peak intensity, absorption corrected
intensity, FWHM, peak position. The vertical lines separate the data
measured in argon (left-hand side), in dry air (centre) and back in argon
(right-hand side).
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J. Appl. Cryst. (2000). 33, 1262±1270
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on subsequent exposure to dried air. The shift is much more
pronounced, 0.15 (2), and is close to that predicted by
Ê.
theory (Kaszkur, 2000) for a cubooctahedron of size 22 A
The slight underestimation of the experimental shift by
modelling may arise from the contribution to the shift of
icosahedral phase. Monitoring peak width reveals that the
apparent particle size (as calculated from the Scherrer formula
for crystallites without strain) rises in dry air by less than
Ê . This is less than for sample 1 and suggests that the
1 A
surface ordering effect for sample 2 is less important. Indeed,
the observed rise of the 111 peak height in dry air is by only
3%. The peak intensity practically does not grow at all, the
height rise being cancelled out by the peak narrowing. The
observed I(111)/I(311) ratio estimated for sample 2 is 3.5.
This value is slightly larger than that for sample 1 and re¯ects
the contribution from icosahedra, for which this ratio is 4.5.
The experimental observations of the peak intensity
presented for sample 1 are in line with those reported for small
platinum particles by Gnutzmann & Vogel (1989). These
authors report only a change of the integral intensity of the
platinum 111 diffraction peak in hydrogen and after evacuaÊ platinum
tion of the gas and exposure to oxygen. For 30 A
particles they report a 12% loss of intensity, which is the same
Ê
as that observed in the present study for sample 1 with 50 A
particle size (31% rise in hydrogen minus 19% rise in dry air).
For smaller platinum particles, they report a greater loss of
intensity on exposure to oxygen, which is not con®rmed here
for palladium. This may be a result of the observation of
icosahedral palladium clusters for sample 2.
The ®nal stage of the measurements for both samples
involved mixing up the samples with a minute amount of quartz, serving as an internal standard in order to put the
results on an absolute angular scale. A sample of the same
standard material was analysed beforehand by high-resolution
diffraction. The Rietveld analysis of the pattern resulted in
Ê . The
lattice parameters of a = 4.9128 (1) and c = 5.4043 (1) A
total error of the estimation of the peak position consists of
statistical error of the average value and systematic error.
Because of the large number of data ®les, the statistical error
of the average value was in both cases below 0.01 . As the
error of peak position for the standard was also estimated as
0.01 , and the systematic error was believed to be measured by
the test measurements (Fig. 2), the total error is about 0.02 ,
and slightly less for sample 1. The error of the peak shift is
therefore only 0.01 .
The resulting absolute values of the peak positions and
lattice constants for the 111 peak are given below in the order:
peak position in argon, peak position in dry air, peak position
in hydrogen; the corresponding values of the lattice constant
are given within parentheses. For sample 1 the values are:
Ê ), 40.13 (3.891 A
Ê ), 38.75 (4.025 A
Ê ). For
40.18 (3.886 A
Ê
Ê ),
sample 2 the values are: 40.19 (3.886 A), 40.04 (3.900 A
Ê
38.76 (4.024 A). The peak shifts corresponding to the exposure to dry air of the samples kept in argon are equal to 0.05
(2) for sample 1 and 0.15 (2) for sample 2, which are in
quantitative agreement with model calculations (Kaszkur,
2000, Fig. 3 therein). Also, the absolute 111 peak positions for
J. Appl. Cryst. (2000). 33, 1262±1270
the samples in argon agree within the experimental error
(0.02 ) with theoretical predictions (Kaszkur, 2000). The
lattice-parameter shift on transition to -Pd-H for both
samples is equal to 3.6%, in agreement with the work of
Benedetti et al. (1981).
All the model calculations presented in this article were
performed using the computer program CLUSTER, written
by the author and described previously (Kaszkur, 2000).
Analysis of the experimental data was performed with the
program INEL, also written by the author, allowing data
reduction and peak analysis for a long series of data sets.
4. Conclusions
The reported experimental results for small palladium clusters
con®rm earlier theoretically predicted (Kaszkur, 2000)
changes in surface-layer contraction on chemisorption of
oxygen. The quantitative extent of this phenomenon agrees
with the predictions for a complete relaxation of the surface
layer. Furthermore, the absolute 111 peak positions for the
measured samples agree within experimental error with the
theoretical predictions for model cubooctahedra. The results
validate the model potentials chosen for the material. The
proposed technique of monitoring of intensity, peak width and
peak position allows a ®rmer veri®cation of any scenario
adopted for a structural evolution of metal nanoclusters than
has been possible using the classic polycrystalline pattern
interpretation. In the case of palladium, the transition to -PdH in hydrogen may be used as an additional structure probe,
thus strengthening the conclusions. The availability of molecular-simulation tools allows the development of thermodynamically consistent models and enables any model of
disorder or dynamics to be directly compared with the
experimental data.
For the nanocrystalline supported palladium catalysts
studied in this work, the proposed approach allowed the
following structural conclusions.
Ê ) in argon,
(a) For the sample of larger particle size (53 A
the surface of the particle consists of palladium atoms at sites
that do not contribute constructively to the scattered intensity.
Ê from the crystalline core.
These atoms are displaced by 5 A
Exposure to hydrogen causes ordering of the cluster. A similar
effect (but less in extent) is observed on exposure to oxygen.
This observation has been veri®ed using a number of samples
(not reported here) with palladium particle sizes exceeding
Ê.
40 A
(b) The shift in 111 peak position on exposure of the sample
to oxygen agrees well with the theoretical predictions for a
cubooctahedron of the same size. The corresponding change
of the peak width was noticeable and agrees with the concept
of the ordering of the surface (and subsurface) layer.
Ê ), the picture is more
(c) For particles of smaller size (20 A
complex. The diffraction pattern and its evolution on exposing
the sample to hydrogen strongly suggest a two-phase model of
the metal particles in the sample. The pattern evolution
suggests that besides the f.c.c. nanoparticles, the second
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Zbigniew Kaszkur
Palladium nanocrystals
1269
research papers
observed phase is icosahedral and under normal conditions
does not form the -Pd-H phase in hydrogen. The 111 peak
shift on exposure to oxygen agrees well with the theoretical
Ê size.
predictions for the cubooctahedron of 20 A
The reported quantitative evolution of the diffraction
patterns of the samples evidences changes of the 111 peak
intensity that can be explained only by assuming signi®cant
Ê ) from the crystalline
displacement of the surface atoms (5 A
core. This effect is dif®cult to understand and can be rationalized considering the chemical environment of the metal
particles in the studied samples. The results suggest surface
reaction of the metal cluster with some weakly scattering
compound placed between the crystalline palladium surface
and the displaced palladium atoms. This compound decomposes in hydrogen, allowing ordering of the surface and the
layer next to the surface layer. Similar phenomena of the
formation of subsurface oxygen at polycrystalline palladium
surfaces have been observed by a number of experimental
techniques and reported in the literature (Epling et al., 1996).
The observed effects of surface-atom disorder/displacement
and their chemical nature certainly warrant further study.
The author wishes to express his gratitude to Professor J.
Pielaszek for helpful discussions. The work has been ®nancially supported by the Committee of Scienti®c Research of
Poland (Komitet Badan Naukowych) under research project
No. 3 T09A 024 16.
1270
Zbigniew Kaszkur
Palladium nanocrystals
References
Apsel, S. E., Emmert, J. W., Deng, J. & Bloom®eld, L. A. (1996). Phys.
Rev. B, 76, 1441±1444.
Barnes, C. J., Ding, M. Q., Lindroos, M., Diehl, R. D. & King, D. A.
(1985). Surf. Sci. 162, 59±73.
Benedetti, A., Cocco, G., Enzo, S., Pinna, F. & Schif®ni, L. (1981). J.
Chim. Phys. 78, 875±879.
Buffat, Ph. & Borel, J.-P. (1976). Phys. Rev. A, 13, 2287±2298.
Epling W. S., Ho¯und, G. B. & Minahan, D. M. (1996). Catal. Lett. 39,
179±182.
Gnutzmann, V. & Vogel, W. (1989). Z. Phys. D, 12, 597±600.
Juszczyk, W., KarpinÂski, Z., Pielaszek, J. & Sobczak, J. W. (1993). New
J. Chem. 17, 573±576.
Kaszkur, Z. (1998). Mater. Sci. Forum, 278±281, 110±114.
Kaszkur, Z. (2000). J. Appl. Cryst. 33, 87±94.
Lamber, R., Wetjen, S. & Jaeger, N. I. (1995). Phys. Rev. B, 51, 10968±
10971.
èomot, D., Juszczyk, W., Pielaszek, J., Kaszkur, Z., Bakuleva, T. N.,
KarpinÂski, Z., Wasowicz, T. & Michalik, J. (1995). New J. Chem. 19,
263±273.
Peters, K. F., Cohen, J. B. & Chung, Y. W. (1998). Phys. Rev. B, 57,
13430±13438.
Pinna, F., Signoretto, M., Strukul, G., Polizzi, S. & Pernicone, N.
(1997). React. Kinet. Catal. Lett. 60, 9±13.
Schaaff, T. G., Sha®gullin, M. N., Khoury, J. T., Vezmar, I., Whetten,
R. L., Cullen, W. G., First, P. N., GutieÂrrez-Wing, C., Ascensio, J. &
Jose-YacamaÂn, M. J. (1997). J. Phys. Chem. B, 101, 7885±7891.
Villars, P. & Calvert, L. D. (1991). Editors. Pearson's Handbook of
Crystallographic Data for Intermetallic Phases, 2nd ed. Materials
Park, OH: The Materials Information Society/ASM International.
ZielinÂski, J. & BorodzinÂski, A. (1985). Appl. Catal. 13, 305±
310.
electronic reprint
J. Appl. Cryst. (2000). 33, 1262±1270