Indian Journal of Pure & Applied Physics
Vol. 44, February 2006, pp. 157-161
Crystallite size estimation of elemental and composite silver
nano-powders using XRD principles
Bharati R Rehani1, P B Joshi1, Kirit N Lad2 & Arun Pratap2
1
Department of Metallurgical Engineering
Faculty of Technology & Engineering, The M S University of Baroda,Vadodara 390 001
2
Applied Physics Department, Faculty of Technology & Engineering, The M S University of Baroda,Vadodara 390 001
E-mail: [email protected]
Received 25 May 2005; revised 8 November 2005; accepted 8 December 2005
Studies on nanocrystalline materials require an accurate determination of crystallite size as well as the microstrains
induced in the material. X-ray diffraction (XRD) and transmission electron microscopy (TEM) are the two well-known
techniques for this purpose. Based on XRD principles, numerous approaches such as use of Scherrer equation, integral
breath analysis, single-line approximation, Hall-Williamson method, etc have been developed for estimation of crystallite
size. Present work deals with a systematic application of Hall-Williamson method for crystallite size estimation of highenergy milled elemental silver and silver-metal oxide (AgMeO) type composite powders and its comparison with Scherrer
equation that does not take into account the peak broadening due to strain. The effect of second phase particles on the
crystallite size of silver matrix in AgMeO composite is also investigated.
Keywords: Crystal size, X-ray diffraction, Transmission electron microscopy
IPC Code: G01N
1 Introduction
Elemental silver and silver-base composites such
as AgMeO composites are widely used for electrical
applications as electrically conductive materials1,2.
Apart from applications as contact materials in
electrical switchgear devices like contactors, relays
and switches, pure silver is also used as a filler
material in conductive polymers3. It is well-known
that altogether different combination of properties
like electrical, electronic, optical, mechanical or
chemical) is attainable with respect to bulk material if
the grain size of the concerned material is in the nanometer regime4.
A multitude of physical and chemical synthesis
techniques has been invented for the production of
nanostructured materials in general and silver and its
composites in particular5-7. High-energy milling or
mechanical alloying (MA) is one such route that is
gaining importance for synthesis of equiaxed (3D)
nanostructured crystallites of silver-metal oxide
composites such as Ag-CdO, Ag-SnO2, Ag-ZnO, AgIn2O3, etc. for electrical contact applications over the
years8,9.
An accurate estimation of grain size/crystallite size
becomes essential when such materials are produced
with their crystallite size of the order of less than 100
nm. Though TEM is one of the powerful techniques
for crystallite size measurement, it has certain
limitations. Since TEM images represent only a local
region, many samples and images are required to
provide an average information for the entire sample.
Not only this, the TEM sample preparation method is
an involved and time consuming one. The XRD
technique is free from these limitations.
X-ray diffraction is, on the other hand, a simpler
and easier approach for the determination of
crystallite size of powder samples. The underlying
principle for such a determination involves precise
quantification of the broadening of the diffraction
peaks. Based on this principle, a few techniques
involving Scherrer equation, integral breath analysis
or Hall-Williamson approach, Fourier method of
Warren-Averbach, etc. have been developed10-13. Out
of these options, the Hall-Williamson method of
crystallite size estimation has been chosen in this
investigation for determining the crystallite size of
elemental silver and silver-cadmium oxide composite
powders subjected to MA.
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INDIAN J PURE & APPL PHYS, VOL 44, FEBRUARY 2006
2 Theory
2.1 Mechanism of High-energy Milling
High-energy milling or mechanical alloying is one
of the proven techniques for producing powders with
nanocrystalline structures. It involves deformation,
fracture and re-welding of powder particles during the
course of milling. In case of a single-phase elemental
powder system subjected to MA, the grain size of the
powder particles continues to decrease with
progressive milling until it reaches a minimum level
below around 25 nm. However, the major mechanism
of grain refinement in such materials is not simply
that of fracturing and re-welding. For example, in
elemental ductile materials like silver the reduction of
crystallite size (grain size) is basically due to
localized plastic deformation of the powder particles
in the form of shear bands. The shear bands contain
high density of dislocations and with sufficiently
large increase in the dislocation density the shear
bands decompose into sub-grains separated by lowangle grain boundaries. With further milling the subgrains transform into grains through a process of
mechanically driven grain rotation and sub-grain
boundary sliding14.
On the other hand, in ductile-brittle system like
AgMeO composites, the mechanism of reduction in
crystallite size is somewhat different. Here, the
metallic ductile phase deforms and fractures with
progressive milling whereas the brittle oxide phase is
mainly fractured into smaller and smaller particles
until such a point that the fracture strength of the fine
dispersoid particles (i.e. oxide phase particles) is
equal to or greater than the stress induced due to
collision of grinding balls8. These fine dispersoid
particles of oxide phase are quite effective in
retarding the grain growth of the matrix phase such as
silver in AgMeO composites15.
2.2 Crystallite Size Estimation
The high-energy milling or MA process not only
leads to reduction in the crystallite size of concerned
powder particles to nanometric size but also causes an
increase in the lattice-strain. The reduced crystallite
size, the lattice strain and the instrumental effects
account for the total broadening of XRD peaks with
progressive milling and the major activity during
crystallite size determination of a milled powder
sample therefore involves quantitative estimation of
each one of these factors responsible for the line
broadening. When the crystallites of a material are
smaller (i.e. less than 100 nm) they have too small a
number of parallel diffraction planes and eventually
they produce broadened diffraction peaks instead of a
sharp peak. Likewise, the non-uniform strains arising
out of heavy plastic deformation during MA
processing cause broadening of diffraction peaks.
Lastly, instrumental factors such as unresolved α1 and
α2 peaks or imperfect focusing also lead to line
broadening.
The first step in crystallite size determination by
Hall-Williamson method is to determine pure
diffraction breadth (i.e. the one which is solely due to
small crystallite size.). It is better to use integrated
width (i.e. integrated intensity/maximum intensity) of
a diffraction peak rather than half-width (also called
as Full Width at Half Maximum, FWHM) particularly
for XRD profiles having broad peaks and where there
is a possibility of introduction of an error due to
wrong estimation of background level. Most modern
diffractometers are equipped with a software for
measurement of integrated intensity of diffraction
peaks. Basically, it is the ratio of area under a peak
above the estimated background to the maximum
height of that peak.
Thus, the observed peak broadening Bo may be
represented as
Bo = Bi + Br
...(1)
where Bo is the observed peak broadening in radians;
Bi the broadening due to instrumental factors, in
radians and Br is the broadening due to crystallite size
and lattice strain.
The instrumental broadening Bi may be assumed to
be that for a coarse-grained, well-annealed highpurity silver powder (standard) sample subjected to
XRD under identical conditions as those for the test
sample. Eq. (1) holds good if the diffraction peaks
exhibit purely Cauchy profile. However, when the
diffraction peaks show a mixed behaviour (i.e. partly
Cauchy and partly Gaussian) for their profiles, the
following relation between Bo, Bi and Br holds good.
(
Br = ( Bo − Bi )( B − B )
2
o
2
i
1
2
)
1
2
...(2)
Now, according to Scherrer equation10, the
broadening due to small crystallite size may be
expressed as
Bc =
kλ
t cos θ
...(3)
REHANI et al.:CRYSTALLITE SIZE ESTIMATION BY XRD PRINCIPLES
where Bc is the broadening solely due to small
crystallite size, k a constant whose value depends on
particle shape and usually taken as 1.0; t the
crystallite size in nanometers; θ the Bragg’s angle; λ
is the wavelength of incident X-ray beam in nm.
Similarly, according to Wilson16, the broadening
due to lattice strain may be expressed by the relation,
Bs = η tan θ
…(4)
where Bs is the peak broadening due to lattice strain
η the strain distribution within the material and
θ is the Bragg’s angle.
Based on Eqs (3) and (4), the total peak broadening
Br may be expressed as:
Br =
kλ
+ η tan θ
t cosθ
…(5)
multiplying both sides of Eq.(5) by cosθ, we get
Br cosθ =
kλ
+ η sin θ
t
…(6)
The plot of Brcosθ versus sinθ gives a straight line
with slope equal to η and the intercept along y-axis as
kλ/t. For a typical value of k equal to 1.0, and the
wavelength of incident X-ray beam as 0.15406 nm for
Cu-target, the crystallite size t can be calculated from
the intercept. The scatter of the points on Brcosθ
against sin θ graph about a mean straight line is a
characteristic feature of a face-centered-cubic (FCC)
metal subjected to heavy plastic deformation and
hence a mean straight line satisfying all the points is
usually drawn. Further, it may be clarified that the
error in evaluating crystallite size turns out to be quite
high due to scattering of data. So, it is not very
meaningful to estimate error in determination of
crystallite size using Hall-Williamson method. In
turn, the so-obtained crystallite size data for samples
milled for different durations of time has been
compared with the corresponding values derived
through Scherrer formula given by Eq. (3), which
does not account for strain in the samples.
3 Experimental Details
The Sisco Research Laboratory (SRL) make silver
powder of AR grade and 99.9% purity was used as
starting material. Similarly, stoichiometric amount of
99.5% purity s.d. Fine make cadmium oxide powder
was used to produce Ag12CdO composite powder.
The elemental silver powder was directly subjected to
159
high-energy milling whereas Ag12CdO was milled
after an initial blending operation in a cylindrical
blender to obtain homogeneous powder mix. In either
case, the dry milling was carried out in a centrifugal
attritor in air without using any process control agent
(PCA) at a ball to charge ratio of 20:1 and milling
speed of 450 rpm. The powder samples were drawn at
periodic intervals for their characterization by XRD
for crystallite size determination. The XRD profiles
were obtained using Rigaku Gieger Flex D-max
model (Japanese make) of X-ray diffractometer
within 2θ range of 30o-75o at a scan speed of 3o per
min using a Cu target and Cu-Kα radiation of 0.15406
nm wavelength at a power rating of 40 kV and 20
mA. The powder samples were mounted on ground
glass sample holder for this purpose. The diffraction
profile for high-purity well-annealed silicon powder
(as standard) was also obtained under identical
conditions. The integrated intensity for silver peaks
for elemental silver as well as Ag12CdO composite
powders and Si powder was measured using
instrument’s software. The crystallite size was
determined by using the step-by-step procedure.
4 Results and Discussion
The data on crystallite size estimation for
elemental silver and Ag12CdO composite powder
based on integral width value is given in Tables 1 and
2, respectively. Based on the data given (for 4 hr
milled powder samples) in Tables 1 and 2 plots for
Table 1 — Data on crystallite size estimation for elemental silver
powder
Milling
time
As-blended
2 hr
4 hr
8 hr
2θ in
deg.
Integrated Brcosθ×(10-3)
width
38.05
0.184
1.211
44.24
0.222
1.931
64.43
0.231
1.970
38.05
0.374
4.697
44.24
0.547
7.486
64.43
0.547
6.839
38.05
0.365
4.541
44.24
0.526
7.137
64.43
0.554
6.944
38.05
0.353
4.333
44.24
0.552
7.568
64.43
0.506
6.219
Crystallite size
(nm)
HW
Scherrer
–
46
44
20
57
21
38
21
INDIAN J PURE & APPL PHYS, VOL 44, FEBRUARY 2006
160
Table 2 — Data on crystallite size estimation for Ag12CdO
powder
Milling time 2θ in Integrated Brcosθ×(10-3)
width
deg.
As- blended 38.10
0.184
1.211
44.26
0.222
1.931
64.41
0.231
1.970
1 hr
4 hr
11 hr
38.10
0.385
4.880
44.26
0.562
7.733
64.41
0.548
6.853
38.10
0.424
5.556
44.26
0.648
9.145
64.41
0.591
7.500
38.10
0.498
6.812
44.26
0.697
10.083
64.41
0.610
7.913
Crystallite size
(nm)
HW
Scherrer
–
46
38
20
28
18
19
16
Fig. 1 — Hall-Williamson plots for elemental silver powder
(„) and Ag12CdO composite powder (S) after 4 hr of milling
Brcos θ versus sin θ (known as Hall-Williamson
plots) for selected diffraction peaks are drawn as
shown in Fig. 1. The reciprocal of the intercept along
y-axis at sin θ = 0 gives the crystallite size in each
case. The last column for data on elemental silver
powder and Ag12CdO composite powder in Tables 1
and 2 report the crystallite size values computed from
Hall-Williamson plots and also through Scherrer
formula.
It is apparent from the data in Tables 1 and 2 that
the crystallite size for Ag12CdO composite powder is
finer than that for elemental silver powder subjected
to milling under a similar set of processing
Fig. 2 — Variation of crystallite size with milling time for
elemental silver („) and Ag12CdO (S) composite powders
conditions. The extensive amount of plastic
deformation produced by the processes such as MA
leads to changes in the grain size and shape
morphology of concerned powder particles. Figure 2
shows the variation in the crystallite size with respect
to milling time for elemental silver and Ag12CdO
composite powders. With increase in milling time, the
crystallite size progressively decreases in each case.
However, the crystallite size values obtained from
Hall-Williamson method come out to be more than
those derived through Scherrer equation. The
crystallite size estimation for as-blended powder has
not been done through Hall-Williamson method as
such sample will not have considerable strain.
However, the crystallite size has been derived by
Scherrer equation which does not consider strain. The
typical values of crystallite size for elemental silver
powder after 4 h of milling are 57 and 21 nm
respectively for Hall-Williamson and Scherrer
methods. Likewise, the corresponding sizes of
crystallites for Ag12CdO milled powder after 4 h of
milling have been found to be equal to 28 and 18 nm
respectively. Thus, the crystallite size obtained using
Scherrer equation is smaller than that computed by
Hall-Williamson method. This is due to the fact that
the Scherrer equation does not take into account the
effect of lattice strain and instrumental factors on
peak broadening. This, in turn, overestimates the
effect of crystallite size on broadening of peaks and
thus underestimates crystallite size.
Besides this, the deformation of any individual
grain within a powder particle is strongly influenced
by its neighbouring grains. Not only this, the
REHANI et al.:CRYSTALLITE SIZE ESTIMATION BY XRD PRINCIPLES
neighbouring grains induce residual strain within this
grain. Incidentally, similar effects are observed when
the second-phase particles such as the oxide particles
are intimately dispersed along the grain boundaries of
the matrix phase due to high-energy milling. The
residual strain induced within the grains of matrix
phase (such as silver) by the uniformly dispersed
second-phase particles (such as CdO particles) not
only restrict the grain growth of the former but also
produce residual strains and thus give rise to
broadening of diffraction peaks. Eventually, the
crystallite size of Ag12CdO composite powder
produced by high-energy milling is finer than that for
the elemental silver powder subjected to milling
under similar set of processing conditions.
Acknowledgement
The help rendered in XRD measurements by Prof.
N.S.S.Murti is gratefully acknowledged.
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5 Conclusion
The Hall-Williamson method is a more accurate
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the former approach to measure pure breadth of the
diffraction peaks i.e. that solely due to smaller
crystallite size. The intimate dispersion of submicroscopic second phase particles imparts finer
crystallite size to the matrix phase within the
composite in view of the residual strain produced
within the matrix by such particles.
161
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