Materials Letters 64 (2010) 1160–1162
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Materials Letters
j o u r n a l h o m e p a g e : w w w. e l s e v i e r. c o m / l o c a t e / m a t l e t
Lattice parameter and expected density of Au nano-structures sputtered on glass
Z. Kolská a,⁎, J. Říha b, V. Hnatowicz c, V. Švorčík d
a
Department of Chemistry, J. E. Purkyně University, 400 96 Usti nad Labem, Czech Republic
New Technologies-Research Centre in Westbohemian Region, University of West Bohemia, 306 14 Plzen, Czech Republic
c
Nuclear Physics Institute of Academy of Sciences of the Czech Republic, 25068 Rez near Prague, Czech Republic
d
Department of Solid State Engineering, Institute of Chemical Technology, 166 28 Prague, Czech Republic
b
a r t i c l e
i n f o
Article history:
Received 29 January 2010
Accepted 16 February 2010
Available online 24 February 2010
Keywords:
Au sputtering
XRD analysis
Au density calculation
Free volume fraction
a b s t r a c t
Gold nano-structures (clusters and layers) were sputtered on the glass substrate. Lattice parameter was
determined by X-ray diffraction. Density of Au nano-structures was calculated depending on structures size.
Density of gold structures increases from the value of 13.6 · 103 to 19.3 · 103 kg m− 3. Free volume fraction of
structures decreases from the value of 48 to 26%.
© 2010 Elsevier B.V. All rights reserved.
1. Introduction
2. Experimental
Vacuum-deposited metal clusters and thin films play an important
role in various fields of technology [1], such as micro- and nanoelectromechanical systems (MEMS and NEMS) [2], sensors [3], electronic
textiles [4], bio-engineering [5], generator of non-linear optical properties [6] or devices for Surface-enhanced Raman scattering [7].
Gold is known as a noble metal that has a face centred cubic
structure, melts at temperature T = 1336 K and has got a density value
of ρ = 19.320 · 103 kg m− 3. In the last decades properties of thin metal
layers were studied intensively and some theories of size-dependent
effects of nano-sized structures were developed [8,9]. Also different
arrangement of metal crystal lattice and a certain volume disorder may
play an important role in properties of nano-sized materials [10–13]. All
hitherto results show that gold nano-structures exhibit different values
of physical and physico-chemical properties in contrast to the bulk, e.g.
chemical activity [8], melting temperature [8,9,14], cohesive energy
[15].
We studied various physical and physico-chemical properties of gold
nano-structures (clusters and layers) sputtered or evaporated on
different substrates, e.g. glass and some polymers [10,16–22]. In this
work Au structures prepared by sputtering on glass was studied by X-ray
diffraction (XRD) analysis. From XRD results and previously presented
AFM [10], AAS [19] experimental data the Au structure density was
calculated as a function of structure size.
2.1. Substrate and Au deposition
⁎ Corresponding author.
E-mail address: [email protected] (Z. Kolská).
0167-577X/$ – see front matter © 2010 Elsevier B.V. All rights reserved.
doi:10.1016/j.matlet.2010.02.038
Gold structures were sputtered onto glass substrate (2 ×2 cm microscopic glass, 1 mm thick, supplied by Glassbel Ltd., Czech Republic). The
roughness of the substrate, Ra =0.34 nm, was measured over 1.5 μm2
area. Gold of 99.99% purity was supplied by Goodfelow Ltd. The
sputtering was accomplished on diode sputter-coater Balzers SCD 050
device for sputtering times from 4 to 500 s [10]. The sputtering conditions were: DC Ar plasma, Ar gas purity of 99.995%, a discharge power of
7.5 W.
2.2. Diagnostic techniques
The apparent thickness of sputtered Au layers was obtained by two
independent techniques AAS [19] and AFM (Digital Instruments CP II
Veeco) [10], working in tapping mode with silicon P-doped probes
RTESPA-CP and with the spring constant 20–80 N m− 1. The scratches
were done at ten different specimen positions (for each examined
layer thickness) by nanointendation tip and the layer thickness was
determined from AFM scan in contact mode [23]. The accuracy of
these determinations (AAS and AFM) are presented as 10% [19,23].
XRD analysis was performed by automatic powder refractometer
Panalytical X'Pert PRO using copper X-ray lamp (λ CuKα1 =
0.1540598 nm) equipped with ultra-fast semiconductor detector
PIXcel. Measurement has passed on a symetric Bragg–Brentano
geometry. Diffractograms were registered in the angle range 2ϑ =
(10–85°). Lattice parameter a of cubic face centered lattice of Au was
calculated from diffraction lines location and their intensities, using
Z. Kolská et al. / Materials Letters 64 (2010) 1160–1162
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Rietvelds method. We were able to satisfactorily determine the lattice
parameter only for layers with thickness exceeding 10 nm. Spectra for
thinner layers exhibit pronounced peek of amorphous glass preventing
gold peak evaluation.
3. Results and discussion
From the XRD data the density of gold structures (clusters or layers)
was calculated. According to previous investigations [10,24] the density
is expected to depend on the layer thickness, the density changes being
related to varying fraction of free volume in nano-structures. This free
volume fraction means the volume between individual atoms in
structure, which play more important role at the smaller dimensions.
In Fig. 1 the effect of decreasing lattice parameter and decreasing free
volume fraction is schematically illustrated. As it has been discussed
previously [10–12], the lattice parameter a of gold thin layer prepared
by a physical deposition is not a material constant but it depends
strongly on the layer thickness. It has been presented that a of deposited
clusters expand [10–12,25,26] in comparison with spherical clusters not
deposited on solid surface, where a dominant effect is compress [27].
Detailed description of these effects was presented [25–27]. Fig. 2
presents the dependence of a on the structure edge or layer thickness as
determined by XRD measurement. Lattice parameter is monotonously
decreasing function of this dimension, the result being in good
agreement with those of previous studies [10–13].
Details of the kinetic of gold deposition onto solid surfaces and of
the gold structures growth was discussed earlier [1]. In initial phase
gold nano-blocks are created and then continuous nano-layer is
formed [1]. The knowledge of the nano-structure shapes is important
for calculation of their volume. From the Figs. 1 and 2 it is clear that
the higher lattice parameter, the higher distance between individual
atoms, larger fraction of the free volume (space between individual
atoms) and the lower number of atoms per unit volume. As was
reported earlier [10,24], the gold layers with the thicknesses above
90 nm (for sputtered layers [10]) or 200 nm (for evaporated layers [24])
exhibits quite uniform density with a mean value of 19.3 × 103 kg m− 3
which is typical for gold bulk.
Density of gold structures was calculated by the equation ρAu =
(NAu·mAu)/(VAu + Vfree), where NAu is a number of all Au atoms in
nano-structure mAu is a mass of one Au atom (mAu = 3.2707135763762 ·
10− 25 kg [28]), V = VAu + Vfree is volume of nano-structure including the
Au atoms volume VAu and free volume Vfree (free space between
individual atoms in nano-structure). Nano-structure volume V is
obtained from determined lattice parameter a, which presents the
Fig. 2. Dependence of gold lattice parameter on structure edge or layer thickness of gold
sputtered on glass.
distance between individual atoms and from knowledge of nanostructure shape. The effects of changing a and free volume fraction on
the ρAu of nano-structure is illustrated by density calculation performed
for two “extreme” lattice parameters a1 = 0.40839± 0.00022 nm and
a2 = 0.40731 ± 0.00011 nm obtained for the thinnest structure and the
thickest layer respectively. The results are shown in Fig. 3 (curves 1 and 2
for two mentioned a1, a2, respectively). Present XRD data were obtained
only for the structure edges or layers thicker than 10 nm. It is clear from
Fig. 3 the ρAu trend is almost independent on a. The difference between
ρAu calculated from a1 or a2 is negligible. It should be noted that, in
principle, ρAu nano-structures could be affected by the properties of
substrate surface [1,10,22] and it is only predicted value. Trend of a and
ρAu changing with the layer thickness agree with those presented
previously [10–12,24].
Free volume fraction of nano-structures (Vfree)fraction, which means
volume between individual atoms, was calculated by the relation
(Vfree)fraction = ((V − VAu)/V) · 100 as a function of the structure edge
or layer thickness. Free volume fraction decreases from 48% for
the smallest Au structure (containing 14 atoms of the edge size
0.7 nm) to 26% for layer thickness above 80 nm. That means the filling
Fig. 1. 2D schematics of gold structures for two different lattice parameters a1 (A) and a2 (B); a1 N a2.
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Z. Kolská et al. / Materials Letters 64 (2010) 1160–1162
decreases from the 48% for the smallest structure to 26% and gold
atoms volume fraction reaches to 74% for the layer thickness above
80 nm. Observed density changes may be a reason for different behavior
of nano-sized structures and bulk gold.
Acknowledgements
This work was supported by the GA CR under the projects 106/09/
0125 and 108/10/1106, Ministry of Education of the CR under
programs 6046137302 and LC 06041, and AS CR under the projects
KAN400480701, KAN200100801 and IAA 400720710.
References
Fig. 3. Dependences of calculated gold density and the free volume fraction on structure
edge or layer thickness. It was calculated for two “extreme” lattice parameters a1 =
0.40839 nm (curves 1 and 1′, resp.) and for a2 = 0.40731 nm (curves 2 and 2′, resp.). Dot
curves are predicted.
of structures by gold atoms is 74%, which is identical with that
reported for bulk gold 74.05% [28]. This trend is shown in Fig. 3
(curves 1′ and 2′ for mentioned a1, a2, respectively).
Gold density was also calculated by the relation ρ = zAu·MAu·
1.66043 · 10− 27/V [28], where zAu = 4, MAu is atomic number of gold
(MAu = 196.9666), V is volume of nano-structure. We obtained the
following values: ρ1 = 19.212· 103 kg m− 3 for a1 and ρ2 = 19.359 ·
103 kg m− 3 for a2.
4. Conclusions
Density of gold nano-sized structures sputtered on glass was
calculated from lattice parameter (XRD) of deposited structures.
While a decreases, ρAu of structures increases with increasing structure
edge from the value of 18.7· 103 kg m− 3 (gold structure of edge 10 nm)
to the 19.3· 103 kg m− 3 (layer thickness above 80 nm). From these data
density value was predicted decreasing to 13.6· 103 kg m− 3 for gold
structure of edge 0.7 nm. Free volume fraction of gold structure
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