Available online at www.sciencedirect.com
Acta Materialia 59 (2011) 5266–5275
www.elsevier.com/locate/actamat
Nanovoids in thermoelectric b-Zn4Sb3: A possibility for
nanoengineering via Zn diffusion
Protima Rauwel a,⇑, Ole Martin Løvvik a,b, Erwan Rauwel c, Johan Taftø a
a
Department of Physics, University of Oslo, PO Box 1048, Blindern, NO-0316 Oslo, Norway
b
SINTEF Materials and Chemistry, NO-0316 Oslo, Norway
c
Department of Chemistry and inGaP, University of Oslo, N-0315 Oslo, Norway
Received 3 January 2011; received in revised form 2 May 2011; accepted 2 May 2011
Available online 31 May 2011
Abstract
The binary Zn4Sb3 phase is a promising material for thermoelectric applications due to its extraordinarily low thermal conductivity.
The present study attempts to rationalize this property by investigating its nanostructure. b-Zn4Sb3 samples with varying Zn content
were thus synthesized, quenched from the melt and annealed at 350 °C. Their nanostructure was observed using transmission electron
microscopy. The samples presented in this work have Zn:Sb atomic ratios of 1.30 and 1.33 and exhibit a single phase of b-Zn4Sb3 in
X-ray diffraction studies. Transmission electron microscopy (TEM) observations revealed nanoporous morphologies for both compositions, with a random distribution of the voids. Both samples contain voids, while the sample with Zn:Sb = 1.33 also consists of Zn nanoinclusions. Density functional theory calculations were carried out to study the stability of atomistic b-Zn4Sb3 models with varying Zn
content. This was used to suggest a mechanism for the formation of Zn nanoparticles and subsequently nanovoids. The calculations
imply that the Zn solubility in the Zn4Sb3 matrix increases with decreasing temperature. Combined with a high Zn diffusivity, this work
explains how Zn could leave the nanoprecipitates during annealing, resulting in the voids seen by TEM.
Ó 2011 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
Keywords: Density functional theory; Electron microscopy; Diffusion; Nanovoids; Thermoelectricity
1. Introduction
Our continuous hunt for sources of green energy has led
to a more in-depth examination of thermoelectricity-based
materials. Despite this, the efficiency of thermoelectricitybased devices can still be improved. The performance of
a thermoelectric material is defined by the dimensionless
figure of merit (ZT) and is associated to its electrical conductivity (r), Seebeck coefficient or thermopower (S) and
thermal conductivity (j) through the following relation:
ZT ¼ ðrS 2 ÞT =j
where rS2 is the power factor. In recent years, thermoelectric materials have been subjected to improvement mainly
⇑ Corresponding author. Tel.: +47 22 84 06 94; fax: +47 22 05 06 51.
E-mail address: protima.rauwel@fys.uio.no (P. Rauwel).
due to nanostructuring [1,2], which includes superlattices
[3], quantum dots [4], nanowires [5] and nanocomposites
[6,7].
A temperature gradient in all these materials is essential
for the generation of electricity. Even though their reported
ZT values show notable improvement, their application on
a large scale still remains to be assessed with regard to stability and cost effectiveness. Some cost-effective techniques
include bulk nanostructuring [8,9]. Nevertheless, tuning a
thermoelectric material to one’s needs is not easy as there
are many interdependent parameters to be taken into
account, as mentioned above. Simply stated, the electrical
conductivity, Seebeck coefficient and electronic contribution to the thermal conductivity all depend on the electronic structure.
Subsequently, in the early 1990s property modification
through low dimensionality was probed and a significant
1359-6454/$36.00 Ó 2011 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
doi:10.1016/j.actamat.2011.05.003
P. Rauwel et al. / Acta Materialia 59 (2011) 5266–5275
decrease in the thermal conductivity was also reported [10].
Using nanoparticles or inducing nanostructures in a matrix
by spinodal decomposition has helped to increase the Seebeck coefficient by filtering out low-energy electrons [11].
Nanostructuring incontestably seems to present effective
scattering centers provided that there are enough of them.
The present objective is to create nanostructured materials
that are stable over a long period of time and over a range
of temperatures, as large temperature gradients could provoke structural modifications and subsequently changes in
thermoelectric performance.
b-Zn4Sb3 is a well-known thermoelectric material boasting a very low thermal conductivity [12]. A ZT > 1 was
reported by Caillat et al. [13]. In this material Zn plays
many important roles to create short-range ordering: first,
Zn in the Zn1 position according to the interstitial model
has an occupancy of only 89%, thus creating Zn vacancies
[12]. Secondly, the rest of the Zn is found in the interstitial
positions (Zn2, Zn3, Zn4), thereby generating local distortions and lattice irregularities [14]. Thirdly, Zn in this material also precipitates into the matrix to form inclusions of
micrometric and nanometric sizes [15]. The presence of
point defects in the form of interstitials and vacancies in
the material is strategic towards the reduction of thermal
conductivity [16]. Even though vacancies can effectively
scatter phonons [17], they tend to worsen the electron conductivity [18]. Considering Rayleigh’s scattering regime,
the effective scattering cross-section of a point defect varies
as a function of the phonon wavelength (k) and the size of
the scattering particle (b) as r b6/k4. The latter implies
that point defects are efficient in scattering short wavelength phonons by Umklapp processes. The longer wavelength phonons seem unaffected by these imperfections.
One therefore reaches the thermal conductivity reduction
limit or the alloying limit.
Overcoming the alloying limit would imply nanostructuring in the Zn4Sb3 matrix, as in the case of PbTe, where
a combination of point defects and nanostructures was
used to reduce the overall thermal conductivity by 75%
[11]. The reason for the reduction in jl is that the Rayleigh’s scattering regime for the mid- to long wavelength
electrons is satisfied by an increase in the scattering particle
size “b”. For practical reasons, a large size distribution of
nanostructures will be required to efficiently scatter various
phonon modes. The mean nanometric size (8 nm) of the
Zn precipitates in Ref. [15] is approximately the mean free
path of phonons in the material at room temperature (RT),
and therefore such precipitates are candidates for efficient
scattering centers [19]. Unequivocally, Zn is therefore
instrumental in creating the phonon glass and can explain
the low thermal conductivity of the material. Recently,
there has also been debate about the decrease in thermal
conductivity due to soft acoustic phonons originating from
the rattling of the Sb2 dimers [20].
In this work, we demonstrate that nanoscale voids or
pores can be generated on a suitable heat treatment. Porous materials have a variety of applications, viz. as cata-
5267
lysts [21], sensors [22], low k-dielectric layers [23] and
hydrogen storage materials [24,25]. The most common
method for the production of the above is template based
[26]. Other well-known examples of void formation in binary systems include Be/Ni core shell microparticles, Nicoated Cd wires and hemispherical shells in Au/Ag systems
[27–31]. These are all formed by the Kirkendall effect,
where the mutual diffusion rates of two components in a
diffusion couple differ by a considerable amount [32]. Since
2004, papers on hollow nanoshell formation based on the
Kirkendall principle have been published [33–35]. Nanovoids in Al-doped ZnO have improved the overall thermoelectric performance of the material [36] whereas in
Bi2Te3 there is an increase in the ZT due to effective phonon scattering [37]. Other examples of reduced thermal
conductivity as a result of nanovoid formation include
AgSbTe2 [38], SiGe [39], Si [40] and Ca3AlSb3 [41].
It is well known that Zn has a very high diffusion rate in
b-Zn4Sb3 as Zn jumps easily from one interstitial site to the
other [42]. Therefore, a suitable heat treatment could dissolve the Zn precipitates by inducing the diffusion of Zn
into the b-Zn4Sb3 matrix [43]. In our case we use Zn precipitates of nanometric size in bulk b-Zn4Sb3 to eventually
create stable nanostructured voids. A previous study highlighted the presence of Zn nanoinclusions in b-Zn4Sb3 [12].
Here, we report on an original way to use these Zn inclusions as a method for producing stable nanostructures in
thermoelectric b-Zn4Sb3. By carefully varying the Zn concentration and by applying a suitable heat treatment, one
is capable of inducing the diffusion of the Zn atoms. The
voids subsequently formed are visible not only at the nanoscale but also at the microscale. Even though, the mid- to
long wavelength phonons are not the most energetic ones,
they nevertheless contribute to the total thermal conductivity of the material, so emphasizing on the nanostructured
voids is relevant. We demonstrate the possibility of engineering a nanoporous bulk material in this work. A combination of transmission electron microscopy (TEM)
observations and density functional theory (DFT) calculations gives us a Zn concentration window within which a
nanoporous material can be obtained.
2. Experimental
2.1. Synthesis
The samples were prepared with various starting compositions ranging from Zn:Sb = 1.28 to Zn:Sb = 1.36.
The elements were directly reacted in a fused-silica
ampoule sealed under vacuum (105 torr). The melt was
heated for 8 h at 800 °C before being quenched in water.
The resulting ingot was ball milled for 4 h and hot pressed
at 350 °C for 1 h. Fine homogeneous powders were
obtained by mechanical alloying under argon in a SPEX
Mixer/Miller 8000 series mill for a total of 3 h. The powder
was hot pressed under argon at 350 °C for 1 h. Finally, it
was annealed without stress for 2 h at 350 °C.
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P. Rauwel et al. / Acta Materialia 59 (2011) 5266–5275
2.2. Characterization
3.2. SEM studies
The samples were characterized by X-ray diffraction
(XRD) to determine the crystal structure using a Philips
XPERT MPD diffractometer operated at 45 kV and
40 mA. Scanning electron microscopy (SEM) images were
recorded on a Quanta 200FEG, FEI instrument. TEM
studies were carried out using a JEM2010F microscope
operating at 200 kV and disposing a point-to-point resolution of 1.9 Å, with Cs = 0.5 mm, Cc = 1.1 mm, DfSch =
42 nm.
In Fig. 1 several SEM images of samples A and B are presented. The dark regions are voids. These voids vary in sizes
on the micrometric scale. In Fig. 1a we observe a large distribution of voids from 100 nm to 1 lm in size. Fig. 1b is a
higher-magnification SEM image showing irregularly faceted voids. Energy-dispersive X-ray analysis performed in
the voids showed Zn–Sb with ratio of 1.29 and no other
elements. Sample B presented a similar morphology, with
large and faceted voids (Fig. 1c). In Fig. 1d depicts a very
large, irregularly faceted void containing another void.
Fig. 1e is another example of a large micrometric void.
For the voids of sample B presented in Fig. 1f, small voids
of around 1 lm along with large faceted voids similar to
those in sample A were observed. No secondary phases were
observed for these two samples, thus confirming the XRD
results as being single-phase b-Zn4Sb3. For the sample with
a higher Zn:Sb ratio of 1.36 (not shown here), no voids were
observed on the micrometer scale; rather, Zn precipitates of
around 1 lm and larger were observed [48]. However, in
samples A and B voids at the micrometer scale are visible.
These voids are most likely a product of the mechanism
explained in this work.
2.3. Modeling
Theoretical calculations based on DFT were performed
to elucidate the atomic and energetic properties of the
Zn4Sb3 phase. The Vienna Ab Initio Simulation Package,
employing the projector-augmented wave method and the
Perdew–Burke–Ernzerhof generalized gradient approximation, was used [44–47]. A plane wave cut-off of 300 eV was
used for the relaxations, while 500 eV was used for the
total energy calculations. The k-point density was at least
0.25 Å1. Together with a criterion for self-consistence of
105 eV change of total energies, we obtained relative energies with less than 1 meV error originating from numerical
sources. Similarly, the forces were converged to within
0.05 eV Å–1. The relaxations allowed simultaneous changing of atomic positions, unit cell shape and cell size.
High-resolution
transmission
electron
microscopy
(HRTEM) simulations were carried out using the multislice
calculations incorporated in the JEMS software.
3. Results
3.1. X-ray diffraction
The XRD performed on our samples showed a Zn4Sb3
structure belonging to the R-3c space group with
a = 12.22 Å and c = 12.40 Å lattice parameters [7]. No evidence of other phases was observed for the sample with
Zn:Sb ratios of 1.30 and 1.33. For samples with Zn:Sb
ratios of 1.28, a secondary ZnSb phase was observed.
Finally, for Zn:Sb of 1.34 and 1.36, a secondary Zn phase
was observed. Table 1 recapitulates the presence of
different phases as a function Zn:Sb ratio. These samples
have previously been studied in detail [48]. Here, we concentrate on the samples with Zn:Sb ratios of 1.30 (sample
A) and 1.33 (sample B), where void formation was
observed.
3.3. (HR)TEM studies
At the nanometer scale, these voids have a different
appearance and are seemingly more regularly faceted.
Fig. 2 presents TEM observations of these voids in sample
A. Fig. 2a depicts the voids at a low magnification in sample A. The samples for TEM studies were prepared by
mechanical thinning and ion milling. Clearly, the voids
are omnipresent, be it at the grain boundary or within
the grain. In order to reinforce the fact that these voids
are not artifacts resulting from preferential ion beam thinning during TEM sample preparation, a crushed sample
dispersed in alcohol was used. The same voids are observed
in Fig. 2b irrespective of the sample preparation technique.
The average size of the voids is around 8 nm in the volume
of the grains (Fig. 2d and Supporting information). The
high-resolution image in Fig. 2c shows the faceting of the
particle at the nanoscale. The void is hexagonally faceted.
The power spectrum (Fig. 2e) of the void in Fig. 2b provides reflections corresponding to the zone axis of the bZn4Sb3. No extra reflections are visible, indicating that
no other phases are present. TEM was also performed on
this sample as a function of temperature. The aim was to
study the stability of the voids with increasing temperature,
Table 1
Presence of secondary phases in the samples as a function of starting Zn:Sb content as obtained from XRD studies [7].
Zn:Sb
1.283
1.280
1.300
1.330
1.341
1.350
1.360
Secondary phase
ZnSb
ZnSb
None
None
Zn
Zn
Zn
P. Rauwel et al. / Acta Materialia 59 (2011) 5266–5275
5269
Fig. 1. SEM images of: (a) a variety of void sizes in sample A; (b) irregularly shaped voids in sample A; (c) voids present in sample B; (d) a void in a void in
sample A; (e) a higher-magnification image of an irregularly shaped void in sample A; and (f) voids present in sample B.
Fig. 2. (a) Nanometric voids in an ion-milled sample A with Zn:Sb = 1.30; (b) high-resolution image of a nanovoid (Zn:Sb = 1.30); (c) high-resolution
image of Zn nanoparticle the bar corresponds to 2 nm; (d) nanovoids in a crushed sample with Zn:Sb = 1.30; (e) fast Fourier transform of the nanovoid in
(b); and (f) power spectrum of the Zn particle in (c). The red circles correspond to reflections from Zn. (For interpretation of the references to color in this
figure legend, the reader is referred to the web version of this article.).
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P. Rauwel et al. / Acta Materialia 59 (2011) 5266–5275
from RT to 350 °C. All the voids seemed to be very stable
under increasing temperature. No change of size and shape
of the voids was observed.
In accordance with a previous study [15], we also found
Zn nanoparticles in our sample. One such Zn nanoparticle
in sample A is shown in Fig. 2e. There are very few of them
and hence they are difficult to observe. Fig. 2f is the power
spectrum of Fig. 2e composed of reflections from the bZn4Sb3 and the Zn particles. The red circles delimit the
reflections from the Zn particle oriented along the h1 0 0i
zone axis of the hexagonal close-packed Zn structure with
space group P63/mmc and lattice parameters a = 2.665 Å
and c = 4.947 Å. In this sample, a ZnSb grain was also
observed with size >600 nm. There are certainly more of
the ZnSb grains, but they are very difficult to isolate. Sample A is mainly single-phase b-Zn4Sb3 with traces of Zn and
ZnSb.
On increasing the Zn:Sb ratio to 1.33, many more Zn
nanoinclusions along with nanovoids were observed.
Fig. 3a is one such example of Zn nanoprecipitates present
in sample B. Fig. 3b is a high-resolution image of a Zn
nanoparticle in sample B. The size of the nanoparticle is
around 6 nm, and it is oriented along the h1 1 1i zone axis,
as indicated by the power spectrum in the inset to Fig. 3b.
The average size of these precipitates is around 8 nm (Supporting information). Selected area diffraction patterns
were collected, but were difficult to index for Zn metal
due to the smallness of the nanoparticles and the many similar d-spacings for Zn and b-Zn4Sb3.
For TEM sample preparation, sample B was crushed,
the powder obtained was suspended in ethanol and a drop
of the suspension was then placed on a perforated carbon
grid for TEM observation. Ion-milled samples were not
observed as local heating due to ion beam thinning is a
source of artifacts in TEM observations. In Zn-precipitate-rich samples, local heating could bring about a change
in the morphology of the sample as Zn has a very high diffusivity. On observation of the crushed sample B, Zn diffusion was very clear. Prolonged exposure to the electron
beam increased the porosity of the material (Supporting
information). During observation, care was taken to study
sample B at low electron beam currents and for a short period of time. No electron-beam-induced damage was
observed in sample A, possibly because there was less free
Zn in sample A compared to sample B. In Fig. 3c, we
observe nanovoids in sample B with void sizes ranging
from 5 to 20 nm. Size distribution histograms showed the
average size of these voids to be around 8 nm (Supporting
information), which corroborates the size distribution histogram plotted for the nanovoids in sample A. Fig. 3d
shows a large number of Zn nanoparticles present everywhere; these are represented by black dots. The Zn inclusions become prominent in Fig. 3e, where the focus is on
only one nanovoid and its surrounding area containing
the precipitates.
A sample with a high Zn concentration (Zn:Sb = 1.36)
was also observed and has been reported elsewhere [48].
A large number of Zn nanoinclusions were observed along
Fig. 3. (a) Zn nanoparticles in sample B (Zn:Sb = 1.33); (b) high-resolution image of a Zn nanoparticle (inset is the power spectrum of the nanoparticle);
(c) nanovoids; (d) nanovoids in sample B surrounded by Zn nanoparticles (black dots); and (e) high-magnification image of a nanovoid in sample B with
Zn:Sb = 1.33. The Zn nanoparticles are prominent.
P. Rauwel et al. / Acta Materialia 59 (2011) 5266–5275
with large Zn grain sizes for this Zn:Sb ratio. This sample,
however, presented almost no nanovoids and hence no
porosity. From our observations, the quantity of the
nanovoids and Zn precipitates depends directly on the
starting content of Zn. These nanovoids and Zn precipitates were observed even in the non-ball-milled sample
for Zn:Sb of 1.33. All the samples observed here were
annealed for 2 h at 350 °C. To understand the diffusivity
of Zn through b-Zn4Sb3 on annealing, knowledge of the
stability of various interstitial models as a function of Zn
concentration is essential. This was calculated by DFT
and is presented below.
3.4. Stability of various b-Zn4Sb3 models
Atomic calculations based on DFT were carried out to
investigate the stability of Zn vacancies and interstitials
in the b-Zn4Sb3 rhombohedral structure. The initial structure was the stoichiometric Zn6Sb5 compound, where no
Zn interstitials or vacancies are present. The stability of
interstitials or vacancies was calculated according to the
following formula:
DH ðZn36þn Sb30 Þ ¼ ðEðZn36þn Sb30 Þ EðZn36 Sb30 Þ nEðZnÞÞ
ð1Þ
Here E is the total electronic energy as calculated by
DFT and n is the number of excess Zn atoms. A negative
n implies vacancies. The energy of Zn is calculated by relaxing the experimental crystal structure of Zn followed by a
single-point total energy calculation.
Fig. 4a shows how Zn vacancies (in models with a Zn:Sb
fraction of less than 1.20) are unstable, while Zn interstitials are stable in the Zn:Sb interval 1.20–1.32. The most
stable composition is Zn:Sb = 1.27. It must be emphasized
that these calculations do not take into account temperature or entropy (they are valid at 0 K), and thus do not
allow quantitative predictions of the Zn solubility at finite
5271
temperatures. Nevertheless, the ground state enthalpies can
give qualitative information about the population of different sites as a function of temperature. In general, sites with
a negative formation enthalpy will be fully occupied at low
temperatures, as we found in the case of the interstitial Zn.
However, as the temperature is increased, a growing fraction of these sites will be deserted by thermally activated
Zn atoms. At the same time, an increasing number of Zn
vacancies will be formed by a corresponding mechanism.
The overall conclusion from these calculations is that
the solubility of Zn in Zn4Sb3 decreases with increasing
temperature. This has a number of important consequences, which are represented in Fig. 5. First of all, it
means that the solubility of Zn at the highest temperatures
(accessed during quenching from the melt) is quite low. The
calculations suggest that if one starts with a Zn:Sb fraction
higher than around 1.20 there will be excess Zn in the sample, which leads to Zn precipitation. The amount and size
of these precipitates should depend on the quenching rate,
since their formation depends upon solid-state diffusion.
The inclusions are frozen into the structure at RT. When
the sample is subsequently heated on annealing, the Zn solubility is higher, and Zn can re-enter the Zn4Sb3 phase
from the inclusions. This relies on the high diffusivity of
Zn in Zn4Sb3 [49] and is proposed as the main mechanism
for creating the nanovoids.
3.5. Zn interstitials and vacancies
Since the DFT calculations were used to relax the various structural models, detailed information about the
interaction between vacancies and interstitial sites was also
obtained. This is quantified in Fig. 4b, where various
Zn37Sb30 models are compared. Similar to the findings of
Toberer et al. [50], the stability of the various models is
within only a few meV, which means that all these interstitial models are accessible at room temperature. We
investigated the interaction between Zn interstices and
Fig. 4. DFT calculated enthalpy of formation DH for Zn vacancies (diamonds) and interstitial Zn (triangles) in the Zn4Sb3 rhombohedral structure as a
function of the Zn content (a). Enthalpy (defined in the text) is plotted in eV per Zn6Sb5 unit, and is defined as stable for negative values. The dashed lines
are drawn as a visual guide the eye only. In (b) DH is listed for various models with a Zn/Sb ratio of 1.23 (Zn37Sb30). The model marked with started with
a Zn3 interstitial only, but relaxed into Zn3 and Zn4 interstitials around a Zn1 vacancy. The Zn site numbering is similar to that of Ref. [9]. The model
marked with started with a Zn1 vacancy and two neighbor Zn4 interstitials, but one of the Zn4 interstitials relaxed into the Zn1 vacancy.
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P. Rauwel et al. / Acta Materialia 59 (2011) 5266–5275
Table 2
The calculated interatomic Zn–Zn distances (DFT) compared to the same
distances in the structural model from diffraction in Ref. [9] (XRD).
Interstitials occupied
Intersites
Distances R
(XRD, Å)
Distances R
(DFT, Å)
Zn2
Zn4
Zn1vac + Zn2 + Zn3
Zn1vac + Zn2 + Zn4
Zn1vac + Zn3 + Zn4
Zn1-Zn2
Zn1-Zn4
Zn2-Zn3
Zn2-Zn4
Zn3-Zn4
1.6
1.7, 2.0
2.0
2.7
2.5
2.5
2.7
2.5
2.6
2.7
The occupancy of Zn2, Zn3 and Zn4 is only a few percent.
Fig. 5. Proposed schematics of the synthesis procedure. When the
temperature (solid, red curve) is high around melt, the Zn solubility
(dotted green curve) is relatively low. This leads to a Zn concentration in
the Zn4Sb3 phase (dashed blue curve) lower than that at lower temperature, and Zn precipitates are formed. (Note that the solubility and
concentration are only defined in the solid, so the relevant temperature is
where the solid is formed during quenching.) These precipitates are frozen
into the microstructure when the sample is quenched, since the solid-state
diffusivity is too low at room temperature to allow the Zn concentration to
increase (despite the higher solubility at room temperature.) The Zn
concentration in Zn4Sb3 increases upon annealing, since the Zn solubility
is higher than it was when starting from the melt. This means that Zn
leaves the precipitates, forming voids in the microstructure. (For
interpretation of the references to color in this figure legend, the reader
is referred to the web version of this article.)
vacancies, which can provide information about the local
geometric structure. We find, in correspondence with
Toberer et al. [50], that the Zn3 interstitial does not exist
together with Zn1; the neighbor Zn1 relaxes to a Zn4 position and leaves a Zn1 interstitial behind (the Zn numbering
follows Ref. [12]). This does not only apply to the
Zn3 + Zn4 pair. When a pair of interstitials is created
along with a Zn1 vacancy, this gives a structure which is
at least as stable as a single interstitial. Thus, the most stable configuration is the Zn3 + Zn4 interstitial pair
(together with a Zn1 vacancy), followed by the Zn2 and
Zn4 single interstitials, then the Zn2 + Zn3 and
Zn2 + Zn4 pairs. This means that, even if lone vacancies
are expensive to form, Zn vacancies should be rather common in combination with interstitial pairs, even at low
temperatures.
The relaxed models in Fig. 4 exhibit quite a large spread
in the interstitial positions, depending on their nearest
neighbors (other interstitials or vacancies). As an example,
the position of the Zn4 site in the “Zn4” model is located
88 pm away from that of the Zn4 site in the “Zn1vac +
Zn3 + Zn4” model. This is significantly more than could
be expected from numerical uncertainties inherent to the
relaxation procedure, and means that the temperature factor for these sites should be relatively high when refining
the structure. It also indicates that the sites will be difficult
to detect by direct spatial techniques. Some interatomic distances from the relaxed DFT models are compared to the
corresponding ones from the diffraction-based structural
model of Ref. [9] in Table 2.
We see that the Zn–Zn distance is always between 2.5
and 2.7 Å in the relaxed DFT models. This is similar to
the Zn–Zn distance in elemental Zn, and should thus be
expected in atomistic calculations which represent snapshots of the local structure. The Zn–Zn distances in the
XRD model exhibit a much larger spread, however, with
some of the distances being unphysically small. This reflects
the fact the XRD model is an average picture of the occupancy. One immediate conclusion from this is that, when
some of the neighboring positions are occupied simultaneously, significant relaxations away from the XRD positions subsequently occur. Some pairs are always
accompanied with a neighboring vacancy. One example is
the Zn3–Zn4 pair, which only exists together with a Zn1
vacancy.
The only spatial resolution techniques known to have
touted the presence of these interstitial atoms are singlecrystal X-ray and powder synchrotron-radiation diffraction
[12]. In this study, HRTEM was used to study the atomic
arrangement in b-Zn4Sb3. The three interstitial Zn sites
are not very different from the Zn1 position and are at reasonable distances from the Sb position (2.5 nm). Therefore, discerning the Zn atomic positions from those of Sb
should be relatively simple. Moreover, from the DFT calculations, stable Zn vacancies and interstitials should be
created for a Zn:Sb ratio of 1.30.
An experimental HRTEM image of the interstitial
model for b-Zn4Sb3 shown in Fig. 6a along the h0 0 1i axis
gives the characteristic sixfold symmetry of the Zn and Sb
atomic arrangement for a defocus of 60 nm. The thin foil
thickness (t) for the sample after simulation (Fig. 6b) was
estimated to be 50 nm. In the experimental and simulated
images (Fig. 6a and b), only Sb atoms (white spots) are visible. The bright white spots correspond to the Sb2 dimer
columns and the dull white spots correspond to the (Sb2)
4
atomic columns. Zn atoms are invisible. On simulation
for thinner cross-sections, 8 and 2.5 nm as in Fig. 6c and
d respectively, the Zn atoms emerge (orange arrows).
Therefore relatively thin cross-sections are required to visualize the Zn atoms. From the HRTEM simulations, it is
very difficult to differentiate between the different Zn sites.
The use of HRTEM to locate the interstitial Zn sites in
P. Rauwel et al. / Acta Materialia 59 (2011) 5266–5275
5273
Fig. 6. (a) Experimental HRTEM image along the h0 0 1i projection for t = 50 nm. (b–d) Simulated HRTEM images along h0 0 1i for t = 50 nm, t = 8 nm
and t = 2.5 nm, respectively.
b-Zn4Sb3 with an instrument equipped with a Cs corrector
will be the subject for future studies.
4. Discussion
Nanostructuring by void formation is possible. We have
observed void formation at the micro- and nanoscales.
These voids are faceted, and their average size is around
8 nm in grains at the nanoscale. Their average size matches
well with the average size of Zn precipitates found in sample B (8 nm). Since we have eliminated the possibility of
void formation from ball milling, ion beam thinning during
sample preparation and TEM observations, we therefore
conclude from our observations and calculations that the
nanovoids are formed during annealing of the samples rich
in Zn precipitates at 350 °C.
From our observations, Zn precipitates are present in
the as-quenched samples for Zn:Sb ratios of 1.33 and
1.36. This is consistent with our calculations, which predict
that the most stable ratio is 1.27; that is, Zn precipitates
should form for any ratio above 1.27. Experimentally, this
can be translated as the creation of a two-phase material:
b-Zn4Sb3 and Zn nanoparticles. On annealing the sample,
we propose that Zn atoms from the precipitates diffuse into
the b-Zn4Sb3 matrix. Diffusion of Zn atoms in crystalline
b-Zn4Sb3 occurs on annealing the sample due to the high
number of available interstitial sites and the high solidstate diffusivity of Zn in the b-Zn4Sb3 matrix at intermediate temperatures [49]. Since the solubility of Zn in Zn4Sb3
should be quite high at room temperature, reprecipitation
of Zn is unlikely after annealing. We therefore obtain a single-phase material with nanovoids for Zn:Sb = 1.30.
As shown above, different combinations of Zn vacancies
and Zn interstitials can accommodate the Zn from the precipitates. Even though visualizing the Zn atom proves to be
a challenge with HRTEM, new-generation microscopes
could help elucidate the presence of Zn1 sites and consequentially the Zn interstitial positions.
The void formation in our material is quite similar to the
nanoscale Kirkendall effect, where hollow materials are
formed due to diffusivity differences between the innerand outer-lying material. However, in all the cases in the
literature, the Kirkendall effect is vacancy mediated. This
could possibly come from the fact that the materials presenting the Kirkendall effect do not harbor interstitial
atoms. In our case, interstitials and vacancies can occur
simultaneously. Hopping between Zn vacancies and interstitials regulates the Zn1 site occupancy at approximately
89% [12]. This diffusion is thus a special case of the Kirkendall effect, as both interstices and vacancies are involved.
The actual diffusion of Zn has been elaborated in a paper
based on first-principles molecular dynamics calculations
[49].
The synthesis path has provided a thermodynamically
stable material which can retain its nanoscale structures
up to 350 °C. This is explained by the interplay between
Zn solubility and diffusivity, which was balanced by the
annealing procedure. The result is the production of a
material with several possibilities for reducing the thermal
conductivity. Short wavelength phonons can be scattered
by Zn vacancies and interstitials, which are randomly distributed at the atomistic level. Furthermore, medium to
long wavelength phonons, which are known to carry a substantial amount of heat, can be scattered by the nanovoids.
We see this as the explanation for the particularly low thermal conductivity of Zn4Sb3.
With regard to the electrical and thermal properties, the
electron mean free paths are much longer than the phonon
mean free paths. This implies that the nanovoids should
not have an adverse effect on the electrical properties.
The b-Zn4Sb3 is known for its “phonon-glass–electroncrystal” character. The aim is to reduce the thermal conductivity without decreasing the electrical conductivity.
The reduction in the total thermal conductivity is usually
brought about by a decrease in the lattice part of the thermal conductivity in this system, whereupon nanostructuring comes into play. The advantage of nanovoids over
nanoprecipitates of Zn lies in their stability at high temperatures, which could be of importance in high-temperature
experiments.
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P. Rauwel et al. / Acta Materialia 59 (2011) 5266–5275
The Zn4Sb3 system forms nanostructures spontaneously
when appropriately heat treated. This has many benefits
related to efficient synthesis and convenient sample handling, and it is interesting to speculate whether this is
unique to this particular material or if these principles
can be employed in other systems as well. We have shown
above that nanovoid formation in Zn4Sb3 seems to depend
on the following prerequisites: formation of precipitates
due to phase separation; control of precipitate size via rate
of quenching; high atomic diffusivity of one of the elements
forming the nanoprecipitates; and presence of a combination of vacancies and interstitials in the crystal structure,
facilitating efficient transport of the diffusing species. It
seems likely that all of these factors need to be present in
order to achieve as flexible synthesis properties as exhibited
by the Zn4Sb3 system. It is difficult to estimate how common such features are among materials with a high thermoelectric power factor, but the extraordinarily low thermal
conductivity of Zn4Sb3 compared to other thermoelectric
materials indicates that this material is unique. Nevertheless, the attributes listed above are quite general, and one
could expect to identify many more systems with similar
properties were a systematic search pursued.
Our understanding of how the processing influences the
nanostructure thus opens the possibility of engineering
nanostructures in this material and other related materials.
First of all, the temperature profile during quenching from
the melt governs not only the initial solubility of Zn in the
pristine Zn4Sb3 matrix, but also the size distribution of Zn
precipitates. How these precipitates are transformed into
voids is governed by the temperature profile during annealing. Thus, choosing optimal processing conditions can
result in materials which are thermodynamically stable
and also have enhanced thermoelectric properties.
5. Conclusion
We have established the presence of nanovoids in the bZn4Sb3 system and have proposed a mechanism for their
formation due to solid-state diffusion of Zn. This mechanism starts with Zn nanoinclusions precipitating during
the synthesis of the b-Zn4Sb3, i.e. high diffusivity and low
solubility of Zn at high temperature leads to precipitation
of Zn when the material is quenched from melt [43]. Subsequent annealing at an intermediate temperature (slightly
below the temperature at which high temperature Zn4Sb3
phases appear) induces the diffusion of Zn from the nanoinclusions into the Zn4Sb3 matrix, thus filling interstitial
sites. This creates a nanoporous material.
The observation of voids at the micro- and nanoscales
using SEM and TEM along with knowledge of the stability
of Zn vacancies and interstices suggests a compositional
range within which these voids can be formed. Based on
the ground state DFT calculations, we estimate that the
Zn:Sb ratio should be at least 1.27 for the precipitates to
form. Rediffusion of Zn into the Zn4Sb3 lattice seems difficult when this ratio is above approximately 1.33.
In summary, Zn nanoparticles precipitate due to a phase
separation during the first step of synthesis. An annealing
treatment reincorporates the Zn from the precipitates via
a plausible nanoscale Kirkendall effect. Moreover, these
nanovoids are stable up to 350 °C (as observed by TEM),
which is around the upper limit of the working range of
b-Zn4Sb3 in devices. Optimizing the formation of these
nanovoids with different annealing temperatures and Zn:Sb
ratios is still required and calls for more experiments. This
could establish a new path towards engineered nanostructures in this compound and other related compounds.
Acknowledgements
The authors would like to thank Ole Bjørn Karlsen for
fruitful scientific discussions and sample synthesis. Eric S.
Toberer and G. Jeffrey Snyder are gratefully acknowledged
for sample synthesis and fruitful discussions. The Norwegian
Research Council and the Marie Curie-PERG05-GA2009-249243 are thanked for financial support.
Appendix A. Supplementary material
Supplementary data associated with this article can be
found, in the online version, at doi:10.1016/j.actamat.2011.
05.003.
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