Sodium Substitution in Lead Telluride

Article abstract of DOI:10.1021/acs.chemmater.7b05091

Sodium is widely used as a substituting element in p-type PbTe-based thermoelectric materials. In this work, two series of polycrystalline samples Pb_1-yNa_yTe_1-y/2 (total charge balance) and Pb_1-xNa_xTe (total charge nonbalance) were examined. Na has limited solubility for both of the series. The MAS ²³Na NMR analysis of Pb_1-xNa_xTe series (for Pb_0.98Na_0.02Te sample after spark-plasma sintering, SPS) reveals only one Na signal, corresponding to Na atoms coordinated by six Te atoms, indicating substitution of Pb by Na without defects in the Te sublattice. In the Pb_1-yNa_yTe_1-y/2 series, clustering of Na atoms with reduced coordination by Te was observed. Additional heat treatment of these samples leads to the reorganization of the Na clusters in PbTe and their equilibration with the homogenized distribution of Na in the whole volume. The maximum ZT values of 1.4-1.6 at 760 K are established for both Pb_1-xNa_xTe and Pb_1-yNa_yTe_1-y/2 series. Upon long-time annealing at 873 K, reorganization and redistribution of Na atoms lead to the change in carrier concentration and, consequently, the thermoelectric properties for both series.

Full text of DOI:10.1021/acs.chemmater.7b05091

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Article
Sodium substitution in lead telluride
Xinke Wang, Igor Veremchuk, Matej Bobnar, Ulrich Burkhardt, Jing-Tai Zhao, and Yuri Grin
Chem. Mater., Just Accepted Manuscript • DOI: 10.1021/acs.chemmater.7b05091 • Publication Date (Web): 29 Jan 2018
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Chemistry of Materials
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Sodium substitution in lead telluride
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Xinke Wang,1 Igor Veremchuk,1 Matej Bobnar,1 Ulrich Burkhardt,1 Jing-Tai Zhao2, 3 and Yuri
Grin1*
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1Max-Planck-Institut für Chemische Physik fester Stoffe, 01187 Dresden, Germany
2School of Materials Science and Engineering, Shanghai University, Shanghai 200444, China
3Nanophotonics Center, Texas Tech University, Lubbock, TX 79409, USA
ABSTRACT: Sodium is widely used as substituting element in p-type PbTe-based thermoelectric materials. In this work,
two series of polycrystalline samples Pb1-yNayTe1-y/2 (total charge balance) and Pb1-xNaxTe (total charge non-balance) were
examined. Na has limited solubility for both of the series. The MAS 23Na NMR analysis of Pb1-xNaxTe series (for
Pb0.98Na0.02Te sample after SPS) reveals only one Na signal, corresponding to Na atoms coordinated by six Te atoms, indi-
cating substitution of Pb by Na without defects in the Te sublattice. In the Pb1-yNayTe1-y/2 series, clustering of Na atoms
with reduced coordination by Te was observed. Additional heat treatment of these samples leads to the reorganization of
the Na-clusters in PbTe and their equilibration with the homogenized distribution of Na in the whole volume. The maxi-
mum ZT values of 1.4 ÷ 1.6 at 760 K are established for both Pb1-xNaxTe and Pb1-yNayTe1-y/2 series. Upon long-time annealing
at 873 K, reorganization and redistribution of Na atoms lead to the change in carrier concentration and, consequently, the
thermoelectric properties for both series.
gress has been made to obtain high ZT in Na-doped PbTe-
Introduction
based bulk materials using various substitutions (Mg, Ca,
Sr, Ba, Hg, Cd, Yb, Mn).26-35
Thermoelectric materials have the ability to interconvert
heat and electricity, which could play an important role in
It is believed that the monovalent Na is substituting
the alternative, environmentally friendly approach within
Pb. Typically Na is added to PbTe and PbTe-based mate-
the global sustainable energy solution.1, 2 The efficiency of
rials in the form of NaTe or Na2Te, thus giving rise to
formation of acceptor centers.15, 31, 36-40 First experiments
thermoelectric materials is quantified by the thermoelec-
tric dimensionless figure of merit ZT = σS2T/(κel+κL),
revealed the diffusion coefficient increasing with increas-
ing Na concentration. If Na diffuses via Pb vacancies, the
respective diffusion coefficient would be expected to de-
crease. Such anomalous concentration dependence of the
where S is the Seebeck coefficient, σ is the electrical con-
ductivity, κel is the electronic thermal conductivity, κL is
the lattice thermal conductivity and T is the absolute
temperature.3-5 The rock-salt structured, narrow-band gap
diffusion coefficient was explained by presence of the Te
lead chalcogenides (PbX, X=Te, Se, S) semiconductors
vacancies, which may indeed reduce the energy barriers
have been previously studied because of their outstanding
for migration, temporarily making it possible for Na to
thermoelectric performance.6-14 Na has been proved as
reside on Te sites. In other words, the diffusion coefficient
one of the most effective dopants in controlling hole-
should increase with increasing Na concentration if Te
carriers concentration in PbX and therefore has been
vacancies take part in the diffusion mechanism.17
extensively utilized in order to optimize their thermoelec-
tric properties.15-19 Experimental and theoretical studies
In a later study, the hole concentration was found to
be considerably smaller than a value calculated from the
indicate that Na substitution will not introduce resonant
amount of Na added to the reaction mixture, assuming
levels in the electronic band structure of PbTe but, rather,
one hole was produced per one Na atom. The maximum
move the Fermi surface close to the heavy-hole valence
band.18,20-21 Due to large mass and radii fluctuations, a
Na solubility in PbTe was experimentally determined to
lie somewhere between 0.5 at. % and 1.75 at. %, although
reduced lattice thermal conductivity can also be achieved
some loss of Na may occur during processing.36, 39 The
by Na substitution.22-23 The Na-doped PbTe, called ‘‘2P-
maximum observed carrier concentration is 2.5 × 1020 cm-
PbTe’’, has been used in 1959 RTG and for several NASA
3. Each Na atom donates about one hole when Na concen-
missions in the 1960’s.24-25 In 2011, Pei et. al. 15 re-evaluated
tration is higher than ~ 6 × 1019 cm-3, which corresponds to
the thermoelectric properties of p-type PbTe:Na using
new reliable high-temperature thermal conductivity data.
As a result, the maximum ZT ~ 1.4 was obtained, instead
of the earlier underestimate of ZT = 0.7. Recently, pro-
0.84 at. %.16 However, at Na concentration less than this
value, one hole produced by two Na atoms was distin-
guished experimentally. For the nature of the acceptor
centers at small Na concentrations, a proposed model
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implies a formation of the significant complex center
annealing at 873 K, with following quenching in ice water
(NaPb□TeNaPb).16
after 900 hours. Na2Te, for the NMR investigations, was
synthesized by melting Na and Te in the stoichiometric
ratio in an Ar atmosphere in a sealed Ta tube at 773 K for
5 hours.
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The systematic study of PbTe-Na2Te and PbTe-NaTe
quasi-binary phase diagrams shows that only Na2Te (anti-
CaF2 crystal structure40) and NaTe phase (own molecular-
like structure41) are found in these systems.42 According to
the chemical analysis by electron microprobe WDS, the
maximum solubility of Na in PbTe was found to be 1.4 ±
0.3 mol % (0.7 at. % Na average values from more than
100 point analysis) at 623 K. While at 513 K, the solubility
value decreases to 0.24 ± 0.14 at. %.39 First-principles
calculations of defect energy in Na-Pb-Te indicate that Na
substituting Pb is the lowest-energy defect (NaPb1-); here
the solubility should increase with increasing tempera-
ture.37 In recent microscopic studies on Na-doped poly-
crystalline PbTe samples, Na-rich nano-segregations at
mesoscale imperfections, dislocations, and grain bounda-
ries even nanoscale precipitates were formed beyond the
solubility limit,43-45 which may provide additional scatter-
ing centers and reduce the thermal conductivity36, 46 or
increase the high-temperature electrical conductivity due
to re-dissolution of Na at elevated temperatures.44 How-
ever, simple 1:1 substitution Pb by Na is mostly considered
in the experimental studies. The complete shape of the
solid solution of Na in PbTe within the ternary system
Na-Pb-Te was not established (cf. Ref. 39). As a conse-
quence, the influence of different Pb-by-Na substitution
mechanisms on the thermoelectric activity of the ternary
materials remains unclear. The possibility of the two sub-
stitution schemes is indicated or assumed by different Na-
additives (NaTe or Na2Te) for formation of acceptor cen-
ters. In a freshly appeared work, the n-type materials were
rather unexpectedly obtained by ball milling of PbTe with
Na2Te.47
Phase identification was performed with the X-ray
Guinier diffraction technique (Huber G670 camera, Cu Kα1
radiation,
λ = 1.54056 Å, Δ2θ = 0.005°, 2θ range 3.0° - 100°,
exposure time 6×15 min). The reflection positions, ob-
tained by profile deconvolution, were corrected using the
internal standard LaB6. Lattice parameter refinements and
other crystallographic calculations were performed with
the program package WinCSD.48
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For the metallographic study, the materials pieces
were embedded in conductive resin, subsequently grind-
ed and polished. The sample homogeneity was examined
by optical microscopy (Zeiss Axioplan2) in bright-field
and polarized light. The element mappings were obtained
by electron microprobe analysis with the energy disper-
sive X-ray spectroscopy (Bruker Quantax 400 system with
the detector XFlash 630) on the polished bulk materials.
Elemental chemical analysis (for Pb, Te, Na, O) was per-
formed by using the inductively-coupled plasma optical-
emission spectrometry (ICP-OES, Agilent 5100 SVDV
setup for Pb, Te, Na) and the carrier-gas hot-extraction
technique (LECO TCH600 setup for oxygen).
Electrical resistivity and Seebeck coefficient were
measured simultaneously with the ZEM-3 setup (Ulvac-
Riko) in the temperature range 300 to 760 K. The Hall
effect (RH) was measured with a standard four-point ac
technique in a physical property measurement system
(PPMS, Quantum Design), with magnetic fields up to 9 T.
The Hall carrier concentrations were calculated by 1 / (RH
· e), where RH is Hall coefficient, e is the electron charge.
Thermal diffusivity (D) measurements were conducted
with the Netzsch LFA 457 equipment (LFA). The heat
capacity per atom (Cp) was estimated from the relation Cp
/ kB = 3.07+0.00047(T - 300)49. Thermal conductivity was
calculated as κ = dCpD, where d is the density obtained
using the mass and the geometric volume of the specimen
disk after SPS. Lattice thermal conductivity (κL) was cal-
culated by subtracting the electronic part κe = LσT (the
Wiedemann-Franz law) from the total conductivity, the
Lorenz number is evaluated from the equation:
In this report, the crystal structure features and ther-
moelectric properties of samples series Pb1-yNayTe1-y/2
(total charge balance) and Pb1-xNaxTe (total charge non-
balance) have been investigated in order to achieve deep-
er understanding of the Na substitution in PbTe.
Experimental details
Bulk polycrystalline samples Pb1-xNaxTe (0 ≤ x ≤ 0.04),
Pb1-yNayTe1-y/2 (0 ≤ y ≤ 0.10), were synthesized by melting
the elements Pb (shot, 99.999 mass %), Te (chunk,
99.9999 mass %), Na (chunk, 99.99%) in a graphite-
coated and fused silica tube at 1273 K for 6 h under a vac-
uum of around 10-4 torr. Then, the temperature was slowly
lowered to 873 K and the samples were annealed for six
days for homogenization. The obtained ingots were
ground into powders by hand using an agate mortar in an
argon atmosphere before spark-plasma sintering (Fuji
SPS-515S) at 673 K under a pressure of 60 MPa for 7
minutes. The polished SPS-manufactured disks (∅ = 10
mm, 2 mm thick) were first used for measurements of the
thermal diffusivity. Then the disks were cut into rectan-
gular blocks (2 × 2 × 8 mm3) by wire saw in order to ob-
tain specimens for measurements of electrical resistivity
and Seebeck coefficient. The cut sample bars were sealed
in Ta tubes under Ar atmosphere in fused silica tube for
|ꢁ|
ꢀ = 1.5 + exp[− ꢂꢂꢃ], which is accurate within 20% for
PbTe.50
Nuclear Magnetic Resonance (NMR) experiments were
performed on a Bruker Avance 500 spectrometer with a
magnetic field of B0 = 11.74 T and standard Bruker MAS
probes. The samples were diluted with GeO2 and packed
into 4 mm ZrO2 rotors. The 23Na signals were referenced
to saturated solution of NaCl with the reference frequency
of 132.29127 MHz. The spectra were obtained either from
the free induction decay after a single pulse of 2 μs or
from the echoes after two 90° pulses of 6 μs. The recovery
time was 10 s. The experiments were performed under
static and spinning conditions with the spinning rates
provided in the text below.
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Chemistry of Materials
this trend is more prominent for the samples before an-
Results and discussion
1
nealing (Figure 1b). In case of Pb1-yNayTe1-y/2, the maxi-
mum solubility of Na is 1.5 at. %, in contrast to 2.5 at. %
before annealing; and for Pb1-xNaxTe, 0.5 at. % as com-
pared to 1.0 at. %.
We prepared two series of the samples (Figure 1a, top).
The first series with the nominal composition Pb1-xNaxTe
(x = 0.005 ÷ 0.04) assumes that Na atoms simply substi-
tute Pb. All as-cast samples are single-phase materials
according to the powder X-ray diffraction (PXRD). The
lattice parameters decrease with the increasing Na con-
centration monotonically up to 1 at.% (Figure 1b, red
squares) being in accord with the respective ionic radii of
the Na+ (0.99 Å) and Pb2+ (1.19 Å).22 This signalizes the
homogeneity range border in direction to the NaTe phase
of about 1 at.% of Na, being well in agreement with the
results obtained at 623 K.39 Relatively small value of Na
concentration can be understood given a strong differ-
ence in the crystal structure: ionic NaCl-type structure of
PbTe vs. Te polyanions in NaTe (Figure 1a). Above 1 at. %,
the gradient of lattice parameter changes, but it is not
zero as expected for the samples in the multiphase region.
This observation may indicate a non-complete homoge-
neity of the material after the primary heat treatment.
After additional SPS treatment (at T = 673 K), the lattice
parameters of the cubic phase for x > 1 at. % remain un-
changed within 2 e.s.d. (Figure 1b, red triangles), confirm-
ing the border of the homogeneity range. The samples
may still not be completely homogeneous, which is also
revealed by the measurements of thermoelectric proper-
ties (see below). The inhomogeneity of the samples can
arise on the atomic level, since DTA (Figure 2) and ele-
ment mapping scanning (Figure 3) experiments do not
reveal any presence of additional phases, phase transfor-
mations, etc. The only exception are small Na-rich ag-
glomeration areas in the microstructures (Figure 3). The
absolute values of the lattice parameters are slightly re-
duced after the SPS treatment, caused by further ordering
in the crystal structure due to the enhanced diffusion
under SPS conditions. During thermoelectric measure-
ments, some Na was lost (Table S1), and the lattice pa-
rameters are becoming slightly larger for each sample
(Figure 1b, red stars).
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This complex behavior of Na substitution raises the
question of where in the crystal structure Na is located.
Because the X-ray powder diffraction cannot yield this
information, the NMR spectroscopy was performed. Fig-
ure 4 shows the MAS 23Na NMR spectra of the selected
samples from the Pb1-yNayTe1-y/2 and the Pb1-xNaxTe series.
The MAS 23Na NMR spectrum of Pb0.98Na0.02Te after SPS
(shown in black in Figure 4, bottom) shows one strong
peak at about -14 ppm. Because there is no evidence for
another phase(s) in this sample, and the Pb-by-Na substi-
tution is the most probable case, the peak at -14 ppm
should come from Na replacing Pb in the PbTe. The Na
atom is coordinated by six Te atoms (Figure 4, top right)
and according to Ref. 51, the higher coordination of Na
atoms by negatively charged atoms results in more nega-
tive chemical shifts. The MAS 23Na NMR spectrum of the
as cast sample Pb0.95Na0.05Te0.975 is more complex (orange
line, Figure 4 bottom). The weak peak at -13 ppm corre-
sponds to the main peak of the Pb0.98Na0.02Te samples,
thus it is assigned to Na replacing Pb in the PbTe struc-
ture. The main peak at +40.6 ppm corresponds to more
complex arrangement of the Na atoms in the structure,
the same signal is also observed in as-cast Pb0.98Na0.02Te
(Figure 4, blue spectra), which disappeared after addi-
tional heat treatment (Figure 4, black spectra).The ratio
of its intensity (including all its sidebands) to the nega-
tively shifted peak is approximately 6:1.
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The position and assignment of this effect is evaluated
by comparison to the spectrum of the binary compound
Na2Te. We synthesized it and performed the NMR exper-
iment. The 23Na NMR signal has practically the same
position at +40.7 ppm (Figure S1). However, the MAS line
of Na2Te is significantly narrower (FWHM of 0.5 ppm
compared to FWHM of 2.8 ppm for Pb0.95Na0.05Te0.975).
The broader line for the Pb0.95Na0.05Te0.975 sample points
toward the disorder in the crystal structure being in
agreement with the behaviour of the lattice parameters
(Figure 1a). The relatively large positive value of chemical
shift is in accordance with Na being four-coordinated by
Te in Na2Te.51 Thus the signal at +40.7 ppm in the spec-
trum of Pb0.95Na0.05Te0.975 is assigned to Na atoms replac-
ing Pb in vicinity of the Te vacancy. The larger shift and
the large relative intensity of the main signal can be un-
derstood assuming the clustering of the Na atoms around
the Te defect in order to reduce the local excess charge
appearing by the vacancy formation (Figure 4, top left).
All these observations echo with the Crocker’s idea about
For the Pb1-yNayTe1-y/2 series (y = 0.005 ÷ 0.10, Figure 1a,
b), the change of the lattice parameters with the substitu-
tion is not as strong as in the previous case. This is under-
standable assuming that the reduction of the lattice pa-
rameters due to the ionic radii of Pb2+ and Na1+ is partially
compensated by the repulsive interaction of the cations
around the Te defect. After thermoelectric measurement,
the monotonic slope of lattice parameter is observed up
to 2.5 at. % of Na toward the Na2Te phase (Figure 1b)
which is possible to understand given the structural simi-
larity of PbTe (NaCl type) and Na2Te (anti-CaF2 type). The
relative changes of the lattice parameter for the Pb1-
yNayTe1-y/2 samples are similar to that of the Pb1-xNaxTe
series, with the increasing Na content. However, depend-
ing on heat treatment, there is an opposite lattice param-
eter change in these two series. In the case of Pb1-xNaxTe,
it increases after LFA measurement, as opposed to Pb1-
yNayTe1-y/2 samples, for which the lattice parameter de-
creases. After annealing, the lattice parameter of both Pb1-
yNayTe1-y/2 and Pb1-xNaxTe series obeys Vegard’s law and
formation
of
the
significant
complex
center
(NaPb□TeNaPb).16
Even small concentration of the Na improves the me-
tallic behavior for all samples in comparison to the binary
PbTe, which is characterized by the metal–semiconductor
transition14 (Figure 5). All Hall measurements were con-
ducted after SPS treatment and thermal diffusivity meas-
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urements. The Hall carrier concentration of Pb1-xNaxTe Although both series of materials show high values of
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and Pb1-yNayTe1-y/2 decreases with increasing temperature,
the values obtained at 300 K are roughly two times small-
er than those at 50 K for all samples (Figure 5a). Similar
behavior is observed for hole mobility values (Figure 5b).
For both substitution series, the carrier concentration is
smoothly increasing with the Na content within the ho-
mogeneity range of the solid solution. According to the
assumption, that one Na+ donates one hole, we calculate
the theoretical carrier concentrations for the Pb1-xNaxTe
series (Figure 5a). The measured values of Hall charge
carrier concentration correspond to 60 ~ 70 % or less of
the calculated one (Figure 5a), which suggests that a sim-
ple chemical one-charge model is not in complete agree-
ment with the band structure of these materials. This
conclusion is further supported by the behavior of the Pb1-
yNayTe1-y/2 series. Here, for the charge balance situation,
the mutual compensation between Na holes and Te de-
fects can be assumed, so the number of charge carriers
should not be directly dependent on y. The presence of
such dependence in Figure 5a can be explained by the fact
that a part of substituting Na atoms follows the behavior
in the Pb1-xNaxTe (cf. NMR results in Figure 4). Additional
explanation is the appearance of new states in the band
structure, caused by the environment of the Te vacancies.
ZT, they degrade during the measurement. The samples
of Pb1-yNayTe1-y/2 oxidized slightly, especially those with
high Na concentration (y ≥ 0.03). During the cyclic ther-
mal conductivity measurements, the samples of Pb1-
xNaxTe (x ≥ 0.02) show obvious change between the first
heating cycle and the following ones, whereas no such
effect was found in Pb1-yNayTe1-y/2, even for the highest Na
concentration
outside
the
homogeneity
range
(Pb0.90Na0.10Te0.95). For example, the thermal conductivity
of samples with x and y of 0.04 (Figure 10) during the first
heating cycle for both samples are almost the same until
650 K, while at higher temperature, the thermal conduc-
tivity of Pb0.96Na0.04Te shows jump-like decrease, in con-
trast to the Pb0.96Na0.04Te0.98. The cooling and all following
measurements yield stable, but lower values, as compared
to the initial heating curve (Figure 10). After full cycle
measurements, including electrical and Seebeck coeffi-
cient, the Pb0.96Na0.04Te material shows visible microscop-
ic cracks or voids and is partially deformed (cf. inset of
Figure 10). Contrary to this, sample of Pb0.96Na0.04Te0.98 did
not show any obvious microscopic changes.
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In order to evaluate the possibility of these materials in
potential application in thermoelectric modules, further
characterization of the thermal stability for samples an-
nealed at 873 K for 900 hours were carried out. The chem-
ical composition, lattice parameters, and carrier concen-
trations of the selected samples are presented in Table S2.
As mentioned above, the solubility of Na is decreased
according to the evolution of the lattice parameters,
which is likely due to reorganization of Na clusters since
no Na loss after annealing was observed in the chemical
analysis (Table S2). The 23Na MAS NMR investigations of
the annealed Pb0.95Na0.05Te0.975 sample (green spectra in
Figure 4) reveal that the ratio between the two main
peaks has changed. The intensity of the peak, which is
assigned to Na replacing Pb in the PbTe, is much higher
as compared to the peak corresponding to a clustering of
the Na atoms around the Te defect. A heat treatment
leads to an equilibration and homogenisation of the sam-
ples by reorganization and distribution of the Na clusters
and Te vacancies. From the powder XRD and chemical
analyses, the maximum solubility of Na is: ~1.0 at. % (cor-
responding to 1.5 at. % nominal Na content. Na loss took
place during the measurements) for Pb1-yNayTe1-y/2 sample
series and 0.5 at. % for Pb1-xNaxTe (Figure 1c). After an-
nealing, the resistivity shows higher values for all sam-
ples, especially for the high temperature range (Figure 11),
which can be attributed the reduced carrier concentra-
tion. The resistivity and Seebeck coefficient values do not
change significantly for Pb1-xNaxTe (x ≥ 0.01) and for Pb1-
yNayTe1-y/2 (y ≥ 0.03), as evident from Figure 11. This is
consistent with the change of the lattice parameters. The
power factors of Pb1-xNaxTe samples are very similar with
before annealing, especially at high temperature range
(Figure 12). However, all Pb1-yNayTe1-y/2 samples show a
significant reduction of the power factors at high temper-
ature range after annealing (Figure 12). As a result, the
calculated ZT values (using same thermal conductivity
All samples of both series are p-type conductors (Fig-
ure 6), in contrast to the binary PbTe, which shows a p-n
transition with temperature. The specimens of the Pb1-
yNayTe1-y/2 series show similar conductive behavior for the
whole temperature range. The Seebeck coefficient values
at 300 K are comparable to the materials of the Pb1-xNaxTe
series, which is consistent with experimental charge carri-
er concentrations (Figure 5). Upon increasing of Na con-
tent, the resistivity decreases up until y ≥ 0.03, the elec-
tronic transport properties of Pb1-yNayTe1-y/2 samples do
not change significantly (x ≥ 0.02 for Pb1-xNaxTe samples).
An exception is the y = 0.10 sample, for which a formation
of the secondary phase is observed. Room temperature
values of Seebeck coefficient S as a function of the Hall
carrier concentration for all studied samples are con-
sistent with the published data for PbTe:Na15, 31, 33 (Figure
7a). However, the carrier mobility values for all studied
samples are much lower compared to the published
PbTe:Na data15, 31, 33, but higher than that for PbTe:Tl13, 28, 52
(Figure 7b).
The total and lattice thermal conductivities of the Pb1-
xNaxTe samples show smaller values compared to that of
Pb1-yNayTe1-y/2 (Figure 8). Generally, lattice thermal con-
ductivity decreases with Na concentration for all samples,
especially for the high temperature range. Therefore, the
maximum ZT values are around 1.4 ~ 1.6 at 760 K for Pb1-
xNaxTe (x ≥ 0.02) and Pb1-yNayTe1-y/2 (0.1 ≥ y ≥ 0.03, Figure
9), comparable with previous results.15 Within the homo-
geneity range of the solid solution, the decrease of the
lattice and total thermal conductivity goes along with the
increasing local structural disorder according to the sub-
stitution schemes above. In the multi-phase samples, the
additional phonon scattering on the phase boundaries
reduces further the total thermal conductivity.
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values as those measured before annealing) of the an-
1
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nealed Pb1-xNaxTe samples are still very high, but some-
what reduced for the annealed Pb1-yNayTe1-y/2 samples
(Figure 13).
AUTHOR INFORMATION
Corresponding Author
* E-Mail: grin@cpfs.mpg.de
Conclusions
ORCID
Two different substitution schemes Pb1-xNaxTe (known
one) and Pb1-yNayTe1-y/2 (new one) were systemically inves-
tigated, and the shape of the solid solution of Na in PbTe
in the ternary system Na-Pb-Te was established. Na has
limited while different solubility range for each series: 1.0
at. % for Pb1-xNaxTe, and 2.5 at. % for Pb1-yNayTe1-y/2. The
samples with high concentration of Na (x ≥ 0.02 in Pb1-
xNaxTe) showed a jump-like behavior above 650 K during
the first heating cycle, which becomes stable and achieves
lower values in further cyclic measurements. However,
thermal conductivities of Pb1-yNayTe1-y/2 samples are stable
during the measurements.
Yuri Grin: 0000-0003-3891-9584
Author Contributions
Y.G. and J.T.Z. designed the project, X.W. prepared the sam-
ples, X.W. and I.V. measured thermoelectric properties, M.B.
performed NMR and Hall measurements, X.W. and U.B.
performed metallographic experiments.
The manuscript was written through contributions of all
authors. All authors have given approval to the final version
of the manuscript.
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Funding
This research was partially supported by National Natural
Science Foundation of China, Science and Technology Com-
mission of Shanghai Municipality, State Administration of
Foreign Experts Affairs.
The local atomic arrangement by different substitution
schemes were revealed by NMR. The MAS 23Na NMR of
the Pb0.98Na0.02Te after SPS revealed only one Na signal,
which is assigned to Na replacing Pb in the PbTe. This
peak had much lower intensity in the sample of
Pb0.95Na0.05Te0.975, however, an additional strong peak was
observed, which was assigned to Na atoms replacing Pb in
vicinity of the Te vacancy. The larger shift and the large
relative intensity of the main signal can be understood
assuming the clustering of the Na atoms around the Te
defect. This suggestion is consistent with Crocker’s idea
about formation of acceptor center NaPb□TeNaPb in PbTe16
and formation of the Na-rich nano-segregations or na-
noscale precipitates.43-44,46 Moreover, those Na-
aggregation structures may also be responsible for the less
than 100% doping efficiency from Pb-by-Na substitution.
A long-term heat treatment leads to an equilibration and
homogenisation of the samples by reorganization and
distribution of the Na clusters and Te vacancies. Concern-
ing powder XRD analysis, the maximum solubility of Na is
reduced upon annealing for both sample series: ~1.0 at. %
for Pb1-yNayTe1-y/2 and 0.5 at. % for Pb1-xNaxTe.
Notes
The authors declare no competing financial interest.
ACKNOWLEDGMENT
Authors thank Dr. Marcus Schmidt (MPI CPfS) for DSC-TG
measurements, Dr. Gudrun Auffermann (MPI CPfS) for
chemical analysis, structure group of MPI CPfS for the pow-
der XRD measurements, Dr. Eteri Svanidze for valuable dis-
cussion. Prof. Dr. Zhao thanks the support of the National
Natural Science Foundation of China under Project No.
21771123, Science and Technology Commission of Shanghai
Municipality under Project No. 15DZ2260300, and State Ad-
ministration of Foreign Experts Affairs under project No.
D16002.
FIGURE CAPTIONS
Figure 1. (a) Phase diagram for Na-substituted PbTe sam-
ples. (b) Lattice parameter vs. nominal Na composition for
the Pb1-xNaxTe (red) and Pb1-yNayTe1-y/2 (black) series. For
comparison, lattice parameter of the binary PbTe is shown14
as a blue dash dot line. (c) Lattice parameter of annealed Na-
substituted PbTe samples.
The thermoelectric properties of the single-phase ma-
terials were proved to be different by different substitu-
tion schemes. The maximum ZT values of 1.4 ÷ 1.6 at 760
K are established for both Pb1-xNaxTe (x ≥ 0.02) and Pb1-
yNayTe1-y/2 (0.1 ≥ y ≥ 0.03) series in the multi-phase sam-
ples due to the additional reduction of the thermal con-
ductivity on the phase boundaries. Pb1-xNaxTe substitu-
tion series exhibit better thermoelectric properties after
long-time annealing. The degradation of thermoelectric
properties by thermal annealing is proven experimentally.
Figure 2. (a) TG / DTA measurement of Pb0.98Na0.02Te after
SPS; (b) DSC measurement of Pb0.98Na0.02Te0.99 after SPS.
Figure 3. Back-scattered electrons (BSE) image (a) and ele-
ment mapping of Pb0.98Na0.02Te sample after SPS for (b) Na
(K line), (c) Te (L lines), (c) Pb (M line).
Figure 4. Magic Angle Spinning (MAS) 23Na NMR spectra of
PbTe substituted with Na: (orange) Pb0.95Na0.05Te0.975 after
synthesis (before SPS); (blue) Pb0.98Na0.02Te after synthesis
(before SPS); (black) Pb0.98Na0.02Te after SPS; (green)
Pb0.95Na0.05Te0.975 after 900 hours annealing. The spinning
rate was 4.5 kHz. Spinning sidebands from the left and right
signals are marked by asterisks and crosses, respectively.
ASSOCIATED CONTENT
Supporting Information.
Chemical compositions and lattice parameters of the synthe-
sized samples; comparison of compositions, lattice parame-
ters and carrier concentrations before and after annealing;
MAS 23Na NMR spectra of Pb0.95Na0.05Te0.975 (before SPS)
and Na2Te.
Figure 5. (a) Hall carrier concentrations and (b) carrier mo-
bility of Pb1-xNaxTe (triangles) and Pb1-yNayTe1-y/2 (circles) at
50 K (blue) and at 300 K (red). The calculated values (green
squares) assuming one Na+ donates one hole.
The Supporting Information is available free of charge on the
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Page 6 of 21
Figure 6. Temperature dependences of (a) electrical resistivi-
ty, (b) Seebeck coefficient for Pb1-xNaxTe and (c) electrical
resistivity, (d) Seebeck coefficient for Pb1-yNayTe1-y/2
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(PbTe)(1-2x)(PbSe)(x)(PbS)(x)
Thermoelectric
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function of Hall carrier concentration n and (b) room-
temperature Hall mobility μ as a function of Hall carrier
concentration n for Pb1-xNaxTe (triangles), Pb1-yNayTe1-y/2
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Figure 8. Temperature dependence of total and lattice ther-
mal conductivity for Pb1-xNaxTe (a, b) and Pb1-yNayTe1-y/2 (c,
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figure of merit ZT for (a) Pb1-xNaxTe and (b) Pb1-yNayTe1-y/2
.
Figure 10. Cyclic measurements of thermal conductivity for
Pb0.96Na0.04Te and Pb0.96Na0.04Te0.98 Inset: image of
.
Pb0.96Na0.04Te (top) and Pb0.96Na0.04Te0.98 (bottom) speci-
mens after measurement.
Figure 11. Temperature dependences of electrical resistivity
and Seebeck coefficient for Pb1-xNaxTe after 900 hours an-
nealing at 873 K (a, b) and Pb1-yNayTe1-y/2 after 900 hours
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xNaxTe before (a) and after (b) 900 hours annealing at 873 K
and for Pb1-yNayTe1-y/2 before (c) and after (d) 900 hours an-
nealing at 873 K.
Figure 13. Temperature dependent of the thermoelectric
figure of merit ZT for (a) Pb1-xNaxTe and for (b) Pb1-yNayTe1-y/2
after 900 hours annealing at 873 K.
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Figure 1. (a) Phase diagram for Na-substituted PbTe samples. (b) Lattice parameter vs. nominal Na
composition for the Pb1-xNaxTe (red) and Pb1-yNayTe1-y/2 (black) series. For comparison, lattice parameter of
the binary PbTe is shown14 as a blue dash dot line. (c) Lattice parameter of annealed Na-substituted PbTe
samples.
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Figure 2. (a) TG / DTA measurement of Pb0.98Na0.02Te after SPS; (b) DSC measurement of Pb0.98Na0.02Te0.99
after SPS.
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Figure 3. Back-scattered electrons (BSE) image (a) and element mapping of Pb0.98Na0.02Te sample after SPS
for (b) Na (K line), (c) Te (L lines), (d) Pb (M line).
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Figure 4. Magic Angle Spinning (MAS) 23Na NMR spectra of PbTe substituted with Na: (orange)
Pb0.95Na0.05Te0.975 after synthesis (before SPS); (blue) Pb0.98Na0.02Te after synthesis (before SPS); (black)
Pb0.98Na0.02Te after SPS; (green) Pb0.95Na0.05Te0.975 after 900 hours annealing. The spinning rate was 4.5 kHz.
Spinning sidebands from the left and right signals are marked by asterisks and crosses, respectively.
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Figure 5. (a) Hall carrier concentrations and (b) carrier mobility of Pb1-xNaxTe (triangles) and Pb1-yNayTe1-
y/2
(circles) at 50 K (blue) and at 300 K (red). The calculated values (green squares) assuming one Na+
donates one hole.
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Figure 6. Temperature dependences of (a) electrical resistivity, (b) Seebeck coefficient for Pb1-xNaxTe and (c)
electrical resistivity, (d) Seebeck coefficient for Pb1-yNayTe1-y/2
.
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Figure 7. (a) Room-temperature Seebeck coefficient as a function of Hall carrier concentration n and (b)
room-temperature Hall mobility µ as a function of Hall carrier concentration n for Pb1-xNaxTe (triangles), Pb1-
yNayTe1-y/2 (circles). The black and the orange lines are literature data for PbTe: Na15, 31, 33 and PbTe: Tl13, 28,
52, respectively.
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Figure 8. Temperature dependence of total and lattice thermal conductivity for Pb1-xNaxTe (a, b) and Pb1-
yNayTe1-y/2 (c, d).
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Figure 9. Temperature dependence of the thermoelectric figure of merit ZT for (a) Pb1-xNaxTe and (b) Pb1-
yNayTe1-y/2
.
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Figure 10. Cyclic measurements of thermal conductivity for Pb0.96Na0.04Te and Pb0.96Na0.04Te0.98. Inset: image
of Pb0.96Na0.04Te (top) and Pb0.96Na0.04Te0.98 (bottom) specimens after measurement.
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Figure 11. Temperature dependences of electrical resistivity and Seebeck coefficient for Pb1-xNaxTe after 900
hours annealing at 873 K (a, b) and Pb1-yNayTe1-y/2 after 900 hours annealing at 873K (c, d).
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Figure 12. Temperature dependences of power factor for Pb1-xNaxTe before (a) and after (b) 900 hours
annealing at 873 K and for Pb1-yNayTe1-y/2 before (c) and after (d) 900 hours annealing at 873 K.
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Figure 13. Temperature dependent of the thermoelectric figure of merit ZT for (a) Pb1-xNaxTe and for (b) Pb1-
yNayTe1-y/2 after 900 hours annealing at 873 K.
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