22 Electrical Properties of the Tungsten Bronzes H. R. SHANKS, P. H. SIDLES, and G. C. DANIELSON
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Institute for Atomic Research and Department Iowa State University, Ames, Iowa
of
Physics,
The electrical resistivity of K WO x
3
Na WO ,
Li WO ,
3
x
of χ values was 0.25 < χ < 0.9.
3
x
has been measured at 300° K.
and
The range
All resistivities
were characteristic of a metal and lie on a single curve.
Extrapolation of the conductivity curve
to zero conductivity indicated that the tungsten bronzes should be semiconductors for χ < 0.25. The resistivities measured for tungsten bronzes with χ < 0.25 showed semiconducting behavior. The resistivity of Li WO x
3
exhibited an anomalous
peak in the ρvs. Τ curve. Li WO 0.37
The Hall coefficient of
indicated one free electron per alkali
3
atom, as
previously found for
Seebeck coefficient of Na WO x
on
x- / , 2
3
3
Na WO . x
3
The
depended linearly
as expected from free electron theory.
The implications of these and other data are dis cussed.
yungsten bronzes are nonstoichiometric compounds, M ^ W C ^ , where M is usually one of the alkali metals. Single crystals of these compounds, large enough for electrical measurements, can be prepared w i t h values of χ ranging from essentially zero to nearly unity. T h e tungsten bronzes undergo several changes of crystal structure as χ changes, but difficulties i n determining quantitative amounts of M have frustrated attempts to delineate the ranges i n χ over w h i c h each of these structures exists. This situation has been a deterrent to studies of the electrical properties of these materials, especially i n the low x-value range. Electrical properties of certain of the high x-value bronzes have been re ported. B r o w n and Banks ( I ) and Gardner and Danielson (3) both measured the electrical resistivity of cubic sodium tungsten bronze, w i t h ^-values ranging from about 0.5 to 0.9, and reported a m i n i m u m i n resistivity near χ = 0.75. G a r d ner and Danielson (3) also reported the results of H a l l coefficient measurements w h i c h indicated that, i n this range of χ values, each sodium atom contributed one electron to conduction processes. Subsequently, Ellerbeck et al. (2) reported that, when careful attention was given to sample homogeneity, no m i n i m u m i n electrical resistivity at χ = 0.75 was observed. A l k a l i metal bronzes of lower χ value have not been so extensively studied. W i t h the exception of some measurements b y Sienko and Truong (8) of the 237 Ward; Nonstoichiometric Compounds Advances in Chemistry; American Chemical Society: Washington, DC, 1963.
238
ADVANCES IN
CHEMISTRY SERIES
electrical conductivity of cubic lithium bronzes, little of significance has been reported. This publication reports the results of electrical resistivity measure ments on several metal-like tungsten bronzes, w i t h χ values down to 0.28, together w i t h preliminary results for H a l l and Seebeck coefficients, and discusses the i m plications of these results. Below about χ = 0.25, all of the alkali tungsten bronzes appear to exhibit properties w h i c h are characteristic of semiconductors. Some preliminary results illustrate this type of behavior.
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Crystal
Preparation
Crystals of the various alkali tungsten bronzes were prepared b y electrolysis from a melt of the appropriate alkali tungstate and W 0 . The electrolytic cell consisted of a glazed ceramic crucible, a Chromel wire cathode, and a graphite anode. Crystals were obtained under the following conditions: temperatures of the melt, 750° to 900° C ; current through the cell, 15 to 50 ma.; time of elec trolysis, 12 to 24 hours. 3
F o r the low x-value sodium tungsten bronzes (x < 0.5), the crystal structure and χ values of the crystals obtained depended strongly on the temperature of the melt. The size and homogeneity of the crystals were dependent on both temperature and electrode current. The best crystals were obtained at the lowest temperature at w h i c h they could be grown. The optimum current for best quality crystals depended upon χ value and crystal structure. Measurements Electrical resistivity was measured by a d.c. method using four-probe tech niques to avoid problems arising from contact resistance. Pressure contacts were used for both current and potential probes. A t low temperatures, the cur rent contacts could be improved b y ultrasonically tinning the ends of the samples. Details of the method employed for measuring Seebeck coefficients have been described b y Heller and Danielson ( 5 ) . The H a l l coefficient of L i W0 was measured b y a d.c. method and is therefore subject to error from the Ettingshausen effect. This error is not expected to exceed ± 1 0 % . 0
Electrical
3 7
3
Resistivity
In Figure 1, the resistivities of several tungsten bronzes at 300° K . are shown as a function of the alkali metal concentrations. Experimental points are shown for cubic N a ^ W O g , tetragonal N a ^ W C ) ^ cubic L i ^ W O s [including data from both Iowa State University and Cornell University (8)] and tetragonal K ^ W O g . A l l these bronzes show metallic conductivity. It is remarkable that the resistivities for a l l these bronzes seem to fall on the same curve. The metal ions themselves cannot, therefore, be important contributors to the scattering of the free electrons. Rather, the mobility must be limited primarily by electron scatter ing from the acoustical and optical modes of the W 0 structure at h i g h temper atures, and from the vacancies at alkali metal sites at low temperatures. The importance of vacancy scattering at low temperatures has been shown b y E l l e r beck et al. (2). The conductivity at 0° K . (see their Figure 4) increased rapidly w i t h increasing sodium concentration, owing to a reduction i n the number of vacancies w h i c h scatter electrons as χ increases. In Figure 2, the conductivities of these same bronzes at 300° K . are plotted against x. These conductivities are simply the reciprocals of the resistivities shown i n Figure 1. B y extrapolation to zero conductivity, the curve i n Figure 3
Ward; Nonstoichiometric Compounds Advances in Chemistry; American Chemical Society: Washington, DC, 1963.
22. SHANKS ET AL.
239
Tungsten Bronzes
600r
ELECTRICAL M W0 x
RESISTIVITY
300 Κ β
3
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500h
o Cubic Sodium (ISU) V Tetragonal Sodium (ISU) Δ Cubic Lithium (ISU)
ε 40oL ο
x Cubic Lithium (Cornell U.) Q Tetragonal Potassium (ISU)
4.
P 300h ço (/>
Lu CC
< α 200 h o LU UJ iooh
0.1
0.2
0.3
0.4
0.5
0.6
0.7
J
0.8
L
0.9
1.0
X - VALUE
Figure 1. Electrical resistivity vs. x value at 300° Κ.
2 strongly suggests that all the bronzes w i l l become insulators (or semiconductors) for values of χ less than some value i n the neighborhood of 0.25. This possi bility has been suggested by Sienko a n d T r u o n g (8) w h o used the theory of M o t t (7) for metal-semiconductor transitions. T h e experimental data d i d not, however, show evidence of the discontinuity that w o u l d be expected from Mott's theory. If small, the discontinuity may be very difficult to observe experimentally, because of insufficient homogeneity of most available crystals. W e have grown a number of tungsten bronze crystals w i t h χ < 0.25, and have found them to be semiconductors. N o crystals w i t h χ < 0.25 have been found to be metallic in conductivity. The electrical resistivity of one of these semiconducting bronzes is shown in Figure 3. T h e crystal is L4WO3 w i t h χ = 0.097. T h e graph of l o g ρ vs. 1 0 0 0 / T shows the typical behavior of an impurity semiconductor. T h e activation energy corresponding to the straight line at l o w temperatures (extrinsic region) was 0.03 e.v., the activation energy corresponding to the straight line at h i g h temperatures was 0.12 e.v. If the straight line at high temperatures corresponded Ward; Nonstoichiometric Compounds Advances in Chemistry; American Chemical Society: Washington, DC, 1963.
ADVANCES IN
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240
CHEMISTRY SERIES
x-VALUE
Figure 2.
Electrical conductivity Ο V A X •
vs. χ value at 300° K.
Cubic sodium (ISU) Tetragonal sodium (ISU) Cubic lithium (ISU) Cubic lithium (Cornell U.) Tetragonal potassium (ISU)
to the intrinsic region, the energy gap for this semiconducting crystal was about 0.24 e.v. The temperature dependence of the resistivity of hi WO is shown i n F i g u r e 4. F o r χ = 0.28, the anomalous peak was very large and occurred at about 600° K . ; for χ = 0.34 the peak was m u c h smaller and occurred at about 300° K . W i t h increasing lithium concentration, therefore, the peak diminished i n size and shifted to lower temperatures. T h e peak was completely reproducible and x-ray diffraction patterns showed that the cubic crystal structure existed both below and above the temperature at w h i c h the peak occurred. However, preliminary thermal analysis measurements indicated some sort of phase change. Mackintosh (6) has suggested the possibility of ordering of the lithium atoms, and neutron diffraction studies of these cubic L i . W 0 crystals should be made below and above the transition temperature. x
a
s
3
Hall Effect The H a l l coefficient, R, of a crystal of cubic L i W 0 has been measured at 300° K . F r o m this measurement, the number of free electrons per unit volume, n, was calculated from η = 1/Re, where e is the charge on one electron. Hence the number of free electrons per mole was obtained. This result for L10.37WO3 is shown i n Figure 5, w i t h similar results for N a ^ W C ^ obtained by Gardner and Danielson ( 3 ) . The straight line corresponds to one free electron per alkali metal atom, and the fact that the point for L i . W O is very near this 0
3 7
3
0
3 7
3
Ward; Nonstoichiometric Compounds Advances in Chemistry; American Chemical Society: Washington, DC, 1963.
22. SHANKS ET AL.
241
Tungsten Bronzes
line strongly suggests that the number of free electrons i n lA WO is equal to the number of alkali metal atoms. œ
as i n N a ^ W O s ,
S9
Seebeck Effect T h e Seebeck coefficients (thermoelectric powers) of N a W O have been measured over a wide range of χ values at room temperature (300° K . ) . A t this temperature, the residual resistance, p , and thermal resistance, p , are comparable, the value of p being between p and 2p . Nevertheless, one w o u l d expect to a first approximation (10) that S = ( 1 / 3 ) (Ά Τ/βζ), where S is the Seebeck coefficient, k is Boltzmann's constant, e is the electronic charge, and ζ is the F e r m i energy. F o r free electrons, the F e r m i energy ζ = (h /2m *) ( 3 η / 8 τ τ ) where h is Planck's constant, m * is the effective mass, and η is the density of free electrons. Since η is proportional to χ, ζ varies as ac and S varies as xr . In Figure 6, the Seebeck coefficient, S, plotted vs. x . The experimental points lie on a straight line w h i c h provides evidence of the validity of free electron theory when discussing transport properties of the tungsten bronzes. F r o m the a ?
0
0
s
t
t
t
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2
2
2/3
2/3
1
2/3
_ 2 / 3
TEMPERATURE °K 600 300 200 ,—ϋ ,
,„o
I0r
I
I50 1
1
IOO 1
80 —!
:
ELECTRICAL RESISTIVITY
2 Figure 3.
4
6 8 Ι000/Τ
I0
I
12
14
Electrical resistivity vs. temperature for a semiconducting lithium bronze
Ward; Nonstoichiometric Compounds Advances in Chemistry; American Chemical Society: Washington, DC, 1963.
ADVANCES IN CHEMISTRY SERIES
242 700i
Ί
I
I
I
ELECTRICAL Li W0 x
1
I
RESISTIVITY
3
600f-
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500h
Χ=0280
400f~
> CO CO LU 0C
300
