- Email: [email protected]
Electronic and ionic conduction in sodium borosilicate glasses
Journal of Non-Crystalline Solids 48 (1982) 345-357 North-Holland Publishing Company
ELECTRONIC AND IONIC CONDUCTION BOROSILICATE GLASSES *
345
IN SODIUM
B i p r o d a s D U T T A a n d D e l b e r t E. D A Y Ceramic Engineering Department and Graduate Center for Materials Research, University of Missouri, Rolla, Missouri 65401, USA
Received 24 August 1981 Revised manuscript received 9 November 1981
Electron and sodium ion motion in sodium borosilicate glasses containing Sb203 has been determined by thermally stimulated polarization and depolarization current (TSPC/TSDC) technique. Whereas a glass containing Sb203 exhibited a TSPC peak, the peak was absent in a similar glass without Sb203. The TSPC peak which appeared in TSPC -1 and TSPC-2 was 103_ 104 times larger than the TSDC peaks and had an activation energy higher than that of the TSDC peaks and ionic dc conduction. Electron hopping between Sb5+ and Sb3+ ion sites is considered responsible for the TSPC peak. All the glasses show two TSDC peaks. The origin of the low temperature TSDC peak is uncertain but the high temperature TSDC peak could be accounted for by the orientation of Na ÷ ions around [BO4] groups. Above ~360 K the dc conduction is due to sodium ion motion.
1. Introduction Some oxide glasses c o n t a i n i n g ions having m u l t i p l e valence states are s e m i c o n d u c t i n g [1-3]. I n V 2 O s - P 2 0 5 glasses, the c o n d u c t i v i t y is due to elect r o n s h o p p i n g b e t w e e n V 4÷ a n d V 5+ ions [1-3]. Similarly, the c o n d u c t i v i t y of iron p h o s p h a t e a n d c o p p e r p h o s p h a t e glasses has been a t t r i b u t e d [4] to electron m o v e m e n t b e t w e e n Fe2 + / F e 3 + a n d C u ÷ / C u 2 + ions, respectively. R e c e n t l y the c o n d u c t i o n , b e l o w 300 K, of s o d i u m b o r o s i l i c a t e glasses cont a i n i n g S b 2 0 3 has been a t t r i b u t e d [5] to the h o p p i n g o f b i p o l a r o n s (pair of electrons) b e t w e e n Sb 3÷ a n d Sb 5+ ions [6]. In these glasses a sharp m a x i m u m in the dc c o n d u c t i v i t y is o b s e r v e d at 308 K as illustrated in fig. 1. T h e initial increase in c o n d u c t i v i t y b e l o w 300 K was a t t r i b u t e d to increased electron mobility. A b o v e - - 3 0 0 K , the c o n c e n t r a t i o n of Sb 5+ ions decreases, so the decline in c o n d u c t i v i t y was a t t r i b u t e d to the lesser n u m b e r of available Sb 5+ sites. T h e increase in c o n d u c t i v i t y a b o v e - 360 K was a t t r i b u t e d to s o d i u m ion motion.
* This work was supported by NSF Grant DMR-79-18425. From a thesis submitted by B. Dutta for the MS Degree in Ceramic Engineering, University of Missouri-Rolla, December, 1981. 0022-3093/82/0000-0000/$02.75
© 1982 N o r t h - H o l l a n d
346
B. Dutta, D.E. Day / Electronic and ionic conduction
-I0
n ql--lonlc
T
I
I
Conductlon-------l~t~Electronlc
I
I
Conductlon~
-II
s
E -J2
•
)II.u 0 z 0 o
-13
-14
¢.9 o
-le
2.0
2.5
3.0 IO00/T
3.5
4.0
(K)-I
Fig. I. TSPC-1, (O), TSPC-2 (IS]), TSPC-3 (A) of sodium borosilicate glass 2, containing Sb203. • Data from ref. 5.
The method used previously [5] to measure the dc conductivity of sodium borosilicate glasses containing Sb203 resembles the thermally stimulated polarization current technique. Thermally stimulated polarization and depolarization current (TSPC/TSDC) technique has been widely employed to investigate charge motion and trap levels in crystalline dielectrics and semiconductors [7-9]. This technique has also been used to study alkali ion motion in alkali silicate [10-16] and germanate [17] glasses and is said to provide evidence of localized and longer range alkali ion motion. Most alkali silicate glasses [10-16] show two TSDC peaks and a high temperature background (HTB) current. In others, only one low temperature TSDC peak and the HTB were found [14,17]. The two TSDC peaks and HTB were attributed to alkali ion motion, the latter being due to the translational alkali ion motion responsible for dc conduction since the activation energy for the HTB is same as that for dc conductivity. The activation energies for the TSDC peaks were less than that for dc conductivity, dielectric loss or alkali diffusion. This is one of the main reasons the TSDC peaks have been attributed to alkali ion motion more localized than the translational motion causing dc conduction. The smaller of the two TSDC peaks with the lower activation energy has been attributed [ 12,14,15] to the localized movement of the alkali ion around the non-bridging oxygen ion (NBO) to which it is bonded. This interpretation is based~on Charles' model [18] and is supported by the fact that the alkali-NBO dipole concentration calculated from the experimental peak area and assumed alkali-NBO dipole moment agree well with the alkali concentration calculated from the glass composition. In sodium germanate glasses [17]
B. Dutta, D.E. Day / Electronic and ionic conduction
347
containing - 1000 ppm Na20, however, the observed TSDC peak is too large to be accounted for by Na-NBO dipole orientation. To explain this, it was assumed that the true activation energy for the low temperature TSDC peak is the same as that for dc conduction, and that the peak is due to the translational alkali motion responsible for dc conductivity. A limited translational motion of the alkali ions has been proposed [10-16] for the second TSDC peak at higher temperatures since it is too large (10-100 times the first peak) to be accounted for by alkali-NBO dipole orientation. This peak is attributed [12,14,16] to the accumulation/depletion of alkali ions at the immiscible phase boundaries of inhomogeneous glasses according to the interracial polarization model of Maxwell-Wagner and Sillars [19,20]. In sodium silicate and sodium borate glasses [12,13], two TSDC peaks were found in the former but only one in the latter. In sodium borosilicate glasses containing 12 mol% Sb203, a large conductivity peak was found [5] which was attributed to the Sb203 present in the glass as explained earlier. However, no Sb203-free glass was measured where such a peak would be absent if this peak was due to electron hopping. Furthermore, the possibility of Na + ion motion, which produces TSDC peaks in alkali silicate glasses [10-17], was apparently not considered. The present investigation was undertaken to re-examine the interpretation previously [5] proposed for the conductivity peak in sodium borosilicate glasses containing Sb203. An Sb:O3-free glass was measured to test the hypothesis that electron hopping between Sb5+ and Sb3÷ ions is responsible for the conductivity peak. It was also of interest to determine whether Sb203 containing glasses showed TSDC peaks due to Na + ion motion and to compare any such TSDC peaks with the large TSPC peak reported previously.
2. Experimental Two glasses (nos. 2 and 3 in table 1) were prepared by melting reagent grade Na2CO3, H3BO3, Sb203 and 99.8% SiO 2 in platinum crucibles. Procedures similar to those described previously [11] were used. The density of the glasses was measured by the Archimedes' method using xylene as the immersion liquid. Glass 1 was from the same melt as measured previously [5]. Samples (-0.15 cm in thickness and ~ 1.5 cm2 in cross-sectional area) were cut from annealed rectangular bars. Circular gold electrodes (0.317 cm2 in area) were evaporated on the large faces of these samples. The electrical measurements were performed on samples contained in a cell, described previously [10,11], which was evacuated (~35 /~m Hg) at either 300 K (TSPC measurement) or ~ 500 K (TSDC measurement) to remove any moisture present. The samples were short circuited during this time. A static helium atmosphere during TSPC and a flowing helium atmosphere during TSDC measurements was maintained to improve heat transfer and minimize temperature gradients.
348
B. Dutta, D.E. Day / Electronic and ionic conduction
Table 1 Composition (tool%) and density of glasses studied Glass No.
SiO2
B203
Sb203
Na 2°
Density (cm- 3)
Annealing treatment
I a
56 64 70
27 19 25
12 12 -
5 5 5
2.71 2.83 2.91
unknown 5500C, 1 h 550°C, 1 h
2 3
a Providedby Dr. D. Chakravortyof Indian Institute of Technology,Kanpur, India.
In the TSPC measurement, the sample was first cooled to - 1 0 0 K, a dc field (2-8 k V / c m ) was applied and the sample heated at a uniform rate (fl) of 4 K / m i n . The current measured by an electrometer* during the first heating was denoted as TSPC-I. Heating was discontinued much below the temperature where space charge polarization appears i.e. at a conductivity, o, of 10-7 (fl c m ) - i . After TSPC-1, the sample was recooled rapidly to - 100 K with the field still applied, reheated, and the current (denoted as TSPC-2) remeasured. Immediately after TSPC-2, the sample was cooled a third time to 100 K, the field removed and the depolarization current (TSDC-3) recorded during heating at the same rate ft. The dc conductivity, o, was calculated from TSPC-2 using the equation
o(T) =i(T)/E?A,
(I)
where E e is the field applied, A is the electrode area, and i(T) is the current. Previous work [I0,I I] has shown that the dc conductivity calculated in this way from TSPC-2 is reproducible and agrees well with the conductivity measured in other ways. The good reproducibility of the ionic conductivity is shown by the data > 4 0 0 K in fig. l, where the curves for TSPC-1, -2 and -3 are indistinguishable. The activation energy for dc conduction, E c, was determined from o = o0 exp -- E c / k T ,
(2)
where o0 is the pre-exponential factor, T is the absolute temperature and k is the Boltzmann constant. E¢ and o0 were determined from the slope of logo versus I / T (fig. 2). The activation energy for the TSPC peak was calculated from the slope of log o versus 1 / T for the low temperature side of the peak (fig. 2). In TSDC measurements, an unpolarized sample was polarized at a constant temperature, Tp, for a fixed time (tp = 10 rain) and then rapidly cooled ( - 7 min) to ~ 100 K with the field applied. The field was then removed and the depolarization current recorded as the sample was heated until completely * Keithley model 610B electrometer.
B. Dutta, D.E. Day / Electronic and ionic conduction I
I
I
349
I
Ionic Conduction •
,
,A
1
2 -II onlc Conduction A 12'
T-.
-12
E
> -13 I-(.3 =) r-, Z 0 (..) t.,,9
q -14
-I
i
%
I
2.0
I
I
2.5
3.0
IO00/T
(K) - I
I
4'.o
Fig. 2. Electronic and ionic conductivity of sodium borosilicate glasses with ( ~ and A) and without (©) Sb203. ~ =glass l, /~ =glass 2, © =glass 3. Prime denotes data interpolated from figs. 4.4 and 4.5 in ref. 5.
discharged. After measuring TSDC, the sample was short circuited and held at a still higher temperature to completely destroy any residual polarization. The sample was repeatedly polarized at successively higher temperatures at l0 K intervals until any TSDC peak observed became saturated. During the TSDC measurements the shunt resistor of the electrometer was kept at least two orders of magnitude lower than the sample resistance so the sample could discharge freely. The activation energy for the TSDC peaks was determined by the partial discharge [12] of a sample previously polarized to saturation. The peak was subsequently depolarized in steps by heating to successively higher temperatures. The activation energy was calculated from the slope of log current versus 1 / T for each partial discharge (PD-1, PD-2 etc.). The activation energy for the first partial discharge (PD-1) was considerably lower than PD-2, PD-3, etc. so the PD-1 value was neglected and the average of the other values taken as the activation energy. The error in the peak temperature, activation energy and area is estimated to be -+2 K, -+4 kJ/mol and -+ 10%, respectively.
B. Dutta, D.E. Day / Electronic and ionic' conduction
350 3. R e s u l t s
3.1. dc conductivity The data for the dc conductivity above and below the TSPC peak, fig. 1, as calculated from TSPC are compared with that measured previously [5] in tables 2 and 3. The present data agrees well with the previous data [5]. The activation energy for electronic conductivity (TSPC peak) is much higher than that for ionic conductivity above 400 K. The ionic and electronic conductivities of the glasses are compared in fig. 2 where only the straight line portion of the data are shown. 3.2. TSPC peak The TSPC data for the glasses measured are provided in table 3. Glasses containing Sb203 exhibit a TSPC peak which is comparable in magnitude but at slightly lower temperature than the conductivity peak observed previously [5] in glasses of the same composition, fig. 1. The peak at (292 ~ 3)K was
Table 2 Data for dc conduction (ionic) above 400 K [Ec: kJ/mol; %: (~ cm)-1] Glass no.
1 2 3
Present work
Ref. 5
Ec
o0
Ec
o0
85.7 108.3 82.8
0.8 × 10 -3 0.1 7.5 × 10 -3
86.7 115.6 -
8.1×10 -3 3.0
Table 3 Data for current peak observed in TSPC-I and -2 Glass no.
! 2 3 a From ref. 5.
Peak temperature (K)
Peak magnitude, Q/EpA ( × 10-l0 C / V cm)
TSPC- 1
TSPC-2
TSPC- 1
293 (308) a 290 (308) a no peak
295
3.9
1.7
292
10.7
1.8
no peak
-
Activation energy (kJ/mol)
TSPC-2
-
209 (193) a 472 (481) a -
B. Dutta, D.E. Day
I
/ Electronic and ionic" conduction
I
I
351
I
I
Low Temperature TSDC Peak
-I0
t High Temperature TSDC Peek T.~ -II 3
E
oN,,..
21
>- -12 I,--
O
0
'~
o -14 o,
-IE
I
I
I
20
2,5
5.0
o 3.5
4.0
IO00/T (K)-I Fig. 3. TSPC-I curves for glass l (~), glass 2 (A) and glass 3 (O).
observed in both TSPC-1 and TSPC-2 as depicted for glass 2 in fig. 1. Similar results, not shown in fig. 1, were obtained for glass 1. A TSPC-3 measurement was made for glass2. After the TSPC-I and -2
-13 m I
R -14
u
u
'q0-'-Hlgh temp TSDC p e o k ~ L 0 w t (HT) ]
!
/ /
romp TSOC peakn,'l (LT) "~
J0 >.
-15
I-
$ 0
J
-,%
I
2.0
I
3.0 IOOO/T (K) "l
I
4.0
5.0
Fig. 4. TSDC peaks in glasses 1 (~), 2 (A), and 3 (O). Polarization conditions were glass I-LT: Tp =420 K, Ep =8525 V/cm; HT: Tp =460 K, Ep =2758 V/cm. Glass 2-LT: Tp =412 K, Ep =7529 V/em; HT: Tp =480 K, Ep =2792 V/cm. Glass 3-LT: Tp =386 K, Ev--5246 V/cm; HT: 405 K, Ep = 5246 V/cm.
1 2 3
Glass no.
278 265 254
Low Temp. peak
431 462 350
High Temp. peak
Temperature (K)
Table 4 Data for saturated TSDC peaks
57.3 53.5 52.5
76.3 89.0 61.0
Activation energy (kJ/mol) Low High Temp. Temp. peak peak
Q/EpA High Temp. peak (X 10 -13
C / V cm) 15.3 5.0 12.7
Peak magnitude, Low Temp. peak (X 10 -14
C / V era) 1.9 1.5 8.6
1.1 1.2 6.8
cm3)
(X 1020/
Low Temp. peak
1.9 0.7 1.3
era3)
(>( 1021/
High Temp. peak
Nd, calculated from eq. (6)
1.8 1.8 2.7
c m 3)
Na + ion concen= tration ( × 102~/
~" ~"
B. Dutta, D.E. D a y / Electronic and ionic conduction
353
measurement in static helium, the cell was evacuated at ~ 500 K for 10 min. The sample was then cooled to - 1 0 0 K and reheated as the TSPC-3 was measured. The peak previously present in TSPC-1 and -2 was absent in TSPC-3 as is evident from fig. 1. There is a slight difference in the peak temperature between TSPC-1 and -2 and the peak area of TSPC-1 is larger than that of TSPC-2, fig. 1. The TSPC peak occurs at a temperature below the HTB, but the activation energy of the TSPC peak is much higher than that of the HTB, tables 2 and 3. The peak present in TSPC-1 and -2 in the two glasses containing Sb203, was absent in the Sb203-free glass (no. 3) measured under similar experimental conditions, see fig. 3. 3.3. T S D C p e a k s
All three glasses exhibited two TSDC peaks as shown in fig. 4, but they are much smaller (10-3 to l 0 - 4 times) than the TSPC peak. The activation energy for the low temperature TSDC peak is lower than that for the high temperature TSDC peak while the activation energies for both TSDC peaks are lower than that for dc conduction (tables 2-4). The magnitude of the low temperature TSDC peak is apparently reduced by Sb203since it is larger in glass 3 than in glasses 1 and 2 which contain Sb203, table 4. For glasses 1 and 2, the low temperature TSDC peak occurs at a temperature corresponding to a conductivity of ~ 10 -13 and - 1 0 -15 (fl cm) 1 respectively, as denoted by the arrows in fig. 3. The high temperature TSDC peak occurs in glasses 1 and 2 at a temperature where the conductivity is 10-14 (fl c m ) - 1, fig. 3. The low temperature TSDC peak in glasses 1 and 2 was unobserved with an Ep ~ 2.8 kV/cm, which was enough to produce the high temperature peak, so higher voltages ( ~ 8 k V / c m ) had to be used. The high temperature TSDC peak in glass 3 occurs at a conductivity of ~ 10-~5 (fl c m ) - ~, but the low temperature TSDC peak occurs at a temperature where the dc conductivity could not be measured with the field used for TSPC, fig. 3.
4. Discussion 4.1. T S P C p e a k
The data for the TSPC peak indicate that it is the same as the conductivity peak reported previously [5]. The absence of the TSPC peak in glass 3 which did not contain Sb203 clearly indicates that this peak is related to the presence of Sb203 in these glasses. Its origin is clearly different from that of the TSDC peaks found in alkali silicate glasses as indicated by its much larger size and presence in TSPC-2 as well as TSPC-1. The present results support the previous interpretation that the TSPC peak in glasses 1 and 2 is due to electron hopping between Sb 3+ and Sb 5+ ions. Its dependence upon Sb203, its ap-
354
B. Dutta, D.E. Day / Electronic and ionic conduction
pearance in TSPC-1 as well as TSPC-2 and its absence in TSPC-3 when the cell was evacuated are all consistent with the prior interpretation [5] that this TSPC peak is due to the following reactions:
(3) (4) (5)
0 2- ~v*1 / 2 0 2 ? + 2 e - , Sb5+ + 2 e - = S b 3+, Sb205 ~:~Sb203 + 02 ~'.
Prior evidence [5] showing that reaction 5 proceeds from left to right during heating consisted of an endothermic DTA peak at 303 K, a TGA weight loss consistent with the amount of oxygen liberated and chemical analyses of the glasses showing a decrease in the SbS+/Sb +3 ratio as depicted in fig. 5. The temperature of the TSPC peak in the present measurements and that for the DTA and TGA peaks measured previously [5] for glasses 1 and 2 differ by only 10 K which is within experimental error. The reversibility of reaction 5 during cooling was indicated by the reversibility of the peak in conductivity [5] during cooling. At low temperatures the conductivity initially increases due to the increased thermal energy of electrons hopping between Sb3+ and Sb 5+ sites, but due to the reduction in Sb5+ ions with increasing temperature, the conductivity eventually reaches a maximum and then decreases with increasing temperature. The appearance of the peak in TSPC-2 is obviously inconsistent with its being due to a type of orientational polarization resulting from ion motion. Any such motion would have been completed during TSPC-1 and therefore should be absent in TSPC-2 [10-17]. However, if reaction 5 was totally
T (K) 310 I
300 I
32O
OD8 m
0.06
~0.04
&
0.02
0.00
t
I
,
3O
I
!
40 T PC)
Fig. 5. Variationof [SbS+]/[Sb3+] as a functionof temperature for glass 2 (from ref. 5).
B. Dutta, D.E. Day / Electronic and ionic conduction
355
reversible, an identical peak in TSPC-2 would be expected if it was due to electron hopping. This is due to the fact that the oxygen previously liberated during the heating for TSPC-1 would recombine during the cooling cycle and the equilibrium SbS+/Sb 3+ ratio would be re-established at the start of the heating for TSPC-2. Within experimental error, the temperature of the peak in TSPC-2 was identical to that in TSPC-1, table 3. The peak in TSPC-2 was smaller than in TSPC-1, but this could be due to incomplete recombination of some of the oxygen liberated during TSPC-1 such that fewer Sb5+ ions were present at the start of TSPC-2. Equally important evidence supporting eq. (5) was the absence of the peak in TSPC-3 for glass 1, fig. 1. Based on eq. (5), a peak would not be expected if the low SbS+/Sb 3+ ratio at high temperatures could be "frozen" into the glass. This was done by removing the oxygen liberated during the TSPC-2 measurement by evacuating the cell at high temperatures, ~ 500 K, at the completion of TSPC-2. Thus, no oxygen was available to re-establish the equilibrium SbS+/Sb 3+ ratio during cooling at the completion of TSPC-2 and no peak was observed during TSPC-3. All of the present results for the TSPC peak in the Sb203 glasses can be explained as its being due to electron hopping between Sb3+ and Sb5+ sites and the change in the Sb~+/Sb 3÷ ratio as determined by the temperature dependence of eq. (5). It is important to note that the TSPC peak was observed only when the surrounding helium atmosphere was static. Initially, this TSPC peak nearly went undetected when the normal procedure of using a flowing helium atmosphere in the cell was followed. Care should be taken, therefore, in the type of surrounding atmosphere when measuring the TSPC/TSDC of glasses where reaction with oxygen is a possibility. 4.2. Low temperature TSDC peak The origin of the low temperature TSDC peak in these glasses is less certain. In glass 3, it occurs at a temperature where no appreciable dc conductivity could be measured with the fields used in the TSPC measurements. In glasses 1 and 2, the peak occurs where the electronic conductivity is 10-13-10-15 (~ cm) -I. In other alkali containing glasses [10-17] it occurred at an ionic conductivity of - 1 0 -14 (fl cm) -I so no correlation can be drawn in this regard. The reason that this peak did not contribute to the TSPC in glass 3 is that a much higher voltage was required to produce it than the voltage used in TSPC and Tp was much higher than the peak temperature. In TSDC, a sample can be polarized at any temperature below which space charge occurs. For that reason, TSDC can reveal certain alkali movements which is not possible in TSPC. No NBO should be present in sodium borosilicate glasses [21-23] unless the Na: B ratio is > 1. Krogh-Moe [22] and Bray [23] suggested that, up to - 30 mol% Na20, excess oxygens are used exclusively to form [BO4]- tetrahedra.
356
B. Dutta, D.E. Day / Electronic and ionic conduction
Beyond this composition, some non-bridging oxygens are formed. The glasses in the present investigation contain only 5 mol% Na20 and the N a / B ratio is much less than 1. Assuming that Sb203 does not change the structure of sodium borosilicate glasses drastically, then NBO ions should be absent in these glasses and the Na + ions should be associated with the [BO4]- tetrahedra [24]. When a dc potential is applied, the Na + ions may orient around the [BO4]- structural groups and this motion could be responsible for the low temperature TSDC peak. This can be viewed as a Na + -[BO4]- dipole which becomes oriented by Na + ion motion. For a TSDC peak caused by dipole orientation, the concentration of dipoles, Nd, can be calculated from [25]
Nd = kTpQ/Aa#2Ep,
(6)
where/~ is the dipole moment, a is a constant, Q is the peak area and the other symbols have been defined previously. For a freely rotating dipole, a is ~. The hindrances to dipole rotation in a glass is unknown so the equation [26] a = ½ { 1 - [ c o t h ( E a / 2 k T p ) -- 2 k Z p / E a ] 2 }
(7)
was used to calculate the values of a. Whereas the value of a for a freely rotating dipole is 0.333, the a for the glasses investigated ranges from 0.051 to 0.063. The moment, /t, for a Na+-[BO4] - dipole is unknown but has been assumed to the product of Na + -[BO4] - ionic distance [0.98 ,~ (Na ÷ ) + 0.88 ,~ (for B in tetrahedral coordination) = 1.86 ,~] and one unit of electronic charge (1.602 × 10-19C). The values of Nd, calculated from eqs. (6) and (7) using Q for the low temperature TSDC peak is only - 0 . 1 of the alkali concentration, table 4. Moreover, the temperature of the low temperature TSDC peak does not correlate with the ionic conductivity as found previously [12,15,16]. Therefore, this peak does not appear to be due to the orientation of Na + ions around [BO4]- units. Further investigation is required to determine its exact origin although its lower activation energy favors some type of ion movement.
4.3. High temperature TSDC peak The ionic conductivity at which this peak occurs, 10- 14 (~ cm)-~, corresponds well with that where the low temperature TSDC peak occurs in alkali silicate and germanate glasses investigated previously [10-17]. The Nd values calculated by assuming that it is caused by dipole orientation [using eqs. (6) and (7)] are in reasonable agreement with the Na + ion concentration, table 4. The origin of the high temperature TSDC peak in these glasses, therefore, could be explained~by the orientation of Na + ions around [BO4]- tetrahedra.
B. Dutta, D.E. Day / Electronic and ionic conduction
357
5. Summary The TSPC peak and TSDC peaks in these sodium borosilicate glasses clearly differ in several major respects indicating that they originate from different mechanisms. The TSPC peak is 103-104 times larger than the two TSDC peaks and has an activation energy significantly higher than that expected for sodium ion motion in these glasses. Furthermore, the TSPC peak is clearly related to the presence of antimony oxide in the glass and its temperature (292-+ 3) K is close to that ( - 3 0 0 K) where the conversion of Sb 5÷ to Sb3÷ has been reported to occur in these glasses. This TSPC peak, therefore, is believed to arise from electron motion such as the previously suggested [5] bipolaron hopping between Sb 5+ and Sb 3+ sites. Above ~ 360 K, the dc conductivity is attributed to Na ÷ motion. The activation energy of the two TSDC peaks present in all three glasses was less than that for the ionic dc conductivity, but they may be caused by some type of Na ÷ motion more localized than that for dc conductivity. The magnitude of the higher temperature TSDC peak can be accounted by the reorientation of Na + ions around BO 4 tetrahedra, but the origin of the TSDC peak at lower temperature is uncertain at present.
References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [1 I] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26]
N.F. Mott, J. Non-Crystalline Solids 1 (1968) 1. R.M. Hill and A.K. Jonscher, J. Non-Crystalline Solids 32 (1979) 53. L. Murewski, C.H. Chung and J.D. McKenzie, J. Non-Crystalline Solids 32 (1979) 91. C.F. Drake and I.F. Scanlan, J. Non-Crystalline Solids 4 (1970) 234. Devendra Kumar, PhD Thesis, Indian Institute of Technology, Kanpur, India (1980). P. Close, H.M. Shephard and C.H. Drummond, J. Am. Ceram. Soc. 41 (1958) 455. C. Bucci, Phys. Rev. 164 (1967) 1200. C. Bucci, R. Fieschi and G. Guidi, Phys. Rev. 148 (1966) 816. M.M. Perlman, J. Electr. Chem. Soc. 119 (1972) 892. C.M. Hong and D.E. Day, J. Mat. Sci. 14 (1979) 2493. C.M. Hong and D.E. Day, J. Appl. Phys. 50 (1979) 5352. C.M. Hong and D.E. Day, J. Am. Ceram. Soc. 64 (1981) 61. C.M. Hong, PhD thesis, University of Missouri, Rolla (1980). B. Dutta and D.E. Day, to be published. A. Agarwal and D.E. Day, J. Am. Ceram. Soc. 65 (1982) 111. D. Jannek and D.E. Day, J. Am. Ceram. Soc. 64 (1981) 227. A. Doi and D.E. Day, J. Appl. Phys. 52 (1981) 3433. R.J. Charles, J. Appl. Phys. 32 (1961) 115. P. Hedvig, Annual Report, Conf. Elec. Insulation and Dielectric Phenomena (Nat. Acad. Sci., Washington DC, (1975) p. 3. J. Vanderschueren and J. Gasiot, Topics in Appl. Phys. Vol. 37, ed.~ P. Br~iunlich (Springer Verlag, New York, 1979) p. 192. M.P. Brungs and E.R. McCartney, Phys. Chem. Glasses 16 (1975) 48. J. Krogh-Moe, Phys. Chem. Glasses 3 (1962) 1. P.J. Bray and S.G. Greenblatt, Phys. Chem. Glasses 8 (1967) 213. R.L. Myuller, Electrical conductivity of vitreous substances (Consultants Bureau, New York, 1971) p. 79. S. Unger and M.M. Perlman, Phys. Rev. B6 (1972) 3973. A.H. White, J. Chem. Phys. 7 (1939) 58.
ELECTRONIC AND IONIC CONDUCTION BOROSILICATE GLASSES *
345
IN SODIUM
B i p r o d a s D U T T A a n d D e l b e r t E. D A Y Ceramic Engineering Department and Graduate Center for Materials Research, University of Missouri, Rolla, Missouri 65401, USA
Received 24 August 1981 Revised manuscript received 9 November 1981
Electron and sodium ion motion in sodium borosilicate glasses containing Sb203 has been determined by thermally stimulated polarization and depolarization current (TSPC/TSDC) technique. Whereas a glass containing Sb203 exhibited a TSPC peak, the peak was absent in a similar glass without Sb203. The TSPC peak which appeared in TSPC -1 and TSPC-2 was 103_ 104 times larger than the TSDC peaks and had an activation energy higher than that of the TSDC peaks and ionic dc conduction. Electron hopping between Sb5+ and Sb3+ ion sites is considered responsible for the TSPC peak. All the glasses show two TSDC peaks. The origin of the low temperature TSDC peak is uncertain but the high temperature TSDC peak could be accounted for by the orientation of Na ÷ ions around [BO4] groups. Above ~360 K the dc conduction is due to sodium ion motion.
1. Introduction Some oxide glasses c o n t a i n i n g ions having m u l t i p l e valence states are s e m i c o n d u c t i n g [1-3]. I n V 2 O s - P 2 0 5 glasses, the c o n d u c t i v i t y is due to elect r o n s h o p p i n g b e t w e e n V 4÷ a n d V 5+ ions [1-3]. Similarly, the c o n d u c t i v i t y of iron p h o s p h a t e a n d c o p p e r p h o s p h a t e glasses has been a t t r i b u t e d [4] to electron m o v e m e n t b e t w e e n Fe2 + / F e 3 + a n d C u ÷ / C u 2 + ions, respectively. R e c e n t l y the c o n d u c t i o n , b e l o w 300 K, of s o d i u m b o r o s i l i c a t e glasses cont a i n i n g S b 2 0 3 has been a t t r i b u t e d [5] to the h o p p i n g o f b i p o l a r o n s (pair of electrons) b e t w e e n Sb 3÷ a n d Sb 5+ ions [6]. In these glasses a sharp m a x i m u m in the dc c o n d u c t i v i t y is o b s e r v e d at 308 K as illustrated in fig. 1. T h e initial increase in c o n d u c t i v i t y b e l o w 300 K was a t t r i b u t e d to increased electron mobility. A b o v e - - 3 0 0 K , the c o n c e n t r a t i o n of Sb 5+ ions decreases, so the decline in c o n d u c t i v i t y was a t t r i b u t e d to the lesser n u m b e r of available Sb 5+ sites. T h e increase in c o n d u c t i v i t y a b o v e - 360 K was a t t r i b u t e d to s o d i u m ion motion.
* This work was supported by NSF Grant DMR-79-18425. From a thesis submitted by B. Dutta for the MS Degree in Ceramic Engineering, University of Missouri-Rolla, December, 1981. 0022-3093/82/0000-0000/$02.75
© 1982 N o r t h - H o l l a n d
346
B. Dutta, D.E. Day / Electronic and ionic conduction
-I0
n ql--lonlc
T
I
I
Conductlon-------l~t~Electronlc
I
I
Conductlon~
-II
s
E -J2
•
)II.u 0 z 0 o
-13
-14
¢.9 o
-le
2.0
2.5
3.0 IO00/T
3.5
4.0
(K)-I
Fig. I. TSPC-1, (O), TSPC-2 (IS]), TSPC-3 (A) of sodium borosilicate glass 2, containing Sb203. • Data from ref. 5.
The method used previously [5] to measure the dc conductivity of sodium borosilicate glasses containing Sb203 resembles the thermally stimulated polarization current technique. Thermally stimulated polarization and depolarization current (TSPC/TSDC) technique has been widely employed to investigate charge motion and trap levels in crystalline dielectrics and semiconductors [7-9]. This technique has also been used to study alkali ion motion in alkali silicate [10-16] and germanate [17] glasses and is said to provide evidence of localized and longer range alkali ion motion. Most alkali silicate glasses [10-16] show two TSDC peaks and a high temperature background (HTB) current. In others, only one low temperature TSDC peak and the HTB were found [14,17]. The two TSDC peaks and HTB were attributed to alkali ion motion, the latter being due to the translational alkali ion motion responsible for dc conduction since the activation energy for the HTB is same as that for dc conductivity. The activation energies for the TSDC peaks were less than that for dc conductivity, dielectric loss or alkali diffusion. This is one of the main reasons the TSDC peaks have been attributed to alkali ion motion more localized than the translational motion causing dc conduction. The smaller of the two TSDC peaks with the lower activation energy has been attributed [ 12,14,15] to the localized movement of the alkali ion around the non-bridging oxygen ion (NBO) to which it is bonded. This interpretation is based~on Charles' model [18] and is supported by the fact that the alkali-NBO dipole concentration calculated from the experimental peak area and assumed alkali-NBO dipole moment agree well with the alkali concentration calculated from the glass composition. In sodium germanate glasses [17]
B. Dutta, D.E. Day / Electronic and ionic conduction
347
containing - 1000 ppm Na20, however, the observed TSDC peak is too large to be accounted for by Na-NBO dipole orientation. To explain this, it was assumed that the true activation energy for the low temperature TSDC peak is the same as that for dc conduction, and that the peak is due to the translational alkali motion responsible for dc conductivity. A limited translational motion of the alkali ions has been proposed [10-16] for the second TSDC peak at higher temperatures since it is too large (10-100 times the first peak) to be accounted for by alkali-NBO dipole orientation. This peak is attributed [12,14,16] to the accumulation/depletion of alkali ions at the immiscible phase boundaries of inhomogeneous glasses according to the interracial polarization model of Maxwell-Wagner and Sillars [19,20]. In sodium silicate and sodium borate glasses [12,13], two TSDC peaks were found in the former but only one in the latter. In sodium borosilicate glasses containing 12 mol% Sb203, a large conductivity peak was found [5] which was attributed to the Sb203 present in the glass as explained earlier. However, no Sb203-free glass was measured where such a peak would be absent if this peak was due to electron hopping. Furthermore, the possibility of Na + ion motion, which produces TSDC peaks in alkali silicate glasses [10-17], was apparently not considered. The present investigation was undertaken to re-examine the interpretation previously [5] proposed for the conductivity peak in sodium borosilicate glasses containing Sb203. An Sb:O3-free glass was measured to test the hypothesis that electron hopping between Sb5+ and Sb3÷ ions is responsible for the conductivity peak. It was also of interest to determine whether Sb203 containing glasses showed TSDC peaks due to Na + ion motion and to compare any such TSDC peaks with the large TSPC peak reported previously.
2. Experimental Two glasses (nos. 2 and 3 in table 1) were prepared by melting reagent grade Na2CO3, H3BO3, Sb203 and 99.8% SiO 2 in platinum crucibles. Procedures similar to those described previously [11] were used. The density of the glasses was measured by the Archimedes' method using xylene as the immersion liquid. Glass 1 was from the same melt as measured previously [5]. Samples (-0.15 cm in thickness and ~ 1.5 cm2 in cross-sectional area) were cut from annealed rectangular bars. Circular gold electrodes (0.317 cm2 in area) were evaporated on the large faces of these samples. The electrical measurements were performed on samples contained in a cell, described previously [10,11], which was evacuated (~35 /~m Hg) at either 300 K (TSPC measurement) or ~ 500 K (TSDC measurement) to remove any moisture present. The samples were short circuited during this time. A static helium atmosphere during TSPC and a flowing helium atmosphere during TSDC measurements was maintained to improve heat transfer and minimize temperature gradients.
348
B. Dutta, D.E. Day / Electronic and ionic conduction
Table 1 Composition (tool%) and density of glasses studied Glass No.
SiO2
B203
Sb203
Na 2°
Density (cm- 3)
Annealing treatment
I a
56 64 70
27 19 25
12 12 -
5 5 5
2.71 2.83 2.91
unknown 5500C, 1 h 550°C, 1 h
2 3
a Providedby Dr. D. Chakravortyof Indian Institute of Technology,Kanpur, India.
In the TSPC measurement, the sample was first cooled to - 1 0 0 K, a dc field (2-8 k V / c m ) was applied and the sample heated at a uniform rate (fl) of 4 K / m i n . The current measured by an electrometer* during the first heating was denoted as TSPC-I. Heating was discontinued much below the temperature where space charge polarization appears i.e. at a conductivity, o, of 10-7 (fl c m ) - i . After TSPC-1, the sample was recooled rapidly to - 100 K with the field still applied, reheated, and the current (denoted as TSPC-2) remeasured. Immediately after TSPC-2, the sample was cooled a third time to 100 K, the field removed and the depolarization current (TSDC-3) recorded during heating at the same rate ft. The dc conductivity, o, was calculated from TSPC-2 using the equation
o(T) =i(T)/E?A,
(I)
where E e is the field applied, A is the electrode area, and i(T) is the current. Previous work [I0,I I] has shown that the dc conductivity calculated in this way from TSPC-2 is reproducible and agrees well with the conductivity measured in other ways. The good reproducibility of the ionic conductivity is shown by the data > 4 0 0 K in fig. l, where the curves for TSPC-1, -2 and -3 are indistinguishable. The activation energy for dc conduction, E c, was determined from o = o0 exp -- E c / k T ,
(2)
where o0 is the pre-exponential factor, T is the absolute temperature and k is the Boltzmann constant. E¢ and o0 were determined from the slope of logo versus I / T (fig. 2). The activation energy for the TSPC peak was calculated from the slope of log o versus 1 / T for the low temperature side of the peak (fig. 2). In TSDC measurements, an unpolarized sample was polarized at a constant temperature, Tp, for a fixed time (tp = 10 rain) and then rapidly cooled ( - 7 min) to ~ 100 K with the field applied. The field was then removed and the depolarization current recorded as the sample was heated until completely * Keithley model 610B electrometer.
B. Dutta, D.E. Day / Electronic and ionic conduction I
I
I
349
I
Ionic Conduction •
,
,A
1
2 -II onlc Conduction A 12'
T-.
-12
E
> -13 I-(.3 =) r-, Z 0 (..) t.,,9
q -14
-I
i
%
I
2.0
I
I
2.5
3.0
IO00/T
(K) - I
I
4'.o
Fig. 2. Electronic and ionic conductivity of sodium borosilicate glasses with ( ~ and A) and without (©) Sb203. ~ =glass l, /~ =glass 2, © =glass 3. Prime denotes data interpolated from figs. 4.4 and 4.5 in ref. 5.
discharged. After measuring TSDC, the sample was short circuited and held at a still higher temperature to completely destroy any residual polarization. The sample was repeatedly polarized at successively higher temperatures at l0 K intervals until any TSDC peak observed became saturated. During the TSDC measurements the shunt resistor of the electrometer was kept at least two orders of magnitude lower than the sample resistance so the sample could discharge freely. The activation energy for the TSDC peaks was determined by the partial discharge [12] of a sample previously polarized to saturation. The peak was subsequently depolarized in steps by heating to successively higher temperatures. The activation energy was calculated from the slope of log current versus 1 / T for each partial discharge (PD-1, PD-2 etc.). The activation energy for the first partial discharge (PD-1) was considerably lower than PD-2, PD-3, etc. so the PD-1 value was neglected and the average of the other values taken as the activation energy. The error in the peak temperature, activation energy and area is estimated to be -+2 K, -+4 kJ/mol and -+ 10%, respectively.
B. Dutta, D.E. Day / Electronic and ionic' conduction
350 3. R e s u l t s
3.1. dc conductivity The data for the dc conductivity above and below the TSPC peak, fig. 1, as calculated from TSPC are compared with that measured previously [5] in tables 2 and 3. The present data agrees well with the previous data [5]. The activation energy for electronic conductivity (TSPC peak) is much higher than that for ionic conductivity above 400 K. The ionic and electronic conductivities of the glasses are compared in fig. 2 where only the straight line portion of the data are shown. 3.2. TSPC peak The TSPC data for the glasses measured are provided in table 3. Glasses containing Sb203 exhibit a TSPC peak which is comparable in magnitude but at slightly lower temperature than the conductivity peak observed previously [5] in glasses of the same composition, fig. 1. The peak at (292 ~ 3)K was
Table 2 Data for dc conduction (ionic) above 400 K [Ec: kJ/mol; %: (~ cm)-1] Glass no.
1 2 3
Present work
Ref. 5
Ec
o0
Ec
o0
85.7 108.3 82.8
0.8 × 10 -3 0.1 7.5 × 10 -3
86.7 115.6 -
8.1×10 -3 3.0
Table 3 Data for current peak observed in TSPC-I and -2 Glass no.
! 2 3 a From ref. 5.
Peak temperature (K)
Peak magnitude, Q/EpA ( × 10-l0 C / V cm)
TSPC- 1
TSPC-2
TSPC- 1
293 (308) a 290 (308) a no peak
295
3.9
1.7
292
10.7
1.8
no peak
-
Activation energy (kJ/mol)
TSPC-2
-
209 (193) a 472 (481) a -
B. Dutta, D.E. Day
I
/ Electronic and ionic" conduction
I
I
351
I
I
Low Temperature TSDC Peak
-I0
t High Temperature TSDC Peek T.~ -II 3
E
oN,,..
21
>- -12 I,--
O
0
'~
o -14 o,
-IE
I
I
I
20
2,5
5.0
o 3.5
4.0
IO00/T (K)-I Fig. 3. TSPC-I curves for glass l (~), glass 2 (A) and glass 3 (O).
observed in both TSPC-1 and TSPC-2 as depicted for glass 2 in fig. 1. Similar results, not shown in fig. 1, were obtained for glass 1. A TSPC-3 measurement was made for glass2. After the TSPC-I and -2
-13 m I
R -14
u
u
'q0-'-Hlgh temp TSDC p e o k ~ L 0 w t (HT) ]
!
/ /
romp TSOC peakn,'l (LT) "~
J0 >.
-15
I-
$ 0
J
-,%
I
2.0
I
3.0 IOOO/T (K) "l
I
4.0
5.0
Fig. 4. TSDC peaks in glasses 1 (~), 2 (A), and 3 (O). Polarization conditions were glass I-LT: Tp =420 K, Ep =8525 V/cm; HT: Tp =460 K, Ep =2758 V/cm. Glass 2-LT: Tp =412 K, Ep =7529 V/em; HT: Tp =480 K, Ep =2792 V/cm. Glass 3-LT: Tp =386 K, Ev--5246 V/cm; HT: 405 K, Ep = 5246 V/cm.
1 2 3
Glass no.
278 265 254
Low Temp. peak
431 462 350
High Temp. peak
Temperature (K)
Table 4 Data for saturated TSDC peaks
57.3 53.5 52.5
76.3 89.0 61.0
Activation energy (kJ/mol) Low High Temp. Temp. peak peak
Q/EpA High Temp. peak (X 10 -13
C / V cm) 15.3 5.0 12.7
Peak magnitude, Low Temp. peak (X 10 -14
C / V era) 1.9 1.5 8.6
1.1 1.2 6.8
cm3)
(X 1020/
Low Temp. peak
1.9 0.7 1.3
era3)
(>( 1021/
High Temp. peak
Nd, calculated from eq. (6)
1.8 1.8 2.7
c m 3)
Na + ion concen= tration ( × 102~/
~" ~"
B. Dutta, D.E. D a y / Electronic and ionic conduction
353
measurement in static helium, the cell was evacuated at ~ 500 K for 10 min. The sample was then cooled to - 1 0 0 K and reheated as the TSPC-3 was measured. The peak previously present in TSPC-1 and -2 was absent in TSPC-3 as is evident from fig. 1. There is a slight difference in the peak temperature between TSPC-1 and -2 and the peak area of TSPC-1 is larger than that of TSPC-2, fig. 1. The TSPC peak occurs at a temperature below the HTB, but the activation energy of the TSPC peak is much higher than that of the HTB, tables 2 and 3. The peak present in TSPC-1 and -2 in the two glasses containing Sb203, was absent in the Sb203-free glass (no. 3) measured under similar experimental conditions, see fig. 3. 3.3. T S D C p e a k s
All three glasses exhibited two TSDC peaks as shown in fig. 4, but they are much smaller (10-3 to l 0 - 4 times) than the TSPC peak. The activation energy for the low temperature TSDC peak is lower than that for the high temperature TSDC peak while the activation energies for both TSDC peaks are lower than that for dc conduction (tables 2-4). The magnitude of the low temperature TSDC peak is apparently reduced by Sb203since it is larger in glass 3 than in glasses 1 and 2 which contain Sb203, table 4. For glasses 1 and 2, the low temperature TSDC peak occurs at a temperature corresponding to a conductivity of ~ 10 -13 and - 1 0 -15 (fl cm) 1 respectively, as denoted by the arrows in fig. 3. The high temperature TSDC peak occurs in glasses 1 and 2 at a temperature where the conductivity is 10-14 (fl c m ) - 1, fig. 3. The low temperature TSDC peak in glasses 1 and 2 was unobserved with an Ep ~ 2.8 kV/cm, which was enough to produce the high temperature peak, so higher voltages ( ~ 8 k V / c m ) had to be used. The high temperature TSDC peak in glass 3 occurs at a conductivity of ~ 10-~5 (fl c m ) - ~, but the low temperature TSDC peak occurs at a temperature where the dc conductivity could not be measured with the field used for TSPC, fig. 3.
4. Discussion 4.1. T S P C p e a k
The data for the TSPC peak indicate that it is the same as the conductivity peak reported previously [5]. The absence of the TSPC peak in glass 3 which did not contain Sb203 clearly indicates that this peak is related to the presence of Sb203 in these glasses. Its origin is clearly different from that of the TSDC peaks found in alkali silicate glasses as indicated by its much larger size and presence in TSPC-2 as well as TSPC-1. The present results support the previous interpretation that the TSPC peak in glasses 1 and 2 is due to electron hopping between Sb 3+ and Sb 5+ ions. Its dependence upon Sb203, its ap-
354
B. Dutta, D.E. Day / Electronic and ionic conduction
pearance in TSPC-1 as well as TSPC-2 and its absence in TSPC-3 when the cell was evacuated are all consistent with the prior interpretation [5] that this TSPC peak is due to the following reactions:
(3) (4) (5)
0 2- ~v*1 / 2 0 2 ? + 2 e - , Sb5+ + 2 e - = S b 3+, Sb205 ~:~Sb203 + 02 ~'.
Prior evidence [5] showing that reaction 5 proceeds from left to right during heating consisted of an endothermic DTA peak at 303 K, a TGA weight loss consistent with the amount of oxygen liberated and chemical analyses of the glasses showing a decrease in the SbS+/Sb +3 ratio as depicted in fig. 5. The temperature of the TSPC peak in the present measurements and that for the DTA and TGA peaks measured previously [5] for glasses 1 and 2 differ by only 10 K which is within experimental error. The reversibility of reaction 5 during cooling was indicated by the reversibility of the peak in conductivity [5] during cooling. At low temperatures the conductivity initially increases due to the increased thermal energy of electrons hopping between Sb3+ and Sb 5+ sites, but due to the reduction in Sb5+ ions with increasing temperature, the conductivity eventually reaches a maximum and then decreases with increasing temperature. The appearance of the peak in TSPC-2 is obviously inconsistent with its being due to a type of orientational polarization resulting from ion motion. Any such motion would have been completed during TSPC-1 and therefore should be absent in TSPC-2 [10-17]. However, if reaction 5 was totally
T (K) 310 I
300 I
32O
OD8 m
0.06
~0.04
&
0.02
0.00
t
I
,
3O
I
!
40 T PC)
Fig. 5. Variationof [SbS+]/[Sb3+] as a functionof temperature for glass 2 (from ref. 5).
B. Dutta, D.E. Day / Electronic and ionic conduction
355
reversible, an identical peak in TSPC-2 would be expected if it was due to electron hopping. This is due to the fact that the oxygen previously liberated during the heating for TSPC-1 would recombine during the cooling cycle and the equilibrium SbS+/Sb 3+ ratio would be re-established at the start of the heating for TSPC-2. Within experimental error, the temperature of the peak in TSPC-2 was identical to that in TSPC-1, table 3. The peak in TSPC-2 was smaller than in TSPC-1, but this could be due to incomplete recombination of some of the oxygen liberated during TSPC-1 such that fewer Sb5+ ions were present at the start of TSPC-2. Equally important evidence supporting eq. (5) was the absence of the peak in TSPC-3 for glass 1, fig. 1. Based on eq. (5), a peak would not be expected if the low SbS+/Sb 3+ ratio at high temperatures could be "frozen" into the glass. This was done by removing the oxygen liberated during the TSPC-2 measurement by evacuating the cell at high temperatures, ~ 500 K, at the completion of TSPC-2. Thus, no oxygen was available to re-establish the equilibrium SbS+/Sb 3+ ratio during cooling at the completion of TSPC-2 and no peak was observed during TSPC-3. All of the present results for the TSPC peak in the Sb203 glasses can be explained as its being due to electron hopping between Sb3+ and Sb5+ sites and the change in the Sb~+/Sb 3÷ ratio as determined by the temperature dependence of eq. (5). It is important to note that the TSPC peak was observed only when the surrounding helium atmosphere was static. Initially, this TSPC peak nearly went undetected when the normal procedure of using a flowing helium atmosphere in the cell was followed. Care should be taken, therefore, in the type of surrounding atmosphere when measuring the TSPC/TSDC of glasses where reaction with oxygen is a possibility. 4.2. Low temperature TSDC peak The origin of the low temperature TSDC peak in these glasses is less certain. In glass 3, it occurs at a temperature where no appreciable dc conductivity could be measured with the fields used in the TSPC measurements. In glasses 1 and 2, the peak occurs where the electronic conductivity is 10-13-10-15 (~ cm) -I. In other alkali containing glasses [10-17] it occurred at an ionic conductivity of - 1 0 -14 (fl cm) -I so no correlation can be drawn in this regard. The reason that this peak did not contribute to the TSPC in glass 3 is that a much higher voltage was required to produce it than the voltage used in TSPC and Tp was much higher than the peak temperature. In TSDC, a sample can be polarized at any temperature below which space charge occurs. For that reason, TSDC can reveal certain alkali movements which is not possible in TSPC. No NBO should be present in sodium borosilicate glasses [21-23] unless the Na: B ratio is > 1. Krogh-Moe [22] and Bray [23] suggested that, up to - 30 mol% Na20, excess oxygens are used exclusively to form [BO4]- tetrahedra.
356
B. Dutta, D.E. Day / Electronic and ionic conduction
Beyond this composition, some non-bridging oxygens are formed. The glasses in the present investigation contain only 5 mol% Na20 and the N a / B ratio is much less than 1. Assuming that Sb203 does not change the structure of sodium borosilicate glasses drastically, then NBO ions should be absent in these glasses and the Na + ions should be associated with the [BO4]- tetrahedra [24]. When a dc potential is applied, the Na + ions may orient around the [BO4]- structural groups and this motion could be responsible for the low temperature TSDC peak. This can be viewed as a Na + -[BO4]- dipole which becomes oriented by Na + ion motion. For a TSDC peak caused by dipole orientation, the concentration of dipoles, Nd, can be calculated from [25]
Nd = kTpQ/Aa#2Ep,
(6)
where/~ is the dipole moment, a is a constant, Q is the peak area and the other symbols have been defined previously. For a freely rotating dipole, a is ~. The hindrances to dipole rotation in a glass is unknown so the equation [26] a = ½ { 1 - [ c o t h ( E a / 2 k T p ) -- 2 k Z p / E a ] 2 }
(7)
was used to calculate the values of a. Whereas the value of a for a freely rotating dipole is 0.333, the a for the glasses investigated ranges from 0.051 to 0.063. The moment, /t, for a Na+-[BO4] - dipole is unknown but has been assumed to the product of Na + -[BO4] - ionic distance [0.98 ,~ (Na ÷ ) + 0.88 ,~ (for B in tetrahedral coordination) = 1.86 ,~] and one unit of electronic charge (1.602 × 10-19C). The values of Nd, calculated from eqs. (6) and (7) using Q for the low temperature TSDC peak is only - 0 . 1 of the alkali concentration, table 4. Moreover, the temperature of the low temperature TSDC peak does not correlate with the ionic conductivity as found previously [12,15,16]. Therefore, this peak does not appear to be due to the orientation of Na + ions around [BO4]- units. Further investigation is required to determine its exact origin although its lower activation energy favors some type of ion movement.
4.3. High temperature TSDC peak The ionic conductivity at which this peak occurs, 10- 14 (~ cm)-~, corresponds well with that where the low temperature TSDC peak occurs in alkali silicate and germanate glasses investigated previously [10-17]. The Nd values calculated by assuming that it is caused by dipole orientation [using eqs. (6) and (7)] are in reasonable agreement with the Na + ion concentration, table 4. The origin of the high temperature TSDC peak in these glasses, therefore, could be explained~by the orientation of Na + ions around [BO4]- tetrahedra.
B. Dutta, D.E. Day / Electronic and ionic conduction
357
5. Summary The TSPC peak and TSDC peaks in these sodium borosilicate glasses clearly differ in several major respects indicating that they originate from different mechanisms. The TSPC peak is 103-104 times larger than the two TSDC peaks and has an activation energy significantly higher than that expected for sodium ion motion in these glasses. Furthermore, the TSPC peak is clearly related to the presence of antimony oxide in the glass and its temperature (292-+ 3) K is close to that ( - 3 0 0 K) where the conversion of Sb 5÷ to Sb3÷ has been reported to occur in these glasses. This TSPC peak, therefore, is believed to arise from electron motion such as the previously suggested [5] bipolaron hopping between Sb 5+ and Sb 3+ sites. Above ~ 360 K, the dc conductivity is attributed to Na ÷ motion. The activation energy of the two TSDC peaks present in all three glasses was less than that for the ionic dc conductivity, but they may be caused by some type of Na ÷ motion more localized than that for dc conductivity. The magnitude of the higher temperature TSDC peak can be accounted by the reorientation of Na + ions around BO 4 tetrahedra, but the origin of the TSDC peak at lower temperature is uncertain at present.
References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [1 I] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26]
N.F. Mott, J. Non-Crystalline Solids 1 (1968) 1. R.M. Hill and A.K. Jonscher, J. Non-Crystalline Solids 32 (1979) 53. L. Murewski, C.H. Chung and J.D. McKenzie, J. Non-Crystalline Solids 32 (1979) 91. C.F. Drake and I.F. Scanlan, J. Non-Crystalline Solids 4 (1970) 234. Devendra Kumar, PhD Thesis, Indian Institute of Technology, Kanpur, India (1980). P. Close, H.M. Shephard and C.H. Drummond, J. Am. Ceram. Soc. 41 (1958) 455. C. Bucci, Phys. Rev. 164 (1967) 1200. C. Bucci, R. Fieschi and G. Guidi, Phys. Rev. 148 (1966) 816. M.M. Perlman, J. Electr. Chem. Soc. 119 (1972) 892. C.M. Hong and D.E. Day, J. Mat. Sci. 14 (1979) 2493. C.M. Hong and D.E. Day, J. Appl. Phys. 50 (1979) 5352. C.M. Hong and D.E. Day, J. Am. Ceram. Soc. 64 (1981) 61. C.M. Hong, PhD thesis, University of Missouri, Rolla (1980). B. Dutta and D.E. Day, to be published. A. Agarwal and D.E. Day, J. Am. Ceram. Soc. 65 (1982) 111. D. Jannek and D.E. Day, J. Am. Ceram. Soc. 64 (1981) 227. A. Doi and D.E. Day, J. Appl. Phys. 52 (1981) 3433. R.J. Charles, J. Appl. Phys. 32 (1961) 115. P. Hedvig, Annual Report, Conf. Elec. Insulation and Dielectric Phenomena (Nat. Acad. Sci., Washington DC, (1975) p. 3. J. Vanderschueren and J. Gasiot, Topics in Appl. Phys. Vol. 37, ed.~ P. Br~iunlich (Springer Verlag, New York, 1979) p. 192. M.P. Brungs and E.R. McCartney, Phys. Chem. Glasses 16 (1975) 48. J. Krogh-Moe, Phys. Chem. Glasses 3 (1962) 1. P.J. Bray and S.G. Greenblatt, Phys. Chem. Glasses 8 (1967) 213. R.L. Myuller, Electrical conductivity of vitreous substances (Consultants Bureau, New York, 1971) p. 79. S. Unger and M.M. Perlman, Phys. Rev. B6 (1972) 3973. A.H. White, J. Chem. Phys. 7 (1939) 58.