4.1. Impedance spectroscopy (IS)
4.2. A. C. Theory
4.3. Equivalent circuit representation
4.3.1. Series combination of R and C
4.3.2. Parallel combination of R and C
4.4. Jonscher's universal power law (JUPI,)
4.5. Complex dielectric constant
4. 6. Complex electric modulus
4.7. Results of low temperature studies
4.7. 1. Electrical Conductivity
4. 7. 2. a.c Conductivity
4. 7. 3. Dielectric Constant
4.7. 4. Electric Modulus
4.8. Conclusions
References
Low TEMPERATURE
STUDIES
ONSLIPER
IONCONDUCTING
SAT, SPT & SVT GI.ASSES
Chapter
-
IV, briefly deals with the a.c theory, complex impedance (Z*). complex
adm~ttance(Y*), complex dielectric pern~~ttivity
(c*) and complex modulus (M*) 13. 71.
L.ater section is presented with detail results of the temperature dependent ulnduct~vity
itudles through impedance measurement to understand ion dynamics in thc SAT. SPT arid
S\'T glassy systems.
4 . 1 . lmpedance spectroscopy (IS)
Impedance spectroscopy (IS) is used to study the electrical properties of SIC
~naterials,where the response of a system to an applied s~nusoidallyvarying nltcrnuting
ic~ltage is rewrded as a hnct~onof frequenc~es. Impdance analysis of
Ionic
solids
~dent~fies
the elementary process such as, thc hulk u~nduct~cln.
ionic transport. gain
houndary conduction and the electrode-electrolyte ~nterfaccprocess In the measured
frequency domain. It is a non-destmct~vetechn~queand also can provide the dynamic
properties to understand the microscopic nature of the SIC materials I 1-91,
4.2. A. C. Theory
Small amplitude of sinusoidal (a.c) signal is applied to perturb the systm and the
fryuency response is recorded as impedance and phase angle are shown in Fig. 4. 1. The
applied potential is given by
E = E,, exp (jot)
(1)
fie output current of the system is also a sinusoidal and it is represented by,
V
.v,
cQul,
Ctl
I = 4 I"*'
Fig. 4.1 Schematic principle of impedance spectroscopy
1 = 1, exp ( I t e t q )
(2)
~ccordlngto Ohm's law, Impedance (Z) of the c~rcultat anv fiquency (o)can bc
represented by
Z* = Ell = ( E,, i I,, ) exp (-J$)
-
Z,, cxp (-]I$)
= Z LO\
4 - J Z s ~ 4n
Z*=Z'-j7"[uhcre,Z'
(7)
Zcos$dndZ"--ZslnI$]
Where J =d-1, Z'and Z" are respcct~velyredl and lmaglnary parts of the ~mpedanceThe
pha\c difference (4) IS represented by
I$
-
tan '( Z"i L' )
(4)
The Impedance spectroscopy IS also ~allcdImlttancc spectrojcopy and 11 I \ ubcd to
mLa\ure the behav~orsof the materials In tenm ot'the ~omplex~mpedancc(I*).
~olnplex
xim~ttance(Y*), complex permltt~v~ty
( I *) and ~omplexrnoduiu\ (M*) [b-9) The Inter
relat~onsh~p
of above four pardmeten are given In 'Table 4 1
Table 4 1 The Inter relat~onsh~p
of ~mpedance,ddm~ttance,permlttrvrty and electnc
modulus parameters.
I.lertrrc modulus
-
M*
JW
'*
CbZ*
M ' + j M"
[WhereC, = E, (AIL), E, = 8 g54* 10 F/m, w=2nf and (AIL) 1s cell constant, A
of the sample and L 1s the thickness of the sample]
IS
the area
The impedance and admittance representations we used for analyzing the electrical
behavior of the sample in terms of bulk resistance (R,,) and its electrical equivalent circuits.
'The complex permittivity and modulus representations are used for analyzing the dielectric
response of the sample.
4.3. Equivalent circuit representation
4.3. 1. Series combination of K and C
Circuit containing a resistance and a capacitance
111 series
are shown in Fig. 4.2a.
The total impedance of the circuit is given by
Z*
(or)
Where,
=
R + (l/jc~)C)
Z* = Z' - J Z"
?'
Z"-
R?
I 1 0,
C
The resultant impedance plot for R and C in series is represented by a vertical line
parallel to the imaginary axis intersecting thc real axis at R, as shown in Fig 4.2a, and the
corresponding admittance plot gives the semicircle intersecting the rctl axis at a point IIR,
as shown in Fig.4.2b.
4.3.2. Parallel combination of R and C
Circuit containing a resistance and a capacitance in parallel are shown in Fig 4.3a
and the total impedance of the circuit is given by
Fig. 4.2. a) Z vs. Z' & b) B vs. G for series and c) Z" vs. Z' & d) B vs.G for parallel
combinations of RC circuits
Fig. 4.3 a,b,c. Impedance spectra of a) ideal, b) real & c) polycrystalline solid electrolytes
= { R I ( I+ ( u ) R c ) ' ) I - ( ~ W R C I ( I ~ W R C ) : ) I
Z*=Z-JZ"
or
Where, Z' = R / ( I
-f
(UJ
(8)
R c)?and Z" = w R C s ( I + (w R c)')
The complex impedance plot for the circuit ccjntain~ng a resistance and a
as shown in FIE4.3b. and the correspcrnd~ng
capacitance m parallel represents a sem~c~rcle
admrttance plot gives the vertrcal stra~ghtline. Intersection of the sem~circlew~ththe real
;!xis at a point R gives the bulk resistance of'thc material. The q u a t ~ o nof'thc sem~circlc
w~thradius RI? and center at Ri2. 0 is
( 2 - R!2 )' +
9
~'14
:
(9
The relationship between the parallel and scrles components is
R, = R, .' [ I + ( co R, C,, )'I
C,= I I + ( to R,
c,)?] / co? K,,?C,?
( 1 0)
(1 1)
Fig. 4.3, a, b shows the equivalent circuits and the impedance plots rcspectively for
an deal and real solid electrolytes. From fig 4 . h the vertical straight I~neand a perfect
scmicircle in the impedance plot represents for an ideal sold electrolyte. In F I 4.33,
~ the
inclined straight line represents the presence of double layer capacitance of electrode-
electrolyte interface and the depressed semicircle corresponds to the parallel combination
of resistance and capacitance. The angle of inclination of the vertical stra~ghtline and
angle of depression of the semicircle indicate the distributed microscopic properties ofthe
material, which is called constant phase element (CPE) [3]. Fig 4 . 3 ~shows the impedance
spectrum for a polyctystalline sample with the two smicircles, ( I ) resistance within thc
gains of the materials (ii) the partial or complete blocking of charge carriers at grain
boundary. The equivalent circuit for the polycrystalline samples is given by the series of
parallel combination of CPE and bulk resistance, CPE & grain boundary resistance and the
CPE of interface effect [13-161.
Boukamp's equivalent circuit software with non-linear least squrire (NLLS) fitting
procedure is used to analyze the measured complex impedance data of each composition of
all three sets of SAT, SPT & SVT glasses and obtained bulk resistance, equivalent circuit
of each sample.
4.4. Jonscher's Universal Power Law (JUPL)
Fig. 4.4 shows the frequency dependence
01'
conductivity spectrum exhibit three
regions (i). High frequency region (ii). Low frequency region (iii). Intermediate plateau
reglon. At the low frequency region. the conductiv~tydecreases with decrease of frequency
and 11s attributed to the pcrlari~ationeffects nt the electrode-electrolyte interfjce [U-141. In
low frequency region, more chargc accumulation occurs which exhihits thc charge flow
;ind hence, drops thc conductivity. In thc lntennediatc plateau region, conductivity is
almost independent of frequency and it is equal to the bulk or d.c conductivity of the
sample. The high frequency d~spers~on
reglon of the ac conductivity was fitted and
txplained using Jonscher's Iinivcrsal power law (JUPL) [ I 51.
o~,,
= a(o) + Am'
where, a(o) is the zero Frequency limit of a,,,, A is constant , (11
(12)
=
2nf and s is power law
exponent, where O <s < 1.
4.5. Complex dielectric constant
The complex dieledricconstant (c*) is ~xpl-essedas
&I
=
w h , E' is
the real (or relative pemuttivity or dielectric m t ) and c" is the imagrnary (or
dielectric loss) of the dielectrica m m t (E*) on be v t e d as [I 81
Dispersive region
Polarisation region
Plateau region
Fig. 4.4. Schemat~crepresentat~onof logo vs log f
b*
= --1-joC,,Z *
(14)
w is the ayllar tkquency and C,,is the capacitance of freeSF.
The E' and c" were calculated tiom the measured impedance data of all three sets of
SAT, SPT and SVT glasses over a tiequency range of 40 I-lz to I 0 kHz and 20 Hz to
I MHz at different low temperatures using the following equations
w h c x o = 2~ A is the am of the sample and c,, - 8.854' 10 ' ? Fim
4.6. Complex Electric Modulus
The complex electric modulus M* is the reciprocal ofthe complex permittivity c*.
M'=
I
c*
M e = M'+,iMV
(17)
(18)
wlicre, M' and M are respectively real and imaginary parts of complex electric modulus. The
complex eledric modulus spectra represcnt a measure of the distribution of ion energies or
configwahons in the structure and also describe the electrical laxa at ion of ionic glasses
a
~ a ~ s o o pp
ir
o
cm [I 8, 191. The real and unag~naryparts of the modulus data are calculated using
the measured vllpedance data for all three sets of SAT, SPT and SW glasses at d i f f i t low
-1
using the following equations
wAc,,Z"
M'=-
ahee, o = 2 d 1 sangular fialuency. t;,1s parmmvlry
duhkngs
of tiw
~psffA IS luca ol mm -on
dt IS
of the matenal
4.7. Results of Low Temperature Studies
4. 7. 1. Electrical Conductivity
F ~ g s 4 5, 4 6 and 4 7 show the lmaglnary (Z")vs real (Z')parts of mmplex
lrnpedaace plots, respect~vely,for the h~ghconducting former composltlon of x
=
0 5 fi)r
\AT. 0 7 for SPT and 0 6 tor SVT glasses mcdsured at low temperatures (104-IHO K. 89195 K and 99-242 K ) The vanous types of open symbols and
'*' respect~velyshow the
rncdsured and the fitted Impedance data of thc SAT or SPT or SVT glasses From Fig 4 5a
J I I ~h,
wlth~nthe measurcd frequency wlndow, the ~ncllncdstra~ghtl ~ n cI \ found to
d~sappearand the format~onof sem~c~rcle
IS observed w~tlldecrease In temperature The
iompletely formed depressed sem~clrcleand the part~allyformed sem~c~rcle
are shown
111
Tlg 4 5c and d, respect~vely Further, 11 1s observed that the ~ntercept of depressed
~ern~c~rclc
w ~ t h the real axis sh~ll towards the lower frequency w~th decreas~ng
temperature The depressed sem~c~rcle
corresponds to the parallel comblnat~onof bulk
realstance and constant phase elements (CPE) [3] In senes w ~ t hanother CPE, from the
lncllned straight Ime, ass~gnedto the double layer capac~tance,for SAT glasses The
equivalent clrcult 1s shown In Inset of Fig 4 5a. The center of each sem~crrclewas found
'0
be below the real axis. whlch revealed that the msoaated relaxat~onsof Ions are of non-
Debye In nature [3, 201. Slmllar behav~or1s observed for the SPT and SVT glasses as
shown m F~gs.4.6 and 4.7.
0
*
180K
I.11 data
.-C
E
$
0
0.0
20x10'
40x10~
2' Real [ohm1
0.0
awd
Z' Real (ohm1
Fig. 4. 5. Impedance (Z" vs. Z') plots, at low temperatures (I04 - 1 KO K), for high conducting
former composition (x
= 0.5) of SAT glass.
0.0
2 ~ d40x1t
Z' Real l o w
a ~ d
awe' lado" i.wd
Z' Real lohml
0.0
(e)
0
a ~ o "1.6~10' 2 4 0 '
Z' Real lohml
089K
A 1EK
0 lllK
Flt data
*
Fig. 4. 6. Impedance (Z" vs. 2') plots, at low temperatures (89-195 K), for high conduding
former composition (x
= 0.7) of
SPT glass
'E
fit data
e
M
*0
0.0
0.0
5.Ox10'
l.kld
Z' real (ohm)
0
1110'
Z' Real (Ohm)
Fig.4.7 Impedance (Z" vs. Z')plots, at low temperatures (99-24210, for high conducting
former composition (x = 0.6) of SVT glass.
Bulk conductivity o is calculated using pellet dimensions and bulk resistance (Rh)
ohtained from the analfled impedance data. measured at low temperatures. h r the high
conducting former composition of x
-
0.5 for SAT, 0.7 for SPT and 0.6 for SVT glasses.
~ h temperature
c
dependent of d.c conductivity for SAT or SPT or SVT glasses is fitted to
~rrheniusequation. Fig. 4.8a, h and c show the plots of log o T vs. IO(M)il', respectively.
for thc high conducting formcr composition of x
0.5 for SAT. 0.7 for SPT and 0.0 fbr
;
SVT glasses in the temperature range of where symhols represent measured conductivity
data and the line represents Arrhenius fit. From the slopewtrf log (aT) vs. 100017' plots, the
activation energy (E,) for Ag' Ion migration
111
each glass system is calculated arid it is
fbund to be 0.270 eV for SAT, 0.205 eV for SPT and 0.102 eV Ibr SVT glasses.
Figs 4.9, 4.10 and 4.1 1 show the ~rnaginary(%") vs. real (Z') pans of wmplcx
impedance plots respectively for the h~ghconductrng niodifi~rto fbrmcr ratio of m i f - I .75
fir SAT. 2.50 for SPT and 2.00 for SVT glasses measured at low tclnpcraturcs ( I 13-228
K. 1 1 2-208 K and 110-232 K). In Fig 4.9, 4.10 and 4.1 I . various typcs of open symbols
and line respectively show the measured and the fitted impdance data ofthc SAT or SPT
or SVT glasses. From Fig. 4.9a and b, within the measured frequency window, the inclined
straight line is found to disappear and the formation of semicircle is observed with
decrease in temperature. The completely formed depressed and the partially fonned
semicircles are shown in Fig. 4.Yc and d. respectively. Further, it is observed that the
Intercept of depressed semicircle with the real axis shift towards the lower frequency with
decrease of temperature. The depressed semicircle corresponds to the parallel combination
Of bulk resistance and constant phase elements (CPE) in series with another CPE due lo the
double layer
@asses[3,20].
obtained from the inclined straight line for SAT or SPT or SVT
Fig. 4.8. Log oT vs. 1000E plots for high conducting former composition of SAT (X
SPT (x = 0.7), and SVT (x = 0.6), glasses.
= 0.5),
0
3001
i
2
6
4
8
Z' Real [ohm]PIO")
Z' Real lohmlp~o'~--.
3q
I
172 K
0181 Y
, 188K
+
-
Flt dntn
Z' Real lohml ('IO'I
Z' Real
-~.
lohml(~lo'j
--I
Fig 4.9. Impedance (Z" vs. Z') plots, at low temperatures (1 13-22810, for high conducting m/f
= 1.75 of SAT glass.
Z'. real. lohnl] (,lo6)
h
h
-E
so-
148 K
Y
PI1 data
-do
C
0
*
**-A
*
i
:1
6
6'
i$
-
OO
0
50
'a , ,
3
%'.real. lohml ("10) .
.
100
3
2'. real. [ohm] 610')
0;
-E
4
5
"
A
t
-
0
.
2 2
.-
6
0
<=
Thy%*
185K
190K
197K
208K
-- Fit *#IB
, , -
8
Z'. real. loha1 elo3) ,
Fig 4. 10. Impedance (Z" vs. Z') plots, at low temperatures (1 12-208 K) for the high
conducting m/f = 2.5 of SPT glass.
.,
h
-
*b
z'.real. ~ohrn~
(~10")
z',
real, lohrnl (*lo3)
A212h'
2 0218K
*225K
ob
.-t
Z',real. (ohm1 (#lo3),
Fig 4.1 1. Impedance (Z"vs. Z')plots, at low temperatures (I 10-23210 for the high conducting
df= 2.0 of SVT glass
The temperature dependent of d.c conductivity obtained him impdance onnlysis
h r SAT or SPT or S W glasses IS fitted to Arrhen~usequation. 1:1g. 4.12 a. h and c shows
the plots of log oT vs. 1000m respect~velyfor the high conduct~ngm:f ratlo of m:f
1.75
:
-
li~rSAT. 2.50 for SPT and -7.00for SVT glasses in the tempcruture nlngc of 1 1 0 lo 132 K.
where symbols represent measured conductivity data q ~ the
d line represents Arrhenius fit.
I:rom the slopes of log (oT) vs. 1000rr plots. the activation energy (E,) for Ag' ion
migration In each glass system is calculated and 11 IS found to he 0.191 eV for SAT. 0.164
c\'
for SPT and 0.1 87 eV fi)r SVT glasses.
Flg 4.13, 4.14 and 4.15 show the unaplnary (%") vs, real (Z')plots, ~ s p e c t ~ v c lfbr
y,
the htgh conductrng dopant salt concentration of I)
50U/o (br SAT. 60
fi)r SPT and 60%
fi)r SVT glasses measured at low temperatures (154 - 230 K. 114 - 236 K ant1 139 - 231
K). In Fig 4.13, 4.14 and 4.15, various types of open synhols and lmc respectively show
the measured and the fitted impedance data of the SAT or SI'I' or SVT glasses. From Fig.
3.13a and b, within the measured frequency window. the ~nclinedstrs~ghtl ~ n cis tbund to
ci~.;appearand the format~onof stm~eirclcIS ohscrved w~thdecrease in tenipuuture. 'fie
completely formed depressed semicircle and the partially fi)rmed scmicirclc are shown In
Fig. 4 . 1 3 ~and d, respectively. Further. it is observed that the intercept of depressed
semicircle with the real axls sh~fltowards the IOWLT
frequency with dw7case of'
Icmperature. The depressed semicircle corresponds to the parallel combmation of bulk
resistance and constant phase elements (CPE) in series with another CPE, due to the
double layer capacitance obtained from the inclined stra~ghtl ~ n efor SAT or SPT or SVT
glasses (3,201.
The temperaiure dependent of d.c conductivity for SAT or SPT or SVT glasses is
fined to Anhenius equation. Fig. 4.16a, b and c show the plots of log nT vs. 1 0 0 0 ~ .
respectively, for the high conducting dopant concentration of D = 500h for SAT, 60 % for
Fig. 4.12. Log oT vs. 1000fI'plots for high conducting d f = I .75 for SAT, mlf =2.50 for SPT
and m/f =2.00 for SVT glasses.
Z'Real lohm] ch 10")fi
w
2
-
cE
1-
-0
-
182K
188K
195K
d
-
b
FII data
b
b
1
2
%' Real lohrnl(-10")
3
'
Z' Real [ohrnl[~~o~)
- ,
Fig 4.13. Impedance ( Z vs. Z') plots, at low temperatures (154 -236 K), for high conducting
dopant concentration (D = 50%) of SAT glass.
Z' Real [ohrnlcr1o3)- ,
Z' Real lohrnlcao3)--,
Fig. 4.14. . Impedance (Z" vs. Z')plots, at low temperatures (I44 -236 K), for high conducting
dopant concentration (D= 60 %) of SPT glass.
*
-
+
+
0
--
139 K
149K
157K
164K
Flt dala
2' " ' 4L ' , 6' '
Z'Real !ohm] c* lob, - ,
-
%' Real lohmj (. lod)
Z' Real [ohml(xlo')
--J
Fig 4. IS. Impedance (2" vs. 2') plots, at low temperatures (139-231 K), for high conducting
dopant concentration (D= 60%)of SVT glass.
Fig. 4.16.Log a T vs. 10001T plots for high conducting of dopant D = 50% for SAT, D = 60 %
for SPT and D = 6O?h for SVT glasses.
SPT and 60% for S M glasses in the temperature range of 139 to 236 K. u11err symhrls
represent measured conductivity data and the line represents Arrhenius fit. F n ~ ms l o p crf
log (oT) vs. IOOOir plots, the activation energy (E.) for Ag' Ion migration In each glass
system is calculated and it is found to he 0.176 eV for SAT. 0.167 eV for SPT and 0. I 88
c.V for SVT glasses.
1. 7. 2. A. C. Conductivity
Figs. 4.17, 4.18 and 4.19 show the log a
ruFtively.
\7;.
log ((I)) plots obtained at low tempeatuns.
for the high conducting former compos~tionof x
=
0.5 for SAT. 0.7 Ihr SPT
and 0.6 for SVT glasses. Fmm Figs. 4.17, 4.18 md 4.19, it is ohsuvcd tlut the hyuemy
d ~ v d e n c eof conductlvity h w s two distinct rg7nia. w~thlnthe m a s d tiqucncy wndow. I)
die low frequency plateau n%on and ii) high tnqucn~ydlspusinn rcpon. l h c platcllu &@on
umqnnds to trequency independent cnnductivity No) 'Ihc Ho) is obtained hy exbapolating the
mnductivity value to the zan trequency limits. Ihc hquency dqxndent of umduclivity at low
tanpatuns in the d i s p i o n Kpon for the h~ghmnducting fnrmer wjmposltion o i x =. 0.5 Ibr
SAT, 0.7 for SPT and 0.6 for SVT glasses
waq
anal@
using Jonscher's linlvclliul Powu
(JI!P) law [15, 161. In Fig 4.17, 4.18 and 4.10, symbols m n q o n d to expcnmental dab^ and
continuous lines represent JUPL fit. Fmm JLlPL analysis, fit paramdm cly s was oblained for the
SATISPTISVT glasses are qxchvely given in Table 4.2.4.3 and 4. 4. From Fig 4.17,4.18 and 4.
19, the frequency at which the dispajion T o n dmated fiom dc undudi~ltyplatcau is defined IS
charactenstic frequency (w,,)). The relation b e e n dc conductivity and &mder&c
. .
fraqutncy is
@venby ofo)= ko, where k is the anpirid w t , which d e p d s on the combation of mobile
Ions, hqemhm and
the condudion m e c h m [21-241. It is
observed Ulat
the duuadaistic
frequency o,at which the relaxabon &eds b c p to appear, moves towards the hi@ h q m y
with imeasein tgnpaahne and it readKs a postion bqond the messured frequency window limit.
Fig. 4.1 7. Log(4 vs, log ((0)plots, at d ~ f mlow
t tunpcxutures (I04 1x0 K), fix high conducting
Ihrmer colnposition (x 0.5) c~fSAT samplc
-
Fig4.18. Log(@ vs. log(w) plots, at different low ternpaaturn(1 11 - 195 K), for high cotlduding
former composition (x = 0.7) of SPT sample.
it is found that w, is thamally acii~lledwith the same activation magy of o,J (251. The
F&,
d o ) value n h W from the conductivity M. tiaquenq plots at diffaat low tmpraturej was m the
order of 10' to 104 sun-'.
The frequency independent wnducti\ity may he atbihuted to UK. long-rayw tmnsi)rt of
mobile silva ions in response to the appl~udclccmc field. wbae only suuzrslbl diffuston u)ntrihutrs
lo dc conductivity ofo).The oh.wed di~qmstonoi'u)nduc~t~ty
nlth f i w q a)dd hc expltuned
thn)ugh Diffusion wntrnlld relaxation (DCK) 1ntdel[2&33].Amnding to the mdcl. it IS ~ s u r n d
dlat
a negative site can occupy ody one cahon. Ille amviil of dtlhing silver ion to that s~tidy
twcul~edsite than thc position of original ton on that stte exatts ad rx, It~ngup s w Uie Iowa
Lnw
amfigation. wh~chw u l b In mutual mrlllgancnt wthtn the wpon to uchicx u 1x-w
lowest mergy site. Ihus, the fnrma ton rclax at a stte is pmumul to tuw altnnst tnstaitanct~usly.
The hoppod ion can mlax hack to its orignal sttc or one ofthe ion%can d~ftirwto ;ux)thu a d j m t
51te. wh~chindicates cation hopping and d~fiiitontnwhmtsm of mohlle silver ton in tlc
sbu~turesof the glass samples In the pn.v'~lccof non-bridging oxygen and illso the f i r ~
l t d
gof' Ad.
lhe s value obmnd h r n JUPL fit varies rmdomly w~thtanpcmturc h)nl 0.9 to 0.4.
rdble 4 2 o#and s paramdm ohmned tnrm the pow cr Idw lit for formu ampstbon\ of SA'J
das at vanou\ low tcmperdtm (104 180K)
- -- -
Temperature [K]
L
~
--
--
- ---
oFcm
)
'
104
0 96
114
0 79
122
0 70
744x10'
132
0 55
199x10~
149
0 48
408x10'~
0 57
133x10"
0 44
4 77x 10"
168
I
--
180
'
Table 4.3. u(o) and s parametas h n e d Fnm the power law fit for fomw wmplsition~of
S I T glass at various low t a n p w h a s (I I I - 195K)
Temperature [K]
5
7- c c m r
-
Flg. 4.20.4.21 and 4.22 show the log cr vs. log (11 plo~sat low tcmpe~twes,m p ~ ~ v c l ylor.
the high conducting modifier to fomier ratio mlf - 1.75 Ibr SAT. 2.50 fbr SPT and 2.00 for
SVT glasses. From Fib 4.20, 4.21 and 4.22 it 1s t b s c v d that the hqwncy d c p d a l w ol
u~ndu~zivity
shows two d~stindnynles. within the mea~unxlfquency window, i) dx low
tiequency plateau w o n and 11) high frqucncy dlspasion re@tm. 'The pkataiu %on u~mqx)nd..to
hquency dependent conductivity n(o). The tiequaxy depndcnt of condudivity at low
ran-
in the dispasion q o n for the h~ghwnducting modifier to former crmpvsrtlon
m:f ~ 1 . 7 5for SAT, 2.50 for SPT and 2.00 for SVT glasses wax analy~dusing Jvnscha's
U n i v d Powa (JUPL) law 115, 161. In Rp. 4.20, 4.21 and 4.22, symbols cocTespnd to
~xpeimentaldata and continuws lines rimsent JUP fit. The s value o b t d @omJUPL fit vans
randomly with tanpaabse h0.7 lo 0.1. From IUP analysis, fit paramdns No), s was crhttuml
for the SAT/SIT/SVl' glassg are given in Table 4.5.4.6 and 4.7. The No) value obta~nedfmm the
mndudivity vs. frequency plots at differentlow tanpadturewas in the orda of 10' to 10'
an.'.
234 K o-t213K
195KbO
DID-
Fig 4.19. log (a)vs, log ((I)) plo~s, at difermt low tempnu~un~
(I(X) 234 K). Ibr h~gh:hw,nducclng
lbrmer composition (x = 0.6) ol'SV7' glass.
Fig 4.20, Log (o)vs, log (a)plots, at diffaent low lanpaatures(138-203 K), for high conducting mlf
=I .75 of SAT glass.
Fig. 4. ? I , Log@) vs, log ((4plts. at low ranpaaturn ( I I2 - ?OH I(), for h~ghconduding mil'
of SPT glass
Fig 4.22, Log@) vs. log (o)plots, at low tempemttm (122- 232 K), for high conducting mlf = 2.00
of SVT glass.
The
d e p a d m t ~ u b i w r )may
. be amibuted to Ihe lWmngc
mn.qxw of'
mobile silve ions in rrsponse to the applied elcbic field, whaP only s w x ~ f udlffisitm
l
amtrihurcs
10 dc conductivity No). The dmmed
d ~ s p r s ~ (ofmaWW1Udivity with hqueny muld k api11KI1
thmugh Diffusion a)ntmlled relaxahon (WR)mniel, a d ~ w u ind the sanai4.7.2. (?h33] R g
1.23,4. 24 and 4.25 show the log n M.log (I) plots at louclunpautures mpx~~vdy
ti)r thc h1gl1
oenducting dopant sall concentratlcnl D
505.0 ti)r SAT, 60
"O
fifi SPPT und 60'4 tirr S V I '
glasses. From Fig 4.23.4.24 and 4.25.11 IS obsavul tho1 the tioquency dyxndalce ofuwducti\lty
stows two distinct regimes, within dic masunxi fquency \r.mdow.
Table 4.4.o(o)and s purdrnct~nohbi~wl h n i the pow67 low fit fhr ti~rnieru)n~pc>sitiola(x
0.6) of SVTpJassat vanouy low tanpuatuns(l06K to 23410.
--
Temperature [K]
- ---
-
106
.
Fig. 4.23. Log (a)vs. log (w) plots, at low t a n p a a m (1 82 - 230 K), for high conducting dopant D
SAT glass
= 50% of
Fig. 4.24, Log (o)vs. log (w) plots, at low tempemhim (a). 191- 236 K (b). 151-186 K, for the hi$
conducting dopant'^ = 60% of SPT glass.
Fig 4.25, Log (a)vs. log (a)plots, at low temperatures(I 39 - 23 1 K), for high conducting dopant D
60% for SVT glass.
Table 4. 5. o(o) and s parametas ob&
\ anous low temperatllres (I 38-203K).
7
Temperature [K]
-/
-
hm the power law fit (m/l'= 1.75) of SAT @nss at
.--
--
v
--
.
.
.
-.
Table4 6 u(o)and r ~mdmobkuncdlnm U~cpowcrIdw fit (nu1 2 50)ol SI'I
vwou\ low tanpcTdtura ( l 12-2OHli)
gli~\\dt
Table 4.7. o(o) and s pawnaasobtaud f i h e power law tit (m!f = ?.(X)) ofSL7' ylw el
various low tanpaalum (I "-232K).
C
~
I)
I??
the low fraluency platcau q o n and
ii)
high tnqucncy disqxnion ng~on.'The platwu &yon
wmqnnds to fralucncy ~ndcpcndentconductivity n(o).7hc tnqucncy dcpuldent ol'u)ndudrvity a1
low tempaatum in the dispasion region fbr the high conducting dopant salt concentration
D
50% for SAT, 60 % for SPT and 60% for SVT glasses was analyLud using Jo~lscher's
Un~versalPower (JUPL) law [ I 5, Ih]. From JUP a n a l ~ i sfit, p m d e r ; No).s w m obtarnd fir the
SAT or SPT or SVT glassesare given in Table 4.8.4.9 and 4.10. The o(o) valuc thtiunul h m the
conductivity w.fraquency plots at d r f f m t low t a n p a a m was in the orda of 10' to lo9 ~ c m " .
The s value obtained from JUPL fit vanes randomly with tempaahnc from 0.8to 0.1.
Table 4.8. o(o) and
,-
J
panunetas&wed
various low 1
Temperature [K]
;
Table 4 9 ofo) and
I
\
- w/o)
fiun the power law fir (D
7 ( I 69-236K).
oaf SAT@ass
UI
s
panmetm ohtamed hnn the power luw f i t (I>
vmou\ low ttll1pcT.ltun-I ( I 5 1-236K)
(A)'%) of SP1
~ L L ut
U
Log (freq)
Fig.4.26. d vs. log (freq) plots, at low temperatures (a) 104 - 132K and (b) 149 - IXO K. for
high conducting former composition (x
= 0.5) of SAT glass
I
1
.
2
.
.
3
.
Fig. 4.27. E' vs. log (freq) plots, at diffaentlow ternformer composition (x = 0.7) of SPT glass.
.
4
.
.
5
.
(102-195 K), for the high conducting
I
1
.
,
2
.
,
3
.
,
4
.
,
5
Fig. 4. 28. E' vs. log (freq) plots, at differenl low tempaatures (106 - 242 K), for the high
conducting former composition (x = 0.6) of SVT glass.
Fig. 4.29. E' vs. log (freq) plots, at different low tanmlf =I .75 of SAT glass
(1 19-228 K). for the high conducting
Fig. 4.30. E' vs. log (freq)plots, at diffaent low ternpahuts (102-148 K), for the high conducting
mif = 2.50 of SPT glass.
2
0
Log (f&)
2
4
6
6
Log (freq)
Fig. 4.31. E' vs. log (freq) plots, at diffml low tanm/f =2.00 of SW glass.
(1 10-232 K), for the high conducting
Fig. 4. 32. I;' vs. log (freq) plots, at diR'auit low taiipcrdtur* (182-236K).fi)r tlir h~ghconducting
dopant D = 50% of SAT glass.
Fig4.33.E' vs. log (fieq) plots, at diffmt low- t
dopant D = 60%of SPT glass.
( I 82-23610, for the high condud~ng
Fig4. 34. 6' vs. log (a)plots, at diffaenl low tanperahrres (139-23710,for the h~ghconducting
dopant D = 60% of SVT glass.
4.7.4. Electric Modulus
Figs. 4. 35.4. 36 and 4.37 show the M" vs. log (frcq) spcytra plotted ~ s p l ~ t t v rLl yI ~
the high conducting former composttlon of n
-
0.5 for SAT. 0.7 (i)r SPT and 0.6 Ibr SV'T
glasses obtained at different low temperatures ( I ( W -180 I().In the modulus cunjes. the
continuous line represents guide to eye of M" vs. log (freq) cuntc, w h t m s tlie s)mh)ls
correspond to the experimental data ofthe SAT or SPT or SVT glasses. It
IS
observed thut
the shape of each curvc is asymmetric of non-l.orcntz~antype exhihlt~nga peak at the
relaxation tiequency, (41.~with a long tall extending In the region of shorter rclsxut~ori
tllne [ 18, 3 I]. From Figs. 4. 35,4. 36 iuld 4.37. 11 IS c~hsen~cul
that w~thtcmpcruture. M",,,.,
value remalns constant and the positlon of' the peak ficqucncy sh~flstowards the h~glier
tiequency region. However, shifl m
(11,-
w~dithe tunpcxaturc u)uld bc explalnod h ; ~ don the
disbihution of antmpt hquencies for the hanicr
LN~SSOVLT or
a distrihut~onof
JUIIII)
or 111Jil
distances following the ~n,ssovm.The bn)adncssof the M" vs. log (hrq)c w e a i n t m a l ~ tcnns
n
ofthe distribution of relaxation time for distinyishable physid prrmw.
Figs. 4.38a, h and c show the M" vs. log (freq) spectra plottcd, rcspect~vely,for the
h~ghconduct~ngmodifier to former ratlo mlf -1.75 for SAT, 2.50 for SPT and 2.00 li)r
SVT glasses obtained at different low temperatures (106-228 K). In the modulus curves.
the continuous line represents &wideto eye of Muvs. log (frcq) curve, whereas the symbols
correspond to the experimental data of the SAT or SPT or SVT glasses.
Figs. 4.39 a, b and c show the M" vs. log (freq) spectra plotted, respectively, for thc
high conducting dopant concentration D
=
50% for SAT, 60 % for SPT and 60% for SVT
glasses obtained at.different low temperatures (168 - 236 K). In the modulus curves, the
continuous line represents guide to eye of M" vs. log (freq) curve, whereas the symbols
correspond to the experimental data of the SATISPTISVT glasses.
Fig. 4.35. M" vs. log (freq) plots, at low temperatures ( I 04 -1 80 K), for high conducting former
composition (x = 0.5) of SAT glass
Fig. 4.36. M "vs. log (freq) plots, at low temperatures ( I 02 - 195 K), for high conducting fbrma
composition (x = 0.7) of SPT glass.
Figd. 37. M" vs. log (freq) plots, at low temperatures (I06 - 195 K), for high conducling
former composition (x = 0.6) of SVT glass
t
t o e lfrea
Fig. 4.38. M" vs. log (freq) plots, at different low temperatures, for high conducting mlf =1.75
for SAT (1 19-228K), m/f =2.50 for SPT (106-206K) and m/f =2.00 for SVT ( 1 10-232K)
k!lasses
-
SAT
236 K
232 K
.. 227K
222 K
* 216 K
.,
195K
188K
,~
':?:k%.,p
,.
.:.,.
',,
,
,
,
q@,
,
,
,
,
'I
*..-,*.',,
,,
-
$ ,
*$>;'yn
: . ,j;'
n;,""
..
:
*
n . ' . ~
. .\ ,
,
'
,,
I
8..<:..
I
,
h
\
Fig. 4.39. M" vs. log (fieq) plots, at low temperatures, for the high conducting dopant D =
50%for SAT (1 88 -23610, D = 60 % for SPT (168 -236 K) and D = 60% for SVT (I 86-23 1 K )
glasses.
4.8. Conclusions
Conductivity is evaluated by analying the measured impedance data nt loa
temperatures (99 to 242 K) between 40 H7 to 100 kH7 8: 20 H7 to IMH7 f i ~ rthe hrgh
conducting former (x), modifier to former (m'f) arid dopanl (D)cc~ncentmlicmsof'the SAT.
SPT and SVT glassy samples. The ohsm,cul dispersion in the a.c conductlwty spc~truut
high frequency region is explained hy the DCR model. The pcrwer law cxpnent s vuluc
evaluated from a.c conductivity is Sound to hc non-linear with teniperatures. In thc M" vs
log (freq) spectra, the peak frequency of shrtts towards the h~ghcrficquericy region wrth
increase in temperature. The hn~adncssof M" \s. log (frcq) c w c s IS ~ n t q m ~Inu ltcnns ot'tlw
diszrihution of relaxatmn times fbr distinpishahle physiciil pn-w.
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