APCOM 041 P. Hockicko a), S. Jurečka b), P. Bury a), M. Jamnický c) and I. Jamnický a) a)...

APCOM 04APCOM 04 11

P. HockickoP. Hockickoa)a) , , S. Jurečka S. Jurečka b)b), , P. Bury P. Bury a) a) , , M. Jamnický M. Jamnický c)c) and I. Jamnický and I. Jamnický a)a)

a)a) University of Žilina, Department of Physics, 010 26 Žilina, University of Žilina, Department of Physics, 010 26 Žilina,b) b) University of Žilina, Department of Engineering Fundamentals, 031 01University of Žilina, Department of Engineering Fundamentals, 031 01

Liptovký Mikuláš, Liptovký Mikuláš, c)c) Slovak Technical University, Department of Ceramic, Glass and Cement, Slovak Technical University, Department of Ceramic, Glass and Cement,

812 19 Bratislava812 19 Bratislava

P. HockickoP. Hockickoa)a) , , S. Jurečka S. Jurečka b)b), , P. Bury P. Bury a) a) , , M. Jamnický M. Jamnický c)c) and I. Jamnický and I. Jamnický a)a)

a)a) University of Žilina, Department of Physics, 010 26 Žilina, University of Žilina, Department of Physics, 010 26 Žilina,b) b) University of Žilina, Department of Engineering Fundamentals, 031 01University of Žilina, Department of Engineering Fundamentals, 031 01

Liptovký Mikuláš, Liptovký Mikuláš, c)c) Slovak Technical University, Department of Ceramic, Glass and Cement, Slovak Technical University, Department of Ceramic, Glass and Cement,

812 19 Bratislava812 19 Bratislava

THETHE ACOUSTIC ATTENUATION ACOUSTIC ATTENUATION THEORETICAL MODELS FOR THE THEORETICAL MODELS FOR THE

ION CONDUCTIVE GLASSESION CONDUCTIVE GLASSES

THETHE ACOUSTIC ATTENUATION ACOUSTIC ATTENUATION THEORETICAL MODELS FOR THE THEORETICAL MODELS FOR THE

ION CONDUCTIVE GLASSESION CONDUCTIVE GLASSES

[email protected]

APCOM 04APCOM 04 22

IntroductionIntroductionIntroductionIntroduction

1)1) Ion Conductive Glasses CharacterizationIon Conductive Glasses Characterization Glasses preparation procedure

2) 2) Experimental Details of MeasurementsExperimental Details of Measurements Electrical measurement details Acoustical measurement details

3)3) Experimental ResultsExperimental Results D. c. electrical measurements A. c. electrical measurements Acoustical measurements

44) ) Theoretical modelsTheoretical models

55) ) Results Results AnalysAnalysiis s and Discussionand Discussion Fitting of the acoustic attenuation spectra Comparison of the models

66) ) ConclusionConclusion

1)1) Ion Conductive Glasses CharacterizationIon Conductive Glasses Characterization Glasses preparation procedure

2) 2) Experimental Details of MeasurementsExperimental Details of Measurements Electrical measurement details Acoustical measurement details

3)3) Experimental ResultsExperimental Results D. c. electrical measurements A. c. electrical measurements Acoustical measurements

44) ) Theoretical modelsTheoretical models

55) ) Results Results AnalysAnalysiis s and Discussionand Discussion Fitting of the acoustic attenuation spectra Comparison of the models

66) ) ConclusionConclusion

APCOM 04APCOM 04 33

1. Ion Conductive Glasses Characterization1. Ion Conductive Glasses Characterization1. Ion Conductive Glasses Characterization1. Ion Conductive Glasses Characterization

AttentionAttention due to the possible application in modern electrochemical devices (solid electrolytes), solid-state batteries, electrochronic displays, sensors

AdvantageAdvantagess compared to crystalline materials: absence of grain boundaries isotropic properties wide composition variability easy preparation reasonable costImportant criterionImportant criterion – high ionic conductivity at room

temperatures Glasses containing Ag+ ions can have the highest

conductivity 25 10-2-1 cm-1. Theoretically the glasses that contain Cu+ ions should

achieve comparable conductivity because of similar electronic configuration and even smaller ionic radii:

InterestInterest in ion conductive glasses that contain Cu+ ionsIn the present contribution the glasses of the system CuI - CuBr CuI - CuBr -- Cu Cu22O - PO - P22OO55 are investigated.

AttentionAttention due to the possible application in modern electrochemical devices (solid electrolytes), solid-state batteries, electrochronic displays, sensors

AdvantageAdvantagess compared to crystalline materials: absence of grain boundaries isotropic properties wide composition variability easy preparation reasonable costImportant criterionImportant criterion – high ionic conductivity at room

temperatures Glasses containing Ag+ ions can have the highest

conductivity 25 10-2-1 cm-1. Theoretically the glasses that contain Cu+ ions should

achieve comparable conductivity because of similar electronic configuration and even smaller ionic radii:

InterestInterest in ion conductive glasses that contain Cu+ ionsIn the present contribution the glasses of the system CuI - CuBr CuI - CuBr -- Cu Cu22O - PO - P22OO55 are investigated.

APCOM 04APCOM 04 44


constituent elementsconstituent elements: : P2O5 – glass forming components

Cu2O – modificator CuI + CuBr – cuprous halides

meltingmelting reagent of the powders CuI, CuBr, Cu2O and P2O5

mixingmixing under a dry argon atmosphere in appropriate portions in

silica ampule at 933 K for 90 min.

rapid quenchingrapid quenching of glass melts pressing them between two brass

plates of the area 1 cm2 to final thicknees 2.0 mm

X-ray diffraction method and differential thermal analysis (DTA)

method has been used to check the noncrystality and

identity Tg

constituent elementsconstituent elements: : P2O5 – glass forming components

Cu2O – modificator CuI + CuBr – cuprous halides

meltingmelting reagent of the powders CuI, CuBr, Cu2O and P2O5

mixingmixing under a dry argon atmosphere in appropriate portions in

silica ampule at 933 K for 90 min.

rapid quenchingrapid quenching of glass melts pressing them between two brass

plates of the area 1 cm2 to final thicknees 2.0 mm

X-ray diffraction method and differential thermal analysis (DTA)

method has been used to check the noncrystality and

identity Tg

Glasses preparation procedure:Glasses preparation procedure:

APCOM 04APCOM 04 55


Starting composition (in mol. %) at prepared ionStarting composition (in mol. %) at prepared ion

conductive glasses:conductive glasses:

Glass

sample

Composition (in mol.%)

CuBrCuBr CuICuI CuCu22OO PP22OO55

BIDP1BIDP1 2.27 15.91 54.55 27.27

BIDPBIDP22 4.55 13.63 54.55 27.27

BIDPBIDP33 6.82 11.36 54.55 27.27

BIDP5BIDP5 9.09 9.09 54.55 27.27

BIDPBIDP66 11.36 6.82 54.55 27.27

BIDP7BIDP7 13.63 4.54 54.55 27.27

BIDPBIDP88 15.91 2.27 54.55 27.27

BDPBDP 18.18 - 54.55 27.27

Table 1 Starting glass compositions (in mol.%)

APCOM 04APCOM 04 66

2. Experimental details2. Experimental details 2. Experimental details2. Experimental details

measurement equipment: FLUKE PM 6306 impedance measurement equipment: FLUKE PM 6306 impedance analyzer (d.c. and a.c. conductivity) analyzer (d.c. and a.c. conductivity)

sputtered gold electrodessputtered gold electrodes frequency range: 50 Hz – 1 MHz, d.c. measurementfrequency range: 50 Hz – 1 MHz, d.c. measurement temperature range: 140 – 425 Ktemperature range: 140 – 425 K

measurement equipment: FLUKE PM 6306 impedance measurement equipment: FLUKE PM 6306 impedance analyzer (d.c. and a.c. conductivity) analyzer (d.c. and a.c. conductivity)

sputtered gold electrodessputtered gold electrodes frequency range: 50 Hz – 1 MHz, d.c. measurementfrequency range: 50 Hz – 1 MHz, d.c. measurement temperature range: 140 – 425 Ktemperature range: 140 – 425 K

aa)) Electrical conductivity measurementsElectrical conductivity measurements

APCOM 04APCOM 04 77

2. Experimental details2. Experimental details2. Experimental details2. Experimental details

bb)) AcousticalAcoustical measurements measurements

Fig. 1.Fig. 1. Experimental arrangement for acoustic attenuation measurement

MeasurementMeasurement equipment:equipment: MATEC attenuation MATEC attenuation comparatorcomparator

longitudinal acoustic wavelongitudinal acoustic wave of frequency of frequency f = 18 MHzf = 18 MHz generated by quartz generated by quartz transducertransducer

quartz rod bufferquartz rod buffer used to used to separate the signal from separate the signal from shorts samplesshorts samples

temperature range: temperature range: 140 – 365 K140 – 365 K

MeasurementMeasurement equipment:equipment: MATEC attenuation MATEC attenuation comparatorcomparator

longitudinal acoustic wavelongitudinal acoustic wave of frequency of frequency f = 18 MHzf = 18 MHz generated by quartz generated by quartz transducertransducer

quartz rod bufferquartz rod buffer used to used to separate the signal from separate the signal from shorts samplesshorts samples

temperature range: temperature range: 140 – 365 K140 – 365 K

APCOM 04APCOM 04 88

33. Experimental . Experimental resultsresults33. Experimental . Experimental resultsresults

aa)) D. c. electricalD. c. electrical measurements measurements

Fig. Fig. 22.. Arrhenius plot of d.c. Arrhenius plot of d.c. conductivity of sample conductivity of sample BIDPBIDP55

D.c. conductivity can be fitted by D.c. conductivity can be fitted by the relation [1]the relation [1]

(1)(1)

EEaa – activation energy – activation energy

00 – pre-exponential factor – pre-exponential factor

[[00 = = 00(T)](T)]

TT – temperature – temperature

kkBB – Boltzman constant – Boltzman constant

D.c. conductivity can be fitted by D.c. conductivity can be fitted by the relation [1]the relation [1]

(1)(1)

EEaa – activation energy – activation energy

00 – pre-exponential factor – pre-exponential factor

[[00 = = 00(T)](T)]

TT – temperature – temperature

kkBB – Boltzman constant – Boltzman constant

= = 0 0 exp(-Eexp(-Ea a / k/ kBBT)T)

[1] K. Funke et al: Solid State Ionics 105 (1998) 195

? Ea4

APCOM 04APCOM 04 99


bb)) A. c. measurements A. c. measurements

Fig. Fig. 33.. The The sset of frequency et of frequency dependences of a.c. dependences of a.c. conductivity measured at conductivity measured at various temperatures for various temperatures for samples BIDP5samples BIDP5

(0(0)) –– the d. c. conductivity, the d. c. conductivity, tt11 – time, – time, denotes the beginning of denotes the beginning of

dispersive regime (dispersive regime (tt11 == 1/1/11))

11 – – corresponding frequencycorresponding frequency

pp11, , pp22 –– tthe exponentshe exponents,, can be can be determined from determined from eexperimental xperimental results (conductivity spectra)results (conductivity spectra)

(0(0)) –– the d. c. conductivity, the d. c. conductivity, tt11 – time, – time, denotes the beginning of denotes the beginning of

dispersive regime (dispersive regime (tt11 == 1/1/11))

11 – – corresponding frequencycorresponding frequency

pp11, , pp22 –– tthe exponentshe exponents,, can be can be determined from determined from eexperimental xperimental results (conductivity spectra)results (conductivity spectra)

?

The high-frequency part of The high-frequency part of the conductivity spectra the conductivity spectra (regime II) caused by hopping (regime II) caused by hopping motion of the mobile Cumotion of the mobile Cu++ ions ions can be fitted by the relation can be fitted by the relation [2][2]

The high-frequency part of The high-frequency part of the conductivity spectra the conductivity spectra (regime II) caused by hopping (regime II) caused by hopping motion of the mobile Cumotion of the mobile Cu++ ions ions can be fitted by the relation can be fitted by the relation [2][2]

21

21

11

110

pp

tB

tA

((22)) ((22))

[2] K. Funke: Solid State Ionics 94 (1997) 27

APCOM 04APCOM 04 1010


cc)) Acoustical measurementsAcoustical measurements

Fig. Fig. 44.. Temperature dependence of acoustic attenuation of ion conductive glasses of the system CuI-CuBr-Cu2O-P2O5 for different glass compositions.

The existence of three thermally activated relaxation processes (Ea

a1, Ea

a2, Eaa3) of ions are connected with

different kinds of sites. Low temperature peak (Ea

a3) can be related to faster ion transport and high temperature peaks (Ea

a1, Eaa2)

can be related to slower mobile ions.

The existence of three thermally activated relaxation processes (Ea

a1, Ea

a2, Eaa3) of ions are connected with

different kinds of sites. Low temperature peak (Ea

a3) can be related to faster ion transport and high temperature peaks (Ea

a1, Eaa2)

can be related to slower mobile ions.

All glasses we studied using acoustic spectroscopy exhibit an Arrhenius – type relaxation between the peak temperature and the applied frequency [3][3]

All glasses we studied using acoustic spectroscopy exhibit an Arrhenius – type relaxation between the peak temperature and the applied frequency [3][3]

= 0 exp (- Ea / kBTpeak) ((33)) ((33))

[3] B. Roling et al: J. Physical Chemistry B 1999, 103, 4122


44. . Theoretical modelTheoretical modelss 44. . Theoretical modelTheoretical modelss

TThe attenuation may be described as a Debye-like, single relaxation he attenuation may be described as a Debye-like, single relaxation time processestime processes [4] [4] TThe attenuation may be described as a Debye-like, single relaxation he attenuation may be described as a Debye-like, single relaxation time processestime processes [4] [4]

22

2

1 Δ

- attenuation, - relaxation strength, - angular frequency, - relaxation time,B - deformation potential,N - number of mobile ions, v - velocity of the sound wave, - density of the solid, T - absolute temperature,kB - Boltzmann constant,EA- activation energy

TkvNB B32 4/ Δ

peakBA TkE /exp0 , [5], [5]

1/0 1013 – 1014 s-1

- typical relaxation frequency of ion hopping

[4] D. Almond, A. West: Solid State Ionics 26 (1988) 265[5] G. Carini et al.: Physical Review B 30 (1984) 7219

Debye model Debye model 44)) Debye model Debye model 44))

when == 1 1 = max= max

when == 1 1 = max= max



The relaxation phenomena observed in a wide variety of materials exhibit a power-lawpower-law type of frequency dependence. The relationship to Debye behaviour is expressed in the form [4]

The relaxation phenomena observed in a wide variety of materials exhibit a power-lawpower-law type of frequency dependence. The relationship to Debye behaviour is expressed in the form [4]

[4] D. Almond, A. West: Solid State Ionics 26 (1988) 265

nm

m

T 11

1

Power-law model Power-law model 55)) Power-law model Power-law model 55))

m, n - power-law exponents, (take values between 0 and 1)

When m = 1 and n = 0, equation (5) reduces to the equation for a single Debye-like process (4).



Two functions have been also used to fit the both mechanical loss data and acoustical attenuation measurements [6]. Two functions have been also used to fit the both mechanical loss data and acoustical attenuation measurements [6].

[6] B. Roling, M. Ingram: Physical Review B 57 (1998) 14192

KWW model KWW model KWW model KWW model - - The first function is the The first function is the Kohlrausch-Williams-Watts Kohlrausch-Williams-Watts (KWW)(KWW) function function (t (t))

- - The first function is the The first function is the Kohlrausch-Williams-Watts Kohlrausch-Williams-Watts (KWW)(KWW) function function (t (t))

0

sin, dttdt

tdT

t

Tt exp,

66)) 66))

with 0 < 1

- - The second function is the double power lawdouble power law ((DPLDPL)) - - The second function is the double power lawdouble power law ((DPLDPL))

mn

T

1, 77)) 77))

DPL model DPL model

DPL model DPL model


To fit the acoustic spectrum the Debye modelDebye model (Eq.(4)) was applied. The measured spectrum in intermediate and high temperature ranges is represented by spotted line in the acoustic spectrum.

To fit the acoustic spectrum the Debye modelDebye model (Eq.(4)) was applied. The measured spectrum in intermediate and high temperature ranges is represented by spotted line in the acoustic spectrum.

Fig. Fig. 55.. The acoustic spectrum of sample BIDP5 (full line) and the Debye fit of the two relaxation processes (dashed lines).

5. Results Analysis and Discussion5. Results Analysis and Discussion

Debye modelDebye modelDebye modelDebye model


Fig. Fig. 66.. Acoustics attenuation spectrum of sample BIDP5 (full line) and its theoretical supposing fit is superposition of two supposed relaxation processes (dashed lines).


The complete spectrum of this sample cannot be fitted using DPL model supposing only two relaxation processes. The additional third relaxation process should be taken into account with maximum at the temperature about 280 K.

The complete spectrum of this sample cannot be fitted using DPL model supposing only two relaxation processes. The additional third relaxation process should be taken into account with maximum at the temperature about 280 K.

DPL model DPL model

DPL model DPL model


To fit the acoustic spectrum the modified DPL modelDPL model was applied and the calculated lines gave an excellent agreement with measured spectrum in intermediate and high temperature range represented by dashed lines in the acoustic spectrum.

To fit the acoustic spectrum the modified DPL modelDPL model was applied and the calculated lines gave an excellent agreement with measured spectrum in intermediate and high temperature range represented by dashed lines in the acoustic spectrum.

Fig. Fig. 77.. Acoustics spectrum of sample BIDP5 (full line). Dashed lines represent the best fit for three relaxation processes and their superposition.


modifiedmodified DPL model DPL model



The complete spectrum of sample BDP was fitted using the modified DPL modelDPL model and the calculated lines gave an excellent agreement with measured spectrum.

The complete spectrum of sample BDP was fitted using the modified DPL modelDPL model and the calculated lines gave an excellent agreement with measured spectrum.

Fig. Fig. 88.. Acoustics spectrum of sample BDP (full line). Dashed lines represent the best fit for three relaxation processes and their superposition.





From the comparison of various samples (BIDP1 - BIDP7BIDP1 - BIDP7) follows that the individual relaxation mechanisms of the same sample have different values EEAA, but the same three relaxation processes with close values EEAA and the same values of coefficients mm, nn can be find in different samples.

From the comparison of various samples (BIDP1 - BIDP7BIDP1 - BIDP7) follows that the individual relaxation mechanisms of the same sample have different values EEAA, but the same three relaxation processes with close values EEAA and the same values of coefficients mm, nn can be find in different samples.

Fig. Fig. 99.. Acoustics spectrum of sample BIDP7 (full line). Cross marked line represents the best fit of superposition of three relaxation processes.





The experimental and theoretical investigation of ion conductive glasses in system CuI-CuBr-Cu2O-P2O5 showed that:

- the acoustical spectroscopy can be a very useful technique for the study of transport processes in fast ion conductive glasses and compared to the electrical ones they have even some advantages,

- the investigated relaxation process could be described by a relaxation theory,

- the superposition attenuation peaks described by theoretical models can fit all acoustic attenuation spectra,

- using the theoretical models we can describe the relaxation processes and find some ion parameters,

The experimental and theoretical investigation of ion conductive glasses in system CuI-CuBr-Cu2O-P2O5 showed that:

- the acoustical spectroscopy can be a very useful technique for the study of transport processes in fast ion conductive glasses and compared to the electrical ones they have even some advantages,

- the investigated relaxation process could be described by a relaxation theory,

- the superposition attenuation peaks described by theoretical models can fit all acoustic attenuation spectra,

- using the theoretical models we can describe the relaxation processes and find some ion parameters,

6. Conclusion6. Conclusion


- the acoustic attenuation spectra of all investigated ion conducting glasses prepared in the system CuI-CuBr-Cu2O-P2O5 consist of at least three thermally activated relaxation processes for temperatures over 220 K,

- the modified DPL model provides a better fit than the KWW model or the Debye model,

- the superposition of three loss peaks with different activation energies can better fit the investigated spectrum of the glasses,

- further analyses of acoustic spectra obtained by investigation of glass samples with different compositions in wider temperature and frequency range should be done for better understanding of ion transport mechanisms for various types of the investigated ion conducting glasses.

- the acoustic attenuation spectra of all investigated ion conducting glasses prepared in the system CuI-CuBr-Cu2O-P2O5 consist of at least three thermally activated relaxation processes for temperatures over 220 K,

- the modified DPL model provides a better fit than the KWW model or the Debye model,

- the superposition of three loss peaks with different activation energies can better fit the investigated spectrum of the glasses,

- further analyses of acoustic spectra obtained by investigation of glass samples with different compositions in wider temperature and frequency range should be done for better understanding of ion transport mechanisms for various types of the investigated ion conducting glasses.

6. Conclusion6. Conclusion


Peter HockickoPeter HockickoPeter HockickoPeter Hockicko

Thank You for Your AttentionThank You for Your AttentionThank You for Your AttentionThank You for Your Attention

[email protected]://hockicko.utc.sk

[email protected]://hockicko.utc.sk

APCOM 041 P. Hockicko a), S. Jurečka b), P. Bury a), M. Jamnický c) and I. Jamnický a) a)...

Documents

Transcript of APCOM 041 P. Hockicko a), S. Jurečka b), P. Bury a), M. Jamnický c) and I. Jamnický a) a)...