APCOM 041 P. Hockicko a), S. Jurečka b), P. Bury a), M. Jamnický c) and I. Jamnický a) a) University of Žilina, Department of Physics, Žilina, b) University of Žilina, Department of Engineering Fundamentals, Liptovký Mikuláš, c) Slovak Technical University, Department of Ceramic, Glass and Cement, Bratislava P. Hockicko a), S. Jurečka b), P. Bury a), M. Jamnický c) and I. Jamnický a) a) University of Žilina, Department of Physics, Žilina, b) University of Žilina, Department of Engineering Fundamentals, Liptovký Mikuláš, c) Slovak Technical University, Department of Ceramic, Glass and Cement, Bratislava THE ACOUSTIC ATTENUATION THEORETICAL MODELS FOR THE ION CONDUCTIVE GLASSES

APCOM 042IntroductionIntroduction 1)Ion Conductive Glasses Characterization  Glasses preparation procedure 2) Experimental Details of Measurements  Electrical measurement details  Acoustical measurement details 3)Experimental Results  D. c. electrical measurements  A. c. electrical measurements  Acoustical measurements 4) Theoretical models 5) Results Analysis and Discussion  Fitting of the acoustic attenuation spectra  Comparison of the models 6) Conclusion 1)Ion Conductive Glasses Characterization  Glasses preparation procedure 2) Experimental Details of Measurements  Electrical measurement details  Acoustical measurement details 3)Experimental Results  D. c. electrical measurements  A. c. electrical measurements  Acoustical measurements 4) Theoretical models 5) Results Analysis and Discussion  Fitting of the acoustic attenuation spectra  Comparison of the models 6) Conclusion

APCOM Ion Conductive Glasses Characterization Attention Attention due to the possible application in modern electrochemical devices (solid electrolytes), solid-state batteries, electrochronic displays, sensors Advantages Advantages compared to crystalline materials:  absence of grain boundaries  isotropic properties  wide composition variability  easy preparation  reasonable cost Important criterion Important criterion – high ionic conductivity at room temperatures  Glasses containing Ag + ions can have the highest conductivity  25   -1 cm -1.  Theoretically the glasses that contain Cu + ions should achieve comparable conductivity because of similar electronic configuration and even smaller ionic radii:  Interest  Interest in ion conductive glasses that contain Cu + ions In the present contribution the glasses of the system CuI - CuBr - Cu 2 O - P 2 O 5 CuI - CuBr - Cu 2 O - P 2 O 5 are investigated. Attention Attention due to the possible application in modern electrochemical devices (solid electrolytes), solid-state batteries, electrochronic displays, sensors Advantages Advantages compared to crystalline materials:  absence of grain boundaries  isotropic properties  wide composition variability  easy preparation  reasonable cost Important criterion Important criterion – high ionic conductivity at room temperatures  Glasses containing Ag + ions can have the highest conductivity  25   -1 cm -1.  Theoretically the glasses that contain Cu + ions should achieve comparable conductivity because of similar electronic configuration and even smaller ionic radii:  Interest  Interest in ion conductive glasses that contain Cu + ions In the present contribution the glasses of the system CuI - CuBr - Cu 2 O - P 2 O 5 CuI - CuBr - Cu 2 O - P 2 O 5 are investigated.

APCOM Ion Conductive Glasses Characterization constituent elements: constituent elements: P 2 O 5 – glass forming components Cu 2 O – modificator CuI + CuBr – cuprous halides melting melting reagent of the powders CuI, CuBr, Cu 2 O and P 2 O 5 mixing mixing under a dry argon atmosphere in appropriate portions in silica ampule at 933 K for 90 min. rapid quenching rapid quenching of glass melts pressing them between two brass plates of the area  1 cm 2 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 T g constituent elements: constituent elements: P 2 O 5 – glass forming components Cu 2 O – modificator CuI + CuBr – cuprous halides melting melting reagent of the powders CuI, CuBr, Cu 2 O and P 2 O 5 mixing mixing under a dry argon atmosphere in appropriate portions in silica ampule at 933 K for 90 min. rapid quenching rapid quenching of glass melts pressing them between two brass plates of the area  1 cm 2 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 T g  Glasses preparation procedure:

APCOM Ion Conductive Glasses Characterization  Starting composition (in mol. %) at prepared ion conductive glasses: conductive glasses: Glass sample Composition (in mol.%)CuBrCuI Cu 2 O P2O5P2O5P2O5P2O5 BIDP BIDP BIDP BIDP BIDP BIDP BIDP BDP Table 1 Starting glass compositions (in mol.%)

APCOM Experimental details  measurement equipment: FLUKE PM 6306 impedance analyzer (d.c. and a.c. conductivity)  sputtered gold electrodes  frequency range: 50 Hz – 1 MHz, d.c. measurement  temperature range: 140 – 425 K  measurement equipment: FLUKE PM 6306 impedance analyzer (d.c. and a.c. conductivity)  sputtered gold electrodes  frequency range: 50 Hz – 1 MHz, d.c. measurement  temperature range: 140 – 425 K  a) Electrical conductivity measurements

APCOM Experimental details  b) Acoustical measurements Fig. 1. Fig. 1. Experimental arrangement for acoustic attenuation measurement  Measurement equipment: MATEC attenuation comparator  longitudinal acoustic wave of frequency f = 18 MHz generated by quartz transducer  quartz rod buffer used to separate the signal from shorts samples  temperature range: 140 – 365 K 140 – 365 K  Measurement equipment: MATEC attenuation comparator  longitudinal acoustic wave of frequency f = 18 MHz generated by quartz transducer  quartz rod buffer used to separate the signal from shorts samples  temperature range: 140 – 365 K 140 – 365 K

APCOM Experimental results  a) D. c. electrical measurements Fig. 2.Arrhenius plot of d.c. conductivity of sample BIDP5 Fig. 2. Arrhenius plot of d.c. conductivity of sample BIDP5 D.c. conductivity can be fitted by the relation [1] (1) (1) E a – activation energy  0 – pre-exponential factor [  0 =  0 (T)] [  0 =  0 (T)] T – temperature k B – Boltzman constant D.c. conductivity can be fitted by the relation [1] (1) (1) E a – activation energy  0 – pre-exponential factor [  0 =  0 (T)] [  0 =  0 (T)] T – temperature k B – Boltzman constant  =  0 exp(-E a / k B T) [1] K. Funke et al: Solid State Ionics 105 (1998) 195 ? E a4

APCOM Experimental results  b) A. c. measurements Fig. 3.The set of frequency dependences of a.c. conductivity measured at various temperatures for samples BIDP5 Fig. 3. The set of frequency dependences of a.c. conductivity measured at various temperatures for samples BIDP5  (0) – the d. c. conductivity, t 1 – time, denotes the beginning of dispersive regime (t 1 = 1/ 1 ) 1 – corresponding frequency 1 – corresponding frequency p 1, p 2 – the exponents, can be determined from experimental results (conductivity spectra)  (0) – the d. c. conductivity, t 1 – time, denotes the beginning of dispersive regime (t 1 = 1/ 1 ) 1 – corresponding frequency 1 – corresponding frequency p 1, p 2 – the exponents, can be determined from experimental results (conductivity spectra) ? The high-frequency part of the conductivity spectra (regime II) caused by hopping motion of the mobile Cu + ions can be fitted by the relation [2] (2) (2) (2) (2) (2) (2) (2) (2) [2] K. Funke: Solid State Ionics 94 (1997) 27

APCOM Experimental results  c) Acoustical measurements Fig. 4. Fig. 4. Temperature dependence of acoustic attenuation of ion conductive glasses of the system CuI-CuBr- Cu 2 O-P 2 O 5 for different glass compositions. The existence of three thermally activated relaxation processes (E a a1, E a a2, E a a3 ) of ions are connected with different kinds of sites. Low temperature peak (E a a3 ) can be related to faster ion transport and high temperature peaks (E a a1, E a a2 ) can be related to slower mobile ions. [3] All glasses we studied using acoustic spectroscopy exhibit an Arrhenius – type relaxation between the peak temperature and the applied frequency [3] = 0 exp (- E a / k B T peak ) (3) (3) (3) (3) (3) (3) (3) (3) [3] B. Roling et al: J. Physical Chemistry B 1999, 103, 4122

APCOM Theoretical models The attenuation may be described as a Debye-like, single relaxation time processes [4]  - 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, k B - Boltzmann constant, E A - activation energy, [5] 1/  0  – 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 4)  = 1  = max when  = 1   = max

APCOM Theoretical models power-law The relaxation phenomena observed in a wide variety of materials exhibit a power-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 Power-law model 5) 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).

APCOM Theoretical models 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) KWW model - The first function is the Kohlrausch-Williams-Watts (KWW) function  (t) 6)6)6)6) 6)6)6)6) with 0 <   1 - double power law (DPL) - The second function is the double power law (DPL) 7) 7) DPL model

APCOM 0414 Debye model To fit the acoustic spectrum the Debye model (Eq.(4)) was applied. The measured spectrum in intermediate and high temperature ranges is represented by spotted line in the acoustic spectrum. Fig. 5. Fig. 5. The acoustic spectrum of sample BIDP5 (full line) and the Debye fit of the two relaxation processes (dashed lines). 5. Results Analysis and Discussion Debye model

APCOM 0415 Fig. 6. Fig. 6. Acoustics attenuation spectrum of sample BIDP5 (full line) and its theoretical supposing fit is superposition of two supposed relaxation processes (dashed lines). 5. Results Analysis and Discussion 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

APCOM 0416 DPL model To fit the acoustic spectrum the modified DPL 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. 7. Fig. 7. Acoustics spectrum of sample BIDP5 (full line). Dashed lines represent the best fit for three relaxation processes and their superposition. 5. Results Analysis and Discussion modified DPL model

APCOM 0417 DPL model The complete spectrum of sample BDP was fitted using the modified DPL model and the calculated lines gave an excellent agreement with measured spectrum. Fig. 8. Fig. 8. Acoustics spectrum of sample BDP (full line). Dashed lines represent the best fit for three relaxation processes and their superposition. 5. Results Analysis and Discussion modified DPL model

APCOM 0418 BIDP1 - BIDP7 E A E A mn From the comparison of various samples (BIDP1 - BIDP7) follows that the individual relaxation mechanisms of the same sample have different values E A, but the same three relaxation processes with close values E A and the same values of coefficients m, n can be find in different samples. Fig. 9. Fig. 9. Acoustics spectrum of sample BIDP7 (full line). Cross marked line represents the best fit of superposition of three relaxation processes. 5. Results Analysis and Discussion modified DPL model

APCOM 0419 The experimental and theoretical investigation of ion conductive glasses in system CuI-CuBr-Cu 2 O-P 2 O 5 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-Cu 2 O-P 2 O 5 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. Conclusion

APCOM the acoustic attenuation spectra of all investigated ion conducting glasses prepared in the system CuI-CuBr-Cu 2 O- P 2 O 5 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-Cu 2 O- P 2 O 5 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. Conclusion

APCOM 0421 Peter Hockicko Thank You for Your Attention