Conductivities and Activation Energies

The impedance data of PSZ and PSZ/mullite composites can be divided into two semicircles corresponding to high and low frequencies. They were modeled by an equivalent circuit consisting of two R-CPE parallel circuits in series, where R and CPE are the resistor and the constant-phase element, respectively.⁴⁹ The impedance spectra of monolithic mullite showed , however, a single imperfect semicircle (i.e., a depressed circular arc), and its data were fit using a model of one R-CPE parallel circuit.⁴⁹ In the other way, the impedance spectra with a perfect semicircle would be fit by the equivalent circuit of one RC parallel circuit.

The conductivities of various composites obey the Arrhenius equation and can be expressed by:

⎟⎠

⎜ ⎞

⎝⎛−

= RT

A E

T exp ^a

σ (3.1)

where σ is the conductivity (ohm^-1 cm^-1), A is a constant, E_a is the activation energy (kJ/mol), R is the gas constant (J/mol K), and T is the absolute temperature (K).

Figure 3.4 displays the Arrhenius plots of ln(σT) as a function of 1/T for all samples. The conductivities of the composites in the high-frequency region increased with increasing PSZ content as shown in Fig. 3.4(a). In contrast, the plots in Fig. 3.4(b) indicate that the conductivities in the low-frequency region exhibited a somewhat different trend. The conductivities of MZY20 at low temperatures were smaller than those of MZY05 and MZY10.

Furthermore, the slope of the ln(σT) versus 1/T curve for MZY20 was much larger than those for MZY05 and MZY10. The electrical conductivity versus 1/T curves of MZY30, MZY40, or MZY50 demonstrate a similar slope.

It was also noted that the conductivity in the high-frequency region (related to grains) of MZY80 was the same as that of PSZ, while the conductivity in the low-frequency region (related to grain boundaries) was much lower than that of PSZ. This can be explained by the fact that mullite grains are located at the grain boundaries of PSZ and the existence of intergranular mullite slightly decreased the conductivity of MZY80 along the grain boundaries. The intergranular mullite, however, did not affect the conductivity across the dense interconnected channels of PSZ grains in MZY80.

Figure 3.5 displays the activation energies of electrical conduction with respect to PSZ content in the high- and low-frequency regions. The activation energy for mullite was found to be about 65 kJ/mol, which is in agreement with previous studies.^{45, 47} For PSZ, the activation energies of the grain conductivity at high frequencies and of the grain-boundary conductivity at low frequencies were found to be about 79 and 93 kJ/mol, respectively, agreeing with the results reported by Guo and Zhang.⁴⁴

The activation energies in the high- and low-frequency regions for MZY05 and MZY10 are approximately the same as that for mullite. The high-frequency measurements of MZY05 and MZY10 could be correlated with the presence of grains of mullite. The grain conductivities of MZY05

and MZY10, however, were different from those of monolithic mullite.

PSZ has a much lower resistivity than mullite and can affect the electrical response in MZY05 and MZY10. That is why the grain conductivities for MZY05 and MZY10 are so different with those for monolithic mullite.

In contrast, the low-frequency regions for MZY05 and MZY10 were correlated to the grain boundaries of PSZ and/or mullite. While a glassy phase was usually observed in the grain boundaries of monolithic mullite, the composites containing PSZ were lacking a glassy phase.^{50, 51} For MZY05 and MZY10, the low-frequency signal would transport through grain boundaries of mullite and/or PSZ instead of the glassy phase.

When the PSZ content was larger than 20 vol%, the activation energies in the low-frequency region were much higher than those of MZY05 and MZY10. This could be explained by the formation of a space charge layer at the interface of mullite and PSZ grains in an electric field. The space charge layer is usually formed at the interface of two phases with dissimilar electrical properties. The presence of a space charge potential would increase the activation energy of the electric conduction through the grain boundaries.⁴⁴ Therefore, the low-frequency arcs of the composites were related to the space charge contribution when the PSZ content was larger than 20 vol%. There was not much difference in the activation energies from MZY20 to MZY60 at low frequencies. In contrast, the activation energies of the electric conduction in the high-frequency region between MZY20 and MZY60 increased gradually with PSZ content.

Figure 3.5 also shows that the activation energies of the electric conduction

for MZY80 were close to those values for PSZ in the corresponding high- and low-frequency regions.

3.3.3 Conductivity versus PSZntent

Various theories describe the physical properties of a multi-phase system.

The general mixing equation is frequently used to predict the electrical properties of a heterogeneous system and can be expressed by:⁵²

( )

zⁿ n

m n

c V σ Vσ

σ = 1− + (3.2)

where V is the volume fraction of PSZ, σ_m, σ_z and σ_c are the conductivities of mullite, PSZ, and composite, respectively, and n is a constant between -1 and 1. For the extreme, case, n = 1 if these two phases are laminated and laid parallel to the direction of electric current; n = -1 if these two phases are laminated and laid perpendicular to the direction of electric current. There is a mixed case where -1 < n < 1. When n → 0, the mixing equation is given by:⁵²

( )

_{m z}

c V σ V σ

σ 1 log log

log = − + . (3.3)

This expression was first proposed by Lichtenecker and was called Lichtenecker’s rule.⁵³ The empirical Lichtenecker’s rule was applied successfully to estimate the dielectric content of a two-phase system in previous studies.^{54, 55} Zakri et al.⁵⁶ demonstrated that Lichtenecker’s rule is not only an empirical relationship based on experimental results, but also a theoretical model that can be derived from the effective medium theory.

To understand the change of electrical properties in composites with various PSZ contents, the resistance (R) of those samples was measured at some fixed low and high frequencies. Then, the conductivity (σ) was calculated using:

A l R⋅

= 1

σ (3.4)

where l and A were the thickness and cross-sectional area of the sample perpendicular to the electric current direction, respectively.

Figures 3.6(a) and 3.6(b) display the real parts of conductivity (σ’) as a function of PSZ content at the frequencies of 1 kHz and 1 MHz, respectively, at 600^oC, indicating that the real part of conductivity increases with PSZ content. It was noted that the plot of ln σ’ versus PSZ content at 1 MHz [Fig. 3.6(a)] demonstrates a linear behavior in agreement with Lichtenecker’s rule. Figure 3.6(b), however, shows that the conductivities measured at 1 kHz with various PSZ contents were fit using the mixing rule [Eqn. (3.2)]. The parameter n was about 0.25.

The different trends for the ln σ’ of composites with various PSZ contents at 1 MHz and 1 kHz were caused by different factors. The conductivities measured at 1 MHz and 1 kHz were gained from the contribution of grains and grain boundaries, respectively. Figure 3.6(b) shows that the conductivities of composites with 30 to 60 vol% PSZ were not much different from the conductivities measured at 1 kHz. This could result from

the existence of space charge at grain boundaries as mentioned previously.

Thought the space charge layer could deplete the charge carriers and cause an increase in resistivity of the grain boundaries,⁴⁴ the resistivity was expected to decrease with increasing PSZ content. These two conflicting factors on the resistivity of grain boundaries resulted in less difference in the conductivity at 1 kHz when the PSZ content was between 30 and 60 vol%.

Oxygen diffusivities of mullite/PSZ composites with various PSZ contents show percolation behavior with respect to PSZ content,⁵⁷ though percolation behavior of electrical conductivities was not observed for mullite/PSZ composites. This could be attributed to less difference in the conductivities between mullite and PSZ. The oxygen diffusivity of PSZ was larger than that of mullite by at least 8 orders of magnitude; however, the difference in electrical conductivities at 1 MHz between mullite and PSZ was only about 2 orders of magnitude. Hence, the electrical conductivities of the composites do not reveal the percolation behavior.

3.3.4 Microstructural View of Point

Figure 3.7 shows that MZY05 exhibited elongated grains of mullite, while mullite grains in MZY30 and MZY80 were equiaxed. From the SEM micrograph of MZY05 [Fig. 3.7(a)], it was concluded that PSZ was located at the grain boundaries of mullite and was isolated by mullite grains. It was inferred that the conductivity was still dominated by mullite as mentioned in previous section, although the grain conductivity in MZY05 was increased because of the addition of PSZ. Figure 3.7(b) reveals that some PSZ particles became interconnected in MZY30. The conductivity would be

significantly affected by PSZ. Figure 3.7(c) showed that mullite grains were surrounded by PSZ grains in MZY80. The rapid path of interconnected PSZ for electrical conductivity was formed in MZY80, and the grain and grain-boundary conductivities in MZY80 were completely controlled by PSZ.

3.4 Conclusions

1. The electrical conductivities of mullite/PSZ composites with PSZ content were measured by the ac impedance spectroscopy. The impedance spectra of monolithic mullite showed only one semicircle, while the monolithic PSZ and mullite/PSZ composites showed two semicircles.

2. The conductivities of mullite/PSZ composites increased with the PSZ content, but no percolation relationship was observed. The real parts of conductivities measured at 1 MHz and 1 KHz were in good agreement with the Lichtenecker’s rule and the mixing rule, respectively.

3. The activation energies of electrical conduction for mullite/PSZ composites were different in the high-frequency and low-frequency regions, depending on the PSZ content. The activation energies of grain conductivities in mullite and PSZ were about 65 and 79 kJ/mol, respectively, while those in the composites were calculated in between these two values. Furthermore, the activation energies sharply increased at 10 to 20 vol% PSZ in the low-frequency region.

4. The electrical conductivities of mullite/PSZ composites were effectively increased by the incorporation of PSZ so that high-PSZ composites

could be used for electrochemical purposes such as a gas sensor at high temperatures.

Table 3.1 Designations, compositions, hot pressing conditions, relative densities, and x-ray phases of various mullite/PSZ composites

* M = mullite; Z = 3 mol% Y2O3-ZrO2; t-Z = tetragonal ZrO2; m-Z = monoclinic ZrO2

Designation Composition* Hot Pressing

Condition^# Relative

Density (%) XRD Phases*

M 100 v/o M 1675^oC/45 min 97.8 M

MZY05 95 v/o M + 5 v/o Z 1600^oC/45 min 97.1 M, t-Z, m-Z MZY10 90 v/o M + 10 v/o Z 1600^oC/45 min 96.7 M, t-Z, m-Z MZY20 80 v/o M + 20 v/o Z 1600^oC/45 min 95.4 M, t-Z, m-Z MZY30 70 v/o M + 30 v/o Z 1600^oC/45 min 96.7 M, t-Z, m-Z MZY40 60 v/o M + 40 v/o Z 1600^oC/45 min 97.5 M, t-Z, m-Z MZY50 50 v/o M + 50 v/o Z 1600^oC/45 min 97.1 M, t-Z, m-Z MZY60 40 v/o M + 60 v/o Z 1600^oC/45 min 97.8 M, t-Z, m-Z MZY80 20 v/o M + 80 v/o Z 1600^oC/45 min 97.7 M, t-Z, m-Z Z 100 v/o Z 1600^oC/45 min 99.9 t-Z, m-Z

# All samples were fabricated under the pressure of 30 MPa in Ar.

HP 4194A

Furnace

Pt plate Sample Pt wire

Al₂O₃ plate

Fig. 3.1 Impedance-measuring system.

0 1 2 3 4 5 6 7

Fig. 3.2 Typical impedance spectra. (a) For MZY10 at temperatures ranging from 400 to 1000^oC; (b) For MZY80 at temperatures ranging from 200 to 450^oC. The enlarged views at low impedances are shown in the inset.

0 1 2 3 4 5 6

Fig. 3.3 Impedance spectra of the composites with various PSZ contents: (a) M, MZY05, MZY10 and MZY20 at 700^oC;

(b) MZY30, MZY40, MZY50, MZY60, MZY80 and Z at 300^oC. The enlarged views at low impedances are shown in the inset.

0.5 1.0 1.5 2.0 2.5 3.0

Fig. 3.4 Arrhenius plots of conductivities determined (a) in the high-frequency region; (b) in the low-frequency region of impedance spectra.

0 20 40 60 80 100 60

70 80 90 100

activation energy (kJ/mol)

zirconia (vol%)

high frequency region low frequency region monolithic mullite

Fig. 3.5 The activation energy versus PSZ content curves of mullite/PSZ composites in the high-frequency and low-frequency regions, respectively, of the impedance spectra.

0 20 40 60 80 100 -11

-10 -9 -8 -7 -6

ln σ' (ohm-1 cm-1 )

(a)

zirconia (vol%)

0 20 40 60 80 100

-18 -16 -14 -12 -10 -8 -6

ln σ' (ohm-1 cm-1 )

(b)

zirconia (vol%)

Fig. 3.6 The real part of conductivity versus PSZ content curve at the frequencies of (a) 1 MHz and (b) 1 KHz at 600°C. The fitting lines in (a) and (b) were determined by Lichtenecker’s rule and the general mixing equation, respectively.

( c ) ( b )

( a )

Fig. 3.7 Scanning electron micrographs of mullite/PSZ composites: (a) MZY05; (b) MZY30; (c) MZY80. The dark phase is mullite and the bright phase is PSZ.

Chapter 4

Oxygen Diffusivities and Surface Exchange Coefficients in Porous Mullite/Zirconia Composites Measured by the Conductivity Relaxation Method

4.1 Introduction

Mullite is a frequently used material for applications at high temperatures due to its advantageous properties, including good creep resistance, excellent chemical stability, and suitable high-temperature strength.¹ In addition, mullite is a potential substrate material because it has a favorable dielectric constant and thermal expansion coefficient.⁵⁸ To further improve its mechanical properties (e.g., fracture toughness), ZrO2 particles and/or SiC whiskers have been incorporated in mullite, as indicated in previous studies.^5,

9, 59, 60

One can modify the properties of composite materials by combining two or more components. The properties of composites are highly dependent upon the size, shape and content of the individual components. Previous studies^{57, 61} investigated the oxygen diffusivities and electrical conductivities of mullite/PSZ composites with various PSZ contents. The percolation phenomenon for oxygen diffusion in mullite/PSZ composites was observed at 30-40 vol% PSZ, while no such a phenomenon was observed for electrical conduction.⁶¹ The electrical conductivities of mullite/PSZ composites followed Lichtenecker’s rule at high frequencies and the general mixing equation at low frequencies.

Recently, the mechanical properties of porous mullite/ZrO2 composites have been investigated.^{62, 63} Haslam and Lange⁶² developed a processing method to strengthen porous mullite/ZrO₂ composites without shrinkage using evaporation/condensation sintering in an HCl atmosphere. Latella and Mehrtens⁶³ indicated that the mullite/ZrO2 composites with 62% porosity showed no strength degradation at temperatures ranging from 25 to 1200^oC.

Because porous composites could be used in hot gas filtration environments, the influence of ZrO₂ content on diffusion and/or surface exchange rate in porous mullite/ZrO₂ composites is an important subject.

To date, little research has been conducted on the character of mass transfer in porous mullite/ZrO₂ composites. In a previous study,⁶⁴ Ganeshananthan and Virkar measured the oxygen surface exchange coefficients of porous La0.6Sr0.4CoO3-δ using the conductivity relaxation method. In this study, the conductivity relaxation method was used to measure the diffusivities and surface exchange coefficients of porous mullite/PSZ composites with various PSZ contents. The effects of PSZ content and oxygen partial pressure on the diffusivities and surface exchange coefficients of porous mullite/PSZ composites were explored.

4.2 Experimental Procedures

Based upon a previous study on the percolation phenomenon, mullite/PSZ composites containing more than 40 vol% PSZ were defined as "high-PSZ composites"; otherwise, the composites were categorized as "low-PSZ composites."

The composites in this study were fabricated by sintering mixtures of mullite (KM-mullite, 71.86 wt% Al2O3, 28.07 wt% SiO2, 0.03 wt% Fe2O3, 0.03 wt%

NaO₂ and 0.01 wt% MgO₂, 0.2 µm on average, Kyoritsu Ceramic Materials Co., Nagoya, Japan), 3 mol% Y₂O₃-stabilized ZrO₂ or 3Y-ZrO₂ powder (TZ-3Y, 94.75 wt% ZrO2, 5.21 wt% Y2O3, 0.005 wt% Al2O3, 0.005 wt%

SiO2, 0.002 wt% Fe2O3 and 0.022 wt% NaO2, 0.3 µm on average, Toyo Soda Mfg., Co., Tokyo, Japan), and carbon (Vulcan XC72, 0.03 µm on average, Cabot Co., Billerica, MA), wherein 30 vol% carbon was used as the pore-forming agent.

The starting powders were first dispersed in alcohol. The pH value was adjusted to 10 using NH₄OH as an electrolyte, and then the powder mixtures were dried on a hot plate. Subsequently, they were uniaxially pressed at 63 MPa for a few minutes. The cold-pressed samples were heated to burn out carbon at 600°C for 30 min and then sintered at 1200-1550°C for 2-3 h depending upon the composition of the powder mixture.

The densities of the sintered bodies were determined by the Archimedes method using de-ionized water as an immersing medium, and the relative densities were then calculated. The designations, compositions, sintering conditions, and relative densities of these composites are listed in Table 4.1.

The sintered composites were cut into pieces about 3.5 × 3.5 × 0.8 mm in size. Samples were ground and polished with a precision polishing machine (Model Minimet 1000, Buehler Ltd, Lake Bluff, IL) using standard procedures as described previously.⁵⁷

The conductivity relaxation method was used to measure the electrical

resistivities of bulk samples under different oxygen partial pressures.

Figure 4.1 shows a schematic diagram of the conductivity-measuring system.

The specimen together with two Pt electrodes was clipped by two plates of Al₂O₃. After being connected to an electric potentiometer, the specimen was placed in an Al2O3 tube furnace. The measuring temperatures were less than the sintering temperature by at least 200°C to avoid densification during the measurements. When the electric conductivity was saturated at a certain oxygen partial pressure (Po₂¹), a gas mixture with a decreased oxygen partial pressure (Po₂²) was introduced into the chamber. While the oxygen partial pressure changed from Po21 to Po22, the variation of electrical resistance was recorded with a multimeter (Model 2000, Keithley Instruments Inc, Cleveland, OH). This procedure was repeated using a stepwise decrease in the oxygen partial pressure after the electric conductivity was saturated again.

It was noted that when the ratio of initial to final Po₂ is larger than 20, linear exchange kinetics are no longer valid.⁶⁵ Thus, a narrow Po₂ change was conducted to make certain that systematic error in measuring the diffusivities and surface exchange coefficients could be avoided. The oxygen partial pressures chosen in this study were 20.2, 14.1, 10.1, 6.07 and 2.02 kPa in sequence. Variation of the oxygen partial pressure was achieved by different flow rates of oxygen and argon.

4.3 Mathematical Background

Transport of oxygen ions in a porous sample consists of two possible rate-controlling processes in series: the surface exchange reaction at the

gas/solid interface and ionic diffusion through the bulk. If the oxygen concentration at any cross-section is kept constant, i.e., the flux into the cross-section is equal to the flux out of the cross-section, a steady state is reached. When the oxygen partial pressure is changed in a steady state system, the variation of oxygen concentration in the solid with time can be correlated with the rates of bulk diffusion and surface exchange by the following equation:⁶⁶

where Mt is the total amount of ions that entered (or left) the sample in time t, M_∞ is the total amount of ions that entered (or left) the sample after an infinite time, τ_n is the relaxation time, and β_n are the positive roots of the following equation:

D L l α β

βtan = = ^⋅ (4.2)

where α is the surface exchange coefficient, D is the diffusivity, and l is the half thickness of the membrane. As a result, the relaxation time τn can be

Either bulk diffusion or surface exchange reactions can be a rate-limiting

step in the relaxation process, and the ratio of diffusivity to the surface exchange coefficient is defined as the characteristic length (Lc).^{67, 68} When the thickness of the membrane is much larger than the characteristic length, diffusion will govern the relaxation process. In such a case, where diffusion controls ionic transport, Eqn. (4.1) can be expressed as

∑^∞

In contrast, when the thickness of the membrane is much smaller than the characteristic length, the relaxation process is mainly dominated by the surface exchange reaction. In such a case, where surface exchange controls ionic transport, Eqn. (4.1) can be simplified as

⎟⎠

The equations mentioned above for the relaxation experiment are derived under the assumption of immediate change of oxygen partial pressure.

When a relaxation experiment is performed in a large reactor volume or at a relatively high temperature, the time needed to change the oxygen partial pressure cannot be neglected. The relaxation time can be close to the flush time of the reactor volume, and a correction should be used. The flush time correction in a relaxation experiment was presented by den Otter et al.⁶⁹ Thus, Eqn. (4.1) can be written in terms of the flush time of the reactor volume:

( )

where g(t) is the normalized conductivity and τ_f is the flush time of the reactor volume or the time needed to flush the reactor volume. Since the relaxation process is controlled by surface exchange, Eqn. (4.6) can be simplified as

where the relaxation time τ =l/α. Additionally, the relationship between the normalized conductivity g(t) and electrical conductivities can be

where the relaxation time τ =l/α. Additionally, the relationship between the normalized conductivity g(t) and electrical conductivities can be

在文檔中 氧化鋯含量對莫來石/氧化鋯複合材料氧擴散與導電性之影響 (頁 41-0)