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Detection of the instantaneous acceleration using superionic conducting ceramics
1997 Electrochimica Acta. Vol. 42, Nos 20-22, pp. 3167-3175, 1997 Published bv Elsevier Science Ltd. All rights reserved. Printed in &eat Britain PII: s0013-4686(97)00170-9 00&4686/97 517.00 + 0.00
0
Pergamon
Detection of the instantaneous acceleration using superionic conducting ceramics G. Pajonk”* “Department bDepartment
and H. Rickertb
of Materials Technology, University of Physical Chemistry 1, University
(Received
28 September
of Dortmund, of Dortmund,
1996; in revised form
44221 Dortmund 44221 Dortmund
14 January
1997)
Abstract-If ionic conducting, highly defective crystals are stopped by impaction, the mobile ions are accelerated inside the conduction plane. Therefore, an electric field corresponding to the separation of positive and negative charges approaches during a period of 1 ps. Simultaneously an inertia emf is measured between the electrodes of the galvanic cell, which is directly proportional to the mass to charge ratio of the mobile charge carriers, to the length of the galvanic cell and to the instantaneous acceleration. In this work the effect of the inertia forces on mobile cations in solid electrolytes for the first time is investigated on ceramic materials. 0 1997 Published by Elsevier Science Ltd Key words: Inertia
effect, solid electrolytes,
/Galumina,
INTRODUCTION /?-alumina generally is the expression for a complex sodium aluminate. This substance class of similar composition was assumed to be a modification of aluminum oxide (A1203) for a long period of time. The typical representatives are sodium /I-alumina (NazO. 1 lAlzO3) and sodium /I”-alumina (Na20.7A1203). /?-alumina is characterized by a hexagonal elementary cell, whose main elements are two spinel-like blocks, formed by oxygen in cubic face-centered order and by aluminum ions on tetrahedral and octahedral sites. p”-alumina is arranged rhomboedrically with three spine1 blocks and a high sodium content per unit. If substituted during sintering by bivalent cations, the p”-type is consolidated. Solid state ionics like /I-alumina, a-silver iodide, rubidium silver iodide (RbAg&) or Y203 doped zirconia (ZrO2) are highly disordered. Therefore, a high ionic conductivity is experimentally observed. In /I-alumina the gap between the elementary units perpendicular to the main crystallographic axis is occupied by highly mobile positive charge carriers like sodium cations, located quasi-liquid inside the conduction plane. Therefore, in single crystals an anisotropy of conductance is obtained. In the case of /l-alumina an interstitial mechanism has been 3167
acceleration,
sensor technique.
formulated, whereas in /I”-alumina mass transport requires vacancies. If hot pressed polycrystalline samples were used for sample preparation, no anisotropy is observed, because the conduction path is spread about the whole volume. /I- and /I”-alumina ceramics, substituted by single, double and triple charged cations, are cationic conductors within a great range of temperatures (Fig. 1). Merely trivalent p”-aluminas already exhibit a detectable electronic conductivity at room temperature. Affected by an external force, which usually corresponds to an electrical field, the random walk ion motion changes to a directed mass transport towards the conduction plane [5-121. PREVIOUS
WORK
Basic investigations on the inertia forces of mobile ions in solid state ionic conductors were reported by Betsch, Rickert and Wagner [I]. In 1985 they measured a voltage pulse between the electrodes of an aperiodically accelerated isothermal galvanic cell. During the experiments rods cut from cc-AgI and contacted by silver electrodes were dropped towards a target made of plasticine. Meanwhile a voltage was observed, due to the length of the galvanic cell, to the mass to charge ratio of the silver cations and to the velocity of the sample just before impaction. Further
3168
G. Pajonk
and H. Rickert
experiments of Betsch, Rickert and Wagner [2] established the inertia effect by detecting impaction caused voltage pulses at samples made of Rb AgdIs. For silver containing cationic conductors a sensoric sensitivity of 0.11 PV g-i cm-i was experimentally proved. On rubidium silver iodide a transference number of the silver ions of nearly unity and a cationic conductivity of 0.26R-’ cm-’ is obtained. Additionally Koch and Rickert [3] observed ACvoltages at sinusoidally accelerated samples for a frequency range between 15 Hz and 5 kHz and for accelerations up to 140g (1 g = 9.81 m ss2). THEORETICAL
CONSIDERATIONS
If superionic conductors are dropped towards a target and stopped at once to velocity zero, different forces work on the rigid crystal lattice as well as on the mobile charge carriers. The force Fdedecelerates the sample, acting in the direction of the instantaneous acceleration a& and inverse to the vector of
1
l,5
the impaction path impacts, the mobile plane are accelerated
p*;, = I?lionX 2,
4 = qi,”
of disordered
p” alumina-ceramics.
X E
(2)
where FE = electric force; mlon = ionic charge; E = electric field strength. Because the electric field appears from a period of 1 ps, but the impaction lasts a few milliseconds, the balance condition
mien
1ooorr (K-l] -b Fig. I. Ionic conductivities
(1)
where F,, = inertia force; mien = ionic mass; a = instantaneous acceleration. Therefore, an electric field corresponding to the separation of positive and negative charges occurs and the mobile charge carriers are inversely redriven to the inertia effect by
2,5
2
(Fig. 2). During short-lasting cations inside the conduction by inertia forces as given by
3
x d =
3.5
qion x
E
4
(4)
Detection of the instantaneous
acceleration using superionic conducting ceramics U = 2.
3169
1*4n2v2t2.xo*sin[2nv.t], U = CJ0sin[2nv*t],
(10)
where z = degree of ionization; e = unit charge; UO = voltage amplitude, should be measured between the electrodes of a sinusoidally accelerated cell. Uo=~.1.4n2v2t2.Xo=~.l.~.
l Ag
0’
Fig. 2. Charge displacement in a-A@ caused by an impact. is fulfilled at every moment of the event. According to the definition of the electric field strength E=
-gradb,
(5)
I
U=-
Edx=-Exl, s0
where inertia entf
(I=-pxu,
(6)
where 4 = electric potential; 1= length of the galvanic cell; U = inertia emf, should be measured between the electrodes of a galvanic cell containing solid electrolytes. It should be directly proportional to the mass to charge ratio of the mobile charge carriers, to the length of the galvanic cell and to the instantaneous acceleration. If solid state ionics are accelerated by harmonic motions, a linear dependency of the inertia voltage on the instantaneous acceleration is still expected. As shown in the following, the acceleration is proportional to the deflection from equilibrium. x = xo.sin[2nv.t], a = g
= -(2nv.f)2.xo.sin[2nv.r]
(7)
= -(237v.t)2.x,
(8) a = uo.sin[2nv.t],
(9)
where x = point function; x0 = maximum of deflection; I = time; v = frequency of the harmonic motion; uo = acceleration amplitude. The point function as well as the acceleration are sinusoidal and complementary phase shifted. The acceleration amplitude Q corresponds to the maximum of deflection from the equilibrium x0 as well as on the square of the exiting frequency v. Therefore, an alternating voltage
(11)
Its voltage amplitude should be proportional to the mass to charge ratio of the charge carriers, to the length of the electrolyte as well as to the amplitude of the acceleration or to the maximum deflection from the balance x0 and its exiting frequency. ION EXCHANGE EXPERIMENTS Many mono-, bi- and trivalent B and b”-alumina isomorphs have been produced from the sodium compound by ion exchange, using salt melts for reagent. If the melting points were skillfully chosen, the high ionic mobility in the melt ensured a fast approximation of the thermodynamic balance. The choice of temperature cohered with the balances as well as with the kinetics of the exchange reaction. The balance conditions depending on the melting composition were described by ion exchange isotherms. If the balance for the exchangable species was established at the solid side, an increase in temperature caused a decrease of the equilibrium constant. Otherwise raising the temperature just assured the exchange of cations preferring the melt. At low exchange temperatures the exchange was kinetically impeded and the reaction proceeded slowly, due to the small coefficients of diffusion. A strong surplus of the melting reagent accelerated the reaction in this case. The balance conditions were influenced by the sphere of cation coordination, the ionic diameters and the structure of the conduction plane. Growing complex compounds with the cations inside the melt, big polarizable anions preferred the equilibrium on the melting side. Because their tendency to form complexes and their melting points of approx. 300°C are generally low, nitrate salts were preferred for exchange reagents (Fig. 3). fl”-alumina based cationic conductors were prepared by ion exchange procedures from polycrystalline raw materials, consisting of 87.5% Al203, 9.0% Na20 and 3.5% MgO (density: 3.16 g/cm’) as reported by ABB Heidelberg. Primarily brick shaped samples (approx. 19 mm x 6 mm x 5.5 mm) were cut from sintered compacts (diameter: 26.5 mm, gauge: 5.8 mm) by water cooled diamond tools, heated to 400°C in vacuum to remove water content, sealed in quartz tubes and immersed in salt melts. The exchange conditions are listed in Table 1.
3170
G. Pajonk
Fig. 3. Ion e:xchange
isotherms
of alkali
fi-aluminas
and H. Rickert
in molten
After the reaction had finished, the samples were taken from the liquid, washed in distilled water for three minutes and dried in vacuum at 150°C. The completeness of the exchange reaction was checked by weight exchange in the case of compact samples or by EDX analysis for pulverized substances. This way Ag+/?“-aluminas, Pbz+a”-aluminas, K+/Y’aluminas and NH:/?“-aluminas were achieved. The samples, immersed in potassium nitrate and ammonium nitrate solutions, were generally cracked by reaction caused microstress. Therefore, it was impossible to carry out inertia experiments on these compounds. The AC-conductivity (1 kHz) of samples, remaining whole, was measured at room temperature afterwards. On Ag+/Y’-alumina contacted by silver electrodes a cationic conductivity of
nitrates
at 300°C [6]
0 = 3.57 x 10-4R-’ cm-’ and on Pb2+/Y’-alumina contacted by lead of Q = 4.2 x lo-‘a-’ cm-’ was observed.
SAMPLE
PREPARATION
To prove the inertia effect on /Y-alumina electrolytes, different kinds of specimen were assembled and accelerated by impaction or by harmonic motion. The different specimens are shown in Figs 4 and 5. To create isothermal galvanic cells of the type MelMe*~“-alumina(porY~, ,IMe with Me z Ag, Cu, Me* z Ag, Na,
Table 1. Exchange
conditions
for fi”alumina
electrolytes
Electrolyte
Starting
Ag+ /I”-alumina K+ p”-alumina NH: 8”-alumina Pb2+ /Y-alumina
Na+ b”-alumina Na+ )?I”-alumina Na+ 8”-alumina Na+ /Y-alumina Na+/Pbr+ B”-alumina
material
Delay for exchange
Reagent AgNO, KNOs NHdNO, PbClz PbClr
350 364 220 378 378
96 h 168h 168h 209 h 200 h
Exchange (Gew%) 100% 100% 100% 10% 95%
Comment
Fractured Fractured 2 step reaction
Detection of the instantaneous
screw
acceleration using superionic conducting ceramics
call
aluminum sleeve
I
braided
cable
electmde
dms adhesive
Galuminia
electrolyte
SMD- sofdetinrl
Fig. 4. Specimen for impactions at low accelerations up to 500g as well as for experiments on the electrodynamic multivibrator. brick shaped p-alumina samples were metallized on the face by burn-in- or vacuum-metallization. Silver wires were fixed to the electrodes, covered by silicon hoses for electrical insulation and externally soldered to a radio-screened twin-cored braided cable. To ensure ohmic contact to the cell, different procedures were investigated, like burn-in varnishing, SMD soldering by a silver containing agent or bonding by a silver-containing, electrically-conducting adhesive. Only by adhesive bonding was a high thermo-mechanical strength achieved. For damage protection as well as for radio screening the electrolytes were clad by aluminum sleeves. .
I=
The range of application of the specimen, displayed in Fig. 4, was limited by its fracturing properties. At high values of acceleration the joins between all parts were fractured more and more by microcracks. Different metal components were plastically deformed. Furthermore, the detected pulses were distorted by deformation-caused interferences. Therefore, the construction should be optimized, diminishing the number of joins to an optimum quantity. To detect the inertia emf at high accelerations a specimen corresponding to Fig. 5 was developed. Its main element, a ceramic carrier, was cut from a ceramic bar, shortened to 45 mm and rounded at the lower end. Along its diameter a small slot was cut by diamond tools, where the /Y-alumina electrolyte was fitted and well adjusted. Towards this kind of sample the mechanical pulse was transmitted across the sample only by ceramic components, except for a very small adhesive area between the carrier and the electrolyte. Corresponding to an increase in the mechanical properties, high accelerations up to 20,OOOg were obtained.
EXPERIMENTAL Aperiodic events, like impacts, have usually been of complex constitution. Lasting only a few milliseconds, their analysis required sensors and measuring devices with a short time of response. The devices used for our investigations are schematically illustrated in Fig. 6. During the experiment a piezo sensor was mounted on the specimen acting as a reference. When the sample was dropped, the electrolyte emitted a voltage pulse, which was a thousandfold preamplified by a microvolt amplifier and sent to a digital memoryscope. Simultaneously the reference transmitted an equivalent signal across a charge amplifier to the scope. The amplitudes of
to the chargeamplifier
I
I
I
,
tc themicrovolt pnzamplifier
we---e-s
.---------
piezo aceelemmeter
aluminumsleeve micmvdt
----------------__ -----_-----
orcamolificr
8”-aluminaelectrolyte dms adhesive ceramiceatlier
Fig. 5. Specimen for impactions at high accelerations up to 20,ooog. EA 42/2&22--G
3171
Fig. 6. Device to detect emfpulses
caused by impactions.
3172
G. Pajonk
and H. Rickert
both pulses were detected in two channel operation mode and analysed afterwards on screen by cursor. To receive a higher resolution, the pulses were copied to a xy-recorder and evaluated. To investigate p-alumina electrolytes under periodical load, specimens were mounted according to Fig. 4 to an electrodynamic shaker and sinusoidally accelerated (Fig. 7). To measure at temperatures above 25°C a stove was assembled on the top of the shaker. To protect the shaker against overheating the lower end of the sample was cooled by pressurized air. The shaker consisted of a permanent magnet, of a coil supplied by a hf-generator and restoring strings. When an ac-current passed the coil, the specimen holder was deflected from its equilibrium by an electric field and on the other hand restored by the resiliency of the strings. This way a sinusoidal motion was generated. The frequency and amplitude of the oscillation were registered by an integrated piezo sensor and adjusted independently from each other as well as digitally displayed at the generators control unit. The ac-voltage emitted by the oscillating electrolyte was sent to a lock-in-amplifier, that allowed the investigation of periodical signals within a small frequency range. The bandwidth around the frequency of the aspected signal was limited to f 1 Hz by bandpass filters, which were calibrated by a reference voltage from the generator. Because interferences were excluded, very low voltage amplitudes were obtained and digitally displayed at a multimeter. DISCUSSION To investigate the inertia force of mobile cations in b-alumina electrolytes and to establish the linear dependency of the inertia voltage on the instantaneous acceleration many experiments have been carried out on Ag/I”-alumina and Nab”-alumina us a lock-in-amplifier
electrodynamic
shaker Fig. 7. Device to mesure inertia emfs caused by harmonic motions.
4
T =25’C
6
2
4
6
6
10
12
14
16
16
a/WOOg+ Fig. 8. Impacts of AgB”-alumina on plasticine: microdynamits of the single shot and dependency of the voltage on the instantaneous acceleration. piezo accelerometer (sensitivity: 10.79 mV/g) acting as a reference. By the choice of target material one can guide the microdynamic of the single shot and the accomplished acceleration. Characteristic voltage pulses are shown in Figs 8 and 9. On plasticine, accelerations up to 200 g were received. The single shot period usually lasted 2-3 ms. Above IOOg the pulses faded out by increasing vibrations, caused by a plastic caving of the specimen into the target. On aluminum oxide plates sequences of impacts were counted as voltage pulses. Corresponding to the high Young’s modulus of ceramic materials the samples were partially rejected, falling repetitively onto the plate, while driven by their own weight. Their kinetic energy was stepwise transformed to heat and distortion. On ceramics higher accelerations up to 20,OOOg were received and voltages of nearly 4 mV recorded. The single shot period was shortened from 250 ns at 180 g to 75 ns at 20,OOOg (1 g = 9.81 m/s2). The expected linear coherence between the inertia emf and the instantaneous acceleration for galvanic cells of AglAg/?“-aluminalAg-type was experimentally verified throughout the whole range examined. For defined lengths of the electrolyte all values between 30 g and 20,000 g were located on the computed line except for a 57% deviation, whereas the sensory sensitivities of the specimen determined the line gradients. The sensitivity per unit length for galvanic cells like AglAg/?“-aluminalAg was calculated to be 0.1095 PV g-’ cm-i (ie 1.121 PV m-* s2). The detection was limited at the upper side by the level of materials fatigue. Above 20,OOOg the joins between the assembled materials of the specimen failed by microcracks. The investigations on aperiodical events were limited by the thermal resistor noise.
Detection of the instantaneous
acceleration using superionic conducting ceramics
By low pass filtering of 10 kHz for, eg an 18 mm long specimen a noise voltage of 3 PV was observed, corresponding to an acceleration of about 30g. When approximated towards the noise, the recorded values below 50 g were still dissolved with deviations of 15-20%. The effective voltage of noise hardly corresponded to the resistance of the specimen. For a given temperature T and a bandwidth Av, chosen at the amplifier, this voltage could be estimated by using the Nyquist-formula
3173
200
T-25-C
150 > ?lOO 3
u s,e,i = J4kTRAv,
uu= UR,cflx J2,
(12)
where UR = noise voltage; k = Boltzmann’s constant; T = temperature; Av = bandwidth of frequencies; R = gas constant, and the limit of recording EC should be calculated from the signal noise ratio SNR. EC = I/ZSNR
= U./~UR,
(13)
where EC = limit of detection; SNR = signal to noise ratio; U, = inertia emf. For the sample presented in Fig. 8 a resistance of 36.5 kR was obtained at 23°C by impedance spectroscopy. Corresponding to the Nyquist formula a voltage of 3.4 PV and a limit of 34g was found. Investigations on Nab”-alumina electrolytes, metallized on the face by silver, copper, tin or lead electrodes, established the expected linear relation between inertia emf and acceleration on sodium cationic conductors (Fig. 10). On samples contacted by silver electrodes acceleration up to 8000g as well as 4000g at copper electrodes were obtained within a random deviation of + 10%. For specimens made of Nab”-alumina a reduced sensory sensitivity per unit length of 2.34 x lo-* PV g-t cm-’ (ie 0.24 PV
0
0,5
2
4
6
8
IQ
12
14
16
10
a/looOg--+ Fig. 9. Reboundings of Agp”-alumina on ceramics: microdynamics of the event and dependency of the voltage on the instantaneous acceleration.
2
2,5
3
3,5
4
all000 g+ Fig. 10. Reboundings of Nap”-alumina on ceramics: microdynamics of the event and dependency of the voltage on the instantaneous acceleration. m-* s*) was found, due to the minor mass to charge
ratio of the sodium cations and according to their lower electric field strength (Fig. 11). For aperiodical events the lower limit of detection was proved to be 15og. Further experiments established that ceramic electrolytes could be used for sensors detecting periodically recurring events. Therefore, galvanic cells of the AglAg/3”-aluminalAg-type were submitted to a harmonic motion in a frequency range between 400 Hz and 3 kHz. Corresponding to the exciting harmonic motion, an alternating voltage was detected between the poles of the galvanic cell (Fig. 13). For
c
0
1,5
1
0
I
1
2
//
3
4
5
6
7
8
a11000gh Fig. 11. Dependency of the electric field on the atomic mass of the mobile charges.
G. Pajonk and H. Rickert
3174
.
15
x
T
x
0
Ag 1AgWdumina v-48oHz
( Ag
*_2yc
v-9M)Hz v-146lHz
10
20
30
40
50
60
70
80
SO
0
5 101~20253035145055606570
a/g -4
aI0 Fig. 12. AgB”-alumina frequencies.
specimen
oscillating
at different
the whole frequency range the proprotionality has been frequency-independent proved with high precision (Fig. 12). Taking the different mass to charge ratio into account, this claim was also valid for other representatives of the /I-alumina class, such as Nab”-alumina (Fig. 13). Subsequently, no proof was found for a temperature dependency of the inertia effect (Fig. 14), instead of a decline of the thermal noise with increasing conductivity. Other features of the assembled components, like phase transformations, various
A~Na8’4umlnalAg I-
Y =
0
10
20
18.8mm. T=
1.2kHz w- 1tiz
30 a/g
40
50
00
Fig. 14. Ag/?“-alumina specimen: oscillating at different temperatures. thermal expansions and high temperature corrosion processes, were responsible for a temperature-dependent limitation. Therefore, above 600°C measurements were impossible.
CONCLUSIONS We have proved that it is possible to detect short lasting aperiodic events as well as periodical processes by means of galvanic cells made from b-alumina ceramics. The microdynamics of a physical event were completely displayed. Particular events lasting a few nanoseconds were still resolved. The time limitation of recording corresponded to the electric time-constant of the material, ie the delay to induce the electric field. The sensory sensitivity per unit length for galvanic cells like AglAg/Y’-aluminalAg was found at 0.1095pV g-l cm-’ (ie 1.121 PV m-* s*) with a maximum measurement deviation of f 7% as well as at 2.34 x lo-* PV g-l cm-’ (ie 0.24 PV m-* s2) and deviations of f 10% for specimens made of Nap”-alumina. The lower limit of detection of accelerations was determined by the thermal noise of resistance of the solid electrolyte, due to its conductivity and the volume of the sample. It was essentially limited on the upper side by the kind of sample construction and by the mechanical qualities of the chosen materials, especially the shear and fracture strengths of the electrolyte, carriers and joins.
d
Fig. 13. Periodically accelerated Nab”-alumina specimen: microdynamics of the event and dependency of the voltage on the instantaneous acceleration.
REFERENCES 1. M. Be&h,
H. Rickert
Phys. 89,
1I3 (1985)
and R. Wagner,
Ber. Eunsenges.
Detection of the instantaneous
acceleration using superionic conducting ceramics
2. M. Betsch, H. Rickert and R. Wagner, SolidS!afe Ionics 3. 4. 5. 6. 7.
18/19, 1193 (1986). W. Koch and H. Rickert, Solid State Ionics 28-30, 1664 (1988). R. C. Tolman and T. D. Stewart, P&s. Rev. 8, 97 (1916). W. L. Roth, J. Solid State Chem. 4, 60 (1972). J. T. Kummer, Progr. Solid State Chem. 7, 141 (1972). Y.-F. Yu Yao and J. T. Kummer, J. Inorg. Nucl. Chem. 29, 2453 (1967).
3175
8. J. T. Kummer, Inorg. Synrh. 19, 51 (1979). 9. W. Maly-Schreiber, P. Linhardt and M. W. Breiter, Solid State Ionics 13, 131 (1987). 10. S. Rohrer and G. C. Farrington, Solid State Ionics 28-30, 142 (1988). Il. J. Tegenfeld, M. Underwood and G. C. Farrington, Solid State Ionics 18 & 19, 668 (1986). 12. H. J. Kennedy, in Topics in Applied Physics, p. 105-141. Springer-Verlag. Berlin, Heidelberg (1977).
0
Pergamon
Detection of the instantaneous acceleration using superionic conducting ceramics G. Pajonk”* “Department bDepartment
and H. Rickertb
of Materials Technology, University of Physical Chemistry 1, University
(Received
28 September
of Dortmund, of Dortmund,
1996; in revised form
44221 Dortmund 44221 Dortmund
14 January
1997)
Abstract-If ionic conducting, highly defective crystals are stopped by impaction, the mobile ions are accelerated inside the conduction plane. Therefore, an electric field corresponding to the separation of positive and negative charges approaches during a period of 1 ps. Simultaneously an inertia emf is measured between the electrodes of the galvanic cell, which is directly proportional to the mass to charge ratio of the mobile charge carriers, to the length of the galvanic cell and to the instantaneous acceleration. In this work the effect of the inertia forces on mobile cations in solid electrolytes for the first time is investigated on ceramic materials. 0 1997 Published by Elsevier Science Ltd Key words: Inertia
effect, solid electrolytes,
/Galumina,
INTRODUCTION /?-alumina generally is the expression for a complex sodium aluminate. This substance class of similar composition was assumed to be a modification of aluminum oxide (A1203) for a long period of time. The typical representatives are sodium /I-alumina (NazO. 1 lAlzO3) and sodium /I”-alumina (Na20.7A1203). /?-alumina is characterized by a hexagonal elementary cell, whose main elements are two spinel-like blocks, formed by oxygen in cubic face-centered order and by aluminum ions on tetrahedral and octahedral sites. p”-alumina is arranged rhomboedrically with three spine1 blocks and a high sodium content per unit. If substituted during sintering by bivalent cations, the p”-type is consolidated. Solid state ionics like /I-alumina, a-silver iodide, rubidium silver iodide (RbAg&) or Y203 doped zirconia (ZrO2) are highly disordered. Therefore, a high ionic conductivity is experimentally observed. In /I-alumina the gap between the elementary units perpendicular to the main crystallographic axis is occupied by highly mobile positive charge carriers like sodium cations, located quasi-liquid inside the conduction plane. Therefore, in single crystals an anisotropy of conductance is obtained. In the case of /l-alumina an interstitial mechanism has been 3167
acceleration,
sensor technique.
formulated, whereas in /I”-alumina mass transport requires vacancies. If hot pressed polycrystalline samples were used for sample preparation, no anisotropy is observed, because the conduction path is spread about the whole volume. /I- and /I”-alumina ceramics, substituted by single, double and triple charged cations, are cationic conductors within a great range of temperatures (Fig. 1). Merely trivalent p”-aluminas already exhibit a detectable electronic conductivity at room temperature. Affected by an external force, which usually corresponds to an electrical field, the random walk ion motion changes to a directed mass transport towards the conduction plane [5-121. PREVIOUS
WORK
Basic investigations on the inertia forces of mobile ions in solid state ionic conductors were reported by Betsch, Rickert and Wagner [I]. In 1985 they measured a voltage pulse between the electrodes of an aperiodically accelerated isothermal galvanic cell. During the experiments rods cut from cc-AgI and contacted by silver electrodes were dropped towards a target made of plasticine. Meanwhile a voltage was observed, due to the length of the galvanic cell, to the mass to charge ratio of the silver cations and to the velocity of the sample just before impaction. Further
3168
G. Pajonk
and H. Rickert
experiments of Betsch, Rickert and Wagner [2] established the inertia effect by detecting impaction caused voltage pulses at samples made of Rb AgdIs. For silver containing cationic conductors a sensoric sensitivity of 0.11 PV g-i cm-i was experimentally proved. On rubidium silver iodide a transference number of the silver ions of nearly unity and a cationic conductivity of 0.26R-’ cm-’ is obtained. Additionally Koch and Rickert [3] observed ACvoltages at sinusoidally accelerated samples for a frequency range between 15 Hz and 5 kHz and for accelerations up to 140g (1 g = 9.81 m ss2). THEORETICAL
CONSIDERATIONS
If superionic conductors are dropped towards a target and stopped at once to velocity zero, different forces work on the rigid crystal lattice as well as on the mobile charge carriers. The force Fdedecelerates the sample, acting in the direction of the instantaneous acceleration a& and inverse to the vector of
1
l,5
the impaction path impacts, the mobile plane are accelerated
p*;, = I?lionX 2,
4 = qi,”
of disordered
p” alumina-ceramics.
X E
(2)
where FE = electric force; mlon = ionic charge; E = electric field strength. Because the electric field appears from a period of 1 ps, but the impaction lasts a few milliseconds, the balance condition
mien
1ooorr (K-l] -b Fig. I. Ionic conductivities
(1)
where F,, = inertia force; mien = ionic mass; a = instantaneous acceleration. Therefore, an electric field corresponding to the separation of positive and negative charges occurs and the mobile charge carriers are inversely redriven to the inertia effect by
2,5
2
(Fig. 2). During short-lasting cations inside the conduction by inertia forces as given by
3
x d =
3.5
qion x
E
4
(4)
Detection of the instantaneous
acceleration using superionic conducting ceramics U = 2.
3169
1*4n2v2t2.xo*sin[2nv.t], U = CJ0sin[2nv*t],
(10)
where z = degree of ionization; e = unit charge; UO = voltage amplitude, should be measured between the electrodes of a sinusoidally accelerated cell. Uo=~.1.4n2v2t2.Xo=~.l.~.
l Ag
0’
Fig. 2. Charge displacement in a-A@ caused by an impact. is fulfilled at every moment of the event. According to the definition of the electric field strength E=
-gradb,
(5)
I
U=-
Edx=-Exl, s0
where inertia entf
(I=-pxu,
(6)
where 4 = electric potential; 1= length of the galvanic cell; U = inertia emf, should be measured between the electrodes of a galvanic cell containing solid electrolytes. It should be directly proportional to the mass to charge ratio of the mobile charge carriers, to the length of the galvanic cell and to the instantaneous acceleration. If solid state ionics are accelerated by harmonic motions, a linear dependency of the inertia voltage on the instantaneous acceleration is still expected. As shown in the following, the acceleration is proportional to the deflection from equilibrium. x = xo.sin[2nv.t], a = g
= -(2nv.f)2.xo.sin[2nv.r]
(7)
= -(237v.t)2.x,
(8) a = uo.sin[2nv.t],
(9)
where x = point function; x0 = maximum of deflection; I = time; v = frequency of the harmonic motion; uo = acceleration amplitude. The point function as well as the acceleration are sinusoidal and complementary phase shifted. The acceleration amplitude Q corresponds to the maximum of deflection from the equilibrium x0 as well as on the square of the exiting frequency v. Therefore, an alternating voltage
(11)
Its voltage amplitude should be proportional to the mass to charge ratio of the charge carriers, to the length of the electrolyte as well as to the amplitude of the acceleration or to the maximum deflection from the balance x0 and its exiting frequency. ION EXCHANGE EXPERIMENTS Many mono-, bi- and trivalent B and b”-alumina isomorphs have been produced from the sodium compound by ion exchange, using salt melts for reagent. If the melting points were skillfully chosen, the high ionic mobility in the melt ensured a fast approximation of the thermodynamic balance. The choice of temperature cohered with the balances as well as with the kinetics of the exchange reaction. The balance conditions depending on the melting composition were described by ion exchange isotherms. If the balance for the exchangable species was established at the solid side, an increase in temperature caused a decrease of the equilibrium constant. Otherwise raising the temperature just assured the exchange of cations preferring the melt. At low exchange temperatures the exchange was kinetically impeded and the reaction proceeded slowly, due to the small coefficients of diffusion. A strong surplus of the melting reagent accelerated the reaction in this case. The balance conditions were influenced by the sphere of cation coordination, the ionic diameters and the structure of the conduction plane. Growing complex compounds with the cations inside the melt, big polarizable anions preferred the equilibrium on the melting side. Because their tendency to form complexes and their melting points of approx. 300°C are generally low, nitrate salts were preferred for exchange reagents (Fig. 3). fl”-alumina based cationic conductors were prepared by ion exchange procedures from polycrystalline raw materials, consisting of 87.5% Al203, 9.0% Na20 and 3.5% MgO (density: 3.16 g/cm’) as reported by ABB Heidelberg. Primarily brick shaped samples (approx. 19 mm x 6 mm x 5.5 mm) were cut from sintered compacts (diameter: 26.5 mm, gauge: 5.8 mm) by water cooled diamond tools, heated to 400°C in vacuum to remove water content, sealed in quartz tubes and immersed in salt melts. The exchange conditions are listed in Table 1.
3170
G. Pajonk
Fig. 3. Ion e:xchange
isotherms
of alkali
fi-aluminas
and H. Rickert
in molten
After the reaction had finished, the samples were taken from the liquid, washed in distilled water for three minutes and dried in vacuum at 150°C. The completeness of the exchange reaction was checked by weight exchange in the case of compact samples or by EDX analysis for pulverized substances. This way Ag+/?“-aluminas, Pbz+a”-aluminas, K+/Y’aluminas and NH:/?“-aluminas were achieved. The samples, immersed in potassium nitrate and ammonium nitrate solutions, were generally cracked by reaction caused microstress. Therefore, it was impossible to carry out inertia experiments on these compounds. The AC-conductivity (1 kHz) of samples, remaining whole, was measured at room temperature afterwards. On Ag+/Y’-alumina contacted by silver electrodes a cationic conductivity of
nitrates
at 300°C [6]
0 = 3.57 x 10-4R-’ cm-’ and on Pb2+/Y’-alumina contacted by lead of Q = 4.2 x lo-‘a-’ cm-’ was observed.
SAMPLE
PREPARATION
To prove the inertia effect on /Y-alumina electrolytes, different kinds of specimen were assembled and accelerated by impaction or by harmonic motion. The different specimens are shown in Figs 4 and 5. To create isothermal galvanic cells of the type MelMe*~“-alumina(porY~, ,IMe with Me z Ag, Cu, Me* z Ag, Na,
Table 1. Exchange
conditions
for fi”alumina
electrolytes
Electrolyte
Starting
Ag+ /I”-alumina K+ p”-alumina NH: 8”-alumina Pb2+ /Y-alumina
Na+ b”-alumina Na+ )?I”-alumina Na+ 8”-alumina Na+ /Y-alumina Na+/Pbr+ B”-alumina
material
Delay for exchange
Reagent AgNO, KNOs NHdNO, PbClz PbClr
350 364 220 378 378
96 h 168h 168h 209 h 200 h
Exchange (Gew%) 100% 100% 100% 10% 95%
Comment
Fractured Fractured 2 step reaction
Detection of the instantaneous
screw
acceleration using superionic conducting ceramics
call
aluminum sleeve
I
braided
cable
electmde
dms adhesive
Galuminia
electrolyte
SMD- sofdetinrl
Fig. 4. Specimen for impactions at low accelerations up to 500g as well as for experiments on the electrodynamic multivibrator. brick shaped p-alumina samples were metallized on the face by burn-in- or vacuum-metallization. Silver wires were fixed to the electrodes, covered by silicon hoses for electrical insulation and externally soldered to a radio-screened twin-cored braided cable. To ensure ohmic contact to the cell, different procedures were investigated, like burn-in varnishing, SMD soldering by a silver containing agent or bonding by a silver-containing, electrically-conducting adhesive. Only by adhesive bonding was a high thermo-mechanical strength achieved. For damage protection as well as for radio screening the electrolytes were clad by aluminum sleeves. .
I=
The range of application of the specimen, displayed in Fig. 4, was limited by its fracturing properties. At high values of acceleration the joins between all parts were fractured more and more by microcracks. Different metal components were plastically deformed. Furthermore, the detected pulses were distorted by deformation-caused interferences. Therefore, the construction should be optimized, diminishing the number of joins to an optimum quantity. To detect the inertia emf at high accelerations a specimen corresponding to Fig. 5 was developed. Its main element, a ceramic carrier, was cut from a ceramic bar, shortened to 45 mm and rounded at the lower end. Along its diameter a small slot was cut by diamond tools, where the /Y-alumina electrolyte was fitted and well adjusted. Towards this kind of sample the mechanical pulse was transmitted across the sample only by ceramic components, except for a very small adhesive area between the carrier and the electrolyte. Corresponding to an increase in the mechanical properties, high accelerations up to 20,OOOg were obtained.
EXPERIMENTAL Aperiodic events, like impacts, have usually been of complex constitution. Lasting only a few milliseconds, their analysis required sensors and measuring devices with a short time of response. The devices used for our investigations are schematically illustrated in Fig. 6. During the experiment a piezo sensor was mounted on the specimen acting as a reference. When the sample was dropped, the electrolyte emitted a voltage pulse, which was a thousandfold preamplified by a microvolt amplifier and sent to a digital memoryscope. Simultaneously the reference transmitted an equivalent signal across a charge amplifier to the scope. The amplitudes of
to the chargeamplifier
I
I
I
,
tc themicrovolt pnzamplifier
we---e-s
.---------
piezo aceelemmeter
aluminumsleeve micmvdt
----------------__ -----_-----
orcamolificr
8”-aluminaelectrolyte dms adhesive ceramiceatlier
Fig. 5. Specimen for impactions at high accelerations up to 20,ooog. EA 42/2&22--G
3171
Fig. 6. Device to detect emfpulses
caused by impactions.
3172
G. Pajonk
and H. Rickert
both pulses were detected in two channel operation mode and analysed afterwards on screen by cursor. To receive a higher resolution, the pulses were copied to a xy-recorder and evaluated. To investigate p-alumina electrolytes under periodical load, specimens were mounted according to Fig. 4 to an electrodynamic shaker and sinusoidally accelerated (Fig. 7). To measure at temperatures above 25°C a stove was assembled on the top of the shaker. To protect the shaker against overheating the lower end of the sample was cooled by pressurized air. The shaker consisted of a permanent magnet, of a coil supplied by a hf-generator and restoring strings. When an ac-current passed the coil, the specimen holder was deflected from its equilibrium by an electric field and on the other hand restored by the resiliency of the strings. This way a sinusoidal motion was generated. The frequency and amplitude of the oscillation were registered by an integrated piezo sensor and adjusted independently from each other as well as digitally displayed at the generators control unit. The ac-voltage emitted by the oscillating electrolyte was sent to a lock-in-amplifier, that allowed the investigation of periodical signals within a small frequency range. The bandwidth around the frequency of the aspected signal was limited to f 1 Hz by bandpass filters, which were calibrated by a reference voltage from the generator. Because interferences were excluded, very low voltage amplitudes were obtained and digitally displayed at a multimeter. DISCUSSION To investigate the inertia force of mobile cations in b-alumina electrolytes and to establish the linear dependency of the inertia voltage on the instantaneous acceleration many experiments have been carried out on Ag/I”-alumina and Nab”-alumina us a lock-in-amplifier
electrodynamic
shaker Fig. 7. Device to mesure inertia emfs caused by harmonic motions.
4
T =25’C
6
2
4
6
6
10
12
14
16
16
a/WOOg+ Fig. 8. Impacts of AgB”-alumina on plasticine: microdynamits of the single shot and dependency of the voltage on the instantaneous acceleration. piezo accelerometer (sensitivity: 10.79 mV/g) acting as a reference. By the choice of target material one can guide the microdynamic of the single shot and the accomplished acceleration. Characteristic voltage pulses are shown in Figs 8 and 9. On plasticine, accelerations up to 200 g were received. The single shot period usually lasted 2-3 ms. Above IOOg the pulses faded out by increasing vibrations, caused by a plastic caving of the specimen into the target. On aluminum oxide plates sequences of impacts were counted as voltage pulses. Corresponding to the high Young’s modulus of ceramic materials the samples were partially rejected, falling repetitively onto the plate, while driven by their own weight. Their kinetic energy was stepwise transformed to heat and distortion. On ceramics higher accelerations up to 20,OOOg were received and voltages of nearly 4 mV recorded. The single shot period was shortened from 250 ns at 180 g to 75 ns at 20,OOOg (1 g = 9.81 m/s2). The expected linear coherence between the inertia emf and the instantaneous acceleration for galvanic cells of AglAg/?“-aluminalAg-type was experimentally verified throughout the whole range examined. For defined lengths of the electrolyte all values between 30 g and 20,000 g were located on the computed line except for a 57% deviation, whereas the sensory sensitivities of the specimen determined the line gradients. The sensitivity per unit length for galvanic cells like AglAg/?“-aluminalAg was calculated to be 0.1095 PV g-’ cm-i (ie 1.121 PV m-* s2). The detection was limited at the upper side by the level of materials fatigue. Above 20,OOOg the joins between the assembled materials of the specimen failed by microcracks. The investigations on aperiodical events were limited by the thermal resistor noise.
Detection of the instantaneous
acceleration using superionic conducting ceramics
By low pass filtering of 10 kHz for, eg an 18 mm long specimen a noise voltage of 3 PV was observed, corresponding to an acceleration of about 30g. When approximated towards the noise, the recorded values below 50 g were still dissolved with deviations of 15-20%. The effective voltage of noise hardly corresponded to the resistance of the specimen. For a given temperature T and a bandwidth Av, chosen at the amplifier, this voltage could be estimated by using the Nyquist-formula
3173
200
T-25-C
150 > ?lOO 3
u s,e,i = J4kTRAv,
uu= UR,cflx J2,
(12)
where UR = noise voltage; k = Boltzmann’s constant; T = temperature; Av = bandwidth of frequencies; R = gas constant, and the limit of recording EC should be calculated from the signal noise ratio SNR. EC = I/ZSNR
= U./~UR,
(13)
where EC = limit of detection; SNR = signal to noise ratio; U, = inertia emf. For the sample presented in Fig. 8 a resistance of 36.5 kR was obtained at 23°C by impedance spectroscopy. Corresponding to the Nyquist formula a voltage of 3.4 PV and a limit of 34g was found. Investigations on Nab”-alumina electrolytes, metallized on the face by silver, copper, tin or lead electrodes, established the expected linear relation between inertia emf and acceleration on sodium cationic conductors (Fig. 10). On samples contacted by silver electrodes acceleration up to 8000g as well as 4000g at copper electrodes were obtained within a random deviation of + 10%. For specimens made of Nab”-alumina a reduced sensory sensitivity per unit length of 2.34 x lo-* PV g-t cm-’ (ie 0.24 PV
0
0,5
2
4
6
8
IQ
12
14
16
10
a/looOg--+ Fig. 9. Reboundings of Agp”-alumina on ceramics: microdynamics of the event and dependency of the voltage on the instantaneous acceleration.
2
2,5
3
3,5
4
all000 g+ Fig. 10. Reboundings of Nap”-alumina on ceramics: microdynamics of the event and dependency of the voltage on the instantaneous acceleration. m-* s*) was found, due to the minor mass to charge
ratio of the sodium cations and according to their lower electric field strength (Fig. 11). For aperiodical events the lower limit of detection was proved to be 15og. Further experiments established that ceramic electrolytes could be used for sensors detecting periodically recurring events. Therefore, galvanic cells of the AglAg/3”-aluminalAg-type were submitted to a harmonic motion in a frequency range between 400 Hz and 3 kHz. Corresponding to the exciting harmonic motion, an alternating voltage was detected between the poles of the galvanic cell (Fig. 13). For
c
0
1,5
1
0
I
1
2
//
3
4
5
6
7
8
a11000gh Fig. 11. Dependency of the electric field on the atomic mass of the mobile charges.
G. Pajonk and H. Rickert
3174
.
15
x
T
x
0
Ag 1AgWdumina v-48oHz
( Ag
*_2yc
v-9M)Hz v-146lHz
10
20
30
40
50
60
70
80
SO
0
5 101~20253035145055606570
a/g -4
aI0 Fig. 12. AgB”-alumina frequencies.
specimen
oscillating
at different
the whole frequency range the proprotionality has been frequency-independent proved with high precision (Fig. 12). Taking the different mass to charge ratio into account, this claim was also valid for other representatives of the /I-alumina class, such as Nab”-alumina (Fig. 13). Subsequently, no proof was found for a temperature dependency of the inertia effect (Fig. 14), instead of a decline of the thermal noise with increasing conductivity. Other features of the assembled components, like phase transformations, various
A~Na8’4umlnalAg I-
Y =
0
10
20
18.8mm. T=
1.2kHz w- 1tiz
30 a/g
40
50
00
Fig. 14. Ag/?“-alumina specimen: oscillating at different temperatures. thermal expansions and high temperature corrosion processes, were responsible for a temperature-dependent limitation. Therefore, above 600°C measurements were impossible.
CONCLUSIONS We have proved that it is possible to detect short lasting aperiodic events as well as periodical processes by means of galvanic cells made from b-alumina ceramics. The microdynamics of a physical event were completely displayed. Particular events lasting a few nanoseconds were still resolved. The time limitation of recording corresponded to the electric time-constant of the material, ie the delay to induce the electric field. The sensory sensitivity per unit length for galvanic cells like AglAg/Y’-aluminalAg was found at 0.1095pV g-l cm-’ (ie 1.121 PV m-* s*) with a maximum measurement deviation of f 7% as well as at 2.34 x lo-* PV g-l cm-’ (ie 0.24 PV m-* s2) and deviations of f 10% for specimens made of Nap”-alumina. The lower limit of detection of accelerations was determined by the thermal noise of resistance of the solid electrolyte, due to its conductivity and the volume of the sample. It was essentially limited on the upper side by the kind of sample construction and by the mechanical qualities of the chosen materials, especially the shear and fracture strengths of the electrolyte, carriers and joins.
d
Fig. 13. Periodically accelerated Nab”-alumina specimen: microdynamics of the event and dependency of the voltage on the instantaneous acceleration.
REFERENCES 1. M. Be&h,
H. Rickert
Phys. 89,
1I3 (1985)
and R. Wagner,
Ber. Eunsenges.
Detection of the instantaneous
acceleration using superionic conducting ceramics
2. M. Betsch, H. Rickert and R. Wagner, SolidS!afe Ionics 3. 4. 5. 6. 7.
18/19, 1193 (1986). W. Koch and H. Rickert, Solid State Ionics 28-30, 1664 (1988). R. C. Tolman and T. D. Stewart, P&s. Rev. 8, 97 (1916). W. L. Roth, J. Solid State Chem. 4, 60 (1972). J. T. Kummer, Progr. Solid State Chem. 7, 141 (1972). Y.-F. Yu Yao and J. T. Kummer, J. Inorg. Nucl. Chem. 29, 2453 (1967).
3175
8. J. T. Kummer, Inorg. Synrh. 19, 51 (1979). 9. W. Maly-Schreiber, P. Linhardt and M. W. Breiter, Solid State Ionics 13, 131 (1987). 10. S. Rohrer and G. C. Farrington, Solid State Ionics 28-30, 142 (1988). Il. J. Tegenfeld, M. Underwood and G. C. Farrington, Solid State Ionics 18 & 19, 668 (1986). 12. H. J. Kennedy, in Topics in Applied Physics, p. 105-141. Springer-Verlag. Berlin, Heidelberg (1977).