Sensors and Actuators B 55 (1999) 217–221

A capacitive pressure gauge as a reliable transfer pressure standard

Yashwant Kumar a, Vinay Kumar a, Kamlesh K. Jain a*, Subhash C. Kashyap b

a Force and Hardness Standards, National Physical Laboratory, New Delhi 110012, Indiab Department of Physics, Indian Institute of Technology, New Delhi 110016, India

Received 20 April 1998; received in revised form 8 December 1998; accepted 13 December 1998

Abstract

This paper describes the performance of an alternative capacitive pressure gauge using lead iron tungstate as a capacitiveelement over a pressure range of 418 MPa. A commercial strain gauge pressure transducer is used to get the consistency in thecalibration equation of the pressure transducer using the piston gauge pressure standard when compared with the calibrationequation of the pressure transducer obtained using the capacitive pressure gauge. A close agreement better than 1×10−3 (overall accuracy of the pressure transducer is 95×10−3) demonstrate for the first time the use of the capacitive pressure gauge asa reliable pressure standard where the required accuracy in the pressure measured is below 1×10−3. © 1999 Elsevier Science S.A.All rights reserved.

Keywords: Transducer; Pressure measurements; Pressure standards; Hydraulic pressures

1. Introduction

The measurement of hydrostatic pressure has tradi-tionally been performed in most national metrologicallaboratories through the use of liquid column manome-ters and piston gauges, generally regarded as first prin-ciple instruments [1–5]. In general, a primary pressurestandard establishes a pressure scale in terms of forceper unit area without resorting to calibration againstthe other pressure standards of higher accuracy. How-ever, when a piston gauge is used as a secondarystandard, its effective area is determined by comparisonagainst another piston gauge of known effective area oragainst a mercury manometer. A piston gauge is suc-cessfully used over a medium range of pressures up to280 MPa, and is serving as a reliable, portable andreproducible pressure transfer standard to promote theuniformity in the pressure measurement. It also helps totrace out the possible systematic errors, if any, in thepressure measured by the standards established in dif-ferent metrological laboratories. These gauges, if re-quired to be used beyond 280 MPa, become bulky and

expensive both to purchase and operate, and can not betransported easily. This seriously limits their utility.

The pressure transfer standard useful in the highpressure region measures pressure in terms of someother suitable physical property whose relation to pres-sure is determined by a calibration, i.e. by comparisonwith an instrument of higher accuracy. A wide choiceof physical properties, which vary with pressure, isavailable for their exploitation as pressure transducer[6]. Though a large variety of high-pressure transducersare available, only the manganin resistive transducer [7]is extensively used as a pressure transfer standard (inthe high-pressure region). Of late, other strain gaugetransducers are also beginning to be used and indeedcalibrated strain gauge transducers [8] are commercialavailable to measure pressures up to a GPa. Thoughthese gauges are in use, these are handicapped with zeroshift with time, hysteresis, low pressure cut-off andlimited sensitivity; and hence need frequent calibrationagainst the primary pressure standards. It thus impliesthat one has to find out an alternative pressure trans-ducer wherein these effects should be minimized, if noteliminated completely.

Efforts have been made for quite some time tounderstand the pressure dependence of relative permit-tivity through the variation of capacitance with applied

* Corresponding author. Tel.: +91-11-5787161; fax: +91-11-5752678.

E-mail address: root@csnpl.ren.nic.in (K.K. Jain)

0925-4005/99/$ - see front matter © 1999 Elsevier Science S.A. All rights reserved.

PII: S 0 9 2 5 -4005 (99 )00088 -X

Y. Kumar et al. / Sensors and Actuators B 55 (1999) 217–221218

pressure. The studies of capacitance as a function of theapplied pressure on a few crystalline and poly-crys-talline materials [9–11] have revealed their limited pres-sure coefficient and relatively large temperaturecoefficient of capacitance. It was only recently that thepresent authors carried out dielectric studies as a func-tion of applied hydrostatic pressures on lead basedferroelectric relaxors [12,13], thereby demonstratingtheir usefulness in pressure gauging. Ferroelectric relax-ors have been known for many years for their uniqueproperties like high relative permittivity, broad max-ima, relatively low firing temperatures with nearly zerothermal expansion and low aging effect, etc. Theseproperties make them attractive for a number of appli-cations like multilayer layer capacitors, actuators, andpiezo-transducer and in medical ultrasonics, etc. [14–17]. These studies [12,13] have thus added one moreapplication of the ferroelectric relaxor, as a pressuregauge, in the already existing long list.

In the present investigation, the systematic studies ofthe capacitance and the dielectric loss are carried outon lead iron tungstate (PFW) as a function of theapplied high hydrostatic pressure ranging from 0.1 to418 MPa, and at temperatures ranging from 291 to 303K, respectively. The experimental data of the relativepermittivity (or) as a function of the applied pressure isexpressed in the form a second order polynomial cali-bration equation of a pressure transducer (herein afterdesignated as transducer). The results of an indepen-dent calibration of a transducer against a laboratorypiston gauge pressure standard and the PFW capaci-tance pressure gauge over a pressure region up to 418MPa are reported here.

2. Experimental

The specimens of PFW were prepared using highpurity oxides (PbO, 99.9%; Fe2O3, 99.5%; and WO3,99.99%, from Aldrich, USA) by the conventional solidstate sintering method. All of the sintered disks of 18mm in diameter and 1.4–1.8 mm in thickness werepolished and silver electrodes with a guard ring on oneface of the disk were deposited by vacuum evaporation,using a special mask. With the given specimen dimen-sions, the width of the guard ring was suitably adjustedto ensure that there was no fringing effect [9].

A specimen was placed in a specially designed cellthat can be pressurized directly to a maximum of 600MPa. The capacitance and the dissipation factor weremeasured at a fixed frequency of 1 kHz using anautomatic digital capacitance bridge with an accuracyof 90.1 ppm in the capacitance range of interest. Forestimating the hysteresis, observations were made overa complete pressure cycle, i.e. first by increasing andthen by decreasing the pressure at the same tempera-

ture. The pressure is transmitted through diethyl hexylsebacate fluid as it does not react with the specimen,and its viscosity does not change appreciably over thepressure range of interest. The pressure was measuredwith accuracy better than 90.03%. The cell was im-mersed in a constant temperature bath capable of main-taining temperature within 90.05 K duringmeasurement. The temperature of a specimen was mea-sured with a chromel–alumel thermocouple placed justnear the specimen using a digital temperature indicatorhaving a resolution of 0.01 K. The pressure effect onthe chromel–alumel thermocouple and the consequenttemperature correction are quite small for the condi-tions in the present experiment.

The dead weight piston gauge [18] used as a sec-ondary pressure standard is equipped with a simple-type piston and cylinder assembly having a full-scalepressure of 500 MPa. The effective area and the pres-sure coefficient of the piston-cylinder assembly of thegauge were estimated in the laboratory by calibratingthe secondary standard against primary controlledclearance pressure standard that has a full pressurerange of 500 MPa. The value of 3s uncertainty (99.7%confidence level) obtained for secondary standard is9300 ppm.

The strain gauge transducer of 1.4 GPa (full scale)has a sensitivity of 0.02 mV MPa−1. The overall accu-racy of the pressure measured by the transducer was95×10−3 (full scale). The input voltage was suppliedwith a highly stabilized DC power supply and itsoutput was measured with an autoranging digital multi-meter having a resolution of 10 mV.

3. Results and discussions

3.1. Capaciti6e pressure gauge

The relative permittivity was calculated from thecapacitance measured directly by the capacitance bridgewithout considering the compressibility of the speci-men, as in the present case only a relative change in thepermittivity is meaningful. The relative permittivity ofPFW as a function of applied hydrostatic pressure ascalculated at 1 kHz while increasing the pressure insteps arbitrarily fixed at 49, 96.5, 142.5, 189,235, 280.5,326, 373 and 418 MPa, respectively and decreasing thesame from 418 MPa to atmospheric pressure, are plot-ted in Fig. 1. At each pressure point, three observationswere made, and three such complete pressure cycleswere carried out under identical conditions. It is ob-served that the relative permittivity (or) decreases nearlylinearly with the increase of applied pressure. The rela-tive permittivity was also calculated at different temper-atures and at atmospheric pressure. From the aboveobservation, the average values of the pressure and

Y. Kumar et al. / Sensors and Actuators B 55 (1999) 217–221 219

temperature coefficients of relative permittivity (or) arecalculated as −530×10−12 Pa and −0.007 K, respec-tively. The behavior of relative permittivity studied as afunction of temperature is observed to follow the samepattern, and the absolute value of or decreases under-standably with an increase in the temperature of aspecimen above transition temperature.

In all of the pressure cycles, the observed smallhysteresis reduces to zero when the applied pressureexceeds 200 MPa. Total hysteresis effect in all the threecycles lies between 2.48×10−4 and 3.80×10−4,whereas its magnitude varies from 3.46×10−5 to3.29×10−4 in a cycle. The maximum zero shift, refer-ence taken as before starting the calibration cycles, wasalways less than 0.5 pF over the entire pressure range.This is well below 0.1% of the full scale of the capac-itive element and is sufficiently below the expecteduncertainty of the capacitive gauge. The typical shortterm reproducibility in any of three cycles varies from2.18×10−7 to 1.49×10−6 with pressure increasing upto 418 MPa and from 2.91×10−7 to 6.91×10−7 withpressure decreasing to atmosphere. The relative permit-tivity value of 1074, as calculated at 1 kHz and at 302K, can not be compared directly as the earlier reportedvalues, are at low temperatures (153–253 K) and athigher frequencies [19,20]. It may be mentioned thatthis is the only reported work describing variation of or

with pressure in PFW and at high temperature. Thevalue of dielectric loss is measured to 0.006. The lowloss is desirable for a reproducible gauge. Comparingthese results with the most commonly used manganinresistive transducer which has the pressure and temper-ature coefficient of 23×10−12 Pa and 500 mV K−1

around 300 K, and a hysteresis of the order of 1×

10−3. This shows that the capacitive pressure gauge iscertainly at an advantageous position over the conven-tional transducers.

The best least square fit, using all of the data of thethree pressure cycles over a pressure range 20–418 MPaobtained as a second order interpolation equation

P(MPa)=3289.155–5101.145X+1814.404X2

s=0.481 MPa (1)

where X (=or/ora, where or is the value of relativepermittivity at any pressure P and ora is its value atatmospheric pressure) is the output of the capacitiveelement, corrected for its value at atmospheric pressure.

4. Calibration of strain gauge pressure transducer

In order to visualize the performance of the capaci-tance pressure gauge under reference, the transducer isfirst calibrated against the piston gauge pressure stan-dard and then against the capacitive pressure gauge.Three pressure cycles at 302 K were taken on differentdays in the pressure range up to 418 MPa. At eachpressure point, three observations were made.

The best least square fit, using the data of all threepressure cycles over the pressure range 49–418 MPaobtained as a second order interpolation equation

P(MPa)=0.330021+707.0366X–21.90383X2

s=0.138 MPa (2)

where X=mV V−1 is the output of the transducercorrected for zero.

Fig. 1. Pressure dependence of relative permittivity of PFW in combined three pressure cycles of one of the capacitive element at 1 KHz and at302 K: �, first cycle; �, third cycle.

Y. Kumar et al. / Sensors and Actuators B 55 (1999) 217–221220

Fig. 2. Deviation in the pressure calculated from the calibration equation of the strain gauge pressure transducer obtained from its calibrationagainst the laboratory piston gauge pressure standard from the pressure value calculated using the calibration equation obtained againstcapacitance pressure gauge.

The transducer is again calibrated against the ca-pacitance pressure gauge over the pressure range upto 418 MPa at 302 K, following the above mentionedprocedure. The best least square fit, using all the dataof all the three pressure cycles over the pressure range49–418 MPa obtained as a second order interpolationequation

P(MPa)=0.931044+702.4893X–15.08775X2

s=0.293 MPa (3)

where X=mV V−1 is the output of the transducercorrected for zero

The pressure difference calculated using the two in-dependent calibration equations (Eqs. (2) and (3)) ofthe transducers were of the order of 6.6×10−4 at thefull scale of 418 MPa and this difference is repre-sented graphically in Fig. 2. Considering the stateduncertainty in the pressure measured by the labora-tory piston gauge pressure standard, and the accuracyof the individual transducer and capacitance pressuregauge, the agreement is excellent. The capacitancepressure gauge under reference can be used as a reli-able pressure gauging instrument where the pressureare to be measured within an accuracy of 91×10−3

on the conservative basis. Efforts are being made tofurther improve its accuracy of measurement by low-ering its hysteresis, aging effect and increasing itslong-term stability.

5. Conclusion

A close agreement with in 6.6×10−4 between thecalibration results of the strain gauge pressure trans-ducer calibrated against the piston gauge pressurestandard and the capacitive pressure gauge is ob-served over the whole pressure range. This demon-strates the use of the capacitive pressure gauge as areliable pressure transfer standard where the estimatedaccuracy of 91×10−3 or below is required in thepressure measured.

Acknowledgements

The work was partly supported by a grant in aidunder the INDO–US project. Kamlesh K. Jain isgrateful to Dr C.R. Tilford, Physicist, Process Mea-surement Division, NIST, Gaithersburg, USA for thestimulating discussion and to Professor A.K. Ray-chaudhrui, Director NPL, for permission to publishthe work.

References

[1] P.L.M. Heydemann, B.E. Welch, Experimental Thermodynam-ics, vol. 2B, Butterworths, London, chp. 4, 1975, pp. 147–200

[2] R.S. Dadson, S.L. Lewis, G.N. Peggs, The pressure Balance:

Y. Kumar et al. / Sensors and Actuators B 55 (1999) 217–221 221

Theory and Practice, National Physical Laboratory, chp. 6, HerMajesty’s Stationary Office, London 1982, pp. 131–157

[3] J.K.N. Sharma, K.K. Jain, Accurate measurement of pressure,Pramana J. Phys. 27 (3) (1986) 417–434.

[4] C.R. Tilford, Pressure and Vacuum Measurements, in: W R.Bryant, C.B. Roger (Eds.), Physical Methods in Chemistry,Wiley, 1992.

[5] F. Pavese, G.F. Molinar, Modern Gas Based Temperature andPressure Measurements, chp. 7, Plenum Press, New York, 1992,pp. 273–353

[6] G.N. Peggs, Secondary-standard gauges for accurate pressuremeasurement up to about 1 GPa, High Temp.–High Press. 12(1980) 1–10.

[7] G.F. Molinar, L. Bianchi, Metrological characterization of man-ganin gauges calibrated against the mercury melting line, IXAIRAPT Conference, Albany, New York, 1983.

[8] A.W. Birks, Stain Gauge Pressure Transducer, Internal ReportNo. 1566, Queen’s University of Belfast, 1981.

[9] C. Andeen, J. Fontanella, D. Schuele, A capacitive gauge for theaccurate measurement of high pressure, Rev. Sci. Instrum. 42(1971) 495–496.

[10] J. Colwell, Proceedings of the Eighth AIRAPT Conference, NewYork, September, 1991.

[11] K.K. Jain, S.C. Kashyap, Dielectric properties of Bi12GeO20

(100) single crystals under hydrostatic pressures, High Temp.–High Press. 27/28 (1996) 371–376.

[12] M.V. Radhika Rao, A.M. Umerji, Y. Kumar, K.K. Jain, E.S.Raja Gopal, Effect of high pressure on the dielectric propertiesof relaxor compositions Pb(Fe1/2 Nb1/2)O3]1-x-y-[Pb(Zn1/3 Nb2/

3)O3]x-[BaTiO3]y, J. Mater. Sci. Lett. 16 (1997) 122–125.[13] D. Arun Vijaykumar, Y. Kumar, K.K. Jain., S.C. Kashyap, A.

Ramanan, Development of a ceramic capacitive sensor for themeasurement of high hydrostatic pressures, Proceedings of theInternational Conference on Instrumentation (ICI-1996) 26 (3)(1996).

[14] M. Yonezawa, Low-firing multilayer capacitor materials, Am.Ceram. Soc. Bull. 62 (12) (1983) 1375–1383.

[15] T. Sakai, M. Ishikiriyama, R. Shimazaki, Durability of piezoele-crtic ceramics for an actuator, Jpn. J. Appl. Phys. 31 (1992)3051–3054.

[16] J. Kuwata, K. Uchino, S. Nomura, Phase transitions in thePb(Zn1/3 Nb2/3)O3–PbTiO3. Ferroelectrics 37 (1981) 579–582

[17] S. Nomura, J. Kuwata, Electrostriction in Pb(Zn1/3 Nb2/3)O3.Mater. Res. Bull. 14 (1979) 769–74

[18] K. Jain, C. Ehrlich, J. Houck, Intercomparision of hydrostaticpressure measurements, Rev. Sci. Instrum. 63 (5) (1992) 3127–3135.

[19] N. Yasuda, S. Fujimoto, K. Tanaka, Dielectric properties of

Pb(Fe2/3 W1/3)O3 under pressure. J. Phys. D: Appl. Phys. 18(1985) 1909–1917

[20] N. Yasuda, S. Fujimoto, T. Yoshmura, Pressure and tempera-ture dependence of dielectric properties of Pb(Mg1/2 W1/2)O3. J.Phys. C: Solid State 19 (1986) 1055.

Biographies

Yashwant Kumar completed his postgraduate fromK.G.K. (P.G.) College. Moradabad, in 1994. He is sresearcher in the National Physical Laboratory, NewDehli 110012.

Vinay Kumar completed his postgraduate from K.G.K.(P.G.) College, Moradabad, in 1994. Presently he is aresearcher in Force and Hardness Standards, NationalPhysical Laboratory, New Dehli 110012.

Kamlesh Kumar Jain completed his doctorate from theIndian Institute of Technology, Dehli, in ExperimentalSolid State Physics in 1973 and joined the NationalPhysical Laboratory as a scientist. He has workedextensively in the field of Polymer Physics, PressurePhysics and Pressure Metrology. His current interest isin the field of Force Metrology and in particular, theSensors. Presently, he is the scientist in charge of Forceand Hardness Standards at the National Physical Labo-ratory, New Dehli 110012, India.

Subhash C. Kashyap completed his doctorate from theIndian Institute of Technology, Dehli in 1971 in Exper-imental Solid State Physics. His vast experience in thefield of Crystal Growth and High Temperature Semi-conductors with particular reference to their surfacestudies has given him more than 100 original researchpapers. Until recently, he was Professor of Physics,Department of Physics, Indian Institute of Technology,Dehli before taking up the responsibility as Director ofKamla Nehru Institute of Technology, Sultanpur, UP(India).

..