NBSIR 75-749

STABLE PRESSURE TRANSDUCER

Jack H. Colwell

National Bureau of Standards

Department of Commerce

Washington, D.C. 20234

July 1975

Annual Report

Prepared for

CCG/Army/Navy

US Army Missile Command

US Army Metrology and Calibration Center

Redstone Arsenal , AL 35809

Naval Plant Representative

Metrology Engineering Center

1675 W. Mission Blvd.

Pomona, CA 91766

ABSTRACT

In this report we describe the progress over the past year in the development of a capacitive pressure transducer which utilizes solid dielectric

capacitors. The pronounced temperature dependence of the individual capacitors is circumvented by measuring the ratio of two capacitors having the same

temperature dependence but markedly different pressure dependence. Of the

materials measured to date, calcite crystals cut parallel and Derpendicul ar to

the crystalline axis most closely meet our criteria. An Invar sample holder

has been fabricated which fits inside a commercial pressure vessel. The combination effectively cancels out adiabatic heating effects within the pressure

vessel which will greatly simplify the thermostating requirements of the transducer.

INTRODUCTION

We are endeavoring to develop a pressure transducer that is capable of

high precision and will possess long term stability. The device is intended

for use as a transfer standard in the dissemination of the absolute pressure

values determined by piston gauges in standards laboratories, but could be used

in any application where pressure measurements of high accuracy are required.

Current developments have centered on a capacitance gauge in which the

capacitor is a disc of solid dielectric material with metallic electrodes

deposited directly on its surfaces. With a capacitor made from a hard, preferably crystalline, material and subjected only to hydrostatic forces within

a pressure vessel, one would not expect any physical deterioration of the

capacitor with use.

For most materials which are of interest to us, the capacitance changes

about VI upon being subjected to a pressure of 140 MPa (20,000 psi), the

maximum pressure we are currently considering. Using modern ac bridge techniques, three terminal capacitors, and accurate ratio transformers,

capacitances can, be readily measured to 1:10 7

, so that pressure resolution of

about 700 Pa (0.1 psi) can be achieved. The major drawback with the device is

that the capacitors are, in general, very temperature dependent. For example,

with the widely studied material CaF 2 > a change of 1 mK is equivalent to a

pressure change of 7000 Pa (1 psi). The search for materials having a

smaller temperature dependence while still maintaining a sufficiently large

pressure dependence has produced some improvement in this regard, but it has

not substantially altered the problem. BN and AS2S3 are the most notable

examples in that their ratios of temperature to pressure dependences are an

order of magnitude smaller than CaF 2 but they would still require millikelvin

thermostating in order for the achievable pressure resolution to be realized.

Two separate schemes have evolved as ways of getting around the temperature problem; both use two transducer-type capacitors in opposite arms of

the measurement bridge so that it is the ratio of the two capacitors that is

being determined. The first approach, which is being pursued by James Miller

of the Redstone Arsenal, uses two capacitors of the same material . One

capacitor is placed in the pressure vessel and the other is outside at atmospheric

pressure. In this arrangement, the temperature dependence of the pressure

measurement is canceled to first order when the two capacitors are at the

same temperature but this condition creates a difficulty since the two

capacitors must be separated by a pressure-bearing wall. The second approach,

the one being pursued in this laboratory, is to place both capacitors in the

pressure vessel and to use two materials having the same temperature

dependence but widely differing pressure dependences. This approach puts

stringent requirements on the choice of materials since the temperature and

pressure derivatives of the ratio measurement

R = Cj/C2

1 dC}

-J dC 2

C 1 dT~ " C2 dT~

1 dC} -j dC 2 Ci dp C 2 HpThe behavior of the pair, therefore, depends on the fractional dependences

which are properties of the material and do not depend on the magnitude of the

individual capacitances. When we began pursuing this course a year ago there

were no known pairs of materials that met our requirements. We began our

search by looking at several anisotropic materials since crystals of these

materials cut parallel and perpendicular to the crystalline axis frequently

can be written as 1 dR

R dT

and

1 dR

I <Jp

have widely different properties. Capacitors with intermediate values could

then be obtained by cutting the crystal at the proper angle between the major

axes. This approach did not produce the anticipated results but we did find

that the parallel and perpendicular cuts of calcite (CaC0 3 ) as a pair came

close to meeting our requirements. We have since made detailed measurements

with the calcite pair against a piston gauge and found the results very

encouraging. Accordingly, we have begun the development of a prototype device

with the idea of using a calcite pair as the capacitor materials. In this

report we describe the pressure vessel and sample holder that has been

fabricated for the device. We discuss the considerations that went into the

design of the device and the thermostating that will be required for its

effective operation.

Thermal Eguil ibration and Thermostating Considerations

To establish the thermal requirements for a pressure transducer

utilizing a pair of calcite capacitors we must first determine the pressure

resolution that is to be sought. We are predicting that the uncertainty in

the capacitance bridge which arises from the limited accuracy of the ratio

transformer will be about 1:10 7

. With the calcite pair this corresponds to

an uncertainty in the pressure determination of about 1700 Pa (0.25 psi).

Since the bridge resolution will exceed this value, let us consider the

thermal requirements we will need to achieve a pressure resolution of

700 Pa = 0.1 psi.

We can identify three ways that thermal effects can cause errors in the

pressure determination. The first and most obvious is for the two capacitors

to be at a different temperature because of a temperature gradient within the

system. This error depends on the temperature dependence of the individual

capacitances and for resolution of 700 Pa requires that the two capacitors be

within 0.1 mK of each other.

The second effect comes from the fact that a pressure determination depends

on a ratio measurement made at high pressure relative to one made at atmospheric pressm

The temperature of the transducer at the two pressures must be within limits

which, for the calcite pair, are determined mainly by the temperature dependence

of the ratio measurement. The pressure resolution of 700 Pa requires that

these two temperatures be within about 10 mK.

The third temperature effect arises because the pressure dependence

of the ratio measurement is itself temperature dependent. As a result the

pressure gauge must be used at the same temperature as it was during its

calibration. The calcite pair is very good in this respect and the

temperature of the device need only be maintained with a precision of

about 75 mK in order to have precision in the pressure measurement to 700 Pa

at pressures as large as 140 MPa.

Ad i aba ti c Heating

The thermostating of the pressure transducer is complicated by the

adiabatic heating effects which occur whenever the pressure is changed. When

the pressure transducer is pressurized, all the material inside the pressure

vessel (the samples, sample holder, and pressurizing oil) are under compressive

stress and increase in temperature. The pressure vessel itself is placed under

a net tensile stress when the nressure increases and as a result, it cools.

The reverse occurs when the transducer is depressurized . Consequently, in

thermostating the transducer one would need, in general, the capability of both

heating and cooling the system. Also, with part of the system warming and others

cooling, a rapidly-responding thermostat would probably prolong the period of

equil ibration

.

We are attempting to get around this Droblem by trying to equate the

heating and cooling that occur within the transducer during any pressure

change, so that there will be little or no temperature change when thermal

equilibrium is reestablished.

The amount of heating that occurs in a piece of material under compressive

or tensile stress is given by

0 = TVsaP ,

where 3 is the average thermal expansion coefficient for the range of the

pressure change, aP, and V is the average volume.

The cooling that occurs in the pressure vessel itself when (see Appendix,

April 1975 report) it is internally pressurized is equal in magnitude to the

amount of heating that would occur upon externally pressurizing a piece of steel

of the same composition as that of the vessel and having the same volume as

the internal volume of the vessel. In other words, if we could completely

fill the inside of the vessel with a steel plug and then pressurize the system

using a negligibly small amount of oil, there would be no temperature change

v/hen equilibrium is reestablished.

For steels such as that of the pressure vessel, the thermal expansion

coefficient is about 55 in units of 10" 6 /K. The paraffin oil we have been using

as a pressurizing fluid has a coefficient of about 750. Since we must have at

least a small quantity of oil in the transducer, we need to offset its large

coefficient by including in the pressure vessel a large amount of material

with a thermal expansion coefficient smaller than steel. Fortunately, there

is a suitable material, Invar, a high nickel steel, that has a thermal expansion

coefficient of only 3.6 units. By limiting the volume of oil in the pressure

vessel to about 7% of the total volume and filling the rest of available volume

With Invar, we calculate (see April, 1975 report for detailed calculations) that

temperature changes can be kept at a negligible level. The heating effects

cannot be eliminated completely because the oil is highly compressible so that

its thermal expansion is a marked function of the pressure. Even so, we

predict that the temperature changes of the transducer for pressure changes in t

range 0 to 140 MPa will not exceed 3 mK. This value is well below the 10 mK

limit required for 700 Pa resolution with a calcite pair transducer.

We have checked out these ideas in a laboratory experiment in which the

constant temperature bath of our experimental system was used as a crude

calorimeter. The pressure vessel was alternately fitted with a steel or Invar

plug which filled about 90% of the internal volume of the vessel. The

relative temperature changes of the system with the different plugs were then

observed for various pressure changes. The results indicate that our

calculations were basically correct. There was an asymmetry in the results in

that there was a snail net heating in the pressuri zi ng-depressuri zi ng cycles.

This could be an experimental error but it ray also be a ramification of the

internal friction of the materials involved. We do not think that this net

heating effect is large enough to be of concern. The results also indicate

that the expansion coefficient of the oil may not be as pronounced a function of

the pressure as originally thought. If 'this is true, it may be possible to keep

the temperature changes in the system smaller than originally calculated.

In any case, the predicted maximum temperature change of 3 mK upon

pressurizing or depressurizing the transducer is sufficiently below the 10 mK

stability requirement stated in the previous section, that the temperature

of the transducer will not require any adjustment for the capacitance measurements. All that is required is that the transducer be well insulated except

for a weak thermal link to a thermostated heat sink so that its long term

temperature stability is assured.

Pressure Vessel and Invar Sample Holder

For the prototype pressure transducer we are using a commercial

(High Pressure Equipment Company) pressure vessel with a pressure rating

of 20,000 psi (138 MPa). The vessel has a \h inch I.D. and a depth of

6 inches and comes with a pressure connection in the bottom of the vessel

and one in the center of the one-piece threaded closure. He have modified

the closure with three additional pressure connections to allow for the

separate entry of the three electrical feed-throughs required for the capacitance measurements

.

An Invar sample holder has been fabricated which attaches to the

bottom of the pressure closure and effectively fills the entire volume of

the pressure vessel. The sample holder, diagramed in Fig. 1, was made from

six V' pi ates, which, when bolted together, form the cylindrical plug shown on

the left. The central two pieces hold the low voltage el ectrode, which is

common to both capacitors, and the capacitors themselves fit into recesses on

the outside of these pieces. The next two pieces hold the high voltage

electrodes, which -make contact with the back of the capacitors. The three

electrodes are made from small gold-deposited bellows, the same as used in

our experimental system. The position of two outer electrodes can be adjusted

to ensure sufficient force on the contacts for electrical continuity. The

outer two plates simply fill out the volume.

The volume of oil which the pressure vessel will hold with this Invar

sample holder in place is less than that estimated for minimizing adiabatic

heating effects. This can easily be adjusted later by machining away part of

the Invar holder or preferably substituting plates fabricated from steel or

some other solid material with a thermal expansion coefficient larger than

Invar.

The sample holder was designed so that the two capacitors are situated

in axially symmetric positions within the pressure vessel. As a result the

capacitors should always see the same temperature gradients and should be at

the same temperature. Whether they will remain within the 0.1 mK temperature

difference desired for the transducer with calcite capacitors will have to

be determined.

The new pressure vessel and sample holder will be tested with

capacitors in place as soon as new electrical feedthroughs can be made.

The feedthroughs will be similar to those in our experimental device which

use the sheathed thermocouple cables.

Capacitor Materials and Deposited Electrodes

Although we are proceeding with the development of a transducer using

calcite capacitors, we have not ruled out the use of other capacitor

combinations. In Fig. 2 are collected together values of the temperature

and pressure dependence of the capacitance of numerous materials. What we

require for a useful transducer are two materials that, on this plot, are

displaced from each other by a considerable distance but along a vertical line.

At this time, the only suitable combinations, in addition to the calcite pair,

are the combinations of a calcite crystal with either KC1 or KBr. The potential

pressure resolution with a parallel -cut calcite. capacitor in combination with

KBr is more than three times that of the calcite pair. For the same resolution,

therefore, the allowable temperature gradient between the two capacitors within

the device could be three times greater with the calcite-KBr combination, but the

other two thermal requirements will be similar for the two combinations.

We have attempted to test these combinations in the laboratory but got

very anomalous behavior with all our potassium halide capacitors. The

aluminum electrodes that had been evaporated onto these crystals looked good,

but the adherence was very poor. The coatings could be removed completely with

scotch tape. We think the erratic behavior we observed may be due to gaps

developing between the crystal and the coating. Facilities to gold sputter

electrodes onto samples may be available to us shortly and we will try th\$ procedu

with the alkali halides to determine if it will improve the adherence of the electrodes. It will also be worthwhile to test the gold sputtering with calcite

crystals, for there is some indication that the aluminum electrodes we have

been using may be reacting with these crystals. We have detected a slight

discoloration of the aluminum coatings on capacitors that have been made up

for about six months. This could be due to oxidation of the outer

aluminum surface, but it must be checked out.

It would be advantageous to find a material with a negative pressure

coefficient and a temperature coefficient matching either BN or As 2 S 3

. A

combination of this type with the smaller temperature dependence of the

individual capacitors would alleviate the requirement of close thermal

equilibration between the two capacitors that is so stringent with the calcite

pair or calcite-potassium halide combination. Since the negative pressure

coefficient is the most typical behavior, the chances are good that such a

material exists. Accordingly, we are continuing to look at other materials

that are appropriate as transducer capacitors. •

Automati c Capaci tance Bridge

The assembly of the limited-range automatic capacitance bridge intended

for use with the pressure transducer is nearly complete. All the logic

circuits have been built as originally designed and are operational. The

bridge has been tested to some extent on the bench top using standard

capacitors and will be check out shortly with the actual transducer.

One additional stage of amplification with additional filtering is

going to be added,which will also include the automatic phase-balancing

circuit. A small preamplifier has been built which will go directly on the

pressure transducer. thereby reducing the effects of the capacitance in the

leads to the bridge. The bridge circuits are completely documented in a way

which should facilitate their reproduction. Complete blue prints have been

maintained and, in addition, wiring locations have been put on punch cards.

Print-outs of different sorting sequences of the cards have been valuable aids

in both the original wiring and in trouble-shooting.

Figure Captions

Fig. 1 Invar sample holder shown assembled on the left and disassembled

to the right. The sample holder is 1^ inches in diameter and

and 6 inches long and fits snugly in the cavity of a commercial

pressure vessel. The dielectric capacitors fit into recesses of

the inner two plates and electrical connections are made using

small bellows as spring contacts.

Fig. 2 The pressure dependence of the capacitance of various materials

as a function of their temperature dependence. The temperature

dependence is the atmospheric pressure yalue and the pressure dependence

was determined at 35°C. The lines shown join the values measured

parallel and perpendicular to the crystalline axis of anisotropic

materials and represent temperature dependences that could be

realized for crystals cut at intermediate angles.