High pressure–low temperature apparatus for electrical conductivity measurementsR. E. Jones Jr., G. C. Anderson, and W. J. Keeler Citation: Review of Scientific Instruments 46, 1025 (1975); doi: 10.1063/1.1134400 View online: http://dx.doi.org/10.1063/1.1134400 View Table of Contents: http://scitation.aip.org/content/aip/journal/rsi/46/8?ver=pdfcov Published by the AIP Publishing Articles you may be interested in High pressure apparatus for PVT measurements of liquids and plastic crystals at low temperatures Rev. Sci. Instrum. 51, 533 (1980); 10.1063/1.1136230 High PressureLow Temperature Electrical Feedthroughs Rev. Sci. Instrum. 42, 1889 (1971); 10.1063/1.1685033 An Apparatus for Microwave Studies at High Pressures and Low Temperatures Rev. Sci. Instrum. 42, 1215 (1971); 10.1063/1.1685345 Clamp Cell for High PressureLow Temperature XRay and Mössbauer Resonance Studies Rev. Sci. Instrum. 40, 169 (1969); 10.1063/1.1683719 A Pressure Counterbalancing Apparatus for the Measurement of the Electrical Conductivity of AqueousSolutions above Their Critical Temperatures Rev. Sci. Instrum. 22, 765 (1951); 10.1063/1.1745758

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High pressure-low temperature apparatus for electrical conductivity measurements*

R. E. Jones Jr., G. C. Anderson, and W. J. Keeler

Department of Physics, Lakehead University, Thunder Bay, Ontario, Canada

(Received 12 March 1975)

Equipment is described for electrical measurements under hydrostatic pressures to 30 kilobar over the low to room temperature range. The piston and cylinder type pressure vessel of the high-pressure cryostat is actuated directly by a hydraulic ram at room temperature. Thermal isolation is achieved through use of long tension and compression members. Details about the self-stressing, double-walled cylinder are provided. Both the Bi I-II transition and an n-InSb manometer have been used for pressure calibration.

A high-pressure cryostat has been developed for electrical conductivity measurements on samples under hydrostatic conditions from low to room temperatures. An important design criterion was the use of nonmagnetic materials to permit studies involving magnetic fields. Since externally pressurized fluid systems produce lower pressures and Bridgman anvils do not provide truly hydrostatic condi­tions, a piston and cylinder device was used. This type of system has the advantages of being relatively easy to con­struct and operate.

The design incorporates a self-stressing, double-walled cylinder geometry, and beryllium-copper was used to keep the vessel nonmagnetic. Force is applied to the piston of the vessel by a hydraulic press with long tension and compression members for thermal isolation. In this respect, the present design is similar to previous high-pressure cryostats1,2; how­ever, utilization of the outer cylinder of the vessel as a part of the tension member provides a more compact design.

PRESSURE VESSEL

The piston and cylinder pressure vessel is shown in Fig. 1. All parts are of hardened Be-Cu 2S alloy, unless otherwise indicated. The maximum internal pressure PI which the cylinder will withstand is increased by using a stressed

-

~

1025

,--

f-

r--r--

~ r----

~

Be-Cu PISTON

PISTON GUIDE

OUTER CYLINDER

WC PISTON

INNER CYLINDER CAPSULE PLUG TEFLON CAPSULE SAMPLE INSULATED LEAD

TAPERED PLUG CLOSURE BLOCK

CLOSURE BOLT

FIG. 1. High-pressure vessel with self-stressing, double­walled cylinder. The Teflon capsule is filled with a 1: 1 mixture of isoamyl alcohol and n-pentane. The feed­through insulation next to the capsule is MgO-filled epoxy while the remainder of the insulation is pyrophyllite. All other parts are of hard­ened Be-Cu, except for the tungsten-carbide piston and the i hard Be-Cu capsule plug.

Rev. Sci. Instrum., Vol. 46, No.8, August 1975

double wall. The geometry which allows the greatest value of PI for the elastic case can be determined readily from the Lame formulas if one makes the simplification of assuming the maximum principal stress theory of elastic failure.3 ,4

The results are that both walls must have the same ratio K of outer to inner radii and also that the pressure across the interface must be given by

when the internal pressure is at its maximum value

where CTII is the tensile yield strength. In the limiting case, as K becomes very large, this equation reduces to PI =3CTII,

rather than CT y as in the case of a single-walled vessel. It is worth noting that if the more accurate maximum energy of distortion theory of von Mises is employed rather than the maximum principal stress theory, the value of PI for elastic conditions will be reduced somewhat from that pre­dicted above.

In order to provide the interface pressure P 2 we have incorporated Bridgman's concept of self stressing. 5 Here the thrust T on the high-pressure piston also drives the tapered inner cylinder into the matching tapered bore of the outer cylinder. Neglecting friction, the pressure developed at the interface is T/7r(R12_R22), where Rl and R2 are the maxi­mum and minimum outside radii, respectively, of the inner cylinder. The values of Rl and R2 are chosen so that this interface pressure is P 2 when the internal pressure reaches Pl. The average of Rl and R2 is taken as the interface radius in determining K since the inner cylinder is loaded near its center. These results determine the geometry of the cyl­inder once the inner bore radius '1 and maximum pressure are chosen.

Heat-treated Be-Cu 2S is one of the strongest, if not the strongest, nonmagnetic structural metal suited to low­temperature applications. However, it is difficult to make accurate high-stress calculations,' since its unusual stress­strain relationship does not provide a well-defined yield

Copyright © 1975 by the American Institute of Physics 1025

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1026 Jones, Anderson, and Keeler: Electric conductivity measurements 1026

FIG. 2. Detail of the Teflon capsule and elec­trical feed through. The leads to the sample are either platinum or cop­per and the thick lower lead supports the sam­ple. The straight bore with a combined closure block and plug is shown. All dimensions are in millimeters.

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9.53

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II.- 5.61

CAPSULE PLUG

TEFLON CAPSULE

ISOAMYL ALCOHOL a PENTANE

SAMPLE

6.35 lIf..'ll'lk--MgO FILLED EPOXY

1.27~ ...."./kf"_ PYROPHYLLITE

8.89

+ 8.89

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COMBINED CLOSURE PLUG a BLOCK

~~-- FEEDTHROUGH

-<II II'- 3.18 ., r- 2.41

strength. For example, the 0.01% offset yield strength is only 7.9 kilobar, whereas the 0.20% offset yield strength is 11.7 kilobar. Because of this, it is not feasilbe to achieve the design pressure of 30 kilobar using Be-Cu without ex­ceeding the elastic limit unless one uses additional stressed cylinder walls. The double cylinder design developed above has proven useful even though the pressure on the inner bore exceeds the elastic limit. Our pressure vessel has '1=0.318 cm, K2=8, Rl=0.980 cm, R2=0.820 cm, and using 0'1/=11.7 kilobar, a predicted maximum Pl=25.3 kilobar. Friction at the tapered interface reduces the amount of self stressing even though molybdenum-disulfide lubricant is used. While this lowers the limit for elastic behavior of the inner cylinder, it also reduces the stress experienced by the outer cylinder. In our experiments no deformation of the outer cylinder has been observed even though the inner cylinder experiences some plastic deforma­tion at pressures of approximately 20 kilobar and greater. The inner cylinder can be pressed out for replacement when necessary, although new cylinders must be carefully ma­chined to match the tapered interface. The design shown in Fig. 1 utilizes a tapered plug as part of the feed through closure. Recently in order to simplify machining, a smaller, straight-through inner bore of 0.561 cm has been used successfully to 27 kilobar. The closure block and plug then are fabricated as a single piece.

Details of the high-pressure chamber are shown in Fig. 2. The thicker, lower electrical lead supports the sample inside a Teflon capsule filled with a 1: 1 mixture of isoamyl alcohol and n-pentane. This capsule is closed at the upper end by a ~ hard Be-Cu plug, which also provides an elec­trical contact to the pressure vessel. The lower end of the capsule is closed by an insulated, stepped electrical feed­through. The large-diameter section of the insulation is MgO-filled epoxy molded about the feedthrough then machined to final dimensions. Armstrong C-7 resin with W activator was mixed with an equal volume of MgO powder and then heat treated. The remainder of the insula­tion is pyrophyllite with the disk under the step having a thickness of 0.127 cm. Kim6 has reported that to prevent

Rev. Sci. Instrum., Vol. 46, No.8, August 1975

leakage, all common surfaces between the Teflon capsule, the end plugs, and the inner bore must be press fits. Since this makes assembly difficult we have adopted the following scheme: The press fit of the Teflon capsule to the other parts is retained, but the plugs are machined to be light push fits to the bore. After assembly the inner cylinder is pressed into the outer cylinder by a 3 X 104 N thrust. This reduces the inner bore diameter slightly and provides the necessary sealing. The high-pressure piston is of cemented tungsten carbide. Above the pressurized sample region, the bore diameter decreases upon self stressing. This, together with the strain in the piston, necessitates an initial 0.004 cm radial clearance between the bore and the piston.

Manganin heater wire is wrapped around the outer cyl­inder and cemented for thermal contact. A platinum re­sistance thermometer mount attaches to the bottom of the cylinder, and epoxy encapsulated thermocouples fit into receptacles at the top and bottom of the cylinder.

CRYOSTAT AND HYDRAULIC SYSTEM

Figure 3 shows the complete high-pressure cryostat, which is similar to the design of Beecroft and Swenson! and that of Compy and Alers.2 Utilization of the outer pressure vessel cylinder as a tension member compacts the present design to fit the spatial limits of Dewars and magnets. A 105 N hydraulic ram at room temperature operates directly on the pressure vessel via a press frame with long stainless­steel compression and tension members. These members are approximately 60 em in length for sufficient thermal isolation and are constructed of austenitic stainless-steel alloys (310 and 316, respectively) for improved tensile strength and resistance to low-temperature embrittlement. The annular space between the concentric members is used as a vacuum line and passage for electrical leads. Necessary ports into the vacuum jacket are provided through the tension member wall.

Hydraulic pressure to 690 bar is developed by a manually operated pump and measured by a Heise Bourdon gauge

FIG. 3. High-pressure cryostat and external hy­draulic system.

HYDRAULIC RAM RESEVOIR PRESSURE

GAUGE

HYDRAULIC PUMP

AXIAL ALIGNMENT ASSEMBLY

PI THERMOMETER

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1027 Jones, Anderson, and Keeler: ElectriC conductivity measurements 1027

(0.1 % full-scale accuracy) equipped with electrical readout. A shutoff valve prevents loss of fluid through the pump. Pressure fluctuations due to differential thermal contraction of the press members are minimized by a 0.5-liter hydraulic reservoir.

EXPERIMENTAL DETAILS AND CALIBRATION

For low-temperature measurements the cryostat is sus­pended in a Dewar of liquid nitrogen. Using a controller, the temperature of the pressure vessel can be maintained to within 0.05 K. However, resistance vs temperature data are often recorded continuously on an x-y plotter while the vessel is allowed to cool slowly. These temperature sweeps have a cooling rate of 0.3 K/min or less. Helium exchange gas is used to make the final approach to 77 K. A similar warming rate is obtained using the heater. Typically, the thermal gradient along the vessel length was 0.1 K. We have used this technique to measure the conductivity curve u(T) of n-I nSb at 9.7 kilobar, and the result is shown in Fig. 4. No thermal hysteresis was observed upon warming. In general, either the pressure or temperature can be varied; however, it must be remembered that below the freezing curve of the pressure transmitting fluid the pressure should not be changed. The isoamyl alcohol and n-pentane mixture has been widely used in the study of superconductors, so that large pressure gradients upon freezing are neither ex­pected nor observed. At pressures under 20 kilobar, the Teflon capsules have been cycled several times in both tem­perature and pressure without failure. At high pressures, however, the capsules sometimes failed after only two or three cyclings.

13 4 0 6 7 B 9 10 " 12 13

IOOO/T (K-')

FIG. 4. The curve shows the experimentally determined conductivity vs inverse temperature for InSb at a pressure of 9.7 kilobar. The points are calculated from a simple semiconductor model fit to the end points of the experimental curve. The mobility is assumed to have a T-! temperature dependence due to acoustic phonon scattering, and the number of carriers is assumed to be the thermally excited electrons plus a constant impurity contribution (n=9X101& cm-& measured at p=o and T= 77 K). The gap is estimated to be 0.38 eV at this pressure from the u(P) curve ami t.he 7.ero pressure gap.

Rev. Sci. Instrum., Vol. 46, No.8, August 1975

0.10

10 P (kbor)

15 20

FIG. 5. The solid curve shows 1 he resistivity of n-InSb vs nominal applied pressure as calculaled from the hydraulic ram pressure. The hysteresis loops are used to determine lhe fric­tional loss and allow the resistivity vs corrected pres­sure to he det crmi ned (dashed (,UT vc).

Neglecting friction, the sample chamber pressure can be calculated from the measured hydraulic pressure and the known area ratios. The Bi I-II phase transition at 25.4 kilobar was used as a fixed point. 7 The hysteresis loop of the Bi resistance vs hydraulic pressure indicated the frictional loss was 6.4% and the loop was centered about a calculated pressure of 25.3 kilobar. Additional measurements of the frictional loss were obtained using n-I nSb as an electrical resistance manometer. This sample has an impurity con­centration n=9XlO13 cm-3 and exhibited intrinsic behavior at room temperature. The pressure dependence of the re­sistivity is due to the rapid increase of the valence to con­duction band gap with increasing pressure. Figure 5 shows the resulting hysteresis loops of resistivity vs the nominal internal pressure calculated from the hydraulic pressure. Upon initial pressurization, the frictional loss increases rapidly in the 6-8 kilobar range due to exceeding the elastic limit of the capsule plug. Above this pressure the absolute frictional loss increases slowly and in a roughly linear fashion from 1.09 kilobar loss at 8.1 kilobar to 1.46 kilobar loss at 25.4 kilobar. In cycling the pressure, the frictional loss tends to be the same as that of the highest previolls pressure.

*This work is supported by grants from the Defence Research floard and the National Research Council of Canada.

Ii{. I. Beecroft and C. A. Swenson, J, Phys. Chern. Solids 18, 329 (1961).

2E. M. Compy and P. B. Alers, ASME Publication 64-WA/PT-12 (1964).

'E. W. Comings, llig.'1 Pressure Tec.'moloKY (McGraw-Hili, New York, 1956), Chap. 6.

'F. B. Seely and J. O. Smith, Advanced Mechanics of Materials (Wiley, New York, 1952), Chap. 10.

'P. W. Bridgman, Proc. R. Soc. (Lond.) A 203, 1 (1950). 'K. S. Kim, Rev. Sci. Instrum. 41, 1102 (1970). 7G. C. Kennedy ann P. N. La Mori, J. Geophys. Res. 67, 8S1 (1962).

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