from it using polymide ferrules [21]. The capillary which admits the sample is soldered into the top of the cell. Much of the interior of the cell is filled by the wire support unit which is made from copper and includes a centerpiece, two covers, a top and a bottom cap. The wire support unit is mounted on the high pressure closure. When assembled the wire support unit provides two cylindrical wells 9 mm in diameter and 11 cm long to accomodate the hot wires. Mounted in the top cap with friction fit are two 5 mm sections of a small coaxial cable. The hot wires are soft soldered to the center leads of these coaxial sections. To the bottom of the long hot wire is soldered a short section of teflon covered wire which terminates in a 4-80 brass nut, the weight. The teflon covered section provides isulation between bottom cap and the extension of the long hot wire as well as centering for it. The long hot wire section is connected to one of the steel pins by a small loop of 12.7 μm copper wire. The short hot wire is soft soldered to the other coaxial section in the top cap. To its bottom end a short length of copper wire centered in a second 4-80 brass nut is soldered. The leads on the short hot wire side are completed by a loop of 12.7 μm copper wire which connects to a 5 cm length of coaxial cable. This section of coax is friction fit into the bottom cap and is sufficiently rigid to stand alone. A second loop of copper connects this coax to the second steel pin. Long and short hot wire sections are connected together above the top cap with the center tap soldered in the middle of this connection. The center tap is a 11 cm long section of the coax which at the bottom end is connected to the third steel pin.

Liquid oxygen safety is one of the additional design considerations for the cell since the interior of the cell will be exposed to very high pressure 70 MPa (10,000 psi) liquid. The materials directly exposed to liquid oxygen have been limited to beryllium copper, copper, stainless steel, silver, teflon, and a polyimide (kapton) all of which have been found to be "oxygen compatible" [22]. Cleaning procedures for cell, wire supports, capillary and sample handling system were extensive [23].

3.3. The Wheatstone Bridge

Precision measurements of resistance can be made by using a four lead technique or by using a Wheatstone bridge. In the present apparatus we follow the general development of the hot wire instrument pioneered by Haarman [2], de Groot, et al. [4], Assael, et al. [10] and de Castro, et al. [12] and use a Wheatstone bridge to measure resistances. End effect compensation is provided by placing the long hot wire in one working arm of the bridge and a shorter, compensating wire on the other. In contrast to other instruments where values of time are measured in the present instrument the voltage developed across the bridge is

measured directly as a function of time with a fast response digital voltmeter (DVM). The DVM is controlled by a minicomputer which also handles the switching of the power and the logging of the data. The automation of the voltage measurement follows the work of Mani [3] who used a similar arrangement with a transient hot wire cell to measure resistance by the four lead technique rather than using a bridge.

Figure 2 shows the Wheatstone bridge circuit. Each arm of the bridge is designed to be 100 , two arms R, and R2 are standard resistors. The resistance in each of the other arms R, and R, is a composite of the hot wire, the leads into the cryostat and an adjustable ballast resistor. The leads are roughly 6 at room temperature and 2 when the cell is at 76 K. The ballast resistors allow each working arm to be adjusted to a value of 100 .

The measurement of thermal conductivity for a single point is accomplished in two phases. In the first phase the bridge is balanced as close to null as is practical. To start with, switch 1 is turned from dummy to the bridge while switch 2 is open. With a very small applied voltage, 0.1 Volts normally, and the cell essentially at constant temperature, the voltages are read on channels 0 through 7. The lead, hot wire, and ballast resistances are calculated from the ratios of the appropriate channel voltgage to the voltage across the standard 100 resistor on channel zero. The ballasts are adjusted until each leg is approximately 100 . Finally, with switch 2 closed, the bridge null is checked on channel 6. The second phase incorporates the actual thermal conductivity measurement. The power supply is set to the applied power desired, switch 2 is closed, and switch 1 is switched from dummy to bridge. The voltage developed across the bridge as a function of time is read on channel 6 and stored. The basic data is a set of 250 readings taken at 3 ms intervals. Finally the voltage on channel O is read to determine the exact applied power, and the power is switched back to the dummy resistor.

3.4. The Cryostat

The cryostat for the apparatus, shown in figure 3, is adapted from a general design first used in a PVT apparatus at this laboratory [24]. The cell is connected by the reflux tube to the inner refrigerant tank. The reflux tube is filled with gas which sometimes corresponds to the liquid used as the refrigerant. Varying the gas pressure changes the amount of refrigeration applied to the cell. A cooling yoke and ring insure that the refrigeration is applied primarily at the bottom of the cell. In this way a slight gradient can be maintained between cell top and cell bottom. To avoid convection inside the cell we normally maintain the cell bottom slightly colder than the cell top. The cell and its radiation shield is located in a vacuum environment. A

tube which serves as the inner vacuum line also admits lead wires and the capillary into the inner vacuum space surrounding the cell. The leads are tempered on two rings, one is attached directly to the inner refrigeration tank, the other is the guard ring which is attached to the reflux tube. The cell radiation shield in turn is attached to the guard ring. The inner refrigerant tank is insulated by the outer vacuum system, which in turn is protected by the outer refrigerant, usually liquid nitrogen, in a dewar. All of the various access tubes, fill and vent lines, and vacuum lines pass through the mounting plate which rests on the mounting bracket attached to the wall. Cell alinement is achieved by adjustment of three set screws.

3.5. Cryostat Temperature Control

A diagram of this circuitry is shown in figure 4. The cell temperature is monitored with the platinum resistance thermometer which is mounted in the cell. The PRT resistance is measured by the four lead method as a ratio against a 10 standard using a microvolt potentiometer, a stable cur

rent supply, and a high gain de null detector. The amplified output of the detector is used in a feedback loop to provide power to the cell heater [25]. The ratio of power applied to cell top and cell bottom is monitored with a thermocouple and adjusted by hand. The temperature of the guard ring and cell radiation shield are maintained close to the cell temperature by the use of a second feedback loop. This loop includes a differential thermocouple and a low level dc voltage detector whose amplified output is routed to a power supply which in turn feeds the ring and shield heater. A separate, manual heater is mounted on the capillary. This heater is operated intermittently as needed. Its function is to ensure that the sample does not freeze in the capillary should by chance some unusual temperature conditions prevail at some spot in the capillary.

3.6. Sample Handling and Vacuum Systems

Block diagrams for both systems are shown in figure 5. The vacuum system is conventional except for an automatic back pressure control with alarm and solenoid valve. These

compressor as pressure intensifier. The compressor uses an oxygen compatible oil and has specially hardened check valves and seals. A pressure relief valve was provided in the cell pump-out line to protect against the possibility of an accidental oxygen overpressure, even though the forepump is charged with an oxygen compatible pump oil. With a few changes the sample system was able to handle a liquid sample, propane. Ordinarily the compressor requires an input pressure of about 5 MPa (700 psi). However, if liquid is provided at the intake and sufficient time between strokes is allowed, then the compressor handles a liquid sample quite well. For propane, removing the molecular sieve and turning the supply bottle upside down ensured a direct flow of liquid.

3.7. The Minicomputer

A simplified block diagram of the minicomputer and its peripherals is shown in figure 6. The CPU uses 18 bits per word with BASIC as the operational language. Program storage is on floppy disks, program input on the CRT, program listings are handled on the printer. Data can be displayed on the CRT and on the printer, and can be stored on floppy disk or magnetic tape. Input voltages, i.e., voltages to be read are routed from the 50 input channels by the multiplexer to the DVM where the analog to digital (A/D) conversion is effected. Output voltages, i.e., voltages to be used for experimental control are processed by the logic control unit where the digital to analog conversion takes place. These voltages are available at any of six output channels.

4. Data Measured

In the course of making a single thermal conductivity measurement a large number of variables are measured and recorded. The minicomputer program which controls the measurement is shown in appendix I. An example of a data file as assembled in the minicomputer and then transferred to magnetic tape is shown in appendix II. The first two lines of the data file are keyed in through the CRT. These lines contain the date, run and point number, the PRT reading from the microvolt potentiometer with the last digit repeated, the reading of the pressure gage, the barometer reading, the wire resistance for both long and short hot wire, the sums of lead and ballast resistance for both long and short hot wire sections, the time increment at which the voltage readings were taken, and lastly the voltage applied to the bridge. The remainder of the file contains the set of 250 voltage readings across the Wheatstone bridge.

4.1. Cell Temperature

The PRT is a standard capsule thermometer. It has been calibrated by the NBS temperature section. The voltage

The cell pressure is read with a commercial high precision steel bourdon tube. The unit was selected because it is "compatible" with high pressure oxygen. The unit is calibrated by the vendor with the calibration traceable to NBS. A digital readout is provided through an optical sensor, with the units of the readout in "counts." At the maximum pressure 96000 counts correspond to approximately 68 MPa. At the higher pressures the bourdon tube displays hysteresis under loading as a function of time. It is this hysteresis that gives rise to the stated uncertainty of ± 0.03 MPa. The pressure gage calibration was represented by a low order polynomial for use in the data reduction program. The error attributable to this curve fit is well within the stated error of the gage. Vapor pressure checks of the gage at approximately 1 MPa with both oxygen [26] and propane [27] confirm the calibration at the lower end of the pressure scale.

4.3. Resistances

Direct resistance measurements are made while balancing the Wheatstone bridge. The resistances of the hot wires, of the leads, and of the ballast resistors are measured with the DVM set at the optimum gain. The resistance measurements are made using the four terminal method; the voltage

across a standard 100 resistor defines the current in the circuit and the voltage reading across the unknown defines the resistance in question. In actual practice each voltage

reading is the average of 100 individual readings. Each hot wire section measurement must be corrected for leads inside the high pressure cell which are short pieces of copper and steel wire. The corrections were calculated from wire dimensions and tabulated resistivities [28]. They are estimated to be 0.22 for the long hot wire section and 0.65 for the short hot wire section at room temperature. The corrections are handled in the data reduction and are program further adjusted for changes in bath temperature.

In order to obtain the temperature increase of the platinum wires from the corresponding resistance increase, we need to know the variation of resistance with temperature for both wires. It has been shown in the past [8, 12, 13, 29] that an in situ calibration of the wires is desirable and also that the resistances per unit length of both wires should be the same to within about 2 percent.

where T is the temperature in kelvin and P the pressure gage reading. The pressure dependence is small but statistically significant and reflects the fact that the calibration measurements are made with a small applied voltage of 0.1 volts. Coefficients for eq (4) were determined in two ranges of temperature with some overlap in the range of the fits as shown in table 1. The standard deviation of the resistance measurements as well as the equivalent temperature errors are shown in table 1. The long wire has a length of 10.453 cm at room temperature, the short wire one of 5.143 cm. Both wires have a nominal diameter of 0.001270 + 0.000001 cm, thus the radius a in eq (1) is 0.000625 cm. If we use these values and the measured resistances we can calculate a resistivity of 10.07 × 10 N-cm at 273.15 K compared to a best value of 9.60 × 10-cm for an annealed high purity specimen [28]. The difference is ascribed to the hard drawn condition of our wires. The a of these wires, defined as (R(373.15)-R(273.15)/(100. R(273.15)) is 0.0037944 which is lower than the value 0.003925 required for use in an annealed platinum resistance thermometer [26]. Finally, we evaluate