NBS TECHNICAL NOTE 765

Low Temperature Thermometry:

Interim Report
NATIONAL BUREAU OF STANDARDS

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ajnai tutfeau u* -»*••

Low Temperature Thermometry:

Interim Report

'7J

George Cataland and Harmon H. Plumb

Heat Division

Institute for Basic Standards

National Bureau of Standards Washington, D.C. 20234

NBS Technical Notes are designed to supplement the Bureau's regular publications program. They provide a means for making available scientific data that are of

transient or limited interest. Technical Notes may be

listed or referred to in the open literature.

^exu of

U.S. DEPARTMENT OF COMMERCE, Frederick B. Dent, Secretary

NATIONAL BUREAU OF STANDARDS, Richard W. Roberts, Director

Issued May 1973
National Bureau of Standards Technical Note 765

Nat. Bur. Stand. (U.S.), Tech. Note 765, 23 pages (May 1973) CODEN: NBTNAE

For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, D.C. 20402 (Order by SD Catalog No. C13.46:765). Price $0.40 domestic postpaid or 80.30 G.P.O. Bookstore.
FOREWORD

In the interest of informing the public on program developments and technical advances within the Division, we are increasing our publications activities, beyond the customary formal publication of complete pieces of work, through the media of NBS Technical Notes

and NBS Reports. The former provide the means to deal with the subject matter at greater

depth than normally tolerated by today's journal editors and the latter afford an opportunity to describe informally the progress toward current goals where the work is incomplete.

This is a progress report. The work is incomplete and is continuing. Results and

conclusions are not necessarily those that will be included in the final, formal publications. The period covered herein is the calendar year 1972.

H. H. Plumb, Chief

Temperature Section

National Bureau of Standards
CONTENTS Page

1. Introduction I

2. Speed of Sound in a Gas and Absolute "Temperature 1

3. Speed of Sound Isotherms 9 K to 21 K 3

h. Recent Acoustical Isotherm Measurements 7

5

Helmholtz-Kirchhoff Equation 11

6 Calibration of Germanium Thermometers 13

7

Discussion 16

8References 18
Low Temperature Thermometry: Interim Report

George Cataland and Harmon H. Plumb

Earlier acoustical thermometer 'speed of sound' isotherms are compared with recent measurements. Where systematic deviations had

appeared in "smoothing" through acoustically derived temperatures via

germanium thermometers, a possible solution has emerged; more precise

temperature control of the acoustical thermometer is desirable and

has been realized. A cursory examination of the applicability of the Helmholtz-Kirchhoff equation was made with a modified sonic chamber. Measurements with the modified instrument have shown no changes in the experimental results

The maintenance of the NBS P2-20 (1965) scale is described. A

new calibration apparatus was constructed to accommodate more germanium thermometers thus reducing the calibration cost per thermometer during a calibration run.

Key words: Acoustical thermometer; calibrator; germanium

thermometers; heat conduction; NBS P2-20 (.1965) scale; 'speed of

sound' isotherms; viscosity.

1. Introduction

A number of years ago the National Bureau of Standards Provisional Temperature Scale

2-20 (1965) was established; it was based upon acoustical thermometry and described in the literature [l] . Since that time the International Practical Temperature Scale of 1968 [2] was defined down to 13.8 kelvins and the NBS P2-20 (1965) has been used extensively not only within the United States but also by external research laboratories. The scale's widespread use has certainly been enhanced by the existence of a calibration facility [3] that could meet the requested calibration needs

Although the low temperature scale met an immediate need for temperature determinations

in the 2 to 20 K range, it was recognized that there were deficiencies in the acoustical

thermometry from which the temperature determinations were derived and it was hoped that improvements could be made in the measurements and techniques of acoustical thermometry.

This report will describe most of the continuing work, describe some of the problems that have been encountered, and indicate what may be the remaining program of measurements

2. Speed of Sound in a Gas and Absolute Temperature

For clarity it is desirable to repeat some of the discussion that was previously

presented [l]

When sound is propagated through a gas, if the frequency of the sound is not too high

relative to the mean collision frequency of the gas molecules, the propagation is nearly

adiabatic, and speed of sound [^,5] is

C v

z

, y CM x 8v T v where p is the density of the medium of molecular weight M and E is the adiabatic bulk

modulus defined by the relation

_J_ v (_i£_) . (2)

C

K 3v V y

' v The symbols v and p refer to the volume per mole and pressure of the medium, and the partial

derivative is at constant entropy or temperature, as indicated; C and C are specific heats at constant pressure and volume, respectively. If the conducting medium were an ideal gas, its equation of state would be expressed by
pv = RT (3) and there would result

v 3v ; T v7 K

' Additionally, the ratio of specific heats would be that of an ideal gas,

C

(c2-) = 5/3 v ideal gas

(if the gas is assumed to be monatomic), and eq. (l) becomes

Equation 5 indicates the simple relationship between the absolute thermodynamic temperature

T and the speed of sound in an ideal gas W . (The gas constant R and the molecular weight M are considered to be accurately known constants.)

In actuality an ideal gas does not exist, so eq. (5) must be modified for application

to real gases.- Of the two gases, 3 He and He, which can be used for sound measurements at temperatures between 2 and 20 K, ^He has been selected for experimental measurements. Its equation of state can be assumed to be represented by the empirical relationship [6]

pv = RT(1 + JL+ JIj. .__) ( 6 )

where B and C are functions of the temperature called the second and third virial co- efficients , respectively. If the quantity

v 3v ; T

is evaluated from eq. (6) and the ratio C /C is evaluated for the real gas, eq. (l) can be written P v

w

2 = &-)„», ^(l + ap+ Sp 2 + ...) (7)

where

"C 'ideal M

v

- iff- *

h~m * <»/«>*•£].

_ «>

3 is a term that includes higher orders of the virial coefficients B and C. From eqs . (5) and (7) we obtain

W

2 = W

2 (1 + ap + 3p 2 + ...). (9)

It is now apparent that, if one determines an isotherm of W

2 as a function of pressure,

the intercept W

2 of the extrapolated (to p = o) isotherm readily affords a means of cal- culating the isotherm temperature on the absolute scale. W a is- the slope of the isotherm

and there is no reason to assume that the slopes are not a smooth or continuous function of temperature

In order to obtain values of the speed of sound as a function of pressure, one must determine the wavelength and the frequency. Several methods are possible but our work is based upon the creation of standing waves in a gas by means of an apparatus with a fixed

frequency and a variable path. A quartz crystal, operating at its resonant frequency,

radiates through **He gas to a reflector surface which is parallel to the quartz crystal;

radiation is reflected back through the gas to the quartz crystal. If the spacing between

the crystal and the reflecting surface is an integral number of half-wavelengths the helium gas will be in resonance and a peak voltage will be measured across the quartz

crystal. The reflecting surface is displaced through detected integral numbers of halfwavelengths and its displacement measured. Thus X is determined, the frequency of the quartz crystal is measured and, consequently, W can be calculated. This value of W is, of
course, the phase speed corresponding to -whatever mode exists in the tube of gas. It is supposed that this mode is sufficiently like the plane wave mode to allow identification of W, for our purpose, as the free-space value. The mode may not be pure hut, if this is the

case, its components are spaced so closely that the ultrasonic interferometer does not resolve them. The cavity that contains the ''He gas is a right circular cylinder with an X-cut quartz crystal covering one end of the cavity and the reflecting surface of a piston,

which can slide freely within the cylinder, nearly fills the other end of the cylinder.

Provision is made for the gas space to connect to an external gas ballast volume and

manometer. The resonating gas volume is maintained at the cryogenic temperature of interest hut displacements of the piston's reflecting surface are measured at room temperature. A

fused quartz rod extends from the piston through temperature gradients of a Dewar to ambient

conditions and reliance has been placed upon the small value of the coefficient of ex- pansion for fused quartz. More extensive details of the instrument and its operation

appear in Metrologia [l]

3. Speed of Sound Isotherms 9 K to 21 K

A number of the isotherms upon which the scale NBS P2-20 (1965) were based did not appear to have been adequately characterized by fitting a linear function to the isotherm

data. This is seen in table 1 where the experimental W

2 and p are listed for the f K, 8.1 K and 9 K isotherms. The A's for each isotherm indicate that there are systematic

discrepancies between the actual data points and the assumed linear representation.

9.0 K

8.1 K

7.0 K

Table 1

F 2 (m/s) 2 P (Atmos) Aa

30,980 .2017 5.0 30,818 .1+076 - 3.0 30,665 .6068 - 6.9

30,521* .8096 2.8 30,380 1.0005 2.2

27,792 .131+3 5.1

27,61+2 .2680 - 1+.1+ 27,U66 .1+380 - 2.0 27,287 .6090 - 2.3 27,120 .TjhO 3.5

23,988 .1326 9.5 23,770 .2680 -10.1

23,532 .1+370 - 1.8

23,287 .601+0 - 2.5 23,069 .7580 1+.9

5.6

1+.8

8.7

a. The columns under A contain the difference between the experimental W

2 at the indicated pressure and the W of the linear function determined by the computer least squares fitting

b. a is the standard deviation in the least squares fitting of an isotherm.

Additionally, continued experimental experience indicated that some of the deviations, and

the standard deviation a (3.1+ is approximately equivalent to 1 mK) , were larger than might

he associated with the inherent limitations of the measurements and the apparatus . The most probable causes of the observed systematic deviations appeared to be: that the linear

representation covered a larger range of pressure than was applicable (the experimental

data were not properly represented by just the linear term of eq. 9) ; or that the lowest pressure points were inaccurate because of experimental difficulties which one encounters

in attempting to conduct measurements at low gas densities ; operational problems in- volving the control of the experimental parameters (germanium resistance thermometry,

frequency control, thermal equilibrium) might be improved upon.
It appeared that the range of linear representation might be the most significant

cause of data misrepresentation so experimentation was initiated to determine acoustical

isotherms at each kelvin from 9 to 21 kelvins and for pressure ranges that extended up to

about two atmospheres . By these measurements we hoped to extend the pressure range for each isotherm to such an extent that significant curvatures would appear at the higher

pressures; this would then be a guide that would be informative in determining the proper

value of pressure for truncating the upper limit of pressure. The reason for conducting

the experimentation between 9 and 21 kelvins, as opposed to below 9 kelvins, was that meetings of the ComitS Consultatif de Thermometrie were to take place in the immediate

future and we were desirous of making a contribution to the selection of thermometry fixed

points in the liquid hydrogen temperature range. (At about the same time that these new acoustical measurements were being made, effort was diverted to conducting liquid hydrogen

vapor pressure measurements). Another reason for initiating the higher temperature

measurements was that the slope of the acoustical isotherms passes through zero at about

13.5 K and there was some question about the adequacy of previously determined isotherms

in the vicinity of this temperature.

After identifying the pressure range for which the isotherms (at nearly integral

temperature intervals) could be represented linearly, isotherms at half kelvin values,

between 9 and 21 K, and at the triple and normal boiling points of equilibrium liquid

hydrogen were measured. The experimental data and appropriate statistical information are given in table 2 for the triple-point-of-hydrogen isotherm.

Table 2

W

2 (m/s] P (Atmosl

13.8057 1+7808.70 it78ll.76

Ii78l3. 07

1+7818.75

1*7820.9!* 1*7823.13

1*7825.32 U7829.25

1*7831.1*1*

37^3 - .208

1*1*16 .191 5216 -1.66

5820 1.63

6621* .61*1 7325 .055 8029 - .5^

8806 .319

951*2 - .1*05 0.96

It is to be noted that the deviations, A, in table 2 are much more random than those

of table 1. In addition, the standard deviation of the least squares fitting is much less than those of table 1. The standard deviations of the 13 and Ik kelvin isotherms that were reported earlier [l] were 5.1* and 8.3, respectively, and the A deviations exhibited

systematic departures from linearity. The pressure ranges of the previously reported 13 and ll* kelvin isotherms extended from 0.1* to 1.1* atmospheres - obviously, this was too

great a pressure range.

When the new isotherms from 9 to 21 kelvins had been determined it was appropriate

to check them for consistency and smoothness. This was done in two ways. It was assumed

that the resistance of a germanium resistance thermometer was a smooth function of temperature and subsequently the resistor was calibrated. Values of resistance were associated

with the values of temperature that had been calculated for the new isotherms and the resistance-temperature values of the thermometer vere computer fitted to a polynomial of the form

n

log R =

I A

n (log T) n m=o

The results are given in table 3.
Table 3

Calibration of Germanium Thermometer 56l

T .. (K) acoustic RGe(fi) T .. ». ++ , (K) acoustic fitted ST(mK) §- (Q/W

8.9917 UI4.U . 14-70 8.9911* -0.3 -133.2

9.1+956 383.300 9.1*961* 0.8 -109.9 9.9951 333.239 9-9955 0.1+ - 91.1*

10 . 1+968 291.1*67 10.1+95!* -1.1* - 76.3 IO.8989 262.810 10.8983 -0.6 - 66.2 II.U9U8 227.069 11.1*958 0.8 - 51*. 12.0127 201.1*32 12.0128 0.1 - 1+5.0 12.4956 181.063 12.1*967 1.1 - 38.9 12.9593 l61*.277 12.9600 0.7 - 33.7 13.4989 11+7.533 13.1*985 -0.1* - 28.7 13.8057 139.ll*0 13.801*7 -1.0 - 26.2 1U.0U8U 132.976 lit. 01*82 -0.2 - 21*. 1*

lit. 5019 122.593 15.5001+ -1.5 - 21.5 lU.9893 112.710 lU.9900 0.7 - 18.90 15.5002 103.661* 15. 501 1* 1.2 - 16.56 16.0U62 95.255 16.01*1*9 -1.3 - H+.1+5 16.5012 89.001* 16.5011* 0.2 - 12.96 16.9676 83.281 16.9673 -0.3 - 11.61*

17. ^980 77-1*30 17.5006 2.6 - 10. 31* 18.0112 72.1*51 18.0090 -2.2 - 9.27

18.1+99 1* 68.123 I8.U999 0.5 - 8.38

18.9I+07 61*. 578 18.91+17 1.0 - 7.68 19.5009 60.51I* 19.5002 -0.7 - 6.90

20.01+36 56.927 20.01*72 3.6 - 6.21+

20.281+0 56.512 20.2789 -5.1 - 5.98

20.1*998 5l*.l9l* 20.5037 3.9 - 5.75 21.0102 51.1*32 21.0056 -It.

- 5.27 22.8236 1*3.136 22.826 2.1* - 3.9!+

T . . -.. . , are the values of temperature that would be obtained in a smooth

3.COUST 1C TITTfifl relationship ofR-T for the germanium thermometer. <5T is the difference between

T ^- *++ j an^ T . Although the 6T's show some systematic deviations, particularly at the lower temperatures, the most noteworthy point is the magnitude of the 6T's from 20 to 21 kelvins . Also, the values of 6T at 17.5 and 18 K are significant. One can probably consider that the values of T may yield more consistent and better acoustic fitted

values of temperature than those associated with the temperature of individual isotherms

"but the approximately ±5 mK for 6T in the vicinity of 20 kelvins is distressing. It appears

to indicate that errors may exist in the acoustical isotherms . Later in this report

specific causes of a possible systematic error will be discussed.
A second method of smoothing the isotherms to detect possible systematic variations

was achieved by fitting the isotherm slopes to expressions of temperature that were similar to experimentally observed dependencies of the second virial coefficient. The three ex- pressions

f(T) = a l + hl/T + cj/T

f(T) = a2 + b2 //¥ + c 2 /T f(T) = a3 + b 3 J>n T + =3 yielded residuals of the same sign (there was one exception)

Table k

T (K)

9.1+956 9.9951

10.1+968 10.9002

II.I+9I+8 12.0127 12.U961

12.9596

13.1+989 13.8057

ll+. 01+81+ 11+.5019 11+.9893 15.5002

16.01+73 16.5012

I6.9676

17.1+980 18.0112

18 . 1+991+ 18.91+07 19.5009

20.01+36

20.281+0 20.1+998 21.0107

22.8236

27.1076

29 . 1+130 33.9758

Temperatures and Slopes of the Speed of Sound Isotherms

Upper Pressure

Slopea Limit (Atm)

11+.892 .16) 0.8 12.098 .17) 1.0

10.201+ .10) 0.8

8.I+58 .12) 0.9

• 5-901+ .11+) 0.8

1+.117 .13) 1.0 2.573 .08) 0.9 1.238 .09) 0.9

.l!+9 .09) 0.8

• 952 .01+) 1.0 1.528 • 13) 0.9 2.356 .05) 1.0

3.51+0 .10) 0.9

I+.63I+ .06) 1.0 5.259 .08) 1.0 6.158 '.21) 1.0 6.870 .09) 0.8 8.178 .09) 0.9 8.121 .06) 0.8

9.187 .09) 0.9 9.888 .06) 1.1

10.381+ .10) 1.0 11.073 .20) 0.9 IO.850 .19) 0.9 II.589 .10) 1.0 11.535 .20) 0.6

13.1+58 .09) 1.0 16.556 .11) 1.0 17.832 .09) 0.7 19.798 .22) 0.8

Residual

-.172

.106 -.276

-.201+ .108

.130 .165

.161+ .117

.157

.155

-.01+1+ .110 .198 -.179

-.059 -.100

.1+01+ -.383

.029

.170 -.006

.071

-.1+11 .101

-.1+72 -.186

.010 .082

.235

a) The standard deviations of the slopes are in parenthesis.

If the isotherm slopes in table 1+ are smooth functions of temperature, then the values of

the slopes (and residuals) at 17.5 and 18 kelvins and between 19.5 and 21 kelvins clearly

indicate the presence of peculiarities . This substantially supports the suggested errors

in acoustical isotherms that were noted in the germanium thermometer "smoothing" of temperatures .

The preceding discrepancies and indeterminacy have prevented us until now from

6
replacing or up-dating the NBS P2-20 (1965) scale, and presenting a liquid hydrogen vapor pressure scale, or values of "*He virial coefficients.

k. Recent Acoustical Isotherm Measurements

A systematic error has "been ascertained in recent acoustical thermometer experimentation. It was observed that not all data points lay on a straight line within the apparent reproducibility of the speed of sound- pressure measurements. Efforts to determine

the cause of this discrepancy were concentrated in measurements at 19 K and 9 K and the cause

of the data variability appears to be related to heat flow problems within the acoustical

thermometer low-temperature chamber.

In order to increase the efficiency of acquiring experimental data certain set procedures have been followed. In general, the vacuum space of the acoustical thermometer was filled with some helium gas to enhance its cooling from room temperature down to the approxi- mate temperature of measurements. Then the helium gas was evacuated by an oil diffusion

pump and vacua of 1 x 10-7 mm of Hg were commonly achieved and maintained during the acoustical measurements . The vacuum gauge was in the pumping line at room temperature and

the pumping tube within the Dewar system was of fused quartz -it was desirable that it be of the same material that was employed in other lines (the displacement measuring tube and rod

that are used in connection with the piston-displacement measurements). Customarily, heat

was applied to the acoustical thermometer through a heater coil that was wound around the copper top of the low-temperature portion of the instrument . A copper radiation shield

surrounded the apparatus. The instrument was brought into temperature control, as indicated

by several germanium resistors that were mounted in the cylinder housing which contained

the helium gas, the quartz crystal and the reflecting surface. A temperature controller

supplied the required heat for the apparatus and the germanium thermometers generally in- dicated a temperature control and temperature differential that were within one millikelvin.

In the customary measurement techniques the acoustical thermometer would be at low temperatures for weeks or even months and experimental data points would be measured in a systematic manner. That is, measurements would be taken at say 19 K, the apparatus would

be permitted to cool to 18 K, and measurements would be taken 18 K and so forth. At particular times the acoustical thermometer was heated to higher temperatures, e.g., 27 K, considerable outgassing of helium gas would be observed, and the instrument's temperature

would again be lowered to obtain additional measurements at the regular isotherm temperatures, e.g., 19 K. After some time it was noted that the isotherm data points which were

achieved after a 27 K outgassing were slightly below the "customarily" measured isotherms. The difference appeared to be greater than the expected reproducibility of the isotherm.

This is supported by the data presented in figure 1 and figure 2 for the 9 K and 19 K

isotherms, respectively. It was decided that, in spite of the indications of the vacuum

gauge, problems of heat flow and temperature gradients existed with the acoustical

thermometer chamber.

Subsequently, the radiation shielding of the instrument was modified. The innermost

shield of figure 3 was incorporated in the apparatus , a heater coil was wound around the

outer radiation shield and additional germanium resistors (for monitoring and controlling

the outer radiation shield temperatures) were installed. The apparatus was then operated

so that sufficient heating power was applied to the outer shield to cause the outer shield

temperature to be a few millikelvins warmer than the cylinder of the acoustical thermometer. After some experience had been acquired in taking measurements under these modified

conditions, it was ascertained that the germanium resistors which were mounted within the acoustical thermometer walls indicated stabilities within a few tenths of a millikelvin.

Also the acoustical resonance peaks were sharper and the instrument could be operated at somewhat lower helium gas pressures than had been possible previously. The vertical posts

that are attached to the lower portion of the inner radiation shield were used for additional thermal anchoring of the inner germanium thermometers ' current leads . The use

of these additional thermal anchors does not seem to noticeably affect the thermometers' stability or the instrument's operation.

When the acoustical thermometer was operated under these new conditions of thermal

control, we measured isotherm data points, ("two shields" in figure 1 and figure 2) that

are in close agreement with those earlier data which were acquired after the thermometer
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fe
IZZZZZZZZZZZZZZ •in/iuiu/ii

r\\ EATERS

-INNER SHIELD

- OUTER SHIELD

-VACUUM CAN

-GAS SPACE

X-CUT QUARTZ CRYSTAL

FIGURE 3

10
had teen outgassed at 27 kelvins . It appears that during prolonged experimentation there may he an accumulation of helium gas in the acoustical thermometer chamber. This could result from helium penetrating the fused quartz evacuation line (within the liquid helium

Dewar) and its subsequent condensation, adsorption or accumulation around the lower temperature portion of the acoustical thermometer. This in turn could cause thermal gradients in the resonating helium gas and between the monitoring germanium resistors . The improved

thermal stability and improved resolution of helium gas resonances which are achieved during

the two shield operating conditions strongly suggest the attainment of better operational

procedures. It is to be noted in figure 1 and figure 2 that this technique has resulted

in isotherm determinations for 9 and 19 K which yield slightly lower temperatures and slightly different slopes than were obtained when the measurements involved the use of a single radiation shield and no special high temperature outgassing of the acoustical

thermometer.

The redefinition of isotherms between 9 and 21 K has not been continued because it was desirable to eliminate another possible source of systematic error. It was mentioned

earlier that the measurement of the reflecting piston's displacement is effected by measuring the displacement at room temperature of the end of a fused quartz rod which extends downward approximately one meter and is connected to the copper piston by a ball joint. The fused quartz rod, and a surrounding fused quartz tube that supports the low temperature

components of the acoustical thermometer, pass through temperature gradients which exist

in the liquid helium Dewar. It is possible that, despite the relatively low coefficient

of expansion for fused quartz, the temperature gradients may change or the fused quartz

rod does not attain adequate thermal equilibrium with its surroundings during the course of the experimental measurements. To eliminate this possible source of error it has been

decided to replace the existing piston-displacement measuring system with a laser interferometer. It will essentially measure the displacement of the upper end of the reflecting

piston relative to a surface in the acoustical thermometer which is maintained at low temperatures — more specifically, a reference corner cube will be mounted on the horizontal

surface, figure 3, of the component that accommodates the main heater coil. This design,

in addition, to providing a more accurate displacement measurement will permit the use of

a thin wall stainless steel tubing for suspending the acoustical thermometer. Fused-quartz

and metal epoxy joints can be replaced by solder joints, the instrument will not be so fragile and the fused quartz evacuation line, which may have been a contributing factor to the thermal instability (described in the previous paragraphs), will be replaced by a stainless steel line. Some of the rebuilding of the acoustical thermometer, to accommodate

the laser interferometer, and preliminary operational checking of the laser system have already been performed. It is also hoped that the detection of gas resonance in the acoustical thermometer can be discerned digitally — it has been detected in the past by

the visual observation of a voltmeter. These apparatus changes should lead to the elimination of possible sources of systematic error and permit the determination of better

isotherms

5. Helmholtz-Kirchhoff Equation

It was stated earlier in this report that the value of W is, of course, the phase

speed corresponding to whatever mode exists in the tube of gas and it is supposed that this

mode is sufficiently like the plane wave mode to allow the identification of W, for our purpose, as the free-space value.

The equations derived by Helmholtz [7] and Kirchhoff [8] are based upon the effects

of viscosity and heat conduction at the boundary walls for a gas that travels along the length of a cylinder. The equations assume that the amplitude of the sound waves are uniform over the whole cross-section of the cylinder and predict that both the speed and

the absorption differ from free space values . For the speed

W

o

[1L iA2b p it f

where W is the speed within a cylinder;

11
W is the free space speed

b is the radius of the tube

p is the density of the gas

f is the frequency of the sound

and n is an effective viscosity that is related to n., the real viscosity of a gas by

n = n, [i + {( Y -1) v4^-}] 2 cp

nrY is the ratio of specific heats

K is the thermal conductivity of the gas and C is the specific heat at constant pressure.

P While these equations [9] have been experimentally investigated at frequencies up to 120 kHz and for tube diameters of a few millimeters, information is lacking at 1 MHz and higher. There is some verification of the equations at the relatively low frequencies but, at the

very least , questions have been raised concerning the effect of the engineering finish of the boundary surface

We thought that it would be both desirable and interesting to determine if the Helmholtz-Kirchhoff (H-K) equations were applicable to the NBS acoustical thermometer.

In the correction term

12b

'n

p I f increases in both the cylinder diameter and the frequency should increase the value of the

measured sound speed within the cylinder. For an acoustical isotherm of W

2 versus pressure

or density there should be a noticeable bending of the isotherm with decreasing pressure. The temperature dependency of ri is such that these effects should be greater at higher

temperatures. For our acoustical thermometer b is close to 0.5 cm and it operates at

1 MHz. At an operating temperature of about 19 K, see figure 1, the H-K equations would

predict that the data point at 0.25 atmospheres would depart from the isotherm linearity by

the equivalent of about 8 millikelvin — there would be a systematic decrease of W from

linearity as p becomes smaller. As yet, both in the plotting of isotherm data and in its analysis by computer, it has not been possible to detect systematic curvatures at low pressures

Another experiment was conducted to check the applicability of the H-K equation for

our acoustical thermometry. Another gas chamber was constructed and its principal dia- meter was close to 2 cm. Figure Ua indicates the usual design of the containing gas space; figure kb shows the design of the chamber of larger diameter.

(a) (b)

FIGURE 4

12
We should have preferred that the entire cylindrical gas volume, to the right of the quartz

crystal, in figure Ub5 be of the 2 cm dimension hut we desired to use the same quartz

crystal that had "been employed in previous experiments. One may assume that the larger

diameter gas volume would cause a higher value for the measured speed of sound because the H-K correction term would be smaller; in figure 2, at 0.25 atmospheres, the measured speed

of sound would be the equivalent of about k millikelvins higher than that which was measured

with a cavity of customary design. The measured data points for the 2 cm cavity do not indicate that this is the case in figure 1 and figure 2.

As an additional check on the applicability of the H-K equations for our measurements it is highly desirable that the acoustical thermometer be operated at higher

frequencies. While it was not convenient to do this during the past investigations of the H-K equations, it must and will be done when the new instrument that is being developed

is finished. Additionally, if the new thermometer can be operated at yet lower pressures,

it will yield greater sensitivity for detecting a possible low pressure curvature of the isotherms

6. Calibration of Germanium Thermometers

Since 1965 the National Bureau of Standards has provided a calibration service for germanium thermometers on the NBS P2-20 (1965) scale for the general public on a reimbursable fee basis. Since the major cost associated with the, calibration facility was for personnel, it was considered advantageous to increase the number of thermometers that could

be calibrated during a calibration run, in order to reduce the unit cost per thermometer. Within the first calibration apparatus [3], the total number of germanium thermometers

that could be accommodated was limited to four and two of the thermometers were calibration

reference standards. Therefore, it was decided to construct a calibrator that could accommodate at least six thermometers and to update the existing support equipment

Below will be discussed the improvements that have been incorporated in the new calibration apparatus and the stability of the two reference germanium thermometer standards

over the last seven years. These two resistors are of a group of six that maintain the

NBS P2-20 (1965) temperature scale.

For the new apparatus a vacuum seal, fabricated from stycast resin, was employed to admit electric lead lines into the evacuated chamber of the calibrator. Twice the necessary

number were cast within the seal to meet possible future needs. In the former apparatus

the absence of an adequate number of leads was a factor that limited the number of thermometers that could be calibrated at a time. Normally, when measurements of resistance

are to be made potentiometrically , the thermometers current leads are wired in series and

if one of the thermometers should become open circuited, the complete calibration would

have to be terminated. To avoid the necessity of such a shut-down, individual leads were wired to the current anchors within the calibrator and terminated at one external multiple

switch box; thus an open circuited germanium resistor could be by-passed and the calibration

continued. A secondary radiation shield was added to the vacuum environment and was attached to the main calibrator core at its base. Another selector switch box was acquired

that contained more terminals and the apparatus can now accommodate seven thermometers and with a few minor changes in the wiring, nine.

During a calibration run it is desired to attain a temperature (via resistance) that

is as close as possible to the "assigned" resistance values of the calibrated germanium

thermometer standards. If the values of the standards are within ±2 mK of their assigned

temperature, measurements of resistance are taken for all of the thermometers within the

calibrator. Since the first derivative (dR/dT) of each of the calibration standards is well defined, it is relatively simple to assign normalized values of temperature to a resistance value. Then the average of temperature of both standard thermometers at each calibration point (temperature) is assigned to each measured resistance value for the other thermometers that are to be calibrated.

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Table 5 typifies the procedure for assigning temperatures to germanium resistors that have been calibrated. The temperature in the Column T (2-20) scale are the temperatures

that are associated with the values of resistance, "R565 (scale)" and "R5^0 (scale)", for the standard resistors 565 and 5^0. The values under "R565 (cal)" and "R5^0 (cal)" are the resistance values at which the actual calibration of unknown germanium resistors were

performed. Through the respective dR/dT's, the "T (cal)..R565" and "T (cal) R5^0" are cal- culated and from these "T (cal) avg" is obtained. "T (cal) avg" are the temperatures that correspond to respective resistance values for the "unknown" germanium thermometers.

When the new calibration apparatus became operational in September, 1971, resistor

56l, which had been compared with 565 and 5^0 twice previously, was again installed to assess the maintenance of the provisional temperature scale. A comparison of the average value of the standards with resistor 5°1 and its previous calibration of 1967 , indicated

that the resistors 565 and 5^0 had maintained their calibration (relative resistance

comparisons) to better than ±0.1 mK.

Since the initiation of the calibration service for germanium thermometers, a record

has been maintained for the two reference standards (565 and 5^0). Their reproducibility

of assigned resistance values is evaluated by the differences (Rsi+o - R565) between their

observed values at each calibration point. Table 6 contains a compilation of the relative

stability of the two standard thermometers and their relative reproducibilities over the

last five years. The data involve 52 calibration runs and also include approximately Uo thermal cyclings of the calibrator from ambient to low temperatures . It also includes data

that were taken after the installation of the monitor resistors within the new calibration

apparatus since our primary concern is the retention and stability of the NBS P2-20 (1965)

t emp er ature s c ale

Table 6

Statistical Review of the Two Reference Standards Within Calibration Apparatus

Ho. Runs 52 Mo. Cycles Up Period Covered Hov 66 - Dec 71 Temperature (K) AT (mK) ±2a (mK) dR/dT(56l) (fl/mK)

2.3

2.8

3.2

U.

5.0 6.0

7.0

8.0 9.0

10.0 11.0

12.0

13.0 lU.O

15.0

16.0

17.0 18.0

18.9

20.0

1.0

1.0

1.0 1.3

0.5

0.5 0.6

0.5 0.U

0.6

0.5 0.6

0.7

0.8

0.6

0.9 0.7

0.8

0.9 1.0

.58

.56

.51

.63

.26 .21

.23 .21

.23

.25 .25

.25 .33 .33

.25

.37

.37 .35

.kk M

13.000

5.800

3.500 1.350

.770

.1*1+0 .290 .190

.130 .093

.065

.0U5

.035 .025 .019

.015 .012

.010 .008

.007

a) Indicates maximum difference in "equivalent temperature" between the two reference

standards (T L5l+0 " T

565

) -

15
Below k.2 and above 16.0 K there appears to "be a larger spread "between the assigned

resistance values and their realization during a calibration run, i.e., both AT and 2a appear to increase at both temperature extremes. At h.2. K and below, the normal procedure

is to admit 4 He exchange gas to the vacuum can to hasten the cool down of the interior of the calibration apparatus and then to reduce the 'vapor pressure of the liquid helium bath

to a pressure below the lambda point. Meanwhile the vacuum chamber is being pumped out and,

when the automatically controlled bridge current approaches a steady-state current to the heater of the calibrator and the vacuum pressure remains at a steady value of 10-7 mm, calibration measurements are made. In the former calibration apparatus there was a time

limitation in which all the resistance values could be taken because of the gradual drift

upwards in the temperature of the calibrator. This could be in part due to the continuing

outgassing of the calibrator. In the present apparatus, temperature controlling at a selected

low temperature is possible for hours and the problem of drift seems to have been eliminated.

Above 16 K the dR/dT's of the resistors become smaller and the uncertainty in the measured

values of resistance is approaching our measurement capability. In our last comparison of resistance thermometer 56l with the two monitoring standards there were indications that resistance thermometer 565 may be experiencing a slight drift in its calibration at the higher temperatures (see table 6).

The new calibration apparatus has made it possible to reduce the germanium thermometer

calibration costs from $1,100 to $600. This of course depends upon the receipt of enough

thermometers so that at least four can be calibrated at one time

7. Discussion

As was indicated previously in this report, the acoustical thermometry at NBS will be continued but a laser interferometer will be employed for wavelength determinations . When

the final measurements have been made they may or may not lead to the revision of the temperature scale NBS P2-20 (1965). At the present time there is considerable activity

concerning temperature determinations below 20 kelvins by several national laboratories.

Under the auspices of the Comitl Consultatif de Thermometrie a committee on thermometry

below 90 kelvins has been formed and the Australian National Standards Laboratory (CSIRO) has undertaken the task of performing measurements to compare temperature scales below

20 or 30 kelvins. The NBS has calibrated three germanium thermometers, which will be sent

to CSIRO, and similar contributions from PRMI, NPL, Leiden, Iowa State University and

CSIRO (and, possibly, other laboratories also) are expected. NBS will submit additional

acoustical thermometry data as they become available. Although our new measurements will

be reported to the public, it may be advantageous to await the extension of IPTS-68, rather

than have the NBS present a modificiation of NBS P2-20 (1965) for calibration purposes.

The reader's attention is called to two papers that will shortly be appearing in Metrologia. The first is a contribution from Professor C. A. Swenson, of Iowa State University: "Relationship from 1 to 3

1* K Between a Paramagnetic Salt Temperature Scale and Other Scales; an Addendum". The second will concern the realization of low temperature fixed points by Dr. K. H. Berry of the National Physical Laboratory.

Table 7

NBS„ , . „ ., Acoustic Smooth

**He NBP (K) U.225 ±.001

e-H2 TP (K) 13.80147 ±.001

e-H2 NBP (K) 20.2789 ±.005

NPL, NPL,- "Acoustic '* P-V Isotherms

It. 2235 ±.0018 U.22i*0 ±.0007

20.26U3 ±.00l+9 20.27^6 ±.0013

16
It is appropriate at this point to make reference to table 7, which includes values

of temperature that have recently been reported from NPL for the normal "boiling points of

'''He and e-H2

. The "NPL acoustic" are values of temperature and their uncertainties that were obtained with the NPL low frequency acoustical thermometer [10], The NPL p-v isotherm

values were obtained by K. H. Berry and reported in the Annual Report 1971 of the Division

of Quantum Metrology of the National Physical Laboratory. The "NBS acoustic smooth" values

have also been cited earlier [ll,12] . It should be repeated for clarity that the limits on

U.225 represent the scatter of the isotherm data points while the limits on 13.80^7 and

20.2789 represent the variations in acoustically determined temperatures of the isotherms

that were fitted with germanium thermometers in the vicinity of 13.8 and 20.27,

respectively — presented in table 3. Unpublished work [13] on 3 He p-v isotherms by

Dr. R. Sherman of the Los Alamos Scientific Laboratory also indicates that the NBP of He

is about 10 mK greater than the temperature that is assigned to this fixed point on the

T58 [l**] He vapor-pressure scale.

17
8. References

[1] H. H. Plumb and G. Cataland, Metrologia 2, 127 (1966).

[2] International Practical Temperature Scale of I968, Metrologia 5_, 35 (1969).

[3] G. Cataland and H. H. Plumb, J. Research Natl. Bur. Standards (U.S.) 70A, 2^3 (1966)

[h] A van Itterbeek, Progress Low Temp. Phys . I, 355, North Holl. Publ.'Co. 1955.

[5] L. Bergman: Der Ultras ohall , S. 501. Stuttgart: Hirzel I95U.

[6] W. H. Keesom: Helium, p. 30, Amsterdam: 19^2.

[7] H. Helmholtz, Verhandlungen des Naturhistorisch-medecinischen Variens zu Heidelberg 3, 16 (1863)

[8] G. Kirchhoff, Ann. Phys. Lpz., 13J+, 177 (.1868).

[9] A. Wood, Acoustics, p. 251 London and Glasgow (19U0)

[10] A. R. Colcough, Vol. h, Temperature, Its Measurement and Control in Science and

Industry, published by Instrument Society of America, Pittsburgh, Pennsylvania

(in Press)

[11] G. Cataland and H. H. Plumb, J. Research Natl. Bur. Standards (U.S.) 69A, 531 (1965).

[12] G. Cataland and H. H. Plumb, Vol. h, Temperature, Its Measurement and Control in Science and Industry, published by Instrument Society of America, Pittsburgh,

Pennsylvania (in Press).

[13] R. Sherman - Oral report presented at the 5th Symposium on Temperature, June 21, 1971,

Washington, D. C.

[lU] F. G. Brickwedde, H. van Dijk, M. Durieux, J. R. Clement and J. K. Logan, J. Research,

Natl. Bur. Standards Gkk, 1 (i960)

U.S. GOVERNMENT PRINTING OFFICE : 1973— 511-325/234

18
FORM NBS-114A (1-71) U.S. DEPT. OF COMM. BIBLIOGRAPHIC DATA

SHEET

1. PUBLICATION OR REPORT NO. NBS TN-765

2. Gov't Accession No.

3. Recipient's Accession No.

4. TITLE AND SUBTITLE Low Temperature Thermometry: Interim Report

5. Publication Date May 1973

6. Performing Organization Code

7. AUTHOR(S)

George Cataland and Harmon H. Plumb

8. Performing Organization

10. Proiect/Task/Work Unit No. 9. PERFORMING ORGANIZATION NAME AND ADDRESS NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

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12. Sponsoring Organization Name and Address

Same as No. 9.

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14. Sponsoring Agency Code

15. SUPPLEMENTARY NOTES

16. ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a significant bibliography or literature survey, mention it here.) Earlier acoustical thermometer 'speed of sound' isotherms are compared with recent measurements. Where systematic deviations had appeared in "smoothing" through

acoustically derived temperatures via germanium thermometers , a possible solution has

emerged; more precise temperature control of the acoustical thermometer is desirable

and has been realized. A cursory examination of the applicability of the HelmholtzKirchhoff equation was made with a modified sonic chamber. Measurements with the

modified instrument have shown no changes in the experimental results

.

The maintenance of the NBS P2-20 (1965) scale is described. A new calibration

apparatus was constructed to accommodate more germanium thermometers thus reducing

the calibration cost per thermometer during a calibration run.

17. key words (Alphabetical order, separated by semicolons) Acoustical thermometer; calibrator;

germanium thermometers; heat conduction; NBS P2-20 (1965) scale; 'speed of sound 1 isotherms: viscosity.

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