MECHANICAL MEASUREMENTS
METHOD OF CONSTRUCTING SECONDARY STANDARDS FOR ABSOLUTE PRESSURE ON THE BASIS OF FIXED POINTS FOR PHASE TRANSITIONS IN PURE SUBSTANCES UDC 53.089.68:531.787
S. N. Afanas'ev, A. Yu. Stepanov, and V. V. Suprunyuk
Mercury and piston standards give the highest accuracy in measuring absolute pressures, hut the equipment is complicated and not capable of being transported, so it is impossible to compare stationary standards directly, and thus to evaluate the unification in absolutepressure measurement. Interest attaches to devices based on the triple point [i] or a continuous part of the first-order transition curve for a pure gas [2] to provide simple and transportable secondary standards giving the necessary stability and reproducibility on comparison with the initial ones. The critical unit for both types of devices consists of means of defining and maintaining a cryogenic temperature with the necessary accuracy. Although cryostats are available with temperatures reproducible to better than 1 mK [3, 4], there are various difficulties in using them in transportable standards because of the TABLE i
Substance
Melting point, K
Vapor pressure, Pa, at
Boiling point, K
TPW
MPG (272,10K)
(303,08 K)
dp/dT, Pa/K, at TPW
MPG
Expected pressure,reproducibility, I0~%, at TPW
MPG
Diethyl ether
150,85
307,63
24610,2
85716,4
1331
2662
2,7
6,0
Cis-2-pentane
121,76
310,i0
23204.7
78129,7
1064,8
3175,8
2,3
8,0
2,2-Dimethylbutane
174,25
322,89
14.~14,4
50977,3
798,6
1437,5
2,7
6,0
Cyclopentane
138
317.39
17352,2
60693,6
1064,8
256~,2
3,1
8,9
Acetone
179,95
329,25
895L6
35803,9
532,4
1863,4
3,2
10,9
2,3-Dimethylbutane
145,18
330,54
10224,7
38226,3
665,5
1597,2
3,3
8,0
Carbon tetrachloride
25:0,35
349,85
4402,9
18367.8
332,8
1224,5
3,8
13,0
Ethyl acetate
I90,55
350,25
3234,3
15799,0
199,7
452,5
3,I
6,0
l-Heptane
154,12
366,79
1939,3
9450,1
159,1
657,5
4,1
14,0
n-Heptane
182,55
371,55
1513,3
7979,9
119,8
391,3
4,0
1O,ff
Ethylcyclopentane
134,63
376,62
1339,0
6660,3
7,99
91,8
0,3
3,0
Toluene
178,16
383,75
894,4
4831,5
73,2
205,0
4,1
8,0
Ethanol
158,65
351,45
1573,2
102A8,7
133,1
585,6
4,2
13,0
Water
273,15
373.15
610,8
4232,5
44,4
255,~
0,04
Naphthalene
353,44
,i91,11
0,399
20,63
0,2~5
1,05
31,7
Ethylbenzene
178,18
409,34
252,9
1663,8
17.3
7.99
3,4
n-Dodecane
263,6
489,43
1,22
23,,16
0,25
2,93
10,3
25,0
Decane
243,5
4"~7,27
22,9
242,2
3,99
18,63
7,3
15,0
247,5,8
;69,13
5,32
76,13
I 1,33
5,32
8,4
13,0
n-
n- Undecane
"'
t
Translated from Izmeritel'naya Tekhnika, No. 6, pp. 23-25, June, 1987.
532
0543-1972/87/3006-0532512.50
9 1987 Plenum Publishing Corporation
0,12 68,0 0,96
TABLE 2
TABLE 3 I
.
Gas
'
Pressure idp/dT Triple, at : ~ Iat ~ triple point,~ Itriple point, point, kPa kPa/K
i
i
JTempera-iExpected ture repressure[ t . produel- repro- i !bility, ducibil-! ~ [5] ity, %
r
Carbon dioxide
216,580
517,98
[ 22,6
30
1,3.10
Argon
83,798
6&890
8,0
0,3
3,4.10
Neon
21,562
,t3,371
19,01
0,4
1,75"10 --2
Nitrogen
63,1462
12,526
2,3
0,7
1,28-10 -:~
Methane
90,6855
11,696
1,5
0,3
Oxygen
54,361
0, t462
0,056
Substance
i[
Water
i
]
'
--O
SD in measurement, %
~-; Pe, Pa
Ethanol
1574,6
Acetone
,'*961 , 4
/'C [)e Pc, Pa - - , PC
%
(;10,8
2,3.10
1
0,20
1573,2
1,0"10 --1
O, 15
8957,6
5.0. I0 --'2
3,8"10 --3
0,7
2,2~10 - 2
TABLE 4 Pei-Pe(i+ i ) Measurement SD, %
~e' Pa
Measurement date September 1985
612.2
0,18
--
January
822.8
0,22
0 . 0 . ~ --1
May 1986
612,6
0.15
6,5-10 --2
September 1986
612,9
0,27
I.l.lO - 1
1986
Y
6
7
/~
,.,~ , ~ - ~ , ~ ~ ~ ~ II ] ~.~ ==
!
..r-/L
"
Y
/
~/----~'L-~- secondary ~ I]
~"~
standard
\7
[q b=~_):--I.- ~i
Fig. 1 complex design and the control of temperature reproduction with the necessary accuracy, while the systems are also unsuitable for transportation. A device based on the triple points [i], which is set by the range of pure gases, as well as various other technical difficulties related to calculating corrections to derive the absolute pressure [4]. This makes it better to construct secondary standards based on fixed (reference) pressure points on phase-transition curves for pure substances. Here we give a theoretical and experimental evaluation of the scope for making such a standard with fixed pressure points. One can obtain such a set of points with a set of substances and a universal (unified) stable temperature sensor, which is best:,built as a device for realizing the triple point of water (TPW) and a device for realizing the melting points of hlgh-purlty fusible metals, such as the melting point of gallium (MPG) of purity 99.99999. The TPW type is widely used, while facilities for MPG have been used in thermometry [5]. The design of these instruments is quite simple, as is the control of the long-term reproduction of temperature, with an error of not more than 0.2 mK. The instruments have 533
satisfactory mass and size together with good working characteristics and are relatively cheap. Our theoretical evaluation shows that even a single device such as TPW extends the number of possible pressure points over a wide range. Table I gives a list of substances [6] for realizing pressure points in the range of low and medium vacuum together with the calculated errors in reproducing these pressures with TPW and MPG temperature sources with reproducibility not worse than 0.05 and 0.2 mK correspondingly. For comparison, Table 2 gives pressures on realizing the triple points of gases together with the likely reproducibilities. Tables 2 and 3 indicate that the reference pressure points given by the TPW and MPG devices are substantially higher than the reference pressures given by the triple points of gases not only as regards number and range but also as regards accuracy. The experimental evaluation is based on a model that implements the static method of determining pressure [7], in which a sealed membrane is used to balance the unknown vapor pressure over a substance in a capsule with the pressure of a gas that can be measured with the necessary accuracy. Figure i shows the essential scheme for an experimental transportable standard. Cell 3 is made of fused silica and is a sealed tube of diameter 12 mm and height 150 mm having the stopcock 4. The tube is filled to half its volume with the manometric substance 2, which in the experiment was distilled water, chemically pure acetone, or ethanol. To exclude operations with contaminated substances, the purity is determined before and after filling the tube. To reduce the effects of volatile impurities, which give rise to systematic errors in reproducing the pressures, the substance in the tube is frozen and the pressure is reduced to i0-s Pa, and then it is thawed with valve 4 closed. The cycle is repeated three or four times. Complete gas removal is indicated by the absence of bubbles released from the liquid. The pressure is reproduced by placing this cell in the temperature source i, which is a TPW device having a temperature reproducibility of 0.2 mK. The capillary 5 of diameter 0.8 mm and length 1500 mm joins the cell to the pressure isolator 8. The capillary is placed in the insulating shell 6 to reduce the effects of external heat fluxes. The pressure separator is a two-chamber membrane-capacitance sensor with sensitivity I0-s Pa/~V. It also serves as a precision gauge for measuring the pressure in the tube. The switching components, which include the pipeline 9 and stopcock 7, connect the specimen in a vacuum-tight fashion to any other device, such as a stationary standard for comparison. The total mass of the transportable standard is about 5 kg, including the electronic unit. The pressure reaches the plateau corresponding to the saturated vapor in 25-30 min after opening stopcock 4, and it is maintained in a stable fashion for 4-6 sec. To ensure unified results and reliable values, the mean and standard deviation (SD) in the pressure measurement are determined from five series with ten observations in each. The measurements are made between minutes 40 and 50 on the plateau. The reproduction error 0 is given by
where Pc is the calculated pressure and Pe is the mean pressure measured by means of the experimental system. The prototype containing distilled water was compared three times in a year with a secondary standard having a residual systematic error of 0.5% and an SD of 0.6%. The instability was evaluated from the differences in the measurements between the first and subsequent comparisons. Tables 3 and 4 show that the reproducibility is at the error level of the primary standard facilities and was not worse than 2.3"i0-~% with SD in the measurements of 0.18, 0.2, and 0.15% correspondingly for water, ethanol, and acetone. The instability over a year is characterized by the differences between the mean values and the SD, which were also within the error limits for the secondary standard. These resultsshow thatthe modelbased onfixed pointscan beused to implement simple and transportable secondary standards for the pressure unit at low and medium absolute pressures.
534
LITERATURE CITED
7.
F. Pavese, Metrologia, 17, No. 2, 35 (1981). M. K. Zhokhovskii et al., Tr. Metrolog. Inst. SSSR, No. 213 (273), 66 (1977). Ya. E. Razhba et al., Izmer. Tekh., No. 3, 50 (1973). J. Bonhoure and R. Pello, Metrologia, 19, No. i, 21 (1983) (fr.). R. E. Bedford, et al., Metrologia, 20, No. 4, 145 (1984). N. B. Vargaftik, Handbook on the Thermophysical Properties of Gases and Liquids [in Russian], Nauka, Moscow (1963). Heat and Mass Transfer: Heat-Engineerlng Experiments, Handbook [in Russian], Energoizdat, Moscow (1982).
POLARIZATION INTERFEROMETER FOR PRECISION PRESSURE MEASUREMENTS N. B. Rozhdestvenskaya and V. A. Zamkov
UDC 531.787.53.082.55
To perform precision pressure measurements one applies, as a rule, piston manometers requiring a hydraulic link with the measured volume and having a long readout stabilization time. Manometers with a deformable elastic element widely applied in less precise measurements, have a poor reproducibility and large hysC~resis. The present authors have developed and tested a membrane pressure sensor, based on application of a thick membrane working at the very beginning of its linear characteristics in conjunction with an automatic polarization interferometer used to measure the displacements of the center of the membrane. The design scheme of the sensor and interferometer is shown in Fig. i. The pressure p brings about a deflection of the membrane (2) of radius R and thickness D which is a planeparallel plate covered with a reflecting layer of fused quartz glass or Elinvar. This diaphragm is held between a fluoroplastic tightening ring (i), a quartz separating ring (3) and a quartz supporting ring (4). The three quartz details are united by optical contact. Ring (4) is covered with a reflecting layer on the side turned to the membrane and on the opposite side with a nonreflecting quarter wavelength layer for the laser wavelength % = 633 nm. All elements of the sensor (i-4) are held in the instrument case in one of the ends of the interferometer body C. In order for the optical paths of the rays reflected from the diaphragm (2) and ring (4) to be equal, it is necessary that the thickness d of the ring (3) correspond to the thickness d/(n -- i) of the ring (4), where n is the index of refraction of the material of the ring (n = 1.4571 for the fuxed quartz glass for % = 633 nm). The displacement of the center of the membrane under the pressure p can be represented by the expression ~=3pR4( I--~2) / ( I6ED~) ,
(i)
where p is the Poisson coefficient; E is the Young's modulus for the membrane's material. In our experimental prototype of the device 2R = 45 mm; D = 3 mm; E = 21500 kg/mm; p = 0.23. For the pressure i01 kPa (760 mmHg) the displacement is 6 = 7.415.10 -~ mm, corresponding to a change in the optical path difference by 2.43 % or a 843 ~ rotation of the interferometer dial. A comparison of the readings of the standard manometer MAD-3 in the Mendeleev Metrological Institute with the diacplement of the membrane measured by the interferometer showed that the observed hysteresis is caused by the inaccuracy of the automatic ellipsometer with a mechanical system of rotation of the dial applied in the prototype. According to the results of five series of measurements, carried out at different times, the correlation coefficient between the readings of the two devices was 0.993 for the theoretical deviation from linearity 3.10-'. The membrane is a part of a polarization interferometer bulit according to the Dyson scheme. The interferometer is mounted in a cylindrical case C in the middle of which there is a lens (5) with the focal distance f. As was shown by previous studies [i], the interferometer is stable with respect to all mechanical deformations, except for the change Translated from Izmeritel'naya Tekhnika, No. 6, pp. 25-26, June, 1987.
0543-1972/87/3006-0535512.50
~ 1987 Plenum Publishing Corporation
535
