techniques for approximating the international temperature ... - BIPM
techniques for approximating the international temperature ... - BIPM techniques for approximating the international temperature ... - BIPM
58 thermometer wires) caused a more remarkable change of resistance, equivalent to as much as 3 mK at 2.1 K and 16 mK at 30 K. This apparently was due to relief of strain in the wire and seems to limit the stability of this model. A limited number of thermal cycling tests on thin-film thermometers indicate that stability to within ± 2 mK is achieved after about 15 cycles between room temperature and 4.2 K, about twice the number of cycles as required for the wire-wound industrial type [Barber et al. (1987)]. 5.4 Self-heating Self-heating has been found to be closely the same for both U and W standard-type thermometers; its magnitude is shown in Fig. 5.3 for currents of 0.1 and 0.3 mA. Near 1.5 K the self-heating falls dramatically as the 4 He filling of the capsule condenses to superfluid liquid and thermal contact is vastly improved. As the temperature further decreases, self- heating rises rapidly again. Self-heating in thin-film thermometers is generally smaller than in wire-wound ones. Fig. 5.3: Typical self-heating effect for a 4 He-filled rhodium-iron thermometer with measuring currents of 0.1 mA and 0.3 mA [Rusby (1982)]. 5.5 Calibration and Interpolation A rhodium-iron thermometer is normally calibrated at many points in the range of interest and the data fitted by least squares as described for germanium. The equation chosen is usually of the form
n ∑ i= 0 59 T = a x i where x = AR + B, and B and A are origin-shifting and scaling constants respectively that i (5.1) change the range of the independent variable to -1 ≤ x ≤ 1. For a wide range such as 0.5 K to 27 K, n ~ 10 is necessary if fitting errors are to be ~ 0.2 mK. For lesser precision or narrower ranges, lower degree can be used - typically n = 4, 8, 9 for ranges 0.5 K to 4.2 K, 20 K, 24 K respectively. For temperatures above 27 K, R is usually replaced by In R or In Z (where Z is defined by Eq. (8.5)) in Eq. (5.1). If a change in calibration occurs, it is possible to account for it by expressing the calibration data in terms of Z with the two calibration points (for Z) near the extremities of the range. Another equation, requiring fewer calibration points, has been found to fit calibrations of 25 thermometers satisfactorily [Rusby (1982)]: n R b [ln( T + τ )] = ∑ i= 0 i i (5.2) For τ of the order of 8 to 10 K, the standard deviation of the residuals is less than 0.3 mK for n = 6 and where the points are weighted by dT/dR. Equation (5.2) is of special interest because it allows interpolation in the range from 0.5 K to 25 K using calibrations at a restricted set of easily realizable temperatures - helium vapour pressures, superconductive transitions, and triple and boiling points. The characteristics of rhodium-iron are such that the constants of the interpolation equation do not vary greatly from thermometer to thermometer from the same batch of wire, in contrast to germanium for which they vary widely from one to another. From the limited information available on the industrial-type thermometer [Besley (1985)], it appears that the ceramic type may approximate the ITS-90 in the range 77 K to 273 K to within about 10 or 25 mK using a reference function together with a deviation function that requires 2 or 3 calibration points respectively.
- Page 27 and 28: Table 1.1: Summary of Some Properti
- Page 29 and 30: PART 1: TECHNIQUES AND THERMOMETERS
- Page 31 and 32: 11 Fig. 2.1: One form of apparatus
- Page 33 and 34: 13 Fig. 2.3: Flow cryostat, shown w
- Page 35 and 36: 15 Fig. 2.4: Stirred liquid bath fo
- Page 37 and 38: 17 contained within a cylindrical c
- Page 39 and 40: 19 Fig. 2.5: Schematic drawing of a
- Page 41 and 42: 21 device SRM 767 [Schooley et al.
- Page 43 and 44: 23 Table 3.1 : Current Best Estimat
- Page 45: 25 The widely-used, but not very re
- Page 48 and 49: 28 fraction of sample melted) can g
- Page 50 and 51: 30 Fig. 3.2a: Apparatus for the cal
- Page 52 and 53: 32 Fig. 3.3: Sealed cell for realiz
- Page 54 and 55: 34 Final readings of the thermomete
- Page 56 and 57: 36 temperatures differ (usually) sy
- Page 58 and 59: 38 Fig. 3.4: Cross sectional drawin
- Page 60 and 61: 40 Fig. 3.5: Miniature graphite bla
- Page 62 and 63: 42 4. Germanium Resistance Thermome
- Page 64 and 65: 44 Fig. 4.3: Example of the Π-type
- Page 66 and 67: 46 Fig. 4.4: Differences between dc
- Page 68 and 69: 48 - conversely, p-doped thermomete
- Page 70 and 71: 50 Fig. 4.6: Effect of a radio-freq
- Page 72 and 73: 52 that it will not be subject to m
- Page 74 and 75: ln R n = ∑ i= 0 54 ⎛ ln T - P
- Page 76 and 77: 56 Fig. 5.1: Resistance (Ω) and s
- Page 80 and 81: 60 6. Vapour Pressure Thermometry*
- Page 82 and 83: 62 transitions, but it could be app
- Page 84 and 85: n ∑ i= 2 64 L x [ Π − k ] P =
- Page 86 and 87: 66 Fig. 6.3: Diagram at constant pr
- Page 88 and 89: 68 Fig. 6.4: Schematic construction
- Page 90 and 91: 70 Fig. 6.6: Use of an evacuated ja
- Page 92 and 93: 72 Following this, the connecting t
- Page 94 and 95: 74 Fig. 6.9: (c) N2, CO, Ar, O2, CH
- Page 96 and 97: 76 the Weber-Schmidt equation [Webe
- Page 98 and 99: 78 Table 6.1: Temperature values (K
- Page 100 and 101: 80 into the bulb (hydrous ferric ox
- Page 102 and 103: 82 Fig. 6.12: Effect on the vapour
- Page 104 and 105: 84 the remaining liquid increases.
- Page 106 and 107: 86 Curie constant (C⊥ is about 0.
- Page 108 and 109: 8.1 General Remarks 88 8. Platinum
- Page 110 and 111: 90 For a group of 45 thermometers h
- Page 112 and 113: 92 More recently, Seifert [(1980),
- Page 114 and 115: 94 For thermometers with W(4.2 K) <
- Page 116 and 117: 96 after 500 h at 1700 °C in air,
- Page 118 and 119: 98 normally extends about 50 cm bac
- Page 120 and 121: 100 inhomogeneities result from the
- Page 122 and 123: 9.5 Approximations to the ITS-90 10
- Page 124 and 125: 104 10. Infrared Radiation Thermome
- Page 126 and 127: 106 almost negligible. The final ac
58<br />
<strong>the</strong>rmometer wires) caused a more remarkable change of resistance, equivalent to as much<br />
as 3 mK at 2.1 K and 16 mK at 30 K. This apparently was due to relief of strain in <strong>the</strong> wire<br />
and seems to limit <strong>the</strong> stability of this model.<br />
A limited number of <strong>the</strong>rmal cycling tests on thin-film <strong>the</strong>rmometers indicate that<br />
stability to within ± 2 mK is achieved after about 15 cycles between room <strong>temperature</strong> and<br />
4.2 K, about twice <strong>the</strong> number of cycles as required <strong>for</strong> <strong>the</strong> wire-wound industrial type<br />
[Barber et al. (1987)].<br />
5.4 Self-heating<br />
Self-heating has been found to be closely <strong>the</strong> same <strong>for</strong> both U and W standard-type<br />
<strong>the</strong>rmometers; its magnitude is shown in Fig. 5.3 <strong>for</strong> currents of 0.1 and 0.3 mA. Near 1.5 K<br />
<strong>the</strong> self-heating falls dramatically as <strong>the</strong> 4 He filling of <strong>the</strong> capsule condenses to superfluid<br />
liquid and <strong>the</strong>rmal contact is vastly improved. As <strong>the</strong> <strong>temperature</strong> fur<strong>the</strong>r decreases, self-<br />
heating rises rapidly again. Self-heating in thin-film <strong>the</strong>rmometers is generally smaller than in<br />
wire-wound ones.<br />
Fig. 5.3: Typical self-heating effect <strong>for</strong> a 4 He-filled rhodium-iron <strong>the</strong>rmometer with measuring<br />
currents of 0.1 mA and 0.3 mA [Rusby (1982)].<br />
5.5 Calibration and Interpolation<br />
A rhodium-iron <strong>the</strong>rmometer is normally calibrated at many points in <strong>the</strong> range of<br />
interest and <strong>the</strong> data fitted by least squares as described <strong>for</strong> germanium. The equation<br />
chosen is usually of <strong>the</strong> <strong>for</strong>m
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