Very low temperature measurements

Seven simulations were carried out at temperatures ranging between 7 and 16 mK. Data used at the various temperatures for the lumped elements are plausible values estimated from very low-temperature measurements. They are reported in Table 15.2. 

The extension of very low temperature measurements toward neutral chemistry or relaxation problems would also be of extreme Interest from an astrochemical point of view. The CRESU technique seems especially suitable for this... 

There are three main families of temperature sensors thermocouples, resistance thermometers and thermistors. Some old reactors still have bimetalic thermometers (binary or with local readings), but it is suggested that they be replaced in order to allow the operator to follow closer any temperature transient from the control room. Other temperature sensors, like semi-conductor thermometers, consisting of doped germanium sensors, have a complex resistance temperature relationship and are useful only for very low temperature measurements. 

Many substances exist in two or more solid allotropic fomis. At 0 K, the themiodynamically stable fomi is of course the one of lowest energy, but in many cases it is possible to make themiodynamic measurements on another (metastable) fomi down to very low temperatures. Using the measured entropy of transition at equilibrium, the measured heat capacities of both fomis and equation (A2.1.73) to extrapolate to 0 K, one can obtain the entropy of transition at 0 K. Within experimental... 

Recent research (1995-) has produced at very low temperatures (nanokelvins) a Bose-Einstein condensation of magnetically trapped alkali metal atoms. Measurements [41] of the fraction of molecules in the ground... 

Voltage measurement have been made at very low temperatures using a superconductor as one leg of a thermocouple. Eor a superconductor, S is zero, so the output of the couple is entirely from the active leg. The Thomson heat is then measured at higher temperatures to extend the absolute values of the Seebeck coefficients (7,8). The Thomson heat is generally an order of magnitude less than the Peltier heat and is often neglected in device design calculations. 

A very low temperature rise at the main joints is a measure to prevent the joints from overheating due to eorrosion. ... 

Langer et al. [10] measured also electrical resistance of individual MWCNTs at very low temperatures and in the presence of a transverse magnetic field. As for the case of the microbundle, the CNTs were synthesised using the standard carbon arc-discharge technique. Electrical gold contacts have been attached to the CNTs via local electron beam lithography with an STM. The measured individual MWCNT had a diameter of about 20 nm and a total length of the order of 1 im. 

In Fig.. I we present the temperature dependence of the conductance for one of the CNTs, measured by means of a three-probe technique, in respectively zero magnetic field, 7 T and 14 T. The zero-field results showed a logarithmic decrease of the conductance at higher temperature, followed by a saturation of the conductance at very low temperature. At zero magnetic field the saturation occurs at a critical temperature, = 0.2 K, which shifts to higher temperatures in the presence of a magnetic field. 

Electrical resistance thermometers, the most widely used of which is Callendar s platinum resistance thermometer. This is probably the most convenient and accurate apparatus for measuring temperatures between the boiling-point of liquid air (—190° C.) and the melting-point of platinum (1,500° C.). Lead has recently been applied at very low temperatures. 

This remarkable result has been verified by experimental measurements of specific heats at very low temperatures, viz., in liquid air and liquid hydrogen (cf. references in Chap. I.). It was formerly believed that the specific heats of solids approached small positive limiting values at the absolute zero, but the form of the curve at very low temperatures alters appreciably, and it may be inferred that the specific heat is vanishingly small at... 

The chemical constants may therefore be determined directly by the measurement of vapour pressures, especially at low temperatures. Equation (9), which is more general, shows that the chemical constant is determined for a. homogeneous gas as soon as we know A, and C, as functions of temperature, and the vapour pressure at one temperature. These data, especially vapour pressures at very low temperatures, are not very well known at present, and some other method must therefore be used in the determination of the chemical constant. Several such methods have been proposed by Nernst (loc. cit. cf. also Haber, Thermodynamics of Technical Gas Reactions, pp. 88—96 Weinstein, Thermodynamik and Kinetik III., 2, pp. 1064—1074). 

By means of the experimental methods briefly referred to in 9 a large number of specific-heat measurements have been made at very low temperatures. In Fig. 91 we haye the atomic heats of some metals, and of the diamond, represented as functions of the temperature. The peculiar shape of the curves will. be at once apparent. At a more or less low temperature, the atomic heat decreases with extraordinary rapidity, then apparently approaches tangentially the value zero in the vicinity of T = 0. The thin curves represent the atomic heats calculated from the equation ... 

One way to make the short-lived intermediates amenable to study is to increase their lifetime, usually by irradiating in the solid state and at very low temperatures. Then, the intermediates can be measured at the end of the irradiation by optical absorption spectroscopy or ESR. 

Rodebush has also implied that the accuracy with which very low temperatures can be measured is restricted by the uncertainty principle and by the nature of the substance under investigation. However, the accuracy of a temperature measurement is not limited in a serious way by the uncertainty principle for energy, inasmuch as the relation between the uncertainty in temperature and the length of time involved in the measurement depends on the size of the thermometer, and the uncertainty in temperature can be made arbitrarily small by sufficiently increasing the size of the thermometer we assume as the temperature of the substance the temperature of the surrounding thermostat with which it is in either stable or metastable equilibrium, provided that thermal equilibrium effective for the time of the investigation is reached. 

Any substance that somehow changes with alterations in its temperature can be used as the basic component in a thermometer. Gas thermometers work best at very low temperatures. Liquid thermometers are the most common type in use. They are simple, inexpensive, long-lasting, and able to measure a wide temperature span. The liquid is almost always mercury, sealed in a glass tube with nitrogen gas making up the rest of the volume of the tube. 

Other thermometers operate by sensing sound waves or magnetic conditions associated with temperature changes. Magnetic thermometers increase in efficiency as temperature decresises, which makes them extremely useful in measuring very low temperatures with precision. Temperatures can also be... 

The advantages of measuring at very low temperatures are well established [4], Because of the increased speed of data collection, it now becomes feasible to consider the use of liquid helium as a cryogen. A prototype open-flow helium cooling device using mainly off-the-shelf components has been developed [3],... 

The fact that the water molecules forming the hydration sheath have limited mobility, i.e. that the solution is to certain degree ordered, results in lower values of the ionic entropies. In special cases, the ionic entropy can be measured (e.g. from the dependence of the standard potential on the temperature for electrodes of the second kind). Otherwise, the heat of solution is the measurable quantity. Knowledge of the lattice energy then permits calculation of the heat of hydration. For a saturated solution, the heat of solution is equal to the product of the temperature and the entropy of solution, from which the entropy of the salt in the solution can be found. However, the absolute value of the entropy of the crystal must be obtained from the dependence of its thermal capacity on the temperature down to very low temperatures. The value of the entropy of the salt can then yield the overall hydration number. It is, however, difficult to separate the contributions of the cation and of the anion. 

For the odd electron systems, tf3 4Z andc 5 6Z+, measurements of the average susceptibility at very low temperatures are not likely to prove as informative as for the even electron, d 32 species. This is because whereas the latter yield a limiting value of 1 as T -+ 0, from which D/g2 can be directly estimated, the former lead only to a limiting value of the (x)-1 vs. T slope, which except for large values of D will be difficult to determine. Nevertheless calculation shows that even in cases for which only very small deviations from the spin-only behaviour are to be expected, e.g. V(Cp)2, the susceptibility may yet show very considerable anisotropy. Thus, with the parameters of Prim and Van Voorst (47), V(Cp)2 is predicted to show an anisotropy, (x — X )Kx of some 5% at liquid nitrogen temperatures, whilst Ni(Cp)2, with the much larger/) value, should show an anisotropy of about 30% at 77K, which is reduced only to some 12% even at room temperature. There is thus considerable scope for the measurement of anisotropic susceptibilities, and although this technique would probably not be applicable to the d8 bis-arenes (97,... 

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