Temperature coefficient of frequency

In its original application as timing reference, special care has been taken to minimize the perturbations on frequency of the selected mode of vibration caused by unavoidable variations in the environment, first of all temperature and acceleration. The breakthrough of quartz crystal resonators in timekeeping is very much correlated to the existence of a specific crysfal cuf, at which the device resonance frequency provides a zero temperature coefficient of frequency at 25 °C and a remarkable temperature stability around room... 

The two most important cuts, AT and BT, provide a zero temperature coefficient of frequency. Actually, when departing from 25 °C the frequency of AT-cut crystals varies in a cubic manner with respect to temperature. The temperature dependence of BT-cut crystals is quadratic. This second-order response to temperature is larger than the cubic variation of AT-cut quartzes. 

Fig. 3 Temperature coefficient of frequency for pure shear mode of rotated 7-cut quartz (courtesy of J. Vetelino [20])...

Ideally a standard cell is constmcted simply and is characterized by a high constancy of emf, a low temperature coefficient of emf, and an emf close to one volt. The Weston cell, which uses a standard cadmium sulfate electrolyte and electrodes of cadmium amalgam and a paste of mercury and mercurous sulfate, essentially meets these conditions. The voltage of the cell is 1.0183 V at 20°C. The a-c Josephson effect, which relates the frequency of a superconducting oscillator to the potential difference between two superconducting components, is used by NIST to maintain the unit of emf. The definition of the volt, however, remains as the Q/A derivation described. 

The CPCM structure also determines the following properties important in practice the temperature coefficient of resistance, dependence of conductivity on frequency, etc. However, the scope of this review does not include the consideration of such dependences and they can be found in [2, 3,12]. 

The temperature coefficient of the reaction is still given by the Arrhenius equation. It is reasonable to assume that the velocity constant of the reaction is proportional to the radiation density. Now chemical heats of activation correspond to frequencies in the short infra-red region, and for these values of v the term ehvlkT in Planck s equation is large in comparison with unity. The expression for Uy thus reduces to... 

Figure 1. Temperature coefficient of the index of refraction of water. Measurements at four different frequencies (60)...

Boos and Flauschildt90) obtained for the model copolymerization of phenylglycidyl ether with hexahydrophthalic anhydride activation energies of 96 kJ/mol up to 75% conversion and 27 kJ/mol for higher conversions. Frequency factors are also very different (log A = 13.7 and 5.5, respectively). The frequency factors as well as the temperature coefficients of the solution viscosities depended on the initiator concentration. The activation energy determined by the same authors 90) for the curing of epoxy resins at conversions lower than 75% was 86.4 kJ/mol and the frequency factor log A = 11.8 whereas at higher conversions these values were not obtained. 

Table 5.1 Microwave properties of the most important microwave dielectrics (SC= bulk single crystals , bc = bulk ceramics , tf = thin films , r/ = temperature coefficient of resonant frequency . The materials marked with are tuneable dielectrics.

High-power transmitter capacitors for the frequency range 0.5-50 MHz for which the main requirement is low loss a negative temperature coefficient of permittivity is tolerable since it limits the power through the unit when its temperature increases. 

A common function of circuits is the provision of an accurate resonance state. For instance, for a resonance frequency to stay within a tolerance of 0.1% over a temperature range of 100 K a temperature coefficient of less than 10 MK 1 would be required. It might be achieved in the 10-100 kHz range by using a manganese zinc ferrite pot-core inductor (see Section 9.5.1) with a small positive temperature coefficient of inductance combined with a ceramic capacitor having an equal, but negative, temperature coefficient. This is clear from the resonance condition... 

A ceramic of relative permittivity 37 is in the form of a cylindrical DR for use at 1 GHz. Estimate the overall dimensions of the DR. The ceramic has a temperature coefficient of linear expansivity of 5MK-1 and a temperature coefficient of permittivity of — 16MK-1. Estimate by how much the resonance frequency will change for a 5°C change in temperature. [Answer diameter 2.5 cm 15 kHz]... 

According to the first postulate the cause of activation is radiation. Perrin was impressed by the fact that reaction rate in a uni-molecular reaction does not depend on the collision frequency, and so he sought for some source of energy other than collisions. Radiation is a natural source to consider. Furthermore, he pointed out that the temperature coefficient of the emission of monochromatic light from a heated solid is the same as the temperature coefficient of most chemical reactions. The similarity might be coincidence, but at the time it seemed significant. 

Quite a different situation is experienced in NQR spectroscopy. Dehmelt and Kriiger (1950/1951) 3-6> found that the temperature dependence of NQR frequencies in organic materials is considerable. For instance, the temperature coefficient of i (35Cl) for chlorine bonded to carbon atoms is found to be in the range... 

Quartz Crystal Thermometer. The temperature coefficient of the resonant frequency of quartz (14-20 MHz), using the piezoelectric effect, is a function of temperature (1 kHz per degree). In the temperature range -80°C to 230°C, an electronically controlled quartz crystal thermometer can be accurate to 0.02°C and has a sensitivity of 10 microdegrees centigrade in temperature difference measurements. 

Further evidence for pi bonding is provided by the temperature coefficients of the resonance frequencies of these complex ions (see Table 6). The temperature coefficient is normally expected to be negative because of the decrease in the effective electric field gradient with increasing molecular bending vibrations (36,68, 69). Stretching vibrations do not reduce the principle electric field gradient (70). From Table 6... 

Table 6. Temperature coefficients of the resonance frequencies of some transition metal hexachloro complexions (58)...

Raman spectra can also be used to determine the degree of dissociation of some molecules, namely, those that react with the solvent to give ions (e.g., HCl). If the Raman frequency shifts for the dissociated molecules are known, then they can be used to calculate equilibrium constants at different temperatures. Then, once the temperature coefficient of the equilibrium constant K is known, one can determine AH° and AS" of the dissociation reaction (Section 2.13). 

With the progress in microwave telecommunication technology, dielectric materials have come to play an important role in the miniaturization and compactness of microwave passive components. The dielectric materials available for micro-wave devices are required to have predictable properties with respect to a high dielectric constant (K), high quality factor (Qf), and small temperature coefficient of resonant frequency (TCP). Numerous microwave dielectric materials have been prepared and investigated for their microwave dielectric properties and for satisfying these requirements. In particular, complex perovskite compounds A(B,B )03... 

FIGURE 22.7 Temperature coefficient of resonant frequency (TCP) of PCCN, PCMT, PCFTN specimens with A-site and B-site bond valence. 

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