Resonance temperature coefficient

All piezoelectric crystals should have a good temperature coefficient, that is. should show as little change in resonant frequency as possible under large variations in temperature. Ideally. Ihe piezoelectric constant of proportionality between the mechanical and electrical variables must be the same for both direct (pressure-to-electricily) and converse effects... 

Nitric oxide exhibits a negative temperature coefficient for vibrational relaxation in self-collisions, below about 700° K. It has been suggested170 that this effect arises because the potential energy of the point of resonance, postulated by Nikitin, is strongly orientation dependent. (In this case the maximum depth of the potential minimum can be no greater than about 3 kcal. mole-1 which will not steepen the potential sufficiently to account for the observed relaxation rate, with l = 0.18 A.)... 

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.

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]... 

There are two ferrite material properties which were not discussed in Section 9.3.1 but which are important in the inductor context they are the temperature and time stabilities of the permeability which, of course, determine the stability of the inductance. The temperature coefficient of permeability must be low, and this has been achieved for certain MnZn ferrite formulations as indicated in Fig. 9.18. A small residual temperature coefficient of inductance can be compensated by a suitable coefficient of opposite sign in the capacitance of the resonant combination. 

When we determine values of 7 for benzene rings attached to polymers, we find that they are much shorter than for benzene itself they are in fact at the lower limit of usefulness of the direct method. We have found (3) that for the phenyl resonance of a low molecular weight polystyrene in carbon disulfide 7 is only about 0.4 0.1 sec. at 25°. For the backbone protons, 7 is even shorter and cannot be measured by the direct method. For the phenyl groups of poly-y-benzylglutamate in trifluoroacetic acid, 7 is 0.7 0.1 sec. Recently, more reliable values have been obtained for polystyrene by the spin echo method (72). For a polymer of molecular weight 63000 in tetrachloroethylene, three 7 X values could be resolved. At 25°, these were 0.033 sec. for the aliphatic protons, 0.076 sec. for the ortho protons and 0.20 sec. for the meta-para protons. The temperature coefficients for all three Tt values correspond to a heat of activation of about 3 kcal/mole. The differences in the absolute Tx values at the aromatic positions can be explained in terms of of differences in the sums of r e in equation (56). The shorter aliphatic Tj value probably reflects also a longer correlation time for backbone... 

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)...

The T in the designations AT, BT, and ST stands for temperature AT and BT were the first two widely recognized temperature-coefficient-optimized cuts for TSM quartz resonators. 

Several low temperature-coefficient materials have been characterized for AW applications. The ST and AT cuts of quartz provide nominal zero temperature coefficients near room temperature for SAW and TSM resonator devices, re-... 

Mossbauer spectroscopy is the study of recoilless resonant fluorescence " Sn Mossbauer spectroscopy has been found to be a most usefifl method for studying the bonding and stereochemistry of tin compounds in the solid state. The two most important parameters are the isomer shift (5, mm s ) and the quadrupole sphtting (A q, nuns ), although the recoil-free fractions and temperature coefficients can also supply useful structural indications. 

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. 

For materials applications, the chemical shifts of methanol and ethylene glycol can be monitored in the liquid state to follow temperature [Hawl]. The most sensitive ehemical shift is the Co resonance of aqueous Co(CN)e with a sensitivity of 0.05 K at 7 T and 0.2 K at 2T [Dorl]. Furthermore, dibromomethane dissolved in a liquid crystal is a temperature sensitive NMR compound [Hed 1 ], and known phase-transition temperatures can be exploited to calibrate the temperature control unit [Hawl J. In temperature imaging of fluids, temperature can be determined from the temperature dependence of the selfdiffusion coefficient but convective motion may arise in temperature gradients [Hedl]. In the solid state, the longitudinal relaxation time of quadrupolar nuclei like Br is a temperature sensitive parameter [Suil, Sui2]. In elastomers, both T2 and Ti depend on temperature (Fig. 7.1.13). In filled SBR, T2 is the more sensitive parameter with a temperature coefficient of about 30 xs/K [Haul]. 

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... 

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