Heterodyne beating

The dipole moment of naphthazarin has been deduced from the measurements of the dielectric constants of its solutions in benzene and dioxan, respectively. A heterodyne beat apparatus has been used at 4 4 Mhz, the temperature of the solution was 20°C. The molecular refraction has been computed [8] from standard bond refractions, the experimental determination being impossible because of the strong... 

An important and precise traditional method of measuring capacitance for dipole moment determinations is the heterodyne beat method, a particular form of the null method mentioned above. The output of an LC oscillator incorporating the capacitance... 

Note the similarity to heterodyne beat and to one- and two-dimensional moire patterns... 

Measurements of e,.—Stability under pressure is the prime requirement for capacitance cells used to determine dielectric virial coefiScients. Cells of both parallel-plate and cylinder-within-a-cjirnder design, stable to a few parts in 10 and usable to over 200 atm, have been described by a number of authors. " Cells for use in the microwave region and cells for measuring refractivity > have also been described. Early measuremoits at radio frequencies relied on the heterodyne beat method, " but more recent work " has utilized the three-terminal transform ratio-aim technique developed by Cole and Gross. This second method eliminates difficulties due to stray capacitances and provides accuracies of better than 1 part in 10 . For an exceUent review of techniques at both ratfio and microwave frequencies see ch. 2 of ref. 53. For refractivity methods see refs. 45,46, and 54. 

The overall dipole moments of many covalent azides were obtained from measurements of the dielectric constants of their benzene solutions by the heterodyne beat method (Table 9). 

The dipole moment of D-fructose was studied by the heterodyne beat method, with pyridine or p-dioxane as the solvent, and a value of 15 Debye units was obtained, whereas other hexoses showed values in the range of 11 to 12. 

The dielectric constants needed for the determination of dipole moments are obtained by a heterodyne beat method or the resonance and bridge methods. The instrument specifically adapted for measurements of dielectric constants for dipole moments is a dipole meter model DM-01 manufactured by Wissenschaflich-Technische Werkstatten, Weilheim, Germany, equipped with two different thermostatted cells for two ranges of dielectric constants (cell DFL-1, e 1.0 to 3.4, cell DFL-2, e 2 0 to 6.9). The other dipole meter which used to be available from Toshniwal Brothers, Ltd., Madras, India, is not sufficiently sensitive for measurements of dielectric constants of diluted solutions and is better suited for measurements of large differences, such as the dielectric constants and dipole moments of different solvents. 

The first term represents the shot noise, the second is the dc term, and the third term gives the heterodyne beat spectrum with the difference (co — coq) and sum (o) -h coo) frequencies. The detector is not fast enough to detect the sum frequency. The output signal of the third term therefore contains only the difference frequency (co — ct)o)- If this difference frequency lies in an inconvenient frequency range, the local oscillator can be shifted with an acousto-optic modulator to the frequency COL Act) in order to bring the difference frequency 0)+ Acd — cog into an easily accessible range [947]. 

The modulation structure of the resulting field ED(t) in front of the photodetector deserves a special discussion. In general, the Raman signal field from the sample cell consists of two components which can be characterized by a phase relationship between carrier and Raman sidebands corresponding to the cases of pure amplitude (AM) and frequency (FM) modulation (see Fig. 2). With the superposition of Eq and E by means of an analyzer, these AM and FM components lead to an amplitude and frequency modulation of the detector field Eo(t), respectively. The heterodyne beat signal of a phase-insensitive, square-lav photodetector now is connected only with the AM component of the Raman signal field and it can therefore be... 

Fig.11.31. Fourier transform heterodyne beat spectrum of CH3F derived from Stark switched two-pulse photon echoes [11.491...

Stark pulse on, but radiates when it is off, the emission is Stark shifted from the laser and four heterodyne beat frequencies are produced at the detector, each beat being due to two transitions M M. The four lines are 170 KHz wide and are spaced at 0.83 MHz [11.50]. The exponential decay of the echo signal with increasing delay time t, which is plotted in Fig.11.31, samples the homogeneous dipole dephasing rate due to elastic and inelastic collisions (see Sect.11.4.1). This technique therefore allows measurement of collision rates separately for different M levels. Since different velocity groups of molecules can be sampled, depending on the Stark shift, information on the velocity dependence of the collision rates can also be obtained (see Chap.12). 

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