Argand plot

Figure 10.6 Cole-Cole (or Argand) plot of /" versus / recorded on a powder sample of 3 at 4.5 K at an external dc field of 500 Oe. The dashed line indicates the expected behaviour for a single relaxation time, while...

Figure 7. Left Schematized Argand plot for microscopes of different sensitivity. Right Sensitivity estimation for STEM (bottom curve) and HRTEM (top curve).

The method extends previous work of W. Sinkler, L.D. Marks and allows for a comparison with the Is-state model that approximates well an Argand plot in the first extinction distance while providing a promising path to go from an exit wave to the crystal structure ". J.R Jinschek et al. demonstrated by simulations and experiments on gold samples that a channeling plot (Figure 8) reveals the discrete nature of... 

Argand Plot Harmonic Variables Input ( ), Pade (o)... 

Argand Plot Input Exact Poles (x), Pade Poles (o), Pade Zeros ( )... 

We shall refer to it as the complex-plane impedance plot, recognizing that the same data can also he represented in the complex-plane capacitance or the complex-plane admittance plots. The terms Cole-Cole plot, Nyqidst plot and Argand plot are also found in the literature. 

Figure 11.10 plots the imaginary -Z" vs. the real part Z" of the complex impedance (Argand plot) exemplary for undoped CoTi03/La at 400°C under synthetic air. All plots showed semicircles and could be described with the impedance function of a parallel RC circuit equivalent. 

Fig. 11.10 Argand plot of CoTi03/La in synthetic air at T = 400°C and the corresponding circuit equivalent...

Samples with depressed semicircles have been adjusted with a CPE. The CPE is a nonintuitive circuit element. In case of a resistance R and a CPE in parallel, we observe the arc of a circle with the center some distance below the x-axis in the Argand plot. The corresponding circuit equivalent is called a ZARC-element.44... 

Figure 4. Argand plot of the flxed-V S-matrlx versus total energy for the process F+D- (v. 0)- DF(v,=3)+D for various. -values,...

The characteristic feature of these results Is the occurrence of a flattened portion of the Argand plot. Earlier colllnear (7 0 ) studies of F+D. with 1 0 showed this same behavlor(21) and It was found In that case to signal a resonance In the presence of strong... 

The reason the resonance In Y=0, 1=0 shows up only as a flattening of the Argand plot Is due to the stronger background for this case compared to that for Y=0, 1=10. 

Immediately recognized that the time delay for Y=0, 1=0 Is over twice as large as that for Y=0, 1=10. This is so In spite of the fact that the Argand plots In Figure 5 show a complete counterclockwise loop for Y=10, 1=0 and not for Y=0, 1=0. The time delay for FH2 Y=0, 1=0 Is about 3.4xl0 s. This corresponds to about 45 vibrations of the (free) molecule. The Y=0, 1=10 resonance lasts... 

Figure 5. Argand plot of the fixed y S-matrlx versus total energy for the process F+H2(v =0)- F(v =2)-HI for Y=0 , (a) 1-0 (b) 1-10.

A calculation of delay times t I/1 and phase shifts S p was the basis for a discussion of interference of direct and resonance processes in reactions of H + H2 (Schatz and Kuppermann, 1973). With their previous potential, these authors found resonances for i = 0, j = 0 at total energies 0-90 and 1-276 eV with widths 0 05 and 0-008 eV, respectively. The maximum delay time Too at the 1-276 eV resonance is about an order of magnitude greater than the period of symmetric stretch vibration of H3 at the saddle point. An Argand plot was also given for these resonances (see Fig. 4). 

Figure 19-5. Different possibilities to represent impedance data. Left Argand plot Right ...

The Argand plot is a very useful diagram by which several important parameters of the relaxation process can be obtained (Fig. 10.12). This type of diagram is also commonly called a Cole-Cole plot. The single relaxation time = 1) data form a half circle with the j-axis intercepts at and fip The symmetrically broadened relaxation p = 0.2) also results in a circular arc with the x-axis intercepts at fi, and 8, but the radius of the circle is considerably larger than in the case of a single relaxation time. The equation for the... 

Figure 10.12 Argand plot showing the circular arcs of the data presented in Fig. 10.11.

Figure 10.13 Argand plot showing two dielectric relaxation processes a and P for a hyper-branched polyester measured at 260 K. Experimental data are indicated by the points and the lines are obtained by fitting the Havrilak-Negami equation to experimental data. After data from Malmstrom et al. (1994).

This equation shows a great flexibility and can be fitted to most dielectric data. Figure 10.13 shows dielectric data presented in an Argand plot. Two circular arcs indicating symmetric broadening (y = 1) of the two relaxation processes OC and P are fitted to the experimental data. From the positions of the centres of the circular arcs, it is evident that the symmetric broadening factor is larger for the a process than for the p process. 

The type of relaxation time distribution can be easily determined from plots of e" versus e for a broad range of frequencies (so-called Cole-Cole plot or Argand plot, Fig. 8.29). The Cole-Cole plot for a single relaxation time is a semicircle between a = 8qo and e =eo centred on the e axis (Debye model) or below the e axis (Cole-Cole model). 

In analyzing the results of reactive scattering calculations, it is useful to use Argand plots of the elements of the scattering matrix. These are Cartesian plots of the imaginary part of S j versus its real part, the collision energy being the parameter on which both these quantities depend. In Fig. 10 we present such... 

For the purpose of data analysis, the complex dielectric relaxation is usually presented in graphical form as an Argand plot of s"((o) vs 8 (co). This graphical representation is commonly known as the Cole-Cole plot. For the case of a simple Debye relaxation (single relaxation time, cf. eqn 4.8), the (e, e") points lie on a semicircle with the center on the e -axis at e = (8o —8qo) and intersections at 8 = 8oo and e = 8o see Fig. 4.2. For a distribution of relaxation times, the Cole-Cole plot always deviates downwards from the semicircle on the interval Sq—Soo, i.e. it lies completely within the semicircle. These deviations take different forms, but... 

Fig. 4.6. Argand plots of dielectric relaxation spectra of the nematic phase of some typical liquid crystals in two principal geometries of measurement. Numbers refer to frequency (in MHz) of the probing electric field. (From Ref. 23).

Fig. 4.15. Typical Argand plots of the complex dielectric permittivity of rod-like poly(n-alkyl isocyanate) solutions in toluene at room temperature, (a) PHIC and (b) copoly(n-butyl, nonyl-isocyanate) (PBNIC). L and L.C. indicate isotropic and liquid-crystalline states of solution, respectively, and / is the frequency. ...

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