Comparison with the Experimental Data

The theoretical curves are in close agreement with the experimentally observed values of the steady-state creep rate in a-iron at 813, 873, 923 and 973 K. 

It can be seen that the theory does not represent the experimental results at 773 K. 

We obtained analogical results for other metals and for solid solutions. For example, the measured rate of the steady-state creep s equals to 13.9 x 10 s for alloy Ni + 9.9 at.% Al at 873 K and o = 136 MPa. In the same conditions, the calculated E value equals to 13.0 x 10 s.  

The present theory is imderstood to be valid within certain limitations. It has a scope of application. When temperature is relatively low, the dislocation climb is depressed and hence the regular sub-boundaries cannot be formed. The lower limit of 

The stable sub-boundaries are of major significance in the process of high-temperature strain for pure metals and solid solutions. The upper stress limit of the sub-boimdary stability depends upon metal properties and temperature. The lower the shear modulus fi and the higher temperature, the lower the limit. An inactivated emission of dislocations from sub-boimdaries occurs when the applied external stress is higher than about 2 x 10 . Then the sub-boimdaries break up. 

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Extensive comparisons of experimental frequencies with HF, MP2 and DFT results have been reported [7-10]. Calculated harmonic vibrational frequencies generally overestimate the wavenumbers of the fundamental vibrations. Given the systematic nature of the errors, calculated raw frequencies are usually scaled uniformly by a scaling factor for comparison with the experimental data. 

For the rate expressions R and R given above, Equations (1) to (6) were solved numerically using the PDEPACK routine of Madsen and Sincovec (33). The computational results as well as their comparison with the experimental data will be discussed in the next section. 

The comparison with the experimental data will then be made in Sections V and VI ... 

Harris and Dranoff [115] appear to have been the first to use the LSPP model to study the performance of a photochemical reactor for scale-up purposes. Experimentally, two sizes of perfectly mixed photochemical reactor were used for the decomposition of hexachloroplatinic acid in dilute aqueous solution, and the result of the theoretical analysis was acceptable in comparison with the experimental data. 

Equation 36 is divided into the contributions to the diffusion of substitutional impurity under nonoxidizing conditions, DSI, and the enhanced contribution due to oxidation, AD0. Figure 16 shows the data of Taniguchi et al. (44) for oxidation-enhanced diffusion of P and B versus the total number of dopant impurities per square centimeter, QT. The calculated values of DSI and AD0 are shown in comparison with the experimental data. Reasonable agreement is obtained. Thus, Taniguchi s model of self-interstitial recombination with vacancies is consistent with the models of high-concentration diffusion of B and P used by Fair in his calculations. 

The fit of the theoretical isotherms calculated using the Si and Ei parameters in comparison with the experimental data is satisfactory, as shown in Figures 2 and 3. The sum of squares error calculated by the expression... 

Within the approximation of considering the complexes in the gas phase, the optimum geometry and vibrational frequencies of bi- and mono-dentate complexes have been obtained from a full geometry optimisation. To the best of our knowledge, no precise geometrical parameters are available for these complexes. Next, the vibrational frequencies have been computed as commented above and comparison with the experimental data is used to validate the particular theoretical approach chosen to carry out the present study. 

In reality several aggregation numbers of the micelles occur, but from the simple equilibrium in (3.2) one can make a number of relevant conclusions. The larger the value of n, the more cooperative is the association and the more one approaches phase separation behavior. This is illustrated in Fig. 3.1 which shows plots, for two values of n, of the fraction of the amphiphile that enters the micelle as a function of the total amphiphile concentrations. A comparison with the experimental data in Figs. 

For an illustrative calculation, we apply the TBI model to predict the number of bound ions (Eq. (22.14)) for a 24-bp DNA duplex immersed in an ionic solution with fixed 2 mM [Na+] and different Mg2 1 ]. As shown in Fig. 22.2, comparison with the experimental data (Bai el al., 2007 Chu et al, 2007) shows that the predictions from the TBI model are more accurate than the results from PB. For example, for 2 mM [Mg2+], the improvement for Mg2 1 -binding number is 20%. 

Figure 22.2 shows the TBI-predicted folding free energy AGj- and melting temperature Tm for short DNA duplexes as functions of [Mg +J (Tan and Chen, 2006a). Comparisons with the experimental data indicate that the TBI model gives much improved predictions than the PB theory (Fig. 22.3). 

Depending on the scheme chosen, the birefringence experiments provide [143,144] direct measurements of either Av or (Av)2. To present the theoretical results in a form suitable for comparison with the experimental data, let us consider the orientational oscillations induced in the dipolar suspension by a harmonic held H = Hq cos (at and analyze the frequency dependencies of the spectra of the order parameters (P2) and (Pi)2- As formula (4.371) shows, the latter quantities are directly proportional to Av and (Av)2, respectively. Since the oscillations are steady, let us expand the time-dependent orientational parameters into the Fourier series... 

The feasibility of some of these radical pathways has been examined using Marcus theory to obtain rate constants for comparison with the experimental data (Eberson, 1984). For some relevant anions, including hydroxide, methoxide, t-butoxide, the anion of benzaldehyde hydrate and di-2-propyl-amide, the necessary E°(RO-/RO) values are available or can be estimated with sufficient accuracy. For the reaction of t-butoxide with benzophenone in THF, or the benzaldehyde hydrate anion with benzaldehyde in aqueous dioxan, direct electron transfers between the anion and the neutral are not feasible the calculated rate constants are orders of magnitude too low to be compatible with the observed reduction rates. Any radicals observed in these reactions must arise by some other more complex mechanism. The behaviour of an aromatic aldehyde hydrate dianion has not been examined in this way, but MNDO calculation (Rzepa and Miller, 1985) suggests that such a species could easily transfer either a single electron or a hydrogen atom to an accepting aldehyde. 

The values given in Table IT and referring to the potassium silicate solution already considered before (paragraph entitled "Comparison with the experimental data obtained by Harris at al. ") show a good agreement between experimental and calculated concentrations for the main oligomers. Satisfactory agreement was found as well for the other species not mentioned in Table IT. 

The results of the application of these equations to a number of polymers are given in Table 13.5 in comparison with the experimental data. The agreement is very satisfactory. 

In table 18, the results of the hyperfine calculations are collected. A comparison with the experimental data for Ax = Ajgo - TZZ and Ay = Aiso + Tzz is given. The isotropic hfcc Aiao is also included, because its strong dependence on the theoretical method is the reason for the variations of A and Ay between different methods. Since the anisotropic term Tzz is nearly constant with respect to the theoretical method, it is not given. For all calculations the QCISD/6-31G optimized geometries (CCO Rcc = 1-371 A, Rco = 1173 A CNN RNn = 1-231 A, Ron = 1-237 A NCN Ron = 1-245 A) were used. All... 

Figures 21a, b show the 4-CP, 4-CC, and HQ concentrations derived from inserting the estimated parameters in the kinetic model and a comparison with the experimental data under different operating conditions. Symbols correspond to experimental data and solid lines to model predictions calculated with Equations (64)-(66) and Equations (71)-(74). Eor these experimental runs, the RMSE was less than 14.4%. These experimental 4-CC and HQ concentrations are in agreement with the proposed kinetic mechanism of parallel formafion of fhe intermediate species (Figure 16), and also with the series-parallel kinetic model reported by Salaices et al. (2004) to describe the photocatalytic conversion of phenol in a slurry reactor under various operating conditions. ...

As far as quantitative comparison with the experimental data is concerned, we decided to compare directly the experimentally determined orientation with the theoretical prediction. This requires a rescaling of the theoretical orientation in order to match it with the experimental data at times of the order of xa- A satisfactory agreement for the average orientation is observed as shown in Figure 14. 

The calculated hyperfine constants for the chosen directions of the C84H7g[NV] cluster in comparison with the experimental data are shown in Fig. 2. 

The final stage in any polymorphic simulation is to check the reliability of the simulated data. This can be achieved by comparing a variety of data, e.g., density, lattice energies, etc. With the advent of reliable software, a simulated diffraction pattern is now used as the primary comparison with the experimental data. Prior research has shown that computer simulations can successfully predict the structure of an unknown polymorph or determine the potential for polymorphisim (37). 

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