Zener ratio

The condition for isotropic elasticity, as has been seen, is C44 = C55 = Cge = Cn C12). Cubic crystals, because of their high symmetry, almost satisfy this condition. Zener introduced the ratio 2C44/(cn - C12) as an elastic anisotropy factor for cubic crystals (Zener, 1948a). In a cubic crystal, if the Zener ratio is positive, the Young s modulus has a... 

The reverse condition holds when the Zener ratio is negative. Similar equations for the Young s moduli for the other crystal classes can be derived from the expressions given in Nye s book (Nye, 1957). 

The parameter Z is known as the Zener ratio or the elastic anisotropy factor. For the Young s modulus representational surface in cubic crystals, this anisotropy... 

How could you recognize from the array of elastic constants that a single crystal would produce a shear strain in response to a normal stress The Zener ratio is the ratio of the shear moduli for deformation on which crystallographic planes in a cubic crystal (include direction of displacement) ... 

For cubic crystals. Young s modulus is a maximum along < 100> if the Zener ratio Z is less than unity. For Z>1, Young s modulus is a maximum along. ... 

If the Zener ratio is unity, the shape of the Young s modulus representational surface for a cubic crystal is. ... 

The Zener ratio is less than unity for most rock-salt structures. The... 

This is also true because any trace inductance here gets multiplied by the square of the turns ratio, and reflects into the primary side, as discussed previously. This greatly increases the dissipation in the primary-side RCD/zener clamp and severely degrades the converter efficiency. We have to really struggle to minimize secondary-side inductances, especially for low output voltage rails, that is, those with higher turns ratios. 

The c/a ratio is greater than for V02, which implies that the n band (i.e. that with d-orbital lobes in the basal plane) is more occupied than in V02 (Goodenough 1971, p. 352). But we think that if it were not ferromagnetic, the n band, in contradistinction to V02, would be wholly above the Fermi energy. The Hubbard correlation term U, however, produces localized moments for the 3d2 states, as explained in Chapter 3, and these, if oriented ferromagnetically, would just fill the tjj band. The filled band (for spin-up electrons) will now overlap the n band, allowing ferromagnetic interaction of Zener or RKK Y type between the d2 moments, as described in Chapter 3. The T2 term in the resistivity could be explained as in Chapter 2, Section 6. 

Another clue to why this branching ratio changes in this counterintuitive way with laser intensity is to note that the three-photon signal is peaked near v = 15, while the two-photon signal is peaked near v = 7. This implies that high vibrational excitation of the ion enhances the curve crossing necessary to produce the two-photon signal. This is exactly the trend observed in the Landau-Zener formula calculations performed by Zavriyev et al. [50], In their calculations on H2 the probability to cross the... 

Table II Comparison of the ratio k/k E °f quantum rate k over k, which is the TST result corrected for zero-point energy in the reactant well. Also shown are the Landail-Zener and centroid calculations67 and the molecular dynamics with quantum transition result.68...

Fourth, Jaime and Salamon (1999) have pointed out that a(T) increases more sharply than exponentially on cooling to rmax in fig. 30 and that the additional entropy transported increases on crossing the () -() phase boundary at tc. This observation is consistent with a progressive transformation from Zener to small polarons in the hole-poor phase as the hole concentration x = 0.30 in this phase is diluted by the trapping of Zener polarons in the hole-rich phase. Such a transformation would double the number of sites available to a polaron and would therefore increase the a of eq. (26) by reducing c = (1 — r)2x toward c = (1 — r)x, where r is the ratio of trapped to free polarons. In the O phase, most of the polarons appear to be small polarons at 7 N. 

Note that if the zener voltage is too close to the chosen Vor, the dissipation in the clamp goes up steeply. Vor therefore always needs to be picked with great care. That simply means that the turns ratio has to be chosen carefully ... 

Note that if we plot the zener dissipation equation presented earlier, as a function of Vz/Vor, we will discover that in all cases, we get a knee in the dissipation curve at around Vz/Vor = 1 4. So here too, we pick this value as an optimum ratio that we would like to target. Therefore... 

This historical work provides a model to describe the evolution of the so-called growth coordinate (e.g. the phase radius in 3D) for isothermal, diffusion-induced transformations ratios of different coexisting phases and morphologies are not considered, (Zener, 1949). 

Electronic nonadiabatic factor (Xeff) as a function of the ratio between nuclear and elfective electronic frequencies Vv/(XeiVei), or adiabaticity parameter (IkqsI ) as a function of the Landau-Zener classical transition probability (plz), illustrating their rapid convergence to the same as5miptotic limits. 

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