Crossover transition

A series of NFS spectra of the spin-crossover complex [Fe(tpa)(NCS)2] were recorded over a wide temperature range [45]. A selection of spectra around the spin-crossover transition temperature is shown in Fig. 9.13. At 133 K, the regular quantum-beat structure reflects the quadrupole splitting from the pure high-spin (HS) phase, and the envelope of the spectrum represents the dynamical beating with a minimum around 200 ns. Below the transition, at 83 K, the QBs appear with lower frequency because of smaller AEq of the low-spin (LS) phase. Here the minima of... 

Example Problem Use the electromagnetic selection rules to identity the character of the crossover transitions that could link the second excited state at 2.080 MeV ( + ) in 23Na with the ground state ( 1 ). 

Fig. 3. Temperature dependence of Raman spectra of [Mn(taa)]. Arrows indicate peaks showing remarkable intensity changes at around spin-crossover transition Tc = 48 K.

Both spin-crossover transitions (HS < LS, FO LS) are first order accompanied by definite jumps of populations, while the cooperative Jahn-Teller transition (HS FO) is weak first-order (very close to a second-order transition). It suggests a possibility of observation of hidden cooperative Jahn-Teller transition (the broken line in Fig. 7) between the metastable HS and FO phases, if the HS phase could be supercooled enough below the spin-crossover transition temperature Tc by a rapid cooling. 

The three adjustable parameters are determined, A/kB = 90 K, Jo/kB = -36 K, and J /kB = 125 K, so as to reproduce the spin-crossover transition temperature Tc = 48 K, the virtual Jahn-Teller transition temperature rJT = 6 = 26 K, and the effective LS-HS gap in the LS phase Acff/kB = 340 K. (Note Aeff is approximated by A + 2Jx in this mean-field model.) This choice of model parameters gives a phase sequence from the LS to HS with increasing temperature, corresponding to the arrow path in Fig. 7. Temperature dependence of thermodynamic quantities (Fig. 8) is calculated along the path indicated by the arrow in Fig. 7, where the discontinuities arising from the first-order spin-crossover transition are recognized Ap0 = 0.99, AH = 0.64 kJ mol-1, and AS = 13.3 J K-1 mol-1 These theoretical... 

Jahn-Teller effects are rarely adopted in theoretical treatments of spin-crossover phenomena, except Kambara s model for Fe(II) complexes [24] and Bersuker s for Fe(III) complexes [19,25]. In the Kambara theory, abrupt spin-crossover transitions are given an FO => LS character, while gradual transitions are of the HS LS type. However, experimental evidences of cooperative Jahn-Teller transitions (FO HS) have not yet been reported for Fe(II) spin-crossover complexes. Kambara s theory ignores the spin-orbit interaction and appears to overestimate the Jahn-Teller coupling, producing an unphysical (for Fe(II) complexes) FO => HS transition. 

Spin-crossover phase transition of a manganese(IU) complex [Mn(taa)] was studied by variable-temperature laser Raman spectroscopy and it was found that the vibrational contribution in the transition entropy is not dominant in contrast to the cases of ordinary iron spin-crossover systems. The discovery of a dynamic disorder in the HS phase by means of dielectric measurements provided an alternative entropy source to explain the thermally induced spin-crossover transition. This dynamic disorder was attributed to the reorienting distortion dipoles accompanying the E e Jahn-Teller effect in HS manganese(III) ions. 

The first term corresponds to a forbidden transition s - s on atom X and is hence zero. The second term is an allowed transition on X, and the third and fourth terms are crossover transitions from orbitals on Y to the vacancy on X. Examination of the magnitudes of valence orbitals of in the region of shows that they will be very small, so that the third and fourth terms above can be ignored. Thus we have ... 

For theoretical calculations of molecular x-ray emission rates, it is usual to neglect the contributions from interatomic transitions, sometimes called crossover transitions, and to use the single-center approximation [6]. This approximation is useful and can often reproduces the experimental spectra quite well. Using a simple molecular orbital (MO) approach, Urch [7,8] showed the validity of the single-center approximation for metal K x-ray emission rates in MX4 and MXg molecules. On the other hand, Adachi and Taniguchi... 

X-ray emission rates in simple molecules have been extensively studied by Larkins and his group [10,11]. Larkins and Rowlands [12] made the MO calculations with the complete-neglect-of-differential-overlap (CNDO/2) method and pointed out that there are significant contributions of interatomic transitions to the C K x-ray emission rates in CO, HCN, and CO2 molecules, but relative intensities are less sensitive to inclusion of crossover transitions. Applying the ab initio MO method to CO, they also examined [13] various factors influencing the molecular x-ray emission rate, such as choice of basis set, choice of length and velocity forms, electronic relaxation effect, and interatomic contributions. Phillips and Larkins extended their calculations to other simple molecules [14,15]. 

Liu L, Mon CY, Chen SH. The fragile-to strong dynamic crossover transition in confined water nuclear magnetic reso- 57. nance results. J. Chem. Phys. 2006 124 161102. 

Note On the topic of beads, note that beads also sometimes have been put in series with the mosfet. But we should not put any such bead in the source. If we do so, then during crossover transitions, the source pin (with bead) can develop spikes. And since the gate is referenced to the source, not the drain, this can lead to a spurious turn-on, resulting in reliability issues. Therefore, a bead, if necessary, should be placed only on the drain side of the mosfet. True, this extra uncoupled inductance can also cause a small spike in principle, but in practice, that is rarely an issue. For the same reason, if we want to monitor the current in the mosfet by means of a current probe, we should place the loop of wire (to slip the probe tip on to) on the drain side, never on the source. 

Note We can ask — since the break point associated with the rise and fall times didn t enter the picture here, does that mean that it doesn t matter how fast we turn-on and turn-off the mosfet Yes from the DM noise viewpoint it really doesn t matter much. However there are parasitics that we have ignored (chiefly the ESL and trace inductances). And since, unlike the ESR, these will produce frequency-dependent voltage spikes, it is in our interest not to keep the mosfet crossover (transition) times too small. 

Thus, MCT indicates the presence of two structures with different density or temperature dependence for their relaxations, with a crossover transition at Tc. However, there are two questions whether the ideal and the experimental (or thermal) Tg s are related, and if so, how they are related. The answer to the first question is affirmative Segmental relaxation dominates at 7 > Tc, whereas structural relaxation dominates at T < Tc, for low-molecular-weight solvents as well as for molten polymers. The answer to the second question is more complex. The existence of transition temperatures Tg... 

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