A-spin configuration

We will describe two cases open and closed chains of sites. For an open chain of sites, the energy of a spin configuration is... 

Upon adsorption of excess ammonia in a Co(II)Y zeolite a white, high-spin cobalt(Il)-ammonia complex with a spin configuration of (fe )5-(eg)2 is formed. According to studies of cobalt (II) complexes in solutions, salts, and in zeolites, a hexacoordinate Co(II)-ammonia complex is the most likely form when an excess of ammonia is present (3, 4> ) Indeed,... 

Fig. 20 Appearance of extended single-particle states by spin-vortices, (a) An antiferromag-netic order without spin-vortices case. Only Kab is nonzero. All electrons are localized, (b) A spin configuration with spin-vortices. Ka and Kb become nonzero around spin-vortices extended single-particle states appear around spin-vortices...

In Fig. 22a, an example of a spin configuration with two spin vortices is depicted. Different current patterns are possible for the same spin configuration by different X. Although each loop current is rather localized around each center of the vortices, a macroscopic current can be generated as a collection of loop currents if the number of loop currents is large enough (Fig. 22d). 

For a spin configuration S,, the ordinary BEG model is described by the Hamiltonian... 

The two common ways to do this are either to use a split coil (such as a Helmholz or a saddle coil) or to use a solenoid oriented perpendicular to the bore. The former scheme allows easy access along the bore for the sample even for a spinning configuration. A representation of a saddle coil is shown at right. The problem with such a split coil is... 

To improve upon die mean-field picture of electronic structure, one must move beyond the singleconfiguration approximation. It is essential to do so to achieve higher accuracy, but it is also important to do so to achieve a conceptually correct view of the chemical electronic structure. Although the picture of configurations in which A electrons occupy A spin orbitals may be familiar and usefiil for systematizing the electronic states of atoms and molecules, these constructs are approximations to the true states of the system. They were introduced when the mean-field approximation was made, and neither orbitals nor configurations can be claimed to describe the proper eigenstates T, . It is thus inconsistent to insist that the carbon atom... 

Given a set of A -electron space- and spin-synnnetty-adapted configuration state fiinctions in tenns of which is to be expanded as T = S. Cj two primary questions arise (1) how to detemiine the 9 coefficients and the energy E and (2) how to find the best spin orbitals ( ). ] Let us first consider the 1 where a single configuration is used so only the question of detemiining the spin orbitals exists. 

The normalisation factor is assumed. It is often convenient to indicate the spin of each electron in the determinant this is done by writing a bar when the spin part is P (spin down) a function without a bar indicates an a spin (spin up). Thus, the following are all commonly used ways to write the Slater determinantal wavefunction for the beryllium atom (which has the electronic configuration ls 2s ) ... 

Figure 7.40 (a) Weak-field, high-spin and (b) strong-field, low-spin configurations in d, d, d ... 

Figure 4-6 illustrates the relaxational eontribution to the motion. Figure 4-6A shows moment vectors for a spin system in the absenee of the rf field (Hi = 0) the magnetization eomponents are = Mq, = 0, My = 0, beeause in the xy plane the magnetization eomponents caneel. In the presenee of the rf field at the resonanee frequency the spin system absorbs energy, increasing the angle between Ho and M and perturbing the thermal equilibrium so that and My components are induced and M < Mo (Fig. 4-6B). With the passage of time (comparable to the relaxation times Tj and Tj), relaxation back to the equilibrium configuration takes place, so M. increases toward Mo, whereas nd My decrease toward zero as a consequence of the gradual loss of coherence of the moment vectors.

Figure 19.16 The possible high-spin and low-spin configurations arising as a result of the imposition of an octahedral crystal field on a transition metal ion.

IS readily obtained hy photolysis of a solution of (Relrj -CsMctl H) in pentane. It is low-spin at loss lemperatutes but has a minor contnbiuion frtim the high-spin configuration at ro m temperature ... 

It is possible to observe spin-allowed, d d bands in the visible region of the. spectra of low-spin cobalt(lll) complexes because of the small value of 0Dq, (A), which is required to induce spin-pairing in the cobalt(lll) ion. This means that the low-spin configuration occurs in complexes with ligands which do not cause the low -energy charge transfer bands whieh so often dominate the spectra of low-spin complexes. 

We define a fee lattice and affect at each site n, a spin or an occupation variable <7 which takes the value +1 or —1 depending on whether site n is occupied by a A or B atom. Within the generalized perturbation method , it has been shown that substitutional binary alloys AcBi-c may be described within a Ising model with effective pair interactions with concentration dependence. Thus, the energy of a configuration c = (<7i,<72,- ) among the 2 accessible configurations for one system can be written... 

Since a considerable amount of review articles on both theoretical frameworks and calculated results have been reported[15-25], the main objective of the present study is placed on the comparisons with experimental results. The organization of the present report is as follows In the next section, for the sake of completeness, a brief theoretical description of the PPM is summarized from the previous articles. In the third section, disorder-LIq transition is focused and visualized atomic (spin) configuration is compared with recent high resolution electron micrograph. In the fourth section, ordering relaxation... 

In the PPF, the first factor Pi describes the statistical average of non-correlated spin fiip events over entire lattice points, and the second factor P2 is the conventional thermal activation factor. Hence, the product of P and P2 corresponds to the Boltzmann factor in the free energy and gives the probability that on<= of the paths specified by a set of path variables occurs. The third factor P3 characterizes the PPM. One may see the similarity with the configurational entropy term of the CVM (see eq.(5)), which gives the multiplicity, i.e. the number of equivalent states. In a similar sense, P can be viewed as the number of equivalent paths, i.e. the degrees of freedom of the microscopic evolution from one state to another. As was pointed out in the Introduction section, mathematical representation of P3 depends on the mechanism of elementary kinetics. It is noted that eqs.(8)-(10) are valid only for a spin kinetics. 

Figure 2 Time sequence of th< spin configuration on a (100) plane at 50% when the system at T=2.5 (snapshot a) is quenched down to T—1.7 and is subject to an isothermal aging. Snapshots demonstrated in figs, b, c and d correspond to time t=20,000, 43,000 and 50,000. The long range and short range order parameters input from the PPM calculations and resultant ones in the simulated lattice are also demonstrated [22, 24, 28]. ...

---