Entropies electronic

Electronic entropy is associated with electrons and holes. It indicates the uncertainty in fixing their energy levels. This uncertainty will increase with 

Similarly, if the Ti3+ ions were to occur in tetrahedral coordination, the single 3d electron could occupy either one of the two e orbitals, dzi or dxi yi, and the electronic entropy would be 

For Cr3 ions in octahedral coordination, there is just one unique electronic configuration in which its three 3d electrons occupy singly each of the t2g orbitals. With probability of occurrence equal to one, the electronic entropy of Cr3+ is given by 

The presence of a Ti3+ ion in a distorted octahedral site would also yield a zero electronic entropy term. This results from removal of the three-fold degeneracy of t2g orbitals in the low-symmetry environment. Other effects of electronic entropy on thermodynamic properties of transition metal-bearing minerals are discussed in chapter 7 ( 7.4). 

Orbitals. Atomic orbitals represent the angular distribution of electron density about a nucleus. The shapes and energies of these amplitude probability functions are obtained as solutions to the Schrodinger wave equation. Corresponding to a given principal quantum number, for example n = 3, there are one 3s, three 3p and five 3d orbitals. The s orbitals are spherical, the p orbitals are dumb-bell shaped and the d orbitals crossed dumb-bell shaped. Each orbital can accomodate two electrons spinning in opposite directions, so that the d orbitals may contain up to ten electrons. 

Transition elements. Elements of the first transition series are characterized by having incompletely filled 3d orbitals in one or more of their common oxidation states. The series includes scandium, titanium, vanadium, chromium, manganese, iron, cobalt, nickel and copper, which have electronic configurations of the form (ls)2(2s)2(2p)6(3s)2(3p)6(3 /)10 (4s)1 or2. 

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The temperature coefficient of the potential of zero charge has often been suggested to indicate the orientation of solvent molecules at the met-al/solution interface. However, this view is based only on the response of a simple two-state model for the interfacial solvent, and on neglecting any contribution from the electronic entropy.76,77 This is in fact not the case. The temperature coefficient of 0in many instances is negative and of the... 

The origin of this heating is the changing distribution of entropy within the paramagnet with the applied field [12-14]. We can write the sum total of entropies according to Equation 9.1, where 5 total is the total entropy, SM is the magnetic entropy, 5,lattice is the lattice entropy and Selectronic is the electronic entropy of the system. 

Deducing the electronic entropy change from the specific heat, it appears that about one-third is due to the electrons. The rest must be the result of soft phonon modes. 

Translational entropy Rotational entropy Vibrational entropy Electronic entropy Total... 

Electronic entropy. As a result of unequal electron occupancies of degenerate t2g orbitals, the Ti3+ and Fe2+ ions in octahedral or tetrahedral sites, for example, may have large electronic entropies compared to zero values for Cr3. Electronic entropies decrease at elevated temperatures and are smaller when cations are located in distorted sites. 

Table 7.3. Electronic entropies for transition metal ions in octahedral and tetrahedral coordinations and high-spin (hs)... 

Figure 7.5 Comparison of the electronic entropy of Fe2+ in regular and distorted octahedral sites (modified from Wood, 1981).

Differences of electronic entropy also exist between high-spin and low-spin configurations (table 7.3). An alternative equation, which is regarded to be more valid than eq. (2.27) (Sherman, 1988), for evaluating the change of electronic entropy during a high-spin to low-spin transition, is... 

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