2. Spin-State Transition: LaCoO3 is a perovskite oxide in which the transition metal ion Co is trivalent (Co³+: d) and it is surrounded by six oxygen ions in an octahedral configuration. The octahedral symmetry partially lifts the orbital degeneracy of 3d levels. It splits the ground state into triply degenerate t2g levels and doubly degenerate eg levels. The eg levels are higher in energy and they are separated by an energy Acry (= 10 meV) from the t2g levels. Because of the closeness of the crystal field (Acry) and intra-atomic exchange (Jex) energies, the spin state of the Co ion can change with increasing temperature. Assume that the spin state of Co³+ ion changes from low spin (S-0) to intermediate spin state (S = 1). (a) Derive an expression for the temperature dependence of magnetic susceptibility for low- to intermediate-spin state transition. At what temperature this transition can take place? (b) Assume that the sample is initially in the low spin state at T = 10 K. A high magnetic field can induce spin state transition from S = 0 to S= 1. What is the magnetic field needed to induce such a transition? (c) Calculate spin entropy change (ASm) due to the spin state transition.

2. Spin-State Transition: LaCoO3 is a perovskite oxide in which the transition metal ion Co is trivalent (Co³+: d) and it is surrounded by six oxygen ions in an octahedral configuration. The octahedral symmetry partially lifts the orbital degeneracy of 3d levels. It splits the ground state into triply degenerate t2g levels and doubly degenerate eg levels. The eg levels are higher in energy and they are separated by an energy Acry (= 10 meV) from the t2g levels. Because of the closeness of the crystal field (Acry) and intra-atomic exchange (Jex) energies, the spin state of the Co ion can change with increasing temperature. Assume that the spin state of Co³+ ion changes from low spin (S-0) to intermediate spin state (S = 1). (a) Derive an expression for the temperature dependence of magnetic susceptibility for low- to intermediate-spin state transition. At what temperature this transition can take place? (b) Assume that the sample is initially in the low spin state at T = 10 K. A high magnetic field can induce spin state transition from S = 0 to S= 1. What is the magnetic field needed to induce such a transition? (c) Calculate spin entropy change (ASm) due to the spin state transition.

Physical Chemistry

2nd Edition

ISBN:9781133958437

Author:Ball, David W. (david Warren), BAER, Tomas

Publisher:Ball, David W. (david Warren), BAER, Tomas

Chapter13: Introduction To Symmetry In Quantum Mechanics

Section: Chapter Questions

Problem 13.22E: Figure 13.27 shows the structure of the molecule porphine. Figure 13.27 The structure of porphine....

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Figure 13.27 shows the structure of the molecule porphine. Figure 13.27 The structure of porphine. Determine the symmetry elements present in the molecule, and its point group. Does the point group change if an Fe2+ ion is substituted for the two hydrogen atoms in the center of the porphine ring?
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