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.

Chemistry

10th Edition

ISBN:9781305957404

Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Chapter1: Chemical Foundations

Section: Chapter Questions

Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...

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