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Register a new userThe alpha-gamma transition of Cerium is entropy-driven
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We emphasize, on the basis of experimental data and theoretical calculations, that the entropic stabilization of the gamma-phase is the main driving force of the alpha-gamma transition of cerium in a wide temperature range below the critical point. Using a formulation of the total energy as a functional of the local density and of the f-orbital local Greens functions, we perform dynamical mean-field theory calculations within a new implementation based on the multiple LMTO method, which allows to include semi-core states. Our results are consistent with the experimental energy differences and with the qualitative picture of an entropy-driven transition, while also confirming the appearance of a stabilization energy of the alpha phase as the quasiparticle Kondo resonance develops.
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The $alpha$-$gamma$ transition in cerium has been studied in both zero and finite temperature by Gutzwiller density functional theory. We find that the first order transition between $alpha$ and $gamma$ phases persists to the zero temperature with negative pressure. By further including the entropy contributed by both electronic quasi-particles and lattice vibration, we obtain the total free energy at given volume and temperature, from which we obtain the $alpha$-$gamma$ transition from the first principle calculation. We also computed the phase diagram and pressure versus volume isotherms of cerium at finite temperature and pressure, finding excellent agreement with the experiments. Our calculation indicate that both the electronic entropy and lattice vibration entropy plays important role in the $alpha$-$gamma$ transition.
The $gamma to alpha$ isostructural transition in the Ce$_{0.9-x}$La$_x$Th$_{0.1}$ system is measured as a function of La alloying using specific heat, magnetic susceptibility, resistivity, thermal expansivity/striction measurements. A line of discontinuous transitions, as indicated by the change in volume, decreases exponentially from 118 K to close to zero with increasing La doping and the transition changes from being first-order to continuous at a critical concentration $0.10 leq x_c leq 0.14$. At the tricritical point, the coefficient of the linear $T$ term in the specific heat $gamma$ and the magnetic susceptibility start to increase rapidly near $x$ = 0.14 and gradually approaches large values at $x$=0.35 signifying that a heavy Fermi-liquid state evolves at large doping. Near $x_c$, the Wilson ratio, $R_W$, has a value of 3.0, signifying the presence of magnetic fluctuations. Also, the low-temperature resistivity shows that the character of the low-temperature Fermi-liquid is changing.
Structural and electronic properties of the alpha- and gamma-phases of cerium sesquisulfide, Ce2S3, are examined by first-principles calculations using the GGA+U extension of density functional theory. The strongly correlated f-electrons of Ce are described by a Hubbard-type on-site Coulomb repulsion parameter. A single parameter of $U^/prime$=4 eV yields excellent results for crystal structures, band gaps, and thermodynamic stability for both Ce2S3 allotropes. This approach gives insights in the difference in color of brownish-black alpha-Ce2S3 and dark red gamma-Ce2S3. The calculations predict that both Ce2S3 modifications are insulators with optical gaps of 0.8 eV (alpha-phase) and 1.8 eV (gamma-phase). The optical gaps are determined by direct electronic excitations at k=Gamma from localized and occupied Ce 4f-orbitals into empty Ce 5d-states. The f-states are situated between the valence and conduction bands. The difference of 1 eV between the optical gaps of the two Ce2S3 modifications is explained by different coordinations of the cerium cations by sulfur anions. For both Ce2S3 modifications the calculations yield an effective local magnetic moment of 2.6 $mu_B$ per cerium cation, which is in agreement with measurements. The electronic energy of the alpha-phase is computed to be 6 kJ/mol lower than that of the gamma-phase, which is consistent with the thermodynamic stability of the two allotropes.
The temperature and pressure dependence of the thermal displacements and lattice parameters were obtained across the $gamma to alpha$ phase transition of Ce using high-pressure, high-resolution neutron and synchrotron x-ray powder diffraction. The estimated vibrational entropy change per atom in the $gamma to alpha$ phase transition, $Delta S^{gamma - alpha}_{rm vib} approx (0.75 pm 0.15)$k$_{rm B}$, is about half of the total entropy change. The bulk modulus follows a power-law pressure dependence which is well described using the framework of electron-phonon coupling. These results clearly demonstrate the importance of lattice vibrations, in addition to the spin and charge degrees of freedom, for a complete description of the $gamma to alpha$ phase transition in elemental Ce.
We report on the most complete investigation to date of the 4f-electron properties at the gamma-alpha transition in elemental Ce by resonant inelastic x-ray scattering (RIXS). The Ce 2p3d-RIXS spectra were measured directly in the bulk material as a function of pressure through the transition. The spectra were simulated within the Anderson impurity model. The occupation number nf was derived from the calculations in both gamma- and alpha-phases in the ground state along with the f doubleoccupancy. We find that the electronic structure changes result mainly from band formation of 4f electrons which concurs with reduced electron correlation and increased Kondo screening at high pressure.
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