Transition In Cerium Research Articles

Equation of state measurements by radiography provide evidence for a liquid-liquid phase transition in cerium

A pressure-volume isotherm in cerium metal at 1100 K was measured in a large volume press of the Paris-Edinburgh type up to 6 GPa. The volume was determined by imaging a rectangular shape of the sample via white X-ray radiography. Energy dispersive x-ray diffraction spectra were recorded to ensure that the highly reactive cerium in the cell assembly remained pure at this temperature. Even at 1100 K the p-V equation of state of liquid cerium shows a pronounced decrease of the bulk modulus above the y-phase region similar to the 775 K isotherm in the solid that also shows an inflection point between y- and a-type cerium. The inflection point in the 1100 K isotherm indicating the minimum in the bulk modulus separating the γ- from the α-type liquid is located at approximately 3.5 GPa.

α-γtransition in cerium: Magnetic form factor and dynamic magnetic susceptibility in dynamical mean-field theory

The nature of the elemental cerium phases, undergoing an isostructural volume collapse transition, cannot be understood using conventional solid state concepts. Using the combination of density functional theory and dynamical mean-field theory, we study the magnetic properties of both the $\alpha$ and the $\gamma$ phases. We compute the magnetic form factor, and show that it is very close to free ion behavior in both the local moment $\gamma$ phase as well as the more itinerant $\alpha$ phase, in agreement with neutron scattering experiments. In sharp contrast, the dynamic local magnetic susceptibility of the two phases is strikingly different. In the $\gamma$ phase, the sharp low energy peak due to local moment formation and consequently low Kondo temperature dominates the spectra. In the $\alpha$ phase two broad peaks can be identified, the first is due to Kondo screening, and the second is due to Hund's coupling. This shows that hybridization plays a central role in the $\alpha-\gamma$ transition in cerium, and that from the point of view of magnetic properties, the $4f$ electrons are strongly correlated in both phases.

Calculation of the volume effect at an electron phase transition in pure cerium and praseodymium

The experimental values of the volume effect at an electronic phase transition in several rare-earth metals are discussed. Specifically, volume changes at phase transitions in cerium and praseodymium are calculated using a semiphenomenological relationship derived in terms of the Falikov-Ramirez-Kimball model. A number of factors influencing the amount of the volume effect at electronic phase transitions are analyzed.

Density-Functional Theory forf-Electron Systems: Theα−γPhase Transition in Cerium

The isostructural α-γ phase transition in cerium is analyzed using density-functional theory with different exchange-correlation functionals, in particular the PBE0 hybrid functional and the exact-exchange plus correlation in the random-phase approximation [(EX+cRPA)@PBE0] approach. We show that the Hartree-Fock exchange part of the hybrid functional gives rise to two distinct solutions at zero temperature that can be associated with the α and γ phases of cerium. However, despite the relatively good structural and magnetic properties, PBE0 predicts the γ phase to be the stable phase at ambient pressure and zero temperature, in contradiction with low temperature experiments. EX+cRPA reverses the energetic ordering, which emphasizes the importance of correlation for rare-earth systems.

Density-Functional Theory for f-Electron Systems: The alpha-gamma Phase Transition in Cerium

The isostructural {\alpha}-{\gamma} phase transition in cerium is analyzed using density-functional theory with different exchange-correlation functionals, in particular the PBE0 hybrid functional and the exact- exchange plus correlation in the random-phase approximation [(EX+cRPA)@PBE0] approach. We show that the Hartree-Fock exchange part of the hybrid functional actuates two distinct solutions at zero temperature that can be associated with the {\alpha} and {\gamma} phases of cerium. However, despite the relatively good structural and magnetic properties, PBE0 predicts the {\gamma} phase to be the stable phase at ambient pressure and zero temperature, in contradiction with low temperature experiments. EX+cRPA reverses the energetic ordering, which emphasizes the importance of correlation for rare- earth systems.

Thermal expansion and transformation behavior of cerium and plutonium alloys: an application of the Aptekar–Ponyatovsky regular solution model

In this paper we apply the Aptekar–Ponyatovsky (AP) regular solution thermodynamic model to the analysis of experimental data for the coefficient of thermal expansion (CTE) and determine the AP model parameters for unalloyed cerium metal, Ce–Th–La alloys, and Pu–Ga alloys. We find that the high temperature CTE of cerium metal follows the predictions of the AP model based on low temperature, high pressure data. For Ce–Th–La alloys we use the AP parameters to track the suppression of the first-order γ–α cerium transition. We show the AP model accounts for the negative CTE observed for Pu–Ga alloys and is equivalent to an earlier invar model. Finally, we apply the AP parameters obtained for Pu–Ga alloys to rationalize the observed δ–α transformation pressures of these alloys. We show that the anomalous values of the Grüneisen and Grüneisen–Anderson parameters are important features of the thermal properties of plutonium. A strong analogy between the properties of plutonium and cerium is confirmed.

Phonons of the anomalous element cerium.

Many physical and chemical properties of the light rare-earths and actinides are governed by the active role of f electrons, and despite intensive efforts the details of the mechanisms of phase stability and transformation are not fully understood. A prominent example which has attracted a lot of interest, both experimentally and theoretically over the years is the isostructural γ - α transition in cerium. We have determined by inelastic X-ray scattering, the complete phonon dispersion scheme of elemental cerium across the γ → α transition, and compared it with theoretical results using ab initio lattice dynamics. Several phonon branches show strong changes in the dispersion shape, indicating large modifications in the interactions between phonons and conduction electrons. This is reflected as well by the lattice Grüneisen parameters, particularly around the X point. We derive a vibrational entropy change ΔS(γ-α)(vib) ≈ (0.33+/-0.03)k(B), illustrating the importance of the lattice contribution to the transition. Additionally, we compare first principles calculations with the experiments to shed light on the mechanism underlying the isostructural volume collapse in cerium under pressure.

Nuclear 111Cd probes detect a hidden symmetry change at the γ → α transition in cerium considered isostructural for 60 years

We use the time-differential perturbed angular correlation technique to study nuclear electric quadupole hyperfine interactions of probe 111Cd nuclei in cerium lattice sites at room temperature under pressures up to 8 GPa. We have found that the well known γ → α phase transition in cerium is not isostructural. In α-Ce, the probe 111Cd nuclei reveal a quadrupole electron charge density component that is absent in γ-Ce. The hidden spacial structure of electronic quadrupoles in α-Ce is triple-q antiferroquadrupolar, as was suggested in [14]. We relate our findings to the current understanding of the γ → α phase transition and also report on nuclear quadrupole interactions in other high-pressure phases of cerium: α″ (C2/m space symmetry) and α′ (α-U structure).

Thermal vibrations and polymorphic β → γ transition in cerium

Method of neutron diffraction was used to determine the temperature dependence of the Debye-Waller factor and the related thermal atomic displacements for two polymorphic modifications of cerium, namely, for β-Ce with a double hexagonal closed-packed (dhcp) structure and for γ-Ce with a face-centered cubic (fcc) structure. It has been shown that the phase transition does not lead to substantial changes in the root-mean-square thermal atomic displacements and that the Debye temperatures of the two modifications are close: 131 K for β-Ce and 127 K for γ-Ce. However, the relative (with respect to the lattice parameters) displacements along the axes change considerably. The transition from the anisotropic hexagonal to the isotropic cubic modification leads, because of a redistribution of thermal atomic displacements along the crystallographic axes, to a decrease in the maximum values of these quantities and to a weakening of their temperature dependence. It has also been shown that a change in the thermal atomic vibrations and in the vibrational contribution to the entropy of the polymorphic transformations is connected with the sign of the volume effect of the transformation (stronger upon a positive effect and weaker, upon a negative one). The reasons for this behavior are discussed.

Lowering of the spatial symmetry at theγ→αphase transition in cerium

Using time-differential perturbed angular correlation spectroscopy we have measured the electric field gradient (EFG) at $^{111}\text{C}\text{d}$ probe nuclei in solid Ce in a pressure range up to 8 GPa. Covering various allotropic phases of Ce, we find that the value of the EFG in the cubic $\ensuremath{\alpha}$ phase is almost four times larger than in the cubic $\ensuremath{\gamma}$ phase and close to values in the noncubic phases ${\ensuremath{\alpha}}^{\ensuremath{'}}$ and ${\ensuremath{\alpha}}^{\ensuremath{''}}$. These results together with the differences in time modulation of the spectra are interpreted as evidence for quadrupolar electronic charge-density ordering and symmetry lowering at the $\ensuremath{\gamma}\ensuremath{\rightarrow}\ensuremath{\alpha}$ transition while the lattice remains face-centered cubic.

Kinetics of the isostructural γ to α transition in cerium investigated by ultrasonics

We performed ultrasonic pulse echo measurements on high-purity polycrystalline cerium across the isostructural γ to α-fcc-to-fcc transition, up to 13 kbar and then back down to 0.3 kbar. Our results confirm the anomalous decrease of the longitudinal sound velocity in the γ-phase approaching the transition, a significant hysteresis loop, and definitively highlight the strong difference in the long wavelength limit of the lattice dynamics of the γ and α phases. We have also studied the kinetics of the transition, which is well described by an Arrhenius behavior, with an activation volume of 10 cm3/mol.

Charge carrier localization and metal to insulator transition in cerium substituted (Bi,Pb)-2212 superconductor

Abstract We report on the details of carrier localization and metal to insulator transition in (Bi,Pb)-2212 by substituting Ce at its Sr site (0.2 ≤ x ≤ 1.0). Structural and compositional analysis confirm good homogeneity of Ce distribution in the (Bi,Pb)-2212 matrix. The resistivity measurements show that x = 0.2 sample is a superconductor while those with x > 0.2 are insulators. Resistivity in the insulating regime (0.4 ≤ x ≤ 1.0) is analyzed using a generalized hopping approach. The increase in normal state resistivity and disorder of the samples leads to a metal to insulator transition at 0.2 x ≤ 0.4 and the insulating phases exhibit Mott's variable range hopping phenomenon. Around the transition, a dimensional change over from two to three dimensions is observed in the variable range hopping regime. Results show that substitution reduces the carrier concentration of (Bi,Pb)-2212, leads to suppression of superconductivity and metal to insulator transition in the system by localizing the electronic states at the Fermi level.

Quantum Monte Carlo impurity solver for cluster dynamical mean-field theory and electronic structure calculations with adjustable cluster base

We generalized the recently introduced new impurity solver based on the diagrammatic expansion around the atomic limit and Quantum Monte Carlo summation of the diagrams. We present generalization to the cluster of impurities, which is at the heart of the cluster Dynamical Mean-Field methods, and to realistic multiplet structure of a correlated atom, which will allow a high precision study of actinide and lanthanide based compounds with the combination of the Dynamical Mean-Field theory and band structure methods. The approach is applied to both, the two dimensional Hubbard and t-J model within Cellular Dynamical Mean Field method. The efficient implementation of the new algorithm, which we describe in detail, allows us to study coherence of the system at low temperature from the underdoped to overdoped regime. We show that the point of maximal superconducting transition temperature coincides with the point of maximum scattering rate although this optimal doped point appears at different electron densities in the two models. The power of the method is further demonstrated on the example of the Kondo volume collapse transition in Cerium. The valence histogram of the DMFT solution is presented showing the importance of the multiplet splitting of the atomic states.

Theα−γTransition of Cerium Is Entropy Driven

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 Green's functions, we perform dynamical mean-field theory calculations within a new implementation based on the multiple linear muffin tin orbital (LMTO) method, which allows us to include semicore 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.

Magnetic Form Factor ofα-Ce: Towards Understanding the Magnetism of Cerium

A favored interpretation of the gamma <--> alpha phase transition in cerium postulates the transformation of the localized 4f state in gamma-Ce to a weakly correlated itinerant 4f band in alpha-Ce. However, results of high-energy neutron inelastic scattering measurements, presented here, show clearly that the magnetic susceptibility response from alpha-Ce follows the Ce3+ form factor despite the large, 30-fold, increase in its spectral width relative to that in gamma-Ce. This observation provides, for the first time, indisputable evidence for the localized character of the 4f state in the alpha phase. The present findings appear consistent with recent calculations combining dynamical mean-field theory with the local density approximation that indicate a strongly correlated 4f state in alpha-Ce. The localized 4f state is also fundamental to the Kondo volume collapse theories for the gamma <--> alpha phase transition in cerium.

Hydrogenation of CeNi: hydride formation, structure and magnetic properties

The hydrogenation at different temperatures and hydrogen pressures of the binary intermetallic compound CeNi was studied. A hydride with the composition CeNiH 2.9(1) was obtained by hydriding the host alloy at 293 K and P H2=1 MPa. With increasing temperature of hydriding a reaction of hydrogenolysis of CeNi occurred with formation of a stable two-phase product composed of CeH 2.51 and CeNi 5. The newly prepared hydride CeNiH 2.9(1) was found to be isostructural with CeNi (orthorhombic, CrB-type, S.G. Cmcm). On the basis of refinement of the XRD patterns of both the intermetallic compound and its hydride, the atomic positions of Ce and Ni and the interatomic distances were determined. The probable sites of hydrogen intersection in the host structure were proposed. Moreover, a valence transition of cerium from intermediate valence (CeNi) to the trivalent state (CeNiH 2.9) was evidenced by magnetization measurements.

Electrical and magnetic properties of the cerium–transition metal intermetallics CeTSb 2 (T: Cu, Au, Ni)

We have succeeded in growing single crystals of the cerium–transition metal intermetallics CeTSb 2 (T: Cu, Au, Ni) with the tetragonal structure via the self-flux method, and measured the electrical resistivity, magnetic susceptibility, magnetization and specific heat. CeCuSb 2 and CeAuSb 2 are antiferromagnets with Néel temperatures of 6.9 and 5.0 K, respectively. CeCuSb 2 is a heavy-fermion antiferromagnet with an electronic specific heat coefficient γ=200 mJ/K 2 mol. CeAuSb 2 also is a similar compound with an antiferromagnetic easy axis along the [0 0 1] direction. CeNiSb 2 is a ferromagnet with a Curie temperature of 6.0 K. The easy axis is oriented along [1 0 0], with a moment of 0.6 μ B/Ce.

Vibrational and electronic entropy of β-cerium and γ-cerium measured by inelastic neutron scattering

Time-of-flight (TOF) inelastic neutron-scattering spectra were measured on \ensuremath{\beta}-cerium (double hcp) and \ensuremath{\gamma}-cerium (fcc) near the phase-transition temperature. Phonon densities of states (DOS) and crystal-field levels were extracted from the TOF spectra. A softening of the phonon DOS occurs in the transition from \ensuremath{\beta}- to \ensuremath{\gamma}-cerium, accounting for an increase in vibrational entropy of $\ensuremath{\Delta}{S}_{\mathrm{vib}}^{\ensuremath{\gamma}\ensuremath{-}\ensuremath{\beta}}=(0.09\ifmmode\pm\else\textpm\fi{}{0.05)k}_{B}/\mathrm{atom}.$ The entropy calculated from the crystal-field levels and a fit to calorimetry data from the literature were significantly larger in \ensuremath{\beta}-cerium than in \ensuremath{\gamma}-cerium below room temperature, but the difference was found to be negligible at the experimental phase-transition temperature. A contribution to the specific heat from Kondo spin fluctuations was consistent with the quasielastic magnetic scattering, but the difference between phases was negligible. To be consistent with the latent heat of the \ensuremath{\beta}-\ensuremath{\gamma} transition, the increase in vibrational entropy at the phase transition may be accompanied by a decrease in electronic entropy not associated with the crystal-field splitting or spin fluctuations. At least three sources of entropy need to be considered for the \ensuremath{\beta}-\ensuremath{\gamma} transition in cerium.

High Temperature-High Pressure Structural Studies of Cerium

Energy dispersive X-ray-diffraction with the large volume press MAX 80 at HASYLAB/DESY is used in the present study for the determination of the p - V - T -relations around the critical point of the f - n -phase transition in Cerium. Furthermore the f - l -phase boundary is studied experimentally to remove the last question marks from the phase diagram of Cerium in the accessible region of pressure and temperature.

On the nature of the γ-α transition in cerium

In 1964 Davis and Adams established that the large increase of the thermal expansion and compressibility in the critical region of the γ-to α-Ce phase transition occurs predominantly in the α phase. This provides strong evidence that a tricritical point is realized in Ce. This also means that the aforementioned transition is not isomorphic and that α-Ce should have a distorted fcc structure. A careful examination of Jayaraman’s data (1965) shows that a second-order transition line continues beyond the tricritical point to the vicinity of a triple point on the melting curve. The phase boundary with the tricritical point and the minimum of the melting curve are reconstructed within the framework of Landau theory.