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Prague August 31- September 4 200 9

Joint US Russia Conference on Advances in Materials Science. Prague August 31- September 4 200 9. Study into phase transformation with volume collapse in f-electron materials Alex Mirmelstein, Russian Federal Nuclear Center - Institute of Technical Physics.

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Prague August 31- September 4 200 9

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  1. Joint US Russia Conference on Advances in Materials Science Prague August 31- September 4 2009

  2. Study into phase transformation with volume collapse in f-electron materials Alex Mirmelstein, Russian Federal Nuclear Center - Institute of Technical Physics • A long standing issue in heavy element science is what role the f-electrons play in chemical and physical behaviors of materials. • Phase transformations accompanied by volume discontinuity demonstrate that the function of f-electrons can be changed by experimental variables such as temperature, pressure and alloying. • Pressure effects in CeNi • Multiple intermediate valence in plutonium

  3. Examples of phase transformations in f-electron materials Atomic volume of Pu as a function of temperature ? •  (fccfcc) transition in Ce 3+4+ Isomorphic transition in YbIn1-xAgxCu4 3+2+ Lattice parameter of fcc Ce0.74Th0.26 as a function of temperature. Inset: hysteresis in the transition region. V/V ~ 17% at room T. The cell volume (V0 is the volume at 300 K) for YbIn0.75Ag0.25Cu4 vs. temperature. V/V ~ 0.5%. Volume difference between - and - phases is ~ 26%.

  4. Mechanism (or mechanisms) of the volume-collapse transitions in f-electronic materials is still an open problem •  transition in Ce • the dominant contribution to the transition entropy in Ce0.9Th0.1 comes from magnetic excitations [M.E. Manley et al., Phys. Rev. B 67 014103 (2003)] • in pure Ce metal about a half of transition entropy is related to lattice vibrations [I.-K. Jeong et al., Phys. Rev. Lett. 92 105702 (2004)] • Pu • only a quarter of the transition entropy between - and -phases can be associated with phonons [M.E. Manley et al., Phys. Rev. B 79 052301 (2009)] Physics of f-electronic materials is not complete until the nature of such transitions obtains a comprehensive explanation

  5. Pressure effects in CeNi • CeNi is well known as a typical intermediate-valence* (IV) systemexhibiting: • anomalous behavior of many physical properties • (T), (T), Cel(T), thermal expansion, thermopower  Tcf ~ 150 K • unusual spin dynamics • anomalous lattice dynamics • pressure-induced first-order phase transition • resembles the stabilized -phase of Pu(to a certain degree) Intermediate valence  deviation of f-element effective valence from integer value

  6. Intermediate valence in CeNi Ce valence > 3 and increases with decreasing temperature Cе ion valence vs. temperature V.N. Lazukov et al. (2002) XAS experiment

  7. CeNi lattice CeNi unit cell c c a b b a Main structural motive : alternating triangles (or trigonal prisms) build of either Ce or Ni ions Orthorhombic CrB-type structure of CeNi (space group Cmcm). a = 3.784 Å, b = 10.543 Å, c = 4.363 Å Ce: 4c (0, 0.139, 1/4) Ni: 4c (0, 0.428, 1/4) CeNi is intermediate-valence system. Ground state: Kondo-singlet

  8. CeNI: pressure-induced first order phase transition D. Gignoux and J. Voiron (1985) D. Gignoux, C. Vettier and J. Voiron (1987) ~ 5% volume discontinuity at the transition The features of this transition are studied rather weakly

  9. Pressure effects in CeNi • Chemical compression: Ce1-xLuxNi (x=0.05, 0.1, 0.2, 0.4) • External pressure up to ~ 9 GPa • Experimental techniques: • magnetic susceptibility (T) vs. temperature (1.8 < T < 300 K) as a function of external pressure up to 1.5 GPa • specific heat vs. temperature (1.8 < T < 300 K) • neutron (up to 5 GPa) and X-ray (up to 9 GPa) powder diffraction

  10. High-pressure neutron scattering measurements up to 5 GPa in a sapphire anvil cell Diffraction patterns for CeNi at ambient pressure, at 2 and 5 GPa measured at 300 K using DN-12 time-of-flight high-pressure spectrometer (Dubna). (hkl) indexes correspond to the Cmcm space group. Clear indication of a first-order phase transition at 2 GPa

  11. Description of elastic neutron scattering spectrum measured at 5 GPa may be achieved assuming the pure high-pressure phase of CeNi to be of a tetragonal symmetry with a =3.748 Å andc= 2  5.796 = 11.592 Å CeNi 5 GPa DN-12-Dubna ΔV/V = 6.5% is independent on the unit cell choice Space group: to be determined (014) (005) (010) (113) The symmetry of high-pressure phase is higher than symmetry of ambient pressure CeNi Line shows the result of Rietveld refinement

  12. X-ray diffraction pattern of Ce0.9Lu0.1Ni under external pressure up to 8.7 GPa (ESRF) 8.7 GPa Phase transition between 2.08 and 2.5 GPa 2.5 GPa 2.08 GPa 0.35 GPa

  13. Pressure dependence of unit cell volume V and bulk modulus B for CeNi and Ce0.9Lu0.1Ni

  14. P-T diagram of ambient pressure orthorhombic and pressure-induced tetragonal phases in CeNi Ttr – maximum of M(T) curve Ptr – linear interpolation between P300K (applied pressure) and P7K (SC transition in Pb) to Ttr

  15. Normalized value of the low temperature magnetic susceptibility (0,P)/(0,P=0) vs. pressure for CeNi and Ce0.9Lu0.1Ni. Typical phase transition curves, also for Ce0.9Lu0.1Ni For a comparison Sommerfeld coefficient (P)/(P=0) is also shown S. Takayanagi et al. J. Phys. Soc. Jap. (2001) Sommerfeld coeeficient =Cmag(T)/TT0

  16. Measurements of magnetic susceptibility and specific heat allow to obtain quantitative characteristics of the f-electron system and their variation as a function of either chemical or external pressure

  17. Positive chemical pressure effect on magnetic susceptibility of CeNI Ce1-xLuxNi x = 0, 0.05, 0.1, 02, 04 (0) = (T)T0 Tmax From magnetic susceptibility and specific heat measurements we obtain: , (0), Tmax 0.35T0 where T0 is the characteristic energy scale (Kondo energy) of IV system

  18. Single-site approximation for Kondo-systems T0 – characteristic energy scale (Kondo temperature) nf - fractional f-orbital occupation N – magnetic degeneracy N=6 for J=5/2 an empirical relation effective f-element valence

  19.  as a function of T0 for Ce1-xLuxNi T0(CeNi)=106K/0.35=298K = 25.7 meV (= 25.7meV from INS) <nf> = 0.864 corresponds to the Ce ion valence 3.136 Chemical compression of CeNi increases f-electron hybridization: T0, <nf>  Ce0.6Lu0.4Ni: T0=550 K, <nf>0.75

  20.  and Tmax = 0.35T0 as function of the unit cell volume for Ce1-xLuxNi (x = 0, 0.05, 0.1, 0.2, 0.4), Ce0.9La0.1Ni and Ce0.9Lu0.1Ni vs. P (Å3)

  21. Ce valence as function of the unit cell volume for Ce1-xLuxNi (x = 0, 0.05, 0.1, 0.2, 0.4), Ce0.9La0.1Ni and Ce0.9Lu0.1Ni vs. P Ce0.9Lu0.1Ni CeNi Ce0.9La0.1Ni (Å3)

  22. From these results we conclude that • both chemical and external pressure increase Ce valence and hybridization between Ce f-electrons and conduction band electrons • independent spectroscopic experiments are required • Kondo physics dominates the behavior of CeNi under variation of the chemical and, perhaps, external pressure. • Single-site Kondo approximation seems to provide good description of the observed behavior

  23. Analysis of low temperature properties of Pu metal in terms of the same formulas If E0 is adjust to provide correct , (0) are also correct excluding  - Pu Wilson criterion is not valid for  - Pu universal Wilson ratio

  24. Temperature dependence of magnetic susceptibility of -Pu may be described in terms of SSA but only below ~ 150 K Experimental data from [S.K. McCall, M.J. Fluss et al. (2006)] Neither temperature dependence of magnetic susceptibility of -Pu (above ~ 150 K) nor the behavior of -Pu can be described by a simple model of the IV regime.

  25. Multiple intermediate valence in plutonium We assume that in Pu fluctuation occurs not between two but minimum between three electronic configurations with valence states |3+, |2+ and |4+. Such a regime can be called multiple intermediate valence (MIV)[E. Clementyev & A. Mirmelstein, JETP 109 (2009) 128] IV regime for Pu (similar for Sm and Yb) for Ce MIV regime where i+ is dynamical fractional occupation of i+ configuration effective valence f count

  26. Multiple intermediate valence in Pu • We assume [A. Mirmelstein et al., JETP Letters 90 (2009) in press] • the ground state of MIV is many-particle Kondo-singlet • [Y. Yafet and C.M. Varma, Phys.Rev. B 32 (1985) 360 • N. Read, K. Dharamvir, J.W. Rasul and D.M. Newns, J. Phys. C: Solid State Phys. 19 (1986) 1597] • magnetic susceptibility, magnetic (electronic) specific heat and atomic volume can be described as follows (T)and(T) are given by V.T. Rajan, Phys. Rev. Lett. 51 (1983) 308

  27. Multiple intermediate valence in Pu Atomic volumes of - () and -Pu ()  - Vi+

  28. Multiple intermediate valence in Pu Magnetic susceptibility of - and -Pu Experimental data from [S.K. McCall, M.J. Fluss et al. (2006)]

  29. Multiple intermediate valence in Pu Magnetic specific heat of - and -Pu J.C. Lashley et al., PRL 91 (2003) 205901

  30. Multiple intermediate valence in Pu Entropy of  transition Smag = 0.7kB /Pu atom Sphonon = 0.4kB /Pu atom[M.F. Manley et al. PRB 79(2009) 052301 ] Stotal = 1.1kB /Pu atom Stotal(exp) = 1.3kB /Pu atom

  31. Multiple intermediate valence in Pu • The simple empirical model of the MIV regime • describes magnetic susceptibility and specific heat of - and -Pu, difference in their volumes and gives the value of S() which is rather close to the experimental one • explains why - and-Pu have comparable magnetic susceptibility while ()/() ~2-3 • In terms of our model both - and -Pu are MIV systems. • In -Pu hybridization of f and conduction band electrons is stronger and the admixture of 4+ configuration is higher than in -Pu

  32. Conclusion • Fluctuation regime in Pu involves more than two electronic configurations (basic difference as compared to 4f IV systems) • In spite of simplicity and rather empirical character the MIV concept seems to serve as a convenient instrument for further studies of the peculiarities of the 5f-electronic states balancing between localized and delocalized behavior. • We are open for collaboration

  33. Collaborators • VNIITP SnezhinskInstitute of Metal JINR DubnaPhysics, RAS • Ekaterinburg • A. Mirmelstein Yu. Akshentsev D. Kozlenko • E. Clementyev* V. Voronin • O. Kerbel I. Berger ESRF Grenoble • Yu. Zuev V. ShchennikovD. Chernyshov • * now at ISSSP, Kurchatov Institute, Moscow

  34. Joint US Russia Conference on Advances in Materials Science Thank you!

  35. Multiple intermediate valence in Pu

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