RFNC-VNIITF Joint US Russia Conference on Advances in Materials Science, Prague, September 2, 2009 Prague August 31- September Joint US Russia Conference on Advances in Materials Science

RFNC-VNIITF Joint US Russia Conference on Advances in Materials Science, Prague, September 2, 2009 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

RFNC-VNIITF Joint US Russia Conference on Advances in Materials Science, Prague, September 2, 2009 Examples of phase transformations in f-electron materials Lattice parameter of fcc Ce0. 74 Th 0.26 as a function of temperature. Inset: hysteresis in the transition region.  V/V ~ 17% at room T.  (fcc  fcc) transition in Ce 3+  4+ Isomorphic transition in YbIn 1-x Ag x Cu 4 3+  2+ The cell volume (V 0 is the volume at 300 K) for YbIn 0.75 Ag 0.25 Cu 4 vs. temperature.  V/V ~ 0.5%. Atomic volume of Pu as a function of temperature ? Volume difference between  - and  - phases is ~ 26%.

RFNC-VNIITF Joint US Russia Conference on Advances in Materials Science, Prague, September 2, 2009 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 Ce 0.9 Th 0.1 comes from magnetic excitations [M.E. Manley et al., Phys. Rev. B (2003)] in pure Ce metal about a half of transition entropy is related to lattice vibrations [I.-K. Jeong et al., Phys. Rev. Lett (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 (2009)] Physics of f-electronic materials is not complete until the nature of such transitions obtains a comprehensive explanation

RFNC-VNIITF Joint US Russia Conference on Advances in Materials Science, Prague, September 2, 2009 Pressure effects in CeNi CeNi is well known as a typical intermediate-valence* (IV) system exhibiting: anomalous behavior of many physical properties  (T),  (T), C el (T), thermal expansion, thermopower  T cf ~ 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

RFNC-VNIITF Joint US Russia Conference on Advances in Materials Science, Prague, September 2, 2009 Intermediate valence in CeNi Cе ion valence vs. temperature V.N. Lazukov et al. (2002) XAS experiment Ce valence > 3 and increases with decreasing temperature

RFNC-VNIITF Joint US Russia Conference on Advances in Materials Science, Prague, September 2, 2009 CeNi unit cell c b a b c a Main structural motive : alternating triangles (or trigonal prisms) build of either Ce or Ni ions CeNi is intermediate- valence system. Ground state: Kondo- singlet CeNi lattice Orthorhombic CrB-type structure of CeNi (space group Cmcm). a = Å, b = Å, c = Å Ce: 4c (0, 0.139, 1/4) Ni: 4c (0, 0.428, 1/4)

RFNC-VNIITF Joint US Russia Conference on Advances in Materials Science, Prague, September 2, 2009 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

RFNC-VNIITF Joint US Russia Conference on Advances in Materials Science, Prague, September 2, 2009 Pressure effects in CeNi Chemical compression: Ce 1-x Lu x Ni (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

RFNC-VNIITF Joint US Russia Conference on Advances in Materials Science, Prague, September 2, 2009 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

RFNC-VNIITF Joint US Russia Conference on Advances in Materials Science, Prague, September 2, 2009 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 and c = 2  = Å Line shows the result of Rietveld refinement ΔV/V = 6.5% is independent on the unit cell choice Space group: to be determined (113) (014)(005) (010) CeNi 5 GPa DN-12-Dubna The symmetry of high-pressure phase is higher than symmetry of ambient pressure CeNi

RFNC-VNIITF Joint US Russia Conference on Advances in Materials Science, Prague, September 2, 2009 X-ray diffraction pattern of Ce 0.9 Lu 0.1 Ni under external pressure up to 8.7 GPa (ESRF) 0.35 GPa 2.5 GPa 8.7 GPa 2.08 GPa Phase transition between 2.08 and 2.5 GPa

RFNC-VNIITF Joint US Russia Conference on Advances in Materials Science, Prague, September 2, 2009 Pressure dependence of unit cell volume V and bulk modulus B for CeNi and Ce 0.9 Lu 0.1 Ni

RFNC-VNIITF Joint US Russia Conference on Advances in Materials Science, Prague, September 2, 2009 P-T diagram of ambient pressure orthorhombic and pressure-induced tetragonal phases in CeNi T tr – maximum of  M(T) curve P tr – linear interpolation between P 300K (applied pressure) and P 7K (SC transition in Pb) to T tr

RFNC-VNIITF Joint US Russia Conference on Advances in Materials Science, Prague, September 2, 2009 Normalized value of the low temperature magnetic susceptibility  (0,P)/  (0,P=0) vs. pressure for CeNi and Ce 0.9 Lu 0.1 Ni. Typical phase transition curves, also for Ce 0.9 Lu 0.1 Ni For a comparison Sommerfeld coefficient  (P)/  (P=0) is also shown S. Takayanagi et al. J. Phys. Soc. Jap. (2001) Sommerfeld coeeficient  =C mag (T)/T T  0

RFNC-VNIITF Joint US Russia Conference on Advances in Materials Science, Prague, September 2, 2009 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

RFNC-VNIITF Joint US Russia Conference on Advances in Materials Science, Prague, September 2, 2009 Positive chemical pressure effect on magnetic susceptibility of CeNI Ce 1-x Lu x Ni x = 0, 0.05, 0.1, 02, 04  (0) =  (T) T  0 T max From magnetic susceptibility and specific heat measurements we obtain: ,  (0), T max  0.35T 0 where T 0 is the characteristic energy scale (Kondo energy) of IV system

RFNC-VNIITF Joint US Russia Conference on Advances in Materials Science, Prague, September 2, 2009 T 0 – characteristic energy scale (Kondo temperature)  n f  - fractional f-orbital occupation N – magnetic degeneracy N=6 for J=5/2 Single-site approximation for Kondo-systems an empirical relation effective f-element valence

RFNC-VNIITF Joint US Russia Conference on Advances in Materials Science, Prague, September 2, 2009  as a function of T 0 for Ce 1-x Lu x Ni = corresponds to the Ce ion valence T 0 (CeNi)=106K/0.35=298K = 25.7 meV (= 25.7meV from INS) Chemical compression of CeNi increases f-electron hybridization: T 0 ,  Ce0.6Lu0.4Ni: T 0 =550 K,  0.75

RFNC-VNIITF Joint US Russia Conference on Advances in Materials Science, Prague, September 2, 2009  and T max = 0.35T 0 as function of the unit cell volume for Ce 1-x Lu x Ni (x = 0, 0.05, 0.1, 0.2, 0.4), Ce 0.9 La 0.1 Ni and Ce 0.9 Lu 0.1 Ni vs. P (Å 3 )

RFNC-VNIITF Joint US Russia Conference on Advances in Materials Science, Prague, September 2, 2009 Ce valence as function of the unit cell volume for Ce 1-x Lu x Ni (x = 0, 0.05, 0.1, 0.2, 0.4), Ce 0.9 La 0.1 Ni and Ce 0.9 Lu 0.1 Ni vs. P CeNi Ce 0.9 La 0.1 Ni (Å 3 ) Ce 0.9 Lu 0.1 Ni

RFNC-VNIITF Joint US Russia Conference on Advances in Materials Science, Prague, September 2, 2009 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

RFNC-VNIITF Joint US Russia Conference on Advances in Materials Science, Prague, September 2, 2009 Analysis of low temperature properties of Pu metal in terms of the same formulas  -Pu CeNi  -Pu  -Ce 0.8 Th 0.2 , mJ/(mol K 2 ) E 0, meV  calc,  emu/mol  exp,  emu/mol R exp R calc (N = 6) 1.2 If E 0 is adjust to provide correct ,  (0) are also correct excluding  - Pu Wilson criterion is not valid for  - Pu universal Wilson ratio

RFNC-VNIITF Joint US Russia Conference on Advances in Materials Science, Prague, September 2, 2009 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.

RFNC-VNIITF Joint US Russia Conference on Advances in Materials Science, Prague, September 2, 2009 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

RFNC-VNIITF Joint US Russia Conference on Advances in Materials Science, Prague, September 2, 2009 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

RFNC-VNIITF Joint US Russia Conference on Advances in Materials Science, Prague, September 2, 2009 Multiple intermediate valence in Pu Atomic volumes of  - (  ) and  -Pu (  )  - V i+

RFNC-VNIITF Joint US Russia Conference on Advances in Materials Science, Prague, September 2, 2009 Multiple intermediate valence in Pu Magnetic susceptibility of  - and  -Pu Experimental data from [S.K. McCall, M.J. Fluss et al. (2006)]

RFNC-VNIITF Joint US Russia Conference on Advances in Materials Science, Prague, September 2, 2009 Multiple intermediate valence in Pu Magnetic specific heat of  - and  -Pu J.C. Lashley et al., PRL 91 (2003)

RFNC-VNIITF Joint US Russia Conference on Advances in Materials Science, Prague, September 2, 2009 Multiple intermediate valence in Pu Entropy of  transition  S mag = 0.7k B /Pu atom  S phonon = 0.4k B /Pu atom [M.F. Manley et al. PRB 79 (2009) ]  S total = 1.1k B /Pu atom  S total (exp) = 1.3k B /Pu atom

RFNC-VNIITF Joint US Russia Conference on Advances in Materials Science, Prague, September 2, 2009 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

RFNC-VNIITF Joint US Russia Conference on Advances in Materials Science, Prague, September 2, 2009 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

RFNC-VNIITF Joint US Russia Conference on Advances in Materials Science, Prague, September 2, 2009 Collaborators VNIITP SnezhinskInstitute of MetalJINR Dubna Physics, RAS Ekaterinburg A. MirmelsteinYu. AkshentsevD. Kozlenko E. Clementyev* V. Voronin O. Kerbel I. Berger ESRF Grenoble Yu. Zuev V. Shchennikov D. Chernyshov * now at ISSSP, Kurchatov Institute, Moscow

RFNC-VNIITF Joint US Russia Conference on Advances in Materials Science, Prague, September 2, 2009 Joint US Russia Conference on Advances in Materials Science Thank you!

RFNC-VNIITF Joint US Russia Conference on Advances in Materials Science, Prague, September 2, 2009 Multiple intermediate valence in Pu