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

RFNC-VNIITF

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

Prague August 31- September 4 2009

Joint US Russia Conference on Advances Joint US Russia Conference on Advances in Materials Sciencein Materials Science

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Study into phase transformation with volume collapse in f-electron materialsAlex 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

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Examples of phase transformations in f-electron materials

Lattice parameter of fcc Ce0.74Th0.26 as a function of temperature.Inset: hysteresis in the transition region.V/V ~ 17% at room T.

(fccfcc) transition in Ce3+4+

Isomorphic transition in YbIn1-xAgxCu4

3+2+

The cell volume (V0 is the volume at 300 K) for YbIn0.75Ag0.25Cu4 vs. temperature. V/V ~ 0.5%.

Atomic volume of Pu as a function of temperature ?

Volume difference between - and - phases is ~ 26%.

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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

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Pressure effects in CeNi

CeNi is well known as a typical intermediate-valence* (IV) system exhibiting:

• 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

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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

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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 = 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)

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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

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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

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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

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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 5.796 = 11.592 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

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X-ray diffraction pattern of Ce0.9Lu0.1Ni 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

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

145

155

165

175

185

0 1 2 3 4P (GPa)

V (

A3 )

CeNi

Ce0.9Lu0.1Ni

0

10

20

30

40

50

0 1 2 3P (GPa)

B (

GP

a)

CeNi

Ce0.9Lu0.1Ni

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P-T diagram of ambient pressure orthorhombic and pressure-induced tetragonal phases in CeNi

0

100

200

300

0 1 2 3

Pressure (GPa)

Tem

pe

ratu

re (

K)

Gignoux & Voiron, 1985

T~ p^1/2

susceptibility, this work

neutron diffraction

Orthorhombicphase

Tetragonal phase

Ttr – maximum of M(T) curve

Ptr – linear interpolation between P300K (applied pressure) and P7K (SC transition in Pb) to Ttr

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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 shownS. Takayanagi et al. J. Phys. Soc. Jap. (2001)

Sommerfeld coeeficient =Cmag(T)/TT0

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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

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Positive chemical pressure effect on magnetic susceptibility of CeNI

Ce1-xLuxNi

x = 0, 0.05, 0.1, 02, 04

(0) = (T)T0

Tmax

0

0.001

0.002

0.003

0.004

0 100 200 300T, K

, e

mu

/Ce

mo

le

CeNi powder

Ce095Lu005Ni powder

Ce09Lu01Ni powder

Ce08Lu02Ni powder

Ce06Lu04Ni powder

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

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)1(

31

)0(

222

0

2

JJg

TknN

BJeff

BfeffA

NN

TknkNC

BfBAmag

13

1/T

0

220T

T0 – characteristic energy scale

(Kondo temperature)

nf - fractional f-orbital occupation

N – magnetic degeneracy

N=6 for J=5/2

)1J(J2

)1L(L)1S(S)1J(J1gJ

Single-site approximation for Kondo-systems

35.0/max0 TT

6.11/00523.01 0Tn f

)()0( 10 Tf )( 1

0 Tf

6.11/00523.03

)1(3

0T

nf

an empirical relation

effective f-element valence

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as a function of T0 for Ce1-xLuxNi

<nf> = 0.864 corresponds to the Ce ion valence 3.136

6.11/00523.01 0Tn f

T0(CeNi)=106K/0.35=298K = 25.7 meV (= 25.7meV from INS)

Chemical compression of CeNi increases f-electron hybridization: T0 , <nf>

Ce0.6Lu0.4Ni: T0=550 K, <nf>0.750

20

40

60

80

100

120

140

0 0.001 0.002 0.003 0.004 0.005

1/T0, K-1

=

Сm

ag/T

, m

J/(C

e m

ole

K2 )

specific heat exp

recalc. from susceptibility

nf ~ To

nf = 0.864

Ce1-xLuxNi

Ce0.9La0.1Ni

CeNix=0.4

x=0.2

x=0.1

x=0.05

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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)

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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

CeNi

Ce0.9La0.1Ni

(Å3)

Ce0.9Lu0.1Ni

6.11/00523.03

)1(3

0T

nf

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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

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Analysis of low temperature properties of Pu metal in terms of the same formulas

-Pu CeNi -Pu -Ce0.8Th0.2

, mJ/(mol K2) 65 65 17 17.4

E0, meV 26 26 98 138

calc, emu/mol 540 2290 140 381

exp, emu/mol 550 2000 510 540

Rexp 1.22 1.05 4.3 1.06

Rcalc (N = 6) 1.2

If E0 is adjust to provide correct , (0) are also correct excluding - Pu

Wilson criterion is not valid for - Pu

1/

/22

2

NN

kR

B

eff

universal Wilson ratio

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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.

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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

kkffkf 44

62

542 5551

where i+ is dynamical fractional occupation of i+ configuration

242424 32)1(34

242424 56)1(54 fN

effective valence

f count

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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

2234244

3342444

3342444

)1(

)()0()1()()0(/)(

)()0()1()()0()(

VVVV

TTTTC

TTT

mag

NN

EkN iiBAi

13

1

0

22

iieffiAi EN

0

2

31

)0(

(T) and (T) are given by V.T. Rajan, Phys. Rev. Lett. 51 (1983) 308

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Atomic volumes of - () and -Pu ()

- Vi+

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Magnetic susceptibility of - and -Pu

Experimental data from [S.K. McCall, M.J. Fluss et al. (2006)]

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Magnetic specific heat of - and -Pu

J.C. Lashley et al., PRL 91 (2003) 205901

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Entropy of transition

''

)'()(

0

dTT

TCTS

Tmag

mag

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

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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

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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

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Collaborators

VNIITP Snezhinsk Institute 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. Shchennikov D. Chernyshov

* now at ISSSP, Kurchatov Institute, Moscow

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Joint US Russia Conference on Advances Joint US Russia Conference on Advances in Materials Sciencein Materials Science

Thank you!

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

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