Interconfigurational fluctuations in Ce cubic compounds

(1)

HAL Id: jpa-00218900

https://hal.archives-ouvertes.fr/jpa-00218900

Submitted on 1 Jan 1979

HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Interconfigurational fluctuations in Ce cubic compounds

J. Sereni, G. Olcese, C. Rizzuto

To cite this version:

J. Sereni, G. Olcese, C. Rizzuto. Interconfigurational fluctuations in Ce cubic compounds. Journal de

Physique Colloques, 1979, 40 (C5), pp.C5-337-C5-339. �10.1051/jphyscol:19795116�. �jpa-00218900�

(2)

JOURNAL DE PHYSIQUE

Colloque C5, supplément au n° 5, Tome 40, Mai 1979, page C5-337

Interconfigurational fluctuations in Ce cubic compounds

J. G. Sereni (*) (**)

Centro Atomico Bariloche (CNEA), Bariloche, Argentina

G. L. Olcese

Istituto di Chimica Fisica, Universita di Genova, Italia

and C. Rizzuto

Istituto di Scienze Fisiche, Universita di Genova, Italia

Résumé. — La susceptibilité magnétique de trente composés cubiques de cérium est analysée, en supposant une dépendance en température des fluctuations de valence. Le schéma des niveaux d'énergie obtenu par l'ajustement de la susceptibilité mesurée est utilisé pour calculer d'autres propriétés physiques. On a trouvé une corrélation entre le rayon ionique du cérium et l'énergie d'excitation interconfigurationnelle.

Abstract. — The magnetic susceptibility of thirty Ce cubic compounds is analyzed, assuming a temperature dependence of the valence fluctuations. The energy level scheme, obtained by fitting the measured susceptibility is used to calculate other physical properties. A correlation between the Ce ionic radius and the interconfigura- tionai excitation energy has been found.

The magnetic susceptibility (MS) of thirty Ce where / ( £ ) = e x p ( - EJTJ is the quasi Boltzmann* cubic intermetallic compounds (IC), of different distribution and « Z »the partition function,

crystal structures (see the table I), which shows magnetic, intermediate and non magnetic behaviours,

**Z = £(2./„ + 1) /„*(£).**

has been analyzed assuming a temperature depen-

dence of the valence fluctuations. We have applied Taking D„(E) ~ e x p [ - ( £ - £„)

²

/2 J

²

] it is possible the concept of interconfigurational fluctuations [

^Q

integrate obtaining:

(ICF) [1, 2] to describe the observed temperature

dependence of the MS [3], taking into account the V(T) = (2J„ + 1) exp[j(AjT„)

2

- EjT„~].

l

lz.

possibility of a dynamical mixing between the two

lower energy Ce configurations (4f* 5d* ^ 4 f ° 5d

2

), Substituting T by T„, the MS can be written as identified as n = 1 and n — 1 = 0 respectively. From

X

(T) = (N/3 X„).£ /i

2

V(T). In the case' of Ce it is : this model we have derived a sufficiently accurate „

c

. ?

n

~ , . . . • . i i i .

t

<. c* -1 i_i Hi = 2.54 w*

R

and n

a

= 0. To apply this expression to energy eye scheme to attempt o fit available expe- ^

c a

^ .

g n

^ ^

t Q a c c o u n t for o t h e r

nmentaldataof differentphysica 1 properties

e w h i c h

^

fee c o n s i d e r e d a s i n d e p e n d e n t

f

^{r o r}

n The probability of occupation of the state « « »

^T

„,„ ' , . „,. . , , . , f. , . ,

^{c F}

_ i . , , , / • • . ^ « , ICF. They are : 1) The possible interactions between (of energy E„ and width Aj, is given at T -> 0 by :

^x

. / , • , •

^A

^ • ™ , •

D

m\ t CIA\ A \ u - \

^t

. u magnetic moments, which give rise to a Curie-Weiss P„(0) ~ e x p ( - EJA„), and at high temperatures by :

t e n

f

n e r a t u r e (T

N

2

)

t h e V a n V l e c k

contribution to PjiT) ~ e x p ( - E„/k

b

T). A good interpolation is 1 \ ^

A{ o),A

\ T vieck contriDmion to*

," ' .\> . '' J'rrJ

B

, ~ .r-s r^ , the MS, independent from temperature, and 3) the done considering PJT) ~ exp(— EJT

n

) [4], where . . , ,...: • . , , ,

t

\ , ,

t A r

T -T+ A and k - 1 urine K L enerev unit P

o s s l b l e

splitting, into a doublet F

7

and a quarted r

8

, c "*. 7"' J

b

Z L I °*

f

the Hund sixfold ground state due to the crystal So, the valence dependence with temperature was _ . , ~ . „ , 5 . .

f

. . , , . ' „

a

' - _ / . , . , x-^i. ^ • field effect. These exchange interactions will be repre- taken as the fractional occupation oi the configuration ^ , , i , r. i r i r- \ i r r*

^{T J}

*i_

4 f

i

^{5 d}

i („ = i) j

e s e n t e d b

y l<

^r

t I

^{J z}

I

^r

j > I =

^J

y

U n d e r t h e s e c o n s 1

' derations the general expression for the MS becomes :

/•GO

K D - I / Z z>,(£) /„*(£) d £ . I f . / ^ 2J,5 \

(*) Supported in part by the GNSM-CNR. "I 2 J„2. ")

(**) Present address : II Physikalisches Institut der Universitat exp(— E„JT„) H — — exp(— t '/T) >

zu Koln, Zulpicher Strasse 77,5 Koln 41, Germany. ' J E — £„ J Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19795116

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3. G. SERENI, G. L. OLCESE AND C. RIZZUTO

Table

1.

Lattice parameter

(A)

-

4.722 4.163 4.025 4.771 4.691 4.875 5.013 5.1 15 5.061

Ce ionic radius

(A)

-

1.013 1.009 0.980 1.034 1.034 1.025 1.020

Specific heat calc. meas.

(mJ/K mole) Structure

type

Magnetic behaviour

-

Compound CeSn, CePd, CeRh, CeTl, Celn, CePb, Ce,A1 Ce,Ga Ce,ln

-

- 190 - 3 6 0 1 - 1 600

E,,

>

E'

550 Intermed.

Magnetic

E,, >

E'

l ^Magnetic

CeNi, CeRu, CeRh, CeOs, Celr, CePt, CeA12 CeN CeP CeA s CeSb CeBi CeAg CeMg CeZn CeH g CeTl CeCd, CeBe,

³

CeB,

Ce2C3

Non mag.

Magnetic Magnetic Non mag.

E,, > E'

-

2 150

700 8 60

Magnetic

E,,

>

E'

1 ^Magnetic

BiLi, NaZn

1 3

CaB,

' ~ 2 ~ 3

E,, > E'

-

320 - 80 - 1 200

Magnetic Intermed.

Intermed.

Non mag.

where g,

=

617 and E' is the energy of the first J-

200 400 600 800

excited level characterized by J'

=

7/2. The level

⁶⁰

-

scheme was obtained by fitting this formula to the actual experimental data [3].

In table I we give the values of the excitation energy -

between configurations

:

E,,

= E,-,

- E,, obtained from this method, as well as the comparison between the calculated and the measured specific heat values

at T

⁼

1 K for some compounds. The calculated

T

thermoelectricpower of CeSn, and CeBe,, [5], nuclear

%l

+---*---

e

1

^-

Fig. 1. - Experimental data and theoretical fitting curve of the temperature dependence of : CeBe,, ( X ) and CeSn, (+) thermo-

electrical power (upper right scale), CeN (0) lattice parameter ₀ ₁₀₀ ₂₀₀^I ₃₀₀^I _4A0

5.10

5

5.05

5.00

-

0.5

O (upper left scale) and CeBe,, (e) nuclear spin-lattice relaxation

rate (lower scale). T (K)

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INTERCONFIGURATIONAL FLUCTUATIONS IN Ce CUBIC COMPOUNDS C5-339

spin-lattice relaxation rate

of CeBe,, [6] and the

latticeparameter

of CeN7 as a hnction of temperature are compared with the experimental data in figure 1.

As it is well known there exists a strong dependence of the Ce atomic volume from the valence. To confirm the fact that all possible behaviours of Ce in inter- metallic compounds can be described from its two lower energy configurations, we have plotted in figure 2 the Ce ionic radius (ri)

[3] vs. E,,

of the com- pounds where E,,

<

E'. It is remarkable that the compounds whose structures are

:

AuCu,, Pu,C,, NaC1, NaZn,, and CaB, are practically on the same line. The departure from this general behaviour of the Laves phases (MgCu, AB,) can be understood taking into account the extra compression supported by the element A to obtain the ratio

r,/r, E

1.33, which characterises these phases.

A more general expression of V ( T ) is actually studied using the Fermi distribution for f,(E) and a Lorentzian function for D,(E) in view of having a better fit also in the case of E,

$

T.

Fig. 2. - Ce ionic radius (rice) versus the interconfigurational excitation energy (E,,) of the compounds having E,, < E'. Only the Ce partner is marked (except in the case of Ce,C,).

References

[l] HIRST, L. L., Phys. Kondens. Mater. 11 (1970) 255.

[2] SALES, B. C., J. LOW Temp. Physics 28 (1977) 107.

[3] OLCESE, G. L. and SERENI, J. G., TO be published.

[4] WOHLLEBEN, D., J. Physique CoNoq. 37 (1976) C4-231.

[5] COOPER, J., RIZZUTO, C. and OLCESE, G. L., J. Physique Colloq.

32 (1971) Cl-1 136.

[6] BORSA, F. and OLCESE, G. L., Phys. Status Solidi (a) 17 (1973) 631.

[7] OLCESE, G. L., TO be published.

Interconfigurational fluctuations in Ce cubic compounds

HAL Id: jpa-00218900

https://hal.archives-ouvertes.fr/jpa-00218900

Submitted on 1 Jan 1979

HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Interconfigurational fluctuations in Ce cubic compounds

J. Sereni, G. Olcese, C. Rizzuto

To cite this version:

J. Sereni, G. Olcese, C. Rizzuto. Interconfigurational fluctuations in Ce cubic compounds. Journal de

Physique Colloques, 1979, 40 (C5), pp.C5-337-C5-339. �10.1051/jphyscol:19795116�. �jpa-00218900�

Colloque C5, supplément au n° 5, Tome 40, Mai 1979, page C5-337

Interconfigurational fluctuations in Ce cubic compounds

J. G. Sereni (*) (**)

G. L. Olcese

and C. Rizzuto

The magnetic susceptibility (MS) of thirty Ce where / * ( £ ) = e x p ( - EJTJ is the quasi Boltzmann cubic intermetallic compounds (IC), of different distribution and « Z »the partition function,

crystal structures (see the table I), which shows magnetic, intermediate and non magnetic behaviours,

Z = £(2./„ + 1) /„*(£).

has been analyzed assuming a temperature depen-

dence of the valence fluctuations. We have applied Taking D„(E) ~ e x p [ - ( £ - £„)

/2 J

] it is possible the concept of interconfigurational fluctuations [

integrate obtaining:

(ICF) [1, 2] to describe the observed temperature

dependence of the MS [3], taking into account the V(T) = (2J„ + 1) exp[j(AjT„)

- EjT„~].

lz.

possibility of a dynamical mixing between the two

lower energy Ce configurations (4f* 5d* ^ 4 f ° 5d

), Substituting T by T„, the MS can be written as identified as n = 1 and n — 1 = 0 respectively. From

(T) = (N/3 X„).£ /i

V(T). In the case' of Ce it is : this model we have derived a sufficiently accurate „

. ?

~ , . . . • . i i i .

<. * c* -1 i_i Hi = 2.54 w

and n

= 0. To apply this expression to energy eye scheme to attempt o fit available expe- ^

^ .

^ ^

nmentaldataof differentphysica 1 properties

^

f

n The probability of occupation of the state « « »

„,„ ' , . „,. . , , . , f. , . ,

_ i . , , , / • • . ^ « , ICF. They are : 1) The possible interactions between (of energy E„ and width Aj, is given at T -> 0 by :

. / , • , •

^ • ™ , •

m\ t CIA\ A \ u - \

. u magnetic moments, which give rise to a Curie-Weiss P„(0) ~ e x p ( - EJA„), and at high temperatures by :

f

N

)

contribution to PjiT) ~ e x p ( - E„/k

T). A good interpolation is 1 \ ^

\ T * vieck contriDmion to

," ' .\> . '' J'rrJ

, ~ .r-s r^ , the MS, independent from temperature, and 3) the done considering PJT) ~ exp(— EJT

) [4], where . . , ,...: • . , , ,

\ , ,

T -T+ A and k - 1 urine K L enerev unit P

splitting, into a doublet F

and a quarted r

, c "*. 7"' J

Z L * I °

the Hund sixfold ground state due to the crystal So, the valence dependence with temperature was _ . , ~ . „ , 5 . .

. . , , . ' „

' - _ / . , . , x-^i. ^ *• field effect. These exchange interactions will be repre- taken as the fractional occupation oi the configuration ^ , , i , r. i r i r- \ i r r

*i_

i

i („ = i) j

y l<

t I

I

j > I =

y

' derations the general expression for the MS becomes :

K D - I / Z z>,(£) /„*(£) d £ . I f . / ^ 2J,5 \

Table

Lattice parameter

The magnetic susceptibility (MS) of thirty Ce where / ( £ ) = e x p ( - EJTJ is the quasi Boltzmann* cubic intermetallic compounds (IC), of different distribution and « Z »the partition function,

**Z = £(2./„ + 1) /„*(£).**

<. c* -1 i_i Hi = 2.54 w*

\ T vieck contriDmion to*

Z L I °*

' - _ / . , . , x-^i. ^ • field effect. These exchange interactions will be repre- taken as the fractional occupation oi the configuration ^ , , i , r. i r i r- \ i r r*

l ^Magnetic

1 ^Magnetic