STRUCTURE OF THE VK, CENTRE IN AMF3 COMPOUNDS

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STRUCTURE OF THE VK, CENTRE IN AMF3 COMPOUNDS

J. Rousseau, Jérome Fayette

To cite this version:

J. Rousseau, Jérome Fayette. STRUCTURE OF THE VK, CENTRE IN AMF3 COMPOUNDS.

Journal de Physique Colloques, 1976, 37 (C7), pp.C7-235-C7-237. �10.1051/jphyscol:1976757�. �jpa- 00216916�

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JOURNAL DE PHYSIQUE Colloque C7, supplkment au no 12, Tome 37, Dkcembre 1976, page C7-235

STRUCTURE OF THE V, CENTRE IN AMF, COMPOUNDS

J. J. ROUSSEAU and J. C. FAYET

Laboratoire de Spectroscopie du Solide, FacultC des Sciences du Mans, 7201 7 Le Mans-Cedex, France

RBsumB. - Le centre VK dans les composes AMF3, prksente une liaison courbe intrinsBque.

Le rkseau perovskite sert de support pour le calcul du melange d'orbitale ^217,dans l'orbitale ^{z Z ,} Iorsque l'on soumet l'ion FZ A un champ cristallin de symetrie Czv. De plus, on montre que le centre VK permet de mettre enevidencela distorsion tktragonalequi se produit A 124 K dans RbCdFs.

Abstract. - The VK centre in AMP3 compounds, exhibits a bent bond configuration. The perovskite lattice is used as a support to calculate the admixture of 217, orbital in ~ Z V orbital on submitting the F F molecular ion to a crystal field of Cz, symmetry. Moreover, one shows that the VK centre may be used to evidence the tetragonal distorsion at 124 K in RbCdF3.

Our purpose is to study the influence of lattice symmetry on the VK centre in AMF, compounds.

a) in the cubic perovskite lattice (KMgF,, KZnF, and CsCdF, at any temperature),

b) in the tetragonaly distorted phase, below T, (RbCaF,, TlCdF, and RbCdF,). In RbCdF, the VK centre is stable on both sides of T, = 124K.

1. Cubic phase. - 1 .1 EXPERIMENTAL. - The structure of the VK centre is shown in figure 1. The intrinsic bent configuration is due t o the local C,, symmetry. A review of E. P. R. measurements and optical data is presented in table I. The near constancy of the main hyperfine parameter in the serie implicates a near constancy of the bond length : 2 d. The bending

angle (deviation of the hyperfine axis from [110])

0

F -

has been measured by E. P. R. which cannot decide

•

^{A +}

of the sign.

The initial work on K M ~ F , is due to [31 ^{FIG. 1.}^-The configuration of the F2 molecular ion on the (001) plane. C, ^q(normal to this plane) and 6 are the principal and we have focused ^Our ^On^CsCdF3 which axes of the hyperfine tensors. x (normal to (OOl)), y and t are exhibits neatly a larger lattice parameter. the ^gtensor axes.

TABLE I

Spectroscopic data for the F i ion in some perovskites and alkali fluorides V, in : KMgF3

I

3

1 (*I

KZnF, CsCdF, (*") LiF

I

1

I

N a F

I

1

I

LiF ( 2 I (V,) Unit

9 x

"

^Qy

A5 A, = A,

6 UV Band

22." -+ 2Z.g IR Band

2.zU + 217%

(*) Perturbed VK centres have been also investigated [ 5 ] . (**) This work.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1976757

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C7-236 J. 5. ROUSSEAU AND J. C. FAYET 1.2 MODEL TO ACCOUNT FOR THE BENDING. - The

perovskite lattice has been used as a support to calculate the bending angle 8 on using the following simple bases :

a) E. P. R. permits to derive a L. C . A. 0. model for the hole density :

which formally transforms into :

+

a sin ~(p;, - pg2)

.

(1) The values aZ = 1.202 and

P2

⁼0.041 obtained on using Froese's orbitals [6] hold for both KMgF, and CsCdF,. E. P. R. cannot decide for the sign of

aIP.

b)

1

Y > may be viewed as an eigenfunction of an effective hamiltonian :

in which the low symmetry components of the crystal field acting on the molecular ion are assumed to be

weak.

Then the perturbation theory leads to :

(2) The

1

'ZU > orbital can be derived from E. P. R., AE is supplied by optical measurements. Formula (2), in comparison with formula (1) permits to calculate 8 when one knows V$ and the bond length 2d.

VC2v

, ,

has been computed on using a point charge model and on allowing the nuclear axis to displace by Yo (Fig. 2).

RG. 2. - Trends for atomic displacements around the Vx centre ((1 10) plane).

When the potential is developed in a sum of Tes- sera1 harmonics, in the x, y, z axes system, only the Z z , , with odd parity for n, have to be considered. These

components have been computed by full lattice summation up to n = 5. For higher orders, the summation can be limited to the nearest neighbouring ions, 1 . 3 RESULTS. - Some details of the calculations are given in reference [7] and the results are summa- rized in figure 3.

- The computed values fall in the same range as the measured values of 8.

FIG. 3. - Values of the bent angle 0 versus yola for several values of d, in KMgFs(3-a) and in CsCdFs(3-b). Full lines :

P/u > 0, dashed lines : p/u > 0.

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STRUCTURE OF THE VK CENTRE IN AMF3 COMPOUNDS C7-237

- It is not trivial to predict the direction of the 2. Tetragonal phase. - The tetragonal distorsion bending unless knowing reliable wave functions. is due to staggered rotations of the ligand octahedra.

- Nevertheless, on assuming that 9 has the same On assuming that the nuclear axis of the V, centre sign in both KMgF, and CsCdF,, one has to choose rotates by the same angle as the [I101 axis, E. P. R.

2d close to 4 atomic units to account for the measured permits [8], in RbCdF, to evidence the rotation below values. This result agrees with the ab-initio calcula- 124 K and to measure the order parameter of the

tions on VK in LiF [I]. transition.

References

[I] JETTE, A. N., GILBERT, T. L. and DAS, T. P., Phys. Rev. [5] RHOADS, J. E., ROSE, B. H. and HALLIBURTON, L. E., J.

184 (1969) 884. Phys. & Chem. Solids 37 (1976) 346.

[2] KANZIG, W., J. Phys. & Chem. Solids 17 (1960) 80.

[3] HALL, T. P. P., Brit. J. Appl. Phys. 17 (1966) 101 1.

[6] SUGANO; S. and SHULMAN, R.'G., ~ h y s . Rev. 130 (1963) 517.

[7] ROUSSEAU, J. J. and FAYET, J. C., Phys. Status Solidi (b) 77 (1976) 195.

[4] KAPPERS, L. A. and HALLIBURTON, L. E., J. Phys. C 7 [8] ROUSSEAU, J. J. and FAYET, J. C., Phys. Status Solidi (b)

(1973) 589. 73 (1976) 625.