Short Notes K107

phys. stat. sol. (a) l7, K107 (1973) Subject classification: 12.2; 22.5

Natural Philosophy Department, Aberdeen University

The Elastic Constants of Cerium Fluoride

BY S. HART

Cerium fluoride is one of the fluorides of the lantlvmide series which crystal-

Uses from the melt in a stable hexagonal structure, the others being LaF3, PrF3,

and NdF3. The other fluorides of the series exhibit both hexagonal and orthorhombic

structures, the latter being the low temperature phase. For these fluorides i t is

extremely difficult to obtain crystals of the hexagonal phase with dimensions larger

than a few millimetres at room temperature since the strain due to the volume

change at the transition temperature usually shatters the specimen.

The lanthanide fluorides have been of interest lately in optical work in con-

nection with quantum counter and laser action and in this Department considerable

work has been done on the Stockbarger and Stober growth of these materials (1).

A s yet no lattice dynamic work has been attempted on the series and no me-

chanical properties have been reported. The present work concerns the measure-

ment of the elastic compliances, s.., of one member of the series, CeF3.

standard Stockbarger methods using a temperature gradient of 50 deg/cm and a

nitrogen atmosphere of 5 Torr pressure. Growth rates of 2 mm/h permitted crys-

tals of up to 3 cm diameter and 7 cm length to be obtained.

11 Since this material exhibits no dimorphism it has been grown fairly readily @

The specimens used in this investigation were cut from the grown boules and

ground to cylinders of 5 mm diameter and lengths of a few centimetres. Optical

orientation was used initially (2) a d the final orientations were done using back

reflexion h u e photographs. The orientations were thus obtained to an accuracy

of 0.5'. Spectrographic analyses revealed calcium present at levels of 1000 parts

per million but no other impurity was observed.

The density of CeF is subject to some uncertainty. Batsanova and Grigoreva (3) 3 -3 quote 5.99 g cm

due to the uncertain purity of the sample. Thoma and Brunton (4) quote X-ray deter-

but say their CeF results (mainly of optical data) are tentative 3

Kl08

mined lattice constants which lead to a density of 6.16 g ~ m - ~ while Jones and

Shand (1) quote X-ray values leading to 6.10 gcm

the present specimens gave a value of (6.16 + - 0.02)gcm

been adopted.

physica status solidi (a) 17

-3 . Buoyancy measurements on -3 and a value of 6.16 has

The elastic measurements consisted of determining the longitudinal (f,) and

torsional (f ) resonant frequencies of the rods of length 1 and density e . The

Young's modulus, E, and rigidity modulus, G, were then determined using the t

well known equations

2 2 4 e l2 f:

t ' and G = 4 e l f K E =

K, the Rayleigh correction factor is nearly unity for the specimens used. The fre-

quency measurements were made using the composite oscillator technique which

has recently been'described, Hart (6).

If the crystal rod has its axis at angle 8 to the c axis of the hexagonal crystal

structure then the Young's modulus is related to the elastic compliances by

1 4 4 2 2 - = s E 11 33 44 sin 8 + s cos 8 + (2s13 + s )sin 8 cos 8

and similarly the rigidity modulus is related by

2 2 - + - 1 GE - 44 2 8 )sin ecos 8 , - S~ + (sll - s12 - 2) sin 8 + 2(s11 + s33 - 2 ~ 1 3 - 44

S

G 2

where 3 - 2s )sin 8 case + (2s13 + sM - 2s )sinBcos8 .

33 -"44 13 33 SA5 = 2(Sll + s

These equations are derived as an application to the hexagonal structure of the

study by Brown (7) into free and pure elastic moduli. They are identical for example

to the equations of Wachtman et al. (8) for trigonal corundum on putting s14 = 0 in

the corundum equations.

It is interesting to note that for hexagonal symmetry only the polar angle 8 is of

importance to the elastic properties.

In Table 1 are listed the relevant values of E , G, and 8 for the 5 specimens

used.

Least squares values of sll, s33, and 2sI3 + s44 were obtainedvia the E equations.

These values were used to set up the G equations which were solved for values of

Short Notes

crystal

NO.

1 2 3 4 5

Kl09

E G e

18.92 3.48 5.5O

11 11 (10 dyncm-2) (10 dyncm-2)

11.84 4.63 30'

12.90 3.93 84.5 13.11 3.94 90'

11.34 4.74 33.50

Table 1

Experimental results for CeF 3

- %, and sll + s33 - 2s13 - s Thus a single value of the com-

and two values of s13 were obtained. Both values sqi' sll - 5 2 2 44'

and s 11' s33' s44' 12 pliances s

agreed within experimental accuracy, but since the second determination of s13

from the G equations had a larger error associated with its derivation the value

quoted is that obtained from the E equations. The s

elastic moduli c.. values. The values so obtained are listed in Table 2 and the

variation of E and G with angle 8 is shown in Fig. 1.

matrix was inverted to give i j

11

It would be of interest to extend this study to the other hexagonal fluorides of

the lanthanum series. The X-ray data of Thoma and Brunton (4) show that there

is virtually no difference in the lattice parameters of W3, CeF3, PrF3, and

NdF3 with a and c approximately 7 % i n the unit cell containing 6 molecules. The

+3 charge ionic radii of L a , Ce, Pr, and

Nd are also very nearly equal so that

variations in the elastic constants would be

primarily due to a simple increase in the

cation atomic number.

1 160-

s 100 - L

Lu 8 a . ; 1 I I I ' ' I , :

Fig. 1. YOUng's.modulus and rigiditg modulus values for CeF as a function of the polar angle 8

"00. 1;- iff ;r ir ;r 60. ;a. bb 90' 8 - 3

8 physlca (a)

K l l O

sll

33

44

12

13

S

S

S

S

physica status solidi (a) 17

( 1 0 - l ~ c m 2 ~ n - 1 )

7.64 + 0.05

5.14 + 0.05 - -

29.2 + 0 . 2

-3.3 + 0.2

-1.22 + 0.06

- - -

Table 2

Elastic constants of CeF, B

(10 11 dyncm-2)

18.0 + 0 . 5

22.5 + 0 . 8 11

33

44

12

13

C

C

C

C

C

- -

3.42 + 0.02

8.8 + 0 . 5

6.4 + 0 . 4

- - -

References

(1) D.A. JONES and W.A. SHAM), J. Crgstal Growth 2, 361 (1968).

(2) S. HART and R.W.H. STEVENSON, J. Phys. D 2, 1789 (1970).

(3) L.R. BATSANOVA and G.N. GRIGOREVA, Izv. Sib. Otdel. Akad. Nauk SSSR 2, . 115 (1962).

(4) R.E. THOMA and G.D. BRUNTON, Inorg. Chem. S, 1937 (1966).

(5) R.W. G. WYCKOFF, Crystal Structures, Interscience Publishers, New York.

(6) S. HART, J. Phys. D S , 430 (1970).

(7) W . F . BROWN, Phys. Rev. 58, 998 (1940).

(8) J.B. WACHTMAN, Jr., W.E. TEFFT, D.G. LAM, Jr., and R.P. STINCHFIELD,

J. Ree. Nat. Bur. Standards s, 213 (1960).

(Received March 21, 1973)