The effect of uniaxial stress on the thermal conductivity at low temperature of Al2O3 and MgO doped with 3dn ions

Solid State Communications,Vol. 19, PP. 9—13, 1976.

Pergamon Press.

Printed in Great Britain

THE EFFECT OF UNIAXIAL STRESS ON THE THERMAL CONDUCTIVITY AT LOW TEMPERATURE OF A12O3 AND MgO DOPED WITH 3d~IONS J. Rivallin, B. Salce and A.M. de Goer C.E.A.

—

C.E.N

—

G, Department de Transfert et Conversion d’Energie, Service des Basses Temperatures, France (Received 28 November 1975 by E.F. Bertaut) Thermal conductivity measurements (1.1—30 K) have been made on single crystals of A12O3 doped with elements different of the Iron group: V, Mn, Cr2~ Ni3t Cr, Ni, and also on Cr-doped MgO. The results show 3~, that theand observed effects of stress Preliminary values areofdue thetoorbit—lattice the Jahn—Teller coupling ions constants Mn are deduced from the quantitative analysis of the curves.

1. INTRODUCTION

i Moving plane

THE THERMAL conductivity of insulating crystals is very sensitive to the presence of small concentrations of paramagnetic ions strongly coupled to the lattice, namely Jahn—Teller ions, which give rise to resonant phonon scatterings. Several systems have been studied, for example d4 ions in Al 2 d1 and d7 ions 2 03 and MgO,”

Fixed plane

I

in A1thermal fies the the energy 3’4 conductivity Theleves application of these would of an ions; be thus uniaxial sensitive one stress expects to stress modithat and 2O3. that a determination of couplingmodel constants to the the lattice can be obtained if a theoretical describing

8

energy levels is available. We have done a study of the thermal conductivity under stress of single crystals of

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--

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a Sample

Al

n1

y~m0mete

Copper piece

Fixed plane

doped with V, Cr, Mn and Ni, and of Cr-doped MgO. Preliminary results have been given shorthave com5’6 Such measurements underasstress munications. been done on semiconductors by Keyes and Sladeck several years ago.7 203

~

n 2

Fig. 1. Schematic experimental arrangement for the application of stress. enclosure, which measures the applied force with a precision of 1%. The thermal conductivity is measured by the classical heat flow method. The heat leak through the pulling wire introduces an error less than 1%. Measurements are made at constant temperature and varying stress; one clamp is maintained at a fixed temperature by a regulation and the relative variations of the thermal conductivity K are plotted as a set of functions: f(u, T = constant) = [K(a, 7) —K(a = o, T)]/K(cr = o, 7). The absolute precision and reproducibility onf= i~K/Ko during a run is ±1% in the range ±20%, and ±2% in the range ±20% to ±200%. After the sample has been taken off and mounted again, the reproducibility is not so good, especially in the case of compression, but the great advantage of working with compression is that the samples never break; doped samples often break in traction, though the maximum applied stress 1400 kgf/cm2 for

2. EXPERIMENTAL The apparatus used is similar to that of reference 7 and the mechanical parts are schematized on Fig. 1. In the case of a traction, the force (maximum 100 kgl) is given by a pneumatic system at room temperature and is transmitted to the sample through a stainless steel wire (2 mm dia.). The ends of the sample are stuck on copper pieces (with stycast 2850 FT and catalyst L24), which are connected respectively to the steel wire and to the fixed plane No.2. To improve the alignment, a kneejoint is used at the bottom. Special care must be taken in sticking and mounting the sample in order that the stress be actually uniaxial. To apply a compressive stress, the force is transmitted under the fixed plane No.2, and it is more difficult to obtain a good alignment in this case. The force is measured by a dynamometer placed in the vacuum 9

UNIAXIAL STRESS OF A12O3 AND MgO DOPED WITH 3d’1 IONS

10 16(

5(

COMPRESSION T~1.35K

.

Vol. 19, No. I

0

120

640 kgf

30

—.60

.

x0

.

40

io

/ A’

.

I

+-~•~

1 -20

-

___________________________________

0

400

800 1cm2)1200 ~T (kgf

1600

Fig. 2. Experimental results for different magnetic ions in Al203: change of the thermal conductivity as a function of applied stress at T = cte. A: chromium; •: nickel; —: manganese; 0: vanadium.

2

5

10

20

50

I (Ic) Fig. 4. Examples of fits for Cr2~in Al 2 (compression). 0: Experimental 203results. at u = 640 kgf/crn line: hypothesis (i) with ~o = 9.2 K and Dashed = 6.5 x l0~ Full line: hypothesis (ii) with w 00 = 7.8 K and w02 = 13K. 51~

____________________________________ 2

50 MgO Cr

160

COMPRESSION = 1200 k~/c~2

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30

.•

o 0

120

.

A

0

~40

.~

~

II 1

0

~ -

cm2 I

1

I

5

10 T (K)

20

II

50

-

-20

2

2

I

I

I

i

—

I

i

5

10

Fig. 5. Example of fits for Cr2~in MgO at a = 530 kgf/ (compression). 0: Experimental results. Dashed lines: hypothesis (i) with w 0 = 9.4 K and D1 = 7.5 x l0~5~. Full line: hypothesis (ii) with w01 = 8K and w02 = 12K.

20

30

I (K)

Fig. 3. Relative change of thermal conductivity as a func-

were supplied from Centre de Reclierches Ugine-

tion of temperature at a = cte for different magnetic ions in A1203. Symbols are the same as in Fig. 2.

Kuhlmann (Jarrie, France) and MgO crystal, from Spicer Ltd (England). Typical results for different systems are

typical specimens of 3mm dia.) is far smaller than the average value of breaking2 modulus of Al203 by traction appliedatatroom 450 ternperature (5 x iO~ kgf/cm from C axes.8 More experimental details are given else-

the stress a at the constant temperature 1.35 K; the Al203 crystals, doped differenteffect ions, in arethe of case similar orientation. There is nowith detectable of the vanadium-doped sample, and the largest effect at this

given in Fig. 2, where eXK/Ko is plotted as a function of

where.9

3. RESULTS AND QUALITATIVE DISCUSSION Several samples of each system have been measured.9

temperature is observed in the case of the -y irradiated

ruby. From the curves obtained at different temperatures, we deduce graphically another set of curves at constant stressf’(T, a = constant) which are easier to

A1 203 single crystals, grown by the Verneuil method,

analyse; examples are given in Fig. 3 for

Vol. 19, No. 1 UNIAXIAL STRESS OF A1203 AND MgO DOPED WITH 3d’1 IONS a = 1200 kgf/cm2 the shape of the curves and the ampli-. tude of the effect are different from one system to !!i~° .Cr2~ another, and in all cases, the stress effect disappears 12 above 30K. These results are in complete agreement with the previous studies at zero stress: the systems . .

which mental doubles: large Mn~,Cr2~ stress effects 1,2ions and arewith Ni3~.4 those In the case of stronglydisplay coupled Jahn—Teller an containing orbital fundaA1 4~ions are detectable in zero stress3 only V of these Kramers ions to the lattice is and2O3:V, the coupling not so strong as in the previous three cases. Moreover, zero-stress splitting is larger, so the relative effect of stress on the levels must be even smaller. On the other hand, the thermal conductivity below 20K of pure A1 203 and 3~state) virgin ruby (where the mainly Cr ionsby is determined are essentially in the and Cr scattering by dislocations. The boundary scattering corresponding phonon relaxation times are independant of stress in the elastic regime and the thermal conductivity should not vary with stress, in agreements with the experimental result for pure A1 2O3 the small effects (less than 4%) seen in the case of ruby are ascribed residual 2~ions9 (these results are not shown on the to figures in Cr view of clarity). In the following, we shall discuss only the Jahn— Teller systems which show large stress effects. A general temperature range as the lowest resonant phonon scatterfeature is that the positive effects appear in the same ing observed in zero stress, and the amplitude is related to the value of Ko, that is to the concentration of active ions: L~K/Koincreases when Ko decreases; this fact is confirmed by the study of a -y-irradiated ruby sample during thermal annealing, which transforms Cr2~to Cr~.9Moreover, this study shows that the negative 2~ions, effects are also due to the Cr We note the analogy of the shape of the curves with those observed1~’11Qualitatively, in magneto-thermalthe conductivity shape of the measurements. L~.K/Kocurves as a function of T (Fig. 3) can be explained by an increase of the lowest resonant frequency observed in zero-stress measurements, or by a splitting of this resonance into two. The second possibility is excluded in the case of Ni~ions, as the levels involved are Kramers doublets. 4. QUANTITATIVE DISCUSSION Analysis of the zero stress thermal conductivity curves have been done previously”2’4 within the Callaway model, using two resonant relaxation times of 4/(w2 ~ for d4 ions. The the form: f’ = can D [~ effect of stress be analysed with either of the two hypothesis indicated above: (i) w 0 and D vary with the stress a (ii) the resonance is split and —

11

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6

200

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400

600

~2O3 .0.2+ 15

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4

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01 I-

C

w s ________________________ 0

500 -

~

000

1500

MII~

4 -

0 .• 0

0

500

1000

~

1500

Fig. 6. Variations of hw 0, hw0j and (d hw1~in function of stress for the three systems studied 4 ions). Dashed lines: variation of w0, hypothesis (i), (+: Computed values obtained from compressions measurements). Full(ii), lines: ofvalues w~and w~(w02> ‘.‘oi) hypothesis (0:variations computed obtained from cornpression measurements, A: values from traction measurements). — —

~--~

=

D ~ w4(l ((w2

—

—

21

F)

~4~)2

— —

+

Fw4 (w2 w~)~ —

if we suppose that the total intensity is conserved. Examples of fits are given in Figs. 4 and 5. In the case of Cr2~ingMgO, the two hypothesis give quite similar results, but for 7-irradiated ruby the second one is much better. Taking F = 0.5, two parameters are adjusted in each case, and the variations of w 0,the ~ three and systems. ~ in function of stress are given in Fig. 6 for A linear variation is observed for large stresses, and the same results are obtained in traction and in compression. The main sources of uncertainty come from the

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UNIAXIAL STRESS OF A1203 AND MgO DOPED WITH 3d” IONS

Vol. 19, No. I

Table 1

2~:MgO Cr Cr2~: Al 3~:A203 l Mn 3 : Al 203 Ni 203

aVE (Experimental)

aVE (Calculated)

10,000 10,000 45,000

130,000 cm~ 190,000cm’ (4700)?

17,000 ±l000cm’ ±5000cm’ ±5000 cm~ ±15,000

cm~

130,000cm’

imperfection of the fits in zero stress, the lack of uniformity of the stress, and the influence of the value of 9

calculated values of d(AE~~)/da at large stresses are not much dependant on other parameters. Thus, the cornparison between the theoretical and experimental slopes

the parameter In the caseF.of Cr2~ions, theoretical models of the

[dwo(o)/da in hypothesis (i), or dwo in even hypothesis (ii)] gives preliminary estimations 1(a)/da of (aVE), in the case of Mn3~(isoelectronic of Cr2~)where no precise Jahn—Teller parameters have been given so far. The results are given in Table 1. In the case of Ni3~,a value of (eVE) has been deduced by the same kind of analysis, but the shape of the resonant phonon relaxation time is more complicated.16 The calculated values of (aVE) in a point charge model also given in Table I are systematically quite different from the experimental ones. A value of (a VE) = 17,000 cm~has been given by Lange17 for Cr2~in MgO, from his measurements of ultrasonic absorption under stress, and is in surprisingly good agreement with our determination. We are currently improving the experimental device to obtain a better precision on the measurements of

2”3 level schemes in MgO and Al2Jahn—Teller 03 have been given,’ taking into account a strong effect in the orbital doublet 5E, in the limit of small tunnelling splitting c5. The energy levels are obtained by numerical diagonalization of 15 x 15 matrices. Additional terms describing the coupling of the ion to the E-type strains 10 and I~are included in the matrix to determine the erl1ergy levels under stress. The calculation of the applied strains lo and l~is done for each sample, using the known elastic constants of MgO’4 and Al 5 The theoretical 203.’ schemes obtained in this way display a quasi-linear variation of the levels vs large stresses. In the case of MgO, the strain is purely tetragonal so that l~= o; analytical expressions for the energy levels have been given by Fletcher.’2 For large stresses, the slopes d(~E~~)/du depend only on the coupling constant (aVx). In the case of Al 203, there are no analytical expressions, but the

(aVE).

REFERENCES I.

DE GOER A.M.,J. dePhys. 30, 389 (1969).

2. 3.

CHALLIS L.J., DE GOER A.M., GUCKELSBERGER K. & SLACK GA., Proc. R. Soc. London A330, 29 (1972). DE GOER A.M. & DEVISMES N., J. Phys. Chem. Solids 33, 1785 (1972).

4.

LOCATELLI M. & DE GOER A.M., Solid State Commun. 14, 111(1974).

5. 6. 7.

DE GOER A.M., DEVISMES N. & RIVALLIN J., 1st mt. Conf on Phonon Scattering in Solids (Edited by ALBANY H.J.), p. 260. Saclay (1972). RIVALLIN J. & SALCE B., 2nd hit. Conf on Phonon Scattering in Solids. Nottingham (1975) (in press). KEYES R.J. & SLADEK R.J., Phys. Rev. 125, 478 (1962).

8.

RYSKFIEVITCH, Oxide Ceramics. Academic Press (1960).

9. 10. 11. 12.

RIVALLIN J., These d’Etat, Grenoble (1974). CHALLIS L.J., MCCONACHIE M.A. & WILLIAM D.J., Proc. R. Soc. A310, 493 (1969). MACCLINTOCK P.V.E. & ROSENBERG H.M., Suppl~mentau Bulletin de l7nstitut International du Froid C’ommission 1, Grenoble, Annexe 1965. 2 (1965). FLETCHER J.R. & STEVENS K.W.H., J. Phys. C(SolidStatePhys.)Ser. 2. 2,444(1969).

13.

BATES C.A., JAUSSAUD P.C. & SMITH W.,J. Phys. C(Solid State Phys.)6 898 (1973).

Vol. 19, No. 1

UNIAXIAL STRESS OF A12O3 AND MgO DOPED WITH 3d” IONS

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14.

Phonons in perfect lattices and in lattice with same defects (Edited by STEVENSON R.W.H.). Oliver and Boyd (1966).

15.

TEFFT W.E.,J. Res. N.B.S. 70A, 4,277 (1966).

16.

SALCE B., 2nd mt. Conf. on Phonon Scattering in Solids. Nottingham (1975) (in press).

17.

LANGE J.N.,Phys. Rev. B8, 12, 5999 (1973).