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Thermal conductivity of MgO:Fe++ below room temperature
volume 27A, number 8
PHYSICS
9 September
LETTERS
1968
au spectre de l’argon; la frequence plasma electronique ne varie alors que .de 1%.
quence plasma ionique _fpi; on obtient cette derniere en divisant la fr&p.rence plasma electronique moyenne (f e) don&e par la methode de perturbation TMOl$ par la racine carree de la masse du gaz consider&. D’autre part, aux hautes pressions l’ecart entre ces dew frequences est grand. De plus, autre caracteristique, la variation de la frequence fm en fonction de la frequence d’excitation (f,,) et par consequent en fonction de la frequence plasma, est a peu pres lineaire et croissante. Enfin, un melange de 5% d’argon dans le neon (250 1) fait passer la frequence de modulation du neon (17 MHz) a 13 MHz, frequence appartenant
Rif&ences 1. R. A. Stern et N. Tzoar, Phys. Rev. Letters 17 (1966) 903. A. M. Pointu et Y. Po2. A. Constantin, Ph. Leprince, meau, J. de Phys., Colloque C3, Supplement au No 4 (1968) 190. 3. J. M. Jones et K. G. Emeleus, Phys. Letters 12 (1964) 18’7. 4. M. Sumi, J. Phys. Sot. Japan 14 (1959) 1093. 88 Conf. Int. sur Phe5. J. P. Jouineau et Ph. Leprince, nomenes dans les milieux ionises, Vienne (1967) 339.
* ****
THERMAL CONDUCTIVITY OF MgO:Fe++ BELOW ROOM TEMPERATURE M. F. LEWIS The General Electric Co. Ltd., Hi& Research East Lane, Wembley, UK
Centre,
and Department
of Physics,
I. P. MORTON The UniverSity , Southampton,
Received
16 July 1968
The thermal conductivity of MgO:Fe++ shows a dip at 800K which we attribute scattering involving the ground and first excited states of the Fe++ ion.
At temperatures in the region of 1-4q( it has been shown that the thermal conductivity of MgO is reduced by the presence of Fe++ centres through spin-phonon interactions involving the ground triplet of the Fe++ ion [ 11. In this note we report briefly the effect of small concentrations of Fe++ on the thermal conductivity of MgO at temperatures above 30°K. We show that, at these temperatures, the thermal conductivity is reduced by spin-phonon transitions involving the spin-orbit split level lying -150 cm-l (15OoK) above the ground triplet [Z]; this level is responsible for a strong Orbach split-lattice relaxation mechanism in MgO:Fe++ [3]. The results of thermal conductivity measurements on two MgO samples are shown in fig. 1. Curve A is for a typical 99.9% pure MgO sample grown by the arc fusion technique and has a total
UK
to resonant
spin-phonon
iron group ion content of N 0.1%. Compared with pure MgO samples [e.g. 41, the thermal conductivity is somewhat reduced by the presence of these impurities, but curve A is otherwise typical of dielectric materials [5]. Curve B shows the thermal conductivity of a sample containing - )% of iron, probably * at least half of which was in the divalent state. There is clearly a dip in curve B at - 80°K. The temperature of this dip is consistent with the presence of a transition with energy 105 cm-l if the dominant thermal phonons responsible for the heat transport have energy nkT with n N 2. The value n N 2 is cer* One can differentiate
between Fe2+ ples with low iron concentration by spin resonance. In our experience, usually show that greater than half divalent state.
and Fe 3+ in sammeans of electron such analyses the iron is in the
547
PHYSICS
Volume 27A, number 8
IO
0. l
3
a
.
.
CurveA*‘-
.
.
.
. .
.
.
.
IXI.* Curve
0.f
l. 0. B
.
-8 . .. . z
zf=+2%,
‘% l
0.:
0.1
io
I 30
9 September 1968
agreement with values of the spin-phonon transition probabilities deduced from the Orbach spinlattice relaxation mechanism in MgO:Fe++ [3], but the accuracy of the calculations is limited by lack of information on the 105 cm-I transition lineshape, and by the usual approximations involved in computing thermal phonon transport properties [ 51. One of our reasons for studying the effect of Fe++ centres on the thermal conductivity of MgO is that the attenuation of microwave ultrasound in dielectrics at high temperatures is caused by a relaxation mechanism involving the mean thermal phonon relaxation time, T [6]. T is related to the thermal conductivity, K, by the familiar approximate equation
K (WcN’de$K)
5
LETTERS
* lrJ*
I 50
100
.* -
-
.
T (OKI
I
300
Fig. 1. Thermal conductivity K versus temperature 2’ for two specimens of MgO. The form factor of each specimen has an uncertainty of 20% which gives a corresponding error in the absolute values of K.
where C is the specific heat/unit volume and v a mean phonon group velocity. It can be seen from fig. 1 that the presence of only 1% Fe++ in MgO can cause a substantial reduction in T, and hence, if the theory can be interpreted this naively, in the ultrasonic attenuation in MgO. Such a reduction in the ultrasonic attenuation (not necessarily in MgO) could be useful in devices such as ultrasonic delay lines. The results of further measurements, and details of the calculations will be published elsewhere.
References tainly in the expected region, but it is notoriously difficult to calculate n accurately [5]. This is
particularly true at temperatures near the thermal conductivity maximum where various mechanisms contribute to thermal resistance through phonon scattering processes with widely differing frequency dependences of the scattering cross section. A preliminary calculation, however, does show that the size of the thermal conductivity dip in curve B, fig. 1 is in good ‘order-of-magnitude’
548
1. P.V. E. McClintock, I. P.Morton and H. M.Rosenberg, Proc. Intern. Conf. on Magnetism, Nottingham, 1964 (Institute of Physics and Physical Society, London 1965) p. 455. 2. J. Y. Wong and A. L. Schawlow, Bull.Am. Phys. Sot. 12 (1967) 655. 3. J. B. Jones and M. F. Lewis, Solid State Communications 5 (1967) 595. 4. G. A. Slack, Phys. Rev. 126 (1962) 427. 5. J. M. Ziman, Electrons and phonons (Oxford University Press, 1960) especially Chapt. 8. 6. W. P. Mason and T.B. Bateman, J. Acoust. Sot. Am. 40 (1966) 852.
PHYSICS
9 September
LETTERS
1968
au spectre de l’argon; la frequence plasma electronique ne varie alors que .de 1%.
quence plasma ionique _fpi; on obtient cette derniere en divisant la fr&p.rence plasma electronique moyenne (f e) don&e par la methode de perturbation TMOl$ par la racine carree de la masse du gaz consider&. D’autre part, aux hautes pressions l’ecart entre ces dew frequences est grand. De plus, autre caracteristique, la variation de la frequence fm en fonction de la frequence d’excitation (f,,) et par consequent en fonction de la frequence plasma, est a peu pres lineaire et croissante. Enfin, un melange de 5% d’argon dans le neon (250 1) fait passer la frequence de modulation du neon (17 MHz) a 13 MHz, frequence appartenant
Rif&ences 1. R. A. Stern et N. Tzoar, Phys. Rev. Letters 17 (1966) 903. A. M. Pointu et Y. Po2. A. Constantin, Ph. Leprince, meau, J. de Phys., Colloque C3, Supplement au No 4 (1968) 190. 3. J. M. Jones et K. G. Emeleus, Phys. Letters 12 (1964) 18’7. 4. M. Sumi, J. Phys. Sot. Japan 14 (1959) 1093. 88 Conf. Int. sur Phe5. J. P. Jouineau et Ph. Leprince, nomenes dans les milieux ionises, Vienne (1967) 339.
* ****
THERMAL CONDUCTIVITY OF MgO:Fe++ BELOW ROOM TEMPERATURE M. F. LEWIS The General Electric Co. Ltd., Hi& Research East Lane, Wembley, UK
Centre,
and Department
of Physics,
I. P. MORTON The UniverSity , Southampton,
Received
16 July 1968
The thermal conductivity of MgO:Fe++ shows a dip at 800K which we attribute scattering involving the ground and first excited states of the Fe++ ion.
At temperatures in the region of 1-4q( it has been shown that the thermal conductivity of MgO is reduced by the presence of Fe++ centres through spin-phonon interactions involving the ground triplet of the Fe++ ion [ 11. In this note we report briefly the effect of small concentrations of Fe++ on the thermal conductivity of MgO at temperatures above 30°K. We show that, at these temperatures, the thermal conductivity is reduced by spin-phonon transitions involving the spin-orbit split level lying -150 cm-l (15OoK) above the ground triplet [Z]; this level is responsible for a strong Orbach split-lattice relaxation mechanism in MgO:Fe++ [3]. The results of thermal conductivity measurements on two MgO samples are shown in fig. 1. Curve A is for a typical 99.9% pure MgO sample grown by the arc fusion technique and has a total
UK
to resonant
spin-phonon
iron group ion content of N 0.1%. Compared with pure MgO samples [e.g. 41, the thermal conductivity is somewhat reduced by the presence of these impurities, but curve A is otherwise typical of dielectric materials [5]. Curve B shows the thermal conductivity of a sample containing - )% of iron, probably * at least half of which was in the divalent state. There is clearly a dip in curve B at - 80°K. The temperature of this dip is consistent with the presence of a transition with energy 105 cm-l if the dominant thermal phonons responsible for the heat transport have energy nkT with n N 2. The value n N 2 is cer* One can differentiate
between Fe2+ ples with low iron concentration by spin resonance. In our experience, usually show that greater than half divalent state.
and Fe 3+ in sammeans of electron such analyses the iron is in the
547
PHYSICS
Volume 27A, number 8
IO
0. l
3
a
.
.
CurveA*‘-
.
.
.
. .
.
.
.
IXI.* Curve
0.f
l. 0. B
.
-8 . .. . z
zf=+2%,
‘% l
0.:
0.1
io
I 30
9 September 1968
agreement with values of the spin-phonon transition probabilities deduced from the Orbach spinlattice relaxation mechanism in MgO:Fe++ [3], but the accuracy of the calculations is limited by lack of information on the 105 cm-I transition lineshape, and by the usual approximations involved in computing thermal phonon transport properties [ 51. One of our reasons for studying the effect of Fe++ centres on the thermal conductivity of MgO is that the attenuation of microwave ultrasound in dielectrics at high temperatures is caused by a relaxation mechanism involving the mean thermal phonon relaxation time, T [6]. T is related to the thermal conductivity, K, by the familiar approximate equation
K (WcN’de$K)
5
LETTERS
* lrJ*
I 50
100
.* -
-
.
T (OKI
I
300
Fig. 1. Thermal conductivity K versus temperature 2’ for two specimens of MgO. The form factor of each specimen has an uncertainty of 20% which gives a corresponding error in the absolute values of K.
where C is the specific heat/unit volume and v a mean phonon group velocity. It can be seen from fig. 1 that the presence of only 1% Fe++ in MgO can cause a substantial reduction in T, and hence, if the theory can be interpreted this naively, in the ultrasonic attenuation in MgO. Such a reduction in the ultrasonic attenuation (not necessarily in MgO) could be useful in devices such as ultrasonic delay lines. The results of further measurements, and details of the calculations will be published elsewhere.
References tainly in the expected region, but it is notoriously difficult to calculate n accurately [5]. This is
particularly true at temperatures near the thermal conductivity maximum where various mechanisms contribute to thermal resistance through phonon scattering processes with widely differing frequency dependences of the scattering cross section. A preliminary calculation, however, does show that the size of the thermal conductivity dip in curve B, fig. 1 is in good ‘order-of-magnitude’
548
1. P.V. E. McClintock, I. P.Morton and H. M.Rosenberg, Proc. Intern. Conf. on Magnetism, Nottingham, 1964 (Institute of Physics and Physical Society, London 1965) p. 455. 2. J. Y. Wong and A. L. Schawlow, Bull.Am. Phys. Sot. 12 (1967) 655. 3. J. B. Jones and M. F. Lewis, Solid State Communications 5 (1967) 595. 4. G. A. Slack, Phys. Rev. 126 (1962) 427. 5. J. M. Ziman, Electrons and phonons (Oxford University Press, 1960) especially Chapt. 8. 6. W. P. Mason and T.B. Bateman, J. Acoust. Sot. Am. 40 (1966) 852.