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ANELASTIC PROPERTIES OF ALKALI HALIDES DOPED WITH OXYGEN
H. Beyeler, J. Muggli, G. Pfister
To cite this version:
H. Beyeler, J. Muggli, G. Pfister. ANELASTIC PROPERTIES OF ALKALI HALIDES DOPED WITH OXYGEN. Journal de Physique Colloques, 1971, 32 (C2), pp.C2-261-C2-263.
�10.1051/jphyscol:1971254�. �jpa-00214580�
JOURNAL DE PHYSIQUE
Colloque C2, supplkment au no 7 , tome 32, Juillet 1971, page C2-261
ANELASTIC PROPERTIES
OF ALKALI HALIDES DOPED WITH OXYGEN
H. U. BEYELER, J. MUGGLI and G. PFISTER
Laboratory of Solid State Physics Swiss Federal Institute of Technology, Ziirich
R6sum6. -
Des mol~cules
0;ont ete incorporees dans des halogenures alcalins
ala place d'ions halogknes. Ces defauts ponctuels rkorientent m2me
abasse tempkature. Le taux de rkorien- tation est proportionnel
Bla temperature au-dessous de
4OK,
cequi permet de conclure que la cinematique de reorientation est un processus un phonon dans ce domaine. L'interaction de deux molCcules
0;a kt6 Btudike d'une maniere directe par la rksonance paramagnetique klectro- nique dans KCl, KBr et KI. Ceci est compare aux rksultats thkoriques de l'elasticite des milieux continus. 11s s'accordent assez bien.
Abstract.
- In alkali halides 0; molecules are built in substituting for halide ions. These point defects reorient even at low temperatures. Below
4OK the reorientation rate is proportional to the temperature, indicating that one phonon processes dominate. The elastic interaction of two
0;molecules has been studied directly by means of electron spin resonance in KCl, KBr and
KI.The results are compared with calculations using continuum elasticity theory. The agreement is quite satisfactory.
Anelasticity due to point defects may not only be due to their diffusion but also to their rotation. This can be the case for molecules of low symmetry built in as an impurity at a lattice site or as an interstitial.
Detailed insight in the behaviour of such systems is gained by studying the relation between their microsco- pic and macroscopic properties. For such an investiga- tion 0; doped alkali halides turned out to be a uni- qually suited system. Oxygen is incorporated into the alkali halide lattice mainly in the form of 0; molecular ions substituting for halide ions. In an unstressed crys- tal the molecular axis has six equivalent orientations, namely along the six [I101 axis of the crystal. The 0;
molecule is paramagnetic. Its spectroscopic splitting factor is anisotropic so that in an electron spin reso- nance experiment the six orientations give rise to six separated resonance lines. Therefore EPR is the ideal tool to count the population of the six orientational states.
A uniaxial external stress applied to the crystal, say along a [OOl] axis lifts the degeneracy between these states. The energy of a molecule in [I101 or [ l i ~ ] orientation is now different from that in the other four orientations. The experiments show that in KC1, KBr and KI the molecule favours the orientations perpendicular to the stress axis whereas in NaI it tends to be parallel to a [OOl] stress. Reorientations between the six orientations are possible even at liquid helium temperatures [I]. After application of a uniaxial stress we can by EPR observe how the populations
approach the new Boltzmann equilibrium. It turns out that the energy splitting between the orientational states is proportional t o the external stress and may at low temperatures exceed kT, so that the Boltzmann factors are extremely large. The energy of the 0, molecule in one of the six equilibrium orientations in an arbitrary external uniaxial stress can be written as U
=- P . E , where
Eis the externally produced strain and P is the so called
((elastic dipole
Mtensor. This tensor has been derived from the measured Boltzmann distribution and from the measured expansion of the lattice as a function of the defect concentration. In the framework of continuum elasticity theory an elastic dipole may be considered as local forces acting on the medium with no net resulting total force and torque. An elementary elastic dipole is a double force in a homogeneous medium. Electric and elastic dipoles are analoguous in the sense that the electric potential and the elastic displacement field both fall off with l/r2.
By observing the time dependence of the populations of the six orientational states after changing the uniaxial stress we can directly investigate the reorientation processes. For a stress along [OOl] or [ I l l ] the molecule has just two different orientational levels. The approach to a new Boltzmann equilibrium can then be descri- bed by a single relaxation time. We investigated this relaxation time in KCl, KBr and K I in the tempera- ture range between 1 OK and 5 OK as a function of stress for the isotopes
160and ''0 [2]. The strain and
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1971254
C2-262 H. U, BEYELER, J. MUGGLI AND
G.
PFISTERtemperature dependence indicate that one phonon
processes dominate below 4 OK. At higher temperatures reorientation through excited vibrational levels beco- mes important. The isotope effect, that is the ratio of the relaxation times for 160 and 180 is large and independent of stress and temperature. This indicates that tunnelling through the potential barrier between equilibrium orientations is an important step in the reorientation process. The experimental results can be interpreted in terms of a theory of Gosar and Pirc [3]. It permits the determination of the tunnelling matrix element, the libration frequency of an orienta- tional state and an effective moment of inertia which accounts for the reorientation of the surrounding elastic field. The potential barrier between two orien- tations is found to be of the order of 20 meV.
We have in addition studied the interaction between two 02 centres. For this one has to use highly doped samples. EPR experiments on such samples revealed resonance lines arising from interacting 0; mole- cules on nearest neighbour sites. The experiment yielded the following results
:The molecular axis of the pairs are still oriented along [IIO]. Therefore we have to consider 36 mutual arrangements of the partners. These arrangements, however, reduce to 9 classes with different elastic energy. The partners of a pair still reorient between different equilibrium orientations so that a Boltzmann equilibrium between the populations of the energetically different classes of arrangements is established. The energy splitting between the classes is such that at liquid He or H, temperatures in KC1 and KI only one and in KBr two classes are populated. The structure of these classes has been determined by EPR. In KC1 an arrangement with symmetry Ci (class 5) in KI one with symmetry C, (class 1) is realised. In KBr both classes (1 and 5) are found the energy splitting between the two classes being only 2.4 meV. Class 5 corresponds to the lower level [4]. A detailed study of the influence of external uniaxial stresses led to the dfollowing results. The energy changes induced by external stresses are of the order of 1 to 2 meV and therefore much smaller than the splitting between the pair classes (with the excep- tion of KBr). Thus one expects that a given pair cannot change its class through reorientation under an external stress. The experiments confirmed that the partners of a pair of 0; molecules behave in an external stress as if they were isolated but with the
very restrictive condition that the class of the pair arrangement remains unchanged. 0; pairs in KBr do not follow this rule because there the energy diffe- rence between the two observed classes is of the same order of magnitude as the energy changes induced by external stresses. Including that case, one can say that the energy change of a pair of 0; molecules in an external stress is equal to the sum of the energy changes which both molecules would undergo if they were isolated from each other but having the same orientations. Evidently the energy change by the exter- nal stress superposes to the interaction energy without changing the latter. An important question is now whether elasticity theory can explain the experimen- tally detected classes have the lowest energy. In the theoretical description we have approximated the discrete crystal lattice by an elastic continuum with the same macroscopic properties. By solving the fun- damental equations of continuum elasticity theory the displacement fields produced by an elastic dipole can be calculated. On this basis the displacement fields (the lattice relaxation) around and 0; molecule has been calculated using the experimentally deter- mined elastic dipole tensor. There exist no direct measurements yet to be compared with this theoreti- cal result. However from this displacement field the strain field
Earound the defect can be deduced.
The interaction energy between two elastic dipoles is just the energy of one dipole P in the strain field
Eof the other. Again this is analoguous to the interaction between two electric dipoles. The interaction of any two elastic dipoles in any cubic medium has been calculated and the results have been tabulated [63.
Comparison of the calculated energy levels for the 9 classes with the experimental data yields the follo- wing results
151 :The energies of the 9 different classes are spread over a range of 35 meV in KC1 to 85 meV in KI. In KC1 and KI the class with lowest calculated energy corresponds to the class identified in the expe- riment. For KBr the two classes with the lowest cal- culated energy are those found experimentally, howe- ver the order is inverted. So the agreement between theory and experiment is quite satisfactory. The small experimental deviation from continuum elasticity calculation may be caused by additional interactions such as covalent bonding and electrical quadrupole interaction. The magnetic interaction is known to be small
[7].DISCUSSION (Confkrence de M. Beyeler).
Prof. SEEGER
:Please explain the effect of the lattice overlapping of the statically displaced surroundings distorsion on the transition rate. of the initial and the final state of the molecule.
Dr. BEYELER
:The transition matrix element con- Prof. SEEGER
:Could you explain the difference sists of a product, one factor accounting for the over- between the theory of and Pirc and the theory lapping of the initial state and the final state of the Sussmann.
naked molecule, the other factor accounting for the Dr. BEYELER
:The difference lies mainly in the
ANELASTIC PROPERTIES OF ALKALI HALIDES DOPED WITH OXYGEN
C2-263assumptions made for the expression describing the hand uses a change of this overlapping due to phonons interaction between the localized states of the molecule for the calculation of the transition rate (such a cou- and the phonons. Gosar and Pirc assume, that this pling is difficult to derive from simple physical models).
interaction does not change the overlapping of the Both theories give a transition rate proportional localized molecular states. Sussmann on the other to temperature for one phonon processes.
El] KANZIG (W.),
J. Phys. Chem. Sol.,1962,
23,479. [4] BEYELER
(H. U.), Phys. Kondens.Mat., 1970,
11,121 PFISTER (G.), KANZIG (W.),
Phys. Kondens.Mat., 1969, 286.
10,
