RELAXATION PHENOMENA IN GLASS

Transcription

1 RELAXATION PHENOMENA IN GLASS J. Stevels To cite this version: J. Stevels. RELAXATION PHENOMENA IN GLASS. Journal de Physique Colloques, 1985, 46 (C8), pp.c8-613-c < /jphyscol: >. <jpa > HAL Id: jpa Submitted on 1 Jan 1985 HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

2 JOURNAL DE PHYSIQUE Colloque C8, supplement au n 12, Tome t6, decembre 1985 page C8-613 RELAXATION PHENOMENA IN GLASS J.M. Stevels Emeritus Professor, Eindhoven University of Technology, Eindhoven, The Netherlands Résumé - Cet article est une brève revue de l'état des connaissances dans le domaine des phénomènes de relaxation diélectriques et mécaniques dans les verres. Abstract - An Abstract is given of the current state of the knowledge of dielectric and mechanical relaxation phenomena in glass. J_. Some General Remarks. Relaxation effects occur if in a system an extensive quantity (for instance a dielectric displacement or a mechanical strain) lags behind in phase compared to a corresponding intensive quantity (i.e. the electric field strength or the mechanical stress). The name retardation effect would be better but in literature the name relaxation is commonly used. The phase difference is called loss angle, $. It can easily be shown that the energy loss per period in an A.C. electric field in a non-ideal dielectric medium is proportional to tan. This is the reason why the behaviour of tan 5 of glasses has been studied in a rather early stage. In the fifties, when the etectrics industry started to construct large transmitting valves, X-ray tubes and similar products, it was very important to know how tan behaves, not only as a function of the frequency of the applied field and the temperature, but also as a function of the composition of the glass. Later it was realised that this knowledge may help a great deal in an understanding of the structure and the transport phenomena in glass. Consequently the study of the electric relaxation phenomena has become more and more important. The study of mechanical relaxation phenomena has also contributed much to the knowledge of the structure and behaviour of glasses. 2_. General theory. The general phenomenological theory of the relaxation processes is well-known. These processes can be described with a complex modulus K = K' - ik' 1, in which K' and K'' may represent the real and the imaginary parts of the modulus. In the "electric" case K'is the dielectric constant and in the "mechanical" case K'is Young's modulus.,, For both cases tan O = ^r~ and also tan d = JJ WZ C^. in which T is the relaxation time, CO = 2"jl f, in which f is the frequency of the A.C. field or, as the case may be the mechanical stress applied and A K is a quantity that will be discussed later. In the "electric" case tan is often called the dielectric loss, where as in the "mechanical" case tan S is called the "internal friction". Article published online by EDP Sciences and available at

3 JOURNAL DE PHYSIQUE Both colloquial names are not quite correct, but they suggest their physical meaning quite well. What is the significance of Z, when considered on a molecular or atomic scale? Suppose we have an ion (or an electron or a group of molecules) in a potential well, that is separated from its surroundings by a potential barrier Q. The ion in question will pick up energy from its surroundings owing to its vibration in the potential well and to the collisions with the walls. After some time (relaxation time Z 1, it will have llcollected" sufficient energy to jump over the potential barrier from cne well to an adjacent one. Ifw7 >> 1, no jumps can be made because the AC field reverses too quickly, in other words, no energy is absorbed and so tan = o. If wt<< 1, the jumps can be made at the beginning of each new period, and since tan 6 is proportional to E* (if E is the electric field at the mcment of the jump), again tan 3 = o. Tan & has a considerable value only if WZ 1, so that tan 6 as a function of w is a rather narrow bell-sha ed curve with its maximum where & = -L For rjt = 1, (tan b max - A R z For values CL, < 4 the m;ree?z1shows jumping ions and for values UJ > 1 polarisation is absent. considerable polarisation because of the This means that in the former cas~modulus K' is higher than in the latter case, the difference being indicated by A K. As to the temperature, relaxation processes are typical rate processes, which means that the relaxation time -C can usually be expressed in a formula of the type C/RT = Toe in which Q is the above potential barrier, RT has the wellknown significance and fs is a characteristic relaxation time. %sically both t e tan & - T and tan 8 - & curves show a maximum in the area where W 5 = w~, '/R~ = 1. In practical experiments the temperature may be kept constant and w be varied, but this means that different types of apparatus have to be used, which makes the experiments laborious and expecsive. It is much easier to keep tu constant and to vary T; very often this can be doce with the same equipment. There is another reason why the latter type of experiments were found interesting. The knowledge of the tan 6 - T curve provides an easy method of determi- ning the value of Q. For the 11electrf611 _cse different apparatus in the wide range.of frequencies f = s-i to 10 s are available to measure koc; tan vanes with T for oce given frequency over a temperature range from Helium temperatures (4 10 to, for example 300 c.- Fo_? the "mechanicalf1 case mea~urements_~can be made by torsion experiments (f" 1 10 s )and acoustic vibration experiments ( f s ), Sending experfmsnt.~ (f fz.s 2000 to 3000 s- ): This provides sufficient variatior, for a study of the dependfnce of tan d on temperature, because the methods nectioned can be used in the temperature range frorr. - 1 OoOc to 800'~. If it is known how Q behaves in a.series of glasses in which the compositions are varied in a systematic way, interesting conclusions can often be drawn about the structure of these glasses, and it can be shown what the mechanism of the relaxation phenomenon is on ar atomic scale. From the above formulae it can be derived, that R T = - m In -0 if Tm is the temperature where tan 6 is maximal as a function of T and w is the given frequency of the A.C. field applied. In other words, if Tm is known, i.e. the ~osition of ( tan 6 )rnax Q in the tan 6 - T diagram, Q can be calculated with a constart proportionality factor, namely Q = (-R In wx.) Tm. In macy cases however,t, is not known. In that case Q can be determind with the formula = R (lnfi - lnf2 if the situation of T and T for two tan 6 -T 1 ITmq - I ITm '"1 m2 L 1 curves is measured zt two different frequencies fl and fl.

4 - 3. Practical Results. The above general theory holds for both crystalline and vitreous systems. In crystals the relaxing particles are regulary distributed in the material. Their surroundings on an atomic scale are exactly the same, so that one welldefined Q value and as a result a very sharp tan & peak in the tan -T diagram can be expected. As in vitreous systems these conditions are not fulfilled, there is a wider distribution of the Q values, which results in much wider tan 3 peaks in the tan 8 -T diagram. Strange enough, very few investigations have been carried out with crystals, whereas for vitreoussystems extensive material is available. Figure 1 gives a representative but simplified overall picture for tan 6 as a function of frequency at two temperatur s (30C' and 50 K) for the complicated glasses used for technical applications These are sections of a general sterical model, where tan 6 is plotted as a function of T and f. An anlyses of the curves of fig. 1 shows that there are 3 types of relaxation phenomena in (non-radiated) glasses, namely the migration lossed (curves I acd 2), the losses due to local motions (curve 3) and the network losses (curve 4) s n characteristics of the various types of relaxation phenomena in vitreous systems Migration losses. Migraf;ion,losses usually occur in the frequency range f = 10' s-' (and lower) to f =-lo0 s-' and they are- due mainly to the jumping of the ~ a ions + in the interstices of the network (through ~ i+ and K+ ions may also give some contribution). They are characterised by activation energies from 0.6 to 1.2 ev. depending on the composition of the glass. Since this value is fairly high, the migration losses are hardly sensitive to the temperature. bny cases are known where besides the activation energy of t,he dielectric relaxation also that of the self-diffusion for ~ a ions + or that of the D.C. electric conductivity or both are known. In these cases the sm,e value is found for each glass, which shows that. the mechanism of the jumping of the ~ a ions + is really r.esponsible for all these three effects. Fig. 1. Showing the general shape of tan d of glasses as a function of the frequencey at 300 K and 50 K. The fuliy drawn curves give the total losses. The four different contributions are given by dotted lines.

5 C8-616 JOURNAL DE PHYSIQUE In a number of recent paped)about measurements with blocking and non-blocking electrodes, it was showr that the migration losses (curves 1 + 2) are really a superposition of (1) "conduction lossesf1 (the Na+ ions jump under the influence of a D.C. field principally in one directiodand (2) the "dipole relaxation losses" (the Na+ ions jump to and fro in a limited area and follow the frequency of an A.C. field applied). Usually the conduction losses for one and the same glass at a given temperature have to be located at much lower frequencies than the dipole relaxation losses. This is why thelformer are usually overruled by the latter, at least in the rarge of f = 10' s- to 1 o6 s-i Losses... due to local motions. Fig. 1 also shows the dielectric losses due to local motions (curve 3), in older literature called deformation losses. These losses are caused by an atoms llwagglingll between several positions in their own interstices se~arated by rather low potential barriers. The Q values involved are very low indeed. They vary between 0.05 and 0.2 ev. This means that they are very sensitive to the temperature. Fig. 1 shows that they can be stu ied onky a? rather low temperatures (50 K) and at medium frequencies (f = lo3 iq to 10 < 1. At room temperature they cannot be detected because they are droxned in the losses represented by curve 4. 4,s N~tw:rll_l:s_sez. Finallv fin. 1 shows the network losses (curve 4), in older literature called the vibration losses. As they are due to the relaxation of mcvements of parts of the network, this type of losses is found mainly in the region where the glass approaches its annealing range. The value of activation energy Q is very high and usually between 2.2 and 4 ev. It is not suprising that this value is about as high as the usual activation energies for viscous flow. This is a very strong evidence that the relaxation indeed is due to movements of parts of the network (rupture and recombination). 5. Concluding remm. - In the preceeding text some general remarks about the four different types of relaxations phenomena in vitreous systems are made. In the last fifteen years the behaviour of many vitreccs systems has been studied. These include silicate, borate and phosphate glasses, as well as the complicated glasses used for technical applications. Many details about the structure of these systems have been revealed. A survey of this work is given in a paper by the author to be published before long in the Journal of Non - Crystalline Solids, References. 1. J.M. Stevels (19571, Encyclop. of Physics 3, p M. Tomozawa and R. H. Dorenus (1974) (1976), J. Non - Crystalline Solids 14, 54, 21, 287. M.H. bar and J.M. Stevels (1978), J. Non- Crystalline Solids 3, 51.