E.P.R. study of electron irradiation defects in the red molybdenum bronze of potassium K0.33MoO3

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E.P.R. study of electron irradiation defects in the red molybdenum bronze of potassium K0.33MoO3

H. Vichery, F. Rullier-Albenque, S. Bouffard

To cite this version:

H. Vichery, F. Rullier-Albenque, S. Bouffard. E.P.R. study of electron irradiation defects in the red molybdenum bronze of potassium K0.33MoO3. Journal de Physique, 1989, 50 (6), pp.685-696.

�10.1051/jphys:01989005006068500�. �jpa-00210946�

E.P.R. study of electron irradiation defects in the red

molybdenum ^{bronze of} potassium K0.33MoO3

H. Vichery, ^F. Rullier-Albenque ^{and S. Bouffard} (*)

Laboratoire des Solides Irradiés, ^Ecole Polytechnique, 91128 Palaiseau Cedex, ^France (Reçu le 27 avril 1988, révisé le 19 septembre 1988, accepté le 14 novembre 1988)

Résumé.

Nous avons étudié par R.P.E. les défauts créés dans K0,33MoO3 par irradiation ^aux électrons. Nous avons ainsi mis en évidence l’existence de deux types de défauts (A ^et B) présentant de nombreux points ^{communs : tous deux sont} constitués d’un électron 4d non apparié

localisé préférentiellement ^{sur un atome de} molybdène ^et couplé beaucoup plus faiblement avec

deux autres atomes de molybdène. Nous proposons ^un modèle très simple pour la ^structure

électronique ^{de ces centres} paramagnétiques. ^{Les mesures du} temps de relaxation spin-réseau ^ont

montré une dépendance ^en température très inhabituelle (lois ^{en T3 et} T5) qui peut ^être expliquée

en considérant un modèle de phonons ^{localisés au} voisinage ^{du défaut.}

Abstract.

Defects induced by ^electron irradiation in the red molybdenum ^{bronze of} potassium K0.33MoO3 ^{have been studied} by ^E.P.R. spectroscopy. ^{Two main} types ^{of centers} (A ^and B) ^have

been observed. They both have been identified as unpaired 4d electrons localized on one

molybdenum ^{atom with a} weak interaction with two other ones. A very simple electronic model is

proposed ^to explain qualitatively the main features of these two paramagnetic ^centers.

Measurements of the spin-lattice relaxation time of defect A show a temperature variation much slower than expected from the standard theory. This unusual dependence (laws ^{in T3 or} T5) ^{can be} explained by ^{an extended} theory which takes into account the contributions of lattice vibrations at the defect sites.

Classification

Physics ^Abstracts

33.30

76.30

1. Introduction. -

Among the series of the potassium molybdenum bronzes of general ^formula KRMo03, ^the

blue bronze Ko.3MO03 ^{has been} intensively ^{studied in} relation with the non-linear transport

properties attributed to the sliding ^{of the} charge density ^wave (C.D.W.) [1]. ^In particular,

irradiation experiments ^have emphasized ^the role of lattice defects in the pinning ^{of the}

C.D.W. [2] ^{and other} associated phenomena ^{such as} metastability ^or hysteresis [3]. ^However,

the nature of irradiation defects is totally unknown in this complicated structure. The interaction between C.D.W. and defects and also the presence of free carriers avoid an

accurate knowledge ^{of the defect structure in such} materials. In this paper, ^we present ^E.P.R.

(*) Present address : C.I.R.I.L., ^{Bd H.} Becquerel, ^B.P. 5133, 14040 Caen Cedex.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:01989005006068500

study of the defects produced by ^electron irradiation in a very neighbour compound ^{of the}

blue bronze : the red potassium molybdenum ^bronze Ko.33MOO3.

2. Crystal ^{structure and} properties ^of Ko.33Mo03.

The red bronze Ko33Mo03 crystallizes, ^{as well as the blue} bronze, in the monoclinic space group C2/m [4]. ^The structures of these two compounds consist of distorted Mo06 ^octahedra

which are arranged ^{to form clusters of 10} (KO.3MO03) ^{or 6} (KO.33MO03) octahedra. In the red

bronze, ^identical clusters form bidimensional infinite layers in the directions (010) ^and (001) by sharing ^corners (see Fig. 1). Adjacent layers ^are joined together by potassium ^ions incorporated in between. If all available potassium ^{sites are} occupied the ideal formula is

Ko.33MO03

K2Mo6018.

The electronic structure of molybdenum ^{bronzes can be} interpreted ^{as follows} [5] : ^{in the} binary ^oxide M06018, ^5s, 5p, 4d Mo orbitals combine with 2s and 2p ^{O orbitals to form an} occupied valence band. The empty antibonding 4d orbitals are lying far above the valence band. As, ^{in first} approximation, ^{Mo is} placed ^{in a cubic} symmetry, 4d (eg) ^{orbitals are shifted}

above 4d (t2 g) ^{orbitals. Actually,} the octahedron is distorted and the triplet ^is probably splitted.

In the bronzes, ^K yields ^{its outer electron so that two} electrons per cluster occupy the

4d(t2g) ^{levels (for the} stoechiometric compound).

Electrical [6] ^and optical [7] measurements have shown the semiconducting character and the strong anisotropy of the red bronze. These properties ^{are bound to} the fact that the

4d (t2 g ) ^{orbitals are only} delocalized over the cluster and that there is no overlap ^{between two}

Fig. ^1.

Crystal ^structure of the red potassium molybdenum ^bronze Ko.33MOO3 [4]. (a) Arrangement

of six Mo-O octahedra forming ^{a cluster.} (b) Projection parallel ^to the monoclinic b-axis. (e) ^{K at}

y

1/2 ; (0) ^K at y

^0. Mo(l) at y

^{0 and} Mo(2) ^at y

0.26.

neighbouring ^{clusters. The two electrons are} necessarily paired ^because magnetic suscepti- bility [6] ^{does not show} strong temperature dependent paramagnetism ^and paramagnetic

centers [8] only represent 10 ppm ^{of the} 4d (t2 g ) ^electrons.

E.P.R. spectra ^{of the non} irradiated material [8] show the existence of several E.P.R.

centers attributed to M05 + (4d’): g ^{tensors have} nearly tetragonal symmetry ^with gb (1.89-1.90) : g1. (1.92-1.93 ). ^{These centers are related to deviation from} potassium stoechiometry. ^The analysis ^{of the} hyperfine ^{structure indicates that the} unpaired d electrons

are delocalized within a domain of 6 Mo06 ^octahedra (namely ^{in one} cluster).

3. Experiments.

The single crystals used in this study ^are grown by electrolysis ; they ^are platelets parallel ^to

the monoclinic b and c axes and easily ^cleave parallel ^{to this} plane. ^The samples ^were

irradiated at 20 K by electrons of energies ranging ^{from 0.6 to} 2.5 MeV. The energy loss by

nuclear collision or electronic excitation is high enough ^to induce atomic displacement. ^The

irradiations were performed ^{in the} VINKAC’low temperature facility ^{installed on} the Van der Graaff accelerator in Fontenay-aux-Roses [9].

E.P.R. spectra ^were recorded with a Bruker ^{E.P.R. 200 D} spectrometer operating ^{at a} frequency of 9.3 GHz (X-band). Using ^a helium continuous-flow cryostat ^{fitted on the} spectrometer, ^{we could} obtain, ^{at the} sample position, temperatures varying ^{from 4 to 300 K.}

Available incident micro-wave power ^was ranging ^{from 0.5} uW ^{to 245 mW.} Samples ^were

rotated in the magnetic field with a one-axis goniometer.

Results reported here refer to two types ^of experiments ^{carried out} differently.

-

In the first _one, samples ^were irradiated by ^{electrons of} energies ranging ^{from 0.6 to 2.5}

MeV and at doses between 0.2 to 1 C/cmz. After irradiation at 20 K, ^these samples ^were kept

in liquid nitrogen, apart ^{from a} rapid warming up ^{to room} temperature (R.T.) ^{for a few}

seconds to transfer the samples in the E.P.R. spectrometer. Unfortunately, further R.T.

annealing experiments ^{show that some defect} recovery ^occurs in this transfer operation, ^so

the evolution of the defect concentration versus irradiation conditions such as electron energy

or dose could not be followed. One of these samples (Sl) ^{has been} especially ^studied (irradiation energy : 800 keV, dose : 0.7 ± 0.1 C/CM2).

-

The second series of experiments ^concerns samples irradiated at 20 K by ^{2.5 MeV}

electrons at relatively high ^doses ( > ² C/cm2) ^and kept ^at R.T. for several weeks before measurement. Results displayed by sample ^S2 (dose ^2.4 C/cm2) ^are representative ^{of this}

series.

4. Results.

First ^of all, ^E.P.R. _spectra ^are very different in the pure and electron irradiated samples.

Whatever the irradiation conditions, ^E.P.R. spectra present ^{the same} general features : four different types ^of signals ^{are observed.} They ^{all are} strongly anisotropic with factor g varying between 1.85 and 1.96 for two of them (spectra ^{A and} B), ^{1.35 to 1.64 for} spectrum C and 1.74 to 1.83 for spectrum ^{D. We have} especially ^studied spectra ^A and B which are the most intense and are strongly ^related together.

4.1 STRUCTURE OF THE SPECTRA A AND B.

Spectrum ^A.

^The spectrum ^A consists in a

central line surrounded by three different series of six identical lines (see Fig. 2) ^and by ^a

group of much weaker satellites. Each series (denoted ^{I, II,} III) corresponds ^{to a} hyperfine

Fig. ^2.

^E.P.R. spectrum of electron irradiated Ko,33MOO3: ^{schematic structure of} spectrum ^A.

interaction with a nucleus spin 5/2. This spectrum ^{can be} explained ^{with the} following

Hamiltonian

in which g ^and Ai ^are symetric ^{tensors and S} = 1/2 ; ^I

^5/2.

In order to explain precisely ^the positions ^{of the} hyperfine ^{lines 1 which} correspond ^{to a}

constant AI ^much larger ^{than the two other ones,} second order corrections for hyperfine

Hamiltonian have to be taken into account [10].

In figure 2, ^{one can see that each line of} hyperfine ^structure (HFS) ^I splits ^{into two} parts (I’, I") ^whose hyperfine ^{constants differ} by ^{2 % and} intensities by - ^{60 %. This} hyperfine ^structure

is consistent with the natural abundance and nuclear moments of 95Mo and 97MO (see ^Tab. 1).

So the HFS I, ^and consequently the HFS’ II and III, ^{are due to} the interaction of an electron

spin 1/2 with the nucleus spin ^I

^{5/2 of the two} isotopes ^{95Mo and 97Mo.}

Table I.

Natural isotopes of molybdenum ^with 1 :¡l: ^0.

In the case of the HFS’s II and III, the differences induced by the presence of ^{the two Mo}

isotopes ^{with I = 5/2 are too small for the two} distinct lines to be separated.

Moreover, numerical simulations (Fig. 3) show that the lines of the three hyperfine

structures have nearly ^{the same} intensity ^{and the} intensity ^{ratio of} the central line to the

hyperfine ^lines (HFS I, II, III) ^{is about 18/1.} Taking ^{into account the natural abundance of the}

isotopes gSMo, 97Mo, ^{the case} ₍₃ ^{Mo with I =} ₀₎ ^is eighteen ^{times as} probable ^{as the case}

Fig. ^3. Comparison of the model with measured spectrum ^near the central line : numerical simulation

assuming ^{one central} line surrounded with two lines from HFS II and from HFS III, ^{each line} having ^the

same width.

(2 Mo ^{with I}

0 and 1 Mo with I

5/2). ^{From this, we can conclude that the} spectrum ^{A is} due to unpaired ^electrons delocalised over three different molybdenum ^sites.

In order to determine the g ^and Ai ^{tensors, the} crystals ^{have been} rotated in relation to the external magnetic ^{field H around the} perpendicular directions a*, ^{b and c. When H is not} parallel ^to the mirror plane ^{of the structure} (a-c plane), ^the spectrum ^{A does not} split ^{into two}

identical spectra corresponding ^{to the} occurrence of two equivalent crystallographic ^sites,

which indicates that the b axis constitutes a principal axis for the g ^and Ai ^{tensors. The} eigenvalues ^{of the g and} Ai ^{tensors are} respectively equal ^{to :}

and

The directions of the principal ^{axes are} represented ⁱⁿ respect ^{to the} crystallographic

directions in figure 4a for the g ^and AI ^{tensors. Given the} measurement precision, ^{it is difficult}

to say if the difference of 5° in the a-c plane between the principal ^{axis of g and} AI ^is significant.

As the AIl ^and AIII ^{tensors are concemed, it is difficult to détermine} precise values because

the HFS’s are not well resolved. Nevertheless one can roughly say that the distances between

two successive lines vary between 6 and 7.5 G for HFS II and between 4 and 5 G for HFS III

Fig. ^4.

Principal ^{axis of tensors in the a-c} plane. ^The third axis is along ^b. (a) g and A ^tensors of spectrum ^A. (b) g ^tensor of spectrum ^B.

whatever orientation of the sample in the extemal magnetic field. These variations are much

weaker than for HFS 1 (39 ^G-96 G). Then it is likely ^{that the} AIl ^and AIII ^{tensors have not the}

same symmetry ^as AI.

As the magnitude ^of Ai ^{tensor is a} measurement of electron density ^{at the} given ⁱ site, ^one

can conclude from the precedent analysis ^{that the} spectrum ^{A is} mainly ^{due to the resonance}

of an unpaired electron localized (electron density is around 80 %) ^{at a Mo atom} (which ^is

denoted site I). Nevertheless the extent of the atomic orbital is such as the electron can also

weakly ^{interact with two other Mo atoms} located in the neighbourhood.

Spectrum ^B. - Spectrum ^B presents ^{the same} main features as spectrum A. It consists in a

central line surrounded by ^{three HFS denoted I, II, III. One of them} (HFS I) ^{has a} hyperfine

constant much more important ^{than the two} others. The line width is too large ^to separate lines from 95Mo and 97Mo but lines of HFS 1 appear wider than the central line because of this

non resolved structure. Figure 5 shows the result of numerical simulation of the spectrum

center. As for spectrum A, the best fit is achieved with the assumption ^{of a} unpaired ^electron

delocalised over three different molybdenum sites. However hyperfine interactions (II ^and III) ^are less intense than for spectrum ^{A and are difficult to resolve near} the central line.

Like spectrum A, _spectrum ^{B does not} split ^{into two identical} spectra by rotating crystal ⁱⁿ

the extemal magnetic field. The measured g ^values are gx

1.881, gy

1.934, gz

^1.924.

Figure 4b shows the direction of principal ^axes of g ^{tensor. The} distance between two successive hyperfine lines varies approximatively ^{from 16 G to 42 G for HFS I.} They ^are respectively around 3 G and 4 G for HFS II and HFS III.

4.2 CONCENTRATION OF DEFECTS.

The line width of spectra ^{A and B do not} depend ^on temperature ^{for T} 150 K. This allows to determine the temperature dependence ^{of the} magnetic susceptibility X by measuring only the intensities of the central lines. Figure ^{6 shows} that y ^{verifies a Curie law} (X ^oc 1/T) ^{for both} types of defects. The number of defects N is deduced by comparison ^{with a} calibrated copper sulfate sample. ^For experiments, ^both samples ^{are at the same time in the} spectrometer, ^{as close as} possible. ^{Non saturated} spectra

are recorded at the same temperature. ^{Values of N are} obtained with a precision ^{around 30 %}

for N around 1019 spin/cm3 and between 40 and 50 % for N around 1018 spins/cm3.

Depending ^{on the} experimental conditions, ^{different results were obtained :}

-

In the samples ^{of the first series} (kept ^{at 77 K after} irradiation), the numbers of defects

A and B are located in the same range of magnitude (1018 ^{to 1019} spins/cm3). For the less

Fig. ^5.

Numerical simulation of the center of the spectrum B with the same assumptions ^{as for} spectrum ^A.

Fig. ^6.

Inverse of the amplitude (10) of the central line of spectra ^{A and B as a} function of T.

Arbitrary ^{units on} y-axis.

irradiated samples, spectrum ^{B is more} intense than spectrum A ; opposite ^{result is observed}

for the most irradiated ones. After a few hours of R.T. annealing, defects B have nearly completely disappeared ^{in the} background ^{of the} spectrum. ^{On the} contrary, within the measurement accuracy, ^{we cannot see} any variation in the concentration of defects A. For the

sample S 1, the concentration is equal ^{to 2.7-4.2 x 1018} spins/cm3.

-

In the samples ^of the second series, ^{which were} studied after a R.T. annealing ^{of several} weeks, ^the spectrum ^{B does not} appear. In sample S2, ^the concentration of defects A is equal

to 1.5-2 x 102° spins/cm3 ^which represents ^two percents ^of damaged cluster. A second R.T.

annealing of several months decreases this value down to less than 1018 spins/cm3.

4.3 RELAXATION TIMES. - To determine the spin-spin (T2) ^and spin-lattice (ri) ^relaxation times, steady ^state saturation method has been used. By using ^{Castner’s method} [11], ^{we have}

calculated the a parameter ^{which measures the} degree ^of inhomogeneous broadening (a = nH G ~HI ^{which AHG the} inhomogeneous absorption ^{line width and} OHL ^{the «} spin packet ^»

~HQ

width). ^Results reported ^{below are limited to the} spectrum ^{A after} annealing. ^{For all} samples

we have studied, a ^{is found to be} superior ^{to one} which allows the assumption ^of homogeneous broadening for the lines of interest here.

4.3.1 Spin-spin relaxation time T2. T2 is deduced directly ^{from the} measurement of the line width OH PP ^{pp by T2 =} 3- -y 2 AH ^{3 ’)’ I1H with y 9 1£ B À T2 2 is found to vary between 5 and}

15 x 10- g s for spectrum ^{A after} annealing.

For samples of the first series, the line width seems to be independent of the concentration of defects A and we note a decrease of I1Hpp after R.T. annealing although the concentration of defects A remains approximately constant : for instance, the line width of sample ^SI

decreases from 1.1 G to 0.6 G.

However, ^for sample S2, ^{the same value of} I1Hpp (1.1-1.4 G) ^{is found} for concentrations of 1.5-2 x 1020 spins/cm3 and less than 1018 spins/cm3.

4.3.2 Spin-lattice relaxation time Tl.

^{Values of} Tl ^{are issued from the} product Tl T2 given by the saturation curves [12], T2 being determined independently ^as previously reported. ^The temperature dependence ^of Tl ^was studied between 10 and 200 K. Below 10 K, Tl ^{is too} long and the lines are satured even at the weakest available power. For both samples

SI and S2, Tl ^{is found to} depend ^{on the field} direction, whatever the temperature. ^{This is} displayed ⁱⁿ figure ^{7 for the} sample ^S2. Moreover, ^a very unusual temperature dependence ^of Tl is observed : experimental ^{data cannot be fitted} by any ^common model [13, 14]. ^{Best fits of}

our results are obtained with a phenomenological ^law (over the range of six orders of

Fig. ^7.

Dependence ^of spin lattice relaxation mechanism of defect A with the magnetic ^{field :}

evolution of Ti ^{when the} sample ^{S2 is} rotating ^{around b-axis} ( T = ³⁰ K ). ^{One can note that the} largest

variation of Tl ^{with the} magnetic field is of the order of 6.

magnitude) ^{such as} 1/T1 proportional ^{to Txwith x between 3 and} 5, which is much slower than

expected by ^standard theory.

5. Discussion.

Results presented ^{in the} previous section show that E.P.R. spectra ^of irradiated red bronzes of potassium ^are quite complex. Moreover, quantitative analysis of the results is hindered by

the not well-controlled recovery of the defects during ^the measurements. In particular,

relations between the two series of experiments performed ^are actually difficult. Nevertheless,

some general conclusions come out from these results.

First of all, although ^the paramagnetic ^{centers are} very different in irradiated and non

irradiated samples [8], they present ^{some common} features : the nearly tetragonal symmetry of g tensors, the range of magnitude (1.85-1.95) of g ^{factor and the} property : 91 - 9 1 These results seem to be characteristic of an ion Mo5 + (4d’) ^{in a} distorted octahedral

configuration (see ^{M05+ in} Ti02 by Kyi [15], Chang [16]). ^However, according [13, 15], ^the property gil g.l. ^{should be} expected.

In non irradiated red bronzes, unpaired ^{electrons are} delocalized over five or six Mo atoms

(approximately ^{over one} cluster) [8]. ^{On the} contrary, irradiation induced centers (A ^and B)

are mainly ^localized (at ⁸⁰ %) ^{around one Mo atom with a weak} interaction with two other

ones.

The tetragonal axis of the g ^tensors for both A and B centers is parallel ^{to the} (a-c) ^mirror plane ^{of the non disturbed} structure. So it is reasonable to think that the Mo atom mainly

concerned is a molybdenum Mo(l) (see Fig. 1) ^{located in that} plane. ^To distinguish ^{two other}

distinct Mo atoms among the four equivalent Mo(2) ^{atoms of the} original structure, ^structural modification within the cluster must be assumed.

As the A and B centers are created with nearly ^{the same} concentration by ^{2 MeV and}

600 keV electrons, ^{their threshold} energies ^must be very weak. Displacement thresholds are

unknown in red bronze but, given the open ^structure of this material they ^are probably ^weak

even for molybdenum. However, ^{as A and B defects have the same} symmetry ^{as the non} disturbed structure, molybdenum vacancy/interstitial within the cluster can be excluded.

Then, ^{we can conclude that A and B centers are induced} by point defects in the sublattices of oxygen ^or potassium. ^This point ^{defect must involve a} little structural modification in the group of six Mo ^atoms and create an unpaired ^electron.

In order to understand qualitatively ^the main features (symmetry, hyperfine coupling) ^{of A}

and B centers, ^{we use a} _very simple model with the following assumptions :

-

We consider the non disturbed structure where octahedra are supposed ^{to be} regular (Fig. 8a). ^We neglect effects of irradiation on the position ^{of Mo atoms but we consider them}

as a perturbation potential applied ^on electronic states.

-

Electronic structure has not been radically changed ^{and we assume that the} unpaired

electron occupies ^a 4d (t2 g) antibonding ^orbital (as ^{the two electrons} yielded by potassium ⁱⁿ

non irradiated bronze).

-

As the unpaired ^{electrons are} strongly localized, ^their ground ^{state can be well}

described with atomic orbitals of Mo(l) ^atoms. By assuming ^small departures ^{from octahedral} crystal ^field, pure (xy ), (xz ), (yz ) ^{orbitals can be used} (see Fig. 8a, b).

Electron densities of (yz ) ^and (xy ) ^{orbitals both have} tetragonal symmetry ^{and the} two

axes (x ^and z) ^are parallel ^{to the} (a-c) plane. ^{Moreover for each} orbital, hyperfine interactions with only ^two Mo(2) ^are possible (Fig. 8b). ^We suggest ^{that A centers} (B centers) ^{are created}

when the perturbation potential ^induced by point ^{defects lowers} (xy ) ^orbitals ( (zy ) orbitals)

(see Fig. 8c).

Fig. ^8.

(a) Projection parallel ^to the b axis of the structure : oxygen ^atoms occupy octahedra vertices.

(b) (xy ) orbital and position of Mo and 0 atoms in (x, y) plane. (c) Electronic model for A center : cubic symmetry ^{has been} assumed for the Mo crystal ^{field so that} 4d (t2 g) ^{orbitals are} degenerate (before irradiation). Actually these orbitals are splitted but the result is the same if the perturbation potential ^is higher ^{than the} splitting.

In this simple model, ^{we have} totally ignored the local deformation of the cluster, ^{so it is}

not surprising ^{that the} experimental directions of the symmetry ^{axes of} g ^{tensors and the} different magnitudes ^of hyperfine coupling ^{can not be found out.}

Results obtained in the first series of experiments ^{show that} spectrum ^{A is} strongly

correlated with spectrum ^B. Annealing experiments ^{indicate that} spectrum ^{B is} less stable than spectrum ^{A : a} few hours R.T. annealing is sufficient to suppress spectrum ^{B almost} completely ^whereas only the line width of spectrum ^A changes. On the other hand, ^an important recovery of defects A is also observed in sample ^{S2 annealed at room} temperature for several months. A parallel ^can be drawn between these two observations and the evolutions of concentrations of defects A and B - decrease of spectrum B and increase of spectrum ^{A - as the} irradiation dose increases. These results could be the sign ^{that defects B}

are progressively transformed into defects A during annealing ^and during irradiation.

Spin lattice relaxation mechanism observed for spectrum ^{A sets} many problems. ^{The main}

features of the phenomena have been described by ^Stevens [14]. Quantitative predictions ^for

the direct process and the Raman processes lead ^to temperature variations of 11 Tl ^{as follows :}

with hw

9 IL B ^{H and} Rd, Rr dependent and Rt ^non dependent ^on the orientation of the

magnetic ^field.

Above 10 K, ^{the direct} _process ^is negligible. As it has been reported ⁱⁿ paragraph 4.3.2,

laws in T 7and 71 can absolutely ^{not fit the} experimental ^{data. These} theoretical temperature dependences essentially result from the assumption ^{of the} Debye ^{model for} lattice vibrations.

Phonon spectrum ^{of the non} irradiated red bronze is totally ^{unknown but it is} likely ^{that at}

low temperatures (T ¹⁰⁰ K) ^{deviation to the} Debye ^{model is not} important enough ^to explain ^the experimental ^{results. As seen} before, paramagnetic ^centers (A ^and B) ^are

associated with structural modification within the cluster and large ^lattice deformation can

induce local strains significantly different from those in a non disturbed lattice. An extended

theory ^of spin-lattice relaxation which takes into account the vibration modes localized at a

structural defect has been proposed by Castle et al. [17]. Instead of the power laws in

T 7and T9, they obtained laws in T3 and T 5 for the Raman process.

With this model, they explain ^the temperature dependence (laws ⁱⁿ T3 observed from 13 to 250 K) ^{for the} relaxation time of the Ei ^{center in} irradiated quartz. It should be noted that the

Ei ^center is associated to a structural defect and that quartz (as molybdenum bronzes) ^{has an}

open structure : according ^to [17], ^{in an} open ^{structure one can} expect ^{the mechanical} properties of defect sites to differ strongly from these of perfect ^sites.

It is shown in figure ^{9 that our} experimental ^{data can} be rather well fitted by ^{a’ linear}

combination of terms in T3 and T5. Different results are reported ^{on this} figure ^{but it is}

difficult to link them together because of the ànisotropy ^of Tl :

-

For sample ^S2, temperature dependences ^of 11T, ^were studied for two different concentrations of defects A but in two different orientations of the magnetic ^{field. For}

1.7 x 1020 spins/cm3 and in the position H//ZG (see Fig. 7), ^{we found :} 1 /Ti

^{2.02 T3. For a}

concentration lower than 1018 spins/cm3 and in the position H//xG :

In this _case, the term in T5 does not appear ^or is very small. Moreover, ratio of the two factors of T3 can not be fully explained by anisotropy of the relaxation time (Fig. 7).

-

For samples ^SI (2.7-4.2 ^{x 1018} spins/cm3), ^{the term in T5 is more} important. ^{One finds}

for H in the (a-c) plane : 1/Fi

^{0.024 T3+ 2.14 x 10-5 T5.} Variations of the different coefficients are not well understood but the spin lattice relaxation mechanisms must be

strongly dependent ^{on the} particular ^{structure of} irradiation defects and then sensibly

Fig. ^9.

Evolution of 1 / Tl (defect A) ^with température. Experimental ^{data are fitted} by :

different in samples SI and S2. Anyway these results show that localized phonons ^{take an} important place ^{in the} spin lattice relaxation mechanism.

7. Conclusion.

In this paper, ^we have reported ^{an E.P.R.} study ^{of defects} in electron irradiated samples ^of

red potassium ^bronze Ko.33MO03. ^{Two different defects have been} especially studied. Their main features (composition, symmetry, hyperfine coupling, ...) ^were well characterized. A

rough ^{model has been} suggested ^{for these two} paramagnetic ^{centers. We} have shown that the standard theory ^{is not able to} explain ^the spin-lattice relaxation rates measured for defects. In this _case, it is _necessary to take into account characteristic vibrational frequencies ^associated

with the defects as proposed by ^{Castle et al.} [17].

Further experiments ^are clearly necessary to connect the results obtained in the two series of experiments performed ^{in the} present study ; ⁱⁿ particular, ^{it would be} interesting ^{to follow}

the relative evolution of the two types of defects with the irradiation dose. Moreover, ^{a more} precise knowledge ^{of the structure} of irradiation defects should allow a better understanding

of the features of spin-lattice relaxation in this damaged compound.

Acknowledgments.

The authors thank J. Marcus for providing ^the samples ^{and F.} Beuneu, J. M. Flesselles for

helpful discussions.

References

[1] ^SCHLENKER C., in NATO ASI on low dimensional conductors and superconductors, ^HAGOG Québec (August 1986).

[2] ^MUTKA H., ^BOUFFARD S., ^DUMAS J., ^SCHLENKER C., ^J. Phys. ^{Lett. 45} (1984) ^L729.

[3] ^MUTKA H. , RULLIER-ALBENQUE F., BOUFFARD S., ^J. Phys. ⁴⁸ (1987) ^425.

[4] STEPHENSON N. C. and WADSLEY A. D., ^Acta Cryst. ¹⁸ (1965) ^241.

[5] GOODENOUGH J. B., ^J. Appl. Phys. ³⁷ (1966) ^1415.

[6] BOUCHARD G. H. Jr., PERLSTEIN J., SIENKO M. J., Inorg. ^{Chem. 6} (1967) ^1682.

[7] TRAVAGLINI G. , ^WACHTER P. , MARCUS J., SCHLENKER C. , Solid State Commun. 42 (1982) ^407.

[8] ^BANG G. , ^SPERLICH G., ^Z. Phys. ^{B 22} (1975) ^1.

[9] ^DURAL J., Rapport CEA-R-5091 (1981).

[10] ^HAUSMANN A., ^SANDER W., Defects ⁱⁿ crystalline solids, ^{Vol. 4} (North ^Holland Publishing Company).

[11] CASTNER T. G., Phys. ^{Rev. 115} (1959) ^1506.

[12] ^{POOLE C. P.} Jr., ^Electron spin ^resonance (Wiley-Interscience Publication).

[13] ^{ABRAGAM A., BLEANEY} B., ^EPR of Transition Ions (Oxford ^Univ. Press, London) ^1970.

[14] STEVENS K. W. H., Rep. Prog. Phys. ³⁰ (1967) ^189.

[15] ^{KYI R.} T., Phys. ^{Rev. 128} (1962) ^151.

[16] ^CHANG T., Phys. ^{Rev. 136} (1964) ^A1413.

[17] ^{CASTLE J.} G., FELDMAN D. W., KLEMENS P. G., ^{WECKS R.} A., Phys. ^{Rev. 130} (1963) ^577.