observed by coherent neutron scattering

PHYSICAL REVIEW B 1 NOVEMBER 1997-IIVOLUME 56, NUMBER 18

Comparative analysis of the fast dynamics in the supercooled nonfragile glass-forming liquidNa0.5Li 0.5PO3 observed by coherent neutron scattering

B. Ruffle, J. Etrillard, B. Toudic, and C. EcolivetGroupe Matiere Condense´e et Materiaux, UMR CNRS 6626, Universite´ Rennes I, 35042 Rennes, France

G. Coddens and J. P. AmbroiseLaboratoire Leon Brillouin,* CE Saclay, 91191 Gif-Sur-Yvette, France

E. Gueguen and R. MarchandGroupe Verres et Ce´raniques, UMR CNRS 6512, Universite´ Rennes I, 35042 Rennes, France

~Received 20 December 1996!

Experimental results obtained by coherent neutron scattering with a time-of-flight spectrometer on thenonfragile glass-forming liquid Na0.5Li 0.5PO3 ~Tg5515 K, Tm5749 K! in a wide temperature range~300–773K! are presented. As predicted by the mode coupling theory~MCT!, the resulting dynamical structure factorhas aq-independent form in the intermediateb fast regime. Furthermore, it is also found that theq dependenceof the dynamical structure factor is the same for the boson peak and the quasielastic region. Thus, a phenom-enological model assuming that the quasielastic component is related to the damping of the localized vibra-tional modes that give rise to the boson peak is discussed. Though the spectra are well described over a widetemperature range, it is shown that the temperatureT* where the boson peak becomes overdamped is signifi-cantly above the melting temperature in this system and thus cannot be associated to any onset of metastabilityas previously suggested. On the other hand, a qualitative discussion of the susceptibility spectra aboveTg in theframe of the MCT leads to a possible crossover temperatureTc near 620 K (;1.2Tg) close to the temperatureof the decoupling phenomenon of the relaxation time scales observed by31P NMR in this system. ThisTc

value is also compatible with a power-law temperature dependence of the structural relaxation time scalededuced from the viscosity data.@S0163-1829~97!04542-6#

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I. INTRODUCTION

During the last decade, the glass transition phenomehas known a renewed interest triggered in particular bydevelopment of a microscopic theoretical approach, thecalled mode coupling theory~MCT!,1 which offers a fullydynamical picture of the supercooled liquid state. This theprovides an approximation scheme allowing the calculatof the time evolution of the density correlation function froa microscopic equation of motion. In a simplified versiothis approach leads to a kinematic instability at a crossotemperatureTc above Tg where the density fluctuationmodes arrest with decreasing temperature. In the viscousdercooled liquid aboveTc , the correlation function of thedensity fluctuations is found to decay into two steps whare identified as thea and theb fast relaxation processes anis described by a set of scaling laws whereas underTc onlythe b fast process remains, as the structural relaxation oaprocess is ideally frozen.

In the MCT scheme, theb fast process is thus the shotime decay of the density correlation function before tstructural relaxation takes place and is ascribed to localmotions associated with the rattling of particles in their caformed by surrounding particles. This fast process occurspicosecond time scale and has to be distinguished fromsecondarybslow processes2 that are a typical feature of supercooled liquids. The strict ergodic to nonergodic transitat Tc predicted by the MCT is not observed in real glas

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forming liquids due to the existence of temperature activahopping processes that break the trapping of moleculecages formed by neighboring molecules and so restoregodicity below Tc . However, an extended version of ththeory, taking these hopping processes into account, replthis sharp transition by a change in the transport mechannearTc from liquidlike to solidlike behavior. Therefore, remnants of the singularity may strongly influence the dynamaroundTc .

Analyzing neutron3–6 and light7–10 scattering spectrasome predictions of this mode coupling theory for the liquglass transition have been verified in particular aboveTc fora class of glass-forming liquids which are called fragile11

These systems often consist of relatively small, weaklyteracting molecules and so are close to the hard-sphereuids for which the MCT has been developed. In these fragsystems, the crossover seems to be correctly described bscaling laws of the simplest version of the MCT with a crosover temperatureTc located at about 1.2Tg . However, it isnot clear up to now whether this dynamic instability is alrelevant in less fragile systems that are characterized bsmoother temperature dependence of the structural relaxatime scale and thus a stronger influence of the temperaactivated hopping processes on the dynamics aroundTc .Furthermore, it is now well established that the lowest fquency inelastic feature in the vibrational contribution to tdynamical structure factorS(q,v), the so-called boson peakstrongly increases when going from fragile towards stro

11 546 © 1997 The American Physical Society

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56 11 547COMPARATIVE ANALYSIS OF THE FAST DYNAMICS . . .

glass-forming liquids.12 This inelastic component that hasbe regarded as specific to disordered materials13 is com-pletely neglected in the asymptotic solution of the MCequations. However, it strongly distorts the dynamical sceptibility above the susceptibility minimum14–17 betweenthe a and b fast processes in the mesoscopic regime thajust the frequency range concerned by some predicted sing laws of the MCT. This inelastic contribution could thube responsible for the departure of the asymptotic exponfrom the constraint imposed by the MCT, already slighobserved in fragile liquids and strongly amplified in lefragile systems.18 So a successful description of the liquglass transition in less fragile systems has to addressinfluence of these low-frequency vibrational modes onrelaxation dynamics.

As already pointed out, there are some experimental incations for a possible common physical origin betweenboson peak and the quasielastic component~the MCT b fast

process!. For most glasses, it is well known that the depolization ratio @r(v)5I VH(v)/I VV(v)# observed in low-frequency Raman spectra is similar for both contributioand independent of temperature. Recently, coherent neuscattering experiments have shown19 that theq dependenceof the dynamical structure factor was the same for the bopeak and the quasielastic region. These results can be tinto account if it is assumed that the quasielastic part cofrom the damping of the vibrational modes that give risethe boson peak as for example in the approach proposeGochiyaevet al.20 Using this model, a good description othe low-frequency Raman spectra has been achieved inile liquids as well as in stronger ones.20–23 Furthermore, aninteresting result can be related to this phenomenologapproach. It has been found that the boson peak becooverdamped at a temperatureT* close to the crossover temperatureTc of the MCT deduced from scaling analysis of thsusceptibility spectra in the different glass-forming liquithat were investigated.23 According to these authors, it meanthat in this temperature range, two independent explanatsupport the idea of a nonmonotonous change of the dynain supercooled liquids.

In the present paper, we report a coherent neutrscattering experiment on Na0.5Li 0.5PO3 initiated in order tostudy the fast dynamics near the liquid glass transition inonfragile glass-forming liquid. The remainder of the papis organized as follows: after mentioning some experimtal details~Sec. II!, we present a detailed analysis and dcussion of the data. The first part of Sec. III is concernwith the factorization problem of theq andv dependences othe dynamical structure factorS(q,v) in the mesoscopic frequency range in connection with the MCTb fast regime and apossible relation between thisb fast process and the bosopeak. Then a phenomenological approach, the convolumodel first proposed by Gochiyaevet al., which associatesthese two low-energy processes is used. The spectra arelyzed within this approach in order to determine whethernot the temperatureT* , where the boson peak becomoverdamped in this system, can be connected with a crover temperature between solidlike and liquidlike dynamas previously suggested. In the last part of Sec. III, a shqualitative discussion of the dynamical susceptibilities in

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framework of the MCT is presented. Our summary and cclusions are given in Sec. IV.

II. EXPERIMENT

Na0.5Li 0.5PO3 is the eutectic composition~Tg5515 K,Tm5749 K! based on the two alkali phosphate compounNaPO3 and LiPO3. The structure consists of covalent twistechains of phosphate tetrahedra PO4 linked through ionicbonds between nonbridging oxygen and alkali ions. Incrystalline state, NaPO3 ~Ref. 24! and LiPO3 ~Ref. 25! arecharacterized by a very different conformational state ofphosphate chain. As the cations are supposed to be randdistributed in the mixed structure, it results in a random mcrostructure which prevents the supercooled liquid frocrystallizing in the whole temperature range betweenTg andTm , thus over more than 200 K. As it is clearly shownFig. 1, the temperature dependence of the viscosity forglass-forming liquid has an intermediate behavior betwefragile liquids and strong ones in the Angell classificatilike two other systems currently under study, glycerol aZnCl2, although the high-temperature limit could be noticably different due to the polymeric structure.

As the liquid glass transition phenomenon seems tomainly concerned with the phosphate chain dynamics insystem, special care has been taken during the synthesthe sample used for this neutron-scattering experiment. Fpure 7Li starting materials have been chosen due to the habsorption cross section of the6Li isotope ~7.5% naturalabundance!. Second, phosphate glasses being slighhygroscopic,28 deuterated compounds have been used forsynthesis in order to avoid contamination of the scatteintensity by the incoherent scattering from the residual waIn this condition Na0.5Li 0.5PO3 is a coherent scattere~93.4%! and furthermore, 87.2% of the total scattering crosection is due to the coherent scattering from the phospchains. Thus neutron scattering is a suitable probe to ana

FIG. 1. Viscosity data of Na0.5Li 0.5PO3 as compared to those oglycerol and ZnCl2 in an Angell plot.11 d are from Ref. 26 andmfrom Ref. 27.

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11 548 56B. RUFFLE et al.

the collective dynamics of the liquid glass transition phnomenon in this system.

Neutron-scattering experiments have been done ontime-of-flight ~TOF! spectrometer MIBEMOL at the reactoOrphee of the Laboratoire Le´on Brillouin ~Saclay, France!.Using cold neutrons with an incident wavelength set toÅ, a resolution of 84meV ~full width at half height! has beenachieved at detector angles 2u ranging from 36° to 141°.Thus, scattering vectors up to 1.9 Å21 at zero energy transfer were allowed. As MIBEMOL is characterized by a reslution function of triangular shape, inelastic and broad quaelastic scattering as low as 0.1 meV can be observedorder to study the dynamics in Na0.5Li 0.5PO3 from well be-low the calorimetric glass transition temperatureTg up to themelting temperatureTm ~about 500 °C!, a hollow niobiumcell has been especially conceived for this experimentconsists roughly of two thin rolled up niobium sheets~0.1mm! forming two cylinders of, respectively, 11 and 15 min diameter, leaving an empty space of 2 mm width. Tvalue has been calculated in order to achieve a transmisof 90% that allows us to neglect multiple scattering corrtions whereas the cylindrical geometry ensures an as isopic scattering as possible. During the experiment, carebeen taken to guarantee absolute intensity calibration soruns have been measured in an uninterrupted series witremoving the sample from the oven. Furthermore, sincescattering cell is filled at room temperature with glass beathe experiment has been started from the highest temperin the stable liquid phase down to room temperature in orto ensure that the same number of scattering nuclei are inneutron beam during the whole experiment. The detectorficiencies have been determined from a scan with a holvanadium cylinder of the same size. The slightemperature-dependent background of the empty canbeen derived from two scans, one at room temperaturethe other at 500 °C. After these usual corrections, the TspectraS(2u,t,T) have been converted in dynamical struture factor spectraS(q,v,T) with q dependent energy rangeby interpolation with a wave vector step of 0.2 Å21 ensuringa rather good signal-to-noise ratio~23 spectra from 0.6 up to5.0 Å21!.

III. RESULTS AND DISCUSSION

In Fig. 2 is shown a representative set of the coherneutron-scattering spectra obtained from belowTg up toaboveTm for the wavevector 1.6 Å21. In order to removethe trivial temperature dependence of the scattered intenthese spectra have been plotted in reduced intenSred(q,v,T)5S(q,v,T)/@vn(v,T)# where n(v,T) is theBose factor. At low temperatures, the inelastic scatteredtensity is mainly due to low-energy vibrational excitatiothat give rise to a broad asymmetric band, the so-calledson peak with a maximum located around 6 meV at 461just belowTg . On varying temperature, the scattered intesity follows the Bose factor distribution for the energy abo6 meV whereas at lower energy an excess scattering appparticularly aboveTg . This broad quasielastic contributiogrows in intensity faster than the Bose factor revealingharmonic processes and is interpreted in the MCT framethe b fast relaxation though alternative phenomenologic

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approaches are also used attempting to connect it todamping of the low-energy vibrational modes.20,29 InNa0.5Li 0.5PO3, the spectrum is not completely quasielasticthe highest temperature studied just aboveTm in good agree-ment with the intermediate fragility of this system.12 Accord-ing to the viscosity data shown in Fig. 1, the structurallaxation should give a strictly elastic component on twhole temperature range investigated. Indeed, it is inferfrom Fig. 1 that at 773 K the width of thea process remainsbelow 1meV that has to be compared to the resolution widof 84 meV. It means that the broad quasielastic componenNa0.5Li 0.5PO3 can be safely studied over a wide temperaturange in the whole supercooled liquid phase. In particuMCT predictions in this mesoscopicb fast regime can betested.

One of the MCT predictions1 concerning theb fast relax-ation region is a decoupling property of the dynamical strture factorS(q,v,T) between a purely frequency-dependeand a purely wavevector-dependent term:Sb(q,v,T)5G(v,T) H(q). According to this expression, the shapethe dynamical structure factor or the susceptibility specx9(q,v,T)5S(q,v,T)/n(v,T) is predicted to be independent of the wavevector in theb fast regime. This factorizationproperty has been tested on the susceptibility spectratained in Na0.5Li 0.5PO3 and reported in Fig. 3 forT5631 K. The data for 0.6 Å21<q<5.0 Å21 are shown tooverlap within experimental error over a wide energy ranTherefore, it is found that this factorization property is vefied in the whole temperature range~300–773 K! not only inthe b fast relaxation region as predicted by the MCT but alfor the boson peak whatever the relative intensities of thtwo processes. Although the verification of this factorizatiproperty is a prerequisite condition for any mode couplianalysis in theb fast regime, it does not exclude other intepretations of the data. In particular, the observed similaqdependence of the dynamical structure factor for the bopeak and the quasielastic region does not preclude a vitional origin for the latter.

Following an idea first proposed by Gochiyaevet al.,20

these observations can be taken into account if it is assuthat each vibrational eigenmode with a frequencyV is

FIG. 2. Coherent neutron-scattering spectra of Na0.5Li 0.5PO3 inreduced intensity obtained on the TOF spectrometer MIBEMOLa momentum transferq51.6 Å21 at selected temperatures frombelow Tg up to aboveTm . Note the coincidence of all spectra foenergy transfers above 6 meV, the energy of the boson peak mmum at 461 K.

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damped via a relaxation memory functionm(v,T),

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resulting in the following susceptibility for each vibrationmode:

x~v,V,T!5@V22v22m~v,T!#21. ~2!

Then, the scattered intensity is simply given by the sumthe contributions of all the vibrational excitations. Replacithe summation by integration, the vibrational densitystatesg(V) is introduced:

I ~v,T!5n~v,T!E g~V!x9~v,V,T!dV. ~3!

The frequency dependence of the vibrational densitystatesg(v) can then be obtained from the shape of the sctered spectra at sufficiently low temperature when there isrelaxation

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whereI 0 is the reduced intensity scattered spectra at thistemperature. Next, the vibrational density of states orI 0 ischaracterized byvbp(T), the slightly temperature-dependefrequency of the boson peak maximum included in the moin order to take into account the commonly observed softing of the boson peak with increasing temperature. Thusassumed that the spectral shape of the boson peak istemperature dependent. This leads to the following expsion for the scattered intensity that has been used to fitexperimental data:

I ~v,T!5n~v,T!E V2I 0@V,vbp~T!#x9~v,V,T!dV.

~5!

In the Debye memory function of Eq.~1!, d(T) is thehomogeneous temperature-dependent coupling strength

FIG. 3. Test of the factorization property predicted by the MCfor theb fast relaxation region. The 23 susceptibility spectra at 631interpolated to constantq between 0.6 and 5.0 Å21 are representedwith different symbols. Note that the boson peak at higher enealso verifies the factorization property with the sameq dependence.

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tween the vibrational and relaxational modes whereast(T)is the relaxation time of the latter. ForT→0, d→0 and Eq.~5! becomes an identity giving an inelastic spectra. Oncreasing temperature,d(T) increases towardsvbp(T) givingrise to a broad quasielastic component untilvbp

2 5d2 at T5T* where the boson peak merges completely intoquasielastic component. By analogy with the soft moformalism,30 the renormalized frequency of the boson pemaximum v0

25vbp2 2d2 is expected to follow a critical

power-law temperature dependence just belowT* : v02

}(T* 2T). It corresponds to a transition of the excitatiothat give rise to the boson peak from vibrational to relaational type of collective motions.

Using this phenomenological approach, Raman speobtained on several glass formers have been fitted leadinvbp

2 5d2 for a temperatureT* close to the crossover temperatureTc of the MCT deduced from scaling analysis of thsusceptibility spectra.23 These results have led the authorsconclude that at this temperatureT* ;Tc a dynamical cross-over occurs in this energy range between a solidlike dynaics for T,Tc characterized by a vibrational spectra towara liquidlike dynamics forT.Tc characterized by a relaxational spectra. This crossover could thus be observed eby the critical behavior of the relaxational spectrum withthe frames of the MCT or by the critical behavior of thboson peak.

As shown in Fig. 4, this phenomenological model wionly three free parameters describes very well the coheneutron-scattering spectra obtained in Na0.5Li 0.5PO3 in thewhole temperature range investigated from belowTg up toaboveTm . According to Eq.~4!, the shape of the vibrationadensity of statesg(v) has been deduced from the room temperature reduced intensity spectra where the quasielacomponent is strongly reduced. But in this glass, the strasymmetric shape of the boson peak is very well describy a phenomenological generalized Lorentzian form:

I 0„v,vbp~T!…}v2

@v21vbp2 ~T!#2 . ~6!

So in the fitting procedure, this analytic function charactized by a unique parametervbp(T) has been used forI 0

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FIG. 4. q-rescaled spectra from belowTg up to aboveTm fittedwith the convolution model Eq.~5! ~Ref. 20! showing a very goodagreement over the whole temperature range investigated.

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rather than the experimental data. It should also be mtioned that no extra intensity parameter has been added infitting procedure as the temperature dependence of the bpeak intensity follows the Bose factor which is includedEq. ~5!.

The relaxation timet derived from these fits is found tbe weakly temperature dependent and in the range ofpicosecond. Thus the strong temperature dependence oscattered spectra is only due to the variations of the coupstrengthd and the position of the maximum of the bosopeakvbp as shown in Fig. 5. In the framework of this modethe boson peak is not overdamped even at the highestperature studied just aboveTm as the temperature depedence of the coupling strengthd2(T) does not cross thevbp

2 (T) one. As shown in the inset of Fig. 5, this leads torenormalized frequency of the boson peak maximumv0

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5vbp2 2d2 that goes to zero aroundT* 5875 K, well above

the melting temperature. Thus, contrary to the suggestiosome authors,23 the temperatureT* at which the boson peamerges into the quasielastic scattering cannot be assocwith any metastability onset in this system sinceT* is foundin the stable liquid phase.

Some of the most detailed predictions of the MCT abased on an asymptotic development of the susceptibspectrum in theb fast region around the minimum that seprates thea process on the low-frequency side from vibrtional modes at higher frequencies.1 For T above but close tothe crossover temperatureTc , the susceptibility minimum ispredicted to exhibit a universal spectral shape characterby a first power lawv2b at low frequencies in the range this the high frequency part of the stretched exponential fora relaxation. For the high-frequency side of the minimumsecond power lawva characterizing theb fast regime is pre-dicted. This susceptibility minimum can be then appromated by an interpolation formula between these two polaws leading to the determination of two parametersvmin andxmin9 , the frequency and the amplitude of the susceptibiminimum. According to the MCT, these two parameters flow critical temperature dependences:vmin}(T2Tc)

1/2a

andxmin9 }(T2Tc)1/2.

FIG. 5. Temperature dependence of the coupling strengthd ~d!and the position of the boson peak maximumvbp ~m! obtainedfrom the fitted spectra of Fig. 4 with the convolution modInset: Critical temperature dependence of the renormalizedquency of the boson peak maximumv0

25vbp2 2d2 leading toT*

5875 K well above the melting temperature in this system.

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Note that the critical exponentsa andb are not indepen-dent but obey a relation involving the gamma function andparameterl with the conditions 0,b,1 and 0,a,0.395.Furthermore, a critical temperature dependence is alsodicted for the structural relaxation time scaleta}(T2Tc)

2g with a critical exponentg also related to the previ-ous onesg5 1

2 a1 12 b. So aboveTc , all these critical behav-

iors are determined by the unique parameterl that could betheoretically calculated from the static structure factorS(q)but is usually left as a free parameter in MCT analysisreal glass formers.

One should keep in mind that these predictions of tidealized MCT in theb fast regime are only asymptotic resultderived from the mode coupling equations for frequencaround the susceptibility minima and for temperaturestoo far from Tc . Furthermore, it has also been shown theven in very fragile liquids, these predictions break dowvery close toTc as hopping processes, neglected in this idalized version, restore ergodicity belowTc .31 It should alsobe remembered that in the mode coupling asymptotic resuthe lowest-frequency vibrational component, namely, theson peak, is not properly taken into account. These limtions notwithstanding, several fragile liquids investigathave exhibited these different critical behaviors for the sceptibility spectrum obtained by neutron scattering32,33 aswell as by light scattering.7–10,34The scaling laws have beeparticularly verified aboveTc , locating the crossover temperature around 1.2Tg . For the temperatures belowTc , onlyone fragile liquid „@Ca(NO3)2#0.4@K(NO3)#0.6… seems toclearly exhibit up to now the knee in theb fast region of thesusceptibility following correctly the MCT predictions.7 Allthe other systems investigated show deviations probablyto a stronger boson peak influence resulting in critical expnentsa andb that cannot fulfill the MCT constraint.

As shown in Fig. 6, the coherent neutron susceptibilspectra obtained on Na0.5Li 0.5PO3 aboveTg are also stronglyinfluenced by the presence of the boson peak around 6 mFurthermore, the structural relaxation remains sufficienslow to not enter the energy window scanned by our exp

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FIG. 6. Temperature dependence of theq-rescaled susceptibilityspectra for some temperatures aboveTg . At high energy, the bosonpeak is clearly seen even for temperatures aboveTm whereas atlower energy theb fast region remains almost flat with an increasinamplitude with temperature.

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ment even for the highest temperature studied, 773 K,aboveTm . All these features result in almost flat suscepbility spectra in theb fast region without any prominent minimum. The slope at high energies is rather close toa'1 asfor other nonfragile glass-forming liquids investigated.14,15,17

So the lack of pronounced susceptibility minima in thespectra do not allow a complete line shape analysis withe framework of the MCT.

Nevertheless, a prediction that can be tested, as it doerequire any determination of a critical exponent, is the teperature dependence of the susceptibility plateau hexmin9 . Its temperature dependence forT.Tg is reported inFig. 7~a! showing a steeper increase above about 650These data are compatible with the MCT scenario leadina possible crossover temperatureTc near 620 K. As shown inFig. 7~b!, the a relaxation time scale that is related to thshear viscosityhs via the Stokes-Einstein relationta

}hs /T can also lead to the same crossover temperatureTc

;620 K. However, theg53 value used to obtain the lineadependence in Fig. 7~b! cannot be checked against the MCconstraint as the other critical exponentsa and b are un-known in this supercooled liquid and cannot be safely demined from the susceptibility spectra.

It is very interesting to note that the possible crossotemperatureTc;620 K found is very close to the temperture where a secondarybslow process emerges from the strutural relaxation as detected by31P NMR measurements35 andmechanical experiments36 in this glass-forming liquid andshown in Fig. 8. This secondary process has been attribto local reorientations of the PO4 tetrahedra forming thephosphate chains. It merges into the structural ora processabove 600 K, thus slightly belowTc (;1.2Tg). In the caseof fragile liquids, the temperature where this decoupling pnomenon between the structural relaxation and a seconbslow process observed by NMR or dielectric spectroscooccurs is also often found just below the crossover tempture Tc deduced from MCT analysis.37

FIG. 7. ~a! Temperature dependence of the susceptibility platheight deduced from the susceptibility spectra of Fig. 6 leadingpossible crossover temperatureTc;620 K. ~b! Critical scaling ofthe structural relaxation time scaleta}hs /T also leading to thesame crossover temperatureTc;620 K with g53.

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IV. CONCLUSION

In this paper, we have shown that in Na0.5Li 0.5PO3, thedynamical structure factor obtained by a coherent neutrscattering experiment is independent of the wave vectothe whole temperature range investigated from belowTg upto aboveTm . This factorization property ofS(q,v,T) is thusin good agreement with the results given by the MCT for tb fast region. Nevertheless, the observed similarq dependenceof the dynamical structure factor for the boson peak andfast relaxational process does not preclude a vibrationalgin for the latter. Using an alternative approach that relathese two contributions, a very good agreement has bfound between the coherent neutron-scattering spectrathe model in the whole temperature range from belowTg upto aboveTm . However, it has been demonstrated thattemperatureT* , where the boson peak becomes ovdamped, cannot be associated with any metastability ofliquid as recently suggested. Indeed, in this systemT* hasbeen found above the melting temperature.

On the other hand, the temperature dependence of theprocess intensity can be accounted for by the predictionthe simplest version of the MCT. It leads to a crossovtemperatureTc;620 K (;1.2Tg) in the supercooled liquidphase, in good agreement with scaling analysis of the sttural relaxation time scale deduced from viscosity data. Fthermore, it is also close to the temperature where a decpling phenomenon between the structural relaxation ansecondarybslow process occurs in this system as alreadyserved by31P NMR. However, it has not been possibleuse the susceptibility spectra for a line-shape analysisthus a more quantitative comparison with the MCT predtions. In particular, the susceptibility spectra obtainedNa0.5Li 0.5PO3 are strongly distorted by low-lying vibrationamodes, the boson peak, not really taken into account byMCT.

These results suggest that in less fragile systems, therelaxational intensity could be the result of two nea

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FIG. 8. Temperature dependence of the structural relaxatime scalets}hs /T ~d! and relaxation times obtained by31P NMR~j,l! ~Ref. 35! and DMA ~m! ~Ref. 36!. Below T;600 K occursa decoupling between thea process and a secondarybslow process.

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equally weighted contributions: one from the structurallaxation as described by the MCT and the other one fromdamping of the boson peak of negligible intensity in mofragile liquids.

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ACKNOWLEDGMENTS

The authors thank Y. Delugeard for fitting the data of F4 and S. Beaufils for fruitful discussions.

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*Laboratoire commun CEA-CNRS.1W. Gotze and L. Sjo¨gren, Rep. Prog. Phys.55, 241 ~1992!.2G. P. Johari and M. Goldstein, J. Chem. Phys.53, 2372~1970!.3F. Fujara and W. Petry, Europhys. Lett.4, 921 ~1987!.4W. Knaak, F. Mezei, and B. Farago, Europhys. Lett.7, 529

~1988!.5B. Frick, B. Farago, and D. Richter, Phys. Rev. Lett.64, 2921

~1990!.6W. Petry, E. Bartsch, F. Fujara, M. Kiebel, H. Sillescu, and B

Farago, Z. Phys. B83, 175 ~1991!.7G. Li, W. M. Du, X. K. Chen, H. Z. Cummins, and N. J. Tao,

Phys. Rev. A45, 3867~1992!.8W. M. Du, G. Li, H. Z. Cummins, M. Fuchs, J. Toulouse, and L

A. Knauss, Phys. Rev. E49, 2192~1994!.9W. Steffen, A. Patkowski, H. Gla¨ser, G. Meier, and E. W. Fis-

cher, Phys. Rev. E49, 2992~1994!.10E. Rossler, A. P. Sokolov, A. Kisliuk, and D. Quitmann, Phys

Rev. B49, 14 967~1994!.11C. A. Angell, in Relaxations in Complex Systems, edited by K. L.

Ngai and G. B. Wright~NRL, Washington, 1984!, p. 3.12A. P. Sokolov, E. Ro¨ssler, A. Kisliuk, and D. Quitmann, Phys.

Rev. Lett.71, 2062~1993!.13Amorphous Solids: Low Temperature Properties, edited by W. A.

Phillips ~Springer-Verlag, Berlin, 1981!.14A. Brodin, L. Borjesson, D. Engberg, L. M. Torell, and A. P.

Sokolov, Phys. Rev. B53, 11 511~1996!.15M. J. Lebon, C. Dreyfus, G. Li, A. Aouadi, H. Z. Cummins, and

R. M. Pick, Phys. Rev. E51, 4537~1995!.16A. Patkowski, W. Steffen, G. Meier, and E. W. Fischer, J. Non

Cryst. Solids172–174, 52 ~1994!.17J. Wuttke, J. Hernandez, G. Li, G. Coddens, H. Z. Cummins,

Fujara, W. Petry, and H. Sillescu, Phys. Rev. Lett.72, 3052~1994!.

18A. P. Sokolov, W. Steffen, and E. Ro¨ssler, Phys. Rev. E52, 5105~1995!.

.

.

.

-

F.

19B. Frick and D. Richter, Science267, 1939~1995!.20V. Z. Gochiyaev, V. K. Malinovsky, V. N. Novikov, and A. P.

Sokolov, Philos. Mag. B63, 777 ~1991!.21M. Kruger, M. Soltwisch, I. Petscherizin, and D. Quitmann, J

Chem. Phys.96, 7352~1992!.22M. Kruger, A. Kisliuk, A. P. Sokolov, M. Soltwisch, and D. Quit-

mann, J. Phys.: Condens. Matter5, 127 ~1993!.23A. P. Sokolov, A. Kisliuk, D. Quitmann, A. Kudlik, and E.

Rossler, J. Non-Cryst. Solids172–174, 138 ~1994!.24K. H. Von Jost, Acta Crystallogr.14, 844 ~1961!.25J. C. Guitel and I. Tordjman, Acta Crystallogr., Sect. B: Struc

Crystallogr. Cryst. Chem.32, 2960~1976!.26B. Ruffle, Thesis, University of Rennes I, 1996.27R. Wasche and R. Bru¨ckner, Phys. Chem. Glasses2, 80 ~1986!; 2,

87 ~1986!.28B. C. Bunker, G. W. Arnold, and J. A. Wilder, J. Non-Cryst.

Solids64, 291 ~1984!.29U. Buchenau, C. Scho¨nfeld, D. Richter, T. Kanaya, K. Kaji, and

R. Wehrmann, Phys. Rev. Lett.73, 2344~1994!.30V. L. Ginzburg, A. P. Levanyuk, and A. A. Sobyanin, Usp. Fiz.

Nauk 130, 615 ~1980!.31H. Z. Cummins, W. M. Du, M. Fuchs, W. Go¨tze, S. Hildebrand,

A. Latz, G. Li, and N. J. Tao, Phys. Rev. E47, 4223~1993!.32M. Kiebel, E. Bartsch, O. Debus, F. Fujara, W. Petry, and H

Sillescu, Phys. Rev. B45, 10 301~1992!.33R. Zorn, D. Richter, B. Frick, and B. Farago, Phys. Rev. A201,

52 ~1993!.34G. Li, W. M. Du, A. Sakai, and H. Z. Cummins, Phys. Rev. A46,

3343 ~1992!.35B. Ruffle, S. Beaufils, and J. Gallier, Chem. Phys.195, 339

~1995!.36P. Green, D. Sidebottom, and R. Brow, J. Non-Cryst. Solids172–

174, 1353~1994!.37E. Rossler, U. Warschewske, P. Eiermann, A. P. Sokolov, and D

Quitmann, J. Non-Cryst. Solids172–174, 113 ~1994!.

observed by coherent neutron scattering

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