Microscopic Dynamics in Liquid MetalsLiquid metals are an outstan<strong>di</strong>ng example of systemscombining great relevance in both industrialapplications and basic science. On the one hand theyfind broad technological application ranging from theproduction of industrial coatings (walls of refinerycoker, drill pipe for oil search) to me<strong>di</strong>cal equipments(reconstructive devices, surgical blades) or highperformance sporting goods. Most metallic materials,indeed, need to be refined in the molten state beforebeing manufactured. On the other hand liquidmetals, in particular the monoatomic ones, havebeen recognized since long to be the prototype ofsimple liquids, in the sense that they encompassmost of the physical properties of real fluids withoutthe complications which may be present in aparticular system Inelastic.Neutron Scattering played a major role since thedevelopment of neutron facilities in the sixties. Thelast ten years, however, saw the development ofthird generation ra<strong>di</strong>ation sources, which opened thepossibility of performing Inelastic Scattering with Xrays, thus <strong>di</strong>sclosing previously unaccessible energymomentumregions. The purely coherent response ofX-rays, moreover, combined with the mixedcoherent/incoherent response typical of neutronscattering, provides enormous potentialities to<strong>di</strong>sentangle aspects related to the collectivity ofmotion from the single particle dynamics.S(Q,ω) [a.u.]B280240200160120804001501209060300Na-K44/56KNaQ = 0.29 Q Max-4 -3 -2 -1 0 1 2 3 4E / E 0180150120Collecting data on a sizeable library of system, bymeans of new X-ray and Neutron experiment andexisting literature, we identified the commonfeatures of microscopic dynamics at <strong>di</strong>fferentwavelengths and frequencies, from a stronglycorrelated regime to the single particle domainthrough the interme<strong>di</strong>ate, hard-sphere like, kineticregime.9060300In liquid alloys a similar scenario holds. In particularthe generalized hydrodynamic theory correctlydescribes for the spectral lineshapes. An ad<strong>di</strong>tionalrelaxation process, however, related to theconcentration fluctuation, has to be accounted forbeside the usual two-step relaxation process rulingthe acoustic properties in monoatomic fluids.References[1] T. Scopigno, G. Ruocco and F. Sette, The Reviewof Modern Physics 77, 881 (2005).[2] T. Scopigno, R. Di Leonardo, L. Comez, A.Q.R.Baron, D. Fioretto and G. Ruocco, Physical ReviewLetters 94, 155301, (2005).In the last few years, we investigated the highfrequency dynamics in several simple liquids,comprising monoatomic fluids and binary mixtures.While the long wavelength regime is well understoo<strong>di</strong>n terms of or<strong>di</strong>nary hydrodynamics, the atomicmotion at lengthscales comparable to the interatomic<strong>di</strong>stance is still debated.AuthorsS. Cazzato (a,b), G. Ruocco (a,b), T. Scopigno (b).(a) <strong>Dipartimento</strong> <strong>di</strong> <strong>Fisica</strong> Universita’ Roma ‘’La<strong>Sapienza</strong>’’, 00185 Roma, Italy.(b) CRS SOFT-INFM-CNR, Roma, Italy65SOFT Scientific <strong>Report</strong> 2004-06
Scientific <strong>Report</strong> – Non Equilibrium Dynamics and ComplexityNon-Ergo<strong>di</strong>city in Locally Ordered SystemsThe current interest in studying the structurallyarrested states of matter is based on searching for abasic mechanism underlying the onset of theparticle-blocking of motion, common to <strong>di</strong>fferentclasses of systems.Suppose a tagged particle is trapped in a transientcage made by its nearest neighbours, which arecaged themselves. With decreasing temperature, theparticle becomes progressively more confined in itscage and partakes correlated collisions.Subsequent <strong>di</strong>ffusion out of the cage needs acooperative rearrangement of many particles andprovides long-range transport motion, which slowsdown drastically as the temperature is lowered. Thiscage effect mechanism can be regarded as themicroscopic origin of the eventual structural arrest ofa simple liquid that occurs at the glass-transition. Inmore complex systems like associated and covalentliquids, the ubiquitous class of liquids inclu<strong>di</strong>ng waterand silica, the cage effect manifests a <strong>di</strong>fferentnature since molecules are blocked in energeticcages of hydrogen or covalent bonds, and bondbreaking and formation is needed for <strong>di</strong>ffusion tooccur. This is why fin<strong>di</strong>ng a unique para<strong>di</strong>gm toexplain the particle dynamics and the particle cagingof <strong>di</strong>fferent classes of systems actually constitutes abig challenge for condensed matter physics.f Qf Q0.90.80.70.6Q=2 nm -10.50.951.00.90.80.70.95Q=4 nm -10.900.900.850.850.80Q=7 nm -1Q=10 nm -10.750.8050 100 150 200 250 300 50 100 150 200 250 300T(K)T(K)Fig. 1: Temperature dependence of the nonergo<strong>di</strong>cityfactor f Q of m-tolui<strong>di</strong>ne for <strong>di</strong>fferent Q-values. The solid lines are the best fits obtainedusing the square-root function pre<strong>di</strong>cted by theMCT.Intensity64200 2 4 6 8 10 12 14 16 18Q (nm -1 )Fig. 2 X-ray <strong>di</strong>ffraction pattern (left axis) of liquidm-tolui<strong>di</strong>ne at ambient temperature taken from Ref.[2], compared with the parameter f Q c (right axis)obtained from the fit of the experimental f Q(T) data(open circles); full squares in<strong>di</strong>cate the values of f Qat T=263 K - a temperature in the plateau region off Q(T) - for all the available Qs.1.00.80.6f QcOriginally, the mode coupling theory (MCT) wasproposed as an approximation approach for the cageeffect in liquids [1]. In its simplest version, thederived equations of motion for the densityfluctuationslead to a bifurcation of the long-timelimit of the density correlators, the so-called nonergo<strong>di</strong>city factor f Q, if a control parameter liketemperature crosses a critical value, T c. Within MCT,specific pre<strong>di</strong>ctions are postulated for thetemperature and wave-vector dependence of f(Q,T):i) A square-root temperature behaviour below T c,i.e., f Q(T)=f c Q +h Q(1-T/T c) 1/2 , where f cQ is the criticalnon-ergo<strong>di</strong>city parameter and h Q the criticalamplitude at a fixed wavevector Q; ii) A Q-cdependence of f Q and of h Q that follows theoscillations of the static structure factor S(Q).While a large number of experimental and theoreticalworks have verified the MCT pre<strong>di</strong>ctions in Van-der-Waals molecular liquids, few investigations havebeen devoted to associated and covalent liquids, andthe results are often not exhaustive. In these liquidsthe local order extends over several neighboringmolecules and reflects on a nontrivial Q behavior inthe low-Q region of the static structure factor, S(Q).We investigated a molecular system, m-tolui<strong>di</strong>ne,which is characterized by a spatial organization ofthe molecules induced by hydrogen bonds exten<strong>di</strong>ngover several molecular <strong>di</strong>ameters and giving rise tonanometer size clusters [2]. The non-ergo<strong>di</strong>cityfactor of supercooled and glassy m-tolui<strong>di</strong>ne hasbeen measured, through IXS experiments (beam lineID16-ESRF), in the mesoscopic Q range between 1and 10 nm -1 , around the prepeak in the staticstructure factor related to the local order (Q pp=5nm -1 ). We proved that the basic pre<strong>di</strong>ctions of MCTabout the non-ergo<strong>di</strong>city factor hold in m-tolui<strong>di</strong>ne(see Figure 1 and Figure 2), provi<strong>di</strong>ng experimentalevidence that the signature of the ergo<strong>di</strong>c to nonergo<strong>di</strong>ctransition, valid for simple liquids, lives on inclustering systems [3]. Our fin<strong>di</strong>ngs suggest that theinitial stage of the cooperative rearrangements,where the cage effect dominates the moleculardynamics, exhibits a universal character, common tosimple liquids and liquids with a local order. Thisconcept is not so obvious, because it places on thesame level the structural arrest in simple and inlocally ordered liquids, though the cage formation iscontrolled by <strong>di</strong>fferent mechanisms.References[1] W. Götze and L. Sjögren, Rep. Prog. Phys. 55,241 (1992).[2] D. Morineau et al., Europhys. Lett. 43, 195(1998); M. Descamps et al., Prog. Theor. Phys.Suppl. 126, 207 (1997).[3] L. Comez et al., Phys. Rev. Lett. 94, 155702(2005).Authors:L. Comez (a), S. Corezzi (b), G. Monaco (c), R.Verbeni (c), and D. Fioretto (a).(a) CRS-SOFT and <strong>Dipartimento</strong> <strong>di</strong> <strong>Fisica</strong>, Università<strong>di</strong> Perugia, Perugia (Italy), (b) CRS-SOFT and<strong>Dipartimento</strong> <strong>di</strong> <strong>Fisica</strong>, Università <strong>di</strong> Roma La<strong>Sapienza</strong>, Roma (Italy), (c) ESRF, Grenoble (France).SOFT Scientific <strong>Report</strong> 2004-0666
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