The low-energy excess of vibrational states inv-SiO2: the role of transverse dynamicsInsulating <strong>di</strong>sordered solids exhibit some commonpeculiarities in their low-temperature and low-energydynamics, inclu<strong>di</strong>ng an excess of modes in thevibrational density of states, known as the bosonpeak (BP). An unambiguous understan<strong>di</strong>ng of theseextra modes, and of their possible relation with otheranomalies, is still lacking, In the case of v-SiO2, themost widely accepted explanation is that the BPoriginates from the piling up of modes near the firstvan Hove singularity of the transverse acousticvibrational branch. In ad<strong>di</strong>tion to the ambientpressure data, useful information is available for v-SiO2 at higher densities: densification results in ashift of the BP towards higher energies and in asimultaneous decrease of its intensity.a weak shoulder in the transverse spectra only at Q> 10 nm −1 . We assign this feature to the longitu<strong>di</strong>nalsound-like branch. The behaviour of the low energyexcitation is complementary: it is always present inthe transverse spectra, while it appears in thelongitu<strong>di</strong>nal currents only at Q > 8 nm−1. At smallQ, the low energy peak <strong>di</strong>sperses linearly with asound velocity of ≈3800 ms −1 (appropriate for thetransverse sound modes), and becomes almost non<strong>di</strong>spersingat Q > 8 nm−1. This feature —which isthe main one in the transverse spectra— is thetransverse acoustic mode. The presence of thesignature of transverse dynamics in the longitu<strong>di</strong>nalcurrent spectra, and vice versa, is due to the factthat the polarization character of the modes becomesill defined at short wavelengths. Spectra for thesample at the highest density stu<strong>di</strong>ed (ρ=4.0 gcm −3 ), are reported in the right panels of the figure.One can observe that no evidence of wronglypolarized modes is present; moreover, the T branchno longer shows a flattening.The conclusion that can be drawn is that the excessof states in the normal sample accumulates in aregion, which is almost coincident with the energyrange where the transverse branch flattens,in<strong>di</strong>cating that the BP arises from the high Q portionof the transverse branch. This assignment isconfirmed by the behaviour of the high-energytransverse dynamics upon densification.Fig. 1 - Longitu<strong>di</strong>nal (full) and transverse (dashed)current spectra at selected Q values (nm −1 ) for ρ =2.2 (left) and 4.0 rigt) g cm −3 .We present here simulation results on v- SiO 2 at<strong>di</strong>fferent densities which help in clarifying the originand the nature of the excess modes, as well as theintensity and shift effects on the BP as a function ofdensity.The systems investigated consist of 680 SiO 2 units(N=2040 ions), enclosed in cubic boxes of <strong>di</strong>fferentlengths (from L=3.1359 nm, ρ=2.2 g*cm −3 for theglass at room pressure, down to L=2.5693 nm,density ρ=4.0 g*cm −3 ), with perio<strong>di</strong>c boundarycon<strong>di</strong>tions. The ions interact through the BKS [31]two-body potential.We have computed the dynamic structure factorS(Q,ω) and the longitu<strong>di</strong>nal (L) and transverse (T)current spectra C L,T(Q,ω). In figure 1, left panel, wereport longitu<strong>di</strong>nal and transverse current spectra atselected Q values for the uncompressed sample (ρ =2.2 g cm−3). For Q larger than about 8 nm −1 , bothCL(Q,ω) and CT(Q,ω) show two <strong>di</strong>stinct maxima, andthis structure becomes more and more evident withincreasing Q. The excitation at higher energy<strong>di</strong>sperses with Q and is observed at all Q values inthe longitu<strong>di</strong>nal current spectra, while it shows up asExperimentally, it is observed that upon densification(i) the BP shifts to higher energy and (ii) its intensitystrongly decreases. From our simulations we observethat, by increasing the density, the T branch flattensat a higher energy and, upon further densification,no flattening is observed at all. A similar behaviour isobserved for the calculated density of states as afunction of density [1]: the low-energy part of theDOS shifts to higher energies and decreases inintensity. As a consequence, the BP stronglydecreases in intensity and shifts to high energies [1].References[1] O. Pilla et al., J. Phys. Cond. Mat. 16, 8519(2004).Authors:O. Pilla (1), S. Caponi (1,2), A. Fontana (1,2), J.R.Goncalves (1,3), M. Montagna (1), F. Rossi (1), G.Viliani (1,2), L. Angelani (4,5), G. Ruocco (2,4), G.Monaco (6), F. Sette (6) - (1) <strong>Dipartimento</strong> <strong>di</strong> <strong>Fisica</strong>,Università <strong>di</strong> Trento, Italy; (2) INFM-CRS SOFT,Università <strong>di</strong> Roma La <strong>Sapienza</strong>, Italy; (3)Departamento de Fısica, Universidade do Cearà,Brazil; (4) <strong>Dipartimento</strong> <strong>di</strong> <strong>Fisica</strong>, Universit`a <strong>di</strong>Roma La <strong>Sapienza</strong>, Italy(5) INFM-CRS SMC,Universit`a <strong>di</strong> Roma La <strong>Sapienza</strong>, Italy; (6) EuropeanSynchrotron Ra<strong>di</strong>ation Facility, Grenoble, France75SOFT Scientific <strong>Report</strong> 2004-06
Scientific <strong>Report</strong> – Non Equilibrium Dynamics and ComplexityDroplets of Liquid Gallium Under High Temperature and HighPressure Con<strong>di</strong>tionsIn the last few years the study of liquidpolymorphism has received a great attention. Theexistence of two possible <strong>di</strong>stinct liquids, with thesame chemical composition but with <strong>di</strong>fferentphysical properties is quite consistent withexperimental data and theoretical pre<strong>di</strong>ctions.Liquid-liquid phase transition has been related to thesoft-core interaction potential characterized by thecoexistence of metallic and covalent behaviour in thebon<strong>di</strong>ng (for example as liquid Sn, Bi, Ga or Ge). Inprinciple Gallium is one of the best can<strong>di</strong>date forshowing liquid polymorphism. This is due to twoprincipal reason: one its ice-type phase <strong>di</strong>agram witha negative temperature dependence and the secondone because its <strong>di</strong>splay extended polymorphism inthe solid phase. The samples we investigatedconsist of gallium droplets (~ 4% weight) inserted inan inert matrix of mixed epoxy resin and LiF. Weperform on our sample <strong>di</strong>fferent spectroscopictechniques: X-ray absorption on Ga K-edge level(XAS) , single x-ray absorption detection (SEXAD)and energy x-ray <strong>di</strong>ffraction (ESXD). Ourmeasurements were performed at the BM29 of theESRF facility using a Paris-E<strong>di</strong>mburgh large volumecell in a range of pressure up to 6.7 Gpa and atemperature range of 298-440 K. In the next figurewe show the behaviour of the x-ray <strong>di</strong>ffractionspectra as function of the pressure where it ispossible to observe clearly the appearance of Ga(III)crystalline phase Bragg peaks above 4.2 GPa(channel 2) whereas no Ga(III) (013) peak isdetected at 2.3 GPa (channel 3). It is important tonote the appearance of Ga(III) in a region wherethat Ga(II) has a stable crystalline phase. In thesame figure on the right side temperature scans(SEXAD) recorded at <strong>di</strong>fferent pressure are reported,and it is possible to see the <strong>di</strong>scontinuities relatedwith the solid-liquid phase transition. The increasing<strong>di</strong>scontinuities observed as function of pressureFig. 2.confirms the occurrence of a partial crystallization ofthe gallium droplets.In the following picture the XAS measurements in anenergy interval close the Ga-edge for two <strong>di</strong>fferentthermal histories are reported. We can observe aobvious change in the absorption in the liquid phaseobtained between 1.6 GPa and 0 GPa and this mayin<strong>di</strong>cate the occurrence of a possible transformationin the microscopic structure or/and in the electronicstate.Moreover the shape of the <strong>di</strong>fference signal (blackcurve) it is quite <strong>di</strong>fferent from the one obtainedbetween the 5.8 and 2.7 GPa spectra and also<strong>di</strong>fferent from a typical Da(E) curve of twoequilibrium liquid Ga XAS spectra (right panel). Thisresult may infer the existence of a <strong>di</strong>fferent liquidphase above 1.6 Gpa.So considering both ESXD and SEXAD spectra wecan observe that the quantity of crystallized galliumdroplets increases as function of pressure while noevidence of crystallization is observed up to 2.6 Gpa,well under the melting point line at roomtemperature.In conclusion the interesting hypothesis of a liquidliquidphase transition occurring between 0 and 1.6GPa is compatible with our results and it spursfurther investigation on this systems.References[1] R. Poloni, S. De Panfilis, A. Di Cicco, G. Pratesi,E. Principi, A. Trapananti, and A. Filipponi "Liquidgallium in confined droplets under high-temperatureand high-pressure con<strong>di</strong>tions", Phys. Rev. B 71,184111 (2005).AuthorsR. Poloni, S. De Panfilis, A. Di Cicco, G. Pratesi, E.Principi, A. Trapananti, and A. FilipponiFig. 1.SOFT Scientific <strong>Report</strong> 2004-0676
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