The collective dynamics of the ‘non-simple’ liquid metal Sn

The dynamic structure factor S(Q, ω) of liquid Sn was measured at 320 °C and 1000 °C in a Q-range between 2 nm⁻¹ and 30 nm⁻¹ using inelastic X-ray scattering. The obtained spectra clearly demonstrate the existence of longitudinal propagating modes in this liquid metal. At 320 °C a positive dispersion is found in the low Q-region, where the mode velocity is about 12% larger than the bulk adiabatic speed of sound. At 1000° this so-called ‘positive dispersion’ reduces to about 6%. The quasielastic lineshape contains a Gaussian contribution near the Q-positions of the first maximum in S(Q), which has not yet been reported in simple liquid metals like, e.g. the liquid alkalis. With increasing temperature, the relative Gaussian contribution increases and can be observed along a wider Q-range. This anomaly is related to a partially covalent nature of liquid Sn in analogy to other liquid non-simple metals.     

High-resolution inelastic X-ray scattering measurements of an Al72Pd20Mn8 alloy above the melting point

The dynamic structure factor S(Q, ω) of the melt of an icosahedral quasicrystal, Al₇₂Pd₂₀Mn₈, was measured at 1223 K near the melting point, T_m = 1140 K, for momentum transfers, Q, from 1.5 nm⁻¹ to 5.55 nm⁻¹ by means of inelastic X-ray scattering technique using synchrotron radiation at SPring-8. The composition of Al₇₂Pd₂₀Mn₈ is a special one in AlPdMn ternary alloys, since icosahedral AlPdMn quasicrystal is formed directly from the melt. The acoustic mode was observed in the low Q region, and a sound velocity was estimated to be 4170 ± 100 m/s.     

High frequency dynamics of an orientationally disordered molecular crystal

The dynamic structure factor of the polycrystalline plastic crystal 1-cyanoadamantane has been measured in the THz frequency region by inelastic X-ray scattering as a function of the exchanged momentum Q in the range 1–10 nm⁻¹ and as a function of the temperature in the two solid disordered phases: plastic crystal and glassy crystal. We find that the dispersion of the acoustic excitations is crystal-like in the two phases and that the attenuation Γ(Q) shows a negligible T dependence similarly to structural glasses and a Q^α behavior with 1.15 < α < 1.50 at variance with structural glasses characterized by a Q² dependence.     

High frequency dynamics of liquid bismuth

The dynamic structure factor S(Q, ω) of liquid Bi was measured at 580 K in the Q range from 0.15 to 0.6 Å⁻¹ using inelastic neutron scattering. The obtained spectra clearly demonstrate the existence of well defined longitudinal propagating modes. A positive dispersion is found in the low Q region, where the mode velocity undergoes a transition between the hydrodynamic value and a high frequency value 20% larger. The damping of the excitations does not follow the hydrodynamic Q² trend and is stronger than in any metallic liquid investigated so far. The quasielastic lineshape contains a broad Q-independent Lorentzian contribution, other than a small sharp peak, which has yet been observed in liquid Hg and Ga.     

Microdynamics of a monoatomic liquid metal

Modified microscopic theory of the collective dynamics of a simple liquid has been used to explain the recently observed accurate detailed coherent dynamical structure factor S(k, ω) of liquid Na at 390 K as measured by high resolution inelastic X-ray scattering (IXS) in the wave-vector, κ, range 1.5 nm^?1 ? κ ? 14.6 nm^?1. The computed values of detailed spectral lineshape of S(k, ω), the dispersion relation and the velocity of sound are in reasonable agreement with the corresponding experimental results. Variation of longitudinal viscosity with κ has also been reported.     

Observation of the collective vibrational modes in Ni42Nb58 metallic glass

The dynamic structure factors, S(Q, E), for Ni₄₂Nb₅₈ metallic glass have been measured using neutron inelastic scattering on the IN4 spectrometer (ILL, Grenoble, France), over a range of momentum transfer, 0.7 < ℏQ/Å⁻¹ < 8, and energy transfer, 2 < E/meV < 50. Three samples with the same chemical composition and different Ni isotope content were investigated. The constant-E and constant-Q cuts through the S(Q, E) functions have been obtained. They reveal the E-and Q-dependencies due to the existence of the collective vibrational excitations in Ni₄₂Nb₅₈ glass. At the same time the difference of Ni and Nb atoms dynamics was observed by isotope contrast in the scattered spectra.     

Hydrogen dynamics in polyethersulfone: A quasielastic neutron scattering study in the high-momentum transfer region

In a previous quasielastic neutron scattering study [I. Quintana, A. Arbe, J. Colmenero, B. Frick, Macromolecules 38 (2005) 3999] we characterized the hydrogen dynamics in glassy polyethersulfone as due to ‘fast processes’ plus flips and oscillations of the phenylene rings. Here we have extended this investigation by using thermal neutrons, that allowed exploring also much higher values of the momentum transfer Q. In the dynamic window accessed, a characterization as best accurate as possible of the fast dynamics is imperative in order to describe the experimental results, especially at very local length scales. While for Q ≲ 2.2 Å⁻¹ (i.e., in the range previously studied) the proposed model perfectly describes the experimental data with the same parameters deduced from the earlier work, in the high Q-range (Q ≈ 3.5–4 Å⁻¹) deviations are found. These could be overcome by assuming some kind of ‘effective softening’ of the fast process and slight deviations from harmonic behavior in the Q-dependence of the associated Debye–Waller factor.     

Acoustic damping in Li2O–2B2O3 glass observed by inelastic X-ray and optical Brillouin scattering

The dynamic structure factor of lithium-diborate glass has been measured at several values of the momentum transfer Q using high resolution inelastic X-ray scattering. Much attention has been devoted to the low-Q-range, below the observed Ioffe–Regel crossover q_IR ≃ 2.1 nm⁻¹. We find that below q_IR, the linewidth of longitudinal acoustic waves increases with a high power of either Q, or of the frequency Ω, up to the crossover frequency Ω_IR ≃ 9 meV that nearly coincides with the center of the boson peak. This new finding strongly supports the view that resonance and hybridization of acoustic waves with a distribution of rather local low frequency modes forming the boson peak is responsible for the end of acoustic branches in strong covalent glasses. Further, we present high resolution Brillouin light-scattering data obtained at much lower frequencies on the same sample. These clearly rule out a simple Ω²-dependence of the acoustic damping over the entire frequency range.     

Pronounced variation in the collective dynamics of highly correlated lightest liquid alkali metal: Lithium

Recently measured inelastic X-ray spectra (IXS) of detailed coherent dynamical structure factor S(κ, ω) and hence the equilibrium collective dynamics, of the lightest liquid alkali metal, lithium at 475 K, have been successfully explained using the modified microscopic theory of the collective dynamics of a simple liquid, in a huge wave-vector, κ, range: 1.4 nm^?1 ≤ κ ≤ 110.0 nm^?1, ?κ is the linear momentum transfer. The role of single particle motion in the collective dynamics of the liquid changes from diffusive for smaller values of wave-vector, κ < 21 nm^?1 to that of a free particle for higher κ-values, 21 nm^?1 ≤ κ ≤ 110 nm^?1. The quantum correction due to detailed balance condition in S(κ, ω) for liquid Li, whose dynamics, unlike that of quantum liquid ⁴He, is essentially classical, yields results in better agreement with the corresponding experimental S(κ, ω) and the quantum correction becomes significant for higher values of κ and ω. The wave-vector dependent variation of longitudinal viscosity, η_l, is in good agreement with the corresponding results obtained from memory function approach. The wave-vector dependent variation of single characteristic relaxation time lies in between the variation of two relaxation times of memory function approach.     

Static and dynamic structures of liquid GeTe mixtures

Neutron diffraction measurements of the liquid Ge–Te system and quasi- and inelastic neutron scattering experiments of the eutectic liquid Ge₁₅Te₈₅ were performed in the temperature range from 400 to 560 °C. The large temperature dependence of the static structure for liquid Ge₁₅Te₈₅ is reconfirmed; however it is found that the compositional dependence obtained at around 80 °C above the liquidus curve is rather small. The dynamic structure factors of liquid Ge₁₅Te₈₅ in the Q-region from 0.2 to 2.6 Å⁻¹ show a normal temperature dependence. From the vibrational density of states, it is found that the Te–Te covalent bond persists in liquid Ge₁₅Te₈₅; however a bending mode was not assigned clearly.     

Microscopic collective dynamics in liquid tellurium

The spectra of collective excitations of liquid tellurium have been studied by means of inelastic neutron scattering. Here we report on the dynamics of liquid Te as measured at two different temperatures, just above melting (T_m = 723 K) and at ∼1000 K. Estimates for the velocity of propagating excitations for both temperatures have been obtained from the experimental data and a contrasting behavior is found with respect to anomalies shown by the adiabatic sound velocity measured by ultrasound methods.     

Molecular dynamics in glass-forming poly(phenyl methyl siloxane) as investigated by broadband thermal,dielectric and neutron spectroscopy

The molecular dynamics of glass-forming poly(methyl phenyl siloxane) (PMPS) is studied by thermal (10⁻³–5 × 10² Hz), dielectric (10⁻³–10⁹ Hz) and neutron (5 × 10⁸–10¹² Hz) spectroscopy. Because of the broad frequency range of 15 orders of magnitude the study provides a precise determination of glassy dynamics in a wide temperature range using different probes. The relaxation rates extracted from the different methods agree quantitatively in both their absolute values and in their temperature dependencies. A detailed analysis of the temperature dependence of the relaxation rate f_p by a derivative technique shows that the α-relaxation of PMPS has to be characterized by a high and a low temperature branch separated by a crossover temperature T_B = 250 K. In both temperature ranges the temperature dependence of f_p has to be described by Vogel/Fulcher/Tammann laws with different Vogel temperatures. Also the analysis of the dielectric strength in its temperature dependence gives a crossover behavior from a low to a high temperature region with a similar value of T_B. T_B can be interpreted as onset of cooperative fluctuations and the formation of dynamical heterogeneities. The dependence of the relaxation rate on the scattering vector Q extracted from neutron scattering obeys a power law τ ∼ Q^−Slope, where the power Slope varies between Slope = 2 and Slope = 3.5 with increasing temperature. This anomalous dependence of the relaxation time on the momentum transfer is discussed in terms of dynamic heterogeneities in the underlying motional processes even at temperatures above T_B. Besides the segmental dynamics the fast Methyl group rotation is considered as well. The relaxation rates of this process have an activated temperature dependence with an activation energy of 8.3 kJ/mol. The data were discussed in the framework of the threefold jump model were the incoherent elastic scattering from ‘fixed’ atoms which are frozen on the time scale of the Methyl group rotation was taken into account.     

Na–Pb liquid alloy structure at low lead concentrations: Neutron-diffraction studies

Na–Pb liquid alloys with the lead concentration of 1.5 and 7.9 at.%, and pure sodium as a reference system are studied by neutron-diffraction at 700 K. A characteristic prepeak of static structure factor, S(Q), at Q ∼ 1.2 Å⁻¹, known from neutron-diffraction studies of the Na–Pb alloys with the lead concentration of 20 at.% and higher, is not observed for the alloys under consideration. The experimental S(Q) values are compared with the results of molecular-dynamics simulations.     

The structure of phosphate glass evidenced by small angle X-ray scattering

Numerous phosphate glass systems with compositions covering the entire glass forming range have been examined by small angle X-ray scattering. The experiments were carried out in a widely extended interval of s values between 0.055 and 31 nm⁻¹. A small angle scattering effect was detected for all samples investigated with the exception of the aluminium metaphosphate glass. The small angle scattering recorded indicates the presence of two differently-sized heterogeneity regions of electron density. The small-scale heterogeneities are present in magnesium and zinc phosphate glasses only. Their size is about 1 nm diameter in the magnesium and about 2 nm in the zinc phosphate glasses. The species do not result from liquid–liquid phase separation. Examinations to extract information on the nature of these heterogeneity regions are described in detail. There is no fundamental knowledge on the large-scale heterogeneities established. The small angle scattering suggests that their occurrence is related to water contamination. Anomalous small angle X-ray scattering experiments of a series of zinc polyphosphate glasses and a strontium metaphosphate glass sample are performed to examine the distribution of the Zn or Sr atoms, respectively.     

The structures of normal and supercooled liquid silicon metal and SiGe alloy

The atomic structures of liquid Si metal and SiGe alloy in the normal and supercooled liquid states have been measured by X-ray diffraction from aerodynamically levitated and laser heated liquid droplets. The measurements covered a wide range of scattering vector Q (0.8–20 A⁻¹) and a wide temperature range that extended into the supercooled region. The present results on liquid Si confirm earlier measurements that showed a decrease in first-shell coordination with increased supercooling. For liquid SiGe, the shoulder on the high-Q side of the first peak in the structure factor S(Q) sharpens with increased supercooling, suggesting an increase in covalent bonding and development of chemical short-range order.     

Structure of potassium germanophosphate glasses by X-ray and neutron diffraction: 3. Reverse Monte Carlo simulations

Reverse Monte Carlo (RMC) is used to investigate the origin of the first sharp diffraction peaks (FSDP) found for K₂O–GeO₂–P₂O₅ glasses at very small scattering vector Q = ～7.5 nm^?1. Structures of the ternary glass with the greatest intensity of FSDP (KGeP5 – 25/50/25 mol% K₂O/GeO₂/P₂O₅), of the binary combinations of the three oxides and of vitreous GeO₂ are modeled. Results are deduced from comparisons of the partial structure factors and inspections of model sections. The P sites are uniformly distributed in the structure of KGeP5. The K⁺ ions interact more with the PO₄ units (via O_T-corners) than with Ge-centered units. Main component of the FSDP comes from the S_GeGe(Q) factor. The FSDP is due to separations of ～1 nm between the longish Ge-rich clusters which are visible in the corresponding models. Different to our tentative structural models reported before, the PO₄ tetrahedra possess a broad distribution of numbers of O_T corners. The FSDP’s of the binary K₂O–GeO₂ and K₂O–P₂O₅ glasses (～10 nm^?1) are due to a chemical order between network former and network modifier regions. The MRO of a mixed GeO₂–P₂O₅ glass of small P₂O₅ content (FSDP at ～16 nm^?1) shows great similarity to the MRO of vitreous GeO₂.     

Structure of molten Al–Si alloys

The temperature variation of the structure and microstructure of molten eutectic Al_1−xSi_x alloys (x = 0.122 and 0.20) have been studied by neutron diffraction and small-angle neutron scattering (SANS), as well as measurements performed on pure liquid Al. All measurements have been performed at five temperatures in a heating–cooling loop. The SANS results unambiguously show that for the eutectic alloy (x = 0.122) the microstructure changes with increasing temperature in a partly reversible way while for the hypereutectic (x = 0.20) alloy the change is almost completely irreversible. This change in microstructure also manifests itself in the shape of the static structure factor S(Q).     

Non-ergodicity in a locally ordered fragile glass former

We measure the dynamic structure factor of m-toluidine through inelastic X-ray scattering in the mesoscopic Q range between 1 and 10 nm⁻¹, where the static structure factor exhibits a prepeak resulting from a molecular spatial organization in nanometer size clusters, due to the formation of hydrogen bonds. We present experimental evidence of the square-root cusp in the temperature behavior of the non-ergodicity factor of m-toluidine which supports the view that the mode-coupling theory succeeds in describing the dynamics of supercooled molecular liquids, even for liquids with a local order, notwithstanding the cage formation is controlled by a mechanism different from the packing constraints typical of simple liquids. Moreover, we report on the behavior of the non-ergodicity factor in the low-temperature and wavevector regimes, finding a confirmation of the phenomenologic law proposed by Scopigno et al. [T. Scopigno, G. Ruocco, F. Sette, G. Monaco, Science 302 (2003) 849] which correlates the vibrational dynamics of the glass to the fragility of the supercooled liquid.     

Quantitative Raman spectroscopy: High-temperature speciation of potassium silicate melts

In situ, high-temperature Raman spectroscopy was used to study the Qⁿ speciation in binary potassium silicate melts. Over 300 Raman spectra in the compositional range from 20 to 38 mol% K₂O were collected at temperatures between 800 and 1200 K. Quantitative information on the relative abundances of species in melts was obtained from the Raman spectra through a quantification procedure that does not require any a priori assumptions about the line shapes or external calibration of the Raman scattering efficiencies for the various Qⁿ species. The ΔH⁰ associated with the speciation reaction 2Q³ = Q⁴ + Q² was found to be 33.1 ± 7.3 kJ/mol.     

Protein–solvent and weak protein–protein interactions in halophilic malate dehydrogenase

With the aim to correlate the solvation, stability and solubility properties of halophilic malate dehydrogenase, we characterized its weak interparticle interactions by small-angle neutron scattering in various solvents. The protein concentration dependence of the apparent radius of gyration and forward scattered intensity extrapolated from Guinier plots, and thus the second virial coefficient, A₂, were determined for each solvent condition. In NaCl 1M+2-methylpentane-2,4-diol 30%, a solvent that promotes protein crystallization, A₂ is negative, −0.4×10⁻⁴ ml mol g⁻² and indicating attractive interactions; in ammonium sulfate 3M, in which the protein precipitates at high concentrations, A₂∼0. In 2–5M NaCl, 1–3.5M NaOAc, 1–4.5M KF or 1–2M (NH₄)₂SO₄, in which the protein is very soluble, A₂ is positive with a value of the order of 0.4×10⁻⁴ ml mol g⁻² which decreases with increasing salt concentration. In MgCl₂ however, A₂ increases with increasing salt concentration from 0.2 to 1.3M.