Nonexponential relaxation in a simple liquid metal

Modified Landau-Placzek ratio of the liquid metal rubidium beyond hydrodynamics

The intensity ratio of the Rayleigh line and the Brillouin lines can be derived within hydrodynamics and is known as the Landau-Placzek (LP) ratio. This ratio is directly related to the ratio of specific heats of the fluid. Within the microscopic wave vector range, which can be probed by inelastic neutron scattering, the intensity ratio for simple liquid metals deviates distinctly from the hydrodynamic prediction of the LP-ratio. We derive the intensity ratio from experimental data of liquid rubidium, which shows an enhanced LP-ratio by a factor 8 compared to the hydrodynamic prediction. This strong deviation indicates a further relaxation process in the microscopic wave vector range beyond hydrodynamics. That relaxation process is the viscoelastic reaction of the simple liquid to density fluctuations. Taking this process into account a modified LP-ratio is able to describe the data quite well.

Non-Arrhenius behaviour of nickel self-diffusion in liquid Ni77Si23

Nickel self-diffusion was measured for a Ni₇₇Si₂₃alloy in the liquid state over a temperature range of about 400 K through quasielastic neutron scattering. At the two lowest temperature points the derived diffusion coefficients deviate from a high-temperature Arrhenius-type behaviour and indicate a change in dynamics above the liquidus temperature. A fit with a power-law temperature dependence as predicted by the mode coupling theory for the liquid to glass transition can describe the diffusion coefficients quite well over the whole measured temperature range. The obtained results agree with predictions from a classical molecular dynamics (MD)-simulation, which evidenced an increasing glass forming ability with increasing silicon content. A crossover to a super-Arrhenius behaviour was reported for metallic glass formers above the liquidus temperature and the here investigated NiSi alloy demonstrates the same signature.

The intimate relationship between structural relaxation and the energy landscape of monatomic liquid metals

The characteristic property of a liquid, discriminating it from a solid, is its fluidity, which can be expressed by a velocity field. The reaction of the velocity field on forces is enshrined in the transport parameter viscosity. In contrast, a solid reacts to forces elastically through a displacement field, the particles are trapped in their potential minimum. The flow in a liquid needs enough thermal energy to overcome the changing potential barriers, which is supported through a continuous rearrangement of surrounding particles. Cooling a liquid will decrease the fluidity of a particle and the mobility of the neighbouring particles, resulting in an increase of the viscosity until the system comes to an arrest. This process with a concomitant slowing down of collective particle rearrangements might already start deep inside the liquid state. The idea of the potential energy landscape provides an attractive picture for these dramatic changes. However, despite the appealing idea there is a scarcity of quantitative assessments, in particular, when it comes to experimental studies. Here we present results on a monatomic liquid metal through a combination of ab initio molecular dynamics, neutron spectroscopy and inelastic x-ray scattering. We investigated the collective dynamics of liquid aluminium to reveal the changes in dynamics when the high temperature liquid is cooled towards solidification. The results demonstrate the main signatures of the energy landscape picture, a reduction in the internal atomic structural energy, a transition to a stretched relaxation process and a deviation from the high-temperature Arrhenius behavior of the relaxation time. All changes occur in the same temperature range at about [Formula: see text], which can be regarded as the temperature when the liquid aluminium enters the landscape influenced phase and enters a more viscous liquid state towards solidification. The similarity in dynamics with other monatomic liquid metals suggests a universal dynamic crossover above the melting point.

Dynamics on next-neighbour distances in liquid and undercooled gallium

Density fluctuations of liquid and 20 K undercooled gallium have been studied by neutron spectroscopy. The decay of density fluctuations has been recorded at the structure factor maximum over a wide temperature range up to twice the melting temperature. The amplitude of the scattering function falls off with rising temperature in a nonlinear way with a changing slope around [Formula: see text]. The derived generalized longitudinal viscosity shows an upturn with decreasing temperature in the same temperature range. This increase in viscosity can be understood that liquid gallium transforms from a more fluid liquid metal to a more viscous liquid metal in that temperature range upon cooling. The change in the amplitude shows a remarkable agreement with results from liquid aluminium, lead and rubidium. This study suggests a universal crossover in dynamics of liquid monatomic metals, despite the many peculiar properties of gallium.

Stokes-Einstein relation of the liquid metal rubidium and its relationship to changes in the microscopic dynamics with increasing temperature

For liquid rubidium the Stokes-Einstein (SE) relation is well fulfilled near the melting point with an effective hydrodynamic diameter, which agrees well with a value from structural investigations. A wealth of thermodynamic and microscopic data exists for a wide range of temperatures for liquid rubidium and hence it represents a good test bed to challenge the SE relation with rising temperature from an experimental point of view. We performed classical molecular dynamics simulations to complement the existing experimental data using a pseudopotential, which describes perfectly the structure and dynamics of liquid rubidium. The derived SE relation from combining experimental shear viscosity data with simulated diffusion coefficients reveals a weak violation at about 1.3T_{melting}≈400 K. The microscopic relaxation dynamics on nearest neighbor distances from neutron spectroscopy demonstrate distinct changes in the amplitude with rising temperature. The derived average relaxation time for density fluctuations on this length scale shows a non-Arrhenius behavior, with a slope change around 1.5T_{melting}≈450 K. Combining the simulated macroscopic self-diffusion coefficient with that microscopic average relaxation time, a distinct violation of the SE relation in the same temperature range can be demonstrated. One can conclude that the changes in the collective dynamics, a mirror of the correlated movements of the particles, are at the origin for the violation of the SE relation. The changes in the dynamics can be understood as a transition from a more viscous liquid metal to a more fluid-like liquid above the crossover temperature range of 1.3-1.5 T_{melting}. The decay of the amplitude of density fluctuations in liquid aluminium, lead, and rubidium demonstrates a remarkable agreement and points to a universal thermal crossover in the dynamics of liquid metals.

Wave vector dependent damping of THz collective modes in a liquid metal

Well-defined damped collective modes have been observed in liquid metals over a wide range of wave vectors. Hydrodynamics predicts that viscosity and thermal conductivity are the cause for the damping of the collective modes. Here we present experimental data from neutron spectroscopy on the damping of collective modes of liquid rubidium over a wide range of wave vectors. We propose a phenomenological model derived from generalized hydrodynamics to describe the damping of the modes and the evolution with increasing wave vector based on the viscoelastic picture of liquid response. As necessary ingredients a wave vector dependent high frequency shear modulus and shear relaxation time appear. We obtain a remarkable good agreement on a quantitative basis between experiment and calculation over a wide range of wave vectors. The emergent picture is that the lifetime of the collective modes in the THz regime is mainly limited through the diffusion of momentum. The proposed methodology might be applicable to a wide range of liquids.

De Gennes Narrowing and Hard-Sphere Approach

The energy width Δω of the quasielastic coherent dynamic structure factor S(Q, ω) for a simple liquid exhibits the oscillating dependence on wavenumber Q with the sharp minimum at Qmax corresponding to the maximum of the structure factor S(Q). The only known expression for Δω(Q) was derived for a dense hard-sphere (HS) fluid (Cohen et al., Phys. Rev. Lett. 1987, 59, 2872). Though this expression has been frequently used for the analysis of the experimental data obtained for liquid metals, until now, it has never been tested against a true HS fluid. A test performed by means of HS molecular dynamic simulations reveals a considerable discrepancy between the simulations results and the examined model. The main output of the analysis is the finding that the ΔωHS(Q) behavior is defined in terms of the average cage size, ⟨Lc⟩, rather than of the HS diameter, σHS. The simulated ΔωHS(Q) has been compared with the results for the soft-spherical potential. The microscopic dynamics of the soft-sphere fluid shows significant difference in comparison to the HS system. Nevertheless, the diffusive mobility of soft spheres can be characterized within the HS approximation using an effective diameter, σeff, and this parameter can be found from Δω(Q) at Q ≈ Qmax. A similar result has been obtained for the neutron scattering data measured for liquid Rb.

Experimental evidence for a dynamical crossover in liquid aluminium

The temperature dependence of the dynamic structure factor at next-neighbour distances has been investigated for liquid aluminium. This correlation function is a sensitive parameter for changes in the local environment and its Fourier transform was measured in a coherent inelastic neutron scattering experiment. The zero frequency amplitude decreases in a nonlinear way and indicates a change in dynamics around 1.4 ∙ Tmelting. From that amplitude a generalized viscosity can be derived which is a measure of local stress correlations on next-neighbour distances. The derived generalized longitudinal viscosity shows a changing slope at the same temperature range. At this temperature the freezing out of degrees of freedom for structural relaxation upon cooling sets in which can be understood as a precursor towards the solid state. That crossover in dynamics of liquid aluminium shows the same signatures as previously observed in liquid rubidium and lead, indicating an universal character.

Exponential series expansion for correlation functions of many-body systems

We demonstrate that in Hamiltonian many-body systems at equilibrium, any kind of time dependent correlation function c(t) can always be expanded in a series of (complex) exponential functions of time when its Laplace transform C̃(z) has single poles. The characteristic frequencies can be identified as the eigenfrequencies of the correlation. This is done without introducing the concepts of fluctuating forces and memory functions, due to Mori and Zwanzig and extensively used in the literature in the last decades. Our method is based on a different projection technique in the Hilbert space S of the system and shows that appropriate approximations of the exponential series are related to the contraction of S to a finite, usually small, number of dimensions. The time dependence of correlation functions is always described in detail by a multiple-exponential functionality also at long times. This result is therefore also valid for correlation functions of many-body Hamiltonian systems for which a power-law dependence, observed in restricted time ranges and predicted to be the asymptotic one, can be considered at most as a useful approximate modeling of long-time behavior.

Expansion in Lorentzian functions of spectra of quantum autocorrelations

We show that in a quantum mechanical many-body system of Boltzmann particles having space inversion symmetry the spectrum of the autocorrelation function of a local observable can always be given, similarly to the classical case [Phys. Rev. E 85, 022102 (2012)], in terms of a series of Lorentzian functions multiplied by the proper quantum detailed balance factor. This is done by transforming the continued fraction representation, which is derived via recurrent relations and without the use of the generalized Langevin equation hierarchy, into a series expansion. In this way characteristic frequencies can be defined, also in quantum mechanics, which refer to the particular autocorrelation. These are the frequencies of the eigenmodes of the relaxation function connected to the observable. We also show that in practical cases of interest in experimental spectroscopy, and particularly in inelastic neutron and x-ray scattering, the use of a finite number of Lorentzian shapes for an approximate description of the data is related to a reduction of the number of the relevant dynamical variables taken into account, equivalent to the lowering of the dimensionality of the orthogonalized space onto which the dynamic of the system is projected. Examples of application are given for the spectrum of the velocity autocorrelation function of liquid parahydrogen, calculated with a quantum simulation algorithm (path-integral centroid molecular dynamics), and for the molecular center-of mass dynamic structure factor in liquid carbon dioxide as computed by means of classical molecular dynamics simulation.