Time-dependent Pair Distribution Function Research Articles

Ultrafast formation of a transient two-dimensional diamondlike structure in twisted bilayer graphene

Due to the absence of matching carbon atoms at honeycomb centers with carbon atoms in adjacent graphene sheets, theorists predicted that a sliding process is needed to form AA, AB, or ABC stacking when directly converting graphite into sp3 bonded diamond. Here, using twisted bilayer graphene, which naturally provides AA and AB stacking configurations, we report the ultrafast formation of a transient 2D diamond-like structure (which is not observed in aligned graphene) under femtosecond laser irradiation. This photo-induced phase transition is evidenced by the appearance of new bond lengths of 1.94A and 3.14A in the time-dependent differential pair distribution function using MeV ultrafast electron diffraction. Molecular dynamics and first principles calculation indicate that sp3 bonds nucleate at AA and AB stacked areas in moire pattern. This work sheds light on the direct graphite-to-diamond transformation mechanism, which has not been fully understood for more than 60 years.

Experimental determination of the temperature-dependent Van Hove function in a Zr80Pt20 liquid

Even though the viscosity is one of the most fundamental properties of liquids, the connection with the atomic structure of the liquid has proven elusive. By combining inelastic neutron scattering with the electrostatic levitation technique, the time-dependent pair-distribution function (i.e., the Van Hove function) has been determined for liquid Zr80Pt20. We show that the decay time of the first peak of the Van Hove function is directly related to the Maxwell relaxation time of the liquid, which is proportional to the shear viscosity. This result demonstrates that the local dynamics for increasing or decreasing the coordination number of local clusters by one determines the viscosity at high temperature, supporting earlier predictions from molecular dynamics simulations.

Time-dependent pair distribution functions based on Smoluchowski equation and application to an electrolyte solution.

Time-dependent pair distribution function characterizes the diffusion of pairs of molecules in liquids. In the diffusion regime, the function is described with three-dimensional Smoluchowski equation. We propose a scheme to numerically calculate the function between polyatomic and monoatomic species based on the Smoluchowski equation. The present scheme is successfully applied to the diffusion of Ar-Ar pair in liquid Ar and ethylene carbonate (EC)-Li+ pair in 1 M LiPF6 /EC electrolyte solution. © 2018 Wiley Periodicals, Inc.

Clustering and percolation theory for continuum systems: Clusters with nonspecific bonds and a residence time in their definition

In this article, dedicated to the memory of Lesser Blum, we develop a theory for the physical clusters which were introduced some time ago in our group (J. Chem Phys. 116, 1097–1108, 2002). The physical cluster definition establishes that a system particle belongs to the cluster if it is (nonspecifically) bonded to other particles of the cluster along a finite time period τ (the residence time). Our theory has as main ingredients the Stillinger criterion of instantaneous connectivity, that involves a connectivity distance d, the generalized time-dependent pair distribution function of Oppenheim and Bloom that acts as a classical propagator and also the cluster pair correlation function for a weaker version of the physical clusters that requires connectivity just at the extremes of the time period no matter what happens in between. With these tools we express the time dependent pair connectedness function for the physical clusters in the strong sense as a path integral. The path integral is solved by means of a perturbation expansion where the nonperturbed connectedness function coincides with the generalized pair distribution function of Oppenheim and Bloom. We apply the theory to Lennard-Jones fluids at low densities and perform molecular dynamics simulations to check the goodness of diverse functions that appear in the theory.

Zwanzig-Mori equation for the time-dependent pair distribution function

We develop a microscopic theoretical framework for the time-dependent pair distribution function starting from the Liouville equation. An exact Zwanzig-Mori equation of motion for the time-dependent pair distribution function is derived based on the projection-operator formalism. It is demonstrated that, under the Markovian approximation, our equation reduces to the so-called telegraph equation that includes the potential of mean force acting between the pair particles. With the additional approximation neglecting the inertia term, our equation takes the form of Smoluchowski's equation, which has been previously introduced with intuitive arguments and shown to satisfactorily reproduce the simulation results of the particle-pair dynamics.

Pair dynamics in a glass-forming binary mixture: simulations and theory.

We have carried out molecular dynamics simulations to understand the dynamics of a tagged pair of atoms in a strongly nonideal glass-forming binary Lennard-Jones mixture. Here atom B is smaller than atom A (sigma(BB)=0.88sigma(AA), where sigma(AA) is the molecular diameter of the A particles) and the AB interaction is stronger than that given by Lorentz-Berthelot mixing rule (epsilon(AB)=1.5epsilon(AA), where epsilon(AA) is the interaction energy strength between the A particles). The generalized time-dependent pair distribution function is calculated separately for the three pairs (AA, BB, and AB). The three pairs are found to behave differently. The relative diffusion constants are found to vary in the order D(BB)(R)>D(AB)(R)>D(AA)(R), with D(BB)(R) approximately 2D(AA)(R), showing the importance of the hopping process (B hops much more than A). We introduce a non-Gaussian parameter [alpha(P)(2)(t)] to monitor the relative motion of a pair of atoms and evaluate it for all the three pairs with initial separations chosen to be at the first peak of the corresponding partial radial distribution functions. At intermediate times, significant deviation from the Gaussian behavior of the pair distribution functions is observed with different degrees for the three pairs. A simple mean-field (MF) model, proposed originally by Haan [Phys. Rev. A 20, 2516 (1979)] for one-component liquid, is applied to the case of a binary mixture and compared with the simulation results. While the MF model successfully describes the dynamics of the AA and AB pairs, the agreement for the BB pair is less satisfactory. This is attributed to the large scale anharmonic motions of the B particles in a weak effective potential. Dynamics of the next nearest neighbor pairs is also investigated.

Vibrational motions of hydrogen bonds from the short time relative pair dynamics

The short time dynamics of pairs of water molecules, initially lying in the first coordination shell, is investigated via molecular dynamics simulation. The introduction of the generalized time-dependent pair distribution function allows to obtain a relationship between the dynamics and the local structure. The relationship explains the different short time behaviors between the hydrogen-bonded molecules and the structural defects, and the lack of the free flight time dependence of the mean-square distance. The centers of mass vibrational motion of hydrogen-bonded molecules influences the relative pair dynamics beyond the short time expansion. An approach, based on the instantaneous normal modes theory, is proposed to derive the vibrational motion of the hydrogen bonds. Its general applicability is stressed and the particular relevance for studying systems whose dynamics is determined by strong oriented interactions is suggested.

Relative motions in atomic fluids: A molecular dynamics investigation

The generalized time-dependent pair distribution function G 2( R, R '; t) is examined for the first time by two molecular dynamics experiments in Lennard-Jones argon at room temperature and different densities. This function gives insight into the relative motion of atoms and plays an important role in all collision-induced phenomena. The results stress the features of G 2 at intermediate and long times; in the latter case they are found to be in agreement with a simple theoretical model. The behavior of some physical quantities dependent on the relative motion of atoms is also discussed.

Time-dependent pair distribution in the mean-field approximation

The time-dependent pair-distribution function, which plays a central role in the description of nuclear magnetic relaxation and collision-induced absorption in classical fluids, is evaluated in a mean-field approximation proposed earlier. In this scheme the binary dynamics of the colliding pair is treated without approximation, and the interaction with the background fluid is taken into account via a renormalization of the pair potential. The result is expressed in terms of orbits having specified end points and specified elapsed times.

Time-dependent pair distribution function: The constant acceleration approximation revisited

The constant-acceleration approximation for the time-dependent pair distribution function as introduced by Bloom and Oppenheim is critically examined. The previously noted inconsistencies for the initial behaviour of the correlation functions are eliminated by a proper treatment of the short time dynamics.

Nuclear quadrupolar relaxation in molten salts

From the straightforward extension of a general theory for nuclear quadrupolar spin–lattice relaxation in monatomic liquids the rate RQ,α for an α ion in a simple uni-univalent ionic melt is expressed in terms of the local electric field gradients (e.f.g.) which originate from unlike or like charges external to the ion of interest, the van Hove time-dependent pair distribution function, and the static pair distribution function between unlike or like ions. RQ,α may be approximated in terms of the partial elastic limit Sγδ(k, 0) of the dynamic liquid structure factor and the partial weighting factor Iαγ, αδ(k) involving the e.f.g. contribution. For a sodium cation in molten NaCl the terms of INaγ,Naδ(k)(γ, δ; Na or Cl) are estimated under an assumption of an electrostatic quadrupolar interaction. These numerical values are 10–100 times greater than those of I(k) for liquid Ne calculated from exchange–van der Waals e.f.g. The experimental results of the partial static-structure factor Sγδ(k) and the static pair radial distribution function gNaγ(r)(γ; Na or Cl) for molten NaCl are of great consequence in calculations of both Sγδ(k, 0) and Iαγ,αδ(k). Numerical calculation of RO,Na for the sodium cation in the molten NaCl is in rough agreement with experiment. The relaxation process of 23Na in molten NaNO3 is caused by both translation and reorientational motions. The rotation-like motion gives rise to the time dependent e.f.g. at the Na nucleus and contributes mainly to the observed relaxation rate. Numerical calculations of the temperature dependence of RQ,Na in molten NaNO3 are in no good agreement with experiment.

Renormalized theory of the time-dependent pair distribution function. I. General formulation

A classical renormalized theory of a time-dependent pair-distribution function (TDPDF), previously introduced by Oppenheim and Bloom, is presented. An equation of motion for the TDPDF is derived in which the memory function of the system appears. This is then split into a part which contains only static correlation functions and a part which describes the dynamics. The mean field approximation is discussed in some detail and contact is made witn the theory of Oppenheim and Bloom.

A theory of the diffusion coefficient in a liquid metal : II

Abstract Calculations are reported of the diffusion coefficient and frequency spectrum of the velocity autocorrelation function for a model of liquid sodium using long-range oscillatory interionic potentials. They are based on a theory of the associated memory function which employs a previously known expression for the timedependent pair distribution function. The latter is introduced to try to solve the difficult problem of describing the relative motion of two atoms, but the results are not consistent with the information obtained from molecular dynamics calculations. On the basis of a physical argument, a modified theory of the pair distribution is then employed and shown to produce results which are in much better agreement with those obtained from computer experiments. Some information is thereby obtained about the relative motion of atoms in a liquid.

A Theory of the Diffusion Coefficient in a Liquid Metal: I

Abstract An expression has been derived for the diffusion coefficient in terms of the interatomic potential, the pair distribution function and the selfcorrelation function in a liquid. By making use of an earlier result for the time-dependent pair distribution function, which includes correlation in the relative motion of two atoms, the expression has been made applicable to any type of interatomic core potential. In particular it will be useful in a liquid metal where a relatively soft core is a generally accepted feature of the effective interionic potential.

Nuclear quadrupole interactions in liquid and solid metals

The nuclear quadrupole relaxation time in liquid metals is calculated, assuming free-ion cores interacting by an oscillatory screened potential, and whose positions in the liquid are described by the time-dependent pair distribution function of Oppenheim and Bloom. The relaxation time depends on two- and three-particle correlation functions, and the three-particle correlations are treated by means of the superposition approximation. Uncertainties in the antishielding factor and the potential oscillations are eliminated by using the experimental value of the quadrupole coupling constant in the solid. Detailed calculations are performed for Ga and In, and good agreement with the observed relaxation time is obtained if the three-particle terms are neglected. The calculated three-particle terms are not negligible, and it is suggested that the superposition approximation introduces serious errors.

NUCLEAR SPIN RELAXATION IN GASES AND LIQUIDS: I. CORRELATION FUNCTIONS

Calculation of nuclear spin–lattice relaxation times T1 in liquids and gases involves the correlation functions of the matrix elements between different spin states of the interaction coupling the nuclear spin to other degrees of freedom of the system. The correlation functions are expressed in terms of a time-dependent pair-distribution function (TDPDF) for the system. The TDPDF is evaluated using the Wigner distribution function to describe the equilibrium ensemble of the gas or liquid. A time expansion of the dynamics of the system to a constant acceleration approximation and use of the symmetry properties of the TDPDF leads to an expression of the form[Formula: see text]This form for the TDPDF is derived for the high temperature dilute gas, for the dilute gas with first quantum correction, and for classical liquids in which the molecular dynamics can be described by the Langevin equation. The quantity g(R) is the radial distribution function appropriate to each case. The quantity P(R2, R′2, t) is the free particle TDPDF for the classical gas; it is the classical free particle TDPDF at an effective temperature for the quantum gas; it is the product of solutions to the diffusion equation for the liquid multiplied by the (density)2.