Lattice Motion Research Articles

Effects of surface motion and electron-hole pair excitations in CO2 dissociation and scattering on Ni(100).

The energy transfer between different channels is an important aspect in chemical reactions at surfaces. We investigate here in detail the energy transfer dynamics in a prototypical system, i.e., reactive and nonreactive scattering of CO2 on Ni(100), which is related to heterogeneous catalytic processes with Ni-based catalysts for CO2 reduction. On the basis of our earlier nine-dimensional potential energy surface for CO2/Ni(100), dynamical calculations have been done using the generalized Langevin oscillator (GLO) model combined with local density friction approximation (LDFA), in which the former accounts for the surface motion and the latter accounts for the low-energy electron-hole pair (EHP) excitation. In spite of its simplicity, it is found that the GLO model yields quite satisfactory results, including the significant energy loss and product energy disposal, trapping, and steering dynamics, all of which agree well with the ab initio molecular dynamics ones where many surface atoms are explicitly involved with high computational cost. However, the GLO model fails to describe the reactivity enhancement due to the lattice motion because it intrinsically does not incorporate the variance of barrier height on the surface atom displacement. On the other hand, in LDFA, the energy transferred to EHPs is found to play a minor role and barely alter the dynamics, except for slightly reducing the dissociation probabilities. In addition, vibrational state-selected dissociative sticking probabilities are calculated and previously observed strong mode specificity is confirmed. Our work suggests that further improvement of the GLO model is needed to consider the lattice-induced barrier lowering.

Direct Observation of Inner-Layer Inward Contractions of Multiwalled Boron Nitride Nanotubes upon in Situ Heating

In situ heating transmission electron microscopy observations clearly reveal remarkable interlayer expansion and inner-layer inward contraction in multi-walled boron nitride nanotubes (BNNTs) as the specimen temperature increases. We interpreted the observed inward contraction as being due to the presence of the strong constraints of the outer layers on radial expansion in the tubular structure upon in situ heating. The increase in specimen temperature upon heating can create pressure and stress toward the tubular center, which drive the lattice motion and yield inner diameter contraction for the multi-walled BNNTs. Using a simple model involving a wave-like pattern of layer-wise distortion, we discuss these peculiar structural alterations and the anisotropic thermal expansion properties of the tubular structures. Moreover, our in situ atomic images also reveal Russian-doll-type BN nanotubes, which show anisotropic thermal expansion behaviors.

Beyond a phenomenological description of magnetostriction

Magnetostriction, the strain induced by a change in magnetization, is a universal effect in magnetic materials. Owing to the difficulty in unraveling its microscopic origin, it has been largely treated phenomenologically. Here, we show how the source of magnetostriction—the underlying magnetoelastic stress—can be separated in the time domain, opening the door for an atomistic understanding. X-ray and electron diffraction are used to separate the sub-picosecond spin and lattice responses of FePt nanoparticles. Following excitation with a 50-fs laser pulse, time-resolved X-ray diffraction demonstrates that magnetic order is lost within the nanoparticles with a time constant of 146 fs. Ultrafast electron diffraction reveals that this demagnetization is followed by an anisotropic, three-dimensional lattice motion. Analysis of the size, speed, and symmetry of the lattice motion, together with ab initio calculations accounting for the stresses due to electrons and phonons, allow us to reveal the magnetoelastic stress generated by demagnetization.

Phonon angular momentum and chiral phonons

In traditional physics, phonon is widely regarded as being linearly polarized, which means that phonon carries zero angular momentum. Thus the angular momentum of lattice related to mechanical rotation only reflects the lattice rigid-body motion. Recently, in a magnetic system with time reversal symmetry broken by spin-phonon interaction, one found that the phonon angular momentum is nonzero and an odd function of magnetization. At zero temperature, phonon was reported to have a zero-point angular momentum and zero-point energy. Thus the gyromagnetic ratio obtained through the Einstein-de Haas effect needs correcting by considering the nonzero phonon angular momentum. As is well known, if phonon has nonzero angular momentum, which means that phonon can have rotation, it can be right-handed or left-handed, that is, the phonon is chiral. Actually, we can define the polarization of phonon to represent the phonon chirality, which comes from the circular vibration of sublattices. When the phonon polarization is larger (less) than zero, the phonon is right (left)-handed. In non-magnetic honeycomb AB lattices, with inversion symmetrybrocken, the chiral phonons are found to be of valley contrasting circular polarization and concentrated in Brillouin-zone corners. At valleys, there is a three-fold rotational symmetry endowing phonons with quantized pseudo angular momentum. Then conversation of pseudo angular momentum, which determines the selection rules in phonon-involved intervalley scattering of electrons, must be satisfied. Chiral valley phonons can be measured by polarized infrared absorption or emission. In addition, since the phonon Berry curvature is reported to be nonzero at valley, it can distort phonon transport under a strain gradient, which can act as an effective magnetic field. Thus, a valley phonon Hall effect is theoretically predicted, which is probably a method of measuring chiral valley phonons. In consideration of phonons angular momentum and chiral phonons, photon helicity changed by phonons at Gamma point will be explained reasonably. In conclusion, chiral phonons are present in systems that break time reversal or spatial inversion symmetries. In a magnetic system, where time reversal symmetry is broken, phonons generally carry a nonzero angular momentum, which can influence the classic Einstein-de Haas effect. In a nonequilibrium system, the phonon Hall effect can be observed due to the chiral phonons. In a non-magnetic crystal, with inversion symmetry brocken, phonons in the Brillouin-zone center and corners are chiral and have a quantized pseudo angular momentum, providing an alternative to valleytronics in insulators. We believe that the findings of the phonon angular momentum and the chiral phonons together with phonon pseudoangular momentum, selection rules, and valley phonon Hall effect will lead to the relevant exploration and new development of phonon related subject in condensed matter physics.

H2 Dissociation on H Precovered Ni(111) Surfaces: Coverage Dependence, Lattice Motion, and Arrangement Effects

Hydrogen molecule dissociation on metal surfaces is a prototype reaction to study the gas–surface interaction. The dissociation rate constants of H2 on H atom precovered Ni(111) surfaces are calculated using the quantum instanton method in full dimensionality. Four different arrangements of the preadsorbed H and the dissociated H2, in which the preadsorbed H is located at the nearest (H2/H1–Ni(111)), second-nearest (H2/H2–Ni(111)), third-nearest (H2/H3–Ni(111)), and fourth-nearest (H2/H4–Ni(111)) neighbor sites of the bridge site where the H2 is dissociated, are considered. Compared to the dissociation rates of H2 on a clean Ni(111) surface (H2/Ni(111)), the dissociation rates of H2/H1–Ni(111) are much smaller. For instance, the former is 5.22 times larger than the latter at 300 K. This is because there is a strong repulsive interaction between the preadsorbed H and H2, which hinders the dissociation of H2. The dissociation rates of the four arrangements increase in the order of H2/H1–Ni(111), H2/H2–Ni(11...

Domain switching behavior in lead zirconate titanate piezoelectric ceramics

The domain switching behaviors of lead zirconate titanate ceramics were monitored via direct, in-situ lattice observation using transmission electron microscopy. The lattice structures were monitored via video as a sample was heated from room temperature to 300°C. The lattices vibrated in the [110] direction several times over a short period, e.g., 0.1s. Moreover, lattice sliding occurred in the [100] direction for about 15Å. Those lattice motions were detected at around 83–84°C. Lattice orientations were analyzed using the domain switching model to substantiate whether these movements can be attributed to domain switching.

An affine quantum cohomology ring for flag manifolds and the periodic Toda lattice

Consider the generalized flag manifold $G/B$ and the corresponding affine flag manifold $\mathcal{Fl}_G$. In this paper we use curve neighborhoods for Schubert varieties in $\mathcal{Fl}_G$ to construct certain affine Gromov-Witten invariants of $\mathcal{Fl}_G$, and to obtain a family of "affine quantum Chevalley" operators $\Lambda_0, \ldots, \Lambda_n$ indexed by the simple roots in the affine root system of $G$. These operators act on the cohomology ring $\mathrm{H}^*(\mathcal{Fl}_G)$ with coefficients in $\mathbb{Z}[q_0, \ldots,q_n]$. By analyzing commutativity and invariance properties of these operators we deduce the existence of two quantum cohomology rings, which satisfy properties conjectured earlier by Guest and Otofuji for $G= \mathrm{SL}_n(\mathbb{C})$. The first quantum ring is a deformation of the subalgebra of $\mathrm{H}^*(\mathcal{Fl}_G)$ generated by divisors. The second ring, denoted $\mathrm{QH}^*_{\mathrm{af}}(G/B)$, deforms the ordinary quantum cohomology ring $\mathrm{QH}^*(G/B)$ by adding an affine quantum parameter $q_0$. We prove that $\mathrm{QH}^*_{\mathrm{af}}(G/B)$ is a Frobenius algebra, and that the new quantum product determines a flat Dubrovin connection. Further, we develop an analogue of Givental and Kim formalism for this ring and we deduce a presentation of $\mathrm{QH}^*_{\mathrm{af}}(G/B)$ by generators and relations. The ideal of relations is generated by the integrals of motion for the periodic Toda lattice associated to the dual of the extended Dynkin diagram of $G$.

Effect of disorder on exciton dissociation in conjugated polymers**Project supported by the National Natural Science Foundation of China (Grant Nos. 11474218 and 11575116).

By using a multi-configurational time-dependent Hartree–Fock (MCTDHF) method for the time-dependent Schrödinger equation and a Newtonian equation of motion for lattice, we investigate the disorder effects on the dissociation process of excitons in conjugated polymer chains. The simulations are performed within the framework of an extended version of the Su–Schrieffer–Heeger model modified to include on-site disorder, off-diagonal, electron–electron interaction, and an external electric field. Our results show that Coulomb correlation effects play an important role in determining the exciton dissociation process. The electric field required to dissociate an exciton can practically impossibly occur in a pure polymer chain, especially in the case of triplet exciton. However, when the on-site disorder effects are taken into account, this leads to a reduction in mean dissociation electric fields. As the disorder strength increases, the dissociation field decreases effectively. On the contrary, the effects of off-diagonal disorder are negative in most cases. Moreover, the dependence of exciton dissociation on the conjugated length is also discussed.

Dislocation Creep: Climb and Glide in the Lattice Continuum

A continuum theory for high temperature creep of polycrystalline solids is developed. It includes the relevant deformation mechanisms for diffusional and dislocation creep: elasticity with eigenstrains resulting from vacancy diffusion, dislocation climb and glide, and the lattice growth/loss at the boundaries enabled by diffusion. All the deformation mechanisms are described with respect to the crystalline lattice, so that the continuum formulation with lattice motion as the basis is necessary. However, dislocation climb serves as the source sink of lattice sites, so that the resulting continuum has a sink/source of its fundamental component, which is reflected in the continuity equation. Climb as a sink/source also affects the diffusion part of the problem, but the most interesting discovery is the climb-glide interaction. The loss/creation of lattice planes through climb affects the geometric definition of crystallographic slip and necessitates the definition of two slip fields: the true slip and the effective slip. The former is the variable on which the dissipative power is expanded during dislocation glide and is thus, the one that must enter the glide constitutive equations. The latter describes the geometry of the slip affected by climb, and is necessary for kinematic analysis.

The dissociation and recombination rates of CH4 through the Ni(111) surface: The effect of lattice motion.

Methane dissociation is a prototypical system for the study of surface reaction dynamics. The dissociation and recombination rates of CH4 through the Ni(111) surface are calculated by using the quantum instanton method with an analytical potential energy surface. The Ni(111) lattice is treated rigidly, classically, and quantum mechanically so as to reveal the effect of lattice motion. The results demonstrate that it is the lateral displacements rather than the upward and downward movements of the surface nickel atoms that affect the rates a lot. Compared with the rigid lattice, the classical relaxation of the lattice can increase the rates by lowering the free energy barriers. For instance, at 300 K, the dissociation and recombination rates with the classical lattice exceed the ones with the rigid lattice by 6 and 10 orders of magnitude, respectively. Compared with the classical lattice, the quantum delocalization rather than the zero-point energy of the Ni atoms further enhances the rates by widening the reaction path. For instance, the dissociation rate with the quantum lattice is about 10 times larger than that with the classical lattice at 300 K. On the rigid lattice, due to the zero-point energy difference between CH4 and CD4, the kinetic isotope effects are larger than 1 for the dissociation process, while they are smaller than 1 for the recombination process. The increasing kinetic isotope effect with decreasing temperature demonstrates that the quantum tunneling effect is remarkable for the dissociation process.

Effect of atomic flux reversal in a fluctuating moving optical lattice

The dynamics of an ensemble of noninteracting cold atoms is considered in the field of a moving optical lattice subjected to random amplitude and phase fluctuations. The effect of the reversal of an atomic ensemble under the action of lattice fluctuations is demonstrated, in which the atoms begin to move in the direction opposite to that of the lattice motion. A kinetic model is constructed that reproduces this effect and makes it possible to relate its emergence to the asymmetry of the amplitudes of the interlevel transitions in a momentum space.

Lattice effects of surface cell: Multilayer multiconfiguration time-dependent Hartree study on surface scattering of CO/Cu(100)

To study the scattering of CO off a movable Cu(100) surface, extensive multilayer multiconfiguration time-dependent Hartree (ML-MCTDH) calculations are performed based on the SAP [R. Marquardt et al., J. Chem. Phys. 132, 074108 (2010)] potential energy surface in conjunction with a recently developed expansion model [Q. Meng and H.-D. Meyer, J. Chem. Phys. 143, 164310 (2015)] for including lattice motion. The surface vibration potential is constructed by a sum of Morse potentials where the parameters are determined by simulating the vibrational energies of a clean Cu(100) surface. Having constructed the total Hamiltonian, extensive dynamical calculations in both time-independent and time-dependent schemes are performed. Two-layer MCTDH (i.e., normal MCTDH) block-improved-relaxations (time-independent scheme) show that increasing the number of included surface vibrational dimensions lets the vibrational energies of CO/Cu(100) decrease for the frustrated translation (T mode), which is of low energy but increase those of the frustrated rotation (R mode) and the CO–Cu stretch (S mode), whose vibrational energies are larger than the energies of the in-plane surface vibrations (∼79 cm−1). This energy-shifting behavior was predicted and discussed by a simple model in our previous publication [Q. Meng and H.-D. Meyer, J. Chem. Phys. 143, 164310 (2015)]. By the flux analysis of the MCTDH/ML-MCTDH propagated wave packets, we calculated the sticking probabilities for the X + 0D, X + 1D, X + 3D, X + 5D, and X + 15D systems, where “X” stands for the used dimensionality of the CO/rigid-surface system and the second entry denotes the number of surface degrees of freedom included. From these sticking probabilities, the X + 5D/15D calculations predict a slower decrease of sticking with increasing energy as compared to the sticking of the X + 0D/1D/3D calculations. This is because the translational energy of CO is more easily transferred to surface vibrations, when the vibrational dimensionality of the surface is enlarged.

Vortex creep at very low temperatures in single crystals of the extreme type-II superconductor Rh9In4S4

We image vortex creep at very low temperatures using Scanning Tunneling Microscopy (STM) in the superconductor Rh$_9$In$_4$S$_4$ ($T_c$=2.25 K). We measure the superconducting gap of Rh$_9$In$_4$S$_4$, finding $\Delta\approx 0.33$meV and image a hexagonal vortex lattice up to close to H$_{c2}$, observing slow vortex creep at temperatures as low as 150 mK. We estimate thermal and quantum barriers for vortex motion and show that thermal fluctuations likely cause vortex creep, in spite of being at temperatures $T/T_c<0.1$. We study creeping vortex lattices by making images during long times and show that the vortex lattice remains hexagonal during creep with vortices moving along one of the high symmetry axis of the vortex lattice. Furthermore, the creep velocity changes with the scanning window suggesting that creep depends on the local arrangements of pinning centers. Vortices fluctuate on small scale erratic paths, indicating that the vortex lattice makes jumps trying different arrangements during its travel along the main direction for creep. The images provide a visual account of how vortex lattice motion maintains hexagonal order, while showing dynamic properties characteristic of a glass.

Ab Initio Molecular Dynamics Study of Dissociative Chemisorption and Scattering of CO2 on Ni(100): Reactivity, Energy Transfer, Steering Dynamics, and Lattice Effects

The dissociative chemisorption of polyatomic molecules on metal surfaces has attracted much interest in recent years due to their industrial and fundamental importance. Comparing with extensively studied systems such as methane and water, however, dissociative chemisorption of CO2, which is important for CO2 activation, has so far received scant attention. We recently reported vibrational enhancement of the dissociative chemisorption of CO2 on a rigid Ni(100) surface using a nine-dimensional potential energy surface (PES) based on a large number of density functional theory calculations. However, that PES is incapable of describing the lattice motion and energy transfer between this heavy molecule and the surface. To overcome these limitations, we present here ab initio molecular dynamics results for CO2 scattering and dissociation. In addition to formation of adsorbed O and CO, CO2 is found to have a large trapping probability in a chemisorption well, along with a substantial amount of energy loss to sur...

Water dissociation on Ni(100), Ni(110), and Ni(111) surfaces: Reaction path approach to mode selectivity.

A comparative study of mode-selectivity of water dissociation on Ni(100), Ni(110), and Ni(111) surfaces is performed at the same level of theory using a fully quantum approach based on the reaction path Hamiltonian. Calculations show that the barrier to water dissociation on the Ni(110) surface is significantly lower compared to its close-packed counterparts. Transition states for this reaction on all three surfaces involve the elongation of one of the O-H bonds. A significant decrease in the symmetric stretching and bending mode frequencies near the transition state is observed in all three cases and in the vibrational adiabatic approximation, excitation of these softened modes results in a significant enhancement in reactivity. Inclusion of non-adiabatic couplings between modes results in the asymmetric stretching mode showing a similar enhancement of reactivity as the symmetric stretching mode. Dissociation probabilities calculated at a surface temperature of 300 K showed higher reactivity at lower collision energies compared to that of the static surface case, underlining the importance of lattice motion in enhancing reactivity. Mode selective behavior is similar on all the surfaces. Molecules with one-quantum of vibrational excitation in the symmetric stretch, at lower energies (up to ∼0.45 eV), are more reactive on Ni(110) than the Ni(100) and Ni(111) surfaces. However, the dissociation probabilities approach saturation on all the surfaces at higher incident energy values. Overall, Ni(110) is found to be highly reactive toward water dissociation among the low-index nickel surfaces owing to a low reaction barrier resulting from the openness and corrugation of the surface. These results show that the mode-selective behavior does not vary with different crystal facets of Ni qualitatively, but there is a significant quantitative effect.

Do All X-ray Structures of Protein-Ligand Complexes Represent Functional States? EPOR, a Case Study

Based on differences between the x-ray crystal structures of ligand-bound and unbound forms, the activation of the erythropoietin receptor (EPOR) was initially proposed to involve a cross-action scissorlike motion. However, the validity of the motions involved in the scissorlike model has been recently challenged. Here, atomistic molecular dynamics simulations are used to examine the structure of the extracellular domain of the EPOR dimer in the presence and absence of erythropoietin and a series of agonistic or antagonistic mimetic peptides free in solution. The simulations suggest that in the absence of crystal packing effects, the EPOR chains in the different dimers adopt very similar conformations with no clear distinction between the agonist and antagonist-bound complexes. This questions whether the available x-ray crystal structures of EPOR truly represent active or inactive conformations. The study demonstrates the difficulty in using such structures to infer a mechanism of action, especially in the case of membrane receptors where just part of the structure has been considered in addition to potential confounding effects that arise from the comparison of structures in a crystal as opposed to a membrane environment. The work highlights the danger of assigning functional significance to small differences between structures of proteins bound to different ligands in a crystal environment without consideration of the effects of the crystal lattice and thermal motion.

Double vibronic process in the quantum spin ice candidate Tb2Ti2O7 revealed by terahertz spectroscopy

The origin of quantum fluctuations responsible for the spin liquid state in Tb$_2$Ti$_2$O$_7$ has remained a long standing problem. By synchrotron-based terahertz measurements, we show evidence of strong coupling between the magnetic and lattice degrees of freedom that provides a path to the quantum melting process. As revealed by hybrid crystal electric field-phonon excitations that appear at 0.67 THz below 200 K, and around 0.42 THz below 50 K, the double vibronic process is unique for Tb$^{3+}$ in the titanate family due to adequate energy matching and strong quadrupolar moments. The results suggest that lattice motion can indeed be the driving force behind spin flips within the hybridized ground and first excited states, promoting quantum terms in the effective Hamiltonian that describes Tb$_2$Ti$_2$O$_7$.

Heat jet approach for finite temperature atomic simulations of two-dimensional square lattice

We propose a heat jet approach for a two-dimensional square lattice with nearest neighbouring harmonic interaction. First, we design a two-way matching boundary condition that linearly relates the displacement and velocity at atoms near the boundary, and a suitable input in terms of given incoming wave modes. Then a phonon representation for finite temperature lattice motion is adopted. The proposed approach is simple and compact. Numerical tests validate the effectiveness of the boundary condition in reflection suppression for outgoing waves. It maintains target temperature for the lattice, with expected kinetic energy distribution and heat flux. Moreover, its linear nature facilitates reliable finite temperature atomic simulations with a correct description for non-thermal motions.

Coherent Excitation of Optical Phonons in GaAs by Broadband Terahertz Pulses.

Coherent excitation and control of lattice motion by electromagnetic radiation in optical frequency range has been reported through variety of indirect interaction mechanisms with phonon modes. However, coherent phonon excitation by direct interaction of electromagnetic radiation and nuclei has not been demonstrated experimentally in terahertz (THz) frequency range mainly due to the lack of THz emitters with broad bandwidth suitable for the purpose. We report the experimental observation of coherent phonon excitation and detection in GaAs using ultrafast THz-pump/optical-probe scheme. From the results of THz pump field dependence, pump/probe polarization dependence, and crystal orientation dependence, we attributed THz wave absorption and linear electro-optic effect to the excitation and detection mechanisms of coherent polar TO phonons. Furthermore, the carrier density dependence of the interaction of coherent phonons and free carriers is reported.

Effects of Lattice Motion on Dissociative Chemisorption: Toward a Rigorous Comparison of Theory with Molecular Beam Experiments.

The dissociative chemisorption of small molecules such as methane and water on metal surfaces is a key step in many important catalyzed reactions. However, it has only very recently become possible to directly compare theory with molecular beam studies of these reactions. For most experimental conditions, such a comparison requires accurate methods for introducing the effects of lattice motion into quantum reactive scattering calculations. We examine these methods and their recent application to methane and water dissociative chemisorption. New results are presented for CO2 chemisorption and methane dissociation at step edges. The type of molecule-lattice coupling that leads to a strong variation in the dissociative sticking of methane with temperature is shown to occur for many polyatomic-metal systems. Improvements to these models are discussed. The ability to accurately compare theory with molecular beam experiments should lead to improved density functionals and consequently more accurate thermal rate constants for these important reactions.