Nearest-neighbor Layers Research Articles

Spin canting and lattice symmetry in La2CuO4

While the dominant magnetic interaction in ${\mathrm{La}}_{2}{\mathrm{CuO}}_{4}$ is superexchange between nearest-neighbor Cu moments, the pinning of the spin direction depends on weak anisotropic effects associated with spin-orbit coupling. The symmetry of the octahedral tilt pattern allows an out-of-plane canting of the Cu spins, which is compensated by an opposite canting in nearest-neighbor layers. A strong magnetic field applied perpendicular to the planes can alter the spin canting pattern to induce a weak ferromagnetic phase. In light of recent evidence that the lattice symmetry is lower than originally assumed, we take another look at the nature of the field-induced spin-rotation transition. Comparing low-temperature neutron diffraction intensities for several magnetic Bragg peaks measured in fields of 0 and 14 T, we find that a better fit is provided by a model in which spins rotate within both neighboring planes but by different amounts, resulting in a noncollinear configuration. This model allows a more consistent relationship between lattice symmetry and spin orientation at all Cu sites.

Magnetic properties of the layered heavy-fermion antiferromagnet CePdGa6

We report the magnetic properties of the layered heavy fermion antiferromagnet CePdGa$_{6}$, and their evolution upon tuning with the application of magnetic field and pressure. CePdGa$_{6}$ orders antiferromagnetically below $T\rm_{N}$ = 5.2 K, where there is evidence for heavy fermion behavior from an enhanced Sommerfeld coefficient. Our results are best explained by a magnetic ground state of ferromagnetically coupled layers of Ce $4f$-moments orientated along the $c$-axis, with antiferromagnetic coupling between layers. At low temperatures we observe two metamagnetic transitions for fields applied along the $c$-axis corresponding to spin-flip transitions, where the lower transition is to a different magnetic phase with a magnetization one-third of the saturated value. From our analysis of the magnetic susceptibility, we propose a CEF level scheme which accounts for the Ising anisotropy at low temperatures, and we find that the evolution of the magnetic ground state can be explained considering both antiferromagnetic exchange between nearest neighbor and next nearest neighbor layers, indicating the influence of long-range interactions. Meanwhile we find little change of $T\rm_{N}$ upon applying hydrostatic pressures up to 2.2 GPa, suggesting that significantly higher pressures are required to examine for possible quantum critical behaviors.

Entropy measurement of ordered patterns in neuronal network with repulsive coupling

Traveling waves, standing waves, and spiral waves occur spontaneously in the brain neural network in some brain states. The occurrence of these ordered spatiotemporal patterns is often related to some neurological diseases. However, the mechanisms behind the generation of the ordered pattern are not fully understood. How to quantitatively describe the nature of these spatiotemporal patterns still needs further exploring. In order to solve these problems, the Hindmarsh-Rose neuron model is used to study the dynamic behavior of the two-dimensional (2D) neuronal network with double-coupling layer, which is composed of nearest-neighbor excitatory coupling and long-range repulsive coupling layers and evolves from an initial state with a random phase distribution. An improved cluster entropy is proposed to describe the spatiotemporal pattern of the neuronal network. The numerical simulation results show that the repulsive coupling can either promote the formation of ordered patterns or suppress the formation of ordered patterns. When the repulsive coupling strength and excitatory coupling strength are appropriately selected, the chaotic network can spontaneously generate single spiral wave, multiple spiral wave, traveling wave, the coexistence of spiral wave and others wave state, the coexistence of target wave and others wave state, the coexistence of traveling wave and standing wave, etc. The probability with which spiral wave and traveling wave occur reach 0.4555 and 0.1667 respectively. The probability with which target wave and other states co-occur, and the probability with which the traveling wave and the standing wave co-occur, are 0.0389 and 0.1056, respectively. These ordered wave patterns and chaotic states can be distinguished by using the proposed cluster entropy. When the repulsive coupling strength is large enough, the neuronal network is generally in chaotic state. It is found by calculating cluster entropy that a large cluster can appear in the neuronal network when the excitatory coupling strength and repulsive coupling strength are both weak. These results can conduce to understanding the self-organization phenomena occurring in the experiments and also to treating various neurological diseases.

An Interpretation for Defect-Induced Structural Transformation in SiC

Silicon carbide (SiC) has been considered as one of the alternative power semiconductor materials due to its excellent properties such as wide band gap, high break down field, and high thermal conductivity. Although SiC with 3C (zinc blende) is suitable for high-frequency power devices from its high electron mobility and high electron-saturation-velocity, SiC is well known as having dozens of polytypes including 4H and 6H in addition to 2H (wurtzite) and 3C that consist of different ordered stacking sequences of SiC atomic double layers. The 3C-SiC is believed to be more stable than the hexagonal structure at low temperatures. In contrast, 2H-SiC, which has the simplest stacking sequence, is rarely observed at high temperatures. Moreover, point defects also affect the stable polytype in SiC. Heavily Nitrogen (N)-doped single crystals of 6H-SiC were completely transformed into 3C-SiC by annealing in vacuum at presence of Si vapor at 2080 K and 2180 K (hereafter Case I). The 3C-SiC-like bands was also observed in 4H-SiC epilayers with heavily N-doping after thermal annealing (hereafter Case II). Presuming that vacancy formation is related to temperature, point defects such as vacancy and N in SiC are crucial factor for the structural transformation between hexagonal and cubic structures. In this study, the structural transformation in SiC is simply interpreted by considering point defect formation with the aid of ab initio calculations. Ab initio total energy calculations in a √3×√3×12 unit cell imply that stable stacking for SiC is 6H with Si-vacancy (VSi), 4H with C-vacancy (VC) and N substituting for Si (NSi), and 3C with N substituting for C (NC), whereas 2H-stacking does not appear as a stable stacking in these systems. Furthermore, the formation energy calculations reveal that vacancy formation depends on C chemical potential m C, where VSi and VC formations are favorable at large m C (corresponding to C-rich) and small m C (Si-rich), respectively. On the other hand, NC formation is more favorable than NSi formation over the entire range of m C and independent of conditions because of very small difference in covalent radius between N and C. Comparing these calculated results with the experimental finding in the Case I for transformation from 6H to 3C, thermal treatment with presence of Si vapor at high temperatures suppresses VSi formation favoring 6H-stacking while it enhances VC formation to be occupied by N (NC) in addition to N substitution for C (NC) that transform 6H to 3C. The Case II can be also interpreted by considering NC. Thermal annealing for N-doped 4H-SiC favored by VC easily produces NC with N occupying VC and substituting for C to realize 3C-SiC bands at high N-doped region in 4H-SiC epilayers. These results suggest that NC is crucial for the transformation from hexagonal stacking such as 6H and 4H to cubic stacking 3C. In order to give physical interpretation for the transformation to 3C-SiC with NC, the interaction energies Jn between nth neighbor SiC double layers are estimated in the range of n ≤ 3 using the axial next nearest neighbor Ising (ANNNI) model and calculated total energies for SiC polytypes obtained in this study. The calculated results elucidate that the absolute value of positive J 1 (51.70 meV) with J 3 (9.92 meV) favoring 3C-stacking is much larger than that of negative J 2 (-16.66 meV) inducing hexagonal stacking. It should be noted that the Jn values are one order of magnitude greater than those of perfect SiC such as J 1 (2.33 meV), J 2 (-1.41 meV), and J 3 (0.51 meV). This implies that the layer interaction in SiC becomes strong and long-range due to N-doping. Considering coordinate of (|J 2|/J 1, J 3/J 1) in the ANNNI phase diagram, it is also found that (0.31, 0.19) for SiC with NC is located in the stable region of 3C and is more distant from the multi-phase degeneracy point (0.5, 0) inducing polytype and phase boundary between 3C and 4H than (0.61, 0.21) for perfect SiC. This clarifies that the large J 1 in SiC with NC stabilizes 3C-stacking to dominate the structural transformation to 3C due to N-doping. Furthermore, atomistic interaction between the nearest neighbor layers corresponding to J 1 is also qualitatively discussed in terms of electrostatic interaction between bond charges located at the center of interatomic bonds and that between ionic charges located at the lattice sites on the basis of a simple energy description and charge distribution obtained by ab initio calculations.

Excitation of hybridized Dirac plasmon polaritons and transition radiation in multi-layer graphene traversed by a fast charged particle

We analyze the energy loss channels for a fast charged particle traversing a multi-layer graphene (MLG) structure with N layers under normal incidence. Focusing on a terahertz (THz) range of frequencies, and assuming equally doped graphene layers with a large enough separation d between them to neglect interlayer electron hopping, we use the Drude model for two-dimensional conductivity of each layer to describe hybridization of graphene’s Dirac plasmon polaritons (DPPs). Performing a layer decomposition of ohmic energy losses, which include excitation of hybridized DPPs (HDPPs), we have found for N = 3 that the middle HDPP eigenfrequency is not excited in the middle layer due to symmetry constraint, whereas the excitation of the lowest HDPP eigenfrequency produces a Fano resonance in the graphene layer that is first traversed by the charged particle. While the angular distribution of transition radiation emitted in the far field region also shows asymmetry with respect to the traversal order by the incident charged particle at supra-THz frequencies, the integrated radiative energy loss is surprisingly independent of both d and N for N ≤ 5, which is explained by a dominant role of the outer graphene layers in transition radiation. We have further found that the integrated ohmic energy loss in optically thin MLG scales as ∝1/N at sub-THz frequencies, which is explained by exposing the role of dissipative processes in graphene at low frequencies. Finally, prominent peaks are observed at supra-THz frequencies in the integrated ohmic energy loss for MLG structures that are not optically thin. The magnitude of those peaks is found to scale with N for N ≥ 2, while their shape and position replicate the peak in a double-layer graphene (N = 2), which is explained by arguing that plasmon hybridization in such MLG structures is dominated by electromagnetic interaction between the nearest-neighbor graphene layers.

Node importance idenfication for temporal network based on inter-layer similarity

Measuring node centrality is important for a wealth of applications, such as influential people identification, information promotion and traffic congestion prevention. Although there are many researches of node centrality proved, most of them have assumed that networks are static. However, many networks in our real life are dynamic, and the edges will appear or disappear over time. Temporal network could describe the interaction order and relationship among network nodes more accurately. It is of more important theoretical and more practical significance to construct proper temporal network model and identify vital nodes. In this paper, by taking into account the coupling strength between different network layers, we present a method, namely similarity-based supra-adjacency matrix (SSAM) method, to represent temporal network and further measure node importance. For a temporal network with N nodes and T layers, the SSAM is a matrix of size NTNT with a collection of both intra-layer relationship and inter-layer relationship. We restrict our attention to inter-layer coupling. Regarding the traditional method of measuring the node similarity of nearest-neighbor layers as one constant value, the neighbor topological overlap information is used to measure the node similarity for the nearest-neighbor layers, which ensures that the couplings of different nodes of inter-layer relationship are different. We then compute the node importance for temporal network based on eigenvector centrality, the dominant eigenvector of similarity-based supra-adjacency matrix, which indicates not only the node i's importance in layer t but also the changing trajectory of the node i's importance across the time. To evaluate the ranking effect of node importance obtained by eigenvector-based centrality, we also study the network robustness and calculate the difference of temporal global efficiency with node deletion approach in this work. In order to compare with the traditional method, we measure the node ranking effect of different time layers by the Kendall rank correlation coefficient of eigenvector centrality and the difference of temporal global efficiency. According to the empirical results on the workspace and Enrons datasets for both SSAM method and tradition method, the SSAM method with neighbor topological overlap information, which takes into account the inter-layer similarity, can effectively avoid overestimating or underestimating the importance of nodes compared with traditional method with one constant value. Furthermore, the experiments for the two datasets show that the average Kendall's could be improved by 17.72% and 12.44% for each layer network, which indicates that the node similarity for different layers is significant to construct temporal network and measure the node importance in temporal network.

Spontaneous formation of ordered waves in chaotic neuronal network with excitory-inhibitory connections

Spiral waves are a particular form of propagating waves, which rotate around a center point known as a rotor. Spiral waves have been found to play an important role in cardiac arrhythmia. Using voltage-sensitive dye imaging, one can find that spiral waves and plannar waves can occur in the mammalian cortex in vivo. The electrode array conduces to discovering that the seizures may manifest as recurrent spiral waves which propagate in the neocortex. However, the formation mechanism of the ordered waves and its potential function in the nervous system remain uncertain. In order to understand the formation mechanism of the ordered waves, we construct a double-layer two-dimensional -network of neuron, which is composed of nearest-neighbor excitatory coupling and long-range inhibitory coupling layers. The inhibitory grid points account for 25% of total number of grid points in the network. We propose a modified Hindmarsh-Rose neuron model to study whether differently ordered waves can occur spontaneously in the chaotic neuronal network evolving from the initial state with a random phase distribution. The numerical simulation results show that when the inhibitory coupling strength is small the spontaneous formation of ordered wave does not generally appear in the network. The larger inhibitory coupling strength, the more easily the system generates an ordered wave for sufficiently large strength of excitatory coupling. The appearance of differently ordered waves is closely related to the initial state of the system and coupling strength. As the excitatory and inhibitory coupling strengths are appropriately selected, the system can spontaneously generate the maze pattern, planar wave, single spiral wave, multiple spiral wave, paired spiral waves rotating in the opposite directions, two-arm spiral wave, target wave and inward square wave and so on. The probability for spontaneously forming a single spiral wave is far less than that for forming a small spiral wave. The occurrence probabilities of spiral wave, maze pattern and inward square wave reach 27.5%, 21.5% and 10%, respectively. The maze pattern is composed of many plane waves with different propagation directions. The occurrence probabilities of other ordered waves are quite small. These results conduce to understanding the self-organization phenomena occurring in the cerebral cortex.

Antiferromagnetic Interlayer Exchange Coupling in Ferromagnetic GaMnAs/GaAs:Be Multilayers

The interlayer exchange coupling (IEC) in magnetic multilayers determines the spin orientation of individual magnetic layers comprising the system. The dependence of the resistance on the resulting spin configuration in turn leads to the phenomenon known as giant magnetoresistance (GMR). [1] The GMR effect is of key importance to the area of spintronics, in which the spin degree of freedom is utilized in the operation of electronic devices. The behavior of IEC in metallic ferromagnetic multilayers has been extensively investigated, and the ability to control the IEC by structural parameters to be either ferromagnetic (FM) or antiferromagnetic (AFM) is now well established. In contrast, in multilayers consisting of FM semiconductors such as GaMnAs, the ability to change the IEC from FM to AFM is not well understood. Recently, however, AMF IEC was observed in GaMnAs/GaAs:Be multilayers [1]. These systems, however, show somewhat different behavior from their metallic counterparts. Specifically, the IEC in the GaMnAs/GaAs:Be multilayer system is observed to be long range, typically of over 10 nm, so that not only interactions between nearest neighbor (NN) layers of the multilayer, but also between next-nearest-neighbor (NNN) layers are involved during the magnetization reversal process. [2].

Effective distance of a ferromagnetic trilayer Ising nanostructure with an ABA stacking sequence

In this study, we investigated the effects of the distance between two nearest-neighbor layers on the magnetization and hysteresis properties (remanence, coercivity and loop area) of a ferromagnetic trilayer Ising nanostructure (TLINS) with an ABA stacking sequence using the Kaneyoshi approach within the effective field theory. We found that the ferromagnetic properties of the TLINS were highly dependent on the distance (d) between the layers. The layers had strong interactions at a certain minimum distance (dmin) ​but no interactions at a certain maximum distance (dmax). Thus, we suggest that there is an effective distance (deff) at dmin≤deff≤dmax for the TLINS. We observed that the critical temperature increased sharply as the distance decreased at d≤dmin,TC ​ increased slowly as the distance decreased at deff, and TC ​had a certain constant value at d≥dmax. The critical field points increased rapidly as the distance decreased and HC ​had different values for the central and edge atoms at d≤dmin. HC ​increased slowly as the distance decreased at deff and HC ​had the same value for the central and edge atoms at deff, while HC ​had a certain constant value at d≥dmax. Distance had no effect on the critical temperature and critical field points of the TLINS and they had a constant value at d≥dmax; thus, the TLINS behaved as a single layer Ising nanostructure at great distances.

Interlayer exchange coupling between next nearest neighbor layers

Interlayer exchange coupling between next nearest neighbor layers

Rigid‐plane phonons in layered crystals

AbstractThe determination of the layer number ${\cal N}$ in nanoscale thin layered crystals is a challenging problem of technological relevance. In addition to innovative experimental techniques, a thorough knowledge of the underlying lattice dynamics is required. Starting from phenomenological atomic interaction potentials we have carried out an analytical study of the low‐frequency optical phonon dispersions in layered crystals. At the gamma point of the two‐dimensional Brillouin zone the optical phonon frequencies correspond to rigid‐plane shearing and compression modes. We have investigated graphene multilayers (GML) and hexagonal boron‐nitride multilayers (BNML). The frequencies show a characteristic dependence on ${\cal N}$. The results which are represented in the form of fan diagrams are very similar for both materials. Due to charge neutrality within layers Coulomb forces play no role, only van der Waals forces between nearest neighbor layers are relevant. The theoretical results agree with recent low‐frequency Raman results on rigid‐layer modes [Tan et al., Nature Mater. 11, 294 (2012)] in GML and double‐resonant Raman scattering data on rigid‐layer compression modes [Herziger et al., Phys. Rev. B 85, 235447 (2012)] in GML.

DYNAMICS ON MULTILAYERED HYPERBRANCHED FRACTALS THROUGH CONTINUOUS TIME RANDOM WALKS

We introduce a new method to generate three-dimensional structures, with mixed topologies. We focus on Multilayered Regular Hyperbranched Fractals (MRHF), three-dimensional networks constructed as a set of identical generalized Vicsek fractals, known as Regular Hyperbranched Fractals (RHF), layered on top of each other. Every node of any layer is directly connected only to copies of itself from nearest-neighbor layers. We found out that also for MRHF the eigenvalue spectrum of the connectivity matrix is determined through a semi-analytical method, which gives the opportunity to analyze very large structures. This fact allows us to study in detail the crossover effects of two basic topologies: linear, corresponding to the way we connect the layers and fractal due to the layers' topology. From the wealth of applications which depends on the eigenvalue spectrum we choose the return-to-the-origin probability. The results show the expected short-time and long-time behaviors. In the intermediate time domain we obtained two different power-law exponents: the first one is given by the combination linear-RHF, while the second one is peculiar either of a single RHF or of a single linear chain.

Metastable noncollinear canted states from a phenomenological model of a symmetric ferromagnetic film

In the present work we developed a theoretical method to find the noncollinear canted magnetic states of ferromagnetic film whose magnetic properties are treated within a simple phenomenological model that takes into account the discrete location of atomic layers. We apply this method to the description of stable and uniform in the film plane magnetic configurations of symmetric ferromagnetic film with equal anisotropy constants at both sides of a film. We demonstrated that besides the ground noncollinear canted state caused by the competition between the energies of surface and bulk anisotropy this film also exhibits metastable noncollinear canted states that are not necessarily caused by the competition between these energies. They represent various kinds of excited Bloch wall-like states with a wall parallel to the film plane. The generalization of the method developed to the case of explicit account of dipole interaction between the nearest-neighbor layers is presented. We considered the fcc and bcc films with (001) surface and demonstrated that novel metastable states discovered in the present work are not the artifact of a simple model of a film used. To prove this statement we demonstrate that these states exist when the dipole interaction between the nearest-neighbor layers is explicitly taken into account.

Ab initio structural simulation and electronic structure of lithium imide

The crystal structure and the locations of the hydrogen of lithium imide （Li2NH） are studied by first-principle plane wave pseudopotential method based on the density function theory（DFT）. Three models are used to investigating the effects of the Li, N and nearest-neighbor N—H bonds to N—H bond orientation, respectively. The calculated results show that Li2NH crystal can be described by a layered tetragonal crystal （P42） structure. Four N—H bonds of each conventional cell align in two layers. The two imide groups in the same layer prefer to be antiparallel and the imide groups in the nearest-neighbor layers tend to be vertical. The density of states （DOS） and the electron local function （ELF） analysis show strong ionic interaction between the Li and N—H dimmer, while the bonding between the N and H has covalent character. Our P42 structure of Li2NH crystal yields a hydrogen storage Li2NH2+H2/LiNH2+LiH reaction enthalpy of 69.6 kJ/mol H2 at T=0 K, in good agreement with experimental reports of 66 kJ/mol H2 for this reaction.

Effective-field theory of the Ising model with three alternative layers on the honeycomb and square lattices

The Ising model with three alternative layers on the honeycomb and square lattices is studied by using the effective-field theory with correlations. We consider that the nearest-neighbor spins of each layer are coupled ferromagnetically and the adjacent spins of the nearest-neighbor layers are coupled either ferromagnetically or anti-ferromagnetically depending on the sign of the bilinear exchange interactions. We investigate the thermal variations of the magnetizations and present the phase diagrams. The phase diagrams contain the paramagnetic, ferromagnetic and anti-ferromagnetic phases, and the system also exhibits a tricritical behavior.

Effects of temperature on mechanical properties of multi-walled carbon nanotubes

This paper reports the results of an investigation into the effect of environmental temperature on mechanical properties of multi-walled carbon nanotubes (CNTs), by means of a molecular structural mechanics model in which the covalent bonds are treaded as dimensional Euler–Bernoulli beam. Here, van der Waals forces between nearest-neighbor tube layers are firstly simulated by using the nonlinear springs. Based on the ionic plus linear Pauli repulsion model, the sectional stiffness parameters in different environmental temperatures are described as functions of bond stretching, bond bending angle and torsional resistance force constants being dependent of environmental temperature. Results obtained by means of nano-scale finite element simulation reveal that the Young’s modulus and Poisson’s ratios of multi-walled carbon nanotubes decreases significantly with the increase of environmental temperatures. It is noticed that the Young’s modulus of multi-walled Zigzag CNTs is m ore sensitive to environmental temperatures due to the tube chirality. Last, the relationship between Young’s modulus of double-walled CNTs and environmental temperature is given by a simple formula.

Long-Range Interlayer Interactions in Ferroelectric Liquid Crystals

Some smectic liquid crystals exhibit a series of phases, including ferroelectric, antiferroelectric, and ferrielectric commensurate structures as well as an incommensurate phase. A long-standing problem has been to understand the origin of the long-range interaction responsible for this rich variety of phases. We study a model that incorporates thermal fluctuations in the flexing of layers and find that it supports commensurate and incommensurate structures. The vibrational entropy competes with an assumed helical interaction between nearest-neighbor layers. An increase in temperature then leads to an unwinding of the helix that proceeds at first through commensurate phases and then into an incommensurate phase. This result is consistent with the experimentally observed "distorted clock model."

Statistical Thermodynamic Treatment of Multilayer Adsorption-Migration Kinetics

The transient multiple-layer (multilayer) adsorption and adsorption-migration phenomena are described with a statistical thermodynamic model. The key postulate for this model is that the transient process can be delineated by considering perturbation of the grand canonical ensemble characterizing either a multilayer adsorption or adsorption-migration system. Also, the derivative of the site partition function or adsorption site number (molecular coverage) for a given layer is affected only by the site distribution of its own layer and the two nearest-neighbor layers. With these postulates, differentiation of the grand partition function with time results in a system of first-order differential equations in terms of adsorption site numbers that describes the transient multilayer adsorption or adsorption-migration process. Its solution determines the time-varying layer-by-layer deposit buildup on a smooth surface under constant molecular impingement. In either the adsorption or adsorption-migration case, the statistical thermodynamic solution has been proven to be equivalent to that based on the classical kinetic theory, which has been verified by laboratory test data.

Dielectric Study on Ferri-like Ordering in Antiferroelectric Liquid Crystals during the Field-Induced Phase Transition

We studied the field-induced ferri-like (FI) ordering in antiferroelectric (AF) liquid crystals based on a simple geometrical model which includes the electrostatic dipolar and quadrupolar interactions between the molecules in two adjacent layers. In this model, the stabilization of the FI ordering during the AF-ferroelectric (FO) transition results from the quadrupolar interactions between the molecules in the nearest neighbor layers. The experimental results for the dielectric behavior at various bias fields near the AF-FI transition temperature are consistent with the theoretical predictions made within the geometrical model.

Second-Order Perturbational Effect on the Interlayer Interactions in Graphite and Graphite Intercalation Compounds

Abstract The role of second-order perturbations in interlayer interactions of two-dimensional electronic systems is examined from simple two-layer models. The preferred nuclear motions are discussed specifically for the preferred stacking of layers in graphite on the basis of transition-density analyses for extended systems. The well-known ABAB stacking of layers in neutral graphite and the AAAA stacking of layers in graphite intercalation compounds (GICs) such as C6Li and C8K complexes are proposed to be consequences of orbital interactions (near the Fermi level) between nearest neighbor layers. This paper raises doubts about a widely accepted belief that the interlayer interaction between graphite layers is of the van der Waals type.