Three parallel algorithms for classical molecular dynamics are presented. The first assigns each processor a fixed subset of atoms; the second assigns each a fixed subset of inter-atomic forces to compute; the third assigns each a fixed spatial region. The algorithms are suitable for molecular dynamics models which can be difficult to parallelize efficiently—those with short-range forces where the neighbors of each atom change rapidly. They can be implemented on any distributed-memory parallel machine which allows for message-passing of data between independently executing processors. The algorithms are tested on a standard Lennard-Jones benchmark problem for system sizes ranging from 500 to 100,000,000 atoms on several parallel supercomputers--the nCUBE 2, Intel iPSC/860 and Paragon, and Cray T3D. Comparing the results to the fastest reported vectorized Cray Y-MP and C90 algorithm shows that the current generation of parallel machines is competitive with conventional vector supercomputers even for small problems. For large problems, the spatial algorithm achieves parallel efficiencies of 90% and a 1840-node Intel Paragon performs up to 165 faster than a single Cray C9O processor. Trade-offs between the three algorithms and guidelines for adapting them to more complex molecular dynamics simulations are also discussed.

Fast parallel algorithms for short-range molecular dynamics

Fabrication techniques developed for graphene research allow the disassembly of many layered crystals (so-called van der Waals materials) into individual atomic planes and their reassembly into designer heterostructures, which reveal new properties and phenomena. Andre Geim and Irina Grigorieva offer a forward-looking review of the potential of layering two-dimensional materials into novel heterostructures held together by weak van der Waals interactions. Dozens of these one-atom- or one-molecule-thick crystals are known. Graphene has already been well studied but others, such as monolayers of hexagonal boron nitride, MoS2, WSe2, graphane, fluorographene, mica and silicene are attracting increasing interest. There are many other monolayers yet to be examined of course, and the possibility of combining graphene with other crystals adds even further options, offering exciting new opportunities for scientific exploration and technological innovation. Research on graphene and other two-dimensional atomic crystals is intense and is likely to remain one of the leading topics in condensed matter physics and materials science for many years. Looking beyond this field, isolated atomic planes can also be reassembled into designer heterostructures made layer by layer in a precisely chosen sequence. The first, already remarkably complex, such heterostructures (often referred to as ‘van der Waals’) have recently been fabricated and investigated, revealing unusual properties and new phenomena. Here we review this emerging research area and identify possible future directions. With steady improvement in fabrication techniques and using graphene’s springboard, van der Waals heterostructures should develop into a large field of their own.

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Van der Waals heterostructures

BACKGROUND Materials by design is an appealing idea that is very hard to realize in practice. Combining the best of different ingredients in one ultimate material is a task for which we currently have no general solution. However, we do have some successful examples to draw upon: Composite materials and III-V heterostructures have revolutionized many aspects of our lives. Still, we need a general strategy to solve the problem of mixing and matching crystals with different properties, creating combinations with predetermined attributes and functionalities. ADVANCES Two-dimensional (2D) materials offer a platform that allows creation of heterostructures with a variety of properties. One-atom-thick crystals now comprise a large family of these materials, collectively covering a very broad range of properties. The first material to be included was graphene, a zero-overlap semimetal. The family of 2D crystals has grown to includes metals (e.g., NbSe 2 ), semiconductors (e.g., MoS 2 ), and insulators [e.g., hexagonal boron nitride (hBN)]. Many of these materials are stable at ambient conditions, and we have come up with strategies for handling those that are not. Surprisingly, the properties of such 2D materials are often very different from those of their 3D counterparts. Furthermore, even the study of familiar phenomena (like superconductivity or ferromagnetism) in the 2D case, where there is no long-range order, raises many thought-provoking questions. A plethora of opportunities appear when we start to combine several 2D crystals in one vertical stack. Held together by van der Waals forces (the same forces that hold layered materials together), such heterostructures allow a far greater number of combinations than any traditional growth method. As the family of 2D crystals is expanding day by day, so too is the complexity of the heterostructures that could be created with atomic precision. When stacking different crystals together, the synergetic effects become very important. In the first-order approximation, charge redistribution might occur between the neighboring (and even more distant) crystals in the stack. Neighboring crystals can also induce structural changes in each other. Furthermore, such changes can be controlled by adjusting the relative orientation between the individual elements. Such heterostructures have already led to the observation of numerous exciting physical phenomena. Thus, spectrum reconstruction in graphene interacting with hBN allowed several groups to study the Hofstadter butterfly effect and topological currents in such a system. The possibility of positioning crystals in very close (but controlled) proximity to one another allows for the study of tunneling and drag effects. The use of semiconducting monolayers leads to the creation of optically active heterostructures. The extended range of functionalities of such heterostructures yields a range of possible applications. Now the highest-mobility graphene transistors are achieved by encapsulating graphene with hBN. Photovoltaic and light-emitting devices have been demonstrated by combining optically active semiconducting layers and graphene as transparent electrodes. OUTLOOK Currently, most 2D heterostructures are composed by direct stacking of individual monolayer flakes of different materials. Although this method allows ultimate flexibility, it is slow and cumbersome. Thus, techniques involving transfer of large-area crystals grown by chemical vapor deposition (CVD), direct growth of heterostructures by CVD or physical epitaxy, or one-step growth in solution are being developed. Currently, we are at the same level as we were with graphene 10 years ago: plenty of interesting science and unclear prospects for mass production. Given the fast progress of graphene technology over the past few years, we can expect similar advances in the production of the heterostructures, making the science and applications more achievable.

2D materials and van der Waals heterostructures

Graphene-Like Two-Dimensional Materials

Heterostructures based on layering of two-dimensional (2D) materials such as graphene and hexagonal boron nitride represent a new class of electronic devices. Realizing this potential, however, depends critically on the ability to make high-quality electrical contact. Here, we report a contact geometry in which we metalize only the 1D edge of a 2D graphene layer. In addition to outperforming conventional surface contacts, the edge-contact geometry allows a complete separation of the layer assembly and contact metallization processes. In graphene heterostructures, this enables high electronic performance, including low-temperature ballistic transport over distances longer than 15 micrometers, and room-temperature mobility comparable to the theoretical phonon-scattering limit. The edge-contact geometry provides new design possibilities for multilayered structures of complimentary 2D materials.

One-dimensional electrical contact to a two-dimensional material.

By growing graphene in patterned hexagonal boron nitride layers, planar heterostructures can be fabricated and used to create two-dimensional devices.

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In-plane heterostructures of graphene and hexagonal boron nitride with controlled domain sizes

While the intrinsic strength of graphene has previously been demonstrated to be high, the fracture toughness remains unknown. Here, the authors perform in situ testing of graphene in a scanning electron microscope and report a critical stress intensity factor of ~4.0 MPa√m.

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Fracture toughness of graphene

Graphene (G) and atomic layers of hexagonal boron nitride (h-BN) are complementary two-dimensional materials, structurally very similar but with vastly different electronic properties. Recent studies indicate that h-BN atomic layers would be excellent dielectric layers to complement graphene electronics. Graphene on h-BN has been realized via peeling of layers from bulk material to create G/h-BN stacks. Considering that both these layers can be independently grown via chemical vapor deposition (CVD) of their precursors on metal substrates, it is feasible that these can be sequentially grown on substrates to create the G/h-BN stacked layers useful for applications. Here we demonstrate the direct CVD growth of h-BN on highly oriented pyrolytic graphite and on mechanically exfoliated graphene, as well as the large area growth of G/h-BN stacks, consisting of few layers of graphene and h-BN, via a two-step CVD process. The G/h-BN film is uniform and continuous and could be transferred onto different substrates...

Direct Growth of Graphene/Hexagonal Boron Nitride Stacked Layers

Quantitative In Situ Mechanical Characterization of the Effects of Chemical Functionalization on Individual Carbon Nanofibers

The effects of carbon nanotube (CNT) sidewall fluorination on the interface toughness of the CNT epoxy interface have been comprehensively investigated. Nanoscale quantitative single-CNT pull-out experiments have been conducted on individual fluorinated CNTs embedded in an epoxy matrix, in situ, within a scanning electron microscope (SEM) using an InSEM® nanoindenter assisted micro-device. Equations that were derived using a continuum fracture mechanics model have been applied to compute the interfacial fracture energy values for the system. The interfacial fracture energy values have also been independently computed by modeling the fluorinated graphene-epoxy interface using molecular dynamics simulations and adhesion mechanisms have been proposed.

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Jiangnan Zhang

Papers

In-plane heterostructures of graphene and hexagonal boron nitride with controlled domain sizes

Fracture toughness of graphene

Direct Growth of Graphene/Hexagonal Boron Nitride Stacked Layers

Quantitative In Situ Mechanical Characterization of the Effects of Chemical Functionalization on Individual Carbon Nanofibers

Fracture toughness of the sidewall fluorinated carbon nanotube-epoxy interface