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

The stability of two-dimensional (2D) layers and membranes is subject of a long standing theoretical debate. According to the so called Mermin-Wagner theorem, long wavelength fluctuations destroy the long-range order for 2D crystals. Similarly, 2D membranes embedded in a 3D space have a tendency to be crumpled. These dangerous fluctuations can, however, be suppressed by anharmonic coupling between bending and stretching modes making that a two-dimensional membrane can exist but should present strong height fluctuations. The discovery of graphene, the first truly 2D crystal and the recent experimental observation of ripples in freely hanging graphene makes these issues especially important. Beside the academic interest, understanding the mechanisms of stability of graphene is crucial for understanding electronic transport in this material that is attracting so much interest for its unusual Dirac spectrum and electronic properties. Here we address the nature of these height fluctuations by means of straightforward atomistic Monte Carlo simulations based on a very accurate many-body interatomic potential for carbon. We find that ripples spontaneously appear due to thermal fluctuations with a size distribution peaked around 70 \AA which is compatible with experimental findings (50-100 \AA) but not with the current understanding of stability of flexible membranes. This unexpected result seems to be due to the multiplicity of chemical bonding in carbon.

Intrinsic ripples in graphene

A review on mechanics and mechanical properties of 2D materials—Graphene and beyond

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

Computational Materials Science X

We show from a series of molecular dynamics simulations that the tensile fracture behavior of a nanocrystalline graphene (nc-graphene) nanostrip can become insensitive to a pre-existing flaw (e.g., a hole or a notch) below a critical length scale in the sense that there exists no stress concentration near the flaw, the ultimate failure does not necessarily initiate at the flaw, and the normalized strength of the strip is independent of the size of the flaw. This study is a first direct atomistic simulation of flaw insensitive fracture in high-strength nanoscale materials and provides significant insights into the deformation and failure mechanisms of nc-graphene.

Flaw insensitive fracture in nanocrystalline graphene.

Phase diagrams provide ‘roadmaps’ to the possible states of matter. Their determination
traditionally rests on the assumption that all phases, even unstable ones, have well-defined
free energies under all conditions. However, this assumption is commonly violated in
condensed phases due to mechanical instabilities. This long-standing problem impedes
thermodynamic database development, as pragmatic attempts at solving this problem involve
delicate extrapolations that are highly nonunique and that lack an underlying theoretical
justification. Here we propose an efficient computational solution to this problem that has
a simple interpretation, both as a topological partitioning of atomic configuration space and as
a minimally constrained physical system. Our natural scheme smoothly extends the free
energy of stable phases, without relying on extrapolation, thus enabling a formal assessment
of widely used extrapolation schemes.

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The free energy of mechanically unstable phases

We present a set of software tools that largely automate the process of converting ab initio data into thermodynamic databases that can readily be imported into standard thermodynamic modeling softwares. These tools are based on the Special Quasirandom Structures (SQS) formalism, extended to transparently handle, not only traditional fcc, bcc and hcp solid solutions, but also multiple-sublattice structures with possible sublattice disorder. A large database of pre-generated SQS is provided that covers over 30 of the most common multi-sublattice structures and spans the composition ranges of each of their sublattices. In addition, we exploit a theoretically justified and robust method to address the issue of assigning free energies to mechanically unstable “virtual” phases, thus providing a compelling solution to a long-standing problem in CALPHAD modeling, especially in the context of ab initio data. We also propose a simple low-order approximation scheme to include short-range order effects that requires no additional ab initio input. The resulting thermodyamic database seamlessly combines ab initio data (formation energies and, optionally, vibrational free energies) with elemental Scientific Group Thermodata Europe (SGTE) data. The proposed tools provide a clear path to expand the coverage of high-throughput efforts towards non-stoichiometric phases and non-zero temperatures. The generated free energy models can also provide very good starting points to perform complex thermodynamic assessments, especially in cases where the available experimental data poorly constrain some thermodynamic parameters. The Cu-Pt-W phase diagram is calculated as an example.

Software tools for high-throughput CALPHAD from first-principles data

The phase diagram of numerous materials of technological importance features high-symmetry high-temperature phases that exhibit phonon instabilities. Leading examples include shape-memory alloys, as well as ferroelectric, refractory, and structural materials. The thermodynamics of these phases have proven challenging to handle by atomistic computational thermodynamic techniques due to the occurrence of constant anharmonicity-driven hopping between local low-symmetry distortions, while maintaining a high-symmetry time-averaged structure. To compute the free energy in such phases, we propose to explore the system's potential-energy surface by discrete sampling of local minima by means of a lattice gas Monte Carlo approach and by continuous sampling by means of a lattice dynamics approach in the vicinity of each local minimum. Given the proximity of the local minima, it is necessary to carefully partition phase space by using a Voronoi tessellation to constrain the domain of integration of the partition function in order to avoid double counting artifacts and enable an accurate harmonic treatment near each local minima. We consider the bcc phase of titanium as a prototypical example to illustrate our approach.

Sara Kadkhodaei

Papers

Flaw insensitive fracture in nanocrystalline graphene.

The free energy of mechanically unstable phases

Software tools for high-throughput CALPHAD from first-principles data

Free energy calculation of mechanically unstable but dynamically stabilized bcc titanium

First-principles calculations of thermal properties of the mechanically unstable phases of the PtTi and NiTi shape memory alloys