There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

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

Two-dimensional materials are attractive for use in next-generation nanoelectronic devices because, compared to one-dimensional materials, it is relatively easy to fabricate complex structures from them. The most widely studied two-dimensional material is graphene, both because of its rich physics and its high mobility. However, pristine graphene does not have a bandgap, a property that is essential for many applications, including transistors. Engineering a graphene bandgap increases fabrication complexity and either reduces mobilities to the level of strained silicon films or requires high voltages. Although single layers of MoS(2) have a large intrinsic bandgap of 1.8 eV (ref. 16), previously reported mobilities in the 0.5-3 cm(2) V(-1) s(-1) range are too low for practical devices. Here, we use a halfnium oxide gate dielectric to demonstrate a room-temperature single-layer MoS(2) mobility of at least 200 cm(2) V(-1) s(-1), similar to that of graphene nanoribbons, and demonstrate transistors with room-temperature current on/off ratios of 1 × 10(8) and ultralow standby power dissipation. Because monolayer MoS(2) has a direct bandgap, it can be used to construct interband tunnel FETs, which offer lower power consumption than classical transistors. Monolayer MoS(2) could also complement graphene in applications that require thin transparent semiconductors, such as optoelectronics and energy harvesting.

/pdf/single-layer-mos2-transistors-6go64w4t3p.pdf

Single-layer MoS2 transistors

Ultralong beltlike (or ribbonlike) nanostructures (so-called nanobelts) were successfully synthesized for semiconducting oxides of zinc, tin, indium, cadmium, and gallium by simply evaporating the desired commercial metal oxide powders at high temperatures. The as-synthesized oxide nanobelts are pure, structurally uniform, and single crystalline, and most of them are free from defects and dislocations. They have a rectanglelike cross section with typical widths of 30 to 300 nanometers, width-to-thickness ratios of 5 to 10, and lengths of up to a few millimeters. The beltlike morphology appears to be a distinctive and common structural characteristic for the family of semiconducting oxides with cations of different valence states and materials of distinct crystallographic structures. The nanobelts could be an ideal system for fully understanding dimensionally confined transport phenomena in functional oxides and building functional devices along individual nanobelts.

https://science.sciencemag.org/content/sci/291/5510/1947.full.pdf

Nanobelts of Semiconducting Oxides

This review summarizes recent developments in the theory of spin glasses, as well as pertinent experimental data. The most characteristic properties of spin glass systems are described, and related phenomena in other glassy systems (dielectric and orientational glasses) are mentioned. The Edwards-Anderson model of spin glasses and its treatment within the replica method and mean-field theory are outlined, and concepts such as "frustration," "broken replica symmetry," "broken ergodicity," etc., are discussed. The dynamic approach to describing the spin glass transition is emphasized. Monte Carlo simulations of spin glasses and the insight gained by them are described. Other topics discussed include site-disorder models, phenomenological theories for the frozen phase and its excitations, phase diagrams in which spin glass order and ferromagnetism or antiferromagnetism compete, the Ne\'el model of superparamagnetism and related approaches, and possible connections between spin glasses and other topics in the theory of disordered condensed-matter systems.

Spin glasses: Experimental facts, theoretical concepts, and open questions

The development of order for the Ising model in the presence of static, random impurities is studied following a quench from high temperature (T\ensuremath{\gg}${T}_{c}$) to T${T}_{c}$. We find that for quenches to T=0, the system becomes pinned for long times for any value of c0 and never reaches its final equilibrium ferromagnetic ground state. The average linear pinned domain size scales as the inverse square root of the concentration c. For quenches to a final T0, the long-time behavior of the correlation length R and the energy E are slower than a power law, suggesting a logarithmic growth law for long times. The time that is required to reach this asymptotic logarithmic behavior increases as the impurity concentration decreases and/or the temperature increases.

Impurity effects on domain-growth kinetics. I. Ising model

Dislocation motion in the presence of diffusing solutes: a computer simulation study

A diffusion equation describing phase separation during co‐deposition of a binary alloy is derived, and solved in the limit of dominant surface diffusion. Linear stability analysis yields results similar to bulk spinodal decomposition, except that long, and possibly all, wavelength are stabilized. Decomposition into two phases is investigated by solving the diffusion equation for lamellar and cylindrical symmetry. For the lamellar geometry, typically observed for near‐equal volume fractions, the diffusion equation does not yield wavelength selection criteria. These can be obtained if free energy minimization is assumed. For the cylindrical geometry, solutions for small volume fractions yield domain dimensions proportional to the deposition‐rate dependent surface diffusion length.

/pdf/phase-separation-during-film-growth-2vvm07ycmi.pdf

Phase separation during film growth

Normal grain growth is characterized by the self-similar coarsening of the microstructure. Therefore, knowledge of the microstructure at one time and the temporal evolution of the mean grain size, , provides all of the information required for a complete statistical description of the evolving microstructure. In contrast, abnormal grain grow:h is characterized by the growth of a small number of grains at a rate in excess to that of the mean grain size and, consequently, a lack of self-similarity. Abnormal grain growth is most frequently observed in samples containing a dispersed second phase and/or in sheet materials.

https://deepblue.lib.umich.edu/bitstream/handle/2027.42/28656/0000473.pdf?sequence=1

Abnormal grain growth in three dimensions

1 Basic laws of thermodynamics 2 Phase equilibria I 3 Thermodynamic theory of solutions 4 Phase equilibria II 5 Thermodyanmics of chemical reactions 6 Interfacial phenomena 7 Thermodynamics of stressed systems 8 Kinetics of homogeneous chemical reactions 9 Thermodynamics of irreversible processes 10 Diffusion 11 Kinetics of heterogeneous processes 12 Introduction to statistical thermodynamics of gases 13 Introduction to statistical thermodynamics of condensed matter Example problem solutions Appendices

David J. Srolovitz

Papers

Impurity effects on domain-growth kinetics. I. Ising model

Dislocation motion in the presence of diffusing solutes: a computer simulation study

Phase separation during film growth

Abnormal grain growth in three dimensions

Thermodynamics and kinetics in materials science : a short course