We report on the existence of discrete breathers in a one-dimensional, mass-in-mass chain with linear intersite coupling and nonlinear, precompressed Hertzian local resonators, which is motivated by recent studies of the dynamics of microspheres adhered to elastic substrates. After predicting theoretically the existence of discrete breathers in the continuum and anticontinuum limits of intersite coupling, we use numerical continuation to compute a family of breathers interpolating between the two regimes in a finite chain, where the displacement profiles of the breathers are localized around one lattice site. We then analyze the frequency-amplitude dependence of the breathers by performing numerical continuation on a linear eigenmode (vanishing amplitude) solution of the system near the upper band gap edge. Finally, we use direct numerical integration of the equations of motion to demonstrate the formation and evolution of the identified localized modes in energy-conserving and dissipative scenarios, including within settings that may be relevant to future experimental studies.

Epitaxial zinc blende structure metastable (GaAs)1−x(Si2)x alloys have been grown with 0<x<0.3 on As-stabilized GaAs(100) substrates by a hybrid sputter deposition/evaporation technique. The films, typically 2–3 μm thick, were deposited at 570 °C with growth rates between 0.7 and 1 μm h−1. Alloys with 0<x<0.12 were defect-free as judged by plan-view and cross-sectional transmission electron microscopy (TEM and XTEM) with x-ray diffraction peak widths approximately the same as that of the substrate, 30 arcsec 2θ. XTEM lattice images showed smooth abrupt interfaces. (GaAs)1−x(Si2)x alloys with x>0.12 exhibited increasing evidence of interfacial defects associated with lattice strain when grown on GaAs. However, defect-free alloys with x up to 0.3 were obtained using (GaAs)1−x(Si2)x/GaAs strained-layer superlattice buffer layers to provide a better lattice match.

Anisotropy in the above-band-gap optical reflectance along the [110] and [110] directions has been used to investigate long-range atomic ordering in metastable epitaxial (GaAs) & (Si~) (001) alloys as a function of Si concentration x. The amplitude of the differentiated reAectance-difference signal was found to decrease monotonically with increasing x and reach zero, corresponding to the critical concentration for the zinc-blendetodiamond transition, at x =0.37, consistent with x-raydiffraction results. The highest sensitivity in the optical-anisotropy spectra was obtained in the spectral region near the Eo critical point (4.5 eV in GaAs).

We consider a variety of settings involving chains with one or more defects stemming from the introduction of nodes bearing internal resonators. Motivated by experimental results in woodpile elastic lattices with one or two defects, we consider a variety of different theoretical scenarios. These include multi-defect chains and their ability to transmit, reflect, and especially trap energy; they also include settings with linear vs. nonlinear defects of variable interaction exponent. Moreover, they involve defects which are spatially separated and either statically, or more effectively dynamically, enable the confinement of energy between the separated defects. Wherever possible, comparisons of the experiments with numerical simulations, as well as with theoretical intuition are also offered, to provide a justification for the observed findings.

The microstructure of single-crystal zincblende-structure (GaAs)1−x(Si2)x metastable semiconducting alloys with 0≤x≤0.40 has been investigated using triple-crystal x-ray diffraction (XRD), plan-view and cross-sectional transmission electron microscopy (TEM and XTEM), scanning transmission electron microscopy, and convergent-beam electron diffraction. The alloys, typically 1–3 μm thick, were grown using a hybrid sputter-deposition/evaporation technique on As-stabilized GaAs(001) and (GaAs)1−x(Si2)x/GaAs(001) strained-layer superlattices, (SLS). Alloy XRD peak widths were approximately equal to those of the GaAs substrates, 30 arcsec, and lattice constants, uncorrected for strain, obeyed Vegard’s ‘‘law’’ and decreased linearly with increasing x. TEM and XTEM examinations of (GaAs)1−x(Si2)x alloys with 0≤x≤0.20 grown on GaAs revealed no evidence of dislocations or other extended defects. Film/substrate lattice misfit strain in alloys with 0.11<x<0.20 was partially accommodated by the formation of a thin interfacial spinodal layer whose average thickness increased with x to ≂70 nm. The spinodal region, which remained epitaxial, consisted of lenticular platelets extending along the [001] direction with a compositional modulation in orthogonal directions. Films with x≥0.20 exhibited, together with the interfacial zones, inhomogeneously distributed a0/2〈110〉-type threading dislocations. Antiphase domains were observed in alloys with x≥0.23. The use of (GaAs)1−x(Si2)x/GaAs SLS buffer layers extended the composition range to x=0.3 over which dislocation-free alloys, with no evidence of interfacial spinodal decomposition, could be obtained.