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All sourcesNASA NTRSDOE OSTI
NASA NTRS1996

Development of High Speed Imaging and Analysis Techniques Compressible Dynamics Stall

Dynamic stall has limited the flight envelope of helicopters for many years. The problem has been studied in the laboratory as well as in flight, but most research, even in the laboratory, has been restricted to surface measurement techniques such as pressure transducers or skin friction gauges, except at low speed. From this research, it became apparent that flow visualization tests performed at Mach numbers representing actual flight conditions were needed if the complex physics associated with dynamic stall was to be properly understood. However, visualization of the flow field during compressible conditions required carefully aligned and meticulously reconstructed holographic interferometry. As part of a long-range effort focused on exposing of the physics of compressible dynamic stall, a research wind tunnel was developed at NASA Ames Research Center which permits visual access to the full flow field surrounding an oscillating airfoil during compressible dynamic stall. Initially, a stroboscopic schlieren technique was used for visualization of the stall process, but the primary research tool has been point diffraction interferometry(PDI), a technique carefully optimized for use in th is project. A review of the process of development of PDI will be presented in the full paper. One of the most valuable aspects of PDI is the fact that interferograms are produced in real time on a continuous basis. The use of a rapidly-pulsed laser makes this practical; a discussion of this approach will be presented in the full paper. This rapid pulsing(up to 40,000 pulses/sec) produces interferograms of the rapidly developing dynamic stall field in sufficient resolution(both in space and time) that the fluid physics of the compressible dynamic stall flowfield can be quantitatively determined, including the gradients of pressure in space and time. This permits analysis of the influence of the effect of pitch rate, Mach number, Reynolds number, amplitude of oscillation, and other parameters on the dynamic stall process. When interferograms can be captured in real time, the potential for real-time mapping of a developing unsteady flow such as dynamic stall becomes a possibility. This has been achieved in the present case through the use of a high-speed drum camera combined with electronic circuitry which has resulted in a series of interferograms obtained during a single cycle of dynamic stall; images obtained at the rate of 20 KHz will be presented as a part of the formal presentation. Interferometry has been available for a long time; however, most of its use has been limited to visualization. The present research has focused on use of interferograms for quantitative mapping of the flow over oscillating airfoils. Instantaneous pressure distributions can now be obtained semi-automatically, making practical the analysis of the thousands of interferograms that are produced in this research. A review of the techniques that have been developed as part of this research effort will be presented in the final paper.

Chandrasekhara, M. S.↗
NASA NTRS1998

Quantitative Interferometry in the Severe Acoustic Environment of Resonant Supersonic Jets

There is renewed interest in the study of supersonic jets due to advances in high speed jet propulsion, supersonic combustion, and jet noise suppression for the next generation supersonic commercial transport. Understanding fundamental fluid dynamic and acoustic processes for these applications requires quantitative velocity, density and temperature measurements. In this paper we present data demonstrating a new, robust interferometer that can provide accurate data even in the presence of intense acoustic fields. This novel interferometer, the Liquid Crystal Point Diffraction Interferometer (LCPDI), was developed earlier for space flight experiments and is applied here to the case of a supersonic shock-containing jet. The LCPDI is briefly described, then integrated line-of-sight density data from the LCPDI for two underexpanded free jets are presented. The experimental shock spacings agree well with theory.

Mercer, Carolyn R.↗
NASA NTRS1971

Lubrication with sputtered MoS2 films.

Sputtered MoS2 films (2000-6500 A) were deposited on highly polished metal surfaces. These films have a low coefficient of friction (0.03-0.04) at speeds of 40-80 rpm and loads of 250-1000 grams. At loads of 250 grams, the wear lives are over 0.5 million cycles, but at 1000 gram loads, it decreases to 38,000 cycles. Friction experiments and tensile tests have indicated that sputtered films have a strong adherence to metal surfaces. Electron transmission, diffraction, and scanning electron microscopy show that these films have an extremely small particle size less than 30 A in diameter and are very dense and free from observable pinholes.

Spalvins, T.↗
NASA NTRS2000

Optimization of Microelectronic Devices for Sensor Applications

The NASA/JPL goal to reduce payload in future space missions while increasing mission capability demands miniaturization of active and passive sensors, analytical instruments and communication systems among others. Currently, typical system requirements include the detection of particular spectral lines, associated data processing, and communication of the acquired data to other systems. Advances in lithography and deposition methods result in more advanced devices for space application, while the sub-micron resolution currently available opens a vast design space. Though an experimental exploration of this widening design space-searching for optimized performance by repeated fabrication efforts-is unfeasible, it does motivate the development of reliable software design tools. These tools necessitate models based on fundamental physics and mathematics of the device to accurately model effects such as diffraction and scattering in opto-electronic devices, or bandstructure and scattering in heterostructure devices. The software tools must have convenient turn-around times and interfaces that allow effective usage. The first issue is addressed by the application of high-performance computers and the second by the development of graphical user interfaces driven by properly developed data structures. These tools can then be integrated into an optimization environment, and with the available memory capacity and computational speed of high performance parallel platforms, simulation of optimized components can proceed. In this paper, specific applications of the electromagnetic modeling of infrared filtering, as well as heterostructure device design will be presented using genetic algorithm global optimization methods.

Cwik, Tom↗
NASA NTRS1990

Near-nadir radar backscatter from a well-developed sea

The Kirchhoff approximation for the case of well-developed seas is analyzed. In this peculiar case, the equilibrium range in the wave number spectrum corresponds to a cascade pattern in the surface geometry. Its high wave number cutoff is shown to be a major factor of the radar backscatter. This intrinsic scale is evaluated, and both the geometrical and the physical optics terms are related to major parameters of wind-wave dynamics. The range of validity of the Kirchhoff approximation and the relative importance of the diffraction correction are analyzed. Finally, the radar cross section sigma exp 0 of well-developed seas is compared with that of poorly developed seas. The great qualitative difference shown in the wind speed dependence of sigma exp 0 for these two regimes is pointed out as a source of a considerable error trend recently discovered in satellite altimeter wind measurements.

Glazman, Roman E.↗
NASA NTRS1982

Evolution of shock-induced pressure on a flat-face/flat-base body and afterbody flow separation

The time-dependent, compressible Reynolds-averaged, Navier-Stokes equations are applied to solve an axisymmetric supersonic flow around a flat-face/flat-base body with and without a sting support. Important transient phenomena, not yet well understood, are investigated, and the significance of the present solution to the phenomena is discussed. The phenomena, described in detail, are as follows: the transient formation of the bow and recompression shock waves; the evolution of a pressure buildup due to diffraction of the incident shock wave in the forebody and afterbody regions, including the luminosity accompanying the pressure buildup; the separation of the flow as influenced by pressure buildup; the location of the separation and the reattachment points; and the transient period of the shock-induced base flow. The important influence of the nonsteady (transient) and steady flow on the aerodynamic characteristics, radiative heat transfer, and, thus, on the survivability or safeguard problems for an aircraft fuselage, missile, or planetary entry probe at very high flight speeds is described.

Yoshikawa, K. K.↗
NASA NTRS2005

Reconfigurable Antennas for High Data Rate Multi-beam Communication Systems

High-speed (2-100 Mb/sec) wireless data communication - whether land- or satellite-based - faces a major challenge: high error rates caused by interference and unpredictable environments. A planar antenna system that can be reconfigured to respond to changing conditions has the potential to dramatically improve data throughput and system reliability. Moreover, new planar antenna designs that reduce array size, weight, and cost can have a significant impact on terrestrial and satellite communication system performance. This research developed new individually-reconfigurable planar antenna array elements that can be adjusted to provide multiple beams while providing increased scan angles and higher aperture efficiency than traditional diffraction-limited arrays. These new elements are microstrip spiral antennas with specialized tuning mechanisms that provide adjustable radiation patterns. We anticipate that these new elements can be used in both large and small arrays for inter-satellite communication as well as tracking of multiple mobile surface-based units. Our work has developed both theoretical descriptions as well as experimental prototypes of the antennas in both single element and array embodiments. The technical summary of the results of this work is divided into six sections: A. Cavity model for analysis and design of pattern reconfigurable antennas; B. Performance of antenna in array configurations for broadside and endfire operation; C. Performance of antenna in array configurations for beam scanning operation; D. Simulation of antennas in infinite phased arrays; E. Demonstration of antenna with commercially-available RF MEMS switches; F. Design of antenna MEMS switch combinations for direct simultaneous fabrication.

Bernhard, Jennifer T.↗
NASA NTRS2007

Active Correction of Aberrations of Low-Quality Telescope Optics

A system of active optics that includes a wavefront sensor and a deformable mirror has been demonstrated to be an effective means of partly correcting wavefront aberrations introduced by fixed optics (lenses and mirrors) in telescopes. It is envisioned that after further development, active optics would be used to reduce wavefront aberrations of about one wave or less in telescopes having aperture diameters of the order of meters or tens of meters. Although this remaining amount of aberration would be considered excessive in scientific applications in which diffraction-limited performance is required, it would be acceptable for free-space optical- communication applications at wavelengths of the order of 1 m. To prevent misunderstanding, it is important to state the following: The technological discipline of active optics, in which the primary or secondary mirror of a telescope is directly and dynamically tilted, distorted, and/or otherwise varied to reduce wavefront aberrations, has existed for decades. The term active optics does not necessarily mean the same thing as does adaptive optics, even though active optics and adaptive optics are related. The term "adaptive optics" is often used to refer to wavefront correction at speeds characterized by frequencies ranging up to between hundreds of hertz and several kilohertz high enough to enable mitigation of adverse effects of fluctuations in atmospheric refraction upon propagation of light beams. The term active optics usually appears in reference to wavefront correction at significantly lower speeds, characterized by times ranging from about 1 second to as long as minutes. Hence, the novelty of the present development lies, not in the basic concept of active or adaptive optics, but in the envisioned application of active optics in conjunction with a deformable mirror to achieve acceptably small wavefront errors in free-space optical communication systems that include multi-meter-diameter telescope mirrors that are relatively inexpensive because their surface figures are characterized by errors as large as about 10 waves. Figure 1 schematically depicts the apparatus used in an experiment to demonstrate such an application on a reduced scale involving a 30-cm-diameter aperture.

Hemmati, Hamid↗
NASA NTRS2002

Phase-Shifting Liquid Crystal Interferometers for Microgravity Fluid Physics

The initial focus of this project was to eliminate both of these problems in the Liquid Crystal Point-Diffraction Interferometer (LCPDI). Progress toward that goal will be described, along with the demonstration of a phase shifting Liquid Crystal Shearing Interferometer (LCSI) that was developed as part of this work. The latest LCPDI, other than a lens to focus the light from a test section onto a diffracting microsphere within the interferometer and a collimated laser for illumination, the pink region contained within the glass plates on the rod-mounted platform is the complete interferometer. The total width is approximately 1.5 inches with 0.25 inches on each side for bonding the electrical leads. It is 1 inch high and there are only four diffracting microspheres within the interferometer. As a result, it is very easy to align, achieving the first goal. The liquid crystal electro-optical response time is a function of layer thickness, with thinner devices switching faster due to a reduction in long-range viscoelastic forces between the LC molecules. The LCPDI has a liquid crystal layer thickness of 10 microns, which is controlled by plastic or glass microspheres embedded in epoxy 'pads' at the corners of the device. The diffracting spheres are composed of polystyrene/divinyl benzene polymer with an initial diameter of 15 microns. The spheres deform slightly when the interferometer is assembled to conform to the spacing produced by the microsphere-filled epoxy spacer pads. While the speed of this interferometer has not yet been tested, previous LCPDIs fabricated at the Laboratory for Laser Energetics switched at a rate of approximately 3.3 Hz, a factor of 10 slower than desired. We anticipate better performance when the speed of these interferometers is tested since they are approximately three times thinner. Phase shifting in these devices is a function of the AC voltage level applied to the liquid crystal. As the voltage increases, the dye in the liquid crystal tends to become more transparent, thus introducing a rather large amount of error into the phase-shifting measurement. While that error can be greatly reduced by normalization, we prefer eliminating the source of the error. To that end, we have pursued development of a 'blend' of custom dyes that will not exhibit these properties. That goal has not yet been fully achieved. Guardalben, et al, presented a similar set of interferograms in a paper partially funded by this grant. Shearing interferometers are a second class of common path interferometers. Typically they consist of a thick glass plate optimized for equal reflection from the front and back surface. While not part of the original thrust of the project, through the course of laboratory work, we demonstrated a prototype of a shearing interferometer capable of phase shifting using a commercial liquid crystal retardation plate. A schematic of this liquid crystal shearing interferometer (LCSI) and a sample set of interferograms are in the reference. This work was also supported by the U.S. Department of Energy Office of Inertial Confinement Fusion under Cooperative Agreement No. DE-FC03-92SF19460, the University of Rochester, and the New York State Energy Research and Development Authority. The support of DOE does not constitute an endorsement by DOE of the views expressed in this article. Additional information is included in the original extended abstract.

Griffin, DeVon W.↗
NASA NTRS2016

Closing the Contrast Gap Between Testbed and Model Prediction with WFIRST-CGI Shaped Pupil Coronagraph

JPL has recently passed an important milestone in its technology development for a proposed NASA WFIRST mission: demonstration of a better than 1x10-8 contrast over broad bandwidth (10%) on both shaped pupil coronagraph (SPC) and hybrid Lyot coronagraph (HLC) testbeds with WFIRST telescope optics. Challenges remain, however, in the technology readiness for the proposed mission. One such is the discrepancy between the achieved contrast on testbeds and their corresponding model predictions. A series of testbed diagnosis and modeling activity were planned and (some) carried out on SPC testbed in order to close the gap. A very useful tool we developed was to analyze the measured testbed Jacobian and compare with its model version that was used to control image plane speckle pattern. The difference between these two is the error in the control Jacobian. When the error, which includes both amplitude and phase, was inserted into a separate prediction model with nominal Jacobian, the model prediction became closely matching the SPC testbed behavior in both contrast floor and contrast convergence speed. This offers a new perspective and is a step closer toward model validation for high contrast coronagraph. Further Jacobian analysis and modeling provided clues to the possible sources for the mismatch: the DM misregistration and the underrepresented testbed optics wavefront error (WFE) and the deformable mirror (DM) setting for correcting this WFE. These analyses suggested that high contrast coronagraph has a tight tolerance in the accuracy of its control Jacobian. Modifications to both testbed control model as well as prediction model are being implemented and future works discussed.

diffraction modeling↗
NASA NTRS2020

ROMAN CGI Testbed WFSC Modeling and Validation

Optical diffraction and wavefront sensing and control (WFSC) models validated against the high-fidelity Roman Space Telescope Coronagraph Instrument (CGI) testbed play a key role in mask design selection and the verification of many requirements that cannot be accomplished until the observatory is in orbit. We have been steadily improving our model fidelity for the as-built CGI testbed system, demonstrating recently good agreement between measurements and model predictions while validating the Hybrid Lyot Coronagraph’s (HLC) performance using the in-orbit high order wavefront sensing and control (HOWFSC) operational scenario. We present modeling and testbed validation results that explain the reason many testbed WFSC iterations were needed for HLC in the past. A new, direct application of model-generated deformable mirror (DM) solutions has since been successfully demonstrated on the testbed with significant speed and performance improvement. The benefit of using such a solution opens up new model-based WFSC approaches for CGI. This can greatly reduce flight risk from potentially insufficient ground solution generation due to schedule or cost constraints or from unexpected post-delivery changes.

Poberezhskiy, Ilya↗
NASA NTRS1995

Robust Quantitative Measurement of Flows and Transparent or Highly Reflective Objects

The liquid crystal point diffraction interferometer (LCPDI) is a new instrument that has been developed for the measurement of phase objects. The LCPDI uses the compact, robust design of Linnik's point diffraction interferometer and adds to it phase stepping capability for quantitative interferogram analysis. The result is a compact, simple to align, environmentally insensitive interferometer capable of accurately measuring optical wave-fronts. A solid state camera provides very high data density and automated data reduction. The instrument can measure either transparent objects like fluids and lenses, or highly reflective opaque objects like mirrors. In the former case, the refractive index distribution is measured and then related to various properties like temperature, density, chemical composition, or thickness. In the latter case, the measured phase distribution is related to the object shape. The objects measured must be stationary or quasisteady state because the measurement requires the acquisition of several frames of image data during which time the object's properties must not have changed. The data acquisition time depends on the speed of the frame grabber and the required number of data frames. Typically, three to five frames taking 1 to 2 seconds are required. The potential for faster data acquisition exists.

Mercer, Carolyn R.↗
NASA NTRS2009

One-Dimensional Scanning Approach to Shock Sensing

Measurement tools for high speed air flow are sought both in industry and academia. Particular interest is shown in air flows that exhibit aerodynamic shocks. Shocks are accompanied by sudden changes in density, pressure, and temperature. Optical detection and characterization of such shocks can be difficult because the medium is normally transparent air. A variety of techniques to analyze these flows are available, but they often require large windows and optical components as in the case of Schlieren measurements and/or large operating powers which precludes their use for in-flight monitoring and applications. The one-dimensional scanning approach in this work is a compact low power technique that can be used to non-intrusively detect shocks. The shock is detected by analyzing the optical pattern generated by a small diameter laser beam as it passes through the shock. The optical properties of a shock result in diffraction and spreading of the beam as well as interference fringes. To investigate the feasibility of this technique a shock is simulated by a 426 m diameter optical fiber. Analysis of results revealed a direct correlation between the optical fiber or shock location and the beam s diffraction pattern. A plot of the width of the diffraction pattern vs. optical fiber location reveals that the width of the diffraction pattern was maximized when the laser beam is directed at the center of the optical fiber. This work indicates that the one-dimensional scanning approach may be able to determine the location of an actual shock. Near and far field effects associated with a small diameter laser beam striking an optical fiber used as a simulated shock are investigated allowing a proper one-dimensional scanning beam technique.

Tokars, Roger↗
NASA NTRSDate not supplied

Building and Breaking Carbon Composites with REACTER

Carbon composites have become indispensable for aerospace and other high-performance applications, and a detailed picture of their morphology and failure mechanisms remains difficult to obtain through experiment. REACTER is a versatile computational modeling tool for atomistic molecular dynamics designed to model chemical reactions at the speed and length scales of classical force fields.1 In this work, several recent features of REACTER were applied to the creation and subsequent mechanical testing of two classes of carbon composites, carbon-fiber reinforced polymers (CFRP) and carbon nanotube (CNT) composites. Carbon fiber core morphologies were created by the method of Desai et al.,2 but using the advanced reaction constraints framework of REACTER, their proposed multistep procedure was reduced to a single uninterrupted molecular dynamics simulation. The carbon fiber filler was embedded into a polymer matrix by simulated in situ polymerization of several thermosetting resins, including bismaleimide and polyarylacetylene, to obtain the final CFRP model. To generate the second class of carbon composite, CNT networks were grown dynamically using the new ‘create atoms’ feature of REACTER, and similarly infiltrated with resin to obtain CNT composites. The resulting models were compared directly to experiment using simulated high resolution transmission electron microscopy and x-ray diffraction. Failure mechanisms were elucidated by simulating mechanically induced bond breaking, as characterized by third-order DFT-based tight-binding (DFTB3) simulations, via a reaction constraint on the total potential energy of the involved atoms.

Molecular Dynamics↗
NASA NTRS1999

Overview of Photonic Materials for Application in Space Environments

Future space systems will he based on components evolving from the development and refinement of new and existing photonic materials. Optically based sensors, inertial guidance, tracking systems, communications, diagnostics, imaging and high speed optical processing are but a few of the applications expected to widely utilize photonic materials. The response of these materials to space environment effects (SEE) such as spacecraft charging, orbital debris, atomic oxygen, ultraviolet irradiation, temperature and ionizing radiation will be paramount to ensuring successful space applications. The intent of this paper is to, address the latter two environments via a succinct comparison of the known sensitivities of selected photonic materials to the temperature and ionizing radiation conditions found in space and enhanced space environments Delineation of the known temperature and radiation induced responses in LiNbO3, AlGaN, AlGsAs,TeO2, Si:Ge, and several organic polymers are presented. Photonic materials are realizing rapid transition into applications for many proposed space components and systems including: optical interconnects, optical gyros, waveguide and spatial light modulators, light emitting diodes, lasers, optical fibers and fiber optic amplifiers. Changes to material parameters such as electrooptic coefficients, absorption coefficients, polarization, conductivity, coupling coefficients, diffraction efficiencies, and other pertinent material properties examined for thermo-optic and radiation induced effect. Conclusions and recommendations provide the reader with an understanding of the limitations or attributes of material choices for specific applications.

Taylor, E. W.↗
NASA NTRS1989

High speed turboprop aeroacoustic study (single rotation). Volume 1: Model development

A frequency-domain noncompact-source theory for the steady loading and volume-displacement (thickness) noise of high speed propellers has been developed and programmed. Both near field and far field effects have been considered. The code utilizes blade surface pressure distributions obtained from three-dimensional nonlinear aerodynamic flow field analysis programs as input for evaluating the steady loading noise. Simplified mathematical models of the velocity fields induced at the propeller disk by nearby wing and fuselage surfaces and by angle-of-attack operation have been developed to provide estimates of the unsteady loading imposed on the propeller by these potential field type interactions. These unsteady blade loadings have been coupled to a chordwise compact propeller unsteady loading noise model to provide predictions of unsteady loading noise caused by these installation effects. Finally, an analysis to estimate the corrections to be applied to the free-field noise predictions in order to arrive at the measurable fuselage sound pressure levels has been formulated and programmed. This analysis considers the effects of fuselage surface reflection and diffraction together with surface boundary layer refraction. The steady loading and thickness model and the unsteady loading model have been verified using NASA-supplied data for the SR-2 and SR-3 model propfans. In addition, the steady loading and thickness model has been compared with data from the SR-6 model propfan. These theoretical models have been employed in the evaluation of the SR-7 powered Gulfstream aircraft in terms of noise characteristics at representative takeoff, cruise, and approach operating conditions. In all cases, agreement between theory and experiment is encouraging.

Whitfield, C. E.↗
NASA NTRS2004

Fabricating Blazed Diffraction Gratings by X-Ray Lithography

Gray-scale x-ray lithography is undergoing development as a technique for fabricating blazed diffraction gratings. As such, gray-scale x-ray lithography now complements such other grating-fabrication techniques as mechanical ruling, holography, ion etching, laser ablation, laser writing, and electron-beam lithography. Each of these techniques offers advantages and disadvantages for implementing specific grating designs; no single one of these techniques can satisfy the design requirements for all applications. Gray-scale x-ray lithography is expected to be advantageous for making gratings on steeper substrates than those that can be made by electron-beam lithography. This technique is not limited to sawtooth groove profiles and flat substrates: various groove profiles can be generated on arbitrarily shaped (including highly curved) substrates with the same ease as sawtooth profiles can be generated on flat substrates. Moreover, the gratings fabricated by this technique can be made free of ghosts (spurious diffraction components attributable to small spurious periodicities in the locations of grooves). The first step in gray-scale x-ray lithography is to conformally coat a substrate with a suitable photoresist. An x-ray mask (see Figure 1) is generated, placed between the substrate and a source of collimated x-rays, and scanned over the substrate so as to create a spatial modulation in the exposure of the photoresist. Development of the exposed photoresist results in a surface corrugation that corresponds to the spatial modulation and that defines the grating surface. The grating pattern is generated by scanning an appropriately shaped x-ray area mask along the substrate. The mask example of Figure 1 would generate a blazed grating profile when scanned in the perpendicular direction at constant speed, assuming the photoresist responds linearly to incident radiation. If the resist response is nonlinear, then the mask shape can be modified to account for the nonlinearity and produce a desired groove profile. An example of grating grooves generated by this technique is shown in Figure 2. A maximum relative efficiency of 88 percent has been demonstrated.

Mouroulis, Pantazis↗
NASA NTRS2009

Lattice-Matched Semiconductor Layers on Single Crystalline Sapphire Substrate

SiGe is an important semiconductor alloy for high-speed field effect transistors (FETs), high-temperature thermoelectric devices, photovoltaic solar cells, and photon detectors. The growth of SiGe layer is difficult because SiGe alloys have different lattice constants from those of the common Si wafers, which leads to a high density of defects, including dislocations, micro-twins, cracks, and delaminations. This innovation utilizes newly developed rhombohedral epitaxy of cubic semiconductors on trigonal substrates in order to solve the lattice mismatch problem of SiGe by using trigonal single crystals like sapphire (Al2O3) as substrate to give a unique growth-orientation to the SiGe layer, which is automatically controlled at the interface upon sapphire (0001). This technology is different from previous silicon on insulator (SOI) or SGOI (SiGe on insulator) technologies that use amorphous SiO2 as the growth plane. A cubic semiconductor crystal is a special case of a rhombohedron with the inter-planar angle, alpha = 90 deg. With a mathematical transformation, all rhombohedrons can be described by trigonal crystal lattice structures. Therefore, all cubic lattice constants and crystal planes (hkl) s can be transformed into those of trigonal crystal parameters. These unique alignments enable a new opportunity of perfect lattice matching conditions, which can eliminate misfit dislocations. Previously, these atomic alignments were thought to be impossible or very difficult. With the invention of a new x-ray diffraction measurement method here, growth of cubic semiconductors on trigonal crystals became possible. This epitaxy and lattice-matching condition can be applied not only to SiGe (111)/sapphire (0001) substrate relations, but also to other crystal structures and other materials, including similar crystal structures which have pointgroup rotational symmetries by 120 because the cubic (111) direction has 120 rotational symmetry. The use of slightly miscut (less than plus or minus 10 deg.) sapphire (0001) substrate can be used to improve epitaxial relationships better by providing attractive atomic steps in the epitaxial process.

Choi, Sang↗