Browsing by Author "Rao, Satish I."

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    The measurement of elastic stresses and energy in cubic single‐crystal films by x‐ray diffraction
    Rao, Satish I.; Houska, Charles R. (American Institute of Physics, 1981)
    Anisotropicelasticity calculations have been made for use in conjunction with strain measurements by x‐ray diffraction for sputtered single‐crystal films. Only the cubic case has been treated. Data from InSb films with (100) and (111) orientations on similarly oriented GaAs substrates are given. It was found that nearly alike planar strains ε yield lower planar stresses σ′ 1 and σ′ 2 and stored energy density U for the (100) orientation. The (100) films exhibit a relatively large strain perpendicular to the film ε3.
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    Quantitative analysis of fiber texture in cubic films
    Rao, Satish I.; Houska, Charles R. (American Institute of Physics, 1983)
    The method of Roe and Krigbaum for determining fiber texture has been extended to thin film applications. It is often desirable to make i n s i t u pole density measurements of a film on a thick substrate. This does not permit complete data to be collected by x‐ray transmission techniques. If the data are restricted to the range 0≤χ≤75°, obtained by reflection, incomplete pole density plots are obtained, and it is necessary to devise a self‐consistent extrapolation technique that extends the pole density data to 90°. This requires least‐squares fitting over the range from χ=0 to 75° and an iterative procedure for extrapolating with functions consistent with a single orientation function. The example of a 1.14‐μ Mo film on a (111) Si substrate requires an expansion of the symmetry relations to order 46. The procedure established herein is readily extended to include the effect of static displacements resulting from embedded gas atoms that are associated with sputtered films.
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    A simplified procedure for obtaining relative x‐ray intensities when a texture and atomic displacements are present
    He, Baoping; Rao, Satish I.; Houska, Charles R. (American Institute of Physics, 1994-05-01)
    The orientation problem in polycrystalline cubic materials has been simplified, using fundamental relationships, so that the determination of a quantitative interrelationship between the various Bragg peak intensities is no longer a formidable task. This is demonstrated with a cubic Cu-Be-Co alloy having a fiber texture, and a conventional focusing diffractometer. Because data are required which extend over a larger range in d spacings, extinction, thermal, and static atomic displacements must be included into the analysis of intensities. The displacement terms and the extinction parameters may be of primary interest or used as a correction. Seventeen diffraction peaks are used in the example. These must be internally consistent with a crystallite orientation function, the cubic symmetry of the sample, extinction effects influencing the two strongest peaks, and attenuation due to atomic displacements. Tabulated coefficients are presented which greatly reduce the task of calculating the orientation function. A correction is given for instrumental smearing which should be considered for stronger textures than the intermediate case examined or for intermediate textures and nonfocusing instrumental conditions.
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    Thermal diffuse scattering in polycrystalline materials with a texture
    Wu, C. H.; Houska, Charles R.; Rao, Satish I. (American Institute of Physics, 1994-05-01)
    A simplified method of calculating thermal diffuse scattering (TDS) for materials at or above their Debye characteristic temperature is presented. This method is based upon the properties of the lattice Green's function and eliminates the need of solving the equations of lattice dynamics. This simplifies the calculation procedure. The general scheme of evaluating the diffuse scattering for polycrystalline materials with a texture is discussed. A sample calculation of the TDS from a polycrystalline material with a fiber texture is given using the simplified procedure just presented.
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    X-ray diffraction from point-like imperfection
    He, Baoping (Virginia Tech, 1992-01-15)
    Displacement fields from point-like defects are investigated by x-ray diffraction. The atomic volume changes in the interstitial compounds using crystallographic information has been found to correlate with the size of filled octahedral sites. Systematic correlations enable estimates to be made of the components of the dipole tensor for interstitials in octahedral sites for binary systems containing N, C, and 0 in V, Nb, Ta, Cr, Mo, W, and Fe lattices. X-ray diffraction analysis of the concentration and residual stress gradients in N implanted Mo crystals and Nb films show that the dominant source of internal strain arises from N located in octahedral sites. For Nb implanted at LNT, these distortion centers are aligned equally along three mutually perpendicular directions to maintain cubic symmetry. Large biaxial residual strains are developed after a 5at% implantation of N into Nb and Mo. Radiation damage is present as small vacancy and interstitial loops. A method was developed to obtain the orientation function for samples containing a fiber texture. A slit correction is included and the final results from this simplified approach are compared with the pole figure measured by direct x-scanning. Knowing the orientation function allows one to correct the integrated intensities to that for an ideal powder, thereby allowing thermal and static displacements to be obtained from textured samples. Anisotropic displacements about coherent Be rich GP zones were investigated in a Cull-at%Be alloy. The results indicate that the attenuation factor 2M which determines the relative integrated intensities of Bragg, quasiline, and static diffuse scattering can be expressed in a simplified form. Experimental data of 2M for aged Cu-Be samples show an anisotropy. The anisotropy increases with increasing aging time when the equiaxed-GP zones formed in the early stage collapse into platelike GP zones.
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    X‐ray diffraction analysis of concentration and residual stress gradients in nitrogen‐implanted niobium and molybdenum
    Rao, Satish I.; He, Baoping; Houska, Charles R.; Grabowski, Kenneth (American Institute of Physics, 1991-06-15)
    Large biaxial residual strains are developed after a 5-at.% implantation of N into Nb and Mo. The results indicate that the dominant source of internal strain arises from N located in interstitial sites. For Nb implanted at liquid-nitrogen temperature, the N atoms are located in octahedral sites. However, the data allow for some clustering as di- or tri-interstitials at the highest concentration (approximately 5 at. % N). Radiation damage is present as small vacancy and interstitial loops. Since vacancies and self-interstitials are present in nearly equal concentrations, the overall bulk dilatation cancels. However, because of their small size, a lesser core expansion has been included as a correction to the overall residual strain. Although one can obtain an estimate of the N distribution from TRIM, a more accurate description must include the distribution of knock-on energy. The latter has an important influence on the redistribution of N relative to that predicted by TRIM. Both host lattices (Nb and Mo) behave like "rigid containers" in directions parallel to the free surface and give a magnified elastic response normal to the free surface.
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    X‐ray diffraction from d spacing gradients along ion‐implanted zones
    Rao, Satish I.; Houska, Charles R. (American Institute of Physics, 1991-06-15)
    Three kinematic diffraction models are described for interpreting diffraction profiles from ion-implanted samples. Each deals with relatively large d spacing gradients. The first treats the full zone as coherent which requires a direct summation of the Fourier series. The Bragg intensity band from the full zone is applied to implanted zones that are subjected to elastic constraints without incoherent interfaces. For high-fluence samples, and foreign interstitials, a static attenuation term becomes important and is included in all models. This term was not included in previous publications by the authors. The last two models deal with finite subgrain elements that may be connected in a continuous way with interfaces. With a linear element model, slope discontinuities give a sawtooth appearance of the d spacing curve. These discontinuities are eliminated by employing a sinusoidal variation in d spacing in a third model. The additional smoothing does not provide significant changes in the fine structure of the measured intensity. The parameters that determine line shape are: DELTA-M, the total change in the attenuation factor M within a subgrain, and s = N3l(DELTA-d/) which contains three additional independent parameters. These are the subgrain size, the order of the Bragg peak l, and the fractional changes in d spacing. The static lattice displacements can be large enough to introduce an asymmetry of the diffraction profiles from individual elements. This occurs when DELTA-M is greater than 0.15. Although this factor has been introduced only in the linear element model, a similar asymmetry should be observed with a sinusoidal variation in d spacing.
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    X‐ray diffuse scattering from a nitrogen‐implanted niobium film
    Rao, Satish I.; Houska, Charles R.; Grabowski, Kenneth; Ice, Gene E.; Sparks, C. J. (American Institute of Physics, 1991-06-15)
    A 2500-angstrom niobium single-crystal film was deposited onto a sapphire substrate and subsequently implanted with nitrogen to an average concentration of 0.5 at. %. Synchrotron radiation was used to measure the difference between the implanted and an unimplanted film to isolate the diffuse scattering from the implanted film near two Bragg reflections. This diffuse intensity arises mainly from elastic displacement fields about radiation-damage-related loops located on (211) planes. A small contribution of the scattering is calculated from the displacements about single interstitial nitrogen in octahedral sites. The Burgers vector of the loops is along the [111BAR] direction and makes an angle of 62-degrees with the loop plane giving a dominant shear component. Vacancy loops have a radius approximately 5 angstrom while interstitials are somewhat larger ranging from 10 to 15 angstrom. The number of vacancies and interstitials are nearly the same.