Department of Materials Science and Engineering (MSE)

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The mission of the Materials Science and Engineering (MSE) Department at Virginia Tech is to lead the multidisciplinary efforts of the College of Engineering, the University, and the Commonwealth in the field of Materials Science and Engineering through our programs of undergraduate and graduate education, research, and continuing education. In service to our many constituencies, we are committed to the excellence of the contributions of faculty members, staff, and students, as judged by the principles and philosophies to which we aspire.

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X‐ray diffraction approach to grain boundary and volume diffusion
Unnam, Jalaiah; Carpenter, Joseph A.; Houska, Charles R. (American Institute of Physics, 1973)
A generalized two‐dimensional diffusionmodel has been developed which consists of an array of boundaries coupled to the free surface and to the substrate lattice. The model makes use of three nonlinear partial differential equations which describe lattice, grain boundary, and surfacediffusion. This two‐dimensional model has been programmed for the IBM 360 computer using a finite‐difference solution to give concentrations as a function of time. An x‐ray intensity simulation program is developed to give integrated diffracted intensity for a given concentration distribution. This simulated intensity is compared with experimental intensity. Data are presented from a sample containing 8 μ of Ni on a (111)‐oriented Cu crystal diffused for various times at 900°C and a similar sample with 6.5 μ of Ni diffused at 600°C. The simulations are in good agreement with experimental intensity bands. Activation energies and frequency factors are given for volume and grain boundarydiffusion which are in good agreement with those literature values that are available. After a diffusion treatment at 600°C, it was found that pipe diffusion makes an important contribution to the volume diffusion coefficient. At 900°C this does not appear to be true. The contribution from pipe diffusion correlates with rocking curve data except for compositions close to that of the free surface.
An x‐ray study of diffusion in the Cu‐Ag system
Unnam, Jalaiah; Houska, Charles R. (American Institute of Physics, 1976)
The interdiffusion coefficients for both solid phases of the Ag‐Cu system have been determined from x‐ray diffraction and electron microprobe data. Specimens containing 3.2 μm of Ag on a (111) ‐oriented Cu crystal were used for the x‐ray studies, while a 15‐μm deposit of Ag was used for the probe specimens. Composition profiles for each phase were obtained from the x‐ray intensity bands and a new iterative one‐dimensional model was applied to determine the composition‐dependent diffusion coefficients. The average diffusion coefficients for both phases are nearly equal at about 10−10 cm2/sec at 750 °C, the diffusion temperature. Also, the solubility for the Ag‐rich phase is about three times the solubility for the Cu‐rich phase. These conditions result in interface reversal, i.e., the interface first moves into the substrate and later moves toward the free surface.Structural damage resulting from atomic diffusion was found to be much smaller for the Ag‐Cu system than for other single‐phase Cu‐base specimens that have been examined. Both crystal misorientation (tilt) and subgrains are formed as a result of diffusion. The subgrain shape in the plating depends upon the ratio of the thickness to the initial grain size of the plating.
Iterative approaches describing atomic diffusion in finite single‐ and two‐phase systems
Houska, Charles R.; Unnam, Jalaiah (American Institute of Physics, 1976)
Iterative solutions are given for planar one‐dimensional atomic diffusion in finite single‐ and two‐phase systems. They are usable for any continuous variation of the interdiffusion coefficient D (C) within each phase, and need not be fitted to special functions such as a power series or an exponential function. Modified integral functions similar to one first proposed by Boltzmann are used along with a conservation criterion to locate the interface position ξ. Computer time for the iterative solutions is about two to three magnitudes shorter than finite‐difference (F‐D) calculations because of the rapid convergence of the integral equations. The accuracy of these approximate forms is considered. Excellent agreement was obtained between F‐D calculations and the iterative approach for semi‐infinite single‐phase systems. Good agreement is also found for two‐phase systems; however, the accuracy varies with the solubility gap size C βα−Cαβ. The best results are obtained for gaps larger than 0.7 which includes most eutectic systems. Calculations of composition profiles which are based upon the maximum solid solubilities for the Cu‐Ag system are within 1% of the F‐D calculations.
Broadening of x‐ray diffraction lines from small subgrains containing gradients of spacing
Houska, Charles R. (American Institute of Physics, 1978)
Recent data on subgrain size and spacing gradients in the Cu‐Ni system allow a more critical examination of a technique currently used to obtain the composition profiles of small diffusion zones. These data support the assumption that the broadening from individual subgrains need not include a spacing gradient term when volume diffusion is predominant. However, care should be taken in the interpretation of the earliest stage of diffusion where grain boundaries,surface, and other defects may introduce large spacing gradients.
Simplifications in the x‐ray line‐shape analysis
Adler, Thomas; Houska, Charles R. (American Institute of Physics, 1979)
It is shown that a Fourier series associated with the Warren‐Averbach line‐shape analysis can be fitted with only five parameters to a pair of peaks. These interrelate the Fourier coefficients and thereby provide a simplified series which has been applied to the study of a Mo film on a Si crystal. The parameters include the average particle size, the first neighbor rms strain, a term which gives the variation in rms strain with cell separation, and two instrumental broadening coefficients. Although considerable simplification is possible, equivalent information can be obtained as compared with the original analysis and the ’’hook effect’’ is eliminated in the fitted coefficients.
Affect of annealing on uniform and nonuniform strains in a sputtered Mo film on Si
Adler, Thomas; Houska, Charles R. (American Institute of Physics, 1979)
Sputtered films of 1.5 μm of Mo deposited on (111) ‐oriented Si failed either by blistering or localized eruptions after various thermal treatments. Investigations were carried out to determine the amount of strain in the film associated with this unstable mechanical behavior. Two types of measurements were employed. One employs macroscopic interferometer measurements to measure deflection and the other x‐ray diffraction. A separation is made of intrinsic and thermally induced strains. The intrinsic strains are believed to be due mainly to Ar atoms embedded during sputtering which remain throughout annealing treatments. These atoms also introduce a broadening of the diffraction lines because of the special constraints associated within films. This effect is separated from the usual line broadening due to dislocations and small particle size. Annealing treatments reconfirm that dislocation mechanisms are not as effective in relieving nonuniform microstrain in films as they are in cold‐work filings of the same material.
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.
Least‐squares analysis of x‐ray diffraction line shapes with analytic functions
Houska, Charles R.; Smith, Terence M. (American Institute of Physics, 1981)
This is a second paper of a sequence that provides a useful analytic function which is based upon the Warren‐Averbach line shape analysis. Once the Fourier coefficients are interrelated in terms of a minimum number of parameters, the rather lengthy Fourier series can be evaluated by reducing it to a convolution of two known functions. One of these functions includes the particle size distribution, strain, and the Cauchy‐like contribution to the instrumental broadening. The second includes another strain parameter and the Gaussian contribution to the instrumental broadening. The resultant convolution integral is readily carried out using a nine‐point Gauss‐Legendre quadrature. Instrumental parameters are obtained from a separate convolution of Cauchy and Gaussian functions. This procedure reduces the computer time to one‐tenth the time required to synthesize the Fourier series and makes it feasible to carry out a least‐squares fitting of the profile data. Examples are given for Mo films and for an InSb film.
On a point defect inside an idealized elastic sphere
Ling, Chih B.; Houska, Charles R. (American Institute of Physics, 1983)
This paper presents a method of solution for the displacement, stress, and strain due to a point defect located inside a sphere. The solution is represented by a Love stress function in spherical coordinates, which is biharmonic in character. Two axisymmetric types of the point defect are considered. One is treated as a center of dilatation and the other as a double force without moment, or a doublet, oriented axisymmetrically. The Love stress function for the point defect in an infinite solid is specified in each case by a single biharmonic function. The residual tractions on the surface of the sphere left by this function are annulled by superposing two series of biharmonic functions. When the Love stress function is determined, the displacement, stress, and strain can be derived straightforwardly.
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.
Modeling of high fluence Ti ion implantation and vacuum carburization in steel
Farkas, Diana; Singer, Irwin L.; Rangaswamy, M. (American Institute of Physics, 1985)
Concentration‐versus‐depth profiles have been calculated for Ti and C in Ti‐implanted 52100 steel. A computer formalism was developed to account for diffusion and mixing processes, as well as sputtering and lattice dilation. A Gaussian distribution of Ti was assumed to be incorporated at each time interval. The effects of sputtering and lattice dilation were then included by means of an appropriate coordinate transformation. C was assumed to be gettered from the vacuum system in a one‐to‐one ratio with the surface Ti concentration up to a saturation point. Both Ti and C were allowed to diffuse. A series of experimental (Auger) concentration‐versus‐depth profiles of Ti‐implanted steel were analyzed using the above‐mentioned assumptions. A best fit procedure for these curves yielded information on the values of the sputtering yield, range, and straggling, as well as the mixing processes that occur during the implantation. The effective diffusivity of Ti was found to be 6×10− 1 5 cm2/sec, a value that is consistent with the cascade mixing mechanism. The effective diffusivity of C was found to be 6×10− 1 5 cm2/sec, and the sputtering yield by Ti atoms was best fit by a value of about 2. The observed range and straggling values were in very good agreement with the values predicted by existing theories, so long as the lattice was allowed to dilate.
Calculation of x‐ray intensity from a rough sample based on a statistical model
Hwang, Bing; Houska, Charles R. (American Institute of Physics, 1988-06-01)
An x‐ray intensity correction is developed which begins with a roughness model that is often used to describe real surfaces. This is based upon a normal distribution of surface asperities relative to a mean plane. Pair correlation between absorbing elements along x‐ray paths either entering or leaving the sample with respect to the signal producing element is accomplished by means of an exponential autocorrelation function. This allows the degree of roughness to be varied on a local scale to fit specific surfaces using statistical data. Equations are developed to describe x‐ray fluorescence and diffraction signals for symmetric and asymmetric beam optics. Theory is compared with experiment using a roughened, fully stabilized zirconia sample.
Residual strain gradients in a fully stabilized zirconia sample
Hwang, Bing; Houska, Charles R.; Ice, Gene E.; Habenschuss, Anthony (American Institute of Physics, 1988-06-01)
Polished and severely ground fully stabilized zirconia samples are examined using primarily x‐ray diffraction(XRD). The XRD (111) profile reflections from both samples were broadened asymmetrically compared to that of an annealed sample. The asymmetry results from a d‐spacing gradient extending from the free surface into undisturbed bulk material. There are two possible origins of this depth gradient, i.e., variations in residual strain or chemical composition. The latter is eliminated by means of x‐ray photoelectron spectroscopy which did not reveal a chemical gradient. d‐spacing profiles for both samples are obtained nondestructively using a trial and error fitting procedure. A maximum compressive strain of ∼4% is obtained at the surface of the ground sample which decreases gradually to zero at greater depths. The overall zone is ∼1–2 μm. A similar but smaller compressive zone is found in the polished sample which is followed by a zone of tension. The maximum compressive strain at the surface is ∼5% and the overall zone of residual strain is ∼0.1 μm.
Grain-boundary ordering, segregation, and melting transitions in a two-dimensional lattice-gas model
Farkas, Diana; Jang, H. (American Physical Society, 1989-06-01)
A two-dimensional lattice-gas model of a binary-ordering-alloy system was used to study the phase transitions and the atomic configuration near a Σ=5 grain boundary. The cluster variation method was used to study order-disorder and melting transitions in the bulk alloys. The complete binary phase diagrams were constructed for two different sets of interaction-energy assumptions. Simulations based on the same model were performed to study these transitions in the grain-boundary region. In addition, the model also yields information on the segregation behavior of the alloying elements in the grain-boundary region.
Empirical many-body interatomic potential for bcc transition metals
Pasianot, R.; Farkas, Diana; Savino, E. J. (American Physical Society, 1991-03-01)
A simple many-body interatomic potential is proposed. This is an empirical extension of the embedded-atom method (EAM). The EAM models the lattice energy and elastic compressibility using a pair interaction plus a many-body term. It does not include any contribution of many-body terms to the crystal elastic shear. This contribution is included in the model developed here. It implies a simplified treatment of the angularity inherent to covalent bonding in transition metals. A set of interatomic potentials is deduced for bcc Nb, Fe, and Cr. While in previous works in the literature the EAM has already been successfully applied to the fitting of interatomic potentials for Nb and Fe, this was not the case for Cr, for which the elastic-constant values implied a negative Cauchy pressure.
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.
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.
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.
Pyrochlore to Perovskite phase-transformation in sol-gel derived lead-zirconate-titanate thin-films
Kwok, C. K.; Desu, Seshu B. (AIP Publishing, 1992-03-01)
Pyrochlore to perovskite phase transformation in sol-gel derived lead-zirconate-titanate (PZT) films was studied by x-ray diffraction and transmission-electron microscopy (TEM). X-ray diffraction studies of PZT films on sapphire substrates indicated that the pyrochlore to perovskite phase transformation was completed at 650-degrees-C. In contrast, TEM investigations of free-standing PZT films showed that the phase transformation was completed at much higher temperatures. This discrepancy in the behavior of free-standing films versus films on substrate can be related to the size effect.
Low-temperature metalorganic chemical vapor-deposition of perovskite PB(ZRXTI1-X)O3 thin-films
Peng, C. H.; Desu, Seshu B. (AIP Publishing, 1992-07-01)
Pb (ZrxTi1-x)O3 thin films with perovskite structure were successfully prepared on sapphire disks, Pt/Ti/SiO2/Si, and RuOx/SiO2/Si substrates at temperatures as low as 550-degrees-C by hot-wall metalorganic chemical vapor deposition. Safe and stable precursors were used, namely: lead tetramethylheptadione [Pb(thd)2], zirconium tetramethylheptadione [Zr(thd)4], and titanium ethoxide. The deposition rates were in the range of 10.0 to 20.0 nm/min. The Auger electron spectroscopy (AES) depth profile showed good uniformity across the bulk of the films. The AES spectra also showed no carbon contamination in the bulk of the films. Zr/Ti ratio were easily controlled by the precursor temperatures and the flow rate of diluent gas. Optical constants were measured by a UV-VIS-NIR spectrophotometer. As-deposited films were dense and showed uniform and fine grain size. The 600-degrees-C annealed film (Pb/Zr/Ti=50/41/9) showed a spontaneous polarization of 23.3-mu-C/cm3 and a coercive field of 64.5 kV/cm.

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