Charles R. Houska

Simplifications in the x‐ray line‐shape analysis

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.

X‐Ray Diffraction from a Binary Diffusion Zone

Prior treatments of the scattered x‐ray intensity from diffusion zones in two component crystalline systems lack a formal basis and tend to be intuitive in approach. Relatively simple and useful results can be obtained if the continuous composition changes are approximated by either a series of steps or by a system of linear segments. This paper develops equations for the coherent scattering from both approximations. Summing the scattering from all segments leads to the formation of intensity bands. Equations, containing an absorption correction, are given for planar diffusion zones in the micron and submicron range.

X‐Ray Diffraction Technique for the Investigation of Small Diffusion Zones

A nondestructive x‐ray diffraction technique has been developed to analyze small diffusion zones. This technique constitutes a new approach to the study of one‐dimensional volume diffusion and only requires intensity measurements from two different reflections. It has the distinct advantages of permitting a determination of both the concentration profile and the atomic arrangements associated with the diffusion zone. Data for the Cu–Ni system is presented to provide an example of the technique. The composition profile resulting from the interdiffusion of an 8‐μ Ni deposit and a Cu single crystal at 900°C for 45 min was determined. Good agreement was found between these experimental results and a composition curve calculated from DaSilva‐Mehl diffusion coefficients. It has also been found that volume diffusion significantly increases the degree of crystalline misorientation along the diffusion zone. The structure of the as‐plated Ni deposits on a Cu single crystal was found to undergo a large misorientatio...

Method for Determining Composition Profiles and Diffusion‐Generated Substructure in Small Diffusion Zones

An x‐ray diffraction technique is described which may be used to determine the composition profile of small diffusion zones as well as the diffusion‐generated substructure. Thus far, this technique is restricted to volume diffusion and has been applied in the case of a single‐phase solid solution; however, the methods may be readily applied to volume diffusion in multiphase systems. Data are presented for a system containing an 8‐μ deposit of Ni on a [111] oriented single crystal of Cu. This composite was diffused at 900 °C for 45 min, 2 h, and 5 h. A Matano‐Boltzmann analysis of the composition profile gave good agreement with recently obtained diffusion coefficients. The degree of diffusion‐generated subgrain misorientation increased with annealing time and zone size up to the maximum time for our experiments. There was no evidence for the existence of nonuniform strain, and the distribution of subgrain misorientation was found to be Gaussian. Also, the widths of the Gaussian misorientation functions ap...

X‐Ray Determinations of the Debye Temperatures and Thermal Expansions for the Pd–Ag–Au System

X‐ray measurements of the Debye characteristic temperatures ΘM and the coefficient of thermal expansion for the Pd–Ag–Au ternary‐alloy system are presented. The integrated intensities of Bragg reflections and lattice parameters were measured in the temperatures range 80–298°K. For all the alloys, the predominant lattice disturbance was due to thermal vibrations. No significant effect due to static displacements was found. Debye temperatures were found to range from a low of 184°K for gold to a high of 290°K for palladium, with silver intermediate at 226°K. The mean coefficient of thermal expansion was found to range from 9.8×10−6 for palladium to 17.9×10−6 for silver. Gruneisens relationship between the meansquare atomic‐vibration amplitude and the thermal expansion for cubic solids has been found to be valid for these alloys and the constant γZ2 was found to be 0.167. The results suggest that a general weakening of the cohesive forces might be taking place as the smaller palladium atoms are replaced by ...

Least‐squares analysis of x‐ray diffraction line shapes with analytic functions

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.

An x‐ray study of diffusion in the Cu‐Ag system

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 specime...

X-ray diffraction analysis of concentration and residual stress gradients in nitrogen-implanted niobium and molybdenum

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 (∼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...

Residual strain gradients in a fully stabilized zirconia sample

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% an...

Affect of annealing on uniform and nonuniform strains in a sputtered Mo film on Si

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 s...