Stacking Fault Probability Research Articles

Structural characterization of cadmium oxide thin films deposited by spray pyrolysis

A series of CdO thin films have been prepared by spray pyrolytic technique at different substrate temperatures. X-ray diffraction scans confirmed the polycrystalline structure of the films. The films exhibit preferential orientation along the (111) plane. To describe the preferential orientation, the texture coefficient has been calculated and the standard deviation factor has also been evaluated to explain the growth mechanism. Various structural parameters such as lattice parameter, crystallite size, strain, dislocation density and stacking fault probability have been calculated. From the optical measurements, the void concentration has been determined and the results are discussed.

X-ray characterisation of eroded 316 stainless steel

Deformation produced during the erosion of 316 stainless steel specimens by the impact of SiC particles is studied by X-ray diffraction. Erosion studies are made, at different impact angles, on samples simultaneously heated to different high temperatures. For the samples eroded at room temperature the deformation stacking fault probability values are found to be 5 × 10 −3 and 3 × 10 −3 for impact angles of 90° and 30° respectively. Variation of deformation stacking fault probability is correlated with the changes in the hardness value.

X-Ray Diffraction Line Broadening: Modeling and Applications to High-Tc Superconductors.

A method to analyze powder-diffraction line broadening is proposed and applied to some novel high-Tc superconductors. Assuming that both size-broadened and strain-broadened profiles of the pure-specimen profile are described with a Voigt function, it is shown that the analysis of Fourier coefficients leads to the Warren-Averbach method of separation of size and strain contributions. The analysis of size coefficients shows that the “hook” effect occurs when the Cauchy content of the size-broadened profile is underestimated. The ratio of volume-weighted and surface-weighted domain sizes can change from ~1.31 for the minimum allowed Cauchy content to 2 when the size-broadened profile is given solely by a Cauchy function. If the distortion co-efficient is approximated by a harmonic term, mean-square strains decrease linearly with the increase of the averaging distance. The local strain is finite only in the case of pure-Gauss strain broadening because strains are then independent of averaging distance. Errors of root-mean-square strains as well as domain sizes were evaluated. The method was applied to two cubic structures with average volume-weighted domain sizes up to 3600 Å, as well as to tetragonal and orthorhombic (La-Sr)2CuO4, which exhibit weak line broadenings and highly overlapping reflections. Comparison with the integral-breadth methods is given. Reliability of the method is discussed in the case of a cluster of the overlapping peaks. The analysis of La2CuO4 and La1.85M0.15CuO4(M = Ca, Ba, Sr) high-Tc superconductors showed that microstrains and incoherently diffracting domain sizes are highly anisotropic. In the superconductors, stacking-fault probability increases with increasing Tc; microstrain decreases. In La2CuO4, different broadening of (h00) and (0k0) reflections is not caused by stacking faults; it might arise from lower crystallographic symmetiy. The analysis of Bi-Cu-O superconductors showed much higher strains in the [001] direction than in the basal a-b plane. This may be caused by stacking disorder along the c-axis, because of the two-dimensional weakly bonded BiO double layers. Results for the specimen containing two related high-Tc phases indicate a possible mechanism for the phase transformation by the growth of faulted regions of the major phase.

X-ray diffraction study of the effect of boron on lattice properties of Ni76Al24

A small addition of boron is suggested to increase the ductility of the polycrystalline Ni3Al when the Al content is less than 25 at.%. Both metallographic and x-ray investigation have shown the alloys of Ni3Al (24 at.% Al) containing 0.20, 0.42, 0.79, 0.98, and 1.22 at.% B to be of single phase and that of 1.76 at.% B to be of two phase. With the addition of boron, the lattice parameter of the Ni3Al phase is found to increase. Microhardness measurements indicate that initially the hardness decreases for the alloy of 0.20 at.% B, while for the rest of the single phase alloys the hardness is found to increase with further addition of boron. The addition of boron increases the deformation stacking fault probability value except for the alloy with 0.20 at.% B.

X-ray diffraction peak-broadening analysis of (La-M)2CuO4 high-Tc superconductors

An X-ray diffraction peak-broadening analysis of four oxides is described: La2CuO4 and La1.85M0.15CuO4 (M = Ca,Ba,Sr) high-Tc superconductors. The diffraction line profiles were fitted with a convolution of specimen and instrumental functions, and the specimen peakbroadening angular dependence was analyzed with the Warren-Averbach method. It was found that microstrains and incoherently diffracting domains are highly anisotropic. In the superconductors, stacking-fault probability increases with increasing Tc; microstrain decreases. In La2CuO4, different broadening of (h00) and (0k0) reflections is not caused by stacking faults; it might arise from lower crystallographic symmetry.

The use of pattern decomposition to study the combined X-ray diffraction effects of crystallite size and stacking faults in ex-oxalate zinc oxide

The microstructure of ZnO powder, obtained from thermal decomposition of the oxalate and studied previously by electron microscopy and adsorption calorimetry, was investigated by means of X-ray powder diffraction pattern decomposition. A Williamson–Hall plot revealed that some lines were broadened solely due to the effects of crystallite size, whereas other breadths included a contribution due to stacking faults. Spherical and cylindrical models are used to describe the form of the crystallites and procedures are presented for separating 'size' effects from `mistake' broadening. This leads to estimates of the mean dimensions of the crystallites and the stacking-fault probability. The analysis demonstrates that, with good-quality data for a large number of reflections, a considerable amount of detailed information can be obtained about microstructure. On the other hand, it reveals some of the limitations of current procedures for modelling diffraction line profiles.

Structural characterization of cadmium selenide thin films by X-ray diffraction and electron microscopy

X-ray diffraction, transmission electron microscopy and transmission electron diffraction studies on cadmium selenide thin films deposited on glass substrates have been carried out. X-ray line profile analysis of the diffraction patterns has been performed to study the microstructural parameters. The variation of different microstructural parameters, such as crystallite size, RMS strain, dislocation density and stacking fault probability with film thickness as well as substrate temperature is studied. The optimum growth condition is fixed to a film thickness of the order of 1.0 mu m. The change of preferred orientation is observed for films deposited at and above 473 K.

Stacking faults and microstrain in La 1.85M 0.15CuO 4 ( M = Ca, Ba, Sr) by analyzing X-ray diffraction line broadening

We obtained x-ray diffraction patterns for three oxides: La 1.85M 0.15CuO 4 ( M= Ca, Ba, Sr). The superconductors show zero-resistance T c values of 19, 28, and 36 K, respectively. Diffraction- line profiles were fit with a convolution of specimen and instrumental functions. The specimen line-broadening angular dependence was analyzed by the Warren-Averbach method of real Fourier coefficients. Stacking-fault probability increases with increasing T c; microstrain decreases.

Assessing stacking faults in Bi-Sr-Ca-Cu-O phases by X-ray diffraction

A Hendricks-Teller analysis of the X-ray diffraction line shifts in Bi-Sr-Ca-Cu-O phases allows an estimate of the stacking fault probabilities (missing or extra Cu-O layers). The probability values suggest some conclusions about the mutual relationships of the 2201, 2212 and 2223 phases and the kinetics of their formation.

Stacking fault probability in β-SiC grown by chemical vapour deposition

The stacking fault probability in β-SiC, grown by chemical vapour deposition (CVD), was measured using the X-ray diffraction method. Stacking faults on the {111} planes shifted the {111} and {200} X-ray diffraction peaks from which the stacking fault probability can be directly determined. The stacking fault probability increased with decreasing deposition temperature owing to low surface atomic mobility at lower deposition temperatures. At a low hydrogen flow rate, the stacking fault probability increased as a result of decreasing the probability of combination of the silicon and carbon atoms. A methyltrichlorosilane flow rate higher than 10 cm3 min−1 had little effect on the stacking fault probability. Increasing the free silicon content also increased the stacking fault probability. A uniform residual stress effect was observed in the transparent deposit using a polarization microscope.

X-ray, electron microscopy and photovoltaic studies on CdTe thin films deposited normally at different substrate temperatures

X-ray diffraction, transmission electron microscopy and electron diffraction studies were conducted on CdTe thin films deposited on glass substrates kept at different substrate temperatures. Variation of the different structural parameters, such as lattice constant, crystallite size, r.m.s. strain, dislocation density and stacking fault probability with substrate temperature, was investigated in the temperature range 300 to 498 K. An increase in the lattice constant and crystallite size values and a decrease in the other parameters with increase in temperature of the substrate was observed. A photovoltage was observed for CdTe film deposited normally on glass substrates kept at higher substrate temperatures. The development of photovoltage in the film is explained in the light of the formation of crystallites of variable structure.

XRLINE, a program to evaluate the crystallite size of supported metal catalysts by single X-ray profile Fourier analysis

The computer program presented is based on the Fourier analysis of a single X-ray diffraction profile. An X-ray diffraction method is presented which is capable of determining the average particle size, microstrain, stacking fault probability as well as the particle size distribution function in crystalline materials. The main numerical methods used are: 1. (i) smoothing and interpolation by 3rd-order piecewice polynomial functions or by cubic splines with the least squares method; 2. (ii) numerical integration by successive five points formulae and numerical derivative by cubic splines with the least squares method; 3. (iii) estimation of parameters by the weighted least squares method. The results for supported platinum catalysts used in teh H/D isotopic exchange reaction are illustrated.

Microstructure of metastable phase induced by rapid quenching in some cobalt-iron alloys

Microstructure of metastable cobalt-based alloys with 0.94, 1.4, 2.6 and 5.4 wt% iron, obtained by rapid quenching from the melt, was studied by X-ray diffraction. The as-quenched alloys of all concentrations show the fcc structure, which is present in the equilibrium diagram in the high-temperature region. The analysis of X-ray diffraction line profiles and line shifts of quenched alloys revealed that the residual strains and the stacking fault probabilities decreased with increasing concentration of iron. This may be explained with local polymorphic changes of f c c structure. Stacking fault energies, Vickers microhardness data and coercivity were measured, while residual stresses were calculated using both X-ray diffraction and magnetometric measurements.

Diffraction Theory of HCP and FCC Crystals Containing Stacking Faults

As stacking faults in the hcp and fcc crystals, both of growth and deformation faults are taken into account, and, moreover, for either of these types of stacking faults, positive and negative sequences are discriminated. Diffraction anomalies caused by such stacking faults occurring with small probabilities are analytically calculated, and the results obtained are numerically examined. A more general theory, where stacking fault probabilities are not small, is dealt with.

Structural characterization of thin films of cadmium telluride

X-ray diffraction patterns of vacuum-deposited thin films of cadmium telluride have been recorded and X-ray line profile analysis studies have been carried out after correcting for instrumental broadening. Size of the crystallites, r.m.s. strain, dislocation density and stacking fault probabilities have been estimated using the method of variance analysis and peak shift of the line profiles. It is observed that with increase in the thickness of the films there is an increase in the stacking fault probability and this inhibits the growth of the crystallites and results in the increase in r.m.s. strain and dislocation density. The photosensitivity of the films is measured and it is observed, that at about 400 nm thickness, the photosensitivity is at a maximum. An attempt is made to correlate the results.

An x-ray diffraction line profile analysis on the microstructure of cold-worked face-centered-cubic Cu-Mn-Si alloys: Effects of Mn and Si as solutes

In continuation of our earlier investigations on the microstructures of cold-worked Cu-(Sn,Ni,Mn)-Zn ternary alloys by x-ray diffraction line profile analysis [J. Appl. Phys. 54, 6652 (1983); ibid. 48, 3560 (1977); ibid. 56, 1213 (1984)] the present work with Cu-Mn-Si alloy system in the fcc phase has been undertaken to elucidate the effects of Mn and Si, when present together, on the cold-worked substructure of this system. From detailed analyses of peak shift, peak asymmetry, and Fourier line shapes, quantitative estimates of the related microstructural parameters, namely, intrinsic (α′), extrinsic (α″), and twin fault (β) probabilities, domain sizes, rms strain, dislocation density, and stacking fault energy (for pure Cu), have been made. The results indicate, as in the earlier cases, increased presence of intrinsic stacking faults (α′)—primarily responsible for the observed peak shift and domain size broadening with relatively small presence of extrinsic faults (α″) and complete absence or very small presence of deformation twins (β) responsible for the observed asymmetry in the profiles. Unlike earlier observations, the presence of transitional solute Mn along with nontransitional Si as another solute appears to have a pronounced effect on the stacking fault probability of the present Cu-base alloys in the fcc phase.

Dislocations and faults in some alloys containing copper and aluminum

By using the method of variance of the respective X-ray diffraction line profile, the effective particle size (p) and r.m.s.. strain (〈S2〉1/2) of four alloys containing copper and aluminium (Al-0.08, 4 and 10 wt% Cu and Cu-5.87 wt% Al) at different annealing stages (starting from the cold filed stages) have been determined. From the peak shift of these samples, their average stacking fault probability α = α′ − α″ where α′ is the intrinsic stacking fault probability and α″ the corresponding extrinsic stacking fault probability, respectively, were determined. Similarly, from the angular distance between the peak and the centroid of the diffraction profiles, the magnitude ofβ + 4.5α″, whereβ is the twinning fault probability, was measured. From these, the true particle sizeT, the stacking and twinning fault probabilities α′, α″ andβ and the minimum stacking fault widthDmin have been determined. The hardness of alloys at different annealing stages was found to be dependent on the dislocation density and the stored energy in the alloys. The relationT 〈S2〉1/2 = constant was found to be valid for the alloys and from this a mechanism of grain growth with annealing has been suggested. With annealing the dislocation density and stored energy per unit volume were found to decrease until finally, in the fully annealed stages, they disappeared. The same was found to be valid for stacking and twinning fault probabilities as well as the minimum stacking fault width. A mechanism for the creation and annihilation of the intrinsic and extrinsic stacking faults has been suggested.

Line-broadening analysis of synchrotron x-ray diffraction data

The advantages of using monochromatic and parallel synchrotron x rays for the microstructure analysis of polycrystalline materials have been studied. Analysis of line broadening from Pd powers showed encouraging results. Warren–Averbach analysis [J. Appl. Phys. 21, 595 (1950)] with respect to the three major crystal axes [111], [100], and [110] was done using 1-Å x rays. Crystallite sizes and microstrains relative to the [111] direction were obtained using three different reflection pairs (111)-(222), (111)-(333), and (111)-(444). The fixed symmetrical instrument profile shape has major advantages in the correction of instrumental broadening and the determination of a low level (10−4 range) of stacking-fault probabilities.

Effect of stacking faults on diffraction: The structure of lithium metal.

A new method for calculating the effect of stacking faults on x-ray and neutron-diffraction patterns is developed. Using a computer-generated, statistically faulted crystal model, we show that it is possible to examine the effect of various types of faults in different lattice types from a simple and unified point of view. As a benchmark on the application of this method, we recover the standard results obtained by approximate analytical techniques for deformation and growth faults in face-centered-cubic lattices. We then use this method to analyze stacking faults in the 9R hexagonal lattice. A detailed comparison of these calculations with our neutron powder-diffraction results on the low-temperature martensitically transformed phase of lithium metal is given. We find that the structure of Li at 20 K is 9R with a deformation stacking-fault probability density of 0.07 per layer. Finally, we show how this method can be extended to more complex stacking-fault types and other crystal structures.

An X-ray diffraction study on the microstructure of AgCdZn (α phase) alloys

The X-ray diffraction profiles of six ternary alloys of AgCdZn in the cubic α phase have been recorded using a Philips diffractometer. Peak shift, peak asymmetry and Fourier line shape analysis of the profiles are made in order to evaluate the microstructural parameters. It is observed that the stacking fault probability increases with combined solute concentration ( Cd + Zn). The root mean square microstrain 〈ϵ 2〉 1 2 and effective particle size D e along [111] and [100] are found to be anisotropic. The particle size due to faulting D SF , the dislocation density ρ and the parameter γ/μ (γ, stacking fault energy; μ, shear modulus) of these alloys are also evaluated.