Values Of Dislocation Density Research Articles

Microstructural characterization of the evoluted phases of ball-milled α-Fe 2O 3 powder in air and oxygen atmosphere by Rietveld analysis

Transformation reaction induced due to ball-milling of iron oxide, α-Fe 2O 3 in both air and oxygen atmospheres under closed milling condition has been studied for detailed characterization of the microstructure of all the evoluted phases on milling up to 10 h. The methodology adopted for characterization involves Rietveld’s whole X-ray profile fitting technique adopting the most recently developed software, material analysis using diffraction (MAUD), which incorporates Popa model for crystallite (domain) size and microstrain (root mean square, r.m.s. strain). The analysis also considers lattice defect related features of the microstructure, viz. stacking, twin, compound fault density and dislocation density parameters. The study also undertakes quantitative estimation of volume fractions of the phases evoluted (Fe 3O 4: Fd-3m:1 and FeO: Fm-3m). The results reveal transformation of α-Fe 2O 3 to Fe 3O 4 and finally to FeO occurs in both air and oxygen atmospheres, and the reaction speed is slower in oxygen environment. The reaction is controlled by oxygen partial pressure, which decreases on continued milling. A critical oxygen partial pressure is reached at 3–4 h of milling, when Fe 3O 4 phase attains maximum saturation with nano-order (7–8 nm) crystallite sizes, reduced r.m.s. strain and high dislocation density (∼10 12 cm −2). Prolonged milling (7–10 h) results in further reduction of oxygen partial pressure, resulting in complete transformation of α-Fe 2O 3 and Fe 3O 4 to FeO, having nano-order (6–7 nm) crystallite sizes, high r.m.s. strain (∼10 −2) and high dislocation density values (∼10 12 cm −2) in both the environments, except that the transformation reaction is slowed down in oxygen.

Microstructural characterization of Fe–Mn–C martensites athermally transformed at low temperature by Rietveld method

The present study concerns X-ray characterization of the microstructures of Fe–Mn–C alloys with compositions 5.6, 5.8 and 6.0 Mn and 1.0 C (mass%), athermally transformed at low temperatures, following γ→α transformation reaction. The methodology applied is Rietveld's whole X-ray profile fitting technique adopting the recently developed software, Materials Analysis Using Diffraction (MAUD) which incorporates Popa model for crystallite (domain) size and microstrain (root mean square, r.m.s strain) and the preferred orientation of the crystallites. The analysis also considers the lattice-defect related features of the evoluted microstructures, viz. stacking, twin, compound fault probabilities and dislocation density values. The study revealed the highest degree of transformations with 36, 40 and 47% volume fractions of martensites for 5.6, 5.8 and 6.0 mass% of Mn at temperatures 190, 185 and 170 K, respectively. The respective microhardness values are 441, 398 and 385 kg mm −2. With increasing Mn concentration the crystallite size values of the respective martensites decrease and r.m.s strains increase, while the dislocation density and stacking fault density values increase with respect to those of the respective austenites. Depth profile study reveals that the martensite percentage decreases with decreasing microhardness values on removal of thin layers from the surface.

Microstructural characterization of stress-induced martensites evolved at low temperature in deformed powders of Fe–Mn–C alloys by the Rietveld method

The present study considers X-ray characterization of the microstructures of deformation-induced martensites of Fe–Mn–C alloy powders of grain size ∼50 μm (hand-filed) having compositions 5.6, 5.8 and 6.0 Mn and 1.0 C (mass%). The cold-worked powders were further subjected to transformation at low temperatures close to Ms and the evolved phases were again characterized microstructurally. The methodology applied for characterization involves Rietveld’s whole X-ray profile fitting technique adopting the most recently developed software, MAUD (Materials Analysis Using Diffraction) which incorporates Popa model for crystallite (domain) size and microstrain (root mean square, r.m.s.) and preferred orientation of the crystallites. The analysis also considers lattice defect-related features of the microstructure viz. stacking, twin, compound fault probabilities and dislocation density value. The cold-worked powders (hand-filed at room temperature) revealed the highest degree of transformation with 47, 43 and 42% volume fractions of martensites with increasing Mn concentration which for the bulk state of the same alloys transformed at low temperatures are 36, 40 and 47%. The same deformed alloy powders when subjected to low temperature transformation, evolved a maximum of 60, 68 and 62% volume fractions of martensites at 170, 175 and 190 K. The analysis reveals the occurrence of a high propensity of stacking faults in the deformed austenites (10−2–10−3) and high values of dislocation densities (1012–1013 cm−2) in the austenite and martensitic phases which assist in the formation of such a high concentration of martensites in the low temperature-treated deformed powder samples.

Anisotropic diffraction peak broadening and dislocation substructure in hydrogen-cycled LaNi5and substitutional derivatives. Erratum

An erroneous equation and some consequently underestimated values of dislocation densities in the paper by Černýet al.[J. Appl. Cryst.(2000),33, 997–1005] are corrected.

X-ray characterization of nanocrystalline Ni3Fe

X-ray microstructure characterization of nanocrystalline Ni3Fe was made employing Rietveld’s powder structure refinement method, the Warren–Averbach’s method and modified Williamson–Hall method. Ni3Fe particles were synthesized within a silica matrix by a sol–gel method. Particle size (10–15) nm and r.m.s. strain (∼10−3) values of Ni3Fe were found to be anisotropic in nature. Stacking faults, change in lattice parameter, dislocation density (edge type) values indicate the amount of disordering in the Ni3Fe phase. Lattice distortion in terms of several microstructural parameters also corroborates the results obtained from Mössbauer spectra analysis. Other associated co-developed phases like, crystalline SiO2, Fe2SiO4 (trace amount) have been identified and NiO has been characterized by X-ray powder diffraction. A significant correlation between these two different types of characterization has been shown to be present.

On the origin of work softening of Ni 3Al deformed along [001] above the peak temperature

Single crystalline specimens of Ni 3Al were compressed along [001] at three different temperatures (600, 835 and 920 °C). Above the peak temperature ( T P=800 °C), the stress–strain curves show a yield drop caused by work softening. Transmission electron microscopy (TEM) methods were used to analyse the structures of the superlattice dislocations formed at different deformation temperatures showing that the Burgers vector and glide plane do not change (±a〈110〉{111}). Below T P, screws and screw dipoles consisting of Kear–Wilsdorf (KW) locks are dominating. Above T P, screw dipoles are not observed indicating their dynamic recovery. Above T P, dislocations of all characters contain antiphase boundary (APB) faults that lie inclined to their glide plane. It is proposed that their motion occurs by APB fault dragging. Calculations were carried out to model the work-softening behaviour observed above T P. It is concluded that both the yield stress and yield drop are governed by the value of the mobile dislocation density and its evolution with strain.

The temperature dependence of the thermal conductivity of single crystal GaN films

The thermal conductivity of both LEO and HVPE single crystals of GaN have been meassured over the temperature range of 60 K to 300 K using an electrical third harmonic technique. In contrast to the previously reported results of Sichel and Pankove, the thermal conductivity increases with decreasing temperature below room temperature, reaches a maximum and then decreases with further decreases in temperature. The thermal conductivity of the LEO-GaN is higher at all temperatures than the HVPE materials. The higher thermal conductivity is correlated with lower values of the threading dislocation density.

Electro-elastic stress analysis on piezoelectric inhomogeneity–crack interaction

Abstract The current study investigates the interaction problem of a fiber-shaped piezoelectric inhomogeneity embedded in a non-piezoelectric elastic matrix, which contains a crack. The matrix is assumed to be infinite in all directions and the crack is near the piezoelectric fiber. Different geometrical crack–inhomogeneity configurations are considered. The body is subjected to a far-field in-plane tension and a far-field anti-plane electric field. With the solution of stress field for a piezoelectric inhomogeneity embedded in an elastic matrix, the solution of current problem is obtained through a decomposition process. A set of singular integral equations in the crack domain is derived through the dislocation theory. The expressions for the stress intensity factors are then obtained in terms of the asymptotic values of dislocation density functions solved from these integral equations. Numerical examples indicate that interaction between the piezoelectric inhomogeneity and the crack is influenced by many factors, such as the configuration, the material properties of the piezoelectric inhomogeneity and matrix, as well as the far-field electrical and mechanical loadings. The stress intensity factors on crack tips obtained have been checked and confirmed by finite element analysis.

X-ray characterization of the microstructure of α-CuTi alloys by Rietveld’s method

The lattice-defect related features of the microstructures and the properties as evoluted in Cu–1.0, 3.0, 4.5 and 6.0 wt.%Ti alloys have been studied using Rietveld’s whole X-ray profile fitting method incorporating Popa model for crystallite (domain) size and microstrain (root mean square, r.m.s. strain) and the preferred orientation of the crystallites. Direct observations of the microstructure have been effected through the optical and scanning electron microscopy studies and the mechanical property has been measured from microhardness studies. The high Ti content alloys are found to decompose into two phases, α-CuTi and β-Cu 3Ti, through spinodal decomposition which is intensified on prolonged aging at 673 K. In the annealed powders aged at 673 K the crystallite sizes of β-Cu 3Ti phase are found to be smaller whereas the microstrains and dislocation densities are higher compared to those of the α-CuTi phase. In the α-matrix of the aged alloy powders the microstrain and the dislocation density increase and the crystallite size decreases with the increase in Ti concentration. The transformation behaviour of the aged bulk reveals β-Cu 3Ti phase has very high values of microstrains and dislocation densities (∼10 12 cm/cm 3) compared to those of α-CuTi. Profuse twinning is found in the α-CuTi phase of both the annealed powders and bulk aged at 673 K. Severe cold working has little effect on the microstructure of β-Cu 3Ti phase but the deformation effect on the α-CuTi phase results in the generation of low densities of deformation stacking faults, high densities of deformation twins and high dislocation densities (∼10 11 cm/cm 3) with increasing Ti concentration. With increasing volume fraction of β-Cu 3Ti phase in aged bulk Cu–6.0 wt.%Ti alloy the microhardness value increases almost 2-fold (from 290 to 490 kg/mm 2) imparting considerable improvement in its mechanical property.

Thermal conductivity of fully and partially coalesced lateral epitaxial overgrown GaN/sapphire (0001) by scanning thermal microscopy

We have measured high spatial/depth resolution (∼2–3 μm) thermal conductivity (κ) at 300 K of both fully and partially coalesced GaN/sapphire (0001) samples fabricated by lateral epitaxial overgrowth. On the fully coalesced sample we found 1.86W/cm K<κ<2.05 W/cm K over a distance of approximately 50 μm. One of the partially coalesced samples had 2.00 W/cm K<κ<2.10 W/cm K on the overgrown regions, as identified by atomic force microscopy imaging. These latter results are the highest thermal conductivity values reported on GaN material. A correlation between low threading dislocation density and high thermal conductivity values was established.

Characterisation of Microstructure of Isothermally Transformed Martensite in Low Temperature in Powder and Bulk State of Fe–23Ni–3.6Mn (mass%) Alloy by Rietveld's Method

The present study concerns X-ray characterisation of the microstructures of the martensites of Fe–23Ni–3.6Mn alloy, transformed isothermally at low temperature. Along with the austenized powder and bulk forms of the alloy, coldworked powders have also been analysed. The methodology adopted is Rietveld's whole profile fitting technique which incorporates correction for preferred orientation of the crystallites. The results reveal important information on the crystallite (domain) sizes, residual microstrains, preferred orientation, stacking and compound fault probabilities, dislocation density etc., for both the austenite and martensite phases of the alloy. The martensite has smaller crystallite sizes and larger microstrain values, both of which are isotropic in nature for the transformed bulk and the austenized powders but anisotropic for the coldworked powders. The transformed matrix revealed high percentage of martensites in coldworked powder and bulk whereas annealed powder revealed about 8% volume fraction of martensites. The dislocation density values evaluated from the respective crystallite sizes and r.m.s. strain values are high (∼1011 cm/cm3) in the martensitic phase by almost an order of magnitude compared to their respective austenite phase. The coldworked powder reveals high propensity of faulting. The hardness value of transformed bulk (191 kg/mm2) is more than double the value for the austenite bulk (95 kg/mm2). The results have been compared and correlated with those in two previous studies on the same alloy system having 3.3 and 3.8 mass% of Mn.

Characterisation of microstructure of isothermal martensite formed at low temperature in powder of Fe–23Ni–3.3Mn alloy by Rietveld method

The present study attempts to characterise and compare the microstructures of martensite in powders prepared by hand-filing Fe–23Ni–3.3Mn alloys at room temperature with those of the martensites formed at low temperature in the austenite powder and bulk forms of the alloy. The X-ray diffraction line profiles obtained from the powder and the bulk specimens of the material have been analysed by Rietveld’s whole profile fitting method incorporating preferred orientations of the crystallites. The results reveal that the martensite formed in cold-worked powder has higher value of the stacking fault density compared to that of the martensite formed at 160 K in annealed powder of Fe–23Ni–3.3Mn. The martensites have higher value of dislocation density (∼10 11 m −2) with smaller crystallite sizes and larger r.m.s. strain values. The bulk martensite has higher hardness value. The volume percentage of martensites formed are 24, 79, 84% for the austenite powder, cold worked powder and bulk sample, respectively.

Crystal microstructure of PbTe/Si and PbTe/SiO 2/Si thin films

A modified ‘hot wall’ technique (HWE) is used for growth of PbTe thin films directly on Si(100) high ohmic substrates both with and without any buffer layers. The previously formed SiO 2 films have been used as buffer layers. The crystal microstructure of PbTe thin films has been studied by an etching pits method, SEM, RHEED and by X-ray analysis which is able to determine the X-ray rocking curve profiles and line width with high precision.. It has been found that these PbTe/Si and PbTe/SiO 2/Si thin films have mosaic single crystal structure with (100) texture without regard to the Si substrate orientation. The investigations of PbTe/Si thin films dislocation density by the etching pits method and by the analysis of X-ray reflection profiles show the average values of about 10 5–10 7 cm −2. The experimental results of these methods have shown that PbTe/SiO 2/Si thin films had better crystallinity perfection. The average values of dislocation density were about 5×10 4–2×10 5 cm −2.

Syndeformational recrystallization - dynamic or compositionally induced?

Dynamic recrystallization in the strict sense of the term is the reconstitution of crystalline material without a change in chemical composition, driven by strain energy in the form of dislocations. Driving potentials additional to internal strain energy may contribute to the recrystallization of naturally deformed minerals, which form solid solutions such as feldspar, amphiboles and pyroxenes, if they change their composition during recrystallization. To estimate the relative importance of these driving potentials, the chemical composition of porphyroclasts and recrystallized grains of plagioclase, clinopyroxene and hornblende have been investigated in samples from a high grade shear zone of the Ivrea Zone, Italy. The plagioclases show two different recrystallization microstructures: bulging recrystallization at grain boundaries and discrete zones of recrystallized grains across porphyroclasts probably involving fracturing. Deformation took place under amphibolite facies conditions on a retrograde P,T-path. Porphyroclast and recrystallized compositions from bulging recrystallization microstructures differ only in their Or-content and yield a ΔG between mean host grain and mean recrystallized grain composition at fixed P,T-conditions of approximately 5 Joules/10−4 m3. Extreme compositional variations yield approximately 60 J/10−4 m3. The increase of free energy due to dislocations calculated for common glide systems in plagioclase are on the order of 100 Joules/10−4 m3 for high values of dislocation densities of 1014 m−2. Thus, the effect of chemically induced driving energies on grain boundary velocity appears small for mean compositions but may be as great as that of deformational energies for larger chemical differences. In the other type of microstructure, porphyroclasts and recrystallized grains in discrete zones differ in their anorthite content. The maximum ΔG induced by the compositional disequilibrium is on the order of 100 J/10−4 m3. This maximum value is of the same magnitude as the ΔG derived from high dislocation densities of 1014 m−2. The resulting combined ΔG is approximately twice as high as for deformational ΔG alone, and heterogeneous nucleation may become a feasible recrystallization mechanism which is evident from the microstructures. The recrystallization mechanism depends on the nature of the driving potential. Grain boundary migration (GBM) and heterogeneous nucleation can release Gibbs free energy induced by compositional disequilibrium, whereas this is not likely for subgrain rotation. Therefore, only GBM and heterogeneous nucleation may link metamorphism and deformation, so that syndeformational recrystallization may represent a transitional process ranging from dynamic recrystallization to metamorphic reaction.

Selective Area Growth of GaN Directly on (0001) Sapphire by the HVPE Technique

In this paper, we report on the selective area growth (SAG) of GaN directly on patterned c-plane sapphire substrates by hydride vapor phase epitaxy (HVPE). A number of researchers have reported that the HVPE growth technique, unlike the MBE and MOCVD methods, is capable of producing device quality GaN films without the need for any low temperature nucleation/buffer layers. The density of edge dislocations in these HVPE films decreases dramatically as the film thickness is increased, and the dislocation density values for thick films (> 10μm) are comparable to those reported for the best GaN films grown by other methods on c-sapphire. These advantages of the HVPE growth technique makes it possible to achieve high quality selective area growth of GaN directly on c-sapphire substrates.C-plane sapphire substrates were coated with PECVD SiO2 and photolithographically patterned with different size and shape openings. Subsequently, these patterned substrates were introduced in a horizontal, hot-wall quartz reactor for the GaN growth. It was observed that single crystal GaN growth was preferentially initiated in the openings in the oxide layer. This selective area growth was followed by epitaxial lateral overgrowth (ELO), leading to the formation of hexagonal GaN prisms terminated in smooth, vertical (100) facets. We have been successful in shearing these pyramid structures from the sapphire substrates as individual devices, which do not require any post-growth etching for feature definition. This procedure allows for the dramatic reduction of the process complexity and the duration and expense for GaN growth for device applications. Stimulated emission results on these self-formed optical cavities are also presented.

Selective ion-channeling study of misfit dislocation grids in semiconductor heterostructures: Theory and experiments

Planar dechanneling by networks of misfit dislocations was measured in a series of ${\mathrm{In}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x}\mathrm{A}\mathrm{s}/\mathrm{G}\mathrm{a}\mathrm{A}\mathrm{s}$ samples (001) grown by molecular-beam epitaxy. At the beginning of the strain-relaxation process the dechanneling probability exhibits different values for nominally equivalent (110) planes. At larger strain relaxation, the dechanneling probability saturates at a value around $$$\frac{1}{2}$ as the beam-energy increases. In order to explain these results a new model for planar dechanneling by dislocations is proposed. This model is based on the harmonic approximation of the continuum potential but anharmonicity effects are taken into account. The perturbation to the harmonic oscillations caused by the lattice plane curvature around a dislocation is written in terms of a distortion function that depends only on the geometrical configuration of the channeling direction and of the dislocation line. This function is explicitly calculated for geometrical configurations relevant to the present samples allowing us then to solve the equation of motion. The results show that the dechanneling probability saturates at a level sensibly lower than 100% due to the quasiplanar distribution of dislocations. Without any adjustable parameter, the comparison between computed and measured dechanneling probabilities supplies dislocation density values in excellent agreement with those measured by transmission electron microscopy and in good agreement with results deduced from previous strain-relaxation data.

Dislocations and grain size in ball-milled iron powder

The microstructure of ball-milled iron powder has been investigated by high resolution X-ray line profile analysis. Analysis of line breadths suggested that the contrast factors related to dislocations have to be taken into account in the Williamson-Hall procedure. This concluded to a modified Williamson-Hall plot which provided, in a straightforward manner, the grain size refinement of nanocrystals ball-milled for different periods of time. At the same time it has been shown that strain broadening, even in these nanoscale small-grain particles, is caused by the presence of dislocations. The line profiles were also studied by the method of Fourier analysis, which gave the absolute values of dislocation densities.

Kinetic approach to multiple pathway diffusion with traps.

Multiple pathway diffusion with traps was analyzed in the kinetic approach in which the diffusion terms in the diffusion-kinetic equations are replaced by kinetic ones. The criteria for applicability of the kinetic approach are discussed. Since the solutions are linear combinations of exponents, both the exponents and the preexponential factors were taken into account. As an example Au diffusion into a Si film was studied taking into account both the dissociative and the kickout mechanisms. To analyze thin-film diffusion, in addition to terms describing the diffusion transport in crystals of infinite sizes, thin-film surfaces were considered as a substantial source and/or sink of point defects. The different diffusion mechanisms and regimes and the conditions of transition from one mechanism and/or regime to another were found. Expressions were obtained for the critical sample thicknesses, dislocation density, swirl and vacancy cluster density, and temperatures, when transitions of the diffusion transport mechanisms and regimes occur. Possible areas for existence of these transport regimes were determined. Quantitative criteria of the critical values of temperature, dislocation density and thin film thickness for transitions of the Au-Si diffusion transport mechanisms were obtained. For fairly long times the results obtained in the kinetic approach coincide with those of the diffusion-kinetic one but the set of pure kinetic equations is much simpler to solve. This implies that the kinetic approach is a valuable approximation to multiple pathway diffusion with traps.

The influence of temperature and grain size on substructure evolution in stainless steel 316L

The flow stress of polycrystals is controlled by the processes occurring in the grain interior as well as in the mantle, i.e. at the grain boundary and its immediate vicinity. The early stages of evolution of dislocation substructure in these two regions with strain in 316L stainless steel polycrystals have been studied at 293 K, 673 K and 1123 K representing the low temperature thermal, the intermediate temperature athermal and the high temperature thermal regimes respectively. Specimens with grain sizes of 4 and 12 μm were employed to determine the effect of grain size. Transmission electron microscopy studies on deformed specimens show the different roles of grain boundary and grain interior in different temperature regimes. In the low temperature regime grain boundaries act as obstacles to moving dislocations and as such high density of dislocation is found in the grain boundary vicinity. In the intermediate temperature regime the dislocations which are easily spread into the grain interior rearrange to form cell walls. In the high temperature regime grain boundaries transform to the equilibrium state and do not contain any grain boundary dislocations, and the distribution of dislocations within grains is homogeneous at all strains. Significantly higher values of dislocation densities in the vicinity as well as in the grain interior were found in the finer grain size material in the whole strain region employed.

Model of the Early Deformation Stage of bee Metals in Low Temperature

A qualitative and quantitative model of the early deformation stage of bcc metals at low temperatures is proposed. Due to a large difference in mobility of screw and edge dislocations, there is a stress range where only edge-segments are mobile. The force for the edge dislocation mobilization has one component connected with the overcoming of local barriers and another one related to the formation out of screw segments. A rapid creation of hardly mobile screw dislocation dipoles is assumed as the main source of strain hardening. At some critical value of the screw dislocation density and sufficiently high applied stress, some local movement and mutual annihilation of long segments of screws is possible. This last process effectively decreases the strain-hardening rate and leads to a smooth, continuous transient between elastic and plastic deformation. The model is confronted with experimental data and a satisfactory agreement is obtained.