The effectiveness of coincidence site lattice criteria in predicting creep cavitation resistance

The coincidence site lattice (CSL) concept is often used in microstructural characterization by researchers studying grain boundary engineering as a method for improving the performance of polycrystalline materials. It is assumed that a high degree of shared lattice sites in the boundary between two grains will result in improved mechanical properties. For practical application of the CSL concept to experimental results, a maximum deviation from ideal CSL orientation relationships must be defined to distinguish potential CSL boundaries from random boundaries that are not likely to exhibit “special” properties. Several different maximum deviation criteria have been proposed in the literature. In this study, four of these criteria are investigated for their effectiveness in predicting the creep cavitation resistance of boundaries of different CSL character in three model alloys: pure Cu, Cu-Bi, and Cu-Sb. Bi and Sb strongly segregate to Cu grain boundaries and are detrimental to creep life. The experimental observations are compared to simulation results for a non-textured polycrystal. It is observed that only boundaries related to cubic annealing twins (Σ3 and Σ9) exhibit special resistance to creep cavitation, that boundaries with Σ > 3 are affected by the presence of segregants, and that the fraction of non-Σ(3,9) boundaries tracks closely with what would be expected from a random polycrystal. It is shown that more restrictive criteria result in more reliable characterization of the fraction of cavitation-resistant boundaries only because they exclude more non-Σ(3,9) boundaries from the analysis.     

Structure of special grain boundaries in SiAlON ceramics

The microstructure of hot-pressed samples of the 15 R polytype phase in the Si-Al-O-N system was studied by means of TEM. Emphasis was put on studies of high angle grain boundaries. In this material high angle boundaries of arbitrary orientation usually possess a vitreous grain boundary phase. However, special grain boundaries were found, which were free of any vitreous grain boundary phase. From the orientation relation of the adjacent grains Σ=1 (coherent reflection twin boundary), Σ=7 and Σ=13 boundaries were found. For their explanation a coincidence site lattice (CSL) model was developed for (0001) twist boundaries. By assuming an exponential form for the potential of atomic interaction, the calculation of minimum grain boundary energies for special twist angles was in accordance with the experimental observations.     

Extended dislocation barriers in tilt boundaries in fcc crystals

 Extended dislocation barriers at tilt boundaries in fcc crystals are considered. For boundaries with a high degree of lattice coincidence, stable extended dislocation barriers, analogous to those occurring within a single crystal, are shown to exist. Other boundaries can have components equivalent to the high coincidence boundaries. The boundary barriers are shown to be possible nucleation sources for mechanical twins or martensite phase transformations. Received: 10 October 1997 / Accepted: 13 December 1997     

The effects of strain annealing on grain boundaries and secure triple junctions in nickel 200

Changes in the microstructure of 99.5% pure nickel as a function of strain annealing have been investigated. The application of moderate amounts of compressive strain (6–7%), and subsequent thermal treatment at 750°C under vacuum is shown to increase the density of Σ3 grain boundaries, where the coincident-site lattice rationale is adopted to characterize the boundaries. A preliminary, post-strain surface oxidation treatment to 500°C is shown to drastically increase the proportion of twin boundaries, a majority of which are identified as being coherent in nature. In addition, a high level of connectivity for these twins is observed, along with greatly increased numbers of secure triple junctions. It is postulated that the mechanism by which grain boundary energy minimization is effected involves grain rotations when treatment is conducted under vacuum, but that annealing twin formation is the predominant process when an oxygen-rich environment exists. This revised version was published online in November 2006 with corrections to the Cover Date.     

Direct observation of grain-boundary dislocations in the FeCo alloy

A unified dislocation theory of grain boundaries proposed earlier for simple cubic crystals has been extended to include the case of ordered and disordered body-centred-cubic structures. Pure symmetric and asymmetric tilt and pure twist boundaries have been treated in detail and extended to an arbitrary grain boundary. It is shown that a unique set of coincidence site lattices exists for both the symmetric and asymmetric boundaries and that each of these sets, in turn, depends upon the rotation axis which characterizes the boundary. Furthermore, a unique set of grain-boundary dislocations is associated with each of these coincidence site lattices. The results are then applied to the transmission electron microscopy studies carried out in Part 2 of the present study.On leave from The Materials Research Group, Department of Metallurgy, Indian Institute of Science Bangalore — 560012, India.     

Relation between microstructures of martensite and prior austenite in 12 wt% Cr ferritic steel

Tempered martensitic 9–12 wt% Cr ferritic steels are used as heat resistant materials in power plant, where service under conditions of high temperature and pressure for several decades is required, and an adequate resistance to creep is one of the key requirements. In this type of steels, failure has been found to occur preferentially at prior austenite grain boundaries if the prior austenite grains are coarse. It appears that the prior austenite grain boundaries can act as a site of especial weakness in the tempered martensitic microstructure. It would therefore be useful to investigate whether the properties of prior austenite grain boundaries could be modified by some appropriate thermomechanical processing method. One approach to this is to attempt to increase the fraction of annealing twins in the austenite phase and to investigate whether this has an effect on the properties of the martensite after transformation and tempering. In this study, thermomechanical treatments involving hot-rolling have been applied and the fraction of austenite twins produced determined using electron backscatter diffraction analysis. The treatment giving the highest fraction of austenite twins was identified and the effect of the increase in twin fraction on the characteristics of the martensite was investigated. It was found that the fraction of coincidence site lattice boundaries in martensite along prior austenite grain boundaries increased with increasing fraction of prior austenite twin boundaries.     

Faceting–roughening of twin grain boundaries

The coincidence site lattice (CSL) plays a similar role for grain boundaries (GB) as the crystal lattice plays for free surfaces. The most densely packed CSL is the twin-related CSL, characterized by an inverse density of coincidence sites Σ = 3. Phase diagrams in coordinates “relative temperature T/T _m—misorientation angle θ—inclination angle φ” were constructed for the twin GBs in Cu, Al, and Mo having different stacking fault energy γ. At low γ the twin GB remains faceted at all φ values and the number of crystallographically different facets increases with decreasing temperature. With increasing γ asymmetric twin GBs become more and more rough, and fewer facets appear with decreasing temperature. Also, with increasing γ the facets start to degenerate of into the first order rough-to-rough ridges. The behavior of twin GBs in Cu, Al, and Mo is compared with that of twin GBs in Zn.     

Metrics, measures, and parametrizations for grain boundaries: a dialog

Analysis of experimental data on grain boundaries (GBs) can involve putting data into angle “bins.” An example is Brandon’s classification: if rotation angle and axis are each within of a perfect coincidence site lattice (CSL) with density 1/Σ, the GBs can also be considered to be in that CSL relationship, and not if otherwise. Other examples of binning are studies of GB distributions in the full 5D angle space. To determine the size of a bin (necessary for densities, gradients, etc.) one must find a useful way, respecting symmetry, of determining metrics and measures on the full 5-dimensional space of both misorientation and interface normal. For a pair of low-angle GBs, the issue of metric is complicated by the fact that both their rotation axes and their GB normals can stay far apart as their rotation angles approach zero. We address all these issues as a dialog, and provide a framework for choosing metrics.

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Morphology and rotation twin in ZnSe on GaAs (111)

ZnSe crystals were grown by a vapour transport method on a GaAs substrate with a (111) A or (¯1¯1¯1) B surface. Crystals obtained on the (111) A surface of the substrate were fine crystals and hexagonal plates. Whereas crystals grown on the (¯1¯1¯1) B were uniform thin films on which trigonal hills and trigonal pyramids developed. These crystallites had a complicated morphology. In addition, the hill and pyramid grown on the (¯1¯1¯1) B surface contained rotation twins around a polar axis parallel to the growth direction or around the other polar axes.     

Dissociation of lattice dislocations in coincidence boundaries

The possible dislocation reactions in coincidence boundaries with Σ ≦19 in fee and b cc crystals were systematically analysed in consideration of energetics according to the coincidence site lattice theory. The elastic energy reduction during dissociation of lattice dislocations suggests to be more easily absorbed into coincidence boundaries with large Σ-values. Transmission electron microscopy showed a large difference in the absorption rate between coincidence and random boundaries in crept specimens. The absorption of the lattice dislocation depends strongly on its Burger's vector even in the same grain boundary. Experimental results showed that most of EGBDs observed in the coincidence boundaries were of the Burger's vectors which give rise to smaller energy reduction due to the dissociation reaction.     

Structures of a Σ = 9, [110]/{221} symmetrical tilt grain boundary in SrTiO<Subscript>3</Subscript>

In this study, we fabricated a bicrystal of SrTiO₃ containing a Σ = 9, [110]/{221} symmetric tilt grain boundary (GB) and its atomistic structure was directly observed by transmission electron microscopy (TEM) and scanning TEM (STEM). We theoretically estimated the most stable structure by first principles calculations, and by combining this with TEM images determined the atomistic structure of the Σ = 9 grain boundary. We found that when the grain boundary is slightly tilted from the coincident site lattice (CSL) orientation, displacement shift complete (DSC) dislocations are introduced at the grain boundary to accommodate the misorientation between the two adjacent crystals while the most stable atomic structure remains unchanged.     

Icosahedral and decagonal quasicrystals,crystalline phases,and multiple twins in rapidly solidified Al13Cr4Si4

Both the icosahedral and decagonal phases have been found in Al₁₃Cr₄Si₄ melt-spun ribbons. A definite orientation relationship existing between these two phases is determined by SAD which is the same as that obtained previously by Schaefer and Bendersky. During the icosahedral quasicrystal-crystal transformation in this Al−Cr−Si alloy, the Al₁₃Cr₄Si₄ crystalline phase forms at low temperature and an unknown phase at high temperature. Both crystalline phases have definite orientation relationships with the icosahedral phase. The five-fold rotational twins of Al₁₃Cr₄Si₄ around the [110] direction formed from the icosahedral phase follow the group-subgroup relationship. The unknown phase has a hexagonal lattice,a=0.73 andc=1.62nm.     

Effect of grain boundary microstructure on fatigue crack propagation in austenitic stainless steel

The effect of grain boundary microstructure on fatigue crack propagation in austenitic stainless steel was investigated in order to control fatigue crack propagation. The fraction of low-Σ coincidence boundaries in specimens was controlled by thermomechanical processing. The specimen with the higher fraction of low-Σ boundaries (73%) showed the lower propagation rate of fatigue crack than the specimen with the lower fraction of low-Σ boundaries (53%). The ratio of intergranular fracture segments to the total crack length was lower for the specimen with the higher fraction of low-Σ boundaries. Moreover, the roles of grain boundaries in the fatigue crack propagation were investigated in connection with grain boundary microstructure, i.e., the character distribution and geometrical configuration of grain boundaries. It is evidenced that the approach to grain boundary engineering is applicable to controlling fatigue crack propagation in austenitic stainless steel.     

Special grain boundaries based on local symmetries

We propose that, in large unit cell structures, the operation of local symmetries rather than a coincidence site lattice (CSL), is important for the creation of special, low energy, grain and twin boundaries. We illustrate this with a Dürer tiling, and its monoclinic realization, as well as with crystals with large icosahedral motifs.

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Computer modeling of grain boundaries in Ni3Al

Computer modeling of symmetric tilt boundaries Σ = 5 [1 0 0] (0 1 2) and Σ = 5 [1 0 0] (0 1 3) in alloy Ni₃Al was carried out. The energy of grain boundaries (GBs) was calculated out by a method of construction of γ-surface by using Morse's empirical centralforce potentials. Researched GBs have four steady states: one is stable and three — metastable. These states of GBs differ by energy and atomic structure. It is shown that GBs in model of coincidence site lattice are unstable, the stabilization is achieved by additional displacement on some vector along plane of defect.     

Electromechanical coupling properties of [001], [011] and [111] poled Pb(Mg1/3Nb2/3)O3-0.32PbTiO3 single crystals

The electric field induced “butterfly” curves and polarization loops, and the stress induced strain and polarization responses of [001], [011] and [111] oriented Pb(Mg_1/3Nb_2/3)O₃-0.32PbTiO₃ (PMN-0.32 PT) relaxor ferroelectric single crystals have been systematically investigated by experiment study. The focus is on the effect of constant compressive bias stress on the electromechanical coupling behavior along three crystallographic directions of PMN-0.32 PT single crystals. Dependence of the coercive field, remnant polarization, dielectric constant, and piezoelectric coefficient on the bias stress has been quantified for PMN-0.32 PT single crystals oriented in three different directions. Obtained results show that the large piezoelectric responses under zero compressive stress in [001] and [011] orientation are dominated by intrinsic crystal lattice while the engineered domain structure has a relatively minor effect. It is found that observed responses under stress cycle for [001] oriented crystals are due to polarization rotation and phase transformations. However, those for [011] and [111] oriented crystals are due to domain switching. The “butterfly” curves and polarization loops driven by electric field under different bias compression are described by two non-180° domain switching.     

Structural,optical and electrical characterization of undoped ZnMgO film grown by spray pyrolysis method

Undoped Zn_1−X Mg _X O poly crystalline films were successfully grown by a spray pyrolysis method at 500 °C. The samples indicated high quality because (0002) orientation was strongly observed in the X-ray diffraction (XRD) pattern below Mg content X = 0.3. A lattice constant of c axis decreased linearly with increasing Mg content, indicating that the lattice constant of c axis followed Vegard’s law. It was deduced that Mg atoms could be successfully substituted in Zn site from lattice constants and optical bandgap.     

Dynamics of grain boundaries under applied mechanical stress

Recent results of experimental research into stress-induced grain boundary migration in aluminum bicrystals are reported. Boundary migration under a shear stress was observed to be coupled to a lateral translation of the grains for planar symmetrical 〈100〉 tilt boundaries. This coupling proved to be the typical migration mode of any 〈100〉 tilt boundary, no matter whether low- or high-angle, low Σ CSL coincidence or non-coincidence boundary. The measured ratios of normal boundary motion to the tangential displacement of grains are in an excellent agreement with theoretical predictions. The migration-shear coupling is also observed for asymmetrical 〈100〉 boundaries. Measurements of the temperature dependence of coupled boundary migration revealed that there is a specific misorientation dependence of migration activation parameters. Grain boundaries can act during their motion under the applied stress as sources of lattice dislocations that leads to the generation and growth of new grains in the boundary region. The rate of stress-induced boundary migration decreases with increasing solute content in aluminum. Both the migration activation enthalpy and the pre-exponential mobility factor were found to increase with rising impurity concentration.     

Microscopic examination of an Alloy 600/182 weld

A microscopic study was carried out to examine the microstructural and compositional features of an Alloy 600/182 weldment. The grain boundaries of the Alloy 600 base metal consisted of low angle boundaries (4.4%), coincidence site lattice boundaries including twins (46.6%), and random high angle grain boundaries (49.0%). The precipitates in the matrix of Alloy 600 were identified as Cr₇C₃, irrespective of the intergranular and intragranular ones. The microstructure of the Alloy 182 weld metal consisted of cellular dendrites in the grains epitaxially solidified from the heat affected zone, and the Mn concentration increased periodically across the dendritic interfaces. Contrary to the Alloy 600 base metal, most of the grain boundaries of the Alloy 182 weld metal were low angle and random high angle grain boundaries, with a negligible fraction of coincidence site lattice boundaries. Tiny Cr-rich M₂₃C₆ and Nb carbides were distributed on the grain boundaries in the weld metal, and a Cr-depletion zone was formed due to the Cr carbide precipitation. Precipitates of (Nb,Ti)C, Al₂O₃ type and TiO₂ type oxides were found in the Alloy 182 weld metal.