Stereographic Triangle Research Articles

モリブデン合金鋳塊の粒界破壊

Bending tests are made using bicrystals prepared from the ingots of arc and electron-beam melted pure Mo and its alloys. The character of grain boundaries, the scavenging effect of alloying elements and their effect on the grain boundary fracture stress are mainly investigated. Most of grain boundaries are mixed types having a common rotation axis distributed randomly in the unit stereographic triangle except for the vicinity of (001) pole. It is anticipated that a large amount of oxygen and carbon segregated at the grain boundaries of arc melted pure Mo can fairly be reduced by the addition of titanium and electron-beam melting. Especially, the scavenging effect of titanium on oxygen is successful. The grain boundary strength has a tendency to decrease with increasing atomic misfit of the alloying elements to the solvent in electron-beam melted dilute molybdenum alloys.

Plastic deformation and dislocation arrangement of Nb[sbnd]34 at.% Ta alloy single crystals

Abstract Nb66 Ta34 alloy single crystals having orientations in the central part of the stereographic triangle and an interstitial impurity content of less than 10p.p.m. (C + N + O) have been deformed in tension at 77, 195, 295, 330 or 470 K. The dislocation behaviour and arrangement have been studied by slip-line observations, Laue X-ray back-reflection, X-ray topography and transmission electron microscopy (TEM). The slip-line investigations indicate that at each deformation temperature the plane that carries the maximum resolved shear stress (MRSS) is the active macroscopic slip plane. At low deformation temperatures (i.e. 77 and 195 K) the work-hardening curves are parabolic and the dislocation arrangement consists of primary and secondary screw dislocations and of tangles of non-screw dislocations. At intermediate temperatures (i.e. 295, 330 and 470 K) the work-hardening curves resemble that of f.c.c. crystals with an extended stage I. However, the experimental findings suggest that a gradual transit...

Anomalous slip in high-purity tantalum single crystals after tensile deformation at 77 K

Abstract High-purity tantalum single crystals having orientations in the central part of the stereographic triangle and a residual resistance ratio of 5760:1 have been deformed in tension at 77 K. In all crystals anomalous slip was observed. This result is remarkable in view of the fact that other authors have observed anomalous slip in crystals of comparable orientation only after deformation in compression. The. reason for this difference lies presumably in the higher purity of the crystals used in the present work, as indicated by etching experiments: etching in an acid solution subsequently suppresses anomalous slip owing to the influence of hydrogen interstitials.

Effect of normal stresses on yield stress of molybdenum single crystals at slip on the plane (211)

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Underpotential deposition of lead on single crystal faces of gold Part I. The influence of crystallographic orientation of the substrate

The influence of the crystallographic orientation of the gold substrate surface on lead deposition and removal in the underpotential region is studied in detail. In order to observe systematic changes in the cyclic voltammograms, the faces of the three main zones of the unit projected stereographic triangle are grouped into five sections following bond order notation or a notation based on the TLK model of the surfaces. Correlations with the potential of zero charge are discussed. A comparison with ionic adsorption is made.

Underpotential deposition of lead on single crystal faces of gold: Part I. The influence of crystallographic orientation of the substrate

The influence of the crystallographic orientation of the gold substrate surface on lead deposition and removal in the underpotential region is studied in detail. In order to observe systematic changes in the cyclic voltammograms, the faces of the three main zones of the unit projected stereographic triangle are grouped into five sections following bond order notation or a notation based on the TLK model of the surfaces. Correlations with the potential of zero charge are discussed. A comparison with ionic adsorption is made.

An interpretation for FEM patterns of a hydrogen-adsorbed tungsten tip and its application to hydrogen adsorption on single-crystal planes

An attempt is made to interpret the FEM patterns of the hydrogen-tungsten adsorption system at 300K. The proposed model predicts that the FEM patterns depend on the contours of the adsite-surface distance drawn on a unit stereographic triangle of BCC crystals. The main outlines of the observed FEM patterns are found systematically to be able to be analysed as circles or circular arcs centered at some crystallographic planes on the tip, and they are found to correspond to parts of the predicted contours. An application to the adsorption on single-crystal planes is also discussed.

The influence of orientation on the stress rupture properties of nickel-base superalloy single crystals

The influence of orientation on the stress rapture properties of MAR-M247 single crystals was studied. Stress rupture tests were performed at 724 MPa and 774 °C where the effect of anisotropy is prominent. The mechanical behavior of the single crystals was rationalized on the basis of the Schmid factors for the operative slip systems and the lattice rotations which the crystals underwent during deformation. The stress rupture lives at 774 °C were found to be greatly influenced by the lattice rotations required to produce intersecting slip, because second-stage creep does not begin until after the onset of intersecting slip. Crystals which required large rotations to become oriented for intersecting slip exhibited a large primary creep strain, a large effective stress level at the onset of steady-state creep, and consequently, a short stress rupture life. Those crystals having orientations within about 25° of the [001] exhibited significantly longer lives when their orientations were closer to the [001]-[011] boundary of the stereographic triangle than to the [001]-[1l 1] boundary, because they required smaller rotations to produce intersecting slip and the onset of second-stage creep. Thus, the direction off the [001], as well as the number of degrees off the [001], has a major influence on the stress rapture lives of single crystals in this temperature regime.

Shape strains associated with thermally-induced and stress-induced martensite in a CuAlNi shape memory alloy

Accurate measurements have been made of the shape strain accompanying the formation of the 2H orthorhombic γ′ 1 martensite during cooling and during compressive stressing of a Cu14%Al3.4%Ni shape memory alloy. In both transformations the displacement vectors have magnitude 0.087 and are near [1̄10] B in the [010] B-[1̄10] B-[1̄11] B stereographic triangle, the habit planes are near (3̄3̄1) B on both sides of the (1̄10) B symmetry plane and the dilatation parameter is unity. Crystallographic analysis using the geometrical theory indicates that the two shape strains, associated with the two kinds of habit plane, are approximately consistent with two different {121} o twinning heterogeneities in the martensite. However, the discrepancies between the measurements and the theoretical calculations are sufficiently large to suggest that the complementary strain is more complex than a simple shear on the martensite twinning elements.

The behaviour of water at stepped surfaces of single crystal gold electrodes

New information concerning the structure of the metal-electrolyte interface is obtained by comparing the electronic work function of metallic single crystals in vacuum and the potential of zero charge (pzc) at the metal-electrolyte interface. The close parallelism of these two properties is notable in comparing our results for the pzc of gold single crystals of a number of orientations located along the sides of the stereographic triangle and those for the work function of copper by Peralta et al. [24]. This comparison shows that the presence of an adsorbed water layer at the metal-electrolyte interface does not perturb to any large extent the atomic arrangement of the outermost metallic surface with respect to the structure assumed to be displayed in vacuum. In the case of stepped gold surfaces near the (111) face, a comparison between the work function measured by Besocke et al. [23] and our results for pzc allows us to conclude that the metal-solvent interaction depends on the nature of the monoatomic step whether it corresponds to a quaternary site in the case of the (100) step structure or to a ternary site for the (111) step structure.

LEED studies of clean high Miller index surfaces of germanium

Clean high Miller index Ge surfaces the poles of which lie on the sides of a unit stereographic triangle were studied by LEED. Clean surfaces of germanium may coincide with the atomic planes of the same indices or consist of the regular steps with (111) or (100) terraces, or contain the “hill and valley” configuration depending on the orientation. Surface atomic planes are reconstructed. On clean Ge surfaces at certain temperatures the reversible order-disorder and order-order transitions take place.

Recherche des systèmes de glissement actifs dans un processus de déformation plastique du polycristal. III. Comportement du facteur de Taylor dans le cas du glissement cristallographique dans les cristaux cubiques

The boundaries of the regions within which a specific set of slip systems maximizes the Taylor factor M (g, q) are plotted in a stereographic triangle for several values of the contraction ratio q and an axially symmetric flow. For q = 0.5 these boundaries are shown to be mostly circles on the unit sphere.

A unique description of the relative orientation of neighbouring grains

If N denotes the number of symmetry rotations of a crystal lattice, the number, n, of different rotations connecting two orientations of this lattice is a multiple of N and a factor of 2N2. Among these n equivalent rotations those with minimum angle are considered. Usually one, but in exceptional cases two or three, of these has its axis in the standard stereographic triangle and is called a disorientation. How equivalent disorientations are connected by symmetry rotations and how the number, n, of equivalent rotations can be found for any disorientation are shown. Additional conditions for selecting a unique reduced rotation among the disorientations are proposed.

Deformation of FeAl single crystals at high temperatures

Abstract Single crystals of the intermetallic compound FeAl with the CsCl structure have been deformed in compression at temperatures between 470 and 1000 K to study the slip geometry and the dislocation arrangements in this material at high temperatures. At temperatures below 0·44 of the melting temperature, T m, slip occurs on the {110}〈111〉 systems, while at 0·44T m, the transitions in the slip directions from 〈111〉 to 〈001〉 takes place for orientations in the right-hand side of the unit stereographic triangle, i.e. near the [011]-[111] boundary and, as the deformation temperature is increased, the region showing the 〈001〉-type slip becomes wider. The critical resolved shear stress for both types of slip exhibits a strong temperature dependence above 0·44T m. The dislocation arrangements in crystals deformed by the slip of 〈001〉 type is found to consist mostly of edge dislocations. The occurrence of the 〈001〉-type slip at such a high temperature is suggested to be associated with compositional deviatio...

Iodide ion adsorption on gold dependence on electrode crystallographic orientation

Specific adsorption of anions on crystal faces of gold is related to the superficial atomic structure. For the iodide ion analysis of the admittance-potential curves for 13 different crystallographic orientations of the three main zones of the stereographic triangle is done. Empirical correlations are established between surface structure and the morphology of the admittance curves.

Orientation dependence of surface segregation in a dilute Ni–Au alloy

Surface segregation theory admits that the degree of surface enrichment depends on surface orientation through the anisotropy of surface properties such as surface energy. This prediction was tested by determining the surface composition of several grains of different surface orientation in a polycrystalline Ni–Au alloy foil. A scanning Auger microprobe provided Auger point analyses which were used to determine the surface segregation characteristics of individual (randomly oriented) grains, while selected area electron channeling patterns, obtained with a scanning electron microscope, allowed the surface orientation of each grain to be determined. A strong anisotropy of gold surface enrichment was observed; for example,the gold surface concentration at 700°C varied by as much as an order of magnitude over the range of surface orientations investigated. A plot of the variation in surface composition within the standard stereographic triangle showed trends that are comparable with the known anisotropy of surface energy in fcc metals. It is concluded that the coupling of the above experimental techniques provides a powerful tool for the study of such phenomena.

Surface morphology of platinum catalysts

Surface morphologies of small (< 0.06 cm diameter) single crystal spheres of Pt and other transition metals are examined using scanning electron microscopy (SEM) following their use as catalysts in NH 3, C 3H 8, and CO oxidation reactions and in NH 3 decomposition at a total pressure of 1 atm. The stabilities of all regions of the stereographic triangle are examined from SEM micrographs and reflectance patterns, and relative areas of planes are estimated. Between one and five stable crystal planes are observed for these reactions, and the planes formed and their relative areas depend strongly on the reaction and reactant composition. Unstable planes break up into facets of these planes, but smooth curved regions and pits are observed under certain conditions. Dependences on time, temperature, sphere diameter, and flow velocity are examined for NH 3 oxidation. It is found that the rate of facet formation is larger on small spheres and that the stable planes and their relative areas are influenced by both sphere diameter and flow velocity. Facet dimensions are 1 to 5 μm for all reactions under most conditions, and facet size increases slowly with reaction time. It is shown that metal transport by either surface diffusion or volatile oxide formation is possible in most cases and that minimum surface free energy considerations can account for unstable and metastable regions and faceting rates. Boundary layer influences on metal transport and the dependence of etching on sphere diameter and flow velocity are also considered.

Simultaneous hardening and softening in a nonisoaxial β brass bicrystal

Nonisoaxial beta brass bicrystals, consisting of a hard (H) orientation, close to , and a soft (S) orientation near the center of the stereographic triangle, were compressed in both continuous and interrupted tests, which permitted slip line observations to be made, in order to ascertain why in previous work5 a similarH-S combination had shown much greater hardening in theH component. Stress-strain behavior of each component was determined by methods developed earlier.5 TheH component initially hardened rapidly with strain, and at 0.5 pct strain, hardened more slowly. TheS component revealed lower strength and strain hardening than the unbonded single crystal up to 1.5 pct plastic strain, after which hardening was much more rapid. From slip line observations considerations of the effect of secondary stresses, and examination of slip systems providing least work at the grain boundary, it appears that the reduced flow strength of theS component is due to pile-up stresses from theH component. Changes in strain hardening rate in bothH andS components were related to the onset or cessation of heavy slip associated with serrated yielding.

Morphologies of Pt catalyst surfaces

Scanning‐electron microscopy is used to examine faceting of Pt single crystals induced by catalytic oxidation of NH3 and C3H8. By using single‐crystal microspheres of Pt, the morphology can be determined as a function of crystallographic orientation. Stereographic triangle constructions of smooth and faceted regions give the crystal planes and relative areas which should be directly applicable to reactions on polycrystalline or polyfaceted catalysts. Transmission‐electron microscopy is used to examine the morphologies and sintering rates of Pt crystallites supported on graphite, amorphous carbon, SiO2, and Al2O3. An environmental stage permits examination in ultra‐high vacuum, in known gases up to ∠10−2 Torr (1.3 Pa) and at temperatures up to 1000°C. Mechanisms and rates of sintering and the influence gases on sintering rates and crystallite morphology will be described and discussed.

Deformation and Fracture Behaviours of Cementite

In order to clarify the deformation and fracture behaviours of cementite, observations by an optical microscope and a scanning electron microscope were made on the slip lines and fracture surfaces which took place around Vickers hardness indenters pressed on the surface of large cementite grain in white pig iron.Although slip lines in cementite were generally straight, wavy slip lines and cross slip lines were occasionally observed under specified conditions of temperature and crystal orientation.Large dependences on deformation temperature and crystal orientation were recognized for the slipping behaviour and hardness of cementite crystal. The slipping region increased and the hardness decreased with increase in deformation temperature. These temperature effects were remarkably large for cementites having the surface orientation around the center or near the [001]θ–[\bar111]θ boundary of a stereographic triangle. The gliding of cementite having these orientations was very easy in comparison with those of the cementites having the orientation around [001]θ or near the [001]θ–[110]θ boundary of the stereographic triangle.It was further made clear that the operation of the slip system of cementite crystal was closely related with the Schmid factor in spite of a strong anisotropy in the crystalline structure.The fracture of cementite at room temperature was of a cleavage type, judging from the topographic features of fracture surfaces. The indeces of these fracture surfaces were determined to be {110}θ, {100}θ and {210}θ.