Low-index Directions Research Articles

Diffraction of Fast Atomic Projectiles during Grazing Scattering from a LiF(001) Surface

Light atoms and molecules with energies from 300 eV to 25 keV are scattered under a grazing angle of incidence from a LiF(001) surface. For impact of neutral projectiles along low index directions for strings of atoms in the surface plane we observe a defined pattern of intensity spots in the angular distribution of reflected particles which is consistently described using concepts of diffraction theory and specific features of grazing scattering of atoms from insulator surfaces. Experimental results for scattering of H, D, 3He, and 4He atoms as well as H2 and D2 molecules can be unequivocally referred to atom diffraction with de Broglie wavelengths as low as about 0.001 Angstroms.

Effect of thermal vibrations and their correlations on grazing scattering of atoms from crystal surfaces

The influence of thermal vibrations of target atoms and their correlations on grazing scattering of keV atoms from crystal surfaces is investigated. Classical 2D and 3D trajectory calculations are performed and thermal vibrations are included using the Debye model as well as its high-temperature limit and uncorrelated thermal vibrations. Ion beam triangulation, rainbow structures for scattering along low-indexed directions of the surface plane, and polar angular distributions for impact along high-indexed directions are studied. We demonstrate that ion beam triangulation can be analyzed using uncorrelated thermal vibrations, while a realistic description of angular distributions requires more detailed modeling. For the peak positions of rainbow structures thermal vibrations play a minor role and they are well described by 2D simulations based on continuum potentials.

Fast Shape Evolution of TiN Microcrystals in Combustion Synthesis

Single-phase TiN crystalline powder consisting of microcrystals has been prepared by combustion synthesis. During the drastic combustion reaction with a high reaction temperature and rapid heating rate, TiN microcrystals undergo a fast shape evolution process and finally develop into various crystallization shapes, such as quasi-spherical grains, faceted cubes or pyramids, and dendrites. The formation mechanisms of different crystal shapes are discussed in light of basic crystal growth theories. It is proposed that, at the initial stage, quasi-spherical TiN crystals are formed first by diffusion-controlled continuous growth; by a faceting process, flat surfaces then appear in several low-index directions on the quasi-spherical crystals, and at last, well-faceted crystals are produced by two-dimensional nucleation and layered growth. In addition, interesting TiN dendrites are observed, probably arising from the fast cooling rate in combustion synthesis. The dendrites grow quickly in three orthogonal directions, with each growth unit exhibiting a 4-fold symmetry and sometimes a half-octahedral pyramid head.

Deformation-induced martensite stabilisation in [1 0 0] single-crystalline Ni–Ti

It is known that deformation causes stabilisation of the thermoelastic martensite in shape memory alloys. Several hypotheses have been proposed in the literature to explain this phenomenon. One such explanation suggests that grain boundaries in polycrystalline materials contribute to the stabilisation effect by acting as a plastic region to resist the shape recovery during the reverse transformation. This study was carried out to verify this hypothesis in single crystal NiTi. It was found that tensile deformation along the low index directions of the austenite caused stabilisation of the martensite. Transmission electron microscopic examination showed that numerous dislocations were generated by deformation, even at low strain levels. However, the stabilisation effect, as measured by the magnitude of the increase of the critical temperature for the reverse transformation, was much weaker than that observed in similar, but polycrystalline NiTi, supporting the hypothesis that grain boundaries contribute to martensite stabilisation in polycrystalline materials.

Stress-induced martensitic transformation of a Ni 54Fe 19Ga 27 single crystal in compression

This study investigated the pseudoelastic behavior of a Ni 54Fe 19Ga 27 single crystal associated with stress-induced martensitic transformations in compression. The single crystal showed complete pseudoelasticity in four low-index crystallographic directions, including [100], [110], [111] and [112], but with clear anisotropy. The anisotropy includes transformation strains, apparent moduli of elasticity, critical stress for the transformation and selection of martensite variants. The critical stress was confirmed to obey Clausius–Clapeyron type relations on temperature, but with varying coefficients of dependence for different deformation directions. The value of ( ⅆ σ f / ⅆ T ) ε f was found to be nearly the same for the three deformation directions of [100], [110] and [111] but different for the [112] direction, implying a different stress-induced martensitic transformation in the [112] direction than that in the other three directions.

Observations of the Gibeon meteorite and the inverse Greninger–Troiano orientation relationship

All the possible parallelism conditions associated with low-index crystallographic planes and directions in face- and body-centred cubic crystals are enumerated in terms of their minimum angle–axis misorientations. These include the Kurdjumov–Sachs (K-S), Nishiyama–Wassermann (N-W) and Pitsch orientation relationships, which are expressed in terms of close-packed (and near-close-packed) planes, close-packed directions, or both in the two crystal systems. By classifying these into either coplanar or codirectional relationships, it is possible to specify intermediate relations with either high-index directions or planes. In such a way, the Greninger–Troiano (G-T) relationship is approximated as a coplanar relation lying between the K-S and N-W relations. Based on geometric symmetry, a further correspondence relationship, which falls into the codirectional category and is located between the K-S and Pitsch relations, is represented both in pole-figure form and in Rodrigues–Frank space. It is referred to here as the inverse G-T, or G-T′. Experimental evidence from the plessite regions of the Gibeon meteorite is presented to support the validity of this relationship. It is shown that, in plessite, all the well known models, as well as their intermediates, are applicable to the γ-to-α transformation. By contrast, in the Widmanstätten portions, the misorientations are largely limited to the K-S, G-T and N-W relations.

Magnetic dichroism in angular resolved XPS on the Fe(110) surface

Magnetic dichroism has been observed in the angular distribution of Fe 2p photoemission spectra from Fe(110) surface by unpolarized Al Kα X-rays. The dichroism asymmetry varies strongly around low-index forward-scattering direction in the Fe thin film. Photoelectron diffraction theory provides explanation for these unpolarized dichroism effects, which should also be generally useful in surface magnetism studies.

Deflection of Light on a Single Domain Wall in GPI Crystal

Deflection of light on a single domain wall in glycine phosphite crystal (GPI) was studied. The angular positions for all crossing the sample beams were measured as a function of the incidence angle ranged in 0 ± 40°. The angles of α o = α cri = 24.7° have been measured. The angular positions of all beams are in agreement with those calculated using the coordinate free method. Angular dependences of all output beam intensities were observed for two polarizations: the polarization along the high-index direction: (beams D B , R B ,A, and A′) and the polarization along the low-index direction: (beams D A , R A ,B, and B′). The experimental data show clearly the exchange of the intensities of the output beams appearing after crossing the sample containing one domain wall. Communicated by Prof. Bozena Hilczer et al.

Fracture of single crystals having layered morphology

The mechanism for relaxation of elastic energy in layered crystals (where interlayer glide is possible) under a point load is discussed. Titanium dichalcogenides are chosen as materials with covalent interatomic bonds, while the Ir-Sn compound is a metallic single crystal. All studied samples have layered morphology with similar parameters, such as the thickness of the sample and the thickness of a single layer. It was found that penetration of a diamond pyramid induces mechanical twins around the indent, whereas the appearance of cracks is a very rare phenomenon. In contrast with bulk samples, cracks in layered crystals move on complicated trajectories, which do not coincide with low-index crystallographic directions. Besides, their growth is limited by the surface single layer. Gliding between neighbouring layers effectively suppresses the propagation of cracks via the interlayer boundary. Glide may be considered an irreversible shift, which prevents the fracture of a material.

Ion-induced low-energy electron diffraction

${\mathrm{H}}^{+}$ and ${\mathrm{He}}^{+}$ ions with an energy of $25\phantom{\rule{0.3em}{0ex}}\mathrm{keV}$ are scattered under a grazing angle of incidence from a clean and flat $\mathrm{Cu}(001)$ surface. For specific azimuthal orientations of the crystal surface with respect to low index directions in the surface plane we observe the ion induced emission of electrons with a conventional $\mathrm{LEED}$ (low energy electron diffraction) setup. By operating the instrument in an energy dispersive mode we find intensity distributions of emitted electrons which can unequivocally be ascribed to diffraction effects at the target surface.

Study of the orientation and frequency of occurrence of elementary steps on the (010) cleavage face of potassium acid phthalate single crystals

Experimental observations of an atomic force microscopy study of the orientation and frequency of occurrence of elementary steps of height 1.386 nm (equal to the lattice parameter b) produced on the freshly cleaved (0 1 0) surfaces of potassium acid phthalate crystals grown from aqueous solutions are described and discussed. It was found that most of the elementary cleavage steps are oriented along low-index crystallographic directions. The relative frequencies of the experimentally observed elementary steps of different orientations were compared with their calculated energies. Van der Waals interactions between neighbouring molecules and Madelung summation of Coulomb interactions between an ion and the surrounding ions were considered to calculate the total surface energy or the total energy of a step of a given orientation. It is shown that: (1) in the case of crystals like potassium acid phthalate containing both Coulomb and Van der Waals bonds, the calculated values of surface and step energies may be incorrect when they are considered purely ionic, (2) the relatively low value of the surface energy, mainly due to Van der Waals interactions, is responsible for the perfect cleavage along the (0 1 0) plane, and (3) some of the observed cleavage steps have orientations that correspond to low step energies.

Study of the orientation and frequency of occurrence of elementary steps on the (0 1 0) cleavage face of potassium acid phthalate single crystals

Experimental observations of an atomic force microscopy study of the orientation and frequency of occurrence of elementary steps of height 1.386 nm (equal to the lattice parameter b) produced on the freshly cleaved (0 1 0) surfaces of potassium acid phthalate crystals grown from aqueous solutions are described and discussed. It was found that most of the elementary cleavage steps are oriented along low-index crystallographic directions. The relative frequencies of the experimentally observed elementary steps of different orientations were compared with their calculated energies. Van der Waals interactions between neighbouring molecules and Madelung summation of Coulomb interactions between an ion and the surrounding ions were considered to calculate the total surface energy or the total energy of a step of a given orientation. It is shown that: (1) in the case of crystals like potassium acid phthalate containing both Coulomb and Van der Waals bonds, the calculated values of surface and step energies may be incorrect when they are considered purely ionic, (2) the relatively low value of the surface energy, mainly due to Van der Waals interactions, is responsible for the perfect cleavage along the (0 1 0) plane, and (3) some of the observed cleavage steps have orientations that correspond to low step energies.

Kinetic electron emission for planar versus axial surface channeling of He atoms and ions

Fast ${\mathrm{He}}^{+}$ ions and $\mathrm{He}\ifmmode^\circ\else\textdegree\fi{}$ atoms are scattered under grazing incidence from a clean and flat Al(111) surface. The target current recorded as function of azimuthal angle with respect to the surface orientation is enhanced for scattering along low-index crystallographic directions. Coincident studies on the number of electrons emitted per ion impact allow us to explore this effect. We find that the increase of the total electron yield for surface channeling along low-index directions stems primarily from projectiles with trajectories in the subsurface region and the consequent emission of a substantially larger number of electrons.

Triangulation of a Cu(0 0 1) surface and an ultra-thin Mn film via grazing ion surface scattering

The structure of crystal surfaces and ultra-thin films can be studied via ion beam triangulation. The method is based on the enhanced kinetic emission of electrons for grazing angle scattering of fast ions from a mono-crystalline surface, whenever the azimuthal orientation of the target surface with respect to the projectile beam coincides with low index directions. In studies with 25 keV protons scattered from a clean Cu(0 0 1) surface as well as from the surface of an ultra-thin Mn film deposited on the Cu(0 0 1) substrate we have explored features concerning the angular width of the signals obtained in the application of this method.

Effect of Mn(II) ions on the growth of ammonium oxalate monohydrate crystals from aqueous solutions: I. Growth habit and surface morphology

AbstractThe effect of concentration of Mn(II) ions on the growth habit and the surface micromorphology of different as‐grown faces of ammonium oxalate monohydrate (AO) single crystals grown from aqueous solutions was studied at a constant temperature of 30 °C and predefined supersaturations up to 20%. It was observed that the growth habit and the surface morphology of the crystals strongly depend on the supersaturation used for growth and the impurity concentration in the solution. The experimental results were analysed in terms of connected nets determined from different projections of the structure of AO crystals. Analysis of the observations revealed that: (1) the directions of connected nets corresponding to basic growth units composed of single (NH4)2C2O4 · H2O molecules are in excellent agreement with the low‐index crystallographic directions of the orientations of growth layers, (2) all faces appearing in the growth morphology of AO crystals are F faces, and (3) the {001} face growing from pure aqueous solutions is essentially a kinetically rough face but the presence of Mn(II) impurity leads to their appearance in the morphology due to increase in the strength of bonds of the connected nets composing the surface graph.

Deformation of thin foil of fcc and bcc metals containing pre-introduced He bubbles

Thin foil of fcc and bcc metals subjected to tensile deformation has been found to exhibit an anomalously high density of small vacancy clusters, probably in the absence of dislocations. Deformation of fcc Au and bcc Fe containing pre-introduced He bubbles is carried out, at strain rates ranging from 10 −3 to 10 5 s −1 to a 10 2% strain at −180 and 25 °C. Microstructures in the deformed regions are examined by transmission electron microscopy. Rows of bubbles are formed due to extreme elongation of bubbles under stress and its subsequent division into smaller pieces in response to vacancy diffusion around the bubble surfaces. The bubble rows are parallel to the low-index crystallographic directions, 〈001〉, 〈011〉, and 〈012〉 for Au and 〈011〉 and 〈001〉 for Fe, which can be resolved into ‘slip directions’. The results indicate that displacement of atoms in these thin-foil specimens during tensile deformation progresses while conforming to the nature of the crystal, even in the absence of dislocations.

Multiphase Crystallography in the Nucleation of Intragranular Ferrite on MnS+V(C,N) Complex Precipitate in Austenite

Crystallographic orientation relationships between intragranular ferrites, the MnS+V(C, N) complex precipitates acting as ferrite nucleation sites, and austenite matrix were studied in Fe-Mn-C alloys by scanning electron and transmission electron microscopy. VC holds a cube-cube orientation relationship (‹001›γ// ‹001›VC) when it is formed directly within austenite grains in an Fe-12Mn-0.8C-0.3V alloy. When VC precipitates nucleate on incoherent MnS particles dispersed in austenite, there is no specific orientation relationship between the three phases. Intragranular ferrite idiomorphs nucleating on the MnS+V(C, N) complex precipitate in austenite in Fe-1.5Mn-0.2C and Fe-2Mn-0.2C alloys often hold the Baker-Nutting orientation relationship ((001)α//(001)V(C, N), [110]α//[100]V(C, N)). Although several irrational ferrite/V(C, N) orientation relationships were observed, misorientation for either low-index planes or directions are relatively small between ferrite and V(C, N) for those relationships. The orientation relationships between intragranular ferrite and austenite were estimated by examining the misorientations between the ferrite and the neighboring martensite lathes from the Kurdjumov-Sachs inter-variant relationships. There is no specific orientation relationship between the intragranular ferrite idiomorph and the austenite matrix because of the low-energy orientation relationships between ferrite and V(C, N).

Self-assembled nanowire formation during Cu deposition on atomically flat Vse2 surfaces studied by microscopic methods

Self-assembled metallic nanostructures gain increasing interest in nanotechnologies and might find application in future electronic device fabrication. Upon UHV deposition of copper onto cleaved layered crystals of VSe2, self-assembled networks of nanowires and nanoclusters are observed to form and found to be remarkably stable even during storage under ambient conditions and at moderately increased temperatures. Transmission and scanning electron microscopy combined with scanning tunneling and atomic force microscopy have been used to characterize the arrangements, structure and dimensions of the nanostructures and the substrate before metal deposition. On the flat parts of the substrate, self-similar nanowire networks form with wire diameters ranging from 8 to 250 nm and mesh dimensions ranging from 0.35 to 10 μm. The nanowires are preferentially aligned along low-index crystal directions and possess polycrystalline structure. Nanoclusters are formed within the meshes of the nanowire network. A model for the self-assembled growth of nanostructures during metal deposition, which takes into account the electronic charge exchange of adsorbed atoms with the substrate, will be discussed.

Peierls barriers, kinks, and flow stress: Recent progress

The intrinsic barriers against the glide of dislocations lying along low-index crystallographic directions, the so-called Peierls barriers, are overcome by the thermally activated and stress-assisted generation of pairs of kinks of opposite sign in the dislocations. In plastically deformed Al four low-temperature mechanical relaxation processes resulting from this are identified. In a sequence of falling temperatures, the corresponding internal-friction peaks are the original Bordoni peak (a o /2 screw dislocations on {111} slip planes; a 0 = edge length of the elementary cube), Ni-blett's 'subsidiary peak' (60°-dislocations on {111}), the Lax-Filson peak (edge dislocations on {111}), and the Kosugi-Kino peak (30°-dislocations on {111}). In other face-centred cubic (fcc) metals (e. g. Cu, Pd) the relaxation processes of the dislocations lying along as well as those lying along (112) overlap, giving rise to just two peaks, namely very broad Bordoni and Niblett-Wilks peaks. In the body-centred cubic (bcc) transition metals, the Peierls barriers of a 0 /2 screw dislocations are exceptionally high. Beyond the microstrain regime, overcoming them by the formation of kink pairs determines the flow stress up to the knee-temperature T K . The theory of the kink-pair formation enthalpy H kp (σ*) (effective stress σ* = difference between applied resolved shear stress σ and long-range internal stress σ M ) has been tested and verified with great accuracy on various high-purity bcc metals using the Ackermann-Mughrabi cyclic-deformation method as well as stress-relaxation measurements. The 'hump' in the flow-stress-temperature relationship of high-purity bcc metals follows from the theory without further assumptions. The comparison experiment-theory shows that the kink-pair generation takes place on {110} planes below the temperature T of the lower bend of the flow-stress-temperature curve and on {112} in the range T {112} slip systems with different slip directions. The {112} slin is also responsible for the tension-compression asymmetry of bcc metals, which, however, cannot be explained entirely in terms of the familiar twinning-antitwinning asymmetry of {112} slip but involves also stress components other than the effective resolved shear stress σ*. In 1971 it was proposed that the generation of kink-pairs in a 0 /2 screw dislocations gives rise to the so-called γ-relaxation in the internal friction of bcc metals. The agreement of the activation enthalpy of this process with twice the enthalpy of formation of isolated kinks in screw dislocations, H k , as deduced from flow-stress measurements not only verifies this proposal but also demonstrates that in the 'classical' γ-relaxation the kink-pair generation takes place on {112} planes. However, recent measurements on Nb and Ta have shown that annealing may lead to a modified γ-relaxation with a smaller activation enthalpy.

Plasmon-Mediated Scattering of Light by Ion Eroded Ag(110) Surfaces

Enhanced scattering of laser light from polished and ion bombarded Ag(110) surfaces is reported. Ar+ ions with energy 500 eV were directed against the sample at angles of incidence between 30° and 45°. The ion current was about 4–6 μA. The experiments were made with a diode pumped solid-state green laser that emitted at 532 nm, with a continuous wave power output around 5 mW. In a controlled series of experiments a sudden increase in scattered intensity could be observed at a fluence of about 2 × 1017 ions/cm2. The scatterograms showed radially oriented intensity streaks, superimposed on a diffuse and isotropic background intensity. No correlations with low-index crystallographic directions were found. The surface structure was studied by means of optical interferometry and atomic force microscopy. The scattered light was found to be dominated by the contribution from shallow surface indentations and scratches remaining from the polishing process. It is demonstrated that the sputtering creates a surface topography with correlation length of a few μm. A mechanism based on surface plasmons is proposed to be responsible for the observed increase in scattered intensity.