<10$$ \bar{1} $$0> Dislocation at a {2$$ \bar{1} $$$$ \bar{1} $$0} low-angle grain boundary in LiNbO3

A LiNbO₃ bicrystal that contains a {2\( \bar{1} \) \( \bar{1} \)0} low-angle grain boundary with both of 2° tilt misorientation and a slight twist misorientation was fabricated, and resulting dislocation structure at the boundary was analyzed by using transmission electron microscopy (TEM) and scanning TEM. The observations revealed that two types of dislocations of b = 1/3 <2\( \bar{1} \) \( \bar{1} \)0> and b = <10\( \bar{1} \)0> are formed at the boundary. A 1/3 <2\( \bar{1} \) \( \bar{1} \)0> dislocation, which dissociates into two partial dislocations with a {2\( \bar{1} \) \( \bar{1} \)0} stacking fault in between, compensates only tilt misorientation of the boundary. On the other hand, it was found that a <10\( \bar{1} \)0> dislocation, which dissociates into three equivalent partial dislocations with b = 1/3 <10\( \bar{1} \)0>, has both edge and screw components in total. That is, the <10\( \bar{1} \)0> dislocations are formed to compensate the twist misorientation of the boundary, in addition to the tilt misorientation. It is interesting that the three partial dislocations from a <10\( \bar{1} \)0> dislocation are arranged in a zigzag pattern with left–right asymmetry. This special configuration is suggested to originate from the presence of stable stacking fault structure on the {2\( \bar{1} \) \( \bar{1} \)3} plane in LiNbO₃.     

The Core Structure and Peierls Stress of $\langle 11\overline {2}0\rangle $ Dislocations in MgB2 with Mg and B Vacancies

The improved Peierls-Nabarro theory is employed to study the core structure and mobility of \(\langle 11\overline {2}0\rangle \) dissociated dislocations of MgB₂. The generalized stacking fault energy entering the theory is calculated by using first-principle methods. The effects of Mg and B vacancies on the properties of \(\langle 11\overline {2}0\rangle \) dislocations are also presented. It is found that Mg vacancy can reduce the antiphase boundary energy and unstable stacking fault energy obviously compared with B vacancy. Peierls stress of MgB₂ with Mg vacancy is about 1/4 ～1/5 of MgB₂ and MgB₂ with B vacancy.     

Dissociated \frac{1}{3}\langle 0\bar{1}11\rangle dislocations in Bi2Te3 and their relationship to seven-layer Bi3Te4 defects

We investigate the structure of $ \frac{1}{3}\langle 0\bar{1}11\rangle $ dislocations observed in Bi₂Te₃ nanowires. This particular type of dislocation is interesting because it has a large Burgers vector (b = 1.048 nm) with a component normal to the basal planes equal to the thickness of one full Bi₂Te₃ quintuple unit (i.e., c/3). Atomic-resolution high-angle annular dark-field scanning transmission electron microscopy observations show that the dislocations form with a complex dissociated core structure. This structure consists of two partial dislocations that separate a defected region consisting of a seven-plane-thick septuple unit, consistent with a local patch of Bi₃Te₄, rather than the normal Bi₂Te₃ quintuple layer structure. As we discuss, details of the core structure can be understood from an analysis of the crystallographic parameters of the observed partial dislocations. This analysis suggests a mechanism to accommodate the loss of tellurium through the heterogeneous nucleation and growth of seven-layer defects at $ \frac{1}{3}\langle 0\bar{1}11\rangle $ —type dislocations.     

Structure of codes over the ring Z_{3}[v]/\langle v^{3}-v\rangle

In this paper, we study the structure of linear codes over the non chain ring $Z_{3}[v]/\langle v^{3}-v\rangle $ . In order to study the codes, we first study the structure of this ring via a distance preserving Gray map which also induces a relation between codes over this ring and ternary codes. Further, the algebraic structure of cyclic and dual codes is also studied. A MacWilliams type Identity between the Gray weight enumerators of the original code and its dual is established. In all cases examples that illustrate the theorems and lemmas are provided. Also, a BCH-type bound and an example that attains this bound is presented.     

The structure of a migrating low-angle tilt grain boundary in strontium titanate

Weak beam transmission electron microscopy and stereomicroscopy have been used to characterize the three-dimensional structure of a severely deformed low-angle tilt grain boundary in a strontium titanate ceramic. Various interactions between crystal lattice dislocations and grain boundary dislocations in this boundary have been analysed. The deformed low-angle tilt grain boundary is a result of partial glide. The boundary is composed of dislocations with Burgers vectorsa [¯100] and the deformation of the boundary is interpreted as having occurred by the interactions of the boundary with crystal lattice dislocations during grain boundary migration. Observed dislocation network in the grain boundary are a result of the reactionb ₃=b₁+b₂=a [¯100]+a [00¯1]=a [¯10¯1], and the resultant dislocations are sessile. Also, many crystal lattice dislocations are pinned by the grain boundary and produce a complex dislocation structure for the boundary.M. Fujimoto is a Visiting Scientist at the Massachusetts Institute of Technology on leave from Taiyo Yuden Co., Ltd., Tokyo, Japan.     

Segregation at the {013} symmetrical tilt grain boundary in dilute Fe-Si alloy bicrystals

The structure and segregation behaviour of the {013} symmetrical tilt grain boundary were studied in Fe-Si dilute alloy bicrystals. Structural features such as twins, cleavage tongues and steps at the grain boundary, revealed by brittle intercrystalline fracture, are described and the identity of the fracture surface with the grain boundary is discussed. The amounts of segregation of phosphorus and silicon obtained by Auger electron spectroscopy are correlated with the structure of the analysed regions. The scatter of measured values of concentration of phosphorus and silicon in different regions of the fracture surface is explained from a structural point of view. A repulsive interaction between phosphorus and silicon atoms was confirmed. Grain-boundary enrichment ratios for phosphorus of 185 and 278, and decreases of the silicon concentration to 63 and 60% of the bulk value, were found at the grain boundary in as-grown and annealed bicrystals, respectively.     

Evolution of the electrical resistance of \bf{\hbox {YBa}_2\hbox {Cu}_3\hbox {O}_{7-\varvec\delta }} single crystals in the course of long-term aging

Investigated are the changes in the basal-plane electrical resistivity of an optimally doped \(\hbox {YBa}_2\hbox {Cu}_3\hbox {O}_{7-\delta }\) single crystal in the course of long-term aging (17 years) at room temperature in air. In consequence of aging the sample has decomposed into three phases with different temperatures of the superconducting transition, while the transition widths of these phases have increased significantly. The temperature dependence of the electrical resistivity has retained a metallic character. The fluctuation conductivity near the critical temperature is described well by the 3D Aslamazov–Larkin model. In the course of aging significant changes in the scattering characteristics have been observed, whereas the Debye temperature has changed slightly and the transverse coherence length has remained constant.     

On the Diophantine equationsax^2 + bx + c = c_0 c_1^{y_1 } \cdots c_r^{y_r }

An algorithm is devised to determine all solutions of any Diophantine equation of the type described in the title.     

$$\hbox {NO}_{2}^{-}$$ and $$\hbox {SCN}^{-}$$SCN--intercalated layered double hydroxides: structure and orientation of anions in the interlayer gallery

\(\hbox {NO}_{2}^{-}\) and \(\hbox {SCN}^{-}\) are two common small inorganic anions. The former is a common industrial pollutant. The latter is linear and is a good mimic for the toxic \(\hbox {CN}^{-}\) ion. The structures of these two anions are refined within the gallery of the [Zn–Al]-layered double hydroxide (LDH). Both LDHs crystallize as mixed anion phases. The nitrite is found to co-exist with the nitrate ion. The nitrite ion is intercalated with its molecular plane inclined to the metal hydroxide layer. In the case of the \(\hbox {SCN}^{-}\) intercalated LDH, no other anion was detected by ion chromatography, suggesting that the \(\hbox {SCN}^{-}\) deficiency is compensated by intercalated hydroxyl ions. In this case, the \(\hbox {SCN}^{-}\) ion is found to be intercalated with its molecular axis inclined to the metal hydroxide layer.     

Synthesis,structure and thermoelectric properties of $$\mathrm{La}_{1-x}\mathrm{Na}_{x}\mathrm{CoO}_{3 }$$ perovskite oxides

Monovalent ion doped lanthanum cobaltate \(\hbox {La}_{1-x}\hbox {Na}_{x}\hbox {CoO}_{3 }\) (\(0 \le x \le 0.25\)) compositions were synthesized by the nitrate–citrate gel combustion method. All the heat treatments were limited to below 1123 K, in order to retain the Na stoichiometry. Structural parameters for all the compounds were confirmed by the Rietveld refinement method using powder X-ray diffraction (XRD) data and exhibit the rhombhohedral crystal structure with space group R-3c (No. 167). The scanning electron microscopy study reveals that the particles are spherical in shape and sizes, in the range of 0.2–0.5 \(\upmu \)m. High temperature electrical resistivity, Seebeck coefficient and thermal conductivity measurements were performed on the high density hot pressed pellets in the temperature range of 300–800 K, which exhibit p-type conductivity of pristine and doped compositions. The X-ray photoelectron spectroscopy (XPS) studies confirm the monotonous increase in \(\hbox {Co}^{4+}\) with doping concentration up to \(x = 0.15\), which is correlated with the electrical resistivity and Seebeck coefficient values of the samples. The highest power factor of \(10~\upmu \hbox {W~mK}^{-2 }\) is achieved for 10 at% Na content at 600 K. Thermoelectric figure of merit is estimated to be \({\sim }1 \times 10^{-2}\) at 780 K for 15 at% Na-doped samples.     

Templated synthesis and characterization of red-emitting $$\hbox {Ca}_{{1-x}}\hbox {Sr}_{1-x}\hbox {Eu}_{2x}^{3+}\hbox {SiO}_{4}$$ phosphor for LED applications

A novel attempt towards the synthesis of red-emitting europium (\(\hbox {Eu}^{3+}\))-doped \(\hbox {CaSrSiO}_{4}\) phosphors has been made through a templated strategy using non-ionic surfactant as template. The concentrations of \(\hbox {Eu}^{3+}\) in the host were altered and the optimized concentration to extract the maximum efficacy was analysed. The crystalline structure and morphologies of the synthesized phosphor were studied and analysed. The results show the aggregated rod-like morphology with a continuous porous network that shows the maximum intensity at 10 mol% of dopant.     

Thermally induced cation ordering in $$\hbox {ZnAl}_{2}\hbox {O}_{4}{:}\hbox {Mg}^{2+}$$ ZnAl 2 O 4 : Mg 2 + , $$\hbox {Fe}^{3+}$$ Fe 3 + for sensing thermal history through photoluminescence

Journal of Materials Science - Applicability of spinel compounds is mainly governed by cation distribution in them. In the presented study, thermally induced cation ordering is found to influence...     

Three-dimensional mixed mode I+II+III singular stress field at the front of a {\varvec{(}}\mathbf{111 }{\varvec{)}[}\bar{\mathbf{1 }}\bar{\mathbf{1 }}\mathbf 2 {\varvec{]}\times [}\mathbf 1 \bar{\mathbf{1 }}\mathbf 0 {\varvec{]}} crack weakening a diamond cubic mono-crystalline plate with crack turning and step/ridge formation

A heretofore-unavailable mixed Frobenius type series, in terms of affine-transformed x-y coordinate variables of the Eshelby–Stroh type, is introduced to develop a new eigenfunction expansion technique. This is used, in conjunction with separation of the z-variable, to derive three-dimensional mixed-mode I+II+III asymptotic displacement and stress fields in the vicinity of the front of a semi-infinite through-thickness $(111)[\bar{{1}}\bar{{1}}2]\times [1\bar{{1}}0]$ crack weakening an infinite diamond cubic mono-crystalline plate. Crack-face boundary conditions and those that are prescribed on the top and bottom (free, fixed or lubricated) surfaces of the diamond cubic mono-crystalline plate are exactly satisfied. Explicit expressions for the mixed mode I+II+III singular stresses in the vicinity of the front of the through-thickness crack, are presented. Most important mixed modes I+II+III response is elicited even though the far-field loading is only mode I or II or III or any combination thereof. Finally, atomistic modeling of cracks requires consideration of both the long range elastic interactions and the short range physico-chemical reactions, such as bond breaking. The Griffith-Irwin approach does not take the latter into account, and nano-structural details such as bond orientation must be accounted for. A new mixed-mode I+II+III crack deflection criterion elucidates the formation of steps and/or triangular ridges on the crack path. The planes of a multiply deflected crack are normal to the directions of broken bonds. Additionally, the mixed-mode (I+II+III) crack deflection and ridge formation are found to be strongly correlated with the elastic stiffness constants, ${c}^{\prime }_{14}$ and ${c}^{\prime }_{56}$ , of the diamond cubic single crystal concerned.     

Formation of $$\hbox {Mg}_{2}\hbox {C}_{3}$$ phase in N220 nanocarbon containing low carbon MgO-C composition

This paper reports a non-conventional microstructure with sequicarbide \((\hbox {Mg}_{2}\hbox {C}_{3})\) formation in N220 nanocarbon containing low carbon magnesia carbon composition having magnesium metal powder as antioxidant. 5 wt% graphite containing MgO-C refractory with and without 1 wt% N220 nanocarbon is studied and 2 wt% magnesium metal powder is used as the lone antioxidant. The compositions were mixed with powder and liquid resin binder, pressed uniaxially at 150 MPa and cured at 220\(^{\circ }\hbox {C}\). Cured samples were coked at 1000\(^{\circ }\hbox {C}\) for 2 h. Matrix of the coked samples was studied in detail for microstructural analysis phase content and formation of nail-shaped sequicarbide was found in the nanocarbon containing compositions. The in-situ sequicarbide formation has resulted in the strength of the batch.