The Elastic Properties, Generalized Stacking Fault Energy and Dissociated Dislocations in MgB2 Under Different Pressure

The $\langle11\overline{2}0\rangle$ perfect dislocation in MgB₂ is suggested to dissociate into two partial dislocations in an energy favorable way $\langle11\overline{2}0\rangle\rightarrow\frac{1}{2}\langle11\overline{2}0\rangle +\mathrm{SF}+\frac{1}{2}\langle11\overline{2}0\rangle$ . This dissociation style is a correction of the previous dissociation $\langle1000\rangle\rightarrow\frac{1}{3}\langle1\overline{1}00\rangle+\mathrm{SF}+\frac{1}{3}\langle2100\rangle$ proposed by Zhu et al. to model the partial dislocations and stacking fault observed by transmission electron microscopy. The latter dissociation results in a maximal stacking fault energy rather than a minimal one according to the generalized stacking fault energy calculated from first-principles methods. Furthermore, the elastic constants and anisotropy of MgB₂ under different pressure are investigated. The core structures and mobilities of the $\langle11\overline{2}0\rangle$ dissociated dislocations are studied within the modified Peierls–Nabarro (P–N) dislocation theory. The variational method is used to solve the modified P–N dislocation equation and the Peierls stress is also determined under different pressure. High pressure effects on elastic anisotropy, core structure and Peierls stress are also presented.     

Dislocation structure at a \{ {\overline{1} 2\overline{1} 0} \}/ {\langle} 10\overline{1} 0 {\rangle} low-angle tilt grain boundary in LiNbO3

LiNbO₃ is a ferroelectric material with a rhombohedral R3c structure at room temperature. A LiNbO₃ bicrystal with a $ \{ {\overline{1} 2\overline{1} 0} \}/ {\langle}10\overline{1} 0{\rangle}$ 1° low-angle tilt grain boundary was successfully fabricated by diffusion bonding. The resultant boundary was then investigated using high-resolution TEM. The boundary composed a periodic array of dislocations with $ b = { 1}/ 3{\langle} \overline{1} 2\overline{1} 0{\rangle} $ . They dissociated into two partial dislocations by climb. A crystallographic consideration suggests that the Burgers vectors of the partial dislocations should be $ 1/ 3{\langle}01\overline{1} 0{\rangle} $ and $ 1/ 3{\langle}\overline{1} 100{\rangle} $ , and a stacking fault on $ \{ {\overline{1} 2\overline{1} 0} \} $ is formed between the two partial dislocations. From the separation distance of a partial dislocation pair, a stacking fault energy on $ \{ {\overline{1} 2\overline{1} 0} \} $ was estimated to be 0.25?J/m² on the basis of isotropic elasticity theory.     

Effect of Previous Milling of Precursors on Magnetoelectric Effect in Multiferroic {\mathrm{Bi}_{5}\mathrm{Ti}_{3}\mathrm{FeO}_{15}} Ceramic

$\mathrm{Bi}_{5}\mathrm{Ti}_{3}\mathrm{FeO}_{15}$ Bi 5 Ti 3 FeO 15 magnetoelectric (ME) ceramics have been synthesized and investigated. The ME effect can be described as an induced electric polarization under an external magnetic field or an induced magnetization under an external electric field. The materials in the ME effect are called ME materials, and they are considered to be a kind of new promising materials for sensors, processors, actuators, and memory systems. Multiferroics, the materials in which both ferromagnetism and ferroelectricity can coexist, are the prospective candidates which can potentially host the gigantic ME effect. $\mathrm{Bi}_{5}\mathrm{Ti}_{3}\mathrm{FeO}_{15}$ Bi 5 Ti 3 FeO 15 , an Aurivillius compound, was synthesized by sintering a mixture of $\mathrm{Bi}_{2}\mathrm{O}_{3}, \mathrm{Fe}_{2}\mathrm{O}_{3}$ Bi 2 O 3 , Fe 2 O 3 , and $\mathrm{TiO}_{2}$ TiO 2 oxides. The precursor materials were prepared in a high-energy attritorial mill for (1, 5, and 10) h. The orthorhombic $\mathrm{Bi}_{5}\mathrm{Ti}_{3}\mathrm{FeO}_{15}$ Bi 5 Ti 3 FeO 15 ceramics were obtained by a solid-state reaction process at 1313 K. The ME voltage coefficient ( $\alpha _\mathrm{ME}$ α ME ) was measured using the dynamic lock-in method. The highest ME voltage coefficient ( $\alpha _\mathrm{ME} = 8.28\,\text{ mV }{\cdot }\text{ cm }^{-1}{\cdot }\text{ Oe }^{-1})$ α ME = 8.28 mV · cm ? 1 · Oe ? 1 ) is obtained for the sample milled for 1 h at $H_\mathrm{DC }= 4$ H DC = 4  Oe (1 Oe = 79.58  $\text{ A }{\cdot }\text{ m }^{-1})$ A · m ? 1 ) .     

Molecular beam epitaxy of semipolar AlN(11\bar{2}2) and GaN(11\bar{2}2) on m-sapphire

We report on the plasma-assisted molecular-beam epitaxy of semipolar $\hbox{AlN}(11\bar{2}2)$ and GaN( $11\bar{2}2$ ) films on $(1\bar{1}00)$ m-plane sapphire. AlN deposited on m-sapphire settles into two main crystalline orientation domains, $\hbox{AlN}(11\bar{2}2)$ and $\hbox{AlN}(10\bar{1}0),$ whose ratio depends on the III/V ratio. Growth under moderate nitrogen-rich conditions enables to isolate the $(11\bar{2}2)$ orientation. The in-plane epitaxial relationships of $\hbox{AlN}(11\bar{2}2)$ on m-plane sapphire are $[11\bar{2}\bar{3}]_{\rm AlN} \vert \vert [0001]_{\rm sapphire}$ and $[1\bar{1}00]_{\rm AlN} \vert \vert [11\bar{2}0]_{\rm sapphire}.$ GaN deposited directly on m-sapphire results in ( $11\bar{2}2$ )-oriented layers with ( $10\bar{1}\bar{3}$ )-oriented inclusions. A ～100 nm-thick AlN( $11\bar{2}2$ ) buffer imposes the ( $11\bar{2}2$ )-orientation for the GaN layer grown on top. By studying the Ga-desorption on GaN( $11\bar{2}2$ ), we conclude that these optimal growth conditions corresponds to a Ga excess of one monolayer on the GaN( $11\bar{2}2$ ) surface.     

Indentation-induced deformation mechanisms in laser-processed directionally solidified WC–W<Subscript>2</Subscript>C eutectoids

Indentation-induced surface and subsurface deformation mechanisms in directionally solidified WC–W₂C eutectoids are investigated. The microstructures of the WC–W₂C composites consist of primary WC regions, W₂C-rich regions, and lamellar-type eutectoid regions, which form during the sequential phase transformations during laser processing. Indentation-induced surface crack profiles indicate little propensity for debonding at the WC–W₂C eutectoid interfaces, although some interactions with larger-scale microstructural features are observed. In the subsurface indentation regions, dislocation networks predominantly composed of partial dislocation pairs having Burgers vectors \( b = \frac{1}{6}\left\langle {2\bar{1}\bar{1}3} \right\rangle \) are observed in the primary WC regions, whereas shear banding and grain refinement are commonly observed in the micrometer-scale W₂C-rich regions. Deformation in the sub-micrometer eutectoid regions is distinct, with the dislocation activity primarily limited to the WC phase, with Burgers vectors of \( b = \frac{1}{3}\left\langle {1\bar{2}13} \right\rangle \) that terminate at the interfaces.     

Further crosscorrelation properties of sequences with the decimation factor {d=\frac{p^n+1}{p+1}-\frac{p^n-1}{2}}

For an odd integer n ≥ 3, an odd prime p ≡ 3(mod4) and ${d=\frac{p^n+1}{p+1}-\frac{p^n-1}{2}}$ , the value distribution of the exponential sum ${\sum\limits_{x\in \mathbb{F}_{p^n}^{\,*}}\omega^{Tr^n_1(x-\gamma x^{d})}\,(\gamma\in \mathbb{F}_{p^n}^{*})}$ is completely determined in this paper, where ω is a primitive complex p-th root of unity. This improves the results of Müller (1999) and Hu et al. (2001) about the crosscorrelation of sequences with the decimation factor d.     

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.     

The Ideal Strengths of Superconducting MgCNi<Subscript>3</Subscript> and CdCNi<Subscript>3</Subscript>

The stress-strain curves under tensile deformation in the 〈100〉, 〈110〉, and 〈111〉 directions and under shear deformation in the (001)〈110〉, \((110)\langle \overline {1}10\rangle \), \((111)\langle 1\overline {1}0\rangle \), and \((111)\langle 11\overline {2}\rangle \) slip systems have been systematically calculated by first-principles method to study the ideal strengths of superconducting MgCNi₃ and CdCNi₃. The ideal strengths in the three tensile directions are found to be reduced in the order of 〈100〉 → 〈110〉 → 〈111〉 and those for the four shear slip systems in the order of \((110)\langle \overline {1}10\rangle \rightarrow (111)\langle 11\overline {2}\rangle \rightarrow (111)\langle 1\overline {1}0\rangle \rightarrow (001)\langle 110\rangle \) for both superconductors. Their lowest ideal tensile strengths are found to be larger than the corresponding highest ideal shear strengths, which could explain why both superconductors have the ductility. The obtained lattice constants and elastic properties coincide well with the the available experimental and theoretical values.     

Dissociation reaction of the 1/3$$ \left\langle {\bar{1}101} \right\rangle $$ edge dislocation in α-Al2O3

It has been reported that dislocations with 1/3\( \left\langle {\bar{1}101} \right\rangle \) edge component of the Burgers vector are formed in {1\( \bar{1} \)04}/\( \left\langle {11\bar{2}0} \right\rangle \) low-angle grain boundaries of alumina (α-Al₂O₃). These dislocations dissociate into two partial dislocations with a stacking fault on the (0001) plane (Tochigi et al. in J Mater Sci 46:4428–4433, 2011). However, the dissociation reaction of these dislocations has not been determined so far. In this study, the structures of the dissociated dislocations and the (0001) stacking fault were investigated by transmission electron microscopy and theoretical calculations. It was revealed that the dissociated dislocations were generated from the 1/3\( \left\langle {\bar{1}101} \right\rangle \) perfect edge dislocation by the reaction of 1/3\( \left\langle {\bar{1}101} \right\rangle \) → 1/18\( \left\langle {\bar{4}223} \right\rangle \) + 1/18\( \left\langle {\bar{2}4\bar{2}3} \right\rangle \). Furthermore, electron energy loss spectroscopy analysis was performed to examine the atomic/electronic structure of the (0001) stacking fault. In the observed spectra, a chemical shift and intensity decrease were found at the oxygen K-edge. Theoretical spectrum analysis using first-principles calculations revealed that the characteristic features of the spectra are originated from the local atomic configurations of the (0001) stacking fault.     

Temperature Dependence of \sqrt{2} \times \sqrt{2} Phase in Superconducting K0.8Fe1.6Se2 Single Crystal

We report the structural phase transition properties of the newly discovered K_0.8Fe_1.6Se₂ superconductor (T _c =31.8 K) using synchrotron single-crystal X-ray diffraction. The basic structure of the sample at room temperature is found to be tetragonal ThCr₂Si₂-type, modulated by a vacancy ordering induced superlattice structure together with a coexisting minority phase having a $\sqrt{2} \times \sqrt{2}$ ordering. At 520 K, the reflections corresponding to the $\sqrt{2} \times \sqrt{2}$ phase merge with the parent tetragonal phase. The superlattice peaks corresponding to the vacancy ordering disappear at 580 K, indicating an order-disorder phase transition at this temperature.     

Dislocations in β-alumina electrolyte material

β-alumina obtained from a number of sources and manufactured by different techniques has been examined in the electron microscope. Dislocations have been observed on the basal plane and the Burgers vector determined as \(b = a/3< 11\bar 20 > \) . The presence of this type of dislocation has been explained on the basis of the crystallographic structure ofβ-alumina. It is also predicted that the unit dislocation dissociates into two and four partials according to the energetically favourable reactions: $$\begin{gathered} \frac{a}{3}< 11\bar 20 > \to \frac{a}{6}< 11\bar 20 > + \frac{a}{6}< 11\bar 20 > \hfill \\ \frac{a}{3}< 11\bar 20 > \to \frac{a}{6}< 1\bar 100 > + \frac{a}{6}< 0\bar 110 > + \frac{a}{6}< 0\bar 110 > + \frac{a}{6}< 0\bar 110 > \hfill \\ \end{gathered} $$ . Experimental evidence has been obtained which shows the presence of dislocations separated into two and four partials inβ-alumina. Microscopic deformation has been shown to occur in thin crystals ofβ-alumina in the electron microscope, by the passage of large numbers of dislocations along basal slip planes.     

Cryptanalysis of a key exchange protocol based on the endomorphisms ring End{(\mathbb{Z}_{p} \times \mathbb{Z}_{p^2})}

Climent et?al. (Appl Algebra Eng Commun Comput 22:91?C108, 2011) identified the elements of the endomorphisms ring End ${(\mathbb{Z}_p \times \mathbb{Z}_{p^2})}$ with elements in a set, E _p , of matrices of size 2?× 2, whose elements in the first row belong to ${\mathbb{Z}_{p}}$ and the elements in the second row belong to ${\mathbb{Z}_{p^2}}$ . By taking advantage of matrix arithmetic, they proposed a key exchange protocol using polynomial functions over E _p defined by polynomials in ${\mathbb{Z}[X]}$ . In this note, we show that this protocol is insecure; it can be broken by solving a set of 10 consistent homogeneous linear equations in 8 unknowns over ${\mathbb{Z}_{p^2}}$ .     

On quasi-cyclic codes over {\mathbb{Z}_q}

Quasi-cyclic (QC) codes are a remarkable generalization of cyclic codes. Many QC codes have been shown to be best for their parameters. In this paper, some structural properties of QC codes over the prime power integer residue ring ${\mathbb{Z}_q}$ are considered. An l-QC code of length lm over ${\mathbb{Z}_q}$ is viewed both as in the conventional row circulant form and also as a ${\frac{\mathbb{Z}_q[x]}{\langle x^m-1 \rangle}}$ -submodule of ${\frac{GR(q,l)[x]}{\langle x^m-1 \rangle}}$ , where GR(q, l) is the Galois extension ring of degree l over ${\mathbb{Z}_q}$ . A necessary and sufficient condition for cyclic codes over Galois rings to be free is obtained and a BCH type bound for them is also given. A sufficient condition for 1-generator QC codes to be ${\mathbb{Z}_q}$ -free is given and a formula to evaluate their ranks is derived. Some distance bounds for 1-generator QC codes are also discussed. The duals of QC codes over ${\mathbb{Z}_q}$ are also briefly discussed.     

Effect of Pressure on Elastic Constants,Generalized Stacking Fault Energy,and Dislocation Properties in Antiperovskite-Type Ni-Rich Nitrides ZnNNi3 and CdNNi3

The elastic properties and generalized stacking fault energy curves of antiperovskite-type Ni-rich nitrides MNNi₃ (M = Zn, Cd) under different pressure have been obtained from the first-principles calculations. By using the variational method, the core width and Peierls stresses of \(\frac {1}{2}\langle 110\rangle \{110\}\) edge dislocation and screw dislocation in ZnNNi₃ and CdNNi₃ within the improved Peierls-Nabarro (P-N) model in which the lattice discrete effect is taken into account have been investigated. Whatever the material or the pressure range, the Peierls stress of edge dislocation is smaller than that of screw dislocation. This also demonstrates that the edge dislocation is considered to be the dominant factor in determining the plastic behavior of MNNi₃ (M = Zn, Cd) in the pressure range of 0–30 GPa.     

<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.     

\text{ CO}_{2} Laser-Based Pulsed Photoacoustic Ammonia Detection

Detecting ammonia traces is relevant in health, manufacturing, and security areas, among others. As ammonia presents a strong absorption band (the $\nu _{2}$ mode) around 10  $\upmu $ m, some of the physical properties which may influence its detection by means of pulsed photoacoustic (PA) spectroscopy with a TEA $\text{ CO}_{2}$ laser have been studied. The characteristics of the ammonia molecule and the laser intensity may result in a nonlinear dependence of the PA signal amplitude on the laser fluence. Ammonia absorption can be described as a simple two-level system with power broadening. As $\text{ NH}_{3}$ is a polar molecule, it strongly undergoes adsorption phenomena in contact with different surfaces. Therefore, physical adsorption–desorption at the cell’s wall is studied. A theoretical model, based on Langmuir’s assumptions, fits well to the experimental results with stainless steel. Related to these studies, measurements led to the conclusion that, at the used fluenced values, dissociation by multiphotonic absorption at the 10P(32) laser line may be discarded. A calibration of the system was performed, and a detection limit around 190 ppb (at 224 $\text{ mJ}\cdot \text{ cm}^{-2}$ ) was achieved.     

Application of Non-Isothermal Thermogravimetric Method to Interpret the Decomposition Kinetics of \hbox {NaNO}_{3}, \hbox {KNO}_{3}, and \hbox {KClO}_{4}

The non-isothermal thermogravimetric method was used to study the thermal decomposition of \(\hbox {KClO}_{4}, \hbox {KNO}_{3}\) , and \(\hbox {NaNO}_{3}\) at heating rates of (5, 10, 15, and 20)  \(\hbox {K}\cdot \hbox {min}^{-1}\) . The activation energy of thermal decomposition reactions was computed by isoconversional methods of Ozawa–Flynn–Wall, Kissinger–Akahiro–Sunose, and Friedman equations. Also, the kinetic triplet of the thermal decomposition of salts was determined by the model-fitting method of the modified Coats–Redfern equation. The activation energies of \(\hbox {KClO}_{4}, \hbox {KNO}_{3}\) , and \(\hbox {NaNO}_{3}\) of (293 to 307, 160 to 209, and 192 to 245)  \(\hbox {kJ}\cdot \hbox {mol}^{-1}\) , respectively, are obtained by non–isothermal isoconversional methods. The modified Coats and Redfern method showed that the most probable mechanism functions \(g(\alpha )\) of \([-\hbox {ln}(1 - \alpha )]^{1/3}\) (model A3: Arami–Erofeev equation) and \((1 - \alpha )^{-1}- 1\) (model F2: second order) can be used to predict the decomposition mechanisms of \(\hbox {KClO}_{4}\) , \(\hbox {KNO}_{3}\) , and \(\hbox {NaNO}_{3}\) , respectively.     

Hyperfine Fields and Magnetic Structure in the B Phase of CeCoIn5

We re-analyze Nuclear Magnetic Resonance (NMR) spectra observed at low temperatures and high magnetic fields in the field-induced B phase of CeCoIn₅. The NMR spectra are consistent with incommensurate antiferromagnetic order of the Ce magnetic moments. However, we find that the spectra of the In(2) sites depend critically on the direction of the ordered moments, the ordering wavevector and the symmetry of the hyperfine coupling to the Ce spins. Assuming isotropic hyperfine coupling, the NMR spectra observed for H ∥[100] are consistent with magnetic order with wavevector $\mathbf{Q}=\pi(\frac{1+\delta}{a},\frac{1}{a},\frac{1}{c})$ and Ce moments ordered antiferromagnetically along the [100] direction in real space. If the hyperfine coupling has dipolar symmetry, then the NMR spectra require Ce moments along the [001] direction. The dipolar scenario is also consistent with recent neutron scattering measurements that find an ordered moment of 0.15μ _B along [001] and $\mathbf{Q_{n}}=\pi(\frac{1+\delta}{a},\frac{1+\delta}{a},\frac{1}{c})$ with incommensuration δ=0.12 for field $\mathbf{H}\parallel[1\bar{1}0]$ . Using these parameters, we find that a hyperfine field with dipolar contribution is consistent with findings from both experiments. We speculate that the B phase of CeCoIn₅ represents an intrinsic phase of modulated superconductivity and antiferromagnetism that can only emerge in a highly clean system.     

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.     

Collisional rates for the inelastic Maxwell model: application to the divergence of anisotropic high-order velocity moments in the homogeneous cooling state

The collisional rates associated with the isotropic velocity moments ${\langle V^{2r}\rangle}$ and the anisotropic moments ${\langle V^{2r}V_i\rangle}$ and ${\langle V^{2r}(V_iV_j-d^{-1}V^2\delta_{ij})\rangle}$ are exactly derived in the case of the inelastic Maxwell model as functions of the exponent r, the coefficient of restitution ??, and the dimensionality d. The results are applied to the evolution of the moments in the homogeneous free cooling state. It is found that, at a given value of ??, not only the isotropic moments of a degree higher than a certain value diverge but also the anisotropic moments do. This implies that, while the scaled distribution function has been proven in the literature to converge to the isotropic self-similar solution in well-defined mathematical terms, nonzero initial anisotropic moments do not decay with time. On the other hand, our results show that the ratio between an anisotropic moment and the isotropic moment of the same degree tends to zero.