Measurements of Microstructural, Mechanical, Electrical, and Thermal Properties of an Al–Ni Alloy

The Al–7.5 wt% Ni alloy was directionally solidified upwards with different temperature gradients, $G$ ( $0.86\,\text{ K}~{\cdot }~ \text{ mm}^{-1}$ to $4.24\,\text{ K}~{\cdot }~\text{ mm}^{-1})$ at a constant growth rate, $V$ ( $8.34\,\upmu \text{ m}~{\cdot }~\text{ s}^{-1})$ . The dependence of dendritic microstructures such as the primary dendrite arm spacing ( $\lambda _{1}$ ), the secondary dendrite arm spacing ( $\lambda _{2}$ ), the dendrite tip radius ( $R$ ), and the mushy zone depth ( $d$ ) on the temperature gradient were analyzed. The dendritic microstructures in this study were also compared with current theoretical models, and similar previous experimental results. Measurements of the microhardness (HV) and electrical resistivity ( $\rho $ ) of the directionally solidified samples were carried out. Variations of the electrical resistivity ( $\rho $ ) with temperature ( $T$ ) were also measured by using a standard dc four-point probe technique. And also, the dependence of the microhardness and electrical resistivity on the temperature gradient was analyzed. According to these results, it has been found that the values of HV and $\rho $ increase with increasing values of $G$ . But, the values of HV and $\rho $ decrease with increasing values of dendritic microstructures ( $\lambda _{1}, \lambda _{2}, R,$ and $d$ ). It has been also found that, on increasing the values of temperature, the values of $\rho $ increase. The enthalpy of fusion ( $\Delta {H}$ ) for the Al–7.5 wt%Ni alloy was determined by a differential scanning calorimeter from a heating trace during the transformation from solid to liquid.     

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.     

Influence of pH and bath composition on properties of Ni–Fe alloy films synthesized by electrodeposition

Fe?CNi films were electrodeposited on ITO glass substrates from the electrolytes with different molar ratio of Ni $^{\boldsymbol{2+}}$ /Fe $^{\boldsymbol{2+}}$ and different pH values (2 $\boldsymbol{\cdot}$ 1, 2 $\boldsymbol{\cdot}$ 9, 3 $\boldsymbol{\cdot}$ 7 and 4 $\boldsymbol{\cdot}$ 3) at 25 $\boldsymbol{^\circ}$ C. The properties of Fe?CNi alloy films depend on both Ni $^{\boldsymbol{2+}}$ and Fe $^{\boldsymbol{2+}}$ concentrations in electrolyte and pH values. The content of Ni increases from 38% to 84% as the mole ratio of NiSO $_{\boldsymbol{4}}$ /FeSO $_{\boldsymbol{4}}$ increasing from 0 $\boldsymbol{\cdot}$ 50/0 $\boldsymbol{\cdot}$ 50 to 0 $\boldsymbol{\cdot}$ 90/0 $\boldsymbol{\cdot}$ 10 in electrolyte and slightly decreases from 65% to 42% as the pH values increase from 2 $\boldsymbol{\cdot}$ 1 to 4 $\boldsymbol{\cdot}$ 3. The X-ray diffraction analysis reveals that the structures of the films strongly depend on the Ni content in the binary films. The magnetic performance of the films shows that the saturation magnetization ( $\boldsymbol{M}_{\boldsymbol{\rm s}})$ decreases from 1775 $\boldsymbol{\cdot}$ 01 emu/cm $^{\boldsymbol{3}}$ to 1501 $\boldsymbol{\cdot}$ 46 emu/cm $^{\boldsymbol{3}}$ with the pH value increasing from 2 $\boldsymbol{\cdot}$ 1 to 4 $\boldsymbol{\cdot}$ 3 and the saturation magnetization ( $\boldsymbol{M}_{\boldsymbol{\rm s}})$ and coercivity ( $\boldsymbol{H}_{\boldsymbol{\rm c}})$ move up from 1150 $\boldsymbol{\cdot}$ 44 emu/cm $^{\boldsymbol{3}}$ and 58 $\boldsymbol{\cdot}$ 86 Oe to 2498 $\boldsymbol{\cdot}$ 88 emu/cm $^{\boldsymbol{3}}$ and 93 $\boldsymbol{\cdot}$ 12 Oe with the increase of Ni $^{\boldsymbol{2+}}$ concentration in the electrolyte, respectively.     

Linear complexity and correlation of a class of binary cyclotomic sequences

Let $p_1,p_2,\ldots ,p_n$ be distinct odd primes and let $e_1,e_2,\ldots ,e_n$ be positive integers. Based on cyclotomic classes proposed by Ding and Helleseth (Finite Fields Appl 4:140–166, 1998), a binary cyclotomic sequence of period $p_1^{e_{1}}p_{2}^{e_{2}}\ldots p_{n}^{e_n}$ is defined and denoted by $\underline{s_\Upsilon }$ . The linear complexity of $\underline{s_\Upsilon }$ is determined and is proved to be greater than or equal to $(p_1^{e_{1}}p_{2}^{e_{2}}\ldots p_{n}^{e_n}-1)/2$ . The autocorrelation function of $\underline{s_\Upsilon }$ is explicitly computed. Let $\ell \in \{1,2,\ldots ,n\}$ . We also explicitly compute the crosscorrelation function of $\underline{s_\Upsilon }$ and the Legendre sequence $\underline{L_{p_\ell }}$ with respect to $p_\ell $ . It is shown that $\underline{s_\Upsilon }$ and $\underline{L_{p_\ell }}$ have two-level or three-level crosscorrelation, and all their two-level crosscorrelation functions are determined.     

Hypersensitive Transition of Nd(III) Complexes in Liquids Detected by Pulsed-Laser-Induced Photoacoustic Spectroscopy

Laser-induced photoacoustic (PA) spectroscopy for the spectral measurements of extremely weak absorption such as a forbidden transition of lanthanide ions in liquids has been established. In spectroscopy, a pulsed Nd:YAG laser connected with a MOPO series optical parametric oscillator which emits a broad spectrum covering UV and visible regions is used as the excitation source, and the induced PA signals are detected by an optimized PA piezoelectric transducer. The absorption spectra of trivalent lanthanide ions ( $\text{ Pr}^{3+}, \text{ Ho}^{3+}$ , and $\text{ Nd}^{3+})$ in aqueous solutions have been obtained by the detection system with a detection-limit absorbance of $1.3\times 10^{-5}\,\text{ cm}^{-1}$ at room temperature. In addition, the effects of different binding environments on the band shapes and oscillator strengths of the hypersensitive transitions of $\text{ Nd}^{3+}$ ions, i.e., $\text{ Nd}(\text{ CH}_{3}\text{ COO})_{3}$ $\cdot $ $\text{ H}_{2}\text{ O}$ dissolved in $0.1\,{\text{ mol}} \cdot \text{ l}^{-1}$ acetic acid and $\text{ Nd(3-butanedione)}_{3}{\cdot } 2\text{ H}_{2} \text{ O}$ dissolved in triglycol compared with $\text{ NdCl}_{3}$ in $0.1\,{\text{ mol}}\cdot \text{ l}^{-1}$ hydrochloric acid, are observed. The results show that the chemical environment around the lanthanide ions has great impact on 4f–4f transitions, which is rationalized as the impact in terms of ligand (or solvent) special structures and coordination properties.     

Evidence for One-Gap Superconductivity in Mg(B_{1-x}C_{x})_{2} Single Crystals at x=0.132 by Point-Contact Spectroscopy

We report the results of directional point-contact measurements in Mg(B $_{1-x}$ C $_{x})_{2}$ single crystals. The amplitudes of the gaps, $\Delta_{\pi}$ and $\Delta_{\sigma}$ , were determined for each C content by fitting the experimental low-temperature normalized conductance curves of our “soft” point contacts with the BTK model generalized to the two-band case. We found that, on increasing the carbon content, $\Delta_{\sigma}$ decreases almost linearly with $T_{c}$ and $\Delta_{\pi}$ slightly increases until, at $x=0.132$ (where $T_{c}=19$ K), they assume the same value $\Delta =3.2 \pm 0.9$ meV. This result is confirmed by the temperature and magnetic-field dependence of the conductance curves at this C content, which do not show any evidence of two distinct gap values. In particular, the Δ versus T curve follows very well a standard BCS curve, with a gap ratio $2\Delta /k_{B} T_{c}=3.9$ . These experimental findings are compared to the theoretical predictions of the two-band model in the Eliashberg formulation.     

Full-Potential Calculation of Structural, Electronic, and Thermodynamic Properties of Fluoroperovskite \text{ CsMF}_{3} (M?=?Be and Mg)

The structural and electronic properties of the cubic fluoroperoveskite $\text{ CsBeF}_{3}$ and $\text{ CsMgF}_{3}$ have been investigated using the full-potential-linearized augmented plane wave method within the density functional theory. The exchange-correlation potential was treated with the local density approximation and the generalized gradient approximation. The calculations of the electronic band structures show that $\text{ CsBeF}_{3 }$ has an indirect bandgap, whereas $\text{ CsMgF}_{3}$ has a direct bandgap. Through the quasi-harmonic Debye model, in which the phononic effects are considered, the effect of pressure $P$ and temperature $T$ on the lattice parameter, bulk modulus, thermal expansion coefficient, Debye temperature, and the heat capacity for $\text{ CsBeF}_{3}$ and $\text{ CsMgF}_{3}$ compounds are investigated for the first time.     

Study of Glass-Transition Kinetics of Pb-Modified Se_{80}In_{20} System by Using Non-isothermal Differential Scanning Calorimetry

Glass-transition kinetics of $\mathrm{Se}_{80}\mathrm{In}_{20-\mathrm{x}}\mathrm{Pb}_{\mathrm{x}}$ ( $x =$ 0, 5, 10, and 15) chalcogenide glasses have been carried out at different heating rates by using differential scanning calorimeter (DSC) under the non-isothermal condition. The glass-transition temperature $T_{\mathrm{g}}$ and peak glass-transition temperature $T_{\mathrm{pg}}$ have been determined from DSC thermograms. The reduced glass temperature $T_{\mathrm{rg}}$ , total relaxation time $\tau _{T_{g}}$ thermal-stability parameters $K^{l}$ and $S$ , the activation energy of glass transition $E_{\mathrm{g}}$ , the fragility index $F_{\mathrm{i}}$ , and the average coordination number $\langle Z\rangle $ have been calculated on the basis of the experimental results. The temperature differences $(T_{\mathrm{c}}-T_{\mathrm{g}}), K_{\mathrm{gl}}, K^{l}, S$ , and $E_{\mathrm{g}}$ are found to be maxima for $\mathrm{Se}_{80}\mathrm{In}_{10}\mathrm{Pb}_{10}$ glass. This indicates that $\mathrm{Se}_{80}\mathrm{In}_{10}\mathrm{Pb}_{10}$ glass has the highest thermal stability and glass-forming ability in the investigated compositional range. These results could be explained on the basis of modification of the chemical bond formation due to incorporation of Pb in the Se–In glassy matrix.     

Specific Heat of K_{0.71}Na_{0.29}Fe_2As_2 at Very Low Temperatures

A commercially available calorimeter has been used to investigate the specific heat of a high-quality K $_{0.71}$ Na $_{0.29}$ Fe $_2$ As $_2$ single crystal. The addenda heat capacity of the calorimeter is determined in the temperature range $0.02 \, \mathrm{K} \le T \le 0.54 \, \mathrm{K}$ . The data of the K $_{0.71}$ Na $_{0.29}$ Fe $_2$ As $_2$ crystal imply the presence of a large $T^2$ contribution to the specific heat which gives evidence of $d$ -wave order parameter symmetry in the superconducting state. To improve the measurements, a novel design for a calorimeter with a paramagnetic temperature sensor is presented. It promises a temperature resolution of $\Delta T \approx 0.1 \, \mathrm{\mu K}$ and an addenda heat capacity less than $200 \, \mathrm{pJ/K}$ at $ T < 100 \, \mathrm{mK}$ .     

Reparametrizing swung surfaces over the reals

Let $\mathbb {K}\subseteq \mathbb {R}$ be a computable subfield of the real numbers (for instance, $\mathbb {Q}$ ). We present an algorithm to decide whether a given parametrization of a rational swung surface, with coefficients in $\mathbb {K}(\mathtt {i})$ , can be reparametrized over a real (i.e., embedded in $\mathbb {R}$ ) finite field extension of $\mathbb {K}$ . Swung surfaces include, in particular, surfaces of revolution.     

An analytical approach and experimental confirmation of dislocation–twin boundary interactions in titanium

The morphology of $ \{ 10\overline{1} 2\} \left\langle {\overline{1} 011} \right\rangle $ { 10 1 ¯ 2 } 〈 1 ¯ 011 〉 deformation twins formed in commercial purity titanium during an initial pass of equal-channel angular pressing was studied by transmission electron microscopy (TEM). The corresponding diffraction patterns show a symmetry line splitting of $ (10\overline{1} 2) $ ( 10 1 ¯ 2 ) twin boundaries (TB) which is related to the presence of interfacial defects. A simple modeling for the interaction between non-screw a-slip lattice dislocations (Burgers vector b =  $ \frac{1}{3}[\overline{1} \overline{1} 20] $ 1 3 [ 1 ¯ 1 ¯ 20 ] ) and the $ (10\overline{1} 2) $ ( 10 1 ¯ 2 ) twin plane is used according to crystallographic geometry and vector conservation. The results show that dislocation dissociation into different Frank partial dislocations on the interfacial plane is more favorable than its transmission to the other side of the interface. The formation of the Frank partials at the TB can produce a small change in the TB misorientation angle and this is consistent with the symmetry line splitting of the $ (10\overline{1} 2) $ ( 10 1 ¯ 2 ) twin boundaries observed by TEM.     

Exact Analysis of a One-Dimensional Weakly Repulsive Bose-Fermi Mixture

We study a one-dimensional system of Bose–Fermi mixture with repulsive $\delta $ -function interactions using the nested Bethe ansatz method. This system is integrable when the masses of bonsons and fermions are equal and the interactions between Bose–Bose and Bose–Fermi particles are equal. By use of the power series expansion method, the Surtherland integral equation, which describes the ground state properties, is solved analytically in the weak coupling regime. Physical quantities such as the ground state energy, the sound velocity, and the chemical potential are explicitly expressed in terms of a dimensionless interaction parameter $\gamma =c/D$ and boson fraction $\alpha =N_{b}/N$ , where $c$ is the interaction strength, $D$ is the number density, $N_{b}$ is the number of bosons, and N is the total number of particles.     

An extension of the (strong) primitive normal basis theorem

An extension of the primitive normal basis theorem and its strong version is proved. Namely, we show that for nearly all \(A = {\small \left( \begin{array}{cc} a&{}b \\ c&{}d \end{array} \right) } \in \mathrm{GL}_2(\mathbb {F}_{q})\) , there exists some \(x\in \mathbb {F}_{q^m}\) such that both \(x\) and \((-dx+b)/(cx-a)\) are simultaneously primitive elements of \(\mathbb {F}_{q^m}\) and produce a normal basis of \(\mathbb {F}_{q^m}\) over \(\mathbb {F}_q\) , granted that \(q\) and \(m\) are large enough.     

1-generator quasi-cyclic codes over finite chain rings

Let R be an arbitrary commutative finite chain ring with $1\ne 0$ . 1-generator quasi-cyclic (QC) codes over R are considered in this paper. Let $\gamma $ be a fixed generator of the maximal ideal of R, $F=R/\langle \gamma \rangle $ and $|F|=q$ . For any positive integers m, n satisfying $\mathrm{gcd}(q,n)=1$ , let $\mathcal{R}_n=R[x]/\langle x^n-1\rangle $ . Then 1-generator QC codes over R of length mn and index m can be regarded as 1-generator $\mathcal{R}_n$ -submodules of the module $\mathcal{R}_n^m$ . First, we consider the parity check polynomial of a 1-generator QC code and the properties of the code determined by the parity check polynomial. Then we give the enumeration of 1-generator QC codes with a fixed parity check polynomial in standard form over R. Finally, under the condition that $\mathrm{gcd}(|q|_n,m)=1$ , where $|q|_n$ denotes the order of q modulo n, we describe an algorithm to list all distinct 1-generator quasi-cyclic codes with a fixed parity check polynomial in standard form over R of length mn and index m.     

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.     

Influence of Magnetic Field and LO Phonon Effects on the Spin Polarization State Energy of Strong-Coupling Bipolaron in a Quantum Dot

On the basis of Lee–Low–Pines unitary transformation, the influence of magnetic field and LO phonon effects on the energy of spin polarization states of strong-coupling bipolarons in a quantum dot (QD) is studied by using the variational method of Pekar type. The variations of the ground state energy $E_0$ and the first excited state the energy $E_1$ of bipolarons in a two-dimensional QD with the confinement strength of QDs $\omega _0$ , dielectric constant ratio $\eta $ , electron–phonon coupling strength $\alpha $ and cyclotron resonance frequency of the magnetic field $\omega _{c}$ are derived when the influence of the spin and external magnetic field is taken into account. The results show that both energies of the ground and first excited states ( $E_0$ and $E_1)$ consist of four parts: the single-particle energy of electrons $E_\mathrm{e}$ , Coulomb interaction energy between two electrons $E_\mathrm{c}$ , interaction energy between the electron spin and magnetic field $E_\mathrm{S}$ and interaction energy between the electron and phonon $E_{\mathrm{e-ph}}$ ; the energy level of the first excited state $E_1$ splits into two lines as $E_1^{(1+1)}$ and $E_1^{(1-1)}$ due to the interaction between the single-particle “orbital” motion and magnetic field, and each energy level of the ground and first excited states splits into three “fine structures” caused by the interaction between the electron spin and magnetic field; the value of $E_{\mathrm{e-ph}}$ is always less than zero and its absolute value increases with increasing $\omega _0$ , $\alpha $ and $\omega _c$ ; the effect of the interaction between the electron and phonon is favorable to forming the binding bipolaron, but the existence of the confinement potential and Coulomb repulsive energy between electrons goes against that; the bipolaron with energy $E_1^{(1-1)}$ is easier and more stable in the binding state than that with $E_1^{(1+1)}$ .     

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.     

The theoretical calculation of the flow rate of granular matter from an inclined orifice

A theoretical calculation method for the flow rate of granular matter from an inclined orifice is discussed in this article and for the inclination angles at $\theta \le 90^{\circ }$ , a theoretical relation between the flow rate $Q$ and inclination angle $\theta $ is derived; and for the inclination angles at $\theta >90^{\circ }$ , a semi-theoretical relation is established. From the relations, we found that the ratio of the flow rate from a vertical orifice, $Q_{90}$ , to that from a horizontal orifice, $Q_{0}$ , is equal to the sine of the angle of repose $\theta _{\mathrm{r}}$ , i.e., $Q_{90} /Q_0 =\sin \theta _{\mathrm{r}} $ . The theoretical relations are tested by means of the experimental data and the results indicate that the theoretical calculating values are in good agreement with the experimental data over a wide range of the inclination angles. Therefore, the formula proposed in this article can be used for the theoretical calculation of the flow rate of granular matter from an inclined orifice. The relation $Q_{90} /Q_0 =\sin \theta _{\mathrm{r}}$ may be used as an alternative approach to obtaining $\theta _{\mathrm{r}}$ : measuring $Q_{90}$ and $Q_{0}$ , and then calculating $\theta _{\mathrm{r}} $ by using formula $\theta _{\mathrm{r}} =\arcsin (Q_{90} /Q_0 )$ .     

Classification of Novikov algebras

We describe a method for classifying the Novikov algebras with a given associated Lie algebra. Subsequently we give the classification of the Novikov algebras of dimension 3 over $\mathbb{R }$ and $\mathbb{C }$ , as well as the classification of the 4-dimensional Novikov algebras over $\mathbb{C }$ whose associated Lie algebra is nilpotent. In particular this includes a list of all 4-dimensional commutative associative algebras over $\mathbb{C }$ .