Nonlinear correction to Darcy’s law for channels with wavy walls

For low Reynolds numbers ${\mathcal{R}}$ , the flow of a viscous fluid through a channel is described by the well-known Darcy’s law which corresponds to a linear relation between the pressure gradient ${\overline{\nabla p}}$ and the average velocity ${\overline{u}}$ . When the channel is not straight and when the Reynolds number is not negligible, additional terms appear in this relation. Some previous authors investigated the first three coefficients in the expansion of ${|\overline{\nabla p}|}$ in the powers of ${\overline{u}}$ and they showed that the coefficient of ${\overline{u}^2}$ vanishes for moderate ${\mathcal{R}}$ . Other authors demonstrated that this coefficient can be non-zero. This question is addressed and solved. It is demonstrated that both cases occur; Forchheimer’s law has a cubic correction for small ${\mathcal{R}}$ and a quadratic one for large ${\mathcal{R}}$ . Two analytical–numerical algorithms are constructed to prove this property. These algorithms are applied to the Navier–Stokes equations in three-dimensional channels enclosed by two wavy walls whose amplitude is proportional to ${b{\varepsilon}}$ , where 2b is the mean clearance of the channels and ${\varepsilon}$ is a small dimensionless parameter. The first algorithm is applied for small ${\mathcal{R}}$ by representing the velocity and the pressure in terms of a double Taylor series in ${\mathcal{R}}$ and ${\varepsilon}$ . The accuracy ${O(\mathcal{R}^2)}$ and ${O(\varepsilon^6)}$ following Padé approximations yield analytical approximate formulae for Forchheimer’s law. The first algorithm is applied to symmetric channels on the theoretical level (all terms on ${\mathcal{R}}$ and ${\varepsilon}$ are taken into account) to show that ${|\overline{\nabla p}|}$ is an odd function of ${\overline{u}}$ . This observation yields, in particular, a cubic correction to Darcy’s law. Numerical examples for non-symmetrical channels yield the same cubic correction. The second algorithm is based on the analytical–numerical solution to the Navier–Stokes equations for arbitrary ${\mathcal{R}}$ up to ${O(\varepsilon^{3})}$ . This algorithm yields, in particular, a quadratic correction to Darcy’s law for higher ${\mathcal{R}}$ .     

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.     

Fabrication and characterization of iron and fluorine co-doped BST thin films for microwave applications

The effects of fluorine co-doping by means of a post-thermal annealing process of iron-doped BST thin films in a fluorine-containing atmosphere have been investigated. XPS and ToF-SIMS sputter depth profiling verified a homogeneous fluorine distribution in the thin films. By employing EPR, it was shown that singly charged ( $ {\text{Fe}}_{\text{Ti}}^{\prime } $ – $ {\text{V}}_{\text{O}}^{ \cdot \cdot } $ )^· defect complexes, as well as ‘isolated’ $ {\text{Fe}}_{\text{Ti}}^{\prime } $ centres with a distribution of $ {\text{F}}_{\text{O}}^{ \cdot } $ sites in remote coordination spheres exist in the fluorinated films. Tunability enhancement due to fluorine co-doping as well as a Q-factor enhancement due to iron doping is demonstrated.     

Determination of thermodynamic interactions of poly(l-lactide) and biphasic calcium phosphate/poly(l-lactide) composite by inverse gas chromatography at infinite dilution

Inverse gas chromatography at infinite dilution was applied to determine the thermodynamic interactions of poly(l-lactide) (PLLA) and the composite of biphasic calcium phosphate and PLLA (BCP/PLLA). The specific retention volumes, $ V_{\text{g}}^{0} $ , of 11 organic compounds of different chemical nature and polarity (non-polar, donor or acceptor) were determined in the temperature range of 308–378 K for PLLA and 308–398 K for BCP/PLLA. The weight fraction activity coefficients of test sorbates, $ \Omega_{1}^{\infty } $ , and the Flory–Huggins interaction parameters, $ \chi_{12}^{\infty } $ , were estimated and discussed in terms of interactions of the sorbates with PLLA and BCP/PLLA. Also, the partial molar free energy, $ \Delta G_{1}^{\infty } $ , the partial molar heat of mixing, $ \Delta H_{1}^{\infty } $ , the sorption molar free energy, $ \Delta G_{1}^{\text{S}} $ , the sorption enthalpy, $ \Delta H_{1}^{\text{S}} $ , and the sorption entropy, $ \Delta S_{1}^{\text{S}} $ , were analyzed. A different chromatographic behavior of the two investigated samples, PLLA and BCP/PLLA, was observed. The values of $ \Omega_{1}^{\infty } $ indicated n-alkanes, diethyl ether, tetrahydrofurane (THF), cyclohexane, benzene, dioxane (except for 338 K), and ethyl acetate (EtAc) (except for 338 K) as non-solvents, and chloroform (CHCl₃) as good solvent (except for 378 K) for PLLA. For BCP/PLLA, CHCl₃, EtAc (for 378 K), dioxane (except for 378 K), and THF were indicated as good solvents.     

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.     

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.     

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}$ .     

On characteristic lengths used in notch fracture mechanics

In this paper, four kinds of characteristic length parameters used in a local notch fracture criterion are presented: (1) a characteristic length ${\uprho }_{\mathrm{c}}$ generally connecting to the notch radius, (2) a characteristic distance $\hbox {X}_{\mathrm{c}}$ considered as intrinsic to material and connected to the microstructure, (3) a critical distance $\hbox {d}_{0}$ considered as intrinsic to material and connected to the fracture process zone, (4) an effective distance $\hbox {X}_{\mathrm{ef}}$ considered as a characteristic of the stress distribution. Each approach is discussed. The paper ends with the author’s opinion about the different methods.     

Thermal Conductivity of Standard Sands. Part III. Full Range of Saturation

The thermal conductivity $(\lambda )$ ( λ ) of three unsaturated standard quartz sands (Ottawa C-109 and C-190, and Toyoura) was measured by a transient thermal-conductivity probe, at room temperature of approximately $25\,^{\circ }\text{ C }$ 25 ° C and at loose and tight compactions. The measurements were carried out at different degrees of saturation $(S_\mathrm{r})$ ( S r ) from dryness to full saturation. In general, a sharp $\lambda $ λ increase was observed at low $S_\mathrm{r}$ S r , followed by a moderate rise until full saturation. However, experiments on loosely compacted C-190 samples revealed $\lambda $ λ deviation from a general trend ( $\lambda $ λ vs $S_\mathrm{r})$ S r ) caused by water percolation. Alternatively, successful experiments were carried out on loosely packed unsaturated C-190 samples using 1 % agar gel. For loosely compacted C-109 and Toyoura, $\lambda $ λ data obtained from 1 % agar gel closely agreed with $\lambda $ λ data for water as a saturation medium. The measured data were used to verify a model by de Vries for unsaturated soils. The model largely underestimates experimental data at $S_\mathrm{r}<0.5$ S r < 0.5 and produces an overall root-mean-square error of about $0.2\, \text{ W }~{\cdot }~\text{ m }^{-1}~{\cdot }~\text{ K }^{-1}$ 0.2 W · m ? 1 · K ? 1 . Measured $\lambda $ λ data agreed with data by a steady-state technique (a guarded hot-plate apparatus) at dryness and full saturation and exceeded the steady-state data in the unsaturated region. However, TCP data can be considered more reliable due to a lower temperature increase during $\lambda $ λ measurements and a shorter testing time. Consequently, in the case of unsaturated soils, evaporation and migration of water and steam can be avoided.     

Rational formulas for traces in zero-dimensional algebras

We present a rational expression for the trace of the multiplication map Times _r : A → A in a finite-dimensional algebra ${A := \mathbb {K}[x_1,\ldots,x_n] /\mathcal {I}}$ in terms of the generalized Chow form of ${\mathcal{I}}$ . Here, ${\mathcal{I} \subset \mathbb {K}[x_1,\ldots,x_n]}$ is a zero-dimensional ideal, ${\mathbb {K}}$ is a field of characteristic zero, and r(x ₁,..., x _n ) a rational function whose denominator is not a zero divisor in A. If ${\mathcal {I}}$ is a complete intersection in the torus, we get numerator and denominator formulas for traces in terms of sparse resultants.     

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.     

Multi-point evaluation in higher dimensions

In this paper, we propose efficient new algorithms for multi-dimensional multi-point evaluation and interpolation on certain subsets of so called tensor product grids. These point-sets naturally occur in the design of efficient multiplication algorithms for finite-dimensional $\mathcal C $ -algebras of the form $\mathcal A =\mathcal C [x_1, {\ldots }, x_n] / I$ , where $I$ is generated by monomials of the form $x_1^{i_1} {\cdots } x_n^{i_n}$ ; one particularly important example is the algebra of truncated power series $\mathcal C [x_1, {\ldots }, x_n] / (x_1, {\ldots }, x_n)^d$ . Similarly to what is known for multi-point evaluation and interpolation in the univariate case, our algorithms have quasi-linear time complexity. As a known consequence Schost (ISSAC’05, ACM, New York, NY, pp 293–300, 2005), we obtain fast multiplication algorithms for algebras $\mathcal A $ of the above form.     

Mass transfer through a single grain boundary in alumina bicrystals under oxygen potential gradients

The mass-transfer behavior through grain boundaries (GBs) in alumina was systematically investigated using four types of alumina bicrystals. The alumina bicrystal wafers were exposed to the constant oxygen potential gradient $ \left( {\Updelta P_{{{\text{O}}_{ 2} }} } \right) $ generated by the combination of two different oxygen partial pressures $ P_{{{\text{O}}_{ 2} }} \left( {\text{II}} \right) $ and $ P_{{{\text{O}}_{ 2} }} \left( {\text{I}} \right) $ of 10⁵ and 1?Pa, respectively, at 1923?K. Ridges were formed along the GBs on the surface subjected to $ P_{{{\text{O}}_{ 2} }} \left( {\text{II}} \right) $ , and deep GB ditches were developed on the $ P_{{{\text{O}}_{ 2} }} \left( {\text{I}} \right) $ surface mainly during the migration of aluminum thorough GBs from the $ P_{{{\text{O}}_{ 2} }} \left( {\text{I}} \right) $ surface to $ P_{{{\text{O}}_{ 2} }} \left( {\text{II}} \right) $ surface. The surface morphology changes in the vicinity of the GBs were observed by atomic force microscopy. It was found that the surface morphology changes indicative of the aluminum GB diffusion were strongly dependent on the GB characteristics. The GB diffusion coefficients of aluminum estimated from the volume of the GB ridges showed a clear correlation to the local bonding environments of GB cores estimated from theoretical calculations reported previously.     

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.     

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.     

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.     

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 $E_1^{(1+1)}$ .     

Spherical and rod-like Gd 2 O 3 :Eu 3?+? nanophosphors—Structural and luminescent properties

A comparative study of spherical and rod-like nanocrystalline Gd $_{\boldsymbol 2}$ O $_{\boldsymbol 3}$ :Eu $^{\boldsymbol{3+}}$ (Gd $_{\boldsymbol{1\cdot92}}$ Eu $_{\boldsymbol{0\cdot08}}$ O $_{\boldsymbol 3}$ ) red phosphors prepared by solution combustion and hydrothermal methods have been reported. Powder X-ray diffraction (PXRD) results confirm the as-formed product in combustion method showing mixed phase of monoclinic and cubic of Gd $_{\boldsymbol 2}$ O $_{\boldsymbol 3}$ :Eu $^{\boldsymbol{3+}}$ . Upon calcinations at 800 $^{\boldsymbol\circ}$ C for 3?h, dominant cubic phase was achieved. The as-formed precursor hydrothermal product shows hexagonal Gd(OH) $_{\boldsymbol 3}$ :Eu $^{\boldsymbol{3+}}$ phase and it converts to pure cubic phase of Gd $_{\boldsymbol 2}$ O $_{\boldsymbol 3}$ :Eu $^{\boldsymbol{3+}}$ on calcination at 600 $^{\boldsymbol \circ}$ C for 3?h. TEM micrographs of hydrothermally prepared cubic Gd $_{\boldsymbol 2}$ O $_{\boldsymbol 3}$ :Eu $^{\boldsymbol{3+}}$ phase shows nanorods with a diameter of 15?nm and length varying from 50 to 150?nm, whereas combustion product shows the particles to be of irregular shape, with different sizes in the range 50?C250?nm. Dominant red emission (612?nm) was observed in cubic Gd $_{\boldsymbol 2}$ O $_{\boldsymbol 3}$ :Eu $^{\boldsymbol{3+}}$ which has been assigned to $^{\boldsymbol 5}{\bf \textit{D}}_{\boldsymbol 0}$ $\boldsymbol \to$ $^{\boldsymbol 7}{\bf \textit{F}}_{\boldsymbol 2}$ transition. However, in hexagonal Gd(OH) $_{\boldsymbol 3}$ :Eu $^{\boldsymbol{3+}}$ , emission peaks at 614 and 621?nm were observed. The strong red emission of cubic Gd $_{\boldsymbol 2}$ O $_{\boldsymbol 3}$ :Eu $^{\boldsymbol{3+}}$ nanophosphors by hydrothermal method are promising for high performance display materials. The variation in optical energy bandgap ( $\boldsymbol{E}_{\boldsymbol{\rm g}}$ ) was noticed in as-formed and heat treated systems in both the techniques. This is due to more ordered structure in heat treated samples and reduction in structural defects.     

Characterization of Silicon Wafers with Combined Photocarrier Radiometry and Free Carrier Absorption

A combined photocarrier radiometry (PCR) and free carrier absorption (FCA) technique was employed to evaluate the electronic transport properties (carrier lifetime $\tau $ , diffusion coefficient $D$ , and the front surface recombination velocity $S_{1})$ of silicon wafers and to monitor the ion implantation and thermal annealing processes in the semiconductor manufacturing. For non-implanted silicon wafers, the experimental results showed that the accuracy of the simultaneous determination of the transport properties was greatly improved by fitting simultaneously the measured PCR and FCA signals to the theoretical models via a multi-parameter fitting procedure. For As $^+$ ion implanted and thermal annealed silicon wafers, the results showed that both PCR and FCA amplitudes increased monotonically with the increasing implantation dose ( $5\times 10^{11}$ cm $^{-2 }$ to $1\times 10^{16 }$ cm $^{-2})$ , the decreasing implantation energy (20 keV to 140 keV), and the increasing annealing temperature (500 $^{\circ }$ C to 1000 $^{\circ }$ C), respectively. To explain the dependences of the PCR signals on the implantation and annealing parameters, a multi-wavelength PCR technique was proposed to extract the electronic transport properties of the implanted and annealed wafers. The results showed that ion implantation and thermal annealing caused significant decreases of the minority carrier lifetime and diffusion coefficient of the implantation layer, as well as the recombination velocity at the front surface. All three parameters decreased with the increasing implantation dose.