Partial permutation decoding for MacDonald codes

We show how to find s-PD-sets of the minimal size \(s+1\) for the \(\left[ \frac{q^n-q^u}{q-1},n,q^{n-1}-q^{u-1}\right] _q \) MacDonald q-ary codes \(C_{n,u}(q)\) where \(n \ge 3\) and \(1 \le u \le n-1\). The construction of [6] can be used and gives s-PD-sets for s up to the bound \(\lfloor \frac{q^{n-u}-1}{(n-u)(q-1)} \rfloor -1\), of effective use for u small; for \(u \ge \lfloor \frac{n}{2} \rfloor \) an alternative construction is given that applies up to a bound that depends on the maximum size of a set of vectors in \(V_u(\mathbb {F}_q)\) with each pair of vectors distance at least 3 apart.     

<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.     

Thermal Conductivity of Pyroclastic Soil (<Emphasis Type="BoldItalic">Pozzolana</Emphasis>) from the Environs of Rome

The paper reveals the experimental procedure and thermo-physical characteristics of a coarse pyroclastic soil (Pozzolana), from the neighborhoods of Rome, Italy. The tested samples are comprised of 70.7 % sand, 25.9 % silt, and 3.4 % clay. Their mineral composition contained 38 % pyroxene, 33 % analcime, 20 % leucite, 6 % illite/muscovite, 3 % magnetite, and no quartz content was noted. The effective thermal conductivity of minerals was assessed to be about \(2.14\,\hbox {W}{\cdot } \hbox {m}^{-1}{\cdot } \hbox {K}^{-1}\). A transient thermal probe method was applied to measure the thermal conductivity (\(\lambda \)) over a full range of the degree of saturation \((S_{\mathrm{r}})\), at two porosities (n) of 0.44 and 0.50, and at room temperature of about \(25\,^{\circ }\hbox {C}\). The \(\lambda \) data obtained were consistent between tests and showed an increasing trend with increasing \(S_{\mathrm{r}}\) and decreasing n. At full saturation (\(S_{\mathrm{r}}=1\)), a nearly quintuple \(\lambda \) increase was observed with respect to full dryness (\(S_{\mathrm{r}}=0\)). In general, the measured data closely followed the natural trend of \(\lambda \) versus \(S_{\mathrm{r}}\) exhibited by published data at room temperature for other unsaturated soils and sands. The measured \(\lambda \) data had an average root-mean-squared error (RMSE) of \(0.007\,\hbox {W}{\cdot } \hbox {m}^{-1}{\cdot } \hbox {K}^{-1}\) and \(0.008\,\hbox {W}{\cdot } \hbox {m}^{-1}{\cdot } \hbox {K}^{-1}\) for n of 0.50 and 0.44, respectively, as well as an average relative standard deviation of the mean at the 95 % confidence level \((\hbox {RSDM}_{0.95})\) of 2.21 % and 2.72  % for n of 0.50 and 0.44, respectively.     

High-pressure studies of superconductivity in $$\hbox {BiO}_{0.75}\hbox {F}_{0.25}\hbox {BiS}_{2}$$

\(\hbox {BiO}_{0.75}\hbox {F}_{0.25}\hbox {BiS}_{2}\) crystallizes in tetragonal CeOBiS\(_{2}\) structure (S. G. P4/nmm). We have investigated the effect of pressure on magnetization measurements. Our studies suggest improved superconducting properties in polycrystalline samples of \(\hbox {BiO}_{0.75}\hbox {F}_{0.25}\hbox {BiS}_{2}\). The \(T_{\mathrm{c}}\) in our sample is 5.3 K, at ambient pressure, which is marginal but definite enhancement over \(T_{\mathrm{c}}\) reported earlier (= 5.1 K). The upper critical field \(H_{\mathrm{c}2}\)(0) is greater than 3 T, which is higher than earlier report on this material. As determined from the M–H curve, both \(H_{\mathrm{c}2}\) and \(H_{\mathrm{c}1}\) decrease under external pressure P (0 \(\le P \le \) 1 GPa). We observe a decrease in critical current density and transition temperature on applying pressure in \(\hbox {BiO}_{0.75}\hbox {F}_{0.25}\hbox {BiS}_{2}\).     

Evolution of magnetic structure of Dy(Co<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>Ni<Subscript>1−<Emphasis Type="Italic">x</Emphasis></Subscript>)<Subscript>2</Subscript>B<Subscript>2</Subscript>C

DyNi\(_{2}\)B\(_{2}\)C superconducts at \(T_{c} \approx 6\,{\text{K}}\) and orders antiferromagnetically at \(T_{N}\approx 10\,{\text{K}}.\) Its non-superconducting isomorph DyCo\(_{2}\)B\(_{2}\)C is a ferromagnet with \(T_{C}\approx 6\,{\text{K}}.\) With the aim of mapping out the magnetic properties, in particular magnetic structures, of their solid solutions, we synthesized \(^{11}\)B-enriched Dy(Co\(_{x}\)Ni\(_{1-x}\))\(_{2}\)B\(_{2}\)C (\(x=0.2,0.4,0.6,0.8\)). We investigated the evolution of their magnetic, thermal and transport properties by means of the magnetization, resistivity, specific heat and neutron diffraction techniques. Their crystal structures were confirmed to be ThCr\(_{2}\)-Si\(_{2}\)-type tetragonal (I4/mmm) phase. The magnetic structure was found to be antiferromagnetic with k_0.2 = (0, 0, 1) for x = 0.2; helicoidal with k\(_{0.4}\) = (0, 0, 0.49) and k\(_{0.6}\) = (0, 0, 0.46) for, respectively, x = 0.4 and 0.6 and ferromagnetic with k\(_{0.8}\) = (0, 0, 0) for x = 0.8. We discuss the evolution of such magnetic modes assuming a scenario of an idealized one-dimensional chain of transverse magnetic moments.     

NRC Microwave Refractive Index Gas Thermometry Implementation Between 24.5 K and 84 K

The implementation of microwave refractive index gas thermometry at the National Research Council between 24.5 K and 84 K is reported. A new gas-handling system for accurate control and measurement of experimental gas pressure has been constructed, and primary thermometry measurements have been taken using a quasi-spherical copper resonator and helium gas at temperatures corresponding to three defining fixed points of the International Temperature Scale of 1990 (ITS-90). These measurements indicate differences between the thermodynamic temperature T and ITS-90 temperature \(T_{90}\) of \(\left( T - T_{90} \right) = -0.60 \pm 0.56\) mK at \(T_{90} = 24.5561\) K, \(\left( T - T_{90} \right) = -2.0 \pm 1.3\) mK at \(T_{90} = 54.3584\) K, and \(\left( T - T_{90} \right) = -4.0 \pm 2.9\) mK at \(T_{90} = 83.8058\) K. The present results at \(T_{90} = 24.5561\) K and \(T_{90} = 83.8058\) K agree with previously reported measurements from other primary thermometry techniques of acoustic gas thermometry and dielectric constant gas thermometry, and the result at \(T_{90} = 54.3584\) K provides new information in a temperature region where there is a gap in other recent data sets.     

Further Estimates of $$(T-T_{90})$$ Close to the Triple Point of Water

Recent advances in primary acoustic gas thermometry (AGT) have revealed significant differences between temperature measurements using the International Temperature Scale of 1990, \(T_{90}\), and thermodynamic temperature, T. In 2015, we published estimates of the differences \((T-T_{90})\) from 118 K to 303 K, which showed interesting behavior in the region around the triple point of water, \(T_\mathrm{TPW}=273.16\) K. In that work, the \(T_{90}\) measurements below \(T_\mathrm{TPW}\) used a different ensemble of capsule standard platinum resistance thermometers (SPRTs) than the \(T_{90}\) measurements above \(T_\mathrm{TPW}\). In this work, we extend our earlier measurements using the same ensemble of SPRTs above and below \(T_\mathrm{TPW}\), enabling a deeper analysis of the slope \(\mathrm{d}(T-T_{90})/\mathrm{d}T\) around \(T_\mathrm{TPW}\). In this article, we present the results of seven AGT isotherms in the temperature range 258 K to 323 K. The derived values of \((T-T_{90})\) have exceptionally low uncertainties and are in good agreement with our previous data and other AGT results. We present the values \((T-T_{90})\) alongside our previous estimates, with the resistance ratios W(T) from two SPRTs which have been used across the full range 118 K to 323 K. Additionally, our measurements show discontinuities in \(\mathrm{d}(T-T_{90})/\mathrm{d}T\) at \(T_\mathrm{TPW}\) which are consistent with the slope discontinuity in the SPRT deviation functions. Since this discontinuity is by definition non-unique, and can take a range of values including zero, we suggest that mathematical representations of \((T-T_{90})\), such as those in the mise en pratique for the kelvin (Fellmuth et al. in Philos Trans R Soc A 374:20150037, 2016. doi: 10.1098/rsta.2015.0037), should have continuity of \(\mathrm{d}(T-T_{90})/\mathrm{d}T\) at \(T_\mathrm{TPW}\).     

Fracture of pre-cracked thin metallic conductors due to electric current induced electromagnetic force

We investigated propagation of a sharp crack in a thin metallic conductor with an edge crack due to electric current induced electromagnetic forces. Finite element method (FEM) simulations showed mode I crack opening in the edge-cracked conductor due to the aforementioned (i.e., self-induced) electromagnetic forces. Mode I stress intensity factor due to the self-induced electromagnetic forces, \(K_{\mathrm{IE},}\) was evaluated numerically as \(K_{\mathrm{IE}}=\upmu l^{2}j^{2}(\uppi a)^{0.5}f(a/w)\), where \(\upmu \) is the magnetic permeability, l is the length of the conductor, a is the crack length, j is the current density, w is the width of the sample and f(a / w) is a geometric factor. Effect of dynamic electric current loading on edge-cracked conductor, incorporating the effects of induced currents, was also studied numerically, and dynamic stress intensity factor, \(K_{\mathrm{IE,d}}\), was observed to vary as \(K_{\mathrm{IE,d}} \sim f_{d}(a/w)j^{2}(\uppi a)^{1.5}\). Consistent with the FEM simulation, experiments conducted using \(12\,\upmu \hbox {m}\) thick Al foil with an edge crack showed propagation of sharp crack due to the self-induced electromagnetic forces at pulsed current densities of \(\ge \) \(1.85\times 10^{9}\,\hbox {A/m}^{2}\) for \(a/w = 0.5\). Further, effects of current density, pulse-width and ambient temperature on the fracture behavior of the Al foil were observed experimentally and corroborated with FEM simulations.     

Interaction of Glycylglycine with Cationic Surfactants—Cetylpyridinium Chloride and Cetylpyridinium Bromide: A Volumetric,Ultrasonic and Conductometric Study

The interactions of glycylglycine (di-peptide of glycine) also known as 2-[(2-aminoacetyl)amino] acetic acid with cationic surfactants cetylpyridinium chloride (CPC) and cetylpyridinium bromide (CPB) as a function of temperature in aqueous medium has been studied by well-know permutation of volumetric, ultrasonic and conductometric techniques. These measurements have been used to evaluate some useful thermodynamic parameters viz. apparent molar volumes, \( \phi_{v} \), partial molar volumes, \( \phi_{v}^{o} \), transfer volumes, \( \phi_{\text{v}}^{0} (tr) \), partial molar expansibility, \( \phi_{E}^{0} \), hydration number, n_H, apparent molal compressibility, \( \phi_{K} \), limiting partial molal adiabatic compressibility, \( \phi_{K}^{0} \). The specific conductivity (κ) was used to calculate the critical micellar concentration (cmc) and other physicochemical parameters of micellization of CPC/CPB with glycylglycine. The critical micelle concentration, cmc and limiting molar conductivity, \( \varLambda_{m}^{o} \) of the two surfactant systems were determined by using the conductivity data at 298.15 K, 303.15 K, 308.15 K and 313.15 K. The acquired data have been discussed as per various interactions taking place in the ternary system of CPC/CPB, glycylglycine and water.     

Reproducibility of the Helium-3 Constant-Volume Gas Thermometry and New Data Down to 1.9 K at NMIJ/AIST

This study confirms reproducibility of the International Temperature Scale of 1990 (ITS-90) realized by interpolation using the constant-volume gas thermometer (CVGT) of National Metrology Institute of Japan (NMIJ)/AIST with \(^{3}\)He as the working gas from 3 K to 24.5561 K by comparing the newly obtained results and those of earlier reports, indicating that the CVGT has retained its capability after renovation undertaken since strong earthquakes struck Japan. The thermodynamic temperature T is also obtained using the single-isotherm fit to four working gas densities (\(127\,\hbox {mol}\cdot \hbox {m}^{-3}\), \(145\,\hbox {mol}\cdot \hbox {m}^{-3}\), \(171\,\hbox {mol}\cdot \hbox {m}^{-3}\) and \(278\,\hbox {mol}\cdot \hbox {m}^{-3})\) down to 1.9 K, using the triple point temperature of Ne as a reference temperature. In this study, only the second virial coefficient is taken into account for the single-isotherm fit. Differences between T and the ITS-90 temperature, \(T-T_{90}\), reported in earlier works down to 3 K were confirmed in this study. At the temperatures below 3 K down to 2.5 K, \(T-T_{90}\) is much smaller than the standard combined uncertainty of thermodynamic temperature measurement. However, \(T- T_{90}\) seems to increase with decreasing temperature below 2.5 K down to 1.9 K, although still within the standard combined uncertainty of thermodynamic temperature measurement. In this study, T is obtained also from the CVGT with a single gas density of \(278\,\hbox {mol}\cdot \hbox {m}^{-3}\) using the triple-point temperature of Ne as a reference temperature by making correction for the deviation from the ideal gas using theoretical values of the second and third virial coefficients down to 2.6 K, which is the lowest temperature of the theoretical values of the third virial coefficient. T values obtained using this method agree well with those obtained from the single-isotherm fit. We also found that the second virial coefficient obtained by the single-isotherm fit to experimental results agrees well with that obtained by the single-isotherm fit to the theoretically expected behavior of \(^{3}\)He gas with the theoretical second and third virial coefficients at four gas densities used in the present work.     

Inhomogeneous Superconducting Behaviour in $$\hbox {La}_{5}\hbox {Ni}_{2}\hbox {Si}_{3}$$

The superconducting phase transition at \(T_\mathrm{c} = 2.3\) K was observed for the electrical resistivity \(\rho ({T})\) and magnetic susceptibility \(\chi (T)\) measurements in the ternary compound La\(_{5}\hbox {Ni}_{2}\hbox {Si}_{3}\) that crystallizes in the hexagonal-type structure. Although a single-phase character with the nominal stoichiometry of the synthesized sample was confirmed, a small trace of the La–Ni phase was found, being probably responsible for the superconducting behaviour in the investigated compound. The magnetization loop recorded at \({T} = 0.5\) K resembles a star-like shape which indicates that the density of the critical current can be strongly suppressed by a magnetic field. The low-\(T _{\rho }(T)\) and specific heat \({C}_\mathrm{p}({T})\) data in the normal state reveal simple metallic behaviour. No clear evidence of a phase transition to any long- or short-range order was found for \(C_\mathrm{p}(T)\) measurements in the T-range of 0.4–300 K.     

Microwave dielectrics: solid solution,ordering and microwave dielectric properties of $$(1{-}x)\hbox {Ba}(\hbox {Mg}_{1/3}\hbox {Nb}_{2/3})\hbox {O}_{3}{-}x\hbox {Ba(Mg}_{1/8}\hbox {Nb}_{3/4})\hbox {O}_{3}$$ ceramics

The effect of Ba(\(\hbox {Mg}_{1/8}\hbox {Nb}_{3/4})\hbox {O}_{3}\) phase on structure and dielectric properties of \(\hbox {Ba(Mg}_{1/3}\hbox {Nb}_{2/3})\hbox {O}_{3}\) was studied by synthesizing \((1{-}x)\hbox {Ba(Mg}_{1/3}\hbox {Nb}_{2/3})\hbox {O}_{3}{-}x\hbox {Ba}(\hbox {Mg}_{1/8}\hbox {Nb}_{3/4})\hbox {O}_{3}\) (\(x = 0\), 0.005, 0.01 and 0.02) ceramics. Superlattice reflections due to 1:2 ordering appear as low as \(1000^{\circ }\hbox {C}\). \(\hbox {Ba}(\hbox {Mg}_{1/3}\hbox {Nb}_{2/3})\hbox {O}_{3}\) forms solid solution with \(\hbox {Ba}(\hbox {Mg}_{1/8}\hbox {Nb}_{3/4})\hbox {O}_{3}\) for all ‘x’ values studied until \(1350^{\circ }\hbox {C}\). Ordering was confirmed by powder X-ray diffraction pattern, Raman study and HRTEM. Ceramic pucks can be sintered to density \({>}92\%\) of theoretical density. Temperature and frequency-stable dielectric constant and nearly zero dielectric loss (tan \(\delta \)) were observed at low frequencies (20 MHz). The sintered samples exhibit dielectric constant (\(\varepsilon _{\mathrm{r}})\) between 30 and 32, high quality factor between 37000 and 74000 GHz and temperature coefficient of resonant frequency (\(\tau _{\mathrm{f}})\) between 21 and \(24\hbox { ppm }^{\circ }\hbox {C}^{-1}\).     

Cyclic codes over $${\mathbb {F}}_{2^m}[u]/\langle u^k\rangle $$ of oddly even length

Let \({\mathbb {F}}_{2^m}\) be a finite field of characteristic 2 and \(R={\mathbb {F}}_{2^m}[u]/\langle u^k\rangle ={\mathbb {F}}_{2^m} +u{\mathbb {F}}_{2^m}+\ldots +u^{k-1}{\mathbb {F}}_{2^m}\) (\(u^k=0\)) where \(k\in {\mathbb {Z}}^{+}\) satisfies \(k\ge 2\). For any odd positive integer n, it is known that cyclic codes over R of length 2n are identified with ideals of the ring \(R[x]/\langle x^{2n}-1\rangle \). In this paper, an explicit representation for each cyclic code over R of length 2n is provided and a formula to count the number of codewords in each code is given. Then a formula to calculate the number of cyclic codes over R of length 2n is obtained. Moreover, the dual code of each cyclic code and self-dual cyclic codes over R of length 2n are investigated.     

Density Functional Study of the Carbon Dependence of the Structural,Mechanic, Thermodynamic,and Dynamic Properties of SiC Alloys

Using a density functional scheme, for the first time the carbon dependence on the structural, dynamic, thermodynamic, and dynamic properties of \(\hbox {Si}_{1-x}\hbox {C}_{x} \) alloys (\(x=0.0\) to 1.0 in steps of 0.125) has been investigated. The structural properties of these materials, in particular, the composition dependence of the lattice parameter and bulk modulus, are in excellent agreement with experimental data and follow a quadratic law in (x). A nonlinear relationship is found between the elastic constants \(C_{11}\), \(C_{12}\), and \(C_{44}\) and the carbon concentration (x). The behavior of the acoustical and optical phonon frequencies at high-symmetry points \(\varGamma \), X, and L is predicted. Through the quasi-harmonic Debye model, in which the photonic effects are taken into account, the Debye temperature, the heat capacity, the Helmholtz free energy, the internal energy, and the entropy are determined for the \(\hbox {Si}_{1-x}\hbox {C}_{x }\) compounds.     

Characterization and optical properties of $$\hbox {Pr}_{2}\hbox {O}_{3}$$-doped molybdenum lead-borate glasses

\(\hbox {Pr}^{3+}\) doped molybdenum lead-borate glasses with the chemical composition 75PbO?[25–(x \(+\) y)\(\hbox {B}_{2}\hbox {O}_{3}]\)–\(y\hbox {MoO}_{3}\)–\(x\hbox {Pr}_{2}\hbox {O}_{3}\) (where \(x = 0.5\) and 1.0 mol% and \(y = 0\) and 5 mol%) were prepared by conventional melt-quenching technique. Thermal, optical and structural analyses are carried out using DSC, UV and FTIR spectra. The physical parameters, like glass transition \((T_{\mathrm{g}})\), stability factor \((\Delta T)\), optical energy band gap \((E_{\mathrm{gopt}})\), of these glasses have been determined as a function of dopant concentration. The \({T}_{\mathrm{g}}\) and optical energy gaps of these glasses were found to be in the range of 290–350\({^{\circ }}\hbox {C}\) and 2.45–2.7 eV, respectively. Stability of the glass doped with \(\hbox {Pr}^{3+}\) is found to be moderate (\(\sim \)40). The results are discussed using the structural model of Mo–lead-borate glass.     

Critical Parameters and Critical-Region ($$p,\rho,T)$$ Data of trans-1,1,1,3-Tetrafluorobut-2-ene [HFO-1354mzy(E)]

This study presents the experimental measurement of the \(p\rho T\) properties and critical parameters of a low GWP type refrigerant, trans-1,1,1,3-Tetrafluorobut-2-ene (HFO-1354mzy(E)). The sample purity of the substance was 99 area %. \(p \rho T\) property measurements and visual observations of the meniscus of HFO-1354mzy(E) were carried out using a metal-bellows volumometer with an optical cell. The critical temperature was determined by observation of the critical opalescence. The critical pressure and critical density were determined as the inflection point of the isothermal \(p \rho T\) property data at the critical temperature. For more precise clarification of the thermodynamic surface in the vicinity of the critical point, additional \(p \rho T\) property measurements were carried out on three isotherms in the supercritical region. The expanded uncertainties (\(k = 2\)) in the temperature, pressure, and density measurements were estimated to be less than 3 mK, 1.2 kPa, and 0.32 \(\hbox {kg} \cdot \hbox {m}^{-3}\), respectively. The expanded uncertainties of the critical parameters were estimated to be less than 13 mK, 1.4 kPa, and 2.3 \(\hbox {kg} \cdot \hbox {m}^{-3}\), respectively. These values are the first reported for HFO-1354mzy(E) and are necessary for the development of its equation of state in the near future.     

Aggregate packing and -void saturation in mortar and concrete proportioning

Proportioning was studied by measuring aggregate packing (C) and filling of aggregate void space (1?C) with varying volumes of cement paste (\(V_{\rm p}\)) or matrix (\(V_{\rm matrix}\)), i.e., all material <0.125 mm. Eleven widely different normal density aggregates with C = 0.57 to 0.71, i.e., aggregate void content (1?C) = 0.29 to 0.43, were used at constant w/c = 0.38 and flowing consistency and varying dosage of water reducer and paste- and matrix volume. Analysing plots of four excess phase volumes (paste with/without air, matrix with/without air) versus aggregate void space showed constant aggregate void saturation ratios. Both paste- and matrix-aggregate void saturation ratio can be used with the best estimate (\(V_{\rm p}-V_{\rm air})/{(1-C)}=1.15\) per \(\hbox{m}^{3}\). Including air voids in paste- or matrix volume improved correlation so air void content must be included in the normalized paste aggregate void saturation ratio (\(k=V_{\rm p}\)/[(1?C) \(V_{\rm tot}\)]). Simple measurements of aggregate packing are thus very useful. Cost per unit material, per unit fresh (slump, flow diameter) or hardened (compressive strength) property were used to show the cost efficiency of the mixes. The ranking of cost/MPa strength and cost/mm consistency is similar to ranking of total concrete cost for the 11 aggregates with a certain scatter though.     

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.