Fracture toughness and crack morphology in indentation fracture of brittle materials

The relationship between the indentation fracture toughness, K _c, and the fractal dimension of the crack, D, has been examined on the indentation-fractured specimens of SiC and AIN ceramics, a soda-lime glass and a WC-8%Co hard metal. A theoretical analysis of the crack morphology based on a fractal geometry model was then made to correlate the fractal dimension of the crack, D, with the fracture toughness, K _IC, in brittle materials. The fractal dimension of the indentation crack, D, was found to be in the range 1.024–1.145 in brittle materials in this study. The indentation fracture toughness, K _c, increased with increasing fractal dimension, D, of the crack in these materials. According to the present analysis, the fracture toughness, K _IC, can be expressed as the following function of the fractal dimension of the crack, D, such that $$In K_{IC} = {1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}\{ In[2\Gamma E/(1 - \nu ^2 )] - (D - 1)In r_L \}$$ Where Γ is the work done in creating a unit crack surface, E is Young's modulus, v is Poisson's ratio, and r _L is r _min/r _max, the ratio of the lower limit, r _min, to the upper limit, r _max, of the scale length, r, between which the crack exhibits a fractal nature (r _min ?r?r _max). The experimental data (except for WC-8%Co hard metal) obtained in this study and by other investigators have been fitted to the above equation. The factors which affect the prediction of the value of K _IC from the above equation have been discussed.     

Self-diffusion of14C in polycrystalline β-SiC

The¹⁴C self-diffusion coefficients for both lattice (D _lc ^* ) and grain boundary (D _bc ^* ) transport in high purity CVDβ-SiC are reported for the range 2128 to 2374 K. The Suzuoka analysis technique revealed thatD _bc ^* is 10⁵ to 10⁶ faster thanD _bc ^* ; the respective equations are given by $$\begin{gathered} D_{I c}^* = (2.62 \pm 1.83) \times 10^8 exp\left\{ { - \frac{{(8.72 \pm 0.14)eV/atom}}{{kT}}} \right\}cm^2 sec^{ - 1} \hfill \\ D_{b c}^* = (4.44 \pm 2.03) \times 10^7 exp\left\{ { - \frac{{(5.84 \pm 0.09)eV/atom}}{{kT}}} \right\}cm^2 sec^{ - 1} \hfill \\ \end{gathered} $$ A vacancy mechanism is assumed to be operative for lattice transport. From the standpoint of crystallography and energetics, reasons are given in support of a path of transport which involves an initial jump to a vacant tetrahedral site succeeded by a jump to a normally occupied C vacancy.     

Generalized fracture mechanics of ductile steels

The generalized fracture mechanics approach is applied to two ductile steels, namely mild steel and 18/8 stainless steel in plane stress. The theory defines a fracture parameter \(\mathcal{T}\) , which is a truly plastic analogue of theJ contour integral and, for an edge crack specimen, is given by $$\mathcal{T} = k_1 ( \in _0 )cW_{0_c } $$ wherek ₁ is an explicit function,c is the crack length andε ₀, W_0c are respectively the strain and input energy density at fracture, remote from the crack. The functionk ₁(ε _o) is derived experimentally and the constancy of \(\mathcal{T}\) with respect to crack length and applied load is demonstrated. The variation of \(\mathcal{T}\) with crack extension during slow growth is investigated, as is the rate dependence of \(\mathcal{T}\) in mild steel.     

How the Surface Resistance R s of Patterned High-T c Superconducting Thin Film Is Affected by the Film's Edge

This paper defines an effective microwave surface resistance $R_{\text{s}}^{{\text{eff}}}$ for the nonuniform distribution of microwave surface resistance R _s in the strip of a microstrip. It is proved that $R_{\text{s}}^{{\text{eff}}}$ is equivalent to the expression of R _s used in experiments, and that the $R_{\text{s}}^{{\text{eff}}}$ is dominated by the edge part, i.e., the area of width λ²/2t from the strip edge, where λ is the magnetic penetration depth and t is the film thickness. Under the assumption that $R_s \sim \left( {H_{{\text{rf}}}^y } \right)^n$ where $H_{{\text{rf}}}^y$ is the component of rf magnetic field along the film thickness and n is an integer, the ratio of the contributions of the edge part and the rest of the strip to $R_s^{{\text{eff}}}$ is calculated by using an approximate analytical expression of the surface current density distribution J _s in the strip and $H_{{\text{rf}}}^y$ calculated by the London equation. The effect of film's edge on R _s was studied using a microstrip resonator. It is found that the perfectness of the edge could affect the magnitude of the power dependence of R _s significantly, which agreed with our analysis.     

Internal oxidation of Fe-Si alloys in γ-phase region

Internal oxidation measurements of Fe-0.070, 0.219, 0.483, and 0.920 wt % Si alloys were made in the γ-phase region in order to discuss kinetics of internal oxidation, to evaluate the diffusion coefficient of oxygen in the internal oxidation layer, and to determine the diffusion coefficient of oxygen in γ-iron. Internal oxidation of these alloys was conducted at temperatures between 1223 and 1323 K using a powder mixture of iron and Fe₂O₃. The internal oxidation front in Fe-Si alloys with between 0.070 and 0.483 wt % Si advances in parallel to the specimen surface. The internal oxidation in these alloys obeys a parabolic rate law, which indicates that the internal oxidation is controlled by an oxygen diffusion process in the alloy. The diffusion coefficient of oxygen, D _O ^IO , in the internal oxidation layer where SiO₂ particles disperse was determined by using the thermodynamic data for the solution of oxygen in γ-iron. D _O ^IO increases with the increase of the volume fraction of the oxide, f ^IO, in the oxidation layer at a given temperature. The diffusion coefficient of oxygen, D _O, in γ-iron was evaluated by extrapolating D _O ^IO to f ^IO=0. D _O may be given by the following equation: $$D_O = \left( {6.42\begin{array}{*{20}c} { + 4.37} \\ { - 2.60} \\ \end{array} } \right) \times 10^{ - 5} exp \left[ { - \frac{{159 \pm 5(kj mol^{ - 1} )}}{{RT}}} \right]m^2 \sec ^{ - 1} $$ .     

Features in the formation of Ge/Si multilayer nanostructures under ion-beam-assisted crystallization

A method of combined ion-beam crystallization of the Ge/Si multilayer nanostructures is proposed. Using atomic-force microscopy and electron microscopy, we observed the formation of an array of germanium quantum dots with lateral dimensions 〈a〉 = 12–15 nm at the following conditions: silicon-substrate temperature T = 330–350°C, ion-beam energies E _Ge + = 30–40 eV, $E_{Ar^ + }^0 = 230 - 240$ eV (primary pulsed defect formation mode), $E_{Ar^ + } = 130 - 140$ eV (permanent diffusion stimulation mode), and ion-beam fluences $f_{Ge^ + } = 1.5 \times 10^{14} cm^{ - 2} s^{ - 1} $ , $f_{Ar^ + } = 5 \times 10^{12} cm^{ - 2} s^{ - 1} $ . The Raman spectroscopy data indicate the experimental possibility of low-temperature ion-stimulated growth of the spacer layers of silicon (T = 420–450°C, $E_{Ar^ + } = 80 - 90$ eV, $E_{Si^ + } = 30 - 40$ eV, $f_{Si^ + } = 3.5 \times 10^{14} cm^{ - 2} s^{ - 1} $ ) and the formation of multilayer structures with Ge _x Si_{1 ? x} quantum dots (x > 0.85).     

An energy based regression method to evaluate critical CTOA of pipeline steels by instrumented drop weight tear tests

An energy based regression method to estimate critical crack-tip-opening-angle ( $\hbox {CTOA}_\mathrm{C}$ ) of high strength and toughness pipeline steels has been established derived from the Martinelli-Venzi ductile fracture model. Key curve method was applied onto the load-displacement curves of standard pressed-notch drop-weight-tear-test specimens to evaluate the dynamic crack extension, providing a way to verify the correlation between the load and remaining ligament width. In the meanwhile, the material based parameter ( $\hbox {A}^{*} \upsigma _\mathrm{f}$ ), usually required by other $\hbox {CTOA}_\mathrm{C}$ estimation algorithm, could also be determined experimentally. As a result, $\hbox {CTOA}_\mathrm{C}$ of a typical high grade pipeline steel plate was acquired as a constant over steady-state stage during crack propagation, independent of specimen geometry.     

Is There a Unified Description of Conductivity of Layered Cuprates ?

We present a novel approach to the analysis of the normal state in-plane $\sigma _{ab} $ and out-of-plane σ_c conductivities of anisotropic layered crystals such as oxygen deficient YBa ₂ Cu ₃ O _x . It can be shown that the resistive anisotropy is determined by the ratio of the phase coherence lengths in the respective directions; i.e., $\sigma _{ab} /\sigma _c = \ell _{ab}^2 /\ell _c^2 $ . From the idea that at all doping levels and temperatures T the out-of-plane transport in these crystals is incoherent, follows that $\ell _c $ is T-independent, equal to the spacing $\ell _0 $ between the neighboring bilayers. Thus, the T-dependence of $\ell _{ab} $ is given by the measured anisotropy, and $\sigma _{ab} (\ell _{ab} )$ dependence is obtained by plotting $\sigma _{ab} {\text{ }}vs{\text{ }}\ell = {\text{ (}}\sigma _{ab} /\sigma _c )^{1/2} \ell _0 $ .The analysis of several single crystals of YBa ₂ Cu ₃ O _x (6.35 < x < 6.93) shows that for all of them $\sigma _{ab} (\ell ) $ is described by a universal dependence $\sigma _{ab} /\overline \sigma = f(\ell /\overline \ell ) $ with doping dependent parameters $\overline \sigma {\text{ }}and{\text{ }}\overline \ell $ .     

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 ${\mathbb{Z}_{p^2}}$ .     

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.     

An approximate approach for the calculation ofM s in iron-base alloys

Having estimated the critical driving force associated with martensitic transformation,ΔG ^α→M, as $$\Delta G^{\alpha \to M} = 2.1 \sigma + 900$$ whereσ is the yield strength of austenite atM _s, in MN m^?2, we can directly deduce theM _s by the following equation: $$\Delta G^{\gamma \to {\rm M}} |_{M_S } = \Delta G^{\gamma \to \alpha } + \Delta G^{\alpha \to M} = 0.$$ The calculatedM _s are in good agreement with the experimental results in Fe-C, Fe-Ni-C and Fe-Cr-C, and are consistent with part of the data in Fe-Ni, Fe-Cr and Fe-Mn alloys. Some higher “M _s” determined in previous works may be identified asM _a,M _s of surface martensite or bainitic temperature. TheM _s of pure iron is about 800 K. TheM _s in Fe-C can be approximately expressed as $$M_S (^\circ {\text{C}}) = 520 {\text{--- }}\left[ {{\text{\% C}}} \right]{\text{ }}x 320.$$ In Fe-X, the effect of the alloying element onM _s depends on its effect onT ₀ and on the strengthening of austenite. An approach for calculation of ΔG ^γ→α in Fe-X-C is suggested. Thus dM _s/dx _c in Fe-X-C is found to increase with the decrease of the activity coefficient of carbon in austenite.     

Pulsed Nuclear Magnetic Resonance on 3He Adsorbed on Bare and 4He Preplated MCM-41 Using DC SQUID Detection

We report low field DC SQUID NMR measurements down to 1.5 K of ³He adsorbed in the pores of the mesoporous molecular sieve MCM-41. In the first experiment measurements were made on ³He adsorbed onto the bare pore walls of MCM-41 with coverages ranging from $n_{^{3}\mathrm{He}}=0.86n_{1}$ to full pores at $n_{^{3}\mathrm{He}}=1.79n_{1}$ , where n ₁ is the coverage for monolayer completion. A second experiment was performed with low ³He coverages ( $n_{^{3}\mathrm{He}}\sim0.01n_{1}$ ) on ⁴He preplated pores, where a crossover to a quasi-1D state is expected to occur at temperatures sufficiently below 700 mK. In both experiments relaxation times T ₁ and T ₂ ^* were measured as a function of temperature and coverage at frequencies from 80 to 240 kHz. The frequency dependence of the linewidth in the pure ³He experiment is extremely weak therefore T ₂ ^* ≈T ₂. The 1.5 K isotherm shows a small minimum in T ₂ ^* at a coverage corresponding to monolayer completion. In the experiment with ⁴He preplating there was no significant change in T ₁ or T ₂ ^* when the ³He coverage was doubled from $n_{^{3}\mathrm{He}}=0.01n_{1}$ to 0.02n ₁ at a ⁴He preplating of $n_{^{4}\mathrm{He}}=1.05n_{1}$ . This suggests that the relaxation times are dominated by single particle effects in the low density regime.     

Evaluating geometric queries using few arithmetic operations

Let ${\mathcal{P}:=(P_1,\ldots,P_s)}$ be a given family of n-variate polynomials with integer coefficients and suppose that the degrees and logarithmic heights of these polynomials are bounded by d and h, respectively. Suppose furthermore that for each 1??? i??? s the polynomial P _i can be evaluated using L arithmetic operations (additions, subtractions, multiplications and the constants 0 and 1). Assume that the family ${\mathcal{P}}$ is in a suitable sense generic. We construct a database ${\mathcal{D}}$ , supported by an algebraic computation tree, such that for each ${x\in [0,1]^n}$ the query for the signs of P ₁(x), . . . , P _s (x) can be answered using ${h d^{\mathcal{O}(n^2)}}$ comparisons and nL arithmetic operations between real numbers. The arithmetic-geometric tools developed for the construction of ${\mathcal{D}}$ are then employed to exhibit example classes of systems of n polynomial equations in n unknowns whose consistency may be checked using only few arithmetic operations, admitting, however, an exponential number of comparisons.     

Precipitation in non-stoichiometric spinel

Precipitation in non-stoichiometric spinel (MgO · 3.5Al₂O₃) single crystals has been investigated in the temperature range 900 to 1600° C. The formation of a coherent intermediate phase precedes precipitation of the equilibriumα-Al₂O₃, and the time-temperature-extent of transformation (T-T-T) curve for the formation of this metastable phase has been determined. Nucleation ofα-Al₂O₃ occurs only at free surfaces, presumably because of the large strain energy accompanying the transformation of the anion sublattice from cubic to hexagonal close-packing. The growth rate ofα-Al₂O₃ from the free surfaces follows a linear law and appears similar to the “autocatalytic reaction” found in some metallic alloys. The following orientation relationship between spinel andα-Al₂O₃ is observed: $$\langle 10\overline 1 0\rangle _{\alpha - {\rm A}l_2 O_3 } \parallel \langle 110\rangle _{spinel} $$ and $$(0001)_{\alpha - {\rm A}l_2 O_3 } \parallel \{ 111\} _{spinel.} $$ .     

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.     

Effect of silica fume addition and repeated loading on chloride diffusion coefficient of concrete

In this paper, the effect of silica fume (SF) on the chloride diffusion coefficient of concrete subjected to repeated loading was examined. Portland cement was replaced by 5 and 10 % SF. Five cycles repeated loadings were applied to concrete specimens, the maximum loadings were 40 and 80 % of the axial cylinder compressive strength ( $ f_{\text{c}}^{\prime } $ ), respectively. The diffusion coefficients were calculated from the steady state in the chloride migration test using the Nernst-Planck equation. The service life of concrete in chloride environment was predicted by Life-365 model. The results indicate that the diffusion coefficients of concrete containing 5 and 10 % SF replacements are lower than that of the control concrete at the age of 28 days. This trend increases with the increase of SF replacement. Five cycles repeated loading at 40 % $ f_{\text{c}}^{\prime } $ or 80 % $ f_{\text{c}}^{\prime } $ increase the diffusion coefficients (D ₂₈) for all mixes investigated in this study. However, the effect of 80 % $ f_{\text{c}}^{\prime } $ on D ₂₈ of concrete with 10 % SF is significantly lower than that of the control concrete without SF. Compared with the control concrete without SF, 10 % SF replacements increase the service life of concrete by more than 10 times.     

Anisotropy of the Adiabatic Relaxation Time of Adsorbed 3He Monolayer

This paper investigates the anisotropy of the adiabatic relaxation time $T_{2}^{\prime}$ (T ₂(ω), ω→∞, where ω is the Larmor frequency) of adsorbed monolayer solid ³He. We calculate $T_{2}^{\prime}$ based on the phenomenological Heisenberg Hamiltonian with the nearest-neighbor and the next nearest-neighbor exchange interactions. Furthermore, the four particle exchange in the triangular plane is also incorporated. To calculate  $T_{2}^{\prime}$ , it is necessary to compute the second and the fourth moments of the resonance line $M_{2}^{0}$ and $M_{4}^{0}$ . To obtain them, we can use the formulas published in previous studies. From the results, we can observe no significant difference between the nearest-neighbor Heisenberg model and the four particle spin interaction models. A comparison of the present results and the experimental data is briefly discussed.     

High-field ESR on Light-Induced Transition of Spin Multiplicity in FeCo Complex

Cyanide-bridged Fe-Co complex [Fe(Tp)(CN)₃]₂Co(bpe)?5H₂O (1?5H₂O; Tp = hydro-tris(pyrazolyl)borate; bpe = 1,2-bis(4-pyridyl)ethane) shows temperature- and light- induced metal-to-metal charge transfer (MMCT) involving spin state changes between magnetic $\mathrm{Fe}^{\mathrm{III}}_{\phantom{\mathrm{III}}\mathrm{LS}}\mbox{--}\mathrm{Co}^{\mathrm{II}}_{\phantom{\mathrm{II}}\mathrm{HS}}$ (HS = high spin, LS = low spin) state and nonmagnetic $\mathrm{Fe}^{\mathrm{II}}_{\phantom{\mathrm{II}}\mathrm{LS}}\mbox{--}\mathrm{Co}^{\mathrm{III}}_{\phantom{\mathrm{III}}\mathrm{LS}}$ state, while the dehydrated material 1 does not show any MMCT and holds $\mathrm{Fe}^{\mathrm{III}}_{\phantom{\mathrm{III}}\mathrm{LS}}\mbox{--}\mathrm{Co}^{\mathrm{II}}_{\phantom{\mathrm{II}}\mathrm{HS}}$ state. We have investigated the magnetic properties of each spin state in 1 and 1?5H₂O by means of magnetization and ESR measurement under pulsed high magnetic field. At low temperature below T _N, in both 1 and 1?5H₂O, the saturation magnetization in the induced ferromagnetic phase is well explained by S and g values derived from the magnetic susceptibility study. In the ESR of 1, we observed characteristic modes corresponding to a spin excitation in the induced ferromagnetic phase where its temperature dependence shows an evolution of spin correlation in the $\mathrm{Fe}^{\mathrm{III}}_{\phantom{\mathrm{III}}\mathrm{LS}}\mbox{--}\mathrm{Co}^{\mathrm{II}}_{\phantom{\mathrm{II}}\mathrm{HS}}$ state at low temperature. We further found that the similar ESR modes grow in the light-induced state of 1?5H₂O. The results strongly suggest that the light-induced magnetization in 1?5H₂O is driven by a light-induced MMCT, which involves transition of spin multiplicity from the nonmagnetic $\mathrm{Fe}^{\mathrm{II}}_{\phantom{\mathrm{II}}\mathrm{LS}}\mbox{--}\mathrm{Co}^{\mathrm{III}}_{\phantom{\mathrm{III}}\mathrm{LS}}$ to the magnetic $\mathrm{Fe}^{\mathrm{III}}_{\phantom{\mathrm{III}}\mathrm{LS}}\mbox{--}\mathrm{Co}^{\mathrm{II}}_{\phantom{\mathrm{\mathrm{II}}}\mathrm{HS}}$ pair.     

The Splitting of SDW State into Commensurable and Incommensurables Ones and the Peculiarities of the Behavior of Thermodynamic Quantities in a Magnetic Field Arbitrarily Oriented to Magnetization in Quasi Two-Dimensional Systems

The quasi-two-dimensional system in which magnetism is caused by spin density wave (SDW) with an anisotropic energy spectrum (with defined impurity concentration x) is examined. The wave vector $\vec{Q}$ is supposed to be different from 2k _F and the umklapp scattering (U-processes) is taken into account. The system is placed in a magnetic field arbitrarily oriented with respect to the vector $\vec{M}_{Q}$ . The basic equations for order parameters $M_{Q}^{z}, M_{Q}', M_{z}, M^{\sigma}$ are obtained and the system of these equations is transformed taking into account the U-processes. The particular cases $( \tilde{H} \Vert \vec{M}_{Q} )$ and $( \tilde{H} \bot \vec{M}_{Q} )$ and the case of small arbitrarily oriented magnetic fields $\vec{\tilde{H}}$ are examined in detail. The conditions of the system transition to commensurable and incommensurable SDW state are analyzed. The phase diagram (T,x) at H=0 is traced. The influence of the magnetic field $\vec{\tilde{H}}$ on the temperature of magnetic transition is researched and the aspect of the phase diagram in magnetic field in the cases H ^z H ^σ =0 is presented. The longitudinal magnetic susceptibility χ _∥ which demonstrates that at x<x _c the temperature behavior is similar to the case when the system has a gap, and at x>x _c to a gapless case. At x～x _c in the dependence X _∥(T) a local maximum appears. The influence of the energy spectrum anisotropy on the system’s properties is researched. Also the angular anisotropy of the quantity χ _∥ at different values of T and x is determined.     

Angular Dependence of the Fluctuation Magnetization Vector Above the Superconducting Transition of a Highly Anisotropic High-T c Cuprate

In highly anisotropic cuprate superconductors it is generally accepted that the reversible magnetization vector, $\vec{M}$ , is essentially perpendicular to the superconducting CuO₂ layers in a wide range of crystal orientations with respect to the applied magnetic field, $\vec{H}$ . In a recent work (Mosqueira et al. in Phys. Rev. B 84:134504, 2011) it is shown, however, that the dependence of $\vec{M}$ on the $\vec{H}$ orientation in the reversible mixed state of a high-quality Tl-based cuprate presents a notable deviation from this behavior. Here we extend these measurements to the fluctuation region above T _c , in order to check whether the above-mentioned effect is also present.