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It is shown how to reconstruct the stacking sequence from the pairwise correlation functions between layers in close-packed structures. First, of theoretical interest, the analytical formulation and solution of the problem are presented when the exact pairwise correlation counts are known. In the second part, the practical problem is approached. A simulated annealing procedure is developed to solve the problem using as initial guess approximate solutions from previous treatments. The robustness of the procedure is tested with synthetic data, followed by an experimental example. The developed approach performs robustly over different synthetic and experimental data, comparing favorably with the reported methods.

This is the second contribution in a series of papers dealing with dynamical models in equilibrium theories of polytypism. A Hamiltonian introduced by Ahmad & Khan [Phys. Status Solidi B(2000),218, 425–430] avoids the unphysical assignment of interaction terms to fictitious entities given by spins in the Hägg coding of the stacking arrangement. In this paper an analysis of polytype generation and disorder in close-packed structures is made for such a Hamiltonian. Results are compared with a previous analysis using the Ising model. Computational mechanics is the framework under which the analysis is performed. The competing effects of disorder and structure, as given by entropy density and excess entropy, respectively, are discussed. It is argued that the Ahmad & Khan model is simpler and predicts a larger set of polytypes than previous treatments.

Written language is complex. A written text can be considered an attempt to convey a meaningful message which ends up being constrained by language rules, context dependence and highly redundant in its use of resources. Despite all these constraints, unpredictability is an essential element of natural language. Here we present the use of entropic measures to assert the balance between predictability and surprise in written text. In short, it is possible to measure innovation and context preservation in a document. It is shown that this can also be done at the different levels of organization of a text. The type of analysis presented is reasonably general, and can also be used to analyze the same balance in other complex messages such as DNA, where a hierarchy of organizational levels are known to exist.

We present the colloidal synthesis of gold nanoparticles (Au NPs) using the chemical reduction of gold precursors by changing the reducing agent (Na3C6H5O7) volume. We aimed at achieving different particle sizes, morphologies, and defect structures. The modified process impacted the overall synthesis time and nanoparticles' microstructures. We used X-ray diffraction profile analysis (XPA) and transmission electron microscopy (TEM) to follow the nanoparticles’ size and lattice strain details. The NPs' size distributions agree well between the indirect XPA and TEM direct measures. Nanocrystal shapes change from triangular, octahedral, and decahedral to hexagonal plate-like; it shows how the NPs minimize their energy formation by creating defects and well-defined crystallographic directions, including crystal fusion. The combined effects of dislocations, twin boundaries, and surface tension add together to broaden the diffracted line profiles. In particular, the density of dislocation and twin boundaries increase toward the smaller NPs.

The correlated biased random walk with latency in one and two dimensions is discussed with regard to the portion of irreducible random movement and structured movement. It is shown how a quantitative analysis can be carried out by using computational mechanics. The stochastic matrix for both dynamics are reported. Latency introduces new states in the finite state machine description of the system in both dimensions, allowing for a full nearest neighbor coordination in the two dimensional case. Complexity analysis is used to characterize the movement, independently of the set of control parameters, making it suitable for the discussion of other random walk models. The complexity map of the system dynamics is reported for the two dimensional case.

A recently introduced model of coupled non linear oscillators in a ring is revisited in terms of its information processing capabilities. The use of Lempel-Ziv based entropic measures allows to study thoroughly the complex patterns appearing in the system for different values of the control parameters. Such behaviors, resembling cellular automata, have been characterized both spatially and temporally. Information distance is used to study the stability of the system to perturbations in the initial conditions and in the control parameters. The latter is not an issue in cellular automata theory, where the rules form a numerable set, contrary to the continuous nature of the parameter space in the system studied in this contribution. The variation in the density of the digits, as a function of time is also studied. Local transitions in the control parameter space are also discussed.

International audience; Extrinsic faulting has been discussed previously within the so-called difference method and random walk calculation. In this contribution it is revisited under the framework of computational mechanics, which allows expressions to be derived for the statistical complexity, entropy density and excess entropy as a function of faulting probability. The approach allows one to compare the disordering process of an extrinsic fault with other faulting types. The "-machine description of the faulting mechanics is presented. Several useful analytical expressions such as probability of consecutive symbols in the Hä gg coding are presented, as well as hexagonality. The analytical expression for the pairwise correlation function of the layers is derived and compared with results previously reported. The effect of faulting on the interference function is discussed in relation to the diffraction pattern.

An inventory of all possible homogenous Hilbert curves in two dimensions are reported. Six new Hilbert curves are described by introducing the reversion operation in the construction algorithm. For each curve, the set of affine transformation defining the generation process is reported. Finally, each curve is also described in terms of a tag system., Comment: accepted in "Applied Mathematics and Computation"

While there has been a keen interest in studying computation at the edge of chaos for dynamical systems undergoing a phase transition, this has come under question for cellular automata. We show that for continuously deformed cellular automata there is an enhancement of computation capabilities as the system moves towards cellular automata with chaotic spatiotemporal behavior. The computation capabilities are followed by looking into the Shannon entropy rate and the excess entropy, which allows identifying the balance between unpredictability and complexity. Enhanced computation power shows as an increase of excess entropy while the system entropy density has a sudden jump to values near one. The analysis is extended to a system of non-linear locally coupled oscillators that have been reported to exhibit spatiotemporal diagrams similar to cellular automata., Comment: Accepted in CHAOS

Magnetic measurements, X-ray diffraction and scanning electron microscopy (SEM) experiments were carried out in the as-cast Gd ( Co 1 − x Cu x ) 5 samples with different Co/Cu content. Already in the as cast state, this system shows high coercive field for x=0.3 and a magnetization driven by nucleation of reversal domain. SEM micrograph and microanalysis show possible spinodal decomposition in the as-cast state, hence regions with different Co/Cu-content are observed, while the Gd-content almost does not change. High resolution X-ray diffraction patterns show a main CaCu5-type structure with traces of a secondary phase and distorted peak profiles as function of the Cu content. The evolution of the microstructure is discussed in relation with the Cu incorporation into the CaCu5-type structure. The Cu addition avoids the formation of the 2:7 phase within the 1:5 matrix, favoring the formation of a more homogeneous Gd(Co,Cu)5 phase. The relation between the observed microstructure and the magnetic behavior is also discussed.

The stacking problem is approached by computational mechanics, using an Ising next nearest neighbor model. Computational mechanics allows to treat the stacking arrangement as an information processing system in the light of a symbol generating process. A general method for solving the stochastic matrix of the random Gibbs field is presented, and then applied to the problem at hand. The corresponding phase diagram is then discussed in terms of the underlying $\epsilon$-machine, or optimal finite state machine, describing statistically the system. The occurrence of higher order polytypes at the borders of the phase diagram is also analyzed. Discussion of the applicability of the model to real system such as ZnS and Cobalt is done. The method derived is directly generalizable to any one dimensional model with finite range interaction.

It is described and explained the dynamics of the transition from in-plane to perpendicular magnetization for dipolar films with close packed structures when the c/a ratio, with c the interlayer separation and a the two-dimensional lattice constant, is varied. Several arrangements of distinct number of stacked layers are considered. Magnetization switching follows a mechanism based on the role of the interlayer coupling, which is understood as the contribution of the interaction between dipoles of different layers to the studied effects. Calculations for sufficiently low temperatures show that each magnetic configuration transition leaves a fingerprint as an entropy maximum when the latter is plotted as a function of c/a. Thus the entropy allows to determine the c/a range of stability of the different magnetic patterns.

A previously introduced formalism for calculating magnetic dipolar anisotropy energy Δ U in atomic layered structures is further developed. Numerical results are presented for ultrathin films with different close-packed (face centered cubic (FCC) [1 1 1]) and non-close-packed (FCC [0 0 1] and body centered cubic (BCC) [0 0 1]) structures. Structural effects become apparent in the magnetocrystalline dipolar anisotropy energy Δ U L when the ratio between the interlayer separation c and the 2D lattice constant a is changed. Despite the long-range character of the dipolar interaction, it is shown that the number of significantly interacting layers, conventially called coupled layers, is limited and depends on the structural aspect ratio c / a . The slope in the observed linear dependence between Δ U L and the inverse of the film thickness t is explained by the number of the so-called coupled layers, and not by a surface contribution to volume values. Size effects appearing in Δ U are unambiguously distinguished from structural effects. Effective anisotropy energy Δ U eff and Δ U are presented for Co [0 0 0 1] and Ni [0 0 1] ultrathin films. It is verified that the dipolar interaction makes an important contribution to Δ U eff , but the spin reorientation transition is determined by non-dipolar interactions. The former favors the magnetization switching only when the size aspect ratio d / t , with d the characteristic lateral dimension of the film, is sufficiently small. Applications to other layered arrays of magnetic dipoles are straightforward.

The magnetostatic interaction in a pure dipole system with constant magnetization is studied. The system consists of identical hexagonal close packed monoatomic layer of dipoles stacked according to some rule. The influence of the interlayer/intralayer atomic distance ratio (c/a) on the dipolar configuration and stability is analyzed. It is found that for the ideal ratio the stacking sequence is irrelevant; however, it becomes significant when its value is sufficiently small, and the sequence type affects the dipolar field and the anisotropy energy. The most stable in-plane configuration is that of the rhombohedral stacking 3R, while the stacking showing a lower energy difference between the axial and planar magnetization configuration is the hexagonal close packed 2H. The dependence of the magnetostatic anisotropy with layer thickness is also studied.

Investigations of the magnetic properties of NbFe 2 were performed by measuring the temperature dependence of hysteresis loops, initial AC-susceptibility and zero field cooled (ZFC)–FC magnetizations in a wide field range of 50 Oe⩽ μ 0 H ⩽8000 Oe. Two well-defined peaks, at 4.8 and 21.4 K, were found in the AC-susceptibility curve, and only the first peak is sensible to a frequency change of the applied field. The peak changes to high temperature and its intensity decreases with increasing frequency, thus showing a relaxation phenomenon. In ZFC magnetization at 50 Oe, the peaks occur at 3.4 and 21.4 K. With increasing DC field, both peaks are shifted to low temperatures; however, the first peak disappears at fields higher than 100 Oe and a field higher than 1250 Oe suppresses the second peak. A third maximum merges from the magnetization curve at around 7 K in a field of 500 Oe, in which case, the maximum is suppressed by an external field higher than 4000 Oe. One can suggest that the ordered state of the stoichiometric NbFe 2 is a spin density wave (SDW) and both ferro- and antiferromagnetic spin fluctuations coexist.

This paper describes a new measuring system to perform local area magnetization measurements on the surface of a magnetic sample in a pulsed field magnetometer at room temperature. A commercial point pick-up coil is used to detect the induction signal along the radius of samples with cylindrical or disc shapes. The relationship between the induced voltage and the sample geometry is treated and a calibration procedure is proposed to obtain the magnetization values in physical units for the case when the point pick-up coil is at the centre of the sample. The local demagnetizing factor is obtained using the measurement of the local anisotropy field applying the single-point detection (SPD) technique. The measurement of this SPD singularity detected in the transverse reversible susceptibility, using a sample with cubic geometry, is demonstrated for the first time in this type of magnetometer. The application of the system for the investigation of commercial permanent magnets is illustrated, and the advantages and disadvantages are discussed.

The use of Hilbert curves to visualize massive vector of data is revisited following previous authors. The Hilbert curve mapping preserves locality and makes meaningful representation of the data. We call such visualization as Hilbert plots. The combination of a Hilbert plot with its Fourier transform allows to identify patterns in the underlying data sequence. The use of different granularity representation also allows to identify periodic intervals within the data. Data from different sources are presented: periodic, aperiodic, logistic map and 1/2-Ising model. A real data example from the study of heartbeat data is also discussed., Accepted at Computer Physics Communications

We explore the relation of nanostructures with the appearance of giant magnetoresistance (GMR) in melt-spun CuCo ribbons. We find by energy-filtered transmission electron microscopy that the ribbons are composed of a periodic distribution of Co within the Cu, as in spinodal decomposition. The lamellar structure should thus be associated with GMR, as only a small percentage of the Co is present in the form of grains. This is counterintuitive, for no clear interfaces are present as required by standard models, and the period of the composition oscillation (43–52 nm) is an order of magnitude larger than the mean free paths for electrons. Upon annealing, a secondary spinodal decomposition appears following the same direction as the original.

High-resolution X-ray diffraction patterns of Fe 78.5 Si 20 Ta 1.5 and Fe 80− x Si 20 Nb x ( x =0.5, 3.0, 10) show the existence of a metastable hexagonal phase (NbFe 2− x Si x and TaFe 2− x Si x ) together with bcc-Fe 100− y Si y solid solution and an amorphous matrix. The grain size of the bcc-Fe 100− y Si y phase decreases with increasing Nb content in Fe–Si compounds resulting in nanocrystalline materials. On the other side, the micro-strain, the lattice constant, coercivity and the Curie temperature increase with Nb concentration. Enhancements of the local strain and local magnetic anisotropy were also observed by means of NMR measurements. On the contrary, the addition of Cr causes a decrease in the coercivity and Curie temperature.

Alternative formulas are given to compute the number of crystallographically nonequivalent monoatomic close packed polytypes of length N: Γ(N). A formula giving the number of sequence, Ω(N), of length N which complies with the neutrality condition (#1 – #0 = 0 mod 3) is deduced. The asymptotic behavior of both Γ(N) and Ω(N) are given.

The structural evolution with increasing Nb content in Fe 80− x Si 20 Nb x alloys (0 x ≤ 12) was investigated by means of high-resolution X-ray diffraction. A metastable NbFe 2− x Si x hexagonal phase was found together with cubic bcc Fe 100− y Si y solid solution and the amorphous matrix. The grain size of the bcc Fe 100− y Si y phase and the strain were determined and their dependencies on the Nb content and heat treatment of the samples were investigated. The strain increases and the grain size decreases with an increasing of Nb content reaching a size down to 37 nm. Upon heat treatment of the samples, the hexagonal phase decomposes in two hexagonal phases with similar compositions.

A systematic use of binary codes derived from the Hagg symbol are used to study close-packed polytypes. Seitz operators acting over the corresponding binary codes are defined and used. The number of non-equivalent polytypes of a given length are calculated through the use of the Seitz operators. The same procedure is applied to the problem of counting the number of polytypes complying with a given symmetry group. All counting problems are reduced to an eigenvector problem in the binary code space. The symmetry of the binary codes leads to the different space groups to which polytypes can belong.

The implication of the use of particular peak profile functions in the fit of diffraction data on the nature and density of stacking faults in layered solids is studied. Common type of profile functions are studied: Gauss, Lorentz, pseudoVoigt and Pearson VII. An additional peak profile is introduced. For each profile function the decaying term of the probability correlation function is determined and the expression for the correlation length is deduced. The form of the asymmetric component of each profile is also reported. Experimental data is fitted using each profile and the results are discussed. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

We have investigated ribbons of the alloy series Cu1−xCox (x=0.05, 0.10, 0.15, and 0.20) using transmission electron microscopy and magnetotransport measurements to correlate nanostructural transformations to its giant magnetoresistance (GMR) behavior. Instead of dealing with a simple granular system, as it is commonly assumed, we show that spinodal decomposition in the form of lamellar phases is in fact the common feature observed in these materials, and that GMR is seen whenever this decomposition is observed. The formation of these nanoscopic lamellae as metastable segregated phases can be understood via a Cahn–Hilliard analysis.

Two different small flat pick-up coil (FPC) devices, a flat pick-up coil developed at the TU-Vienna using a thin film technique, and a wire-wound flat pick-up coil commercially available, are compared for the characterization of magnetic materials in high pulsed magnetic fields. The FPC devices allow measuring the local surface magnetization. A small Hall probe to perform local magnetization measurements at high pulse field was also tested. The non-linear dependence of such probe was corrected mathematically and the results were compared with pick-up coils measurements. Magnetic viscosity measurement using the Hall probe is presented.

The so-called direct solution of the powder diffraction pattern for a faulted layered crystal is discussed. It is shown how, in the general case, peak profiles can be split into a symmetric and an antisymmetric component. The relationships between peak profile parameters and the underlying faulting structure, as given by the probability correlation function, are evidenced. The formalism reduces to known equations when applied to particular faulting models. Warren's equations for peak profile of fcc materials with {111} planar faulting are derived within the framework of a general theory. Possible strategies for incorporating the proposed formalism into a general powder pattern refinement procedure are also discussed.

We studied the microstructural transformations of Co 10 Cu 90 ribbons by analyzing the in situ resistivity versus temperature, the giant magnetoresistance (GMR) and Transmission Electron Microscopy (TEM) images for isochronous treatments interrupted at different temperatures T f =494–873 K. Resistivity results indicate that several processes take place during the annealing and they should relate to the changes in GMR. The largest GMR (25% at 4.2 K) is close to the second maximum in resistivity, with T f being at about 823 K, while for higher T f , GMR decreases abruptly. All samples show grains with a spinodal decomposition characterized by long stripes with periods from 30 to 45 nm running across the whole grain. For T f >823 K some grains show large Co precipitates, about 30 nm in size, indicating nucleation processes as well. At T f =873 K there is an additional finer decomposition starting at the grain boundaries. The abrupt decrease in GMR coincides in temperature with the latter decomposition. Therefore, the usual description of these materials as purely granular systems is insufficient to explain magnetoresistance effects.

Planar faulting in R2Co17 intermetallic alloys were studied by high-resolution X-ray diffraction. For the light rare-earth elements, the Th2Zn17 rhombohedral structure is found, while for the heavy rare-earth atoms, the Th2Ni17 structure prevails. For intermediate rare-earth atom, the R2Co17 structure shows planar disorder. The occurrence of planar faulting is associated with the interlayer distance in the structure. A correlation was found between interlayer distance and stacking order. Simple qualitative explanation is given for the energy preference for one particular type of stacking order. Planar disorder does not introduce new nearest-neighbors environments for the rare-earth atoms apart from those already found in the hexagonal and rhombohedral variants, but merely changes the probability of occurrence of each neighborhood. Simple stacking fault models should prove insufficient to explain the observed planar disorder.

The practical aspects of a recently deduced formalism for the direct solution of the powder diffraction pattern of a layer crystal are addressed. It is shown that the obtained solution is particularly well suited to combination with a deconvolution procedure based on a series development of the peak profile. The influence of noise and step size on the obtained solution is discussed. Computer simulation is used to assess the robustness of the proposed procedure. The developed procedure is applied to a powder sample of Y2Co17that is affected by planar disorder.

Hysteresis loops in SmCo5−xCux as-cast and annealed magnets (1

Magnetic measurements, X-ray and microstructural studies are carried out in as-cast and in annealed Sm(Co 0.5 ,Cu 0.5 ) 5 showing high coercive field. In the as-cast state three regions with different (Sm, Co, Cu)-content were found. The annealed samples showed a more homogenised composition but still with a two region microstructure. One of the regions has a higher (Sm, Cu)-content. X-ray diffraction patterns show only a CaCu 5 -type structure while microprobe analysis shows a higher Sm content than the Sm(Co, Cu) 5 composition for all regions in the as-cast and the annealed sample. Optical micrographs and Kerr microscopy show for the annealed sample grains with heavy faulting. The evolution of the microstructure upon annealing is discussed in relation with the Sm excess and Cu incorporation into the CaCu 5 -type structure. The relation between the observed microstructure and the magnetic behaviour is also discussed.

Microstructural studies were performed in Sm(Co 1− x Cu x ) 5 alloys with x =0.0, 0.2, 0.3, 0.4 and 0.5. The coercivity increases with Cu content in the studied range of compositions, while the Curie temperature decreased. X-ray diffraction only showed the presence of the hexagonal CaCu 5 -type structure belonging to a Sm(Co,Cu) 5 phase in all the studied compositions. The solubility of excess Sm in the Sm(Co,Cu) 5 phase increases with Cu content. The x =0.3 sample showed needle-like coherent precipitates inside the matrix grains and platelet precipitates at grain boundaries. Both precipitates had a composition close to a Sm 2 (Co,Cu) 7 phase. The x =0.5 sample showed a different microstructure with regions which are thought to be the result of twinning. Evidence of heavy faulting was also found. The occurrence of a disordered CaCu 5 -type structure with Sm excess is discussed in terms of its possible magnetic significance in the observed pinning driven magnetization mechanism.

Transmission electron microscopy studies have been carried out in heat-treated Sm(Co 0.5 Cu 0.5 ) 5 samples. The occurrence of heavily planar faulted regions have been observed. X-ray microanalysis shows a relative increase of Sm and Cu content in the faulted regions compared to the non-faulted ones. The origin and type of disorder is discussed from the crystallographic point of view and related to the pinning magnetisation mechanism reported for this type of alloy.

PbFe 12 O 19 powders were obtained by thermal decomposition of hydroxide–carbonate coprecipitated salts and metal–organic precursors at 920°C. Significant microstructural differences have been found between both specimens. The MOD powder comprised submicronic particles of remarkably high coercivity (5 kOe), and the magnetization mechanism was dominated by coherent rotation. In contrast, the coercivity for chemically coprecipitated powders was very poor (1.6 kOe), when compared with Ba- and Sr-compounds prepared following the same method, a behavior associated with excessive grain growth. Cell parameters, microstructure, Curie temperature, hysteretic properties, anisotropy field and the saturation magnetization as a function of the temperature in the interval 77–300 K are reported.

Magnetic transitions of the melt-spun Fe 70 Si 20 Nb 10 and Fe 77.9 Si 12.1 Nb 10 ribbons were investigated by means of temperature dependence of the initial AC-susceptibility measurements on these ribbons, and additionally, on stoichiometric and off-stoichiometric NbFe 2 . The coexistence of nanocrystalline BCC Fe–Si and hexagonal Nb(Fe 1+ y Si y ) 2 could be evidenced from these measurements and also from Mossbauer experiment.

The coercive field of the as-cast Fe 68 Si 20 Nb 12 and Fe 60 Si 20 Nb 20 ribbons decreases with increasing temperature abruptly up to 35 K, then slowly up to around 200 K. Above this temperature the coercive field increases. Qualitatively this is attributed to the point that this unusual coercive field curve behavior is related mainly to the nano-crystalline material containing two nanocrystalline phases (BCC Fe–Si and hexagonal NbFe 2 - y Si y ), where exchange interactions among these small particles occur. The fraction of the hexagonal phase increases with increasing Nb and after annealing decomposes in two hexagonal phases with similar composition. For the Fe 60 Si 20 Nb 20 alloy the quantity of NbFe 2 - y Si y nanocrystallites is almost the same of that BCC Fe–Si particles.