The relation between giant magnetoresistance (GMR) and phase separated nanostructures in ${\mathrm{Cu}}_{90}{\mathrm{Co}}_{10}$ is studied using magnetotransport measurements together with transmission electron microscopy and x-ray microanalysis. The samples were melt-spun ribbons isochronally annealed up to 873 K, and all show in their grains a homogeneous spinodal decomposition characterized by long parallel Co-excess stripes. These stripes have 40-nm modulation periods and develop along the crystalline directions of each grain. Different anneals do not change appreciably the observed microstructures, while the magnetoresistance is initially enhanced by a factor of 2, followed by a 35% drop above 823 K. The latter coincides with the observation of a secondary lamellar decomposition of 4 nm modulation length. We propose that the GMR effects in CuCo alloys originate from these nanoscopic modulations of the constituents induced by nonequilibrium processes.

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.

Random sequences attain the highest entropy rate. The estimation of entropy rate for an ergodic source can be done using the Lempel Ziv complexity measure yet, the exact entropy rate value is only reached in the infinite limit. We prove that typical random sequences of finite length fall short of the maximum Lempel-Ziv complexity, contrary to common belief. We discuss that, for a finite length, maximum Lempel-Ziv sequences can be built from a well defined generating algorithm, which makes them of low Kolmogorov-Chaitin complexity, quite the opposite to randomness. It will be discussed that Lempel-Ziv measure is, in this sense, less general than Kolmogorov-Chaitin complexity, as it can be fooled by an intelligent enough agent. The latter will be shown to be the case for the binary expansion of certain irrational numbers. Maximum Lempel-Ziv sequences induce a normalization that gives good estimates of entropy rate for several sources, while keeping bounded values for all sequence length, making it an alternative to other normalization schemes in use.