In this article, we have tried to extend the Neumann–Kopp law concerning the heat capacity of solid compounds to other physical observables for materials represented as mixtures of chemical compounds, alloys, and ceramics. The main goal of this study is to find the intervals of external or internal parameters for a solid compound, within which its physical observable - the magnetic transition temperature for this work, can be expressed in terms of the atomic or molar weighted sum of the magnetic transition temperatures of the constituent elements of a compound. Outside these intervals, we tried to figure out the structure of the variable by which the weighted sum should be multiplied. Thus, for USb–x(ThSb) mixtures with a mole fraction x from 0.36 to 0.55, the magnetic transition temperature of this mixture is expressed in term of the molar weighted sum of the temperature of uranium structural transition associated with a change in the magnetic properties of uranium and of the temperature at which the nature of the magnetic susceptibility of antimony changes. For the magnetic Laves phase compounds Er(Fe_0.8–xMn_0.2–yCo_x+y)₂, the Curie temperature of the compound is equal to the weighted sum of the Curie temperatures of all elements of the compound, except for Mn, at x = 0.1, y = 0 and y = 0.1. For the paramagnetic Curie temperature of intercalated dichalcogenides Cr_xМоSe₂, it can be expressed in terms of the weighted Neel temperature of chromium multiplied by a variable depending on x, on the atomic numbers of all elements of the compound, and on a parameter proportional to the derivatives with respect to x of the dichalcogenide’s crystal lattice parameters.

The Heisenberg {\it ab initio} theory of magnetization is developed to apply for multilayer nanoparticles. The theory is based on distribution and partition functions modification with account the difference between exchange integral and closest neighbour numbers, that change the system of resulting transcendental equation for magnetization and its reversal to form either a paramagnetic type curve or hysteresis loops patterns. The equations are obtained within the Heisenberg partition function construction by Heitler diagonalization of energy matrix via irreducible representations of permutation symmetry group. A combination with the Gauss distribution gives the explicit expression for the partition function in the asymptotic limit] at large spin range in terms of transcendent function. The exchange integral, as a parameter of the equation of state (material equation) is evaluated from Curie temperature value by means of a formula derived within the presented theory. Methods of data processing from the simultaneous solution of the material equation system are proposed. The multi-valued function of hysteresis loop is found by combination of graphical approach and special procedure for elimination of mistaken peaks and prolapses of the patterns. The theory and computation methods are applied to spherical particles with separate surface layers consideration. The contribution of the surface layers, that are specified by number of closest neighbors and exchange integrals into overall magnetization, is studied for two-layer and three-layer models, that are discussed and compared graphically.

The effect of transition metal substitution for Fe and the structural and magnetic properties of Gd2Fe16Ga0.5TM0.5 (TM=Cr, Mn, Co, Ni, Cu, and Zn) compounds were investigated. Rietveld analysis of X-ray diffraction indicates that all the samples crystallize in the hexagonal Th2Ni17 structure. The lattice parameters: a, c and unit cell volume show TM ionic radii dependence. Both Ga and TM atoms show preferred site occupancy for 12j and 12k sites. The saturation magnetization at maximum room temperature was observed for Co, Ni, and Cu of 69, 73, and 77 emu/g, respectively while minimum value was observed for Zn (62emu/g) doping Gd2Fe16Ga0.5TM0.5. Highest Curie temperature of 590 K was observed for Cu doping which is 15% and 5% and thesehigher than Gd2Fe17 and Gd2Fe16Ga compounds, respectively. The hyperfine parameters viz. hyperfine field and isomer shift, show systematic dependence on the TM atomic number. The observed magnetic and Curie temperature behavior in Gd2Fe16Ga0.5TM0.5 is explained on the basis of Fe(3d)-TM(3d) hybridization. The superior Curie temperature and magnetization value of Co, Ni, and Cu doped Gd2Fe16Ga0.5TM0.5 compounds as compared to pure Gd2Fe17 or Gd2Fe16Ga makes Gd2Fe16Ga0.5TM0.5 a potential candidate for high-temperature industrial magnet applications.

In this article, the effect of substitution of Zr and Ga in Dy2Fe17 prepared by arc melting technique are studied. The substitution of Zr and Ga in Dy2Fe17 was found to have an important effect on their structure and magnetic properties. The Rietveld analysis conformed that the crystalline system wereTh2Ni17 structure. Lattice parameters a (Å) and c (Å), unit cell volume (Å3), bonding distance (Å) were calculated by using Rietveld analysis. The unit cell volume of Dy2Fe17-xZrx and Dy2Fe16Ga1-xZrx increase linearly with the Zr and Ga substitution. The substitution of Zr and Ga are limited up to x=1 in order to avoid the decrease in saturation magnetization. The Curie temperature (Tc) of Dy2Fe17-xZrx and Dy2Fe16Ga1-xZrx are found to be Zr content dependent. The Curie temperature is found to be increasing first and then decrease for higher Zr content. The maximum curie temperature was observed 510K at x = 0.75 for Dy2Fe17-xZrx and 505.1 K at x = 0.5 for Dy2Fe17-xZrx which are102 K and 97 K higher than Dy2Fe17. The room temperature Mössbauer analysis shows the decrease in average hyperfine field and increase in isomer shift with Zr doping.

Physical roots, exemplifications and consequences of periodic and aperiodic ordering (represented by Fibonacci series) in biological systems are discussed. The role and physical and biological roots of symmetry and asymmetry appearing in biological patterns is addressed. Generalization of the Curie-Neumann Principle as applied to biological objects is presented, briefly summarized as: “asymmetry is what creates a biological phenomenon”. The “up-bottom approach” and “bottom up” approaches to the explanation of symmetry in organisms are presented in detail. The “up-bottom approach”, implies that the symmetry of the biological structure follows the symmetry of media in which this structure is functioning; the “bottom-up” approach, in turn, adopt that the symmetry of biological structures emerges from the symmetry of molecules constituting the structure. A diversity of mathematical measures applicable for quantification of ordering in biological patterns is introduced. The continuous, Shannon and Voronoi measures of symmetry/ordering and their application to biology objects are addressed. The fine structure of the notion of “ordering” is discussed. Informational/algorithmic roots of ordering inherent for the biological systems are considered. Ordered/symmetrical patterns provide economy of biological information, necessary for algorithmic description of a biological entity. Application of the Landauer principle bridging physics and theory of information to the biological systems is discussed.

A time interval only description necessarily needs its own independent definitions, without one moment time coordinates to it. In this paper derived are time interval only set properties, including commutation relations, addition, multiplication and derivatives. Time interval only set commutation relations, consistent with one moment time set properties, are introduced by defining correspondence relations for these sets. Time development and equilibrium within the time interval description depend on the well-known ‘mean velocity theorem’ and the time interval version of the Legendre transform. In contrast, usually applied is only the traditional vector and one moment time coordinate kinematic approach from Newton’s laws. The main results of this paper are correspondences and time interval only set commutation relations. All other properties are derived from these results, while for the time interval only set, different from the one moment time set the canonical property is not valid. The time interval only description can be applied assuming spherical symmetric star-source radiation propagation, with finite time intervals for realistic measurement events. From time development with (a-)symmetry of time intervals, and from Curie’s principle, change can be described with a set theoretic approach. Time interval only set properties include the time interval only version of Noether charges and structure constants. A time interval only description for wave propagation, including group-velocity, for zero and non-zero mass wave particles, relates to the properties of the time interval only set. A second result in terms of the time interval only description is propagation wave energy equivalence with gravitation energy, derived from time interval only set commutation relations. A time interval approach, however including one moment time description dependence, was introduced in earlier publications of this author. In part 1 investigated are the time interval only set and its properties, a forthcoming part 2 to application of the time interval only description to specific groups of stars as emission sources.