Lajos Károly Varga

First, the properties of the linear magnetizing curve and low static permeability are summarized. Second, a design for technical implementation of mechanical stress-induced anisotropy in metal-amorphous nanocomposites (MANCs) is presented. Stress annealing, which creates the conditions for a linear magnetizing curve, is an order of magnitude more effective with Co-based MANCs than with Fe-based ones. Permeabilities between 3000 and 100 and between 100 and 10 can be obtained in Fe- and Co-based nanocomposites, respectively, at similar applied tensile stresses. A measure of linearity is introduced based on the parameters of the hysteresis loop, which is proven to be equal to the fraction of the crystalline phase responsible for the induced anisotropy. Lastly, experimental results concerning linearity and related properties are discussed.

Correlations have been found for the base value of hardness (as the ratio between the heat of fusion and molar volume) and the softening temperature (as the ratio of heat of fusion and specific heat capacity). The relative change of bulk hardness as a function of temperature, H(T), is studied by three new parametric formulas beside the well-known exponential decay and Arrhenius-type expressions. Mathematically, two formulas can be considered as deriving from the exponential decay; the third one is a new rational fraction expression based on the power of normalized temperature. The normalizing temperature is taken as the softening temperature. In the Arrhenius expression, a temperature-dependent activation energy is introduced, which increases steadily with heating but never surpasses the value of self-diffusion. This rational fracture expression has been shown to be applicable to both pure metals and alloys with arbitrary H(T) curve shapes, from convex (pure metals) to concave (alloys). A detailed description of the fitting of these parametric formulas is given, applying the H(T) data from the literature and from our own measurements. Measuring our refractory high entropy alloy (RHEA) samples, an early softening temperature, smaller than the expected half of the melting point (Ts < Tm/2) was detected, signaling a phase instability in the case of Ti-, Zr- and Hf-containing alloys.

First, we discuss a common feature of single-phase pure metals and amorphous and high-entropy alloys: the maximum value of hardness corresponding to a valence electron count (VEC) value of around 6.5–7. This correlation is explained by the coincidence that by subtracting the number of sp valence electrons (Nsp = 2) from the VEC we obtain the maximal number of unpaired d electrons, N_d = 4.5–5 in the 3d, 4d, and 5d rows of transition elements. These unpaired d electrons form orbital overlap bonding, which is stronger than the isotropic metallic bonds of a delocalized electron cloud. The more unpaired d electrons there are, the higher the bonding strength. Second, we will discuss the hardness formulas derived from cohesion energy and shear modulus. We will demonstrate that both types of formulas originate in the electrostatic energy density of metallic bonds, expressing a 1/R⁴ dependence. Finally, we show that only two parameters are sufficient to estimate hardness: the atomic radius and the cohesion-based valence. In the case of alloys, our formula gives a lower bound on the hardness only. It is not suitable for calculation of the hardness increase caused by solid solution, grain size, precipitation, and phase mixture.

Home-built equipment will be presented able to measure the thermal expansion (with a flat indenter) and indentation depth (with a pointed indenter) up to 1100 °C. In dilatometer mode, the allotropic phase transformations can be studied. For hardness, a Rockwell-type measurement is adopted. First, we apply a small load and measure the displacement consisting of a dominant positive thermal expansion and a small negative indentation depth contribution. Then, we repeat the thermal cycle with such a high load that the compensation appears at around 250–300 °C. With increasing temperature, the indentation depth starts to dominate and we can notice a contraction. The indentation depth as a function of temperature, ID(T), will be obtained by subtracting the high load curve from the low load curve. A new rational fraction expression will be tested to describe the thermal softening of pure metals and refractory HEAs. Still, we are working on improving the equipment to extend the working temperature up to 1200 °C.

A home-built equipment will be presented able to measure thermal expansion and indentation up to 1100 oC. The principle of operation is similar to that of Rockwell hardness measurement. First, we apply a small load and measure the thermal expansion of the construction consisting of the sample holder quartz tube, the conical in-denter and the sample. Then we repeat the thermal cycle with such a high load that produces a deviation in thermal expansion already after 200-300 oC, compared to the previous thermal expansion measurement with low load. With increasing temperature, the indentation depth increases and at higher temperatures we already notice a contraction. The evolution of indentation depth as a function of temperature, d(T), we can obtain by sub-tracting the high load curve from the low load curve. Newly created phenomenological expressions will be tested to describe the thermal softening of pure metals and refractory HEAs. The results will be interpreted taking into account the allotropic transformations and temperature dependencies of elastic moduli. We are working on the instrument to extend the working temperature up to 1200 oC.

The big advantage of refractory high entropy alloys (RHEAs) is their strength at high temperatures, but their big disadvantage is their brittleness at room temperature, which prevents their machining. There is a great need to classify the alloys in terms of brittle-ductile (B-D) properties, with easily obtainable ductility indices (DIs) ready to help design these refractory alloys. Usually, the DIs are checked by representing them as a function of fraction strain, ε. The critical values of DI and ε divide the DI—ε area into four squares. In the case of a successful DI, the points representing the alloys are located in the two diagonal opposite squares, well separating the alloys with (B-D) properties. However, due to the scatter of the data, the B-D separation is not perfect, and it is difficult to establish the critical value of DI. In this paper, we solve this problem by replacing the fracture strain parameter with new DIs that scale with the old DIs. These new DIs are based on the force constant and amplitude of thermal vibration around the Debye temperature. All of them are easily available and can be calculated from tabulated data.

According to some recent studies, the magnetoresistance curves of ferromagnetic strip-shaped samples can significantly differ depending on whether the in-plane external applied magnetic field H is oriented in parallel to either the long or the short edge of the strip. To address this problem, in the present work magnetization curves M(H) were measured for similarly shaped samples with both magnetic field orientations used in the magnetoresistance measurements. It was found that the M(H) curves strongly depend on the saturation magnetization and shape of the samples as well as on the magnetic field orientations. For some samples with sufficiently large saturation magnetization, the effective demagnetizing factors could be deduced from the measured M(H) curves. By considering the investigated samples as a ferromagnetic slab, and approximating them with a general ellipsoid, the demagnetizing factors were calculated from known formulae and compared to the experimental values. A fairly good matching was observed, although the latter data were systematically slightly larger, certainly due to the not completely homogeneous magnetization within the rectangular slab as opposed to the case of a general ellipsoid. The differences in the M(H) curves for the two orientations of the magnetic field could be completely attributed to demagnetizing effects.

In order to facilitate the prediction of some physical properties, we propose several simple formulas based on two parameters only, the metallic valence and metallic atomic radii. Knowing the composition, for single-phase alloys, the average parameters can be calculated by the rule of mixture. The input parameters can be obtained from tabulated databases. Adopting from the literature the results of Coulomb crystal model for metals and single-phase high-entropy alloys, we have derived formulas for the shear modulus (G) and the cohesion energy (E_coh). Based on these parameters separately, we set up two formulas to estimate the hardness in the case of pure metals. For single-phase (solid-solution) HEAs, by simplifying the Maresca and Curtin model, we obtained a formula for estimating the hardness, which takes into account the atomic misfit in addition to G. The maximal hardness for single-phase HEA is approximately 600 kg/mm² and is obtained for a composition with a valence electron concentration of approximately 6 ÷ 7.

Multi-component alloys have received increasing interest for functional applications in recent years. Here, we explore the magnetocaloric response for Al–Cr–Mn–Co medium-entropy alloys by integrated theoretical and experimental methods. Under the guidance of thermodynamic and ab initio calculations, a dual-phase system with large magnetic moment, i.e., Al50Cr19Mn19Co12, is synthesized, and the structural and magnetocaloric properties are confirmed via characterization. The obtained results indicate that the selected alloy exhibits a co-continuous mixture of a disordered body-centered cubic and an ordered B2 phase. The ab initio and Monte Carlo calculations indicate that the presence of the ordered B2 phase is responsible for the substantial magnetocaloric effect. The magnetization measurements demonstrated that this alloy undergoes a second-order magnetic transition with the Curie temperature of ∼300 K. The magnetocaloric properties are examined using magnetic entropy change, refrigeration capacity, and adiabatic temperature change. The property-directed strategy explored here is intended to contribute to the study of potential multi-component alloys in magnetocaloric applications.

The present work investigates how the vanadium (V) content in a series of Al₅₀V _x (Cr_0.33Mn_0.33Co_0.33)_(50−x) (x = 12.5, 6.5, 3.5, and 0.5 at.%) high-entropy alloys affects the local magnetic moment and magnetic transition temperature as a step towards developing high-entropy functional materials for magnetic refrigeration. This has been achieved by carrying out experimental investigations on induction melted alloys and comparison to ab initio and thermodynamic calculations. Structural characterization by x-ray diffraction and scanning electron microscopy indicates a dual-phase microstructure containing a disordered body-centered cubic (BCC) phase and a B2 phase with long-range order, which significantly differ in the Co and V contents. Ab initio calculations demonstrate a weaker magnetization and lower magnetic transition temperature (T _C) of the BCC phase in comparison with the B2 phase. We find that lower V content increases the B2 phase fraction, the saturation magnetization, and the Curie point, in line with the calculations. This trend is primarily connected with the preferential partition of V in the BCC phase, which however hinders the theoretically predicted antiferromagnetic B2 phase stabilizing effect of V. On the other hand, the chemistry-dependent properties of the ferromagnetic B2 phase suggest that a careful tuning of the composition and phase fractions can open the way towards promising high-entropy magnetic materials.