Direction Of Temperature Gradient Research Articles

Bimodal structure formation and texture transition mechanism in laser remelted Mg–Al-based alloy

Texture inheritance, texture weakening, and a complete texture transition within different solidified molten pool (MP) have been achieved by manipulating various processing parameters of conduction mode in laser remelted magnesium-aluminum (Mg–Al)-based AZ31 alloy. At a low laser power (P = 100 W), restricted number of temperature gradient directions on moving solid/liquid (S/L) interfaces within small MP leads to strong texture inheritance. Tilting angles 20°–45° away from building direction (B.D.) in {0001} plane is a preferential growth direction of texture inheritance. In contrast, spontaneous texture weakening has occurred due to frequently varied temperature gradient directions within increasing MP size in higher P cases. Meanwhile, increasing scanning speed V has a significant effect on weakening the texture as well as refining grains in the solidified MP. Furthermore, fine grains formation with random orientations in MP bottom at both high P (400 W) and high V (20, 30, and 50 mm/s) leads to the occurrence of a bimodal structure, which is affected by solidification characteristics as well as thermal convection. For the case of the highest P and the highest V, a texture transition has occurred as tilting angles of 45°–90° away from B.D. in {0001} plane within MP, compared to 0°–45° texture of base material for the Mg–Al-based alloy in the study.

Disrupting variant selection memory effect in laser powder bed fusion to improve strength-ductility synergy of Ti-6Al-4V alloys

Texture formation is frequently observed in parts produced by Laser Powder Bed Fusion (L-PBF), which can induce anisotropy and may potentially degrade plasticity. In this study, we introduce a laser remelting strategy to mitigate these adverse effects. By employing experimental observations and numerical simulations, we established the relationship between melt pool thermal history, variant selection, and mechanical properties. Our results indicate that the strengthening of texture can be prevented by disrupting the variant selection memory effect when there is a difference in scanning speeds between the printing and remelting lasers. The achieved random variant orientation is attributed to the altered cooling rates and temperature gradient directions during solidification across different layers. The optimized Ti-6Al-4V alloy demonstrates high strength (1211.5 ± 13 MPa) and significant elongation (12.3% ± 0.8%), exhibiting a superior strength-ductility synergy compared to samples produced by direct printing or laser remelting with consistent parameters, as well as most reported L-PBF processed Ti-6Al-4V alloys. Our findings provide new insights into phase transformation kinetics in L-PBF of Ti-6Al-4V alloys and facilitate the optimization of this process for manufacturing high-performance components.

Microstructural characterization of Stellite 6 alloy processed by electron beam melting

Stellite 6 alloy was subjected to electron beam melting (EBM) processing in this study. The main phases in the alloy are α-Co, ε-Co, M23C6 (M = Cr, Co, W, etc.), and M7C3 (M = Cr, Co, W, etc.) carbides. The microstructure of the EBM-processed Stellite 6 alloy comprises grains of relatively uniform sizes, with an average grain size of 11.1 μm. There is a relatively minor internal strain within the alloy. The majority of grains exhibit low intragranular misorientations, approximately around 0.5°, while a minority of grains display relatively larger intragranular misorientations, around 2.8°. The dominant {100} texture was developed in the build direction because of the fast growth of the <100> direction for a cubic crystal structure during solidification. The vertically aligned columnar grains contribute to the development of the <100> texture along the build direction. The elongated direction of columnar grains was parallel to the temperature gradient direction. This competitive growth direction at the solid-liquid interface results in slight tilts in the pole figures. The eutectic carbide phases are uniformly distributed along the grain boundaries. The cube–cube orientation relationships between the matrix and M23C6 carbide phase were identified as [001]α//[111]M23C6. The low stacking fault energy of the Stellite 6 alloy resulted in the formation of a high density of stacking faults within the grains. The interactions between stacking faults of different orientations were observed. Primary M7C3 carbides were found to transform into secondary M23C6 carbides, with a phase transition process observed where secondary carbides M23C6 surrounded primary carbides M7C3.

Manipulating scanning strategies towards controlled microstructure of laser remelted Mg–3Al–1Zn alloy

Various laser scanning strategies of multitrack products, consisting of a default Raster pattern (R1), a Raster pattern with a changed line order (R2), and a default Zigzag pattern (Z1), with different overlap rates ranged from 0.7 to 0.5, have been conducted to investigate microstructure evolution for Mg–3Al–1Zn alloy. As the overlap rate changes from 0.7 to 0.5, the average grain size decreases and the texture is slightly concentrated, except for R2 pattern. For effect of different scanning pattern, a relatively small average grain size can be obtained using the R1, R2 patterns compared to using the Z1 pattern; a relatively weak texture can be obtained using the R1, Z1 patterns compared to using the R2 pattern. The utilization of Z1 pattern results in a further texture weakening compared to that of the R1 pattern. Microstructure evolution of scanning strategy is mainly determined by low-undercooling-required epitaxial growth along temperature gradient directions at the solid/liquid interface. Combined with computational thermal-fluid dynamics simulation, a strong fluid flow within the molten pool promotes side expansion of the molten pool, resulting in the larger overlap area, the corresponding three-times remelting domain and continuous deflections of grain major axes.

Numerical investigation of parameter distributions in high-temperature PEMFCs under various cooling surface temperature gradients

Non-uniform current density distribution can lead to localized hotspots, resulting in shortened lifespans of fuel cells. The temperature distributions on the bipolar plate cooling surface significantly influence various parameters within a fuel cell. This study develops a mathematical model for a high-temperature proton exchange membrane fuel cell (HT-PEMFC) to simulate its operation in four different directions of temperature gradient on the cooling surface. The distributions of membrane temperature, proton conductivity, oxygen concentration, activation loss, and current density were obtained to clarify the interaction mechanism between cooling surface temperature and these parameters in fuel cell. The results show that the membrane temperature and proton conductivity increase and the oxygen concentrations decrease with increasing cooling surface temperature. A lower temperature in the catalyst layer regions leads to a decrease in the current density. In particular, when the cooling surface temperature distribution is characterized by a temperature decrease in the upstream area with a high reactant concentration and an increase in the downstream area with a low reactant concentration, the fuel cell has an excellent current density uniformity, which reaches 92.61 % at a voltage of 0.6 V and a cooling surface temperature difference of 10 K.

Grain growth competition and formation of grain boundaries during solidification of hcp alloys

Grain growth competition during directional solidification of a polycrystal with hexagonal (hcp) symmetry (Mg-1wt%Gd alloy) is studied by phase-field modeling, exploring the effect of the temperature gradient G on the resulting grain boundary (GB) orientation selection. Results show that selection mechanisms and scaling laws derived for cubic (fcc, bcc) crystals also apply to hcp materials (within their basal plane), provided a re-estimation of fitting parameters and re-scaling to account for the sixfold symmetry. While grain growth competition remains stochastic with rare events of unexpected elimination or side-branching along the developing GBs, we also confirm an overall transition from a geometrical limit to a favorably oriented grain limit behavior with an increase of thermal gradient within the dendritic regime, and the progressive alignment of dendrites and GBs toward the temperature gradient direction with an increase of G during the dendritic-to-cellular morphological transition. Comparisons with original thin-sample directional solidification experiments show a qualitative agreement with PF results, yet with notable discrepancies, which nonetheless can be explained based on the stochastic variability of selected GB orientations, and the statistically limited experimental sample size. Overall, our results extend the understanding of GB formation and grain growth competition during solidification of hcp materials, and the effect of thermal conditions, nonetheless concluding on the challenges of extending the current studies to three dimensions, and the need for much broader (statistically significant) data sets of GB orientation selected under well-identified solidification conditions.

Modeling of anomalous thermal conduction in thermoelectric magnetohydrodynamics: Couette formulation with a multiphase pressure gradient

A metal/liquid-metal junction is a practical thermoelectric cell causing heat absorption or release according to the direction of electric current and temperature gradient. During thermoelectric processes, the possibility of activating the anomalous heat transfer is considered in this work based on adopting a fractional version of Jeffreys equation with three fractional parameters. Because of the connection between the mean-squared displacement of diffusive hot particles and the thermal conductivity, the fractional Jeffreys law is employed to simulate the low thermal conductivity with crossovers; accelerated or retarded transition, and the transition from high (superconductivity—above the Fourier heat conduction) to low (subconductivity—below the Fourier heat conduction) thermal conductivity. The Couette formulation describing a pressure-driven flow of a viscous thick liquid-metal layer bounded by two similar metallic plates, in the presence of a constant transverse magnetic field, is investigated. A triple-phase pressure gradient, consisting of the phases: (i) ramp-up, (ii) dwell, and (iii) exponential decay, is applied as a real-life flow cause and compared with the classical constant pressure gradient and the impulsive pressure gradient case. The velocity and temperature are obtained in the Laplace domain, and then a suitable numerical technique based on the Fourier series approximation is used to recover the solutions in the real domain. It is found that the retarded crossover of low thermal conduction shows “ultraslow” temperature propagation within the thick layer, which indicates to a case of ultralow heat conduction. As well as the strong correlation between the pressure gradient type (constant, impulsive, or three-phase) and direction (favorable or adverse) and its induced velocity, the temperature gradient between the two plates plays a key role in the determination of the velocity direction and magnitude.

Mixed Convection in an Idealized Coastal Urban Environment With Momentum and Thermal Surface Heterogeneities

AbstractCoastal marine heatwaves (MHWs) modulate coastal climate through ocean‐land‐atmosphere interactions, but little is known about how coastal MHWs interact with coastal cities and modify urban thermal environment. In this study, a representative urban coastal environment under MHWs is simplified to a mixed convection problem. Fourteen large‐eddy simulations (LESs) are conducted to investigate how coastal cities interact with MHWs. We consider the simulations by simple urban roughness setup (Set A) as well as explicit urban roughness representation (Set B). Besides, different MHW intensities, synoptic wind speeds, surface fluxes of urban and sea patches are considered. Results suggest that increasing MHW intensity alters streamwise potential temperature gradient and vertical velocity direction. The magnitude of vertical velocity and urban heat island (UHI) intensity decrease with increasing synoptic wind speed. Changing urban or sea surface heat flux also leads to important differences in flow and temperature fields. Comparison between Set A and B reveals a significant increase of vertical velocity magnitude and UHI intensity. To further understand this phenomenon, a canopy layer UHI model is proposed to show the relationship between UHI intensity and urban canopy, thermal heterogeneity and mean advection. The effect of urban canopy is considered in terms of an additional vertical velocity scale that facilitates heat transport from the heated surface and therefore increases UHI intensity. The model can well explain the trend of the simulated results and implies that overlooking the effect of urban canopy underestimates canopy UHI in urban coastal environment.

Manipulating melt pool thermofluidic transport in directed energy deposition driven by a laser intensity spatial shaping strategy

ABSTRACT A three-dimensional thermofluidic coupling transport model is proposed to investigate the influences of different spatial laser intensity profiles (SLIPs), including circular super-Gaussian profile (C-SGP), transverse elliptical Gaussian profile (TE-GP) and longitudinal elliptical Gaussian profile (LE-GP), on the thermofluidic transport characteristics within the melt pool. The results demonstrate that the SLIPs dramatically influence the melt pool geometries, temperature gradient (both in magnitude and direction) at the solidification interface, and fluid flow dynamics. Under the TE-GP strategy, the highest average temperature gradients are observed at the solidification interface. The LE-GP strategy yields the smallest magnitudes and narrowest variation range of the temperature gradient direction angles. The heat transport of the melt pool under the C-SGP and TE-GP strategies are jointly dominated by convective and conductive heat transfer, while those under the LE-GP strategy are dominated by convective heat transfer. Marangoni convection is strongest in the LE-GP strategy and weakest in the TE-GP strategy.

Acoustic characteristics and performance analysis of a solid-state thermoacoustic oscillator

Thermoacoustic instability in solids paves the way for the development of solid-state thermoacoustic (SSTA) engines with superior reliability. Acoustic characteristics with respect to the performance of SSTA oscillators are investigated, where growth ratio is taken as a performance metric. Numerical analyses show that the acoustic characteristics not only determine the temperature gradient direction for strengthening the oscillation, but also affect the maximum growth ratio. A high growth ratio is obtained at a low angular frequency and an acoustic field around 1/8 wavelength from the strain antinode. To realize appropriate acoustic characteristics, the angular frequencies and acoustic fields under different boundary conditions are studied, based on which the method to adjust the acoustic characteristics is discussed. This work aims to reveal the relationship between the acoustic characteristics and the performance of SSTA oscillators, and to provide new insights on adjusting the acoustic characteristics for improving SSTA oscillators.

Programming Crystallographic Orientation in Additive-Manufactured Beta-Type Titanium Alloy.

Additively manufactured metallic materials typically exhibit preferential <001> or <110> crystallographic orientations along the build direction. Nowadays, the challenge is to program crystallographic orientation along arbitrary 3D direction in additive-manufactured materials. In this work, it is established a technique of multitrack coupled directional solidification (MTCDS) to program the <001> crystallographic orientation along an arbitrary 3D direction in biomedical beta-type Ti-Nb-Zr-Ta alloys via laser powder bed fusion (LPBF). MTCDS can be achieved via directional solidification of coupled multi-track melt pools with a specific temperature gradient direction. This results in continuous epitaxial growth of the β-Ti phase and consequently sets the <001> crystallographic orientation along an arbitrary 3D direction. This way, relatively low elastic modulus values of approximately 60 ± 1.2GPa are customized along an arbitrary 3D direction. It is expected that MTCDS can be generalized to a wide range of applications for programming specific crystallographic orientations and, respectively, tailoring desired properties of different metallic materials.

Multiscale analysis of pore structure in clay due to freeze-thaw

The variation of pore structure due to freeze-thaw (F-T) plays a vital role in revealing the thaw settlement mechanism of soils. In this study, remolded saturated clay specimens experienced unidirectional freezing and natural thawing in an open or closed system (i.e., with or without water supply). X-ray computed tomography (CT) and mercury intrusion porosimetry (MIP) were conducted to analyze pore structural characteristics, including macropores, mesopores, and micropores, along the temperature gradient direction before and after F-T. The longitudinal pore binary images, obtained by processing CT images, were used to assess the changes in porosity, pore shape, and orientation of macropores and mesopores due to F-T. The results indicate that the total longitudinal-sectional porosity and macropore percentage increased, whereas the mesopore percentage decreased. F-T considerably influenced the shape and orientation of macropores but had minimal effects on mesopores. The most significant changes occurred in the unfrozen zone due to F-T in an open system but near the final freezing front in a closed system. Additionally, Micropore porosity, diameter, and thermal fractal dimension were analyzed based on MIP data. The results showed that micropore porosity and diameter decreased, with significant changes occurring in the unfrozen zone of the open and closed systems. The micropore porosity and diameter decreased more in the unfrozen zone and near the final freezing front after F-T in a closed system, whereas a smaller decrease occurred in the frozen zone. The thermal fractal dimension value increases after F-T, indicating that the micropore structure became complex. In general, the multiscale pore analysis demonstrated that pore structure, including macropores, mesopores, and micropores, is significantly affected by F-T in the open system compared to the closed system.

Study of thermal behavior and microstructure formation mechanism of CuCrZr alloy melted by laser powder bed fusion

The properties of CuCrZr alloy parts subjected to laser powder bed fusion (LPBF) are severely affected by the thermal behavior of the molten pool in relation to the solidified structure. Detailed understanding of the changes in the thermal behavior of the molten pool and the relationship between the thermal behavior and the solidified structure are required to achieve high-performance LPBF parts. In this study, a numerical simulation of temperature field changes was used to model the heat transfer and molten pool characteristics during the LPBF of CuCrZr alloys. The effect of linear energy density (LED) on the morphology and flow of the molten pool was studied using a finite element model (FEM), and the microstructure of the alloy was analyzed in combination with the temperature field. The results show that the shape of the molten pool obtained by the simulation is approximately circular, which differs from the typical comet-shaped molten pool for other alloys. The LED affects both the size of the molten pool and the flow of bubbles in the melt. When the LED is 800 J/m, the size of the molten pool is optimal, the bubbles in the melt can escape smoothly, and the highest relative density is achieved (98.23±1.4%). The simulation results are also in good agreement with the experimental data. The simulation obtained the difference in the temperature gradient along different directions as well. This anisotropy caused the solidified structure to form a large number of equiaxed crystals in the horizontal plane. At the same time, the circular shape of the molten pool caused a large deflection in the temperature gradient direction. The grain orientation of the horizontal plane formed an angle of 45° to the scanning direction. As a result of this larger temperature gradient in the vertical plane, a large number of columnar crystals are epitaxially grown.

Tip Splitting Dynamics in Degenerate Seaweed Patterns of Aluminum Alloys Induced by Anisotropic Surface Tension

The formation of degenerate seaweed in Al-4.5 wt % Cu, Al-3 wt % Mg, and commercial A356 alloys during quasi-two-dimensional directional solidification is studied. By designing (100)[011]-and (−211)[111]-oriented planar-front seeds, the surface tension profiles are symmetrically arranged with respect to the temperature gradient direction. The results show that growth toward the surface tension maxima is preferred, and the tips tend to grow outward in both directions, leading to degenerate seaweed formation. The comparison of the degenerate seaweeds in the three Al alloys shows that the morphologic features are qualitatively similar. However, the anisotropic surface tension has a significant effect on the growth dynamics of the degenerate seaweed. This quantitatively indicates that Al alloys with a larger anisotropy tend to exhibit growth with a smaller tip spacing (λ) and a higher splitting frequency (f).

Giant thermal rectification efficiency by geometrically enhanced asymmetric non-linear radiation.

Thermal rectification is an asymmetric heat transport phenomenon where thermal conductance changes depending on the temperature gradient direction. The experimentally reported efficiency of thermal rectification materials and devices, which are applicable for a wide range of temperatures, is relatively low. Here we report a giant thermal rectification efficiency of 218% by maximizing asymmetry in parameters of the Stefan-Boltzmann law for highly non-linear thermal radiation. The asymmetry in emissivity is realized by sputter-depositing manganese (ε = ∼0.38) on the top right half surface of a polyurethane specimen (ε = ∼0.98). The surface area of the polyurethane side is also dramatically increased (1302%) by 3D printing to realize asymmetry in geometry. There is an excellent agreement between the experimentally measured temperature profiles and finite element simulation results, demonstrating the reliability of the analysis. Machine learning analysis reveals that the surface area is a dominant factor for thermal rectification and suggests novel light-weight designs with high efficiencies. This work may find applications in energy efficient thermal rectification management of electronic devices and housings.

Thermally driven Marangoni effects on the spreading dynamics of droplets

The influence of the thermally-induced Marangoni stresses on the falling and spreading dynamics of a droplet surrounded by another liquid phase is numerically studied. A water droplet is released in a three-dimensional (3D) domain filled with oil. The droplet descends, comes at an apparent resting position above an oil film close to the bottom surface, and eventually wets the solid surface when the underneath film ruptures. A linear vertical temperature gradient is applied in the solution domain (with the bottom surface as the cold side) which imposes a surface tension gradient across the oil-water interface. The Marangoni source term is added to the momentum equation coupling the momentum and the energy equations. It is assumed that the dynamic contact angle changes according to the Kistler relation during the spreading. The Volume of Fluid (VOF) method is used to capture the interface between the phases. The solver is validated for both the falling and spreading phases. During the buoyancy-driven falling regime, the droplet retains its spherical shape at the low Reynolds number O(1) and finite Bond number O(0.001). It is revealed that the spreading rate of the droplet is a decreasing function of Marangoni number (Ma). Unlike the isothermal systems, where the bottom side of the droplet becomes slightly flattened at the resting stage, the Marangoni stress imposes an upward force on the droplet which elongates the shape of droplet in the temperature gradient direction. Consequently, the ultimate spreading radius at the equilibrium state is smaller at larger Ma. The slow rate of spreading and also the small wetted area at large temperature gradients adversely affect the heat transfer rate from the liquid to the cold plate where the local convective heat transfer coefficient and the average Nusselt number (Nu) are decreasing functions of the Marangoni stress.

Comparative study on process-structure-property relationships of TiC/Ti6Al4V and Ti6Al4V by selective laser melting

Titanium matrix composites (TMCs) have gained tremendous attention due to their excellent mechanical properties by combining the advantages of Ti6Al4V matrix and ceramic reinforcement. In current study, the selective laser melting (SLM) technique is applied to manufacture TiC/Ti6Al4V and Ti6Al4V. Systematic characterization and analysis are conducted to reveal and compare their process-structure-property relationships. The results reveal that the near fully dense parts could be manufactured by process optimization upon the systematic investigation on their densification behaviors. The addition of TiC effectively refines the matrix grain and changes the microstructures. The SLM-manufactured (SLM-ed) Ti6Al4V exhibits typical coarse columnar grains with ultrafine lamellar α+β microstructures distributed inside (average α-lath thickness: 282 nm). Nevertheless, the SLM-ed TMCs possess a peculiar molten pool morphology, in which the sub-columnar grains grow upward along the direction of the steepest temperature gradient. The acicular nanoscale TiC is dispersed inside the sub-columnar grains, while the chain-like TiC is distributed along the boundary. Meanwhile, an evolution process is proposed to describe the microstructure evolution of the SLM-ed TMCs. The interrelationships between energy density and resulting microstructures are also identified, based on which, strong and ductile Ti6Al4V specimens (tensile strength: 1390 MPa, elongation: 9.66%) and ultra-strong TMCs specimens (tensile strength: 1538 MPa) are manufactured. The strengthening effects are mainly attributed to the Hall-Petch strengthening and load-bearing transformation. Fracture analysis indicates that the failure of the SLM-ed Ti6Al4V is caused by the micro-voids nucleation and coalescence at the interface of α and β phases, whereas the premature fracture of the SLM-ed TMCs is originated from the chain-like TiC.

Penetration of a Heating Electromagnetic Pulse into Plasma in Magnetic Field

Penetration of a heating pulse of quasistationary electromagnetic field into plasma in constant magnetic field directed along its surface was studied. Weakening of electron heat transfer across the magnetic field leads to more efficient heating of electrons near the plasma surface. As a result, the penetration of the field into the plasma decreases, which is accompanied by suppression of the “inverse” skin effect. Inhomogeneous heating of electrons across the magnetic field leads to generation of an electric field strength component orthogonal to both the magnetic field and the direction of temperature gradient. Appearance of the additional field strength component leads to a change in polarization of the reflected pulse. In a sufficiently strong magnetic field, due to suppression of the electron heat flux and less significant effect of the magnetic field on the ion heat flux, a state with large difference of electron and ion temperatures occurs.

Lattice Boltzmann simulation of the melting enhancement of composite phase change material with highly conductive additives - Effect of discrete particulate phase and continuous conductive network

The melting process of paraffin-aluminum composite PCM in a 2D enclosure is numerically investigated by means of an enthalpy-based lattice Boltzmann method. The aluminum is deployed in discrete particles with size around 100 μm and the continuous fibrous network in the composite PCM, respectively. The effects of equivalent particle diameter, the volume fraction of aluminum additives as well as the local structural rearrangement are systematically investigated. The results demonstrate that the appending of discrete aluminum particles at a low volume fraction (ϕ ≤ 0.2 in this work) even has a negative effect on the melting process, because of the inhibition of the natural convection. By concentrating the particles in either back and top area, the melting performance could be slightly promoted. However, the improvement is very limited. Instead, it is more effective to utilize the continuous conductive fibrous network structure to accelerate the melting, which is suggested to be bespread over the entire PCM with larger local space in the direction of temperature gradient. Furthermore, it is discovered that the critical melting time reduces exponentially with the increase of fiber volume fraction. This work gives a comprehensive understanding of the differences between the discrete particles and continuous structures in the heat transfer enhancement of composite PCM, and offers an optimization strategy in the fabrication of fiber/foam structures.

Directionally solidified electron beam welding: A novel method to optimize soft magnetic properties for welded permalloy

Welding for permalloy is potentially applied in forming of permalloy devices in large volume and complex shape. The key point for permalloy welding is to guarantee the soft magnetic properties of joint. The new method of directionally solidified electron beam welding is conducted to optimize soft magnetic properties of 1J85 welded joint achieved by changing the direction of temperature gradient. The growth orientation of columnar crystalline clusters deflects from the original direction perpendicular to the fusion line to that towards weld center, corresponding to the direction of external magnetic field. The initial permeability is consequently increased from 3.54 mH/m (67% of the annealed 1J85) of the ordinary welded joint to 5.86 mH/m (higher than that of annealed 1J85) with the 14% decreased coercivity. The cooling rate of the weld is decreased from 12.5 * 10 3 ℃/s to 9.7 * 10 3 ℃/s, favorable for the growth of cellular grains and the consequently easier movement of magnetic domain boundary during magnetization process. The cellular grain boundary is proved to be element segregation instead of the conventional dislocation-walls in view of the distribution of low-angle grain boundaries. The alleviated distortion deriving from the decrease in stress is the underlying cause of the optimization of magnetic properties.