Nominal Thickness Research Articles

Tunability of the optical constants of tantalum-cobalt alloy thin films in the extreme ultraviolet

The optical constants of two Ta-Co binary alloys are determined in the spectral range 8.0 nm–22.0 nm using angle-dependent reflectometry (ADR). The extreme-ultraviolet reflectivity (EUVR) profiles of the alloys were measured using highly monochromatized synchrotron radiation from sputtered thin films, each with a nominal thickness of 30.0 nm. Concerning the alloys, the inability to predict the variability of the optical constants' profiles in the vicinity of cobalt’s M-absorption edge region gives unique proof for the need to derive a more complete theory for predicting the optical constants. Markov chain Monte Carlo (MCMC) based Bayesian inferences, and frequency analysis of X-ray reflectivity (XRR) data were utilized to treat the relevant inverse-problem needed for determining the optical constants. An approach is presented here where both the optical constants of the alloys and their surface layers are simultaneously sampled. The results of this report are apropos to strengthen customizing multilayer mirrors (MLMs) and similar ad hoc optical components intended for the extreme-ultraviolet (EUV) spectral range.

High-quality friction pull plug welding of AA2219-T87 plate with a thickness of 18 mm: Experimental characterization on shaping, microstructure and mechanical properties

In this study, the friction pull plug welding (FPPW) of a thick AA2219-T87 plate (nominal thickness = 18 mm) was conducted. The shaping, microstructure, and mechanical properties of the FPPW joint were characterized and discussed. The experimental results indicated that the defects accounted for the most influencing factor of the tensile properties of the FPPW joint. Further, the lack of bonding at the top and bottom of the joint was caused by insufficient dynamic recrystallization and the necking of the plug, respectively. Notably, the tensile tests revealed that kissing bonds were the main sources of the crack, which were significantly affected by dynamic recrystallization; they are readily formed at the top or bottom of FPPW joints. The detrimental phase, mainly the eutectics at the bonding interface, exerted less influence on the bonding strength. After adjusting the joint structure to achieve sufficient dynamic recrystallization at the top and preventing plug necking, high-quality FPPW joints were obtained; the average tensile strengths of their top, middle, and bottom layers were 323.4, 304.2, and 301.7 MPa, respectively, and their corresponding average elongations were 6.8%, 6.4%, and 5.5%, respectively.

Electromechanical Behavior of Al/Al2O3Multilayers on Flexible Substrates: Insights from In Situ Film Stress and Resistance Measurements

A series of Al and Al/Al2O3thin‐film multilayer structures on flexible polymer substrates are fabricated with a unique deposition chamber combining magnetron sputtering (Al) and atomic layer deposition (ALD, Al2O3, nominal thickness 2.4–9.4 nm) without breaking vacuum and thoroughly characterized using transmission electron microscopy (TEM). The electromechanical behavior of the multilayers and Al reference films is investigated in tension with in situ X‐ray diffraction (XRD) and four‐point probe resistance measurements. All films exhibit excellent interfacial adhesion, with no delamination in the investigated strain range (12%). For the first time, an adhesion‐promoting naturally forming amorphous interlayer is confirmed for thin films sputter deposited onto polymers under laboratory conditions. The evolution of Al film stresses and electrical resistance reveal changes in the deformation behavior as a function of oxide thickness. Strengthening of Al is observed with increasing oxide thickness. Significant embrittlement can be avoided for oxide layer thicknesses ≤2.4 nm.

Temperature-Dependent Material Property Databases for Marine Steels—Part 3: HSLA-80

Integrated Computational Materials Engineering (ICME)-based tools and techniques have been identified as the best path forward for distortion mitigation in thin-plate steel construction at shipyards. ICME tools require temperature-dependent material properties—including specific heat, thermal conductivity, coefficient of thermal expansion, elastic modulus, yield strength, flow stress, and microstructural evolution—to achieve accurate computational results for distortion and residual stress. However, the required temperature-dependent material property databases of US Navy-relevant steels are not available in the literature. Therefore, a comprehensive testing plan for some of the most common marine steels used in the construction of US Naval vessels was completed. This testing plan included DH36, HSLA-65, HSLA-80, HSLA-100, HY-80, and HY-100 steel with a nominal thickness of 4.76 mm (3/16-in.). This report is the second part of a seven-part series detailing the pedigreed steel data. The first six reports will report the material properties for each of the individual steel grades, whereas the final report will compare and contrast the measured steel properties across all six steels. This report will focus specifically on the data associated with HSLA-80 steel.

Effect of periodic thickness on the helium bubble evolution and irradiation hardening in Cu/W(Re) multi-layered films under helium ion irradiation

Based on the basic understanding of prominent helium (He) bubble storage and defect annihilation in the dual-phase heterogeneous interfaces designed in nano-meter materials, the Cu/W(5.31 at.% Re) multilayered films with nominal periodic thickness (h) ranging from 2 nm to 50 nm were irradiated by 60 keV He+ at irradiation temperature of 725 K. At the fluence of 2×1017 cm-2, the lamellated interfaces in the Cu/W(Re) multilayered film of h = 2 nm were broken down due to the irradiation-induced intermixing between the Cu-W(Re) neighbouring interfaces, resulting in a stable distribution of bubble in grains or at grain boundaries. However, at He concentration peak region, the bubble clusters inside the Cu layers and the blurred interfaces were formed in the Cu/W(Re) multilayered film of h = 10 nm. The W phase structure was changed by the aggregated bubbles in lattices, and the Cu layers were damaged due to the distribution scope of aggregated bubble-cluster approximately increased to a critical periodic thickness (10 nm). The lamellated interfaces still kept stable at low He concentration region. The calculated bubble pressure and He density inside bubbles can effectively explain the lattice distortion induced partial phase transformation from α-W to γ-W in the W(Re) layers. Moreover, the effects of interfaces, He bubbles and dislocations on the increase of nano-hardness in the irradiated multilayers were discussed in detail.

On Crashworthiness and Energy-Absorbing Mechanisms of Thick CFRP Structures for Railway Vehicles.

This study aims to provide important guidelines for the crashworthiness design of composite energy-absorbing structures, especially railway vehicles. An experimental and numerical investigation was carried out to explore the crushing response of circular composite tubes reinforced with plain woven carbon fiber-reinforced polymers (CFRP). Quasi-static and dynamic axial crushing tests were performed on CFRP tubes with an inner diameter of 100 mm and a nominal wall thickness of 12 mm. Experimental results showed that increasing loading velocity led to a 21.8% reduction in specific energy absorption (from 99.7 kJ/kg to 78.7 kJ/kg) but had negligible influence on failure modes. Finite element models were also established and validated against the experimental results using ABAQUS/Explicit software. The effects of several different parameters such as the number of shell layers, friction coefficient, and interface properties on the simulated results, were also investigated and analyzed. A small variation in these parameters could change the total energy absorption of CFRP tubes. The comparisons between the predicted and experimental results indicated that a finite element model with 10 shell layers could effectively replicate the crushing response. In addition, the simulated results indicated that the damage of tubal wall materials dominated the major energy-absorbing mechanisms of CFRP tubes under quasi-static loads, which was 69.1% of the total energy. The energy dissipated by friction effects between the loading platen and the crushed fronds was 24.1% of the total energy. The increase in the loading velocity led to a decrease in the composite damage energy except for friction energy, resulting in a decrease in the total energy absorption.

A Simulation Study on the Effect of Layer Thickness Variation in Selective Laser Melting

Abstract Selective laser melting (SLM) has gained prominence in the manufacturing industry for its ability to produce lightweight components. As the raw material used is in powder form, the stochastic nature of the powder distribution influences the powder layer thickness and affects the final build quality. In this paper, a multi-layer multi-track simulation study is conducted to investigate the effect of stochastic powder distribution on the layer thickness and plastic strain in a printed geometry. A faster simulation approach is employed to simulate multiple layers. First, the powder distribution and the melt layer thickness of the first layer are obtained from discrete element method (DEM) and computational fluid dynamics (CFD) simulations respectively. Next, the melt layer thickness of the first layer is used as an input to the finite element (FE) based structural mechanics solver to predict the deformation and layer thickness of subsequent layers. Two nominal layer thicknesses 67.4 μm and 20 μm were considered. Two particle size distribution (PSD) configurations and two scanning strategies were tested. The results showed that variation in PSD and scanning strategy leads to variation in layer thickness which in turn leads to variation in the plastic strain that is known to drive the deformation. However, the nominal layer thickness of 20 μm was found to be less influenced by the PSD configuration. The proposed simulation approach and the insights achieved can be used as inputs in the part-scale simulations for geometric robustness evaluation in the early design stages of SLM products.

Optimal Threshold for Automatic Slice Thickness Measurement using Images of the American College of Radiology (ACR) CT Accreditation Phantom

This study aims to find the optimum threshold for the automatic measurement of slice thickness using ACR CT accreditation phantom. The ACR CT accreditation phantom was scanned using Siemens Somatom Perspective CT scanner. The nominal slice thicknesses of 1.5, 3, 5, 6, 7, and 10 mm were investigated. Our automated method was developed to obtain accurate slice thickness values. Several threshold values from 0.10 to 0.50 with increment of 0.05 to find optimum value were investigated. The results obtained from each threshold were then compared with the nominal slice thickness to determine the optimal threshold value. It is found that the optimum threshold in the automatic measurement of slice thickness with nominal slice thickness values from 1.5 to 10.0 mm is from 0.35 to 0.40. Using this range, the different between the nominal slice thickness and measured slice thickness is within 0.5 mm. The optimal threshold for automatic slice thickness measurement has been determined. The optimal threshold would lead to more accurately automated slice thickness measurement.

In-situ monitoring of powder bed fusion of polymers using laser profilometry

Process monitoring allows for unique opportunities to capture information at intermediate layers during fabrication for part qualification, but also to improve process robustness by identifying issues before yield or quality is reduced. An industrial-grade laser profilometer has been integrated for the first time in a commercial polymer laser sintering machine and used to monitor powder bed quality and potentially qualify parts during production. Powder layer quality was measured in different conditions and changed drastically as a function of recoating speed, preheating temperature but also particle shape. The effective layer thickness was obtained for the first time in PBF of polymers, and gradually increased with the layer count until reaching a plateau at the nominal layer thickness. Powder layer density could be calculated as well and lies between 34 and 65 %, depending on the powder type and layer count. Finally, curling increased with decreasing preheating temperature, ranging from 70 µm to 350 µm i.e. until collision with the recoater. Based on the measured degree of curling, mitigation strategies could be integrated using a closed-loop feedback control. Effective process monitoring such as the one provided with laser profilometry may enable the development of new materials featuring more complex processing conditions, but also larger machines where thermal uniformity might be an issue.

Study on the dose profile in CT-fluoroscopy

This work aims to contribute to the description of the dose profile in Computed Tomography Fluoroscopy (CTF). Our approach uses a function model to fit the single slice dose profiles (SSDP) for any point inside the gantry of the CT unit, with special attention to points off the rotation axis. The function model was successfully tested with measurements performed using GafChromic film. The parameters of the SSDP at the rotation axis (isocenter) and at 8 cm and 16 cm off the isocenter were determined. The model allows an estimation of the slice thickness at the isocenter and for points at 8 cm and 16 cm off the isocenter. The differences between the slice thicknesses results in overestimation of the Computed Tomography Dose Index, CTDI, by values as high as 20% if the nominal slice thickness instead of the model estimated value is used. The results obtained in this work provided a good description of the dose profiles, which can be used in further studies such as comparisons with measurements performed with phantoms and patients.

Local buckling behaviour of stainless-clad bimetallic steel built-up square hollow section stub columns

The local buckling behaviour and design of built-up square hollow section (SHS) stub columns made of the stainless-clad (SC) bimetallic steel is addressed in this paper by experimental and numerical investigations. A total of seven stub column specimens fabricated from hot-rolling bonded SC bimetallic steel plates with nominal thicknesses of 8 mm and 13 mm were tested and analysed.​ Precise measurements of dimensions and geometrical imperfections of the specimens were conducted with the assistance of a non-contact 3D laser scanner. The scanned data was processed by a novel approach to provide a more accurate analysis of imperfections. Finite-element (FE) models with geometric imperfections obtained from 3D-scanned data were developed and validated against the dependent test results herein and independent ones. Comprehensive parametric studies considering various clad ratios, normalized plate slendernesses and steel grades were carried out by using the verified FE models. The applicability of current codified design methods to the SC bimetallic steel SHS stub columns was evaluated through comparisons with the numerical results. A normalized slenderness limit as well as an effective width formula were proposed based on the parametric studies and the evaluation of existing design methods. With improved efficiency and consistency, the design methods proposed herein can be utilized in the future application of the SC bimetallic steel structures.

Thick thermal barrier coatings with different segmentation crack densities: Microstructure analysis and thermal oxidation behavior

Thick thermal barrier coatings (TTBCs) have been developed to increase the lifetime of hot section parts in gas turbines by increasing the thermal insulating function. The premeditated forming of segmentation cracks was found to be a valuable way for such an aim without adding a new layer. The TTBC introduced in the current study are coatings with nominal thickness ranging from 1 to 1.1 consisting of MCrAlY bond coat and 8YSZ top coat deposited by air plasma spray technique (APS). TTBCs with segmented crack densities of 0.65 mm−1 (type-A) and 1 mm−1 (type-B) were deposited on a superalloy substrate by adjusting the coating conditions. It was found that the substrate temperature has an influential role in creating the segmentation crack density. The crack density was found to increase with substrate temperature and liquid splat temperature. The two types of coatings (type-A and B) with different densities of segmentation crack were heat-treated at 1000 °C (up to 100 h) and 1100 °C (up to 500 h). The variation of hardness measured by indentation testing indicates a similar trend in both types of coatings after heat treatments at 1000 °C and 1100 °C. Weibull analysis of results demonstrates that higher preheating coating during the deposition results in a denser YSZ coating. The growth rate of TGO for TTBCs was evaluated for cyclic and isothermal oxidation routes at 1000 °C and 1100 °C. The TGO shows the parabolic trend for both two types of coatings. The Kps value for two oxidation types is between 5.84 × 10−17 m2/s and 6.81 × 10−17 m2/s. Besides, the type B coating endures a lifetime of more than 40 cycles at thermal cycling at 1000 °C.

Recent Advances in Electrodeposition of Copper Ultrathin Films on Cobalt Substrate

As the miniaturization trend in integrated circuits fabrication continues, alternative liner materials in copper interconnects have been actively explored. Cobalt has been widely investigated and employed due to its low resistance at nanoscales, integration compatibility, as well as benefit of improving copper electromigration resistance. However, direct electrodeposition of copper onto cobalt remains less explored due to the stability issue of cobalt in acidic copper damascene process. Subsequent processes of copper seeding and copper electroplating face increasing technical difficulties when widths and aspect ratios of electro-fill features become more challenging.Direct electrodeposition of copper on cobalt has been explored in acidic and alkaline chemistries, both of which were formulated by MacDermid Alpha Semiconductor Solutions. In both cases, well-adherent, nearly-pinhole-free, and ultrathin Cu has been successfully electrodeposited onto cobalt substrate with less than 10% cobalt loss. SEM images in Figure 1 imply uniform dispersion of copper on cobalt. XRF and ICP analysis confirm that the thinnest copper films deposited could be no thicker than 2 nm. Corrosion test in acidic copper plating bath shows that an ultrathin copper layer of thickness less than 2 nm can effectively suppress cobalt dissolution by a factor of three in comparison to non-coated bare cobalt.This work could pave the avenue towards direct copper electrodeposition onto cobalt liner in semiconductor manufacturing for advanced technology nodes. Figure 1. Top-down SEM images. (left) As-received cobalt substrate; (center) Cu of 2 nm nominal thickness electrodeposited on cobalt from an acidic solution; (right) Cu of 2 nm nominal thickness electrodeposited on cobalt from an alkaline solution. All three images have the same scale and scale bars are 200 nm. Figure 1

Qualitative and quantitative interdependence of mechanical properties of industrially extruded AA6063 alloy on process parameters and profile characteristics

PurposeThis study aims to investigate and model interrelationships between process parameters, geometrical profile characteristics and mechanical properties of industrially extruded aluminum alloys.Design/methodology/approachStatistical design of experiments (DOE) was applied to investigate and model the effects of eight factors including extrusion ratio, stem speed, billet-preheat temperature, number of die cavities, quenching media (water/air), time and temperature of artificial aging treatment and profile nominal thickness on four mechanical properties (yield strength, ultimate tensile strength, percent elongation and hardness). Experiments were carried out at an actual extrusion plant using 8-in. diameter billets on an extrusion press with 2,200 ton capacity.FindingsMain factors and factor interactions controlling mechanical properties were identified and discussed qualitatively. Quantitative models with high prediction accuracy (in excess of 95%) were also obtained and discussed.Practical implicationsThe obtained results are believed to be of great importance to researchers and industrial practitioners in the aluminum extrusion industry.Originality/valueAll practical and relevant parameters have been used to model all important mechanical properties in a collective manner in one study and within actual industrial setup. This is in contrast to all previous studies where either a partial set of parameters and/or mechanical properties are discussed and mostly under limited laboratory setup.

Surface regression in opposed flow flame spread: Transitions, correlations and partition factors

Surface regression was studied during opposed flow flame spread over thermally thick polymethyl-methacrylate (2.54 cm) under variable forced flows in a horizontal Narrow Channel Apparatus (NCA). The sample nominal thickness was 2.54 cm and opposed flow velocities varied from 8 - 45 cm/s. The post-burn samples were examined for the regressed surface shape. A formula was derived whose primary input is the regression profile: either the spread rate or the mass flux can be calculated from other inputs. The experimental video record gives the flame spread rate. The measured surface profile, along with the flame spread rate, gives the mass flux from the surface. The regression depth increases with increased mass average flow velocity. For mass average flow velocities below 12 cm/s, when the surface barely regresses (2 mm over an ≈ 12 cm length), the average power law exponent for mass loss rate approximates to -1/2. For mass average flow velocities greater than 25 cm/s, the average power law dependency approximates to -1/4. The transition from the -1/2 to -1/4 power occurs over a narrow range of opposed flow stretch rates and mass mean flow velocities. For the higher opposed flow velocities the regression depth is a prominent feature of the burned sample. Based on the hypothesis of partitioning of physical influences, the contributions to flame spread of the flow field, finite rate chemistry and surface regression are evaluated from the experimental data. A semi-empirical flame spread formula is developed.

Design and Characterization of ITO-Covered Resonant Nanopillars for Dual Optical and Electrochemical Sensing

In this work we present a dual optical and electrochemical sensor based on SiO2/Si3N4 resonant nanopillars covered with an indium tin oxide (ITO) thin film. A 25–30 nm thick ITO layer deposited by magnetron sputtering acts as an electrode when incorporated onto the nanostructured array, without compromising the optical sensing capability of the nanopillars. Bulk sensing performances before and after ITO deposition have been measured and compared in accordance with theoretical calculations. The electrochemical activity has been determined by the ferri/ferrocyanide redox reaction, showing a remarkably higher activity than that of flat thin films of similar ITO nominal thickness, and proving that the nanopillar system covered by ITO presents electrical continuity. A label-free optical biological detection has been performed, where the presence of amyloid-β has been detected through an immunoassay enhanced with gold nanoparticles. Again, the experimental results have been corroborated by theoretical simulations. We have demonstrated that ITO can be a beneficial component for resonant nanopillars sensors by adding potential electrochemical sensing capabilities, without significantly altering their optical properties. We foresee that resonant nanopillars coated with a continuous ITO film could be used for simultaneous optical and electrochemical biosensing, improving the robustness of biomolecular identification.

Archimedes Spiral Wind Turbine performance study using different aerofoiled blade profiles: Experimental and numerical analyses

Wind power is one of the most quickly expanding forms of clean energy. A novel horizontal axis wind turbine type, the Archimedes Spiral Wind Turbine (ASWT), is built for residential applications. The influence of the rotor pitch to diameter ratio (2s/D) and the aerofoil blade profile on the productivity of ASWT is investigated using experimentation and computer simulation. To fulfill the validation of the experimental work, the ANSYS Fluent solver provides the numerical solution. The tests are performed on a modified ASWT with a nominal blade thickness and blade angles of α1 = 25°, α2 = 50°, and α3 = 60° for the first, middle, and third blades. Wind speeds of 8 and 10 m/s were used. The NACA4401 ASWT with (2s/D) = 0.30 is the best-studied design. At a wind speed of 10 m/s, the maximum CP of the conventional, modified, and aerofoiled ASWTs is 0.243, 0.286, and 0.3045, respectively, at tip speed ratios (λ) of 1.5, 2, and 2. Compared to the conventional and modified ASWT, the aerofoiled ASWT exhibits a 26.88% and 6.47% improvement in the peak CP.

Electrochemical Fabrication and Characterization of Organic Electrochemical Transistors Using poly(3,4-ethylenedioxythiophene) with Various Counterions

Organic electrochemical transistors (OECTs) are promising bioelectronic devices, especially because of their ability to transport charge both ionically and electronically. Conductive polymers are typically used as the active materials of OECTs. Crosslinked, cast, and dried films of commercially available poly(3,4-ethylenedioxythiophene):poly(styrene sulfonate) (PEDOT:PSS) suspensions are commonly and widely used for OECTs so far. Electrochemical polymerization of PEDOT from 3,4-ethylenedioxythiophene (EDOT) monomer can also be used to fabricate OECTs; however, this approach has not been investigated in as much detail. In particular, the role of various counterions that can be incorporated into the PEDOT films of OECTs has not been systematically studied. Here, we report the electrochemical fabrication and characterization of OECTs using PEDOT with several different counterion salts including lithium perchlorate (LiClO4), sodium p-toluene sulfonate (pTS), and poly(sodium 4-styrene sulfonate) (PSS). We found that the characteristic dimensions of PEDOT films deposited on the electrodes could be precisely controlled by total charge density, with a nominal thickness of about one micron requiring a current density of about 0.6 C/cm2 regardless of the choice of counterion. The films with the PSS counterion were relatively smooth, while PEDOT films prepared with the pTS and LiClO4 were much rougher due to the sizes of counterions. The PEDOT films with pTS and PSS grew along the substrate surface (in-plane direction) much faster than with LiClO4. The maximum transconductance (gm) of a PEDOT OECT was 46 mS with pTS as the counterion with the high on-current level (>10 mA) based on the large channel area. These results provide an effective and efficient way to fabricate OECTs with various monomers and additives as active materials in order to modify the device characteristics for further applications.

Effect of Impurity Scattering on Percolation of Bosonic Islands and Superconductivity in Fe Implanted NbN Thin Films.

A reentrant temperature dependence of the thermoresistivity between an onset local superconducting ordering temperature and a global superconducting transition at has been reported in disordered conventional 3-dimensional (3D) superconductors. The disorder of these superconductors is a result of either an extrinsic granularity due to grain boundaries, or of an intrinsic granularity ascribable to the electronic disorder originating from impurity dopants. Here, the effects of Fe doping on the electronic properties of sputtered NbN layers with a nominal thickness of 100 nm are studied by means of low-T/high- magnetotransport measurements. The doping of NbN is achieved via implantation of 35 keV Fe ions. In the as-grown NbN films, a local onset of superconductivity at is found, while the global superconducting ordering is achieved at , with a normal state resistivity . Moreover, upon Fe doping of NbN, is estimated, while and are measured to be 15.1 K and 13.5 K, respectively. In Fe:NbN, the intrinsic granularity leads to the emergence of a bosonic insulator state and the normal-metal-to-superconductor transition is accompanied by six different electronic phases characterized by a N-shaped T dependence of . The bosonic insulator state in a s-wave conventional superconductor doped with dilute magnetic impurities is predicted to represent a workbench for emergent phenomena, such as gapless superconductivity, triplet Cooper pairings and topological odd frequency superconductivity.

Oxygen contribution to the magnetic response of ultrathin Fe/Ni multilayers grown on Fe-p(1 × 1)O

We investigated the magnetic behaviour of an Fe overlayer on a Ni buffer layer (Fe/Ni multilayer system) grown on top of the Fe-p(1 × 1)O surface, with a particular focus on the modifications observed in the spin-resolved electronic structure and the role of oxygen, introduced in the system in a well-defined amount at the substrate preparation stage. The structural properties are investigated by means of low energy electron diffraction, that confirms the formation of an epitaxial system featuring a metastable surface lattice. Spin-resolved photoemission spectroscopy testifies a strong decrease of the spectral spin polarization for increasing thickness of the Ni buffer layer, reaching a minimum from a nominal thickness of 6 Ni atomic layers. Surprisingly, the growth of a single Fe overlayer is sufficient to restore most of the original polarization signal, thus creating an ultrathin bcc Fe film seemingly decoupled from the substrate. Ab initio calculations track the modifications of the magnetic moments of the surface layers that quench upon Ni deposition and restore with additional Fe growth. Spin-resolved inverse photoemission highlights a notable reduction of the density of majority states just above the Fermi level, possibly influencing the magnetic response of the system.