Alloy Melt Research Articles

Effect of in-situ forging assisted squeeze casting on the forming quality and mechanical properties of automobile control arm

The squeeze casting technique offers promising prospects for a wide range of applications, as it provides an effective solution to address the challenges associated with the poor casting performance of wrought aluminum alloys. In this paper, we implemented in-situ forging assisted squeeze casting (IFSC) to form an automobile control arm using a high-strength Al–Zn–Mg–Cu alloy modified with Zr and Er. The solidification defects, microstructures, and mechanical properties of the part were investigated under different pressures and in-situ forging using various analytical techniques. With the increase of squeezing pressure from 0 MPa to 120 MPa, the ultimate tensile strength (UTS) of the sample increases from 500 MPa to 593.3 MPa, and the elongation is 4.35 %. After in-situ forging, the tensile strength of the sample is 600.9 MPa and the elongation is 5.59 %. UTS is comparable to squeeze casting, but the elongation is increased by 28.5 %. The results indicate that increasing the forming pressure enhances the surface quality of the parts and reduces the solidification defects. In addition, increasing the forming pressure not only refines the grain but also improves the grain morphology and enhances the uniformity of the structure. The squeezing pressure can enhance the contact between the alloy melt and the mold, increasing the metal's cooling rate and promoting nucleation for grain refinement. In-situ forging further facilitates liquid phase feeding, reduces alloy defects, and improves the overall mechanical properties.

Super high strength of annealed Fe32Cr33Ni29Al3Ti3 manufactured by selective laser melting

Selective laser melting (SLM) of high entropy alloys (HEAs) shows great potential in industry applications and annealing was always used as a post-processing method after SLM. A dual-phase (DP) Co-free HEA was manufactured by SLM and annealed at 900 ℃ in this work. The annealed HEA exhibited super high yield and tensile strengths (∼1224 and ∼1363MPa, respectively), higher than those of the as-printed sample, primarily attributed to grain refinement and spinodal decomposition with FCC phase (rich in Ni/Al/Ti) and BCC phase (rich in Cr/Fe) decomposing into FCC (rich in Fe), B2 (rich in Cr, poor in Ni), and L12 (rich in Ni/Al/Ti, poor in Fe/Cr) during annealing. The annealed DP Co-free HEA exhibits notably superior strength to other Co-free HEAs or medium entropy alloys (MEAs) produced via SLM. Due to their affordability, Co-free HEAs show immense potential for widespread commercial use, and this study explores annealing in SLM to improve the mechanical properties of HEAs. The high-strength annealed DP Co-free HEA could be especially valuable for structural elements in construction applications.

Preliminary study on smelting micro-carbon ferromanganese alloy by electro silicon thermal one-step process

Abstract In this paper, the related thermodynamic analysis of the one-step electro silicon thermal smelting process of micro-C-ferroalloy was carried out, and the effects of smelting temperature (T), slag alkalinity (R), silicon ratio (KSi) and holding time (t) on the appearance quality of the alloy, the Mn content, the Si content of the alloy and the Mn element recovery rate were studied. It is concluded that under the conditions of a smelting temperature of 1400°C, the basicity of slag R is 1.2, the silicon addition coefficient KSi is 1.0, the holding time is 60 min, the alloy appearance quality is good, Mn content of the alloy is high, Si content is low, and Mn yield is relatively high. Under laboratory conditions, the Mn yield of the alloy obtained by this method is low, and the thermodynamic equilibrium and reaction kinetics of the alloy melt and slag system of this method still need to be further studied to provide a theoretical basis for the expansion test.

The temperature field characteristics and amorphous formation ability during the continuous casting process of Zr-based bulk metallic glass

This study utilized FLUENT dynamic mesh simulation technology to simulate the temperature field distribution characteristics during the continuous casting (CC) process of 5 mm thick Zr41.2Ti13.8Cu12.5Ni10.0Be22.5 (Vit1) bulk metallic glass (BMG), analyzed and discussed the amorphous forming ability of the Vit1 BMG plate prepared through CC. The results indicate that during the CC process, the temperature gradient and cooling rate of Vit1 BMG plate decrease with increasing distance from the cooling copper block surface and prolonged solidification time. Even at the lowest cooling rate, it still remains significantly higher than the critical cooling rate (Rc) of Vit1 bulk amorphous alloy. The temperature variations recorded by the thermocouple during the alloy melt solidification process are in basic agreement with the simulation data. The experimental test and simulation results show that 5 mm thick Vit1 BMG slab can be prepared theoretically by continuous casting technology. Finally, XRD, DSC and TEM were used to analyze the amorphous formation ability and microstructure of the Vit1 BMG slab.

The fate of nitrogen during early silicate differentiation of rocky bodies constrained by experimental mineral-melt partitioning

Nitrogen (N) is an essential element for life. Yet the processes of planet formation and early planetary evolution through which rocky planets like Earth obtained their atmospheric and surface nitrogen inventory are poorly understood. In order to understand the effect of early silicate differentiation of the rocky bodies on N inventory, here we study the elemental partitioning of N between the silicate minerals and melts. We conducted laboratory experiments using tholeiitic basalts and Fe + Si alloy mixtures at 1.5 – 4.0 GPa and 1300 to 1550 °C under graphite saturation at an oxygen fugacity range of IW–1.1 to IW–3.0. The experiments yielded an assemblage of Fe-rich alloy melt (am) + silicate melt (sm) + clinopyroxene (cpx) ± garnet (grt) ± orthopyroxene (opx) ± plagioclase (plag). Using electron microprobe, we determine that under the experimental conditions, N act as an incompatible element with DNcpx/sm (0.11 – 0.47) >DNplag/sm (0.41) >DNopx/sm (0.25) >DNgrt/sm(0.06 – 0.21). The DNmineral/sm do not show any strong dependence on temperature, pressure, and melt composition. However, through comparison with previous estimates, it appears that with decreasing fO2, N becomes less incompatible. Under our experimental conditions of alloy melt-mineral equilibria, N behaves as a siderophile element (DNam/mineral ranging from 4.1 to 60.6) with fO2 playing the strongest control on DNam/mineral. Our data suggest that under reducing conditions, in the early stages of a magma ocean (MO) and/or deeper mantle, silicate minerals would hold a non-negligible fraction of N as N becomes less atmophile and siderophile. Therefore, reduced parent bodies could also retain substantial N in the residual mantle during partial melting. The extraction of N from an internal MO or a solid planetary mantle is thus enhanced only as the system becomes more oxidizing, enriching the surficial reservoirs in N. Thus, Earth’s N2-rich atmosphere may be intrinsically linked to its mantle oxidation, whereas other rocky planets of the Solar System, such as Mars and Mercury, may have retained a significant portion of their N inventory in nominally N-free mantle silicates through episodes of MO crystallization and mantle melting.

Optimization of impurity removal and purification flux components and their application in the production of A356 aluminum alloy

Abstract Taking into account the thermodynamic and kinetic conditions of impurity removal and purification, three impurity removal and purification fluxes were designed for comparative experiments. It was found that the impurity and hydrogen removal rates of experimental flux II were the best, with a decrease of 28.1% in micro grain size 28.1 μ m. The spacing between secondary dendrites is significantly reduced. The eutectic silicon phase of the alloy treated with experimental flux II is granular, with small and dispersed inclusions. The fracture structure of the alloy exhibits ductile fracture characteristics, mainly in the form of transgranular microporous aggregation, which helps to improve the plasticity and fatigue resistance of the alloy. The flux purification method, which focuses on impurity removal, can provide a reference for the actual impurity removal in aluminum alloy smelting.

The reduced alloy in Earth's upper mantle: Experimental constraints on Fe-Ni-S-C(-O) melt compositions and deep mantle oxygen fugacity (5–16 GPa)

High-pressure experiments conducted at upper mantle conditions reveal increased Fe3+ contents in majoritic garnet with increasing pressure. Consequently, at ∼8 GPa, Fe2+ disproportionation is expected to generate Fe0, leading to a higher metal/sulfur ratio of the initially present monosulfidic melt. This study experimentally investigates equilibrium systematics between the reduced Fe-Ni-S-C(-O) melt and mantle silicates at 5–16 GPa and near-adiabatic temperatures (1420–1590∘C), aiming to constrain the alloy melt composition in equilibrium with bulk silicate Earth-like (BSE) mantle silicates. As analysis of unquenchable liquid alloys requires large melt pools, experimental charges were designed towards a 50:50 ratio of alloy:silicates, with Fe/Ni ratios, sulfur and carbon scaled to correspond to a BSE with 200–250 ppm S and 100–150 ppm C.Observed phase assemblages consist of Fe-Ni-S-C(-O) melt (metal/(S+O): 0.9–3.5, Ni/(Fe+Ni): ∼0.3–0.6 and 0.2–1.6 wt.% oxygen) saturated with graphite/diamond and coexisting with olivine/wadsleyite (XMg: 0.76–0.91), garnet and cpx ± low-Ca pyroxene. Oxygen fugacities (fO2) range from -0.5 to +4.0 relative to the iron-wüstite (IW) buffer. In most runs, Fe0–Fe2+ redox equilibration affected silicate XMg's, resulting in values <0.90. Therefore, an empirical model was developed to predict KDNi-Fealloy-olivine, allowing to recalculate the experimental results for a primitive BSE mantle composition with XMg of 0.90.Modeling BSE, the alloy's metal/(S+O) increases from 1.1 to ∼7 while Ni/(Fe+Ni) decreases from 0.35 to 0.19 at 5–16 GPa. With BSE-like S concentrations, the abundance of the Fe-Ni-S-C(-O) melt increases from 600–750 ppm at 5 GPa to ∼3800 ppm at 16 GPa, 100–150 ppm bulk carbon lead to graphite/diamond saturation to ∼14 GPa. Finally, a method is presented to derive fO2 from modeled liquid alloy compositions, which act as a “redox-sensor”. For a BSE-like mantle with 250 ppm S, fO2 decreases from IW+2.6 at 5 GPa to IW at 8 GPa, further decreasing to IW-1.0 at 12–16 GPa.

Unconventionally Large Exchange Bias and Cluster Spin Glass State in Mn2(Ni,Sn) Heusler Alloys Melt Spun Ribbons

Unconventionally Large Exchange Bias and Cluster Spin Glass State in Mn₂(Ni,Sn) Heusler Alloys Melt Spun Ribbons

Water-Etched Porous Ti: Surface Manipulation of Ti Foam Fabricated by Liquid Metal Dealloying Technique.

The liquid metal dealloying (LMD) process enables the fabrication of porous metals with various chemical compositions. Despite its advantages, LMD still faces key challenges such as maintaining the high-temperature molten metal bath for a prolonged time, avoiding the use of toxic etchants, and so on. To overcome these challenges, the study develops a water-leachable and oxidation-resistant alloy melt (AM) in Ca-Mg binary system. Specifically, Ca72Mg28 eutectic AM is designed, which exhibits higher oxidation resistance and lower melting temperature compared to pure Mg, allowing LMD to be conducted in atmospheric conditions as well as temperatures >200K lower. The AM also enables an innovative process to fabricate Ti foams with a hexagonal faceted surface structure by carefully manipulating the etching rate during the water etching process. This approach allows for the creation of foam with a surface area over 13% larger than that of foams with smooth surfaces via normal acid etching, potentially enhancing efficiency in applications such as electrodes for electrochemical systems or biomedical materials where increased cell adhesion can be beneficial. This study paves the way for efficiently manipulating the LMD process to fabricate metal foams with customized compositions and enhanced surface properties.

Cellular automata-lattice Boltzmann model for polycrystalline solidification with motion of numerous dendrites

A GPU-accelerated cellular automata-lattice Boltzmann combinatorial model is developed for calculating the preferred growth, movement, and collision behavior of equiaxed crystals in supercooled melts of binary alloys. For moving dendrites, the growth is computed in a dynamic grid that grows with the body, and continuous movement is achieved by moving the dynamic grid. The impulse-based method is used for the collision of dendrites to calculate the post-collision velocity. Each module of the model was rigorously benchmarked, proving that the model has good computational accuracy and efficiency. The model was used for modeling the solidification of an Al-3 wt% Cu alloy, simulating the growth of abundant kinematic equiaxed crystals in a rotating flow and the falling and stacking of dendrites in droves and subsequent grain growth during the columnar to equiaxed transition, respectively.

Sustainable recycling of aluminum scraps to recycled aerospace-grade 7075 aluminum alloy sheets

The production of aerospace-grade aluminum alloy sheet is characterized by stringent demands, resulting in a low yield rate. The processing of this material generates considerable amounts of highly alloyed scrap, complicating its recycling due to the challenge of maintaining melt cleanliness. This study employed an aerospace-grade melt refining system to purify the recycled 7075 alloy melt obtained from comprehensive scrap remelting. The melt's cleanliness was assessed using Porous Disc Filtration Analysis (PoDFA) and Liquid Metal Cleanliness Analyzer (LiMCA) and Alscan. The microstructure of the ingots and sheets was examined through Scanning Electron Microscopy (SEM) and Electron Backscatter Diffraction (EBSD), whereas the mechanical properties of recycled sheets were evaluated and benchmarked against those of primary sheet at an aerospace-certified testing facility. The findings indicate that the recycled 7075 sheet meets aviation standards, with no significant differences in microstructure or performance when compared to primary sheet. Furthermore, the study highlights the economic benefits of recycling scrap, revealing a potential cost saving of $4210.8 per ton of recycled sheet. The findings presented herein offer a theoretical framework and empirical evidence supporting the development of a recycling system for aerospace scraps and the certification of airworthiness for recycled aerospace aluminum alloy.

Hydrogen production from wastewater using interdigitated printed electrode-based Single-Chamber microbial electrolysis cells

In the ever-increasing quest for alternative energy sources, hydrogen emerged as a promising green option, but efficient and economical production and management have been the primary constraints. Converting wastewater into H2 and other forms of energy attracted significant attention in terms of simultaneously and sustainably managing both the wastewater and the energy generation problems. Microbial Electrolysis Cells (MEC) evolved recently as promising options for converting wastewater into H2 and electricity but with serious constraints on scalability. The current research aims to explore design and manufacturing solutions to build structurally strong and electrochemically effective electrodes that can also lead to scalable MEC. Two designs based on the interdigitated and spiral electrode architectures are proposed and evaluated. The added design freedom with additive manufacturing by selective laser melting of specific alloys of choice is effectively utilised in physically prototyping the interdigitated and spiral electrode forms designed with controlled porosity constraints. Microstructural, electrochemical, and cell performance characterisations led to the understanding that the spiral electrode configuration with polypyrrole-coated stainless steel 316L anode is a promising design option for both longitudinal and lateral scale-up of the MEC.

A unified model of tensile and creep deformation for use in niobium alloy materials selection and design for high-temperature applications

There is renewed interest in refractory alloys that possess higher service temperatures than incumbent Ni-based superalloys (e.g., ⪆1100 °C). This study provides a review of the high-temperature constitutive responses of Nb-alloys measured over a wide range of temperatures (≈860 °C < T < ≈1760 °C) and strain rates (≈10–9 s-1< ε˙ < ≈10–1 s-1). Nevertheless, the extant data is sparse and informed materials selection decisions require constitutive expressions to interpolate and reliably extrapolate. The Larson-Miller parameter approach to describe creep-life provides a conservative estimate of material response at the highest temperatures and lowest strain rates, whereas the Sellars-Tegart model describes both steady-state creep and high-temperature tensile test data with a single, universal equation. A minimum flow stress based on the combination of these two models is proposed for design considerations to address the overprediction of strength that can arise from applying one or the other independently. This effort highlights the fact that refractory alloys exhibit strain rate sensitive flow strengths in the temperature range of interest for applications. The roles of alloying, thermomechanical processing, and impurity levels are discussed, and highlight the fact that these advanced Nb-alloys evidence Class 1 (Class A) solute drag controlled creep behavior, except the carbide precipitation strengthened alloy, D-43. In addition, the high-temperature strengths are confirmed to be strongly correlated with alloy melting point.

Characteristics of Gasless Combustion of Core-Shell Al@NiO Microparticles with Boosted Exothermic Performance.

The microstructures and thermochemical behavior of the energetic composites composed of core-shell structured μAl@NiO microparticles were characterized. These core-shell microparticles were synthesized using a wet-chemistry-based one-pot process, where the assembly was proposed to be driven by the electrostatic force between negatively charged Al and positively charged Ni-NH3 ions. Electron microscopic images demonstrated the formation of NiO nanoparticles adhering to the surface of microsized Al particles with different equivalence ratios. Thermal analysis revealed two consecutive exothermic peaks resulting from the initial thermite reaction between 890 and 960 °C and subsequently the intermetallic/alloy formation reactions between 1000 and 1040 °C. The latter was further confirmed by the endothermic peaks of Al-Ni alloy melting at higher temperatures. The formation of alloy was substantiated by the melting of AlNi3, AlNi, and Al3Ni. The onset temperature of the first exothermic peak decreased with increasing nominal equivalence ratio of the core-shell. Compared to the physically mixed (PM) composite, the core-shell structures decreased the activation energy of the thermite reaction by a mere 9.24 kJ/mol; however, it increased the combustibility by the manifold. The PM composite was not able to be ignited at all by a 5 W laser, while the core-shell counterpart ignited at 2.55 ms and was completely combusted within 6.50 ms accompanying a violent impulse.

Reaction of a Molten Cr-Si-Base Alloy with Ceramics and a High Entropy Oxide

Due to their higher thermal and chemical stability than other high-temperature materials, chromium-silicon-base (Cr-Si-base) alloys are promising materials for future gas turbines and other high-temperature applications operating under harsh conditions. To enable near-net-shape casting of Cr-Si-base alloys, a compatibility of the alloy melt with the ceramic crucibles and molds is necessary. Additionally, a metal-ceramic contact exists at the interface between thermal barrier coating (TBC) and alloy, where metallic may melts play a role in the case of coating failure and overheating. In this study, molten Cr92Si8 (in at. %) alloy is brought into contact with powders of ceramics commonly used for casting molds or crucibles (e.g. ZrSiO4, Al2O3, 3YSZ), to investigate liquid metal corrosion, interdiffusion, and stabilities. Additionally, the high entropy oxide (Sm0.2Gd0.2Dy0.2Er0.2Yb0.2)2Zr2O7 (HEO), a potential future TBC material, is investigated. Before melting using an electric arc furnace, the powders of the investigated ceramics were mixed with pulverized Cr92Si8 and pressed into alloy-ceramic pairs, to maximize the contact area between molten metal and ceramic. For microstructural investigations and phase analysis, the materials were assessed using scanning electron microscopy (SEM) equipped with energy-dispersive X-ray spectroscopy (EDS), and X-ray diffraction (XRD). The widely used mold material ZrSiO4 and the coating BN were found to decompose, while reaction products of SiO2 and CoAl2O4 with the melt were detected. Al2O3, 3YSZ, and the HEO did not show decomposition or corrosion by the melt. Al2O3, 3YSZ, and the HEO are therefore considered as promising crucible, mold, and TBC materials for Cr-Si-base alloys.

Investigating creep performance of Wel-lok BiSN plug for sealing of offshore wells

In this study, we explore the long-term creep performance of the Wel-lok BiSN plug, a novel bismuth alloy-based sealing technology developed for the efficient abandonment of offshore oil wells. Unlike conventional cement-based solutions, the Wel-lok system leverages a thermite reaction to melt a bismuth alloy in situ, which flows into the wellbore to create a robust, leak-proof seal upon solidification. This process, completed within minutes, offers a rapid and environmentally friendly alternative to traditional methods. We conducted a comprehensive experimental and numerical analysis to assess the plug's durability under simulated downhole conditions, including a 50-year pressure buildup scenario.The primary merit of this method is its ability to provide a quick and reliable seal, significantly reducing the time and environmental impact associated with well abandonment. The thermite reaction and subsequent bismuth alloy flow ensure a high-density seal less prone to leakage than conventional cement-based plugs. Additionally, the Wel-lok system's resilience under long-term pressure buildup, as confirmed by our finite element simulations using ABAQUS, indicates its potential for extended durability.However, the method also has its disadvantages. Relying on a thermite reaction necessitates precise control over the reaction conditions to ensure consistent alloy melting and flow. Any deviation could result in incomplete sealing. Furthermore, while the bismuth alloy offers superior sealing performance, its behaviour under extreme downhole conditions, particularly over extended periods, still requires further empirical validation.Our findings, derived from laboratory thermite reaction modelling and finite element simulations, confirm that the material properties of the Wel-lok system, particularly its creep behaviour, significantly enhance sealing performance. This research validates the Wel-lok system's potential for widespread application in offshore well abandonment and contributes to developing sustainable and reliable well-sealing technologies.

Stability of oxide crucibles and implications for the fabrication of Zr-based bulk metallic glass master alloys

In this study, a systematic evaluation was conducted on the performance of Al2O3, MgO, BaZrO3 and Y2O3 crucibles for melting Zr-based bulk metallic glass master alloys. The interaction between the crucibles and the alloy melts was investigated, focusing on the effect of crucible type and the addition of Y element on the interaction. The results indicated that the relative stability of the evaluated oxide crucibles, in order of decreasing interaction extent, followed the sequence: MgO→Y2O3→Al2O3→BaZrO3. The grading did not follow the free energy data of the formation of these oxides. It was because that the Y combined with O in the alloy melts to form Y2O3 products, which adhered to the inner surface of the crucible. This further prevented the dissolution of the crucible refractory. Among the tested crucibles, the Y2O3 product layer exhibited the most complete structure on the surface of BaZrO3 crucible, thereby minimizing both the corrosion of the crucible and the contamination of the alloy melts.

Effect of rare earth Ce and Y on microstructure and viscosity of ZL114A alloy

To investigate the impact of rare earth on the fluidity of casting aluminum alloy during the filling process, the study measured the effects of rare earth (Ce, Y) content and the mischmetal (Ce / Y) on the viscosity of ZL114A alloy melt using a viscosimeter. The results show that for a single rare earth element, when the addition amount of Ce and Y is 0.4 wt%, the grain size and viscosity reach a minimum, with average grain sizes of 45.42μm and 43.54μm respectively, and the solidification range decreases by 4.23°C and 4.61°C respectively, with Y having a better effect than Ce; compared with the alloy without rare earth elements, the grain growth mode changes from independent nucleation to outward extension form. For mixed rare earth elements, the refinement effect is better than that of a single rare earth element, but the viscosity is higher. When the Ce/Y mass ratio is 1/3, the grain size and viscosity reach a minimum, with an average grain size of 40.75μm and a solidification range shortened by 8.92°C; when the proportion of Y is higher, the alloy shows better refinement of the microstructure and viscosity improvement. Rare earth elements have the potential to enhance the fluidity and solidification structure of ZL114A alloy. This study offers valuable technical insights for optimizing the casting process and mold design.

Study on the Migration Patterns of Oxygen Elements during the Refining Process of Ti-48Al Scrap under Electromagnetic Levitation.

This study investigated the migration patterns of oxygen in the deoxidation process of Ti-48Al alloy scrap using electromagnetic levitation (EML) technology. Scanning electron microscopy (SEM), X-ray diffraction (XRD), and X-ray photoelectron spectroscopy (XPS) were employed to analyze the oxygen distribution patterns and migration path during EML. The refining process resulted in three types of oxygen migration: (1) escape from the lattice and evaporation in the form of AlO, Al2O; (2) formation of metal oxides and remaining in the alloy melt; (3) attachment to the quartz tube wall in the form of metal oxides such as Al2O3 and Cr2O3. The oxygen content of the scrap was dropped with a deoxidation ratio of 62%. It indicated that EML can greatly promote the migration and removal of oxygen elements in Ti-Al alloy scrap.

Optimizing the microstructure and enhancing the mechanical prsoperties of hypereutectic Al–Si alloys by Mg addition

The impact of Mg on the solidification structure of hypereutectic Al–Si alloys with different Si contents (15 wt% and 18 wt%) was investigated. 3%Mg was added to Al–15Si alloy to modify the phases in the solidification structure for the improvement of mechanical properties, and T6 heat treatment was used to optimize the microstructure and precipitate strengthening phase. The solidification structure was observed by OM and TEM respectively, and the precipitation behavior of each phase was detected through DSC. The results show that the addition of Mg decreased the undercooling of the alloy melt, thus suppressing the precipitation of primary Si phase. Nanoscale β” precipitates were precipitated in the matrix after T6 heat treatment. This resulted in an increase of 54% and 165% in the UTS and EL of the alloy, reaching 252 MP and 15.1%, respectively. Primary Si crystals were present in two forms in Al–18Si–8Mg alloy: spinel twin and non-twin, while Mg2Si always maintained the faceted crystals during the growing process, where only (100) and (111) crystal planes were observed. XRD, SEM and EBSD have been used to prove that Mg2Si crystals with different morphologies could become the heterogeneous nuclei of two types of primary Si crystals. The process of nucleation and growth of primary Si with Mg2Si as the heterogeneous nuclei was experimentally analyzed and theoretically predicted.