Mixed Ceramics Research Articles

Mathematical Modeling of the Bearing Ratio Curve Rmr (50% Rz), through Investigation of the Effect of Process Parameters in Hard Turning of Steel C55 (DIN) with Mixed Ceramics MC2 (Al2O3 + TiC)

The subject of modeling and predicting roughness parameters in hard machining has been discussed in many literature sources. However, most of these sources cover only the amplitude parameters such as Ra and Rz, leaving it unexplored to the right extent compared to its importance the roughness parameter bearing ratio curve (the Abbott–Firestone curve) which is essential in understanding the actual contact area of mating surfaces. To bridge this gap, this research has developed a mathematical model using the design of experiments method through investigation of the effect of process parameters in hard turning of Steel C55 (DIN) with mixed ceramics MC2 (Al2O3 + TiC). The model predicts the bearing ratio curve parameter Rmr (50% Rz), statistically processed using CADEX and Matlab. The research includes the ANOVA as a complementary tool in validating the generated mathematical model. The research analyzes the effects of material properties, cutting forces, and tool geometry as factors that affect the machining process. Additionally, it emphasizes the robustness of hard turning in consistently producing waviness patterns. Overall, this research provides valuable insights into the predictable effects of parameters on machined surfaces, which contributes to a better understanding of surface finish in metalworking.

Enhancement of superior dielectric performance in ZnTiNb2O8 systems by multi‐layer architecture

AbstractZn0.995Cu0.005TiNb2O8@TiO2 mixed ceramics and Zn0.995Cu0.005TiNb2O8‐TiO2‐Zn0.995Cu0.005TiNb2O8 layered ceramics with different TiO2 contents were designed and manufactured to adjust the microwave dielectric performances of Zn0.995Cu0.005TiNb2O8/TiO2 composite ceramics. The effects of random distribution and laminated co‐firing processes on the microwave dielectric properties of the ZnTiNb2O8 systems were fully investigated and compared. During the random distribution process, the compound transforms from the original ZnTiNb2O8 phase to the Zn0.17Nb0.33Ti0.5O2 phase with the increase of TiO2 content. Its value can be adjusted to near zero, but its Q× f value decreases severely. For the laminated co‐firing process, the distinctive tri‐layer architecture allows the reaction between Zn0.995Cu0.005TiNb2O8 and TiO2 to be limited to a narrow region of about 20 µm width and can play a role similar to that of “glue” to connect the layers well. The process significantly minimizes the probability of Q× f values deteriorating. Compared with the random distribution Zn0.995Cu0.005TiNb2O8@TiO2, the Q× f value of the tri‐layer architecture ceramics is improved by about 85% with no significant decrease in dielectric permittivity while ensuring high‐temperature stability. When stacked with 0.04 wt% TiO2, the Zn0.995Cu0.005TiNb2O8‐TiO2‐Zn0.995Cu0.005TiNb2O8 tri‐layer architecture ceramic exhibits superior dielectric properties: = 39.96, Q× f = 51,987 GHz, and = ‐1.31 ppm/°C.

Selective Nitridation of Ceramic Open Cell Foams for Efficient Photothermal Heating

AbstractThis study presents the synthesis of ceramic open cell foams as a new platform for photothermal energy conversion based on the inert structural ceramic alumina and the plasmonic transition metal nitride TiN. TiO2 precursor grains inside the mixed ceramic matrix are converted to TiN via the molten salt synthesis route. Photothermal measurements using an 850 nm LED as a light source show that the ceramic foams with only ≈5% TiN in the alumina matrix showed a 34% increased efficiency in converting light to heat compared to flat ceramic discs of the same composition. The TiN content in the flat discs does not affect the heat conversion efficiency, indicating that the available surface area and the material's ability to trap and direct light to the plasmonic nanostructures are the most important parameters for its photothermal activity. These results show the feasibility of synthesizing mixed ceramics based on inert materials like alumina and transition metal nitrides. Applications in solar heating, water evaporation, and related use cases of photothermal energy conversion can be realized with improved performance over 2D materials. Particularly processes that are based on continuous flow like solar thermal heating or photothermal catalysis will benefit from this new material platform.

Effect of synthesis route on optical properties of Cr:Al2O3 transparent ceramics sintered under high pressure

Transparent polycrystalline ceramics doped with active ions are suitable for many potential optical applications. Fabrication methods that utilize applied external pressure show promise as they allow reducing sintering temperatures and produce transparent non-cubic ceramics. However, not much attention has been given to the dissolution of doping elements while sintering under relatively high pressure and low temperature conditions. In this study, we employed high-pressure spark plasma sintering (HPSPS) for fabrication of Cr:Al 2 O 3 ceramics and investigated the effect of two different synthesis routes on densification and optical properties. Namely, HPSPS of Cr-doped alumina powders prepared by directly doping with 0.05, 0.2, and 0.5 Cr at.% via co-precipitation and alumina mixed with similar mol.% of Cr 2 O 3 nanoparticles towards doping via solid-state reactive sintering (so-called ‘synthesized’ and ‘mixed’, respectively). Remarkable differences in optical properties between samples obtained by each method were observed. The ceramics fabricated from synthesized powders exhibited pink shades of ruby, high transparency, and strong photoluminescence. In contrast, the mixed ceramics exhibited green color, low transparency, and weak photoluminescence. It was found that in the green samples, most of the Cr 2 O 3 nanoparticles remain as undissolved nano-inclusions. These inclusions are detrimental to optical properties and cause green pigmentation of the alumina. Post-sintering heat treatment dissolved the inclusions and the added Cr 3+ in alumina increased photoluminescence. Evidently, doping transparent alumina via reactive sintering is not viable for processes such as HPSPS. Nevertheless, rapid low temperature densification might enable the design of functional translucent ceramics with integrated second phase nanoparticles. • High-pressure spark plasma sintering was used to fabricate polycrystalline Cr:Al 2 O 3 . • Cr-doping via co-precipitation yielded highly transparent Cr 3+ :Al 2 O 3 ceramics. • Mixed Cr 2 O 3 -Al 2 O 3 yielded green translucent ceramics due to Cr 2 O 3 nano-inclusions. • Post-sintering heat treatment dissolved Cr 2 O 3 and increased photoluminescence. • Reactive sintering is not a viable synthesis route for doped transparent alumina.

Incidence, Risk Factors, and Outcome of Ceramic-On-Ceramic Bearing Breakage in Total Hip Arthroplasty

BackgroundCeramic-on-ceramic bearing breakage is a rare but significant complication of total hip arthroplasty. This study aimed to identify risk factors for breakage and to determine the outcome of different revision options. MethodsAll ceramic-on-ceramic primary total hip arthroplasty procedures reported to the Australian Joint Replacement Registry from September 1999 to December 2019 were included. Procedures were subdivided into alumina or mixed ceramic (alumina/zirconia). All breakages were identified. The association between ceramic type and head size was assessed. Subsequent revision rates were compared and cause of revision assessed. ResultsThere were 23,534 alumina and 71,144 mixed ceramic procedures. Breakage was the reason for 1st revision in 84 alumina (5.27% of all revisions and 0.36% of procedures) and 56 mixed ceramic procedures (2.46% of all revisions; 0.08% of procedures). Alumina had a higher breakage rate than mixed ceramic (HR 2.50 (95% CI 1.75, 3.59), P < .001), and breakage was higher for 36-38mm head sizes using alumina (HR 2.84 (1.52, 5.31), P = .001). 17.8% of 2nd revisions occur by 3 years, due to dislocation, infection, metal-related pathology, and loosening. A neck adapter sleeve did not reduce 2nd revisions. Numbers were too low to compare revision bearing surface options. ConclusionCeramic breakage has reduced with mixed ceramics but has a 0.79/1000 incidence at 15-year follow-up. It is unclear what the risk factors are for modern ceramics with increasing head size a risk for alumina only. Risk of 2nd revision is high and occurs early. The optimal revision option is unknown.

Mechanical Stress Issues of La&lt;sub&gt;0.6&lt;/sub&gt;Sr&lt;sub&gt;0.4&lt;/sub&gt;Co&lt;sub&gt;0.2&lt;/sub&gt;Fe&lt;sub&gt;0.8&lt;/sub&gt;O&lt;sub&gt;3-δ&lt;/sub&gt;

Ionic devices consisted of ion-conductive ceramics such as solid oxide fuel cells (SOFC) and oxygen separation membranes have been developed in the last decades. La0.6Sr0.4Co0.2Fe0.8O3-δ (LSCF), which is a mixed ionic-electronic conductive ceramics, is especially expected to play an important role in those ionic devices and so its electrochemical properties have been intensively studied.

Optical properties of transparent ZnSe0.9S0.1 mixed crystal ceramics prepared by hot isostatic pressing

Mid-infrared ZnSe 0.9 S 0.1 transparent mixed crystal ceramics were successfully fabricated by hot pressing (HP) in combination with post hot isostatic pressing (HIP). The phase structure of the as-fabricated mixed ceramics was found to be composed of cubic sphalerite, and the existence of any secondary phase was not detected. It was noticed that after post HIP treatment, the grain size increased greatly, and many closed pores in the samples disappeared. The specimens HP sintered at 1000 °C under 60 MPa and post HIP treated at 1300 °C under 196 MPa in the Ar atmosphere for six hours had the best transmission of 62.3% at 14 μm. • Mid-infrared ZnSe 0.9 S 0.1 transparent ceramics were fabricated by hot pressing in combination with hot isostatic pressing. • The samples pre-sintered at 1000°C and hot isostatic pressing treated at 1300 °C under 196 MPa had the best transmission. • The optimum transmission of ZnSe 0.9 S 0.1 ceramic reach 62.3% at 14 μm.

A Novel Precursor for the Synthesis of Mixed Non-oxide Ultra High Temperature Ceramics

Polymer-derived ceramics have gained importance due to ease of processability, less processing time and flexibility in tailoring the composition of ceramics by altering the monomer ratios in the polymer. In the present work, a preceramic oligomer containing both zirconium and titanium, viz., Zirconotitanoborosiloxane was synthesized by non-aqueous sol–gel process. Oligomer was characterized by GPC, spectral and thermal techniques. Ceramics formed at 1500 °C reveal the formation of Zr and Ti based UHTCs along with some oxides. To study the feasibility of using Zirconotitanoborosiloxane oligomer as precursor for mixed non-oxide ceramics, carbothermic and borothermic reductions were carried out by blending the precursor with phenolic resin as source of carbon and elemental boron as source of boron. XRD study confirms the formation of mixed non-oxide UHTC system containing Zr, Ti, B, Si and C. SEM–EDS analysis revealed the micro-structure of the ceramics and elemental composition.

Tool wear rate of the PCBN, mixed ceramic, and coated cemented carbide in the hard turning of the AISI 52100 steel

The hard turning process is generally performed by PCBN or mixed ceramics tools, which have the mechanical properties that withstand the tribological conditions of the process imposed by the hardened machined material. Coated cemented carbides are also an option for hard machining processes, although relying on the coating deterioration. This paper aims to evaluate the tool wear rate in function of the cutting speed in the hard turning of the steel AISI 52100 with a hardness of 50 HRC for three different types of cutting tool materials: coated cemented carbide, mixed ceramic, and PCBN. The methodology applied to assess the tool wear is based on three-dimensional parameters (volumetric) obtained from a focus variation microscope (FVM). The tool wear rate (WRRM) is calculated based on ordinary least squares (OLS) adopting five values of WRM in five machining time intervals. The face turning experiments were performed at four cutting speeds: vc = 120, 150, 187.5, and 234 m/min. At vc = 120 m/min, the PCBN presented the lowest tool wear rate (182 μm3/s); at vc = 150 m/min, the coated cemented carbide (tool wear rate on the coating) had the best performance (417 μm3/s). The mixed ceramic tool presented a better performance at the higher cutting speeds of vc = 187.5 and 234 m/min, 1206 and 1878 μm3/s, respectively. The methodology applied was reliable to understand and discuss the performance of the machining process through the tool wear rate (WRRM), which is based on the volume of removed material from the tool (WRM). The three-dimensional tool wear parameters can also be applied to machining process optimization, cutting tool wear model creation, benchmarking, and development of new cutting tool materials and grades. Furthermore, the methodology can be considered more agile and precise when compared to the current industrial methodology of tool performance evaluation. Thus, this innovative methodology promotes important information for cutting tool manufacturers and for its customers such as automotive and aeronautic industry.

Lanthanide-Doping Effects on the Formation of Leucite KAlSi2O6

In this study, the lanthanide-doping (Ce3+, Sm3+, Eu3+ and Tb3+) effects on the formation of leucite (KAlSi2O6) by sol-gel synthesis were investigated. The phase purity and morphological properties of lanthanide-doped specimens have been estimated. The proposed sol-gel synthesis route is suitable for the preparation of mixed leucite-kalsilite ceramics doped with Sm3+, Eu3+ and Tb3+ (up to 10 M %). This simple and successful synthetic approach offers a feasible way to obtain lanthanide-doped potassium alumosilicate ceramics with possible application in odontology. The synthesis products were characterized using thermal analysis (TG/DTA), X-ray powder diffraction (XRD) analysis, infrared spectroscopy (FTIR) and scanning electron microscopy (SEM). Moreover, the optical properties of lanthanide-doped synthesis products were also investigated.

Effect of Ba:Ti on ferroelectric properties of LiF doped BaTiO3 ceramics

We prepare three different LiF doped BaTiO3 ceramics by solid state reaction, i.e., (i) the Ba1−xLixTiO3−xFx ceramics (abbreviated as BLiFT-x), (ii) the BaTi1−xLixO3−2xFx ceramics (abbreviated as BTLiF-x), and (iii) the xLiF + BaTiO3 mixed ceramics (abbreviated as LiFBT-x). Through XRD analysis and electrical properties comparison, it is concluded that Li+ ions occupy Ba site and F− ions occupy O site in BLiFT-x and LiFBT-x ceramics, but the solubility of Li+ and F− ions are small and most of them occupy the interstitial site. Thus there are two peaks near Curie point. The d33 and kp increase firstly and then decrease with the increase of LiF content. However, Li+ ions occupy Ti site in BTLiF-x ceramics. The [LiTi-FO]2− defect dipoles are formed, which have a pinning effect and appear thin waist hysteresis loops. The d33 and kp decrease with the increase of LiF content. For all three group of ceramics, the Curie temperature decreases while the dielectric constant increases with the increase of LiF content. Compared Li2CO3 doped BaTiO3 (Ba/Ti 1 and Ba/Ti = 1) ceramics with LiF doped BaTiO3 (Ba/Ti 1 and Ba/Ti = 1) ceramics, the positions of Li+ ions occupying BaTiO3 are different with Li2CO3 doped BaTiO3 ceramics due to F− ions entering BaTiO3 in LiF doped BaTiO3 ceramics, which affect the structure, morphology and properties of BaTiO3 ceramic. This will provide some guidances to choose sintering additives and prepare methods for low temperature sintering in the future.

Synthesis and characterization of multi functional NaNbO3-KNbO3 mixed ceramics

The Ferroelectric perovskite oxides in the form of single crystals, polycrystalline ceramics and thin or thick films constitute an important class of materials widely used in capacitors, electro mechanical systems, ferroelectric memories, etc. Ferroelectric ceramic materials NaxK1-x NbO3(NKN) are synthesized by solid state double sintering method. The synthesized materials are characterized using X-ray diffraction, SEM, EDS and DSC. Dielectric properties and impedance are studied.NKN is a highly researched material as a lead-free piezoelectric ceramic. It is a mixture between ferroelectric KNbO3 and anti-ferroelectric NaNbO3 where there is a morphotropic phase boundary (MPB) for the (Na0.52K0.48)NbO3 formulation; most research, however, is conducted at an equal ratio of sodium to potassium. Like BNT, NKN is known for its sintering difficulties, and suffers from deliquescence (degradation in contact with moisture). Typical properties of NKN include Pr and Ec of 15 µC/cm2 and 13 kV/cm. Doping NKN significantly improve the density, microstructure and piezoelectric properties. In the present study NKN samples with x= 0.0, 0.4, 0.5, 0.6 and 1 compositions are synthesized and characterized. The SEM micrographs indicate a gradual change in the morphology of the samples. For NaNbO3 samples spherical grains are observed. Growth of microfibers is observed in x= 0.5 samples. For higher compositions the microfiber morphology is changed to elongated grains. DSC of the samples showed phase transitions at around 320°C temperature. The x-ray diffraction studies indicate orthorhombic structure except x = 0.4. Dielectric constant versus temperature plots indicated ferroelectric to paraelectric phase transitions. These transitions are of diffuse type. Ferroelectric hysteresis loops are observed to be lossy type without saturation. Impedance spectroscopy studies show relaxation in the samples. The relaxations are observed in the temperature region of 400-600°C. The complex impedance plots in this temperature range indicate single semi-circle. The relaxations are observed to be of non-Debye type. The equivalent circuits contain parallel combinations of resistance and capacitance elements. The mechanism of relaxation is discussed in the paper. An attempt is made to understand the results obtained in terms of possible charge accumulation mechanism.

Electronic structure and dielectric properties of ZrO2-CeO2 mixed oxides

ZrO2–CeO2 mixed ceramics were studied for their local electronic structure and dielectric properties. X-ray diffraction (XRD), scanning electron microscope (SEM), X-ray absorption fine structure (XAFS) and frequency dependence dielectric constant measurements were performed on the samples. Rietveld refinements and quantitative phase analysis of ZrO2-CeO2 ceramics showed an increased concentration of tetragonal ZrO2 and cubic Zr0.5Ce0.5O2 phases at the expense of parent monoclinic ZrO2. The morphology of the ZrO2-CeO2 ceramics remained invariant for all of the fractional percentages of CeO2 loading. O K-edge and Ce M5,4-edge NEXAFS showed the oxygen vacancies and Ce3+-Ce4+ redox pair formation in ZrO2CeO2 ceramics, which is further corroborated by Ce L3-edge XAFS. The higher CeO2 molar ratios containing ZrO2–CeO2 ceramics showed higher ε′, ε″ and σac and lower tan δ.

Comparative assessment of coated and uncoated ceramic tools on cutting force components and tool wear in hard turning of AISI H11 steel using Taguchi plan and RMS

This study investigated the cutting performance of coated CC6050 and uncoated CC650 mixed ceramics in hard turning of hardened steel. The cutting performance was mainly evaluated by cutting force components and tool wear. The planning of experiments was based on Taguchi’s L36 orthogonal array. The response surface methodology and analysis of variance were used to check the validity of multiple linear regression models and to determine the significant parameter affecting the cutting force components. Tool wear progressions and, hence, tool life, different tool wear forms and wear mechanisms observed for tools coated with TiN and uncoated mixed ceramics are presented along with the images captured by digital and electron microscope. Experimental observations indicate higher tool life with uncoated ceramic tools, which shows encouraging potential of these tools to hard turning of AISI H11 (50 HRC). Finally, tool performance indices are based on units which characterise machined cutting force components and wear when hard turning.

Specifics of Wear of Ceramic Cutting Tool Inserts Featuring Al&lt;sub&gt;2&lt;/sub&gt;O&lt;sub&gt;3&lt;/sub&gt;-TiC Dies when Face Milling Hardened Cast Iron

This work studies wear kinetics of index able inserts (II) made of mixed ceramics based on Russian-manufactured in case of fine milling of special hardened cast iron with globular graphite. In a wide range of cutting parameters typical for fine milling, an impact of tool insert wearing parameters on qualitative and quantitative characteristics of the cutting process have been studied. Morphological traits and nature of wear of work surfaces has been studied using optical and scanning electron microscopy. Criteria of II states, as well as specifics of contact work surface transformation, correlating with force parameters of the face milling process, have been determined.

Ceramic-on-ceramic bearings in total hip arthroplasty (THA)

The main reason for total hip arthroplasty (THA) revision is the wear-related aseptic loosening. Younger and active patients after total joint replacement create high demands, in particular, on the bearings. The progress, especially for alumina ceramic-on-ceramic bearings and mixed ceramics have solved many problems of the past and lead to good in vitro results. Modern ceramics (alumina or mixed ceramics containing alumina) are extremely hard, scratch-resistant, biocompatible, offer a low coefficient of friction, superior lubrication and have the lowest wear rates in comparison to all other bearings in THA. The disadvantage of ceramic is the risk of material failure, i.e., of ceramic fracture. The new generation of mixed ceramics (delta ceramic), has reduced the risk of head fractures to 0.03-0.05 %, but the risk for liner fractures remains unchanged at about 0.02 %. Assuming a non-impinging component implantation, ceramic-on-ceramic bearings have substantial advantages over all other bearings in THA. Due to the superior hardness, ceramic bearings produce less third body wear and are virtually impervious to damage from instruments during the implantation process. A specific complication for ceramic-on-ceramic bearings is "squeaking". The high rate of reported squeaking (0.45 to 10.7 %) highlights the importance of precise implant positioning and the stem and patient selection. With precise implant positioning this problem is rare with many implant designs and without clinical relevance. The improved tribology and the presumable resulting implant longevity make ceramic-on-ceramic the bearing of choice for young and active patients.

Performance of mixed ceramics and CBN tools during hard turning of martensitic stainless steel

This paper describes the wear behavior of a ceramic and a PcBN cutting tool during the turning of AISI 440B stainless steels at different machining conditions. Experimental results showed that the wear mechanism for ceramic cutting tool is predominantly abrasive wear and for cBN tools was adhesive wear and abrasive wear. The abrasive wear is as a result of hard carbide particles in the workpiece material resulting in grooves formed on the flank face. There was formation of transferred layer followed by plastic deformation on the rake face of PcBN tool when cutting at low speed and feed rate. Better surface finish (Ra) was recorded for ceramics but with deteriorating surface topography. The results also show that good dimensional accuracy can be achieved with cBN tools using CNC machine with high static and dimensional stiffness coupled with high-precision hard turning.

The history of the technological progress of hardmetals

The impressive history of hardmetals starts with the search for a proper and cheaper material for drawing dies for the drawing of non-sag tungsten (NS-W) after the First World War. The OSRAM R&D group tried to reduce the brittleness of pure WC by adding nickel at first and soon thereafter cobalt, which was utterly successful. Hence, a project aimed to find the solution to a specific problem can unexpectedly lead to a much more important application: The classical hardmetal was born at the OSRAM Studiengesellschaft in Berlin. The famous respective Schröter patent was issued in 1923. Since nobody at OSRAM was realizing the significance of this invention, the patent was offered to the Krupp Company where the development of a production technology for the manufacture of hardmetals was started. Especially in the prewar and war-years (1935–1945) the hardmetal production at KRUPP increased exponentially from ca. 30t/year to 500t/year.The further development of hardmetals is characterized by other carbide and binder combinations. TiC-based hardmetals are a great step forward in the machining of steels and so are fine-grained hardmetals for a wide spectrum of applications. Coating technologies have greatly increased the wear resistance of hardmetals.With the rising tendency of automation in metal cutting, indexable inserts with quite complex geometries were developed for the application in lathes and milling centers working with computer numerical control (CNC). Coating technologies by chemical vapor deposition (CVD) and physical vapor deposition (PVD) have greatly increased the wear resistance of hard metals. Coating with aluminum oxide multilayers and with diamond was devised as well as compact nonmetallic hard materials such as cubic boron nitride, oxide and nitride ceramics and mixed ceramics. Cermets are only briefly discussed here.Hence, after a period of almost 90years, cemented carbides have evolved from a temporary solution in industry (as a substitute for diamond in W-wire-drawing in the lighting industry) to a very successful and almost irreplaceable material for the manufacturing industry. It is also one of the best characterized materials and makes for 36% of global PM-production.The authors of this presentation consider it remarkable that from the very beginning of hardmetals, the optimal combination of WC and Co was chosen. Even today, 90years later, there is no better combination of hard carbide and metallic binder in sight.Finally, a short survey of the literature of hardmetals and hard materials is given.

Roughness Improvement in Hard Turning when Changing Cutting Parameters and Using Differently Shaped Ceramic Tools

This article deals with hard turning using wiper and conventional geometry of cutting tool. The aim of this paper is to compare surface roughness when using different feeds and different cutting speeds when turning with different cutting tool ́s geometries. For the experimental research was used hardened steel 100Cr6 with Rockwell hardness 62 HRC. There is a possibility to use two different cutting tool materials for finish machining of hardened steels with hardness 45 65 HRC: PCBN and mixed ceramics. Aluminum oxide plus TiC was used in this experiment.

Solvation phenomena and revision of solid–liquid equilibria in aqueous solutions of two precursors of mixed oxides, the hydrates of cobalt and nickel nitrates

The hydrates of cobalt and nickel nitrates are highly relevant as precursors for the preparation of mixed ceramics. In order to verify the numerous bibliographical data, systematic solubility measurements in aqueous medium under atmospheric pressure and a critical evaluation have been undertaken. By taking solvation phenomena into account, it has proved possible to correlate all the phenomena observed, to obtain equations representative of the liquidus curves, and to refine and extrapolate the experimental curves. The whole stable and metastable coordinates of the invariant transformations in both binary systems have been calculated or more accurately determined.