There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Tribological behaviour of nano-zirconia reinforced iron-based self-lubricating composites for bearing applications

The CALPHAD approach was used to derive thermodynamic parameters of the Mn–Zr system based on experimental results and critical evaluation of available data. Novel ab-initio calculations as well as experimental data on enthalpy of formation and heat capacity measurements for the C14–ZrMn2 Laves phase were taken into account. The congruent melting point of the C14–ZrMn2 Laves phase was determined using differential thermal analysis (DTA) at 1765 K. Data on heat capacity for the C14–ZrMn2 phase were extended to high temperature range up to 980 K using differential scanning calorimetry (DSC). Standard entropy for C14–ZrMn2 was calculated using an extended Einstein model based on newly obtained results. Additionally, the sublattice model based on antisite substitution in the C14–ZrMn2 Laves phase has been used in order to describe its homogeneity range. Based on the currently obtained results and novel literature data, thermodynamic parameters for the Mn–Zr system were re-optimized. The self-consistent thermodynamic description derived in the present work reproduces all experimental data well.

Heat capacity measurement of C14–ZrMn2 and thermodynamic re-assessment of the Mn–Zr system

The Co–Fe–Zr system and its Co–Zr subsystem were optimized using the CALculation of PHAse Diagram (CALPHAD) approach. The substitutional solution model was used for describing the phases liquid, fcc_A1, bcc_A2 and hcp_A3. Two Laves phases were modeled as (Co,Fe,Zr)2(Co,Fe,Zr)1, and the phases CoFe and CoZr with the bcc_B2 crystal structure were described as the ordered one of bcc_A2 in the formula (Co,Fe,Va,Zr)0.5(Co,Fe,Va,Zr)0.5Va3. With limited solubility ranges, all other phases were treated as the line compounds (Co,Fe)mZrn. An excellent agreement between the reported and calculated results was reached. The reliable thermodynamic parameters of the Co–Fe–Zr system were acquired, which can be well applied to various thermodynamic calculations and materials design.

https://link.springer.com/content/pdf/10.1007/s11669-020-00859-5.pdf

Thermodynamic Descriptions of the Co–Zr and Co–Fe–Zr Systems

The stability of the Fe23Zr6 phase in Fe–Zr system was studied, and the partial Fe–Zr phase diagram was revised by means of X-ray diffraction, electron probe microanalysis and differential thermal analysis methods. On the basis of the experimental results in the present work and literature, the Fe–Zr system was reassessed using CALculation of PHAse Diagram (CALPHAD) method. Solution phases, liquid, fcc, bcc and hcp, are modeled as the substitutional solution. The intermetallic compounds, hex.-Fe2Zr, Fe2Zr, FeZr2 and FeZr3 phases, are treated as Fe2(Fe, Zr)1, (Fe, Zr)2(Fe, Zr)1, (Fe, Zr)1Zr2 and (Fe, Zr)1(Fe, Zr)3 by a two-sublattice model, respectively. The Fe23Zr6 phase is treated as stoichiometric compound. A set of self-consistent thermodynamic parameters of the Fe–Zr system was obtained. The results confirm the stability of Fe23Zr6 phase, improve the phase diagram of the Fe–Zr system and provide a theoretical reference for the development of Zr alloys.

Phase stability of Fe 23 Zr 6 and thermodynamic reassessment of Fe–Zr system

Thermodynamic and physical properties of Zr3Fe and ZrFe2 intermetallic compounds

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Thermodynamic and physical properties of Zr3Fe and ZrFe2 intermetallic compounds