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A simple theory of thermodynamic properties of liquid nitrogen solution in Fe–Mn alloys is proposed. This theory is completely analogous to the theory for liquid nitrogen solution in alloys of the Fe–Cr system proposed previously by the authors in 2019. The theory is based on the lattice model of the considered Fe–Mn solutions. The model assumes a FCC lattice. The atoms of Fe and Mn are in these lattice sites. Nitrogen atoms are located in octahedral interstices. The nitrogen atom interacts only with the metal atoms located in the lattice sites neighboring to it. This interaction is pairwise and it is assumed that the energy of this interaction depends neither on the composition nor on the temperature. Furthermore, the solution in the Fe–Mn system is assumed to be perfect. Within the framework of the proposed theory, a relation was obtained that expresses the value of the Sieverts law constant for N solubility in liquid Mn through the similar constant for the N solubility in liquid Fe and the Wagner N–Mn interaction coefficient in liquid Fe. The values of the Sieverts law constants in this relation are taken directly from the experimental measurements of the solubility of N in liquid Fe and in liquid Mn. In this case, the obtained relation is considered as an equation with respect to the Wagner interaction coefficient $$\varepsilon _{{\text{N}}}^{{{\text{Mn}}}}$$ . The equation’s solution gives the value of Wagner interaction coefficient $$\varepsilon _{{\text{N}}}^{{{\text{Mn}}}}$$ = –5.25 in liquid steel at a temperature of 1873 K. Wagner interaction coefficient $$\varepsilon _{{\text{N}}}^{{{\text{Mn}}}}$$ is related with Langenberg interaction coefficient $$e_{{\text{N}}}^{{{\text{Mn}}}}$$ by the relation deduced by Lupis and Elliott in 1965. The relation includes the atomic masses of Fe and Mn. By substituting the value $$\varepsilon _{{\text{N}}}^{{{\text{Mn}}}}$$ = –5.25 and solving the resulting equation with respect to $$e_{{\text{N}}}^{{{\text{Mn}}}}$$ , we obtain the value $$e_{{\text{N}}}^{{{\text{Mn}}}}$$ = –0.0230. This value corresponds to the experimental data of Beer (1961), which is likely one of the most probable of all experimental values of $$e_{{\text{N}}}^{{{\text{Mn}}}}$$ for liquid steel at 1873 K. Another such value is $$e_{{\text{N}}}^{{{\text{Mn}}}}$$ = 0.0209 obtained by Shin with coworkers in 2011.

Ceramic in the system Ca2P2O7–Ca(PO3)2 was obtained by firing cement stone fabricated from a powder mixture which included β-tricalcium phosphate β-Ca3(PO4)2 and monocalcium phosphate monohydrate Ca(H2PO4)2 ∙ H2O. The molar ratio Ca/P of the initial powder mixtures was set as Ca/P ≤ 1. X-ray phase analysis shows all ceramic samples after firing at 1000°C to include β-calcium pyrophosphate β-Ca2P2O7, and a sample of the ceramic made from a powder mixture with the maximum content of monocalcium phosphate monohydrate Ca(H2PO4)2 ∙ H2O also contained β-calcium polyphosphate β-Ca(PO3)2. The obtained calcium phosphate ceramic with reduced firing temperature can be used to develop a resorbable matrix for tissue engineering structures.

A simple theory is proposed for the thermodynamic properties of nitrogen solutions in Fe–Cr melts. The theory is based on a lattice model of the solution. An fcc model lattice is adopted. Iron and chromium atoms are distributed at the lattice sites. Nitrogen atoms are located in octahedral interstices. The nitrogen atoms only interact with metal atoms at neighboring lattice sites. The energy of this interaction is assumed to depend neither on the composition nor on the temperature. The liquid Fe–Cr solutions are assumed perfect. Within this framework, the constant in the Sieverts law governing the solubility of nitrogen in liquid chromium may be expressed in terms of its value for the solubility of nitrogen in liquid iron and the value of the Wagner parameter for N–Cr interaction in liquid iron alloys. In addition, the partial enthalpy of solution of nitrogen in liquid chromium at infinite dilution is expressed in terms of the corresponding enthalpy for the solution of nitrogen in liquid iron and the Wagner parameter for N–Cr interaction in liquid iron alloys. A relation is also established between the Wagner parameter for N–Fe interaction in liquid chromium alloys and the Wagner parameter for N–Cr interaction in liquid iron alloys. On that basis, the constant in the Sieverts law governing the solubility of nitrogen in liquid chromium is calculated, along with enthalpy of solution of nitrogen in liquid chromium at infinite dilution and the Wagner parameter for N‒Fe interaction in liquid chromium alloys at 1873 K. The calculation results are compared with experimental data regarding the solubility of nitrogen in liquid chromium and Cr–Fe alloys obtained by various methods. The theoretical data are in best agreement with experimental data obtained by quenching. The values of the Wagner parameter for N–N interaction in liquid chromium alloys and iron alloys are discussed.

Biphase ceramic containing hydroxyapatite Ca10(PO4)6(OH)2 and -tricalcium phosphate -Ca3(PO4)2 has been obtained from a uniform nanocrystalline calcium phosphate powder with the structure of apatite, synthesized from water solutions of calcium apatite and ammonium hydrophosphate with molar ratio CaP = 1.5 at room temperature without pH regulation. After firing at 1100°C the material contained 75% -Ca3(PO4)2 and the grain size did not exceed 600 nm. It is suggested that the carbon formed in the interval 200 – 500°C, as a result of the carbonization of the organic components of synthesis adsorbed by particles of powder, be used as a physical barrier impeding intense mass transfer up to 800°C, which makes it possible to obtain an ultradisperse ceramic with grains smaller than 1 m.

The properties of hydroxyapatite powder synthesized from calcium acetate and potassium hydrophosphate and hydroxide were investigated. The associated reaction product (ARP), whose basic component is potassium acetate, modifies the surface of the hydroxyapatite nanocrystals. The components of the ARP can play the role of a salt matrix by preventing coalescence of nanocrystallites and can also serve as a source for a sintering additive which is uniformly distributed due to adsorption during synthesis. A ceramic based on hydroxyapatite with a uniform microstructure and a maximum grain size of 300 nm was obtained by incorporation of sintering additives in the form of ARP at a temperature of 700°C. The ARP is the cause of different solid-phase processes and processes involving the liquid phase. The sites where these processes occur are the boundaries of the grains, which also restrains their growth.

Calcium hydroxyapatite (HAP) powder was synthesized from a water solution of potassium hydrophosphate and a suspension of calcium hydroxide in a water solution containing calcium and potassium ions, hydroxide ions, and acetate ions. The Ca(OH)2 amount in the calcium containing component was 50, 75, and 100%. The HAP powder synthesized was used to produce ceramic. After kilning at 700°C the density of the ceramic obtained from the HAP powder containing a by-product of the reaction was 2.9 – 2.6 g/cm3 and bending strength 35 – 45 MPa with grain size 200 nm. The phase composition was represented by HAP and calciumpotassium double orthophosphate. After kilning at 1200°C the density of the HAP-based ceramic made from powder with no by-product of the reaction was 2.2 – 2.3 g/cm3 and the bending strength was 45 – 55 MPa with grain size 500 – 1000 nm.