The partial (Δ\documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}
$$(\Delta \overline H _i )$$
\end{document} and the integral (ΔH) enthalpies of mixing of liquid Ni-Zr and Cu-Ni-Zr alloys have been determined by high-temperature isoperibolic calorimetry at 1565 ± 5 K. The heat capacity (Cp) of liquid Ni26Zr74 has been measured by adiabatic calorimetry (Cp=53.5±2.2 J mol−1 K−1 at 1261±15 K). The integral enthalpy of mixing changes with composition from a small positive (Cu-Ni, ΔH (xNi=0.50, T=1473 to 1750 K)=2.9 kJ mol−1) to a moderate negative (Cu-Zr; ΔH(xZr=0.46, T=1485 K)=−16.2 kJ mol−1) and a high negative value (Ni-Zr; ΔH(xZr=0.37, T=1565 K)=−45.8 kJ mol−1). Regression analysis of new data, together with the literature data for liquid Ni-Zr alloys, results in the following relationships in kJ mol−1 (standard states: Cu (1), Ni (1), and Zr (1)):for Ni-Zr (1281≤T≤2270 K), \documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}
$$\begin{gathered} \Delta \bar H_{Ni} = x^2 \hfill \\ \left( {\begin{array}{*{20}c} {(333 \pm 55) + ( - 1.39 \pm 0.20) \cdot \frac{{10^5 }}{T} + (3.89 \pm 0.40) \cdot \frac{{10^7 }}{{T^2 }} + ( - 4468 \pm 226)x} \\ { + (1.29 \pm 0.36) \cdot \frac{{10^5 x}}{T} + (11,451 \pm 1178)x^2 + ( - 11,431 \pm 1473)x^3 + (4053 \pm 826)x^4 } \\ \end{array} } \right) \hfill \\ \end{gathered} $$
\end{document}\documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}
$$\begin{gathered} \Delta \bar H_{Zr} = (1 - x)^2 \hfill \\ \left( {\begin{array}{*{20}c} {( - 130.0 \pm 7.9) + ( - 7.45 \pm 0.32) \cdot \frac{{10^4 }}{T} + (3.89 \pm 0.40) \cdot \frac{{10^7 }}{{T^2 }} + ( - 928 \pm 108)x} \\ { + (1.29 \pm 0.36) \cdot \frac{{10^5 x}}{T} + (5310 \pm 658)x^2 + ( - 8189 \pm 1302)x^3 + (4053 \pm 826)x^4 } \\ \end{array} } \right) \hfill \\ \end{gathered} $$
\end{document}\documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}
$$\Delta H = (1 - x)\alpha _{Ni - Zr} $$
\end{document}\documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}
$$\begin{array}{*{20}c} {\alpha _{Ni - Zr} = ( - 130.0 \pm 7.9) + ( - 7.45 \pm 0.32) \cdot \frac{{10^4 }}{T} + (3.89 \pm 0.40) \cdot \frac{{10^7 }}{{T^2 }} + ( - 464 \pm 54)x} \\ { + (6.43 \pm 1.82) \cdot \frac{{10^4 x}}{T} + (1769 \pm 219)x^2 + ( - 2047 \pm 326)x^3 + (811 \pm 171)x^4 } \\ \end{array}$$
\end{document} for Cu-Ni-Zr (T=1565±5 K), \documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}
$$\Delta H = x_{Cu} x_{Ni} \alpha _{Cu - Ni} + x_{Cu} x_{Zr} \alpha _{Cu - Zr} + x_{Ni} x_{Zr} \alpha _{Ni - Zr} + x_{Cu} x_{Ni} x_{Zr} \alpha _{Cu - Ni - Zr} $$
\end{document}\documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}
$$\begin{gathered} \alpha _{Cu - Ni} = (11.1 \pm 0.6) + (1.1 \pm 0.1)x_{Ni} \hfill \\ \alpha _{Cu - Zr} = ( - 42.9 \pm 5.2) + ( - 44.2 \pm 10.3)x_{Cu} + (30.2 \pm 10.6)x_{Cu}^5 \hfill \\ \alpha _{Cu - Ni - Zr} = ( - 570.4 \pm 28.8) + (3010.9 \pm 184.9)x_{Zr} - (3349.8 \pm 268.6)x_{Zr}^2 + ( - 942.8 \pm 55.7)x \hfill \\ \end{gathered} $$
\end{document}
