Erratum to: METALLURGICAL AND MATERIALS TRANSACTIONS B, 2014, Volume 45, Number 4, pp. 1545–1556 DOI: 10.1007/s11663-014-0079-y

Eq. (40) in page 1554 should be:

$$ H_{\alpha ,c} = \left\{ \begin{aligned} &1000 \cdot \left( {5188T(K)^{ - 1} - 86 + 0.505T(K)} \right. \\ & \left. { - 6.55 \cdot 10^{ - 5} T(K)^{2} + 1.5 \cdot 10^{ - 7} T(K)^{3} } \right) \quad T\left( K \right) \le 800 \, \\ & 1000 \cdot \left( { - 1.11 \cdot 10^{6} T(K)^{ - 1} + 4056 - 4.72T(K)} \right. \\ & \left. { + 2.292 \cdot 10^{ - 3} T(K)^{2} } \right) \quad 800 < T\left( K \right) \le 1000 \\ & 1000 \cdot \left( {5780 - 11.5T(K) + 6.238 \cdot 10^{ - 3} T(K)^{2} } \right) \\ & \qquad \qquad \qquad { 1000} < T\left( K \right) \le 1042 \\ & 1000 \cdot \left( { - 18379 + 34.87T(K) - 0.016013T(K)^{2} } \right) \\ & \qquad \qquad \qquad {1042} \le T\left( K \right) \le 1060 \\ & 1000 \cdot \left( { - 5.21766 \cdot 10^{6} T(K)^{ - 1} + 12822 - 10.068T(K)} \right. \\ & \left. { + 2.9934 \cdot 10^{ - 3} T(K)^{2} } \right) \quad { 1060} < T\left( K \right) \le 1184 \\ \end{aligned} \right. $$
(40)

instead of:

$$ H_{\alpha ,c} = \left\{ \begin{aligned} &1000 \cdot \left( {5188T(K)^{ - 1} - 86 + 0.505T(K)} \right. \\ & \left. { - 6.55 \cdot 10^{ - 5} T(K)^{2} + 1.5 \cdot 10^{ - 7} T(K)^{3} } \right) \quad T\left( K \right) \le 800 \, \\ & 1000 \cdot \left( { - 1.11 \cdot 10^{6} T(K)^{ - 1} + 4056 - 4.72T(K)} \right. \\ & \left. { + 2.292 \cdot 10^{ - 3} T(K)^{2} } \right) \quad 800 < T\left( K \right) \le 1000 \\ & 1000 \cdot \left( {{\mathbf{5720}} - 11.5T(K) + 6.238 \cdot 10^{ - 3} T(K)^{2} } \right) \\ & \qquad \qquad \qquad { 1000} < T\left( K \right) \le 1042 \\ & 1000 \cdot \left( { - {\mathbf{18.379}} + 34.87T(K) - 0.016013T(K)^{2} } \right) \\ & \qquad \qquad \qquad {1042} \le T\left( K \right) \le 1060 \\ & 1000 \cdot \left( { - 5.21766 \cdot 10^{6} T(K)^{ - 1} + {\mathbf{12.822}} - 10.068T(K)} \right. \\ & \left. { + 2.9934 \cdot 10^{ - 3} T(K)^{2} } \right) \quad { 1060} < T\left( K \right) \le 1184 \\ \end{aligned} \right. $$
(40)