1 Erratum to: METALLURGICAL AND MATERIALS TRANSACTIONS A, Volume 47A, June 2016, pp. 2625–2641 DOI 10.1007/s11661-016-3430-x

The following are corrections to the original article:

In Appendix A, temperature formulas

$$ {\text{T}}_{{{\text{a}}_{\text{T}} }}^{{{\alpha }}}= - \left( {\sqrt { 1. 1 0 \times 10^{ 1 1} + 2.74 \times 10^{ 3 5} \left( {{\text{C}}_{\text{Si}} } \right)^{ 2} -3.25 \times 10^{ 3 5} {\text{C}}_{\text{Si}} +1.46 \times 10^{ 3 4} } + 1.74 \times 10^{ 2 3} {\text{C}}_{\text{Si}} -1.0 2 \times 10^{ 2 3} } \right) / 8. 5 3 \times 10^{ 1 9} $$
$$ {\text{T}}_{{{\text{A}}_{ 1} }}^{{{\alpha }}} = - \left( {\sqrt { 3. 4 7 \times 10^{ 1 1} +1.60 \times 10^{ 2 2} \left( {{\text{C}}_{\text{Si}} } \right)^{ 2} -2.19 \times 10^{ 2 1} {\text{C}}_{\text{Si}} +5.85 \times 10^{ 1 9} } + 7.4 \times 10^{ 1 6} {\text{C}}_{\text{Si}} -9.8 5 \times 10^{ 1 5} } \right) / 7. 6 9 \times 10^{ 1 2} $$
$$ {\text{T}}_{{{\text{a}}_{\text{T}} }}^{\text{P}} = -\left( {\sqrt { 2. 1 6 \times 10^{ 1 0}+ 5.07 \times 10^{ 2 0} \left( {{\text{C}}_{\text{Si}} } \right)^{ 2} -3.94 \times 10^{ 2 0} {\text{C}}_{\text{Si}} + 5.2 3 \times 10^{ 1 9} }+3.0 8 \times 10^{ 1 5} {\text{C}}_{\text{Si}} -2.82 \times 10^{ 1 5} } \right) / 2. 3 2 \times 10^{ 1 2} $$
$$ {\text{T}}_{{{\text{A}}_{ 1} }}^{\text{P}} = - \left( {\sqrt { 4. 0 5 \times 10^{ 1 1}+6.7 2 \times 10^{ 2 1} \left( {{\text{C}}_{\text{Si}} } \right)^{ 2} -7.3 \times 10^{ 2 0} {\text{C}}_{\text{Si}}+7.5 \times 10^{ 1 9} }+5.4 6 \times 10^{ 1 6} {\text{C}}_{\text{Si}} +1.1 6 \times 10^{ 1 6} } \right) / 2. 4 \times 10^{ 1 3} $$

should be replaced by

$$ {\text{T}}_{{{\text{a}}_{\text{T}} }}^{{{\alpha }}} = - \left( {\sqrt { 1. 1 0 \times 10^{ 1 1} } \sqrt { 2. 7 4 \times 10^{ 3 5} \left( {{\text{C}}_{\text{Si}} } \right)^{ 2} -3.2 5 \times 10^{ 3 5} {\text{C}}_{\text{Si}} +1.46 \times 10^{ 3 4} } +1.74 \times 10^{ 2 3} {\text{C}}_{\text{Si}} -1.02 \times 10^{ 2 3} } \right) / 8. 5 3 \times 10^{ 1 9} $$
$$ {\text{T}}_{{{\text{A}}_{ 1} }}^{{{\alpha }}} = - \left( {\sqrt { 3. 4 7 \times 10^{ 1 1} } \sqrt { 1. 6 0 \times 10^{ 2 2} \left( {{\text{C}}_{\text{Si}} } \right)^{ 2} -2.1 9 \times 10^{ 2 1} {\text{C}}_{\text{Si}}+5.85 \times 10^{ 1 9} }+7.4 \times 10^{ 1 6} {\text{C}}_{\text{Si}} -9.85 \times 10^{ 1 5} } \right) / 7. 6 9 \times 10^{ 1 2} $$
$$ {\text{T}}_{{{\text{a}}_{\text{T}} }}^{\text{P}} = -\left( {\sqrt { 2. 1 6 \times 10^{ 1 0} } \sqrt { 5. 0 7 \times 10^{ 2 0} \left( {{\text{C}}_{\text{Si}} } \right)^{ 2} -3.9 4 \times 10^{ 2 0} {\text{C}}_{\text{Si}}+5.23 \times 10^{ 1 9} }+3.08 \times 10^{ 1 5} {\text{C}}_{\text{Si}} -2.82 \times 10^{ 1 5} } \right) / 2. 3 2 \times 10^{ 1 2} $$
$$ {\text{T}}_{{{\text{A}}_{ 1} }}^{\text{P}} = \left( {\sqrt { 4. 0 5 \times 10^{ 1 1} } \sqrt { 6. 7 2 \times 10^{ 2 1} \left( {{\text{C}}_{\text{Si}} } \right)^{ 2} -7.3 \times 10^{ 2 0} {\text{C}}_{\text{Si}}+7.5 \times 10^{ 1 9} }+5.4 6 \times 10^{ 1 6} {\text{C}}_{\text{Si}}+1.16 \times 10^{ 1 6} } \right) / 2. 4 \times 10^{ 1 3} $$

In Appendix B, Table B-IV, diffusion coefficient of carbon in the liquid (\( {\text{D}}_{\text{C}}^{\text{l}} {{ = 5 \times 10}}^{ 1 0} \)) is corrected as \( {\text{D}}_{\text{C}}^{\text{l}} {{ = 5 \times 10}}^{-10}. \)