TY - JOUR
T1 - Corrigendum to “Evaluation of an Al-Ce alloy for additive manufacturing” [Acta Mater. 126 (2017) 507–519](S1359645416310138)(10.1016/j.actamat.2016.12.065))
AU - Plotkowski, A.
AU - Mohammadpour, P.
AU - Phillion, A. B.
AU - Babu, S. S.
N1 - Publisher Copyright:
© 2018 Acta Materialia Inc.
PY - 2018/10/15
Y1 - 2018/10/15
N2 - The authors regret in the construction of the microstructure selection model presented in the appendix of the original paper [1], a mistake in implementation affected the values presented based on the theoretical calculations. While these errors impact the quantitative values in these results, the conclusions of the paper are not affected. First, in the numerical implementation of the model, the velocity dependent partition coefficient was calculated incorrectly. In addition, two typographical errors were made in the original paper. The value for the liquid composition at the dendrite tip (Equation (21) in Ref. [1]) incorrectly used the equilibrium partition coefficient instead of the velocity dependent value. The correct expression is: [Formula presented] A similar typographical error was made in Equation (16) which was inherited from an error in Ref. [2] (Reference 30 in the original paper). The appropriate equation is: [Formula presented] While not technical errors, we would also like to take the opportunity to clarify three additional points. The dendrite tip radius (Equation (18)) may be more generally expressed in terms of the dendrite tip selection parameter: [Formula presented] The sign of the solutal undercooling term in the dendrite tip undercooling expression (Equation (12)) depends on the convention adopted for the liquidus slope, which, if defined positive, results in a change in sign for this term compared to the original expression: [Formula presented] Finally, the mathematical formulation of the non-equilibrium eutectic composition range was not given explicitly. The expression used here was [Formula presented] The above corrections impact Figures 10, 11, and 14. It was found that similar results were obtained if a Gibbs-Thomson coefficient of 3.5 × 10−7 mK was used for the Al11Ce3 intermetallic. Given the lack of knowledge of the relevant thermodynamic parameters for Al11Ce3, arbitrarily changing the Gibbs-Thomson coefficient in this way may be considered a rough calibration of the model, and only qualitative trends, rather than quantitative predictions, should be expected as a result. Using the mass diffusion coefficient in the liquid for the Al-Si system, the eutectic spacing may then be approximately matched to the experimental values as shown in Fig. 1 (Figure 10 in Ref. [1]). The microstructure selection maps show some differences in the shapes of the various microstructure regions, and due to the corrected planar undercooling resulting from the velocity dependent partitioning behavior, banded and planar Al11Ce3 microstructures are now absent. The new maps are shown in Fig. 2 and may be compared to Figure 11 in Ref. [1]. Finally, the examples of the dendrite tip and interface response functions from Figure 14 in Ref. [1] may be updated as shown in Fig. 3. For reference, the same thermodynamic values are used as those in the original work. The dendrite tip functions show similar shapes but terminate near the high-velocity planar growth limit at lower radius values. The interface response functions are similar except at high velocities where the planar growth shows a significantly larger undercooling. The interpretation of these results is the same as the original paper. Specifically, while this approach to understanding solidification microstructure evolution and phase selection is useful for rationalizing the observed behavior, the uncertainty in the thermodynamic properties of the phases under consideration significantly impacts the ability to make quantitative predictions. References [1] A. Plotkowski, O. Rios, N. Sridharan, Z. Sims, K. Unocic, R.T. Ott, R.R. Dehoff, S.S. Babu, Evaluation of an Al-Ce alloy for laser additive manufacturing, Acta Mater. 126 (2017). doi:10.1016/j.actamat.2016.12.065. [2] R. Trivedi, W. Kurz, Dendritic growth, Int. Mater. Rev. 39 (1994). The Authors Would like to Apologise for Any Inconvenience Caused.
AB - The authors regret in the construction of the microstructure selection model presented in the appendix of the original paper [1], a mistake in implementation affected the values presented based on the theoretical calculations. While these errors impact the quantitative values in these results, the conclusions of the paper are not affected. First, in the numerical implementation of the model, the velocity dependent partition coefficient was calculated incorrectly. In addition, two typographical errors were made in the original paper. The value for the liquid composition at the dendrite tip (Equation (21) in Ref. [1]) incorrectly used the equilibrium partition coefficient instead of the velocity dependent value. The correct expression is: [Formula presented] A similar typographical error was made in Equation (16) which was inherited from an error in Ref. [2] (Reference 30 in the original paper). The appropriate equation is: [Formula presented] While not technical errors, we would also like to take the opportunity to clarify three additional points. The dendrite tip radius (Equation (18)) may be more generally expressed in terms of the dendrite tip selection parameter: [Formula presented] The sign of the solutal undercooling term in the dendrite tip undercooling expression (Equation (12)) depends on the convention adopted for the liquidus slope, which, if defined positive, results in a change in sign for this term compared to the original expression: [Formula presented] Finally, the mathematical formulation of the non-equilibrium eutectic composition range was not given explicitly. The expression used here was [Formula presented] The above corrections impact Figures 10, 11, and 14. It was found that similar results were obtained if a Gibbs-Thomson coefficient of 3.5 × 10−7 mK was used for the Al11Ce3 intermetallic. Given the lack of knowledge of the relevant thermodynamic parameters for Al11Ce3, arbitrarily changing the Gibbs-Thomson coefficient in this way may be considered a rough calibration of the model, and only qualitative trends, rather than quantitative predictions, should be expected as a result. Using the mass diffusion coefficient in the liquid for the Al-Si system, the eutectic spacing may then be approximately matched to the experimental values as shown in Fig. 1 (Figure 10 in Ref. [1]). The microstructure selection maps show some differences in the shapes of the various microstructure regions, and due to the corrected planar undercooling resulting from the velocity dependent partitioning behavior, banded and planar Al11Ce3 microstructures are now absent. The new maps are shown in Fig. 2 and may be compared to Figure 11 in Ref. [1]. Finally, the examples of the dendrite tip and interface response functions from Figure 14 in Ref. [1] may be updated as shown in Fig. 3. For reference, the same thermodynamic values are used as those in the original work. The dendrite tip functions show similar shapes but terminate near the high-velocity planar growth limit at lower radius values. The interface response functions are similar except at high velocities where the planar growth shows a significantly larger undercooling. The interpretation of these results is the same as the original paper. Specifically, while this approach to understanding solidification microstructure evolution and phase selection is useful for rationalizing the observed behavior, the uncertainty in the thermodynamic properties of the phases under consideration significantly impacts the ability to make quantitative predictions. References [1] A. Plotkowski, O. Rios, N. Sridharan, Z. Sims, K. Unocic, R.T. Ott, R.R. Dehoff, S.S. Babu, Evaluation of an Al-Ce alloy for laser additive manufacturing, Acta Mater. 126 (2017). doi:10.1016/j.actamat.2016.12.065. [2] R. Trivedi, W. Kurz, Dendritic growth, Int. Mater. Rev. 39 (1994). The Authors Would like to Apologise for Any Inconvenience Caused.
UR - http://www.scopus.com/inward/record.url?scp=85051739965&partnerID=8YFLogxK
U2 - 10.1016/j.actamat.2018.08.016
DO - 10.1016/j.actamat.2018.08.016
M3 - Comment/debate
AN - SCOPUS:85051739965
SN - 1359-6454
VL - 159
SP - 439
EP - 441
JO - Acta Materialia
JF - Acta Materialia
ER -