Homogeneous and heterogeneous precipitation mechanisms in a binary Mg–Nd alloy

Abstract

Parallel modes of precipitation mechanisms in an Mg–Nd alloy were revealed by examining an isothermally annealed high pressure die cast alloy at 177 °C for up to 100 h. Broadly, precipitate evolution was observed to occur concurrently on dislocations and within the surrounding α-Mg matrix. However, it was observed that the presence of dislocation accelerated the precipitate formation kinetics significantly. In contrast to the accepted precipitation pathway in the Mg–Nd system, i.e., SSSS → GP zones → β″ → β′ → β₁ → β → β_e, dislocations were found to preferentially facilitate the formation of β′ and β₁ precipitates even at the very early stages (5 h) of annealing. Within the same time frame, a homogeneous distribution of Nd-rich pockets was observed throughout the α-Mg matrix, along with the β′ and β₁ precipitates decorating dislocation lines. Results further indicate that these Nd-rich regions initiated precipitation within the parent α-Mg matrix. The formation of these Nd-rich pockets was explained on the basis of a miscibility gap in the α-Mg phase at 177 °C. Our results demonstrate that the presence of dislocations influence strongly the phase-transformation pathways in Mg-rare earth alloys by facilitating the formation of selective precipitate phases.

Appendix

Parameters used for thermodynamic modeling

Standard free energies as a function of temperature (T) for Mg (HCP_A3) and Nd (DHCP) [33]

$$ G_{\text{Mg}}^{0} = - 8367.34 + 143.675547 \times T - 26.1849782 \times T \times \log \left( T \right) + \left( {0.4858 \times 10^{ - 3} } \right) \times T^{2} - \left( {1.393669 \times 10^{ - 6} } \right) \times T^{3} + 78950/T, $$

$$ G_{\text{Nd}}^{0} = - 8402.93 + 111.10239 \times T - 27.0858 \times T \times \log \left( T \right) + \left( {0.556125 \times 10^{ - 3} } \right) \times T^{2} - \left( {2.6923 \times 10^{ - 6} } \right) \times T^{3} + 34887/T. $$

Interaction parameters used to describe the excess free energy (G _excess) by Niu et al. [30]

$$ L_{0}^{{\alpha {\text{ - Mg}}}} = - 300 3. 300 \times { \exp }\left( { - 0.00 60 1 4\times T} \right), $$

$$ L_{1}^{{\alpha - {\text{Mg}}}} = 17928.198 \times \exp \left( { - 0.000617 \times T} \right), $$

$$ L_{2}^{{\alpha {\text{ - Mg}}}} = 4 5. 5 20 \times { \exp }\left( { - 0.000 6 9 9\times T} \right), $$

$$ L_{ 3}^{{\alpha {\text{ - Mg}}}} = 3 8 1 2. 5 5 5\times { \exp }\left( { - 0.00 1 1\times T} \right). $$

Stress field around edge dislocation in a hcp crystal structure [34]

Coordinate system of the following formulations is shown in Fig. 11a

$$ \sigma^{\text{edge}} = \left( {\begin{array}{*{20}c} {\sigma_{\text{xx}} } & {\sigma_{\text{xy}} } & 0 \\ {\sigma_{\text{yx}} } & {\sigma_{\text{yy}} } & 0 \\ 0 & 0 & {\sigma_{\text{zz}} } \\ \end{array} } \right). $$

Components of σ _ij for an edge dislocation are given by

$$ \sigma_{{ {\text{xx}}}} = - \frac{{K_{\text{edge}} b_{\text{edge}} }}{2\pi }\zeta^{2} \frac{{y[\left( {C + 3} \right)x^{2} + \zeta^{2} y^{2} ]}}{{(x^{2} - \zeta^{2} y^{2} )^{2} + (C + 4)\zeta^{2} x^{2} y^{2} }}, $$

$$ \sigma_{{ {\text{yy}}}} = \frac{{K_{\text{edge}} b_{\text{edge}} }}{2\pi }\frac{{y\left( {x^{2} - \zeta^{2} y^{2} } \right)}}{{\left( {x^{2} - \zeta^{2} y^{2} } \right)^{2} + \left( {C + 4} \right)\zeta^{2} x^{2} y^{2} }}, $$

$$ \sigma_{zz} = \left( {\frac{{C_{12} C_{33} - C_{13}^{2} }}{{\overline{C}^{2} - C_{13}^{2} }}} \right)\sigma_{xx} + \left( {\frac{{C_{11} C_{13} - C_{12} C_{13} }}{{\overline{C}^{2} - C_{13}^{2} }}} \right)\sigma_{yy} , $$

$$ \sigma_{{ {\text{xy}}}} = \frac{{K_{\text{edge}} b_{\text{edge}} }}{2\pi }\frac{{y(x^{2} - \zeta^{2} y^{2} )}}{{(x^{2} - \zeta^{2} y^{2} )^{2} + (C + 4)\zeta^{2} x^{2} y^{2} }}, $$

$$ K_{\text{edge}} = \left( {\overline{C} + C_{13} } \right)\sqrt {\left[ {\frac{{C_{44} \left( {\overline{C} - C_{13} } \right)}}{{C_{33} \left( {\overline{C} + C_{13} + 2C_{44} } \right)}}} \right]} ,\quad \zeta^{2} = \sqrt {\frac{{C_{11} }}{{C_{13} }}} = (\overline{C} + C_{13} ),\quad \overline{C} = \sqrt {(C_{11} C_{33} )} , $$

where b _edge is the Burgers vector. Elastic constants of Mg were obtained from Gao et al. [36]: C ₁₁ = 63.5 GPa, C ₁₂ = 24.85 GPa, C ₁₃ = 19.33 GPa, C ₃₃ = 20.0 GPa, and C ₄₄ = 50.8 GPa. Note that edge dislocation stress fields have both dilatation ($\sigma_{\text{mm}} = \frac{1}{3} [\sigma_{\text{xx}} + \sigma_{\text{yy}} + \sigma_{\text{yy}} ]$) and shear ($\sigma_{{ {\text{xy}}}}$) componentss.