J. Mater. Sci. Technol. ›› 2022, Vol. 97: 147-155.DOI: 10.1016/j.jmst.2021.04.044
• Research Article • Previous Articles Next Articles
Tianci Xie, Hui Shi, Hongbin Wang, Qun Luo*(), Qian Li, Kuo-Chih Chou
Received:
2020-11-29
Revised:
2021-04-09
Accepted:
2021-04-28
Published:
2021-06-26
Online:
2021-06-26
Contact:
Qun Luo
About author:
* E-mail address: qunluo@shu.edu.cn (Q. Luo).1 These authors contributed equally to this work.
Tianci Xie, Hui Shi, Hongbin Wang, Qun Luo, Qian Li, Kuo-Chih Chou. Thermodynamic prediction of thermal diffusivity and thermal conductivity in Mg-Zn-La/Ce system[J]. J. Mater. Sci. Technol., 2022, 97: 147-155.
Fig. 1. Heat dissipating alloys marked on the calculated isothermal section of (a) Mg-Zn-La and (b) Mg-Zn-Ce systems at 623 K, XRD patterns of (c) as-cast Mg-Zn-La alloys #L7-L9 and (d) as-cast Mg-Zn-Ce alloys #C7-C9.
Alloys in Mg-Zn-La system | Phase constitutions (mol%) | Solubility of Zn in α-Mg (at.%) | Alloys in Mg-Zn-Ce system | Phase constitutions (mol%) | Solubility of Zn in α-Mg (at.%) |
---|---|---|---|---|---|
#L1-Mg99.8La0.2 | 2.4 LaMg12 | 0 | #C1-Mg99.8Ce0.2 | 2.2 CeMg12 | 0 |
#L2-Mg98.3Zn1.5La0.2 | 2.1 τ1 | 1.41 | #C2-Mg98.3Zn1.6Ce0.1 | 1.7 τ1 | 1.33 |
#L3-Mg97.4Zn2.4La0.2 | 2.2 τ1 | 1.90 | #C3-Mg97.2Zn2.7Ce0.1 | 1.8 τ1 | 2.22 |
#L4-Mg99.6La0.4 | 4.7 LaMg12 | 0 | #C4-Mg99.7Ce0.3 | 3.9 CeMg12 | 0 |
#L5-Mg97.8Zn1.8La0.4 | 4.5 τ1 | 1.30 | #C5-Mg97.7Zn2.0Ce0.3 | 3.4 τ1 | 1.37 |
#L6-Mg97.0Zn2.6La0.4 | 4.5 τ1 | 1.66 | #C6-Mg96.9Zn2.8Ce0.3 | 4.0 τ1 | 1.80 |
#L7-Mg99.4La0.6 | 7.3 LaMg12 | 0 | #C7-Mg99.5Ce0.5 | 6.5 CeMg12 | 0 |
#L8-Mg97.5Zn1.9La0.6 | 6.7 τ1 | 1.54 | #C8-Mg96.9Zn2.6Ce0.5 | 6.1 τ1 | 1.38 |
#L9-Mg96.0Zn3.4La0.6 | 6.7 τ1 | 1.95 | #C9-Mg95.5Zn4.0Ce0.5 | 6.5 τ1 | 2.20 |
Table 1 Alloys compositions, phase constitutions and solid solubility of Zn in α-Mg calculated from thermodynamic database [19,20]. The composition of alloys determined by ICP.
Alloys in Mg-Zn-La system | Phase constitutions (mol%) | Solubility of Zn in α-Mg (at.%) | Alloys in Mg-Zn-Ce system | Phase constitutions (mol%) | Solubility of Zn in α-Mg (at.%) |
---|---|---|---|---|---|
#L1-Mg99.8La0.2 | 2.4 LaMg12 | 0 | #C1-Mg99.8Ce0.2 | 2.2 CeMg12 | 0 |
#L2-Mg98.3Zn1.5La0.2 | 2.1 τ1 | 1.41 | #C2-Mg98.3Zn1.6Ce0.1 | 1.7 τ1 | 1.33 |
#L3-Mg97.4Zn2.4La0.2 | 2.2 τ1 | 1.90 | #C3-Mg97.2Zn2.7Ce0.1 | 1.8 τ1 | 2.22 |
#L4-Mg99.6La0.4 | 4.7 LaMg12 | 0 | #C4-Mg99.7Ce0.3 | 3.9 CeMg12 | 0 |
#L5-Mg97.8Zn1.8La0.4 | 4.5 τ1 | 1.30 | #C5-Mg97.7Zn2.0Ce0.3 | 3.4 τ1 | 1.37 |
#L6-Mg97.0Zn2.6La0.4 | 4.5 τ1 | 1.66 | #C6-Mg96.9Zn2.8Ce0.3 | 4.0 τ1 | 1.80 |
#L7-Mg99.4La0.6 | 7.3 LaMg12 | 0 | #C7-Mg99.5Ce0.5 | 6.5 CeMg12 | 0 |
#L8-Mg97.5Zn1.9La0.6 | 6.7 τ1 | 1.54 | #C8-Mg96.9Zn2.6Ce0.5 | 6.1 τ1 | 1.38 |
#L9-Mg96.0Zn3.4La0.6 | 6.7 τ1 | 1.95 | #C9-Mg95.5Zn4.0Ce0.5 | 6.5 τ1 | 2.20 |
Alloy No. | Elements | Phases | ||
---|---|---|---|---|
α-Mg | REMg12 | τ1 | ||
#L1-Mg99.8La0.2 | Mg | 100.0 | 97.4 | |
La | 0.0 | 2.6 | ||
Zn | 0.0 | 0.0 | ||
#C1-Mg99.8Ce0.2 | Mg | 100.0 | 96.4 | |
Ce | 0.0 | 3.6 | ||
Zn | 0.0 | 0.0 | ||
#L2-Mg98.3Zn1.5La0.2 | Mg | 98.7 | 84.0 | |
La | 0.0 | 2.6 | ||
Zn | 1.3 | 13.4 | ||
#C2-Mg98.3Zn1.6Ce0.1 | Mg | 99.3 | 77.3 | |
Ce | 0.0 | 4.0 | ||
Zn | 0.7 | 18.7 | ||
#L3-Mg97.4Zn2.4La0.2 | Mg | 98.2 | 74.7 | |
La | 0.0 | 3.4 | ||
Zn | 1.8 | 21.9 | ||
#C3-Mg97.2Zn2.7Ce0.1 | Mg | 98.9 | 69.7 | |
Ce | 0.0 | 4.2 | ||
Zn | 1.1 | 26.1 |
Table 2 Composition of phases in the alloys #L1-#L3 and #C1-#C3 (at.%).
Alloy No. | Elements | Phases | ||
---|---|---|---|---|
α-Mg | REMg12 | τ1 | ||
#L1-Mg99.8La0.2 | Mg | 100.0 | 97.4 | |
La | 0.0 | 2.6 | ||
Zn | 0.0 | 0.0 | ||
#C1-Mg99.8Ce0.2 | Mg | 100.0 | 96.4 | |
Ce | 0.0 | 3.6 | ||
Zn | 0.0 | 0.0 | ||
#L2-Mg98.3Zn1.5La0.2 | Mg | 98.7 | 84.0 | |
La | 0.0 | 2.6 | ||
Zn | 1.3 | 13.4 | ||
#C2-Mg98.3Zn1.6Ce0.1 | Mg | 99.3 | 77.3 | |
Ce | 0.0 | 4.0 | ||
Zn | 0.7 | 18.7 | ||
#L3-Mg97.4Zn2.4La0.2 | Mg | 98.2 | 74.7 | |
La | 0.0 | 3.4 | ||
Zn | 1.8 | 21.9 | ||
#C3-Mg97.2Zn2.7Ce0.1 | Mg | 98.9 | 69.7 | |
Ce | 0.0 | 4.2 | ||
Zn | 1.1 | 26.1 |
Fig. 3. Strength and elongation of different Mg-Zn-La (a)/Ce (b) alloys with different second phases (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.).
Element/Phase | Evaluated parameters |
---|---|
Mg | 10.614+0.004·T -103.549·T-1 |
Zn | 6.965+0.034·T +1987.722·T -1 |
Mg12Zn13 | -28.537+0.057·T +25,078.583·T -1 |
LaMg12 | 35.186-0.003·T +8018.229·T -1 |
CeMg12 | 70.244-0.029·T +3743.845·T -1 |
Table 3 Optimized parameters for thermal diffusion resistivity of pure elements and intermetallic compounds.
Element/Phase | Evaluated parameters |
---|---|
Mg | 10.614+0.004·T -103.549·T-1 |
Zn | 6.965+0.034·T +1987.722·T -1 |
Mg12Zn13 | -28.537+0.057·T +25,078.583·T -1 |
LaMg12 | 35.186-0.003·T +8018.229·T -1 |
CeMg12 | 70.244-0.029·T +3743.845·T -1 |
Phase region | Alloy system | Evaluated parameters |
---|---|---|
α-Mg+Mg12Zn13 | Mg-Zn | $M_{\text{Hcp}+\text{M}{{\text{g}}_{12}}\text{Z}{{\text{n}}_{13}}}^{0}=136.002-0.337\cdot T$ |
α-Mg+LaMg12 | Mg-La | $M_{\text{Hcp}+\text{LaM}{{\text{g}}_{12}}}^{0}=19.0402+0.168\cdot T$ |
$M_{\text{Hcp}+\text{LaM}{{\text{g}}_{12}}}^{1}=-63.5293-0.166\cdot T$ | ||
α-Mg+CeMg12 | Mg-Ce | $M_{\text{Hcp}+\text{CeM}{{\text{g}}_{12}}}^{0}=-779.154+0.735995\cdot T$ |
$M_{\text{Hcp}+\text{CeM}{{\text{g}}_{12}}}^{1}=894.143-0.86521\cdot T$ | ||
τ1 | Mg-Zn-La | $^{0}L_{{{\tau }_{1}}}^{La}=-105.186+0.20923\cdot T+43696.987/T$ |
$^{0}L_{{{\tau }_{1}}}^{Mg}=-57.133+0.20923\cdot T+43696.987/T$ | ||
$^{0}L_{{{\tau }_{1}}}^{Zn}=-204.823+0.20923\cdot T+43696.987/T$ | ||
$^{0}L_{{{\tau }_{1}}}^{Mg,\ Zn}=119.6790-0.196\cdot T$ | ||
$^{2}L_{{{\tau }_{1}}}^{Mg,\ Zn}=-1079.680+1.778\cdot T$ | ||
Mg-Zn-Ce | $^{0}L_{{{\tau }_{1}}}^{Ce}=-37.505+0.092\cdot T+20128.308/T$ | |
$^{0}L_{{{\tau }_{1}}}^{Mg}=-35.281+0.092\cdot T+20128.308/T$ | ||
$^{0}L_{{{\tau }_{1}}}^{Zn}=-40.216+0.092\cdot T+20128.308/T$ | ||
$^{0}L_{{{\tau }_{1}}}^{Mg,\ Zn}=-2053.910+2.664\cdot T$ | ||
α-Mg+τ1 | Mg-Zn-La | $M_{\text{Hcp}+{{\tau }_{1}}}^{0}=-249.026+0.385\cdot T$ |
$M_{\text{Hcp}+{{\tau }_{1}}}^{1}=286.952-0.541\cdot T$ | ||
Mg-Zn-Ce | $M_{\text{Hcp}+{{\tau }_{1}}}^{0}=534.759-0.889\cdot T$ | |
$M_{\text{Hcp}+{{\tau }_{1}}}^{1}=-62.155+0.248\cdot T$ |
Table 4 Parameters for thermal diffusion resistivity of Mg-Zn-La/Ce alloys in two-phase region.
Phase region | Alloy system | Evaluated parameters |
---|---|---|
α-Mg+Mg12Zn13 | Mg-Zn | $M_{\text{Hcp}+\text{M}{{\text{g}}_{12}}\text{Z}{{\text{n}}_{13}}}^{0}=136.002-0.337\cdot T$ |
α-Mg+LaMg12 | Mg-La | $M_{\text{Hcp}+\text{LaM}{{\text{g}}_{12}}}^{0}=19.0402+0.168\cdot T$ |
$M_{\text{Hcp}+\text{LaM}{{\text{g}}_{12}}}^{1}=-63.5293-0.166\cdot T$ | ||
α-Mg+CeMg12 | Mg-Ce | $M_{\text{Hcp}+\text{CeM}{{\text{g}}_{12}}}^{0}=-779.154+0.735995\cdot T$ |
$M_{\text{Hcp}+\text{CeM}{{\text{g}}_{12}}}^{1}=894.143-0.86521\cdot T$ | ||
τ1 | Mg-Zn-La | $^{0}L_{{{\tau }_{1}}}^{La}=-105.186+0.20923\cdot T+43696.987/T$ |
$^{0}L_{{{\tau }_{1}}}^{Mg}=-57.133+0.20923\cdot T+43696.987/T$ | ||
$^{0}L_{{{\tau }_{1}}}^{Zn}=-204.823+0.20923\cdot T+43696.987/T$ | ||
$^{0}L_{{{\tau }_{1}}}^{Mg,\ Zn}=119.6790-0.196\cdot T$ | ||
$^{2}L_{{{\tau }_{1}}}^{Mg,\ Zn}=-1079.680+1.778\cdot T$ | ||
Mg-Zn-Ce | $^{0}L_{{{\tau }_{1}}}^{Ce}=-37.505+0.092\cdot T+20128.308/T$ | |
$^{0}L_{{{\tau }_{1}}}^{Mg}=-35.281+0.092\cdot T+20128.308/T$ | ||
$^{0}L_{{{\tau }_{1}}}^{Zn}=-40.216+0.092\cdot T+20128.308/T$ | ||
$^{0}L_{{{\tau }_{1}}}^{Mg,\ Zn}=-2053.910+2.664\cdot T$ | ||
α-Mg+τ1 | Mg-Zn-La | $M_{\text{Hcp}+{{\tau }_{1}}}^{0}=-249.026+0.385\cdot T$ |
$M_{\text{Hcp}+{{\tau }_{1}}}^{1}=286.952-0.541\cdot T$ | ||
Mg-Zn-Ce | $M_{\text{Hcp}+{{\tau }_{1}}}^{0}=534.759-0.889\cdot T$ | |
$M_{\text{Hcp}+{{\tau }_{1}}}^{1}=-62.155+0.248\cdot T$ |
Fig. 7. Predicted thermal conductivities (λ) in (a) Mg-Zn-La system and (b) Mg-Zn-Ce system, (c) the calculated thermal conductivity vs experimental values (experimental data: Mg-Zn alloys [24] at 323 K, Mg-Zn-La alloys and Mg-Zn-Ce alloys at 323 K from present work) and (d) the thermal conductivity and yield strength analysis of Mg alloys [26].
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