Formation of coherent, core-shelled nano-particles in dilute Al-Sc-Zr alloys from the first-principles

doi:10.1016/j.jmst.2018.11.004

Abstract

Abstract:

We present a systematic first-principles based study on the formation of coherent L1₂-phase nano-particles in dilute Al-Sc-Zr alloys. Bulk structures and properties, solute substitution, interface formation energies, and interfacial coherent strains are all calculated. Nucleation modeling and relevant energetic calculations are performed on various possible structures of L1₂-phase nano-precipitates, i.e. individual L1₂-Al₃Sc and L1₂-Al₃Zr, homogeneous L1₂-Al₃(Sc_xZr_1-_x) and the core-shelled L1₂-Al₃Sc(Al₃Zr) and L1₂-Al₃Zr(Al₃Sc). The following insights are obtained. Matrix-dissolved Sc or Zr strongly prefers to substitute the X sublattice sites in L1₂-Al₃X (X = Zr or Sc), while the inter-substitution between L1₂-Al₃Sc and Al₃Zr is only weakly feasible. The cube-on-cube orientation with the (100)/(100) contacting facets is the most energy favored for the Al/Al₃Sc(L1₂), Al/Al₃Zr(L1₂) and Al₃Sc (L1₂)/Al₃Zr(L1₂) interfaces. All these interfaces are highly coherent, with fairly low formation energy. And particularly, the Al₃Sc(L1₂)/Al₃Zr(L1₂) interface has essentially zero formation energy. Ternary L1₂-Al₃(Sc_xZr_1-_x) precipitates tend to form a Al₃Sc-based core and Al₃Zr-based shell structure, with a relatively sharp inner interface of Al₃Sc(L1₂)/Al₃Zr(L1₂). This core-shelled structure becomes energetically more favorable for the particle size R > 1-2 nm. The potential influence of the Sc/Zr ratio and temperature on the relative stabilities of L1₂-phases in Al is also evaluated and discussed.

Key words: Al-Sc-Zr, Precipitation, Interface, Core-shell structure, First principles

Chaomin Zhang, Yong Jiang, Fuhua Cao, Tao Hu, Yiren Wang, Dengfeng Yin. Formation of coherent, core-shelled nano-particles in dilute Al-Sc-Zr alloys from the first-principles[J]. J. Mater. Sci. Technol., 2019, 35(5): 930-938.

Figures/Tables 6

Table 1 Calculated bulk structures and elastic properties of Al, L12-Al3Sc, and L12-Al3Zr.

	fcc-Al			Al₃Sc-L1₂			Al₃Zr-L1₂
	PAW-PBE	Other Calc.	Expt.	PAW-PBE	Other Calc.	Expt.	PAW-PBE	Other Calc	Expt.
a₀(?)	4.04	3.97 [21] ^a4.03 [15] ^b	4.05 [26]	4.106	4.038 [20] ^a4.103 [15] ^b	4.101 [20]	4.107	4.04 [22]4.097 [32] ^c4.11 [32] ^d	4.05 [23]4.09 [24]
C₁₁(GPa)	125.8	106 [21] ^a109 [15] ^b	114.3 [21]	180.0	191 [20] ^a188 [15] ^b	183.0 [20]	179.3	189.3 [22]185.7 [32] ^c175.9 [32] ^d
C₁₂(GPa)	54.0	68.6 [21] ^a64.5 [15] ^b	61.9 [21]	39.6	43 [20] ^a43.7 [15] ^b	46.0 [20]	64.0	66.1 [22]59.2 [32] ^c62.6 [32] ^d
C₄₄(GPa)	37.9	33.6 [21] ^a32.4 [15] ^b	31.6 [21]	71.0	82 [20] ^a71.4 [15] ^b	68.0 [20]	72.8	84.4 [22]62.7 [32] ^c69.6 [32] ^d
B(GPa)	77.9	79.2 [21] ^a79.3 [15] ^b	75.8 [21]	86.7	91.6 [20] ^a91.8 [15] ^b	91.7 [20]	102.0	107.2 [22]103.1 [32] ^c100.3 [32] ^d
G(GPa)	37.0	28.3 [15] ^b	29.4 [21]	71.0	71.7 [15] ^b	68.2 [20]	66.0	67.5 [32] ^c 64.1 [32] ^d
E(GPa)	96.0		78.1 [21]	167.0			164.0	166.1 [32] ^c 158.6 [32] ^d

Table 2 Calculated substitution formation energies (eV) for Zr and Sc.

Substituting element	Substituted element	ΔG (eV)
Substituting element	Substituted element	Substituted element goes into Al	Substituted element goes Into Al₃X
ZrinAl	Al(in Al₃Sc)	1.835	1.835
	Sc(in Al₃Sc)	-0.170	-0.945
Zr(in Al₃Zr)	Al(in Al₃Sc)	2.665	2.665
	Sc(in Al₃Sc)	0.661	-0.115
ScinAl	Al(in Al₃Zr)	1.275	1.275
	Zr(in Al₃Zr)	-0.020	-0.850
Sc(in Al₃Sc)	Al(in Al₃Zr)	2.051	2.051
	Zr(in Al₃Zr)	0.755	-0.075

Fig. 1 (a) The possible 001Al/001Al3X interface structures: (a1) the Al-terminated and top-coordinated, (a2) the Al-terminated and bridge-coordinated, (a3) the AlX-terminated and top-coordinated, (a4) the AlX-terminated and bridge-coordinated. (b) The possible 110Al/110Al3X interface structures: (b1) the Al-terminated and top-coordinated, (b2) the Al-terminated and hollow-coordinated, (b3) the AlX-terminated and top-coordinated, (b4) the AlX-terminated and hollow-coordinated. (c) The possible 111Al/111Al3X interface structures: (c1) the AlX-terminated and top-coordinated, (c2) the AlX-terminated and hollow-coordinated. Note the two nearest-neighboring atomic layers around the interfaces are highlighted as red-dashed lines.

Fig. 2 Prediction of interface energy γ (J/m2) and coherent strain energy ΔGcs (eV/atom) of (a) Al/Al3Sc, (b) Al/Al3Zr, and (c) Al3Sc/Al3Zr interfaces, with various contacting facets of (001)/(001), (110)/(110), and (111)/(111).

Fig. 3 Calculated volumetric formation energies ΔGV of Al3X(L12) (X?=?Sc/Zr) in Al at different temperatures.

Fig. 4 Calculated total formation energies versus precipitate radius for four candidate precipitation structures under various aging temperatures and the Sc/Zr atom ratios. The black curve denotes the formation of two separated Al3Zr(L12) and Al3Sc(L12) particles, the blue curve denotes the core-shelled Sc(Zr) structure, the green curve denotes the homogeneous Al3(ScxZr1-x)structure, and the red curve denotes the core-shelled Zr(Sc) structure.

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