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Thermodynamic Modeling of the Al-Ce-Cu-Mg-Si System and Its Application to Aluminum-Cerium Alloy Design

Recently discovered AlCe alloys have shown promise in a number of applications, but the propensity of Ce to react with Al and other alloying elements can complicate the phase equilibria and design approach. To solve this, the CALPHAD method is used to explore an alloy within the quinary Al-Ce-Cu-Mg-Si system by developing a thermodynamic database with self-consistent parameters. The database includes a description of all 10 binary systems and 8 ternary systems consisting of: (i) 6 Al-containing ternaries (Al-Ce-Cu, Al-Ce-Mg, Al-Ce-Si, Al-Cu-Mg, Al-Cu-Si and Al-Mg-Si); and (ii) 2 additional ternaries that include Mg and Si (i.e., Ce-Mg-Si and Cu-Mg-Si). The thermodynamic description for the Al-Ce-Mg and Al-Mg-Si systems were reassessed to ensure consistency with the binary systems and the Ce-Mg-Si system is presented for the first time and compared to theoretical data from DFT (Density Functional Theory). In addition to the ternary interactions, the quaternary compound Al3Cu2Mg9Si7 and solid solution extending from the ternary Al2CuMg phase (Al,Si)2CuMg are incorporated. The CALPHAD method is employed and leveraged through the use of a Materials Design Simulator (MDS) to accelerate the design of novel aluminum-cerium-based alloys. The combination of a CALPHAD-based framework with experimental efforts and industrial insight permits the development of three new Al-Ce alloys: Al-3.5Ce-0.4Mg-7Si (Ce-modified A356), Al-5Ce-1Cu-0.5Mg-10Si and Al-19Ce-0.9Mg-1.1Si.

36 MATERIALS SCIENCE↗

Materials Data on Mg2Cu3Si by Materials Project

Mg2Cu3Si is Hexagonal Laves-derived structured and crystallizes in the hexagonal P6_3/mmc space group. The structure is three-dimensional. Mg is bonded in a 12-coordinate geometry to nine equivalent Cu and three equivalent Si atoms. There are three shorter (2.84 Å) and six longer (2.92 Å) Mg–Cu bond lengths. All Mg–Si bond lengths are 2.94 Å. Cu is bonded to six equivalent Mg, four equivalent Cu, and two equivalent Si atoms to form CuMg6Cu4Si2 cuboctahedra that share corners with four equivalent SiMg6Cu6 cuboctahedra, corners with fourteen equivalent CuMg6Cu4Si2 cuboctahedra, edges with six equivalent CuMg6Cu4Si2 cuboctahedra, faces with six equivalent SiMg6Cu6 cuboctahedra, and faces with twelve equivalent CuMg6Cu4Si2 cuboctahedra. There are two shorter (2.48 Å) and two longer (2.54 Å) Cu–Cu bond lengths. Both Cu–Si bond lengths are 2.45 Å. Si is bonded to six equivalent Mg and six equivalent Cu atoms to form SiMg6Cu6 cuboctahedra that share corners with twelve equivalent CuMg6Cu4Si2 cuboctahedra, edges with six equivalent SiMg6Cu6 cuboctahedra, faces with two equivalent SiMg6Cu6 cuboctahedra, and faces with eighteen equivalent CuMg6Cu4Si2 cuboctahedra.

36 MATERIALS SCIENCE↗

Materials Data on Mg6Cu16Si7 by Materials Project

Mg6Cu16Si7 crystallizes in the cubic Fm-3m space group. The structure is three-dimensional. Mg2+ is bonded in a distorted square co-planar geometry to four equivalent Si4- atoms. All Mg–Si bond lengths are 2.97 Å. There are two inequivalent Cu1+ sites. In the first Cu1+ site, Cu1+ is bonded in a trigonal planar geometry to three equivalent Si4- atoms. All Cu–Si bond lengths are 2.38 Å. In the second Cu1+ site, Cu1+ is bonded to four Si4- atoms to form a mixture of distorted corner and edge-sharing CuSi4 tetrahedra. There are one shorter (2.42 Å) and three longer (2.56 Å) Cu–Si bond lengths. There are two inequivalent Si4- sites. In the first Si4- site, Si4- is bonded to four equivalent Mg2+ and eight Cu1+ atoms to form a mixture of corner and face-sharing SiMg4Cu8 cuboctahedra. In the second Si4- site, Si4- is bonded in a body-centered cubic geometry to eight equivalent Cu1+ atoms.

36 MATERIALS SCIENCE↗

Materials Data on Mg14CuSi by Materials Project

Mg14CuSi crystallizes in the hexagonal P-6m2 space group. The structure is three-dimensional. there are seven inequivalent Mg sites. In the first Mg site, Mg is bonded to ten Mg and two equivalent Cu atoms to form distorted MgMg10Cu2 cuboctahedra that share corners with four equivalent SiMg12 cuboctahedra, corners with fourteen MgMg10Cu2 cuboctahedra, edges with two equivalent CuMg12 cuboctahedra, edges with sixteen MgMg10Cu2 cuboctahedra, faces with two equivalent CuMg12 cuboctahedra, and faces with eighteen MgMg10Cu2 cuboctahedra. There are a spread of Mg–Mg bond distances ranging from 3.08–3.10 Å. Both Mg–Cu bond lengths are 3.09 Å. In the second Mg site, Mg is bonded to ten Mg and two equivalent Si atoms to form distorted MgMg10Si2 cuboctahedra that share corners with four equivalent CuMg12 cuboctahedra, corners with fourteen MgMg10Cu2 cuboctahedra, edges with two equivalent SiMg12 cuboctahedra, edges with sixteen MgMg10Si2 cuboctahedra, faces with two equivalent SiMg12 cuboctahedra, and faces with eighteen MgMg10Cu2 cuboctahedra. There are a spread of Mg–Mg bond distances ranging from 3.08–3.14 Å. Both Mg–Si bond lengths are 3.09 Å. In the third Mg site, Mg is bonded to ten Mg and two equivalent Cu atoms to form distorted MgMg10Cu2 cuboctahedra that share corners with four equivalent SiMg12 cuboctahedra, corners with fourteen MgMg10Si2 cuboctahedra, edges with two equivalent CuMg12 cuboctahedra, edges with sixteen MgMg10Cu2 cuboctahedra, faces with two equivalent CuMg12 cuboctahedra, and faces with eighteen MgMg10Cu2 cuboctahedra. There are two shorter (3.09 Å) and four longer (3.10 Å) Mg–Mg bond lengths. Both Mg–Cu bond lengths are 3.09 Å. In the fourth Mg site, Mg is bonded to ten Mg and two equivalent Si atoms to form distorted MgMg10Si2 cuboctahedra that share corners with four equivalent CuMg12 cuboctahedra, corners with fourteen MgMg10Cu2 cuboctahedra, edges with two equivalent SiMg12 cuboctahedra, edges with sixteen MgMg10Si2 cuboctahedra, faces with two equivalent SiMg12 cuboctahedra, and faces with eighteen MgMg10Si2 cuboctahedra. There are two shorter (3.12 Å) and four longer (3.14 Å) Mg–Mg bond lengths. Both Mg–Si bond lengths are 3.09 Å. In the fifth Mg site, Mg is bonded to ten Mg, one Cu, and one Si atom to form distorted MgMg10CuSi cuboctahedra that share corners with eighteen MgMg10CuSi cuboctahedra, edges with two equivalent CuMg12 cuboctahedra, edges with two equivalent SiMg12 cuboctahedra, edges with fourteen MgMg10Cu2 cuboctahedra, a faceface with one CuMg12 cuboctahedra, a faceface with one SiMg12 cuboctahedra, and faces with eighteen MgMg10Cu2 cuboctahedra. There are a spread of Mg–Mg bond distances ranging from 3.01–3.17 Å. The Mg–Cu bond length is 3.06 Å. The Mg–Si bond length is 3.10 Å. In the sixth Mg site, Mg is bonded to ten Mg, one Cu, and one Si atom to form distorted MgMg10CuSi cuboctahedra that share corners with eighteen MgMg10CuSi cuboctahedra, edges with two equivalent CuMg12 cuboctahedra, edges with two equivalent SiMg12 cuboctahedra, edges with fourteen MgMg10Cu2 cuboctahedra, a faceface with one CuMg12 cuboctahedra, a faceface with one SiMg12 cuboctahedra, and faces with eighteen MgMg10Cu2 cuboctahedra. There are a spread of Mg–Mg bond distances ranging from 3.09–3.14 Å. The Mg–Cu bond length is 3.06 Å. The Mg–Si bond length is 3.10 Å. In the seventh Mg site, Mg is bonded to twelve Mg atoms to form MgMg12 cuboctahedra that share corners with eighteen MgMg10CuSi cuboctahedra, edges with eighteen MgMg10Cu2 cuboctahedra, faces with three equivalent CuMg12 cuboctahedra, faces with three equivalent SiMg12 cuboctahedra, and faces with fourteen MgMg10Cu2 cuboctahedra. Cu is bonded to twelve Mg atoms to form CuMg12 cuboctahedra that share corners with six equivalent CuMg12 cuboctahedra, corners with twelve MgMg10Si2 cuboctahedra, edges with eighteen MgMg10Cu2 cuboctahedra, faces with two equivalent SiMg12 cuboctahedra, and faces with eighteen MgMg10Cu2 cuboctahedra. Si is bonded to twelve Mg atoms to form SiMg12 cuboctahedra that share corners with six equivalent SiMg12 cuboctahedra, corners with twelve MgMg10Cu2 cuboctahedra, edges with eighteen MgMg10Si2 cuboctahedra, faces with two equivalent CuMg12 cuboctahedra, and faces with eighteen MgMg10Si2 cuboctahedra.

36 MATERIALS SCIENCE↗

Materials Data on Mg6CuSi by Materials Project

Mg6CuSi crystallizes in the orthorhombic Amm2 space group. The structure is three-dimensional. there are seven inequivalent Mg sites. In the first Mg site, Mg is bonded to eight Mg, two equivalent Cu, and two equivalent Si atoms to form a mixture of distorted face, edge, and corner-sharing MgMg8Cu2Si2 cuboctahedra. There are a spread of Mg–Mg bond distances ranging from 3.01–3.10 Å. There are one shorter (3.00 Å) and one longer (3.02 Å) Mg–Cu bond lengths. There are one shorter (3.00 Å) and one longer (3.03 Å) Mg–Si bond lengths. In the second Mg site, Mg is bonded to eight Mg, two equivalent Cu, and two equivalent Si atoms to form a mixture of distorted face, edge, and corner-sharing MgMg8Cu2Si2 cuboctahedra. There are a spread of Mg–Mg bond distances ranging from 3.01–3.10 Å. There are one shorter (3.00 Å) and one longer (3.02 Å) Mg–Cu bond lengths. There are one shorter (3.00 Å) and one longer (3.03 Å) Mg–Si bond lengths. In the third Mg site, Mg is bonded to eight Mg, two equivalent Cu, and two equivalent Si atoms to form a mixture of distorted face, edge, and corner-sharing MgMg8Cu2Si2 cuboctahedra. There are a spread of Mg–Mg bond distances ranging from 2.92–3.15 Å. Both Mg–Cu bond lengths are 2.98 Å. Both Mg–Si bond lengths are 3.01 Å. In the fourth Mg site, Mg is bonded to eight Mg, two equivalent Cu, and two equivalent Si atoms to form a mixture of distorted face, edge, and corner-sharing MgMg8Cu2Si2 cuboctahedra. There are a spread of Mg–Mg bond distances ranging from 2.92–3.11 Å. Both Mg–Cu bond lengths are 2.98 Å. Both Mg–Si bond lengths are 3.01 Å. In the fifth Mg site, Mg is bonded to ten Mg and two equivalent Cu atoms to form a mixture of distorted face, edge, and corner-sharing MgMg10Cu2 cuboctahedra. There are two shorter (3.01 Å) and two longer (3.10 Å) Mg–Mg bond lengths. Both Mg–Cu bond lengths are 2.95 Å. In the sixth Mg site, Mg is bonded to ten Mg and two equivalent Si atoms to form a mixture of distorted face, edge, and corner-sharing MgMg10Si2 cuboctahedra. Both Mg–Mg bond lengths are 3.01 Å. Both Mg–Si bond lengths are 2.95 Å. In the seventh Mg site, Mg is bonded to eight Mg, two equivalent Cu, and two equivalent Si atoms to form a mixture of distorted face, edge, and corner-sharing MgMg8Cu2Si2 cuboctahedra. Both Mg–Mg bond lengths are 3.01 Å. There are one shorter (3.00 Å) and one longer (3.02 Å) Mg–Cu bond lengths. There are one shorter (3.00 Å) and one longer (3.03 Å) Mg–Si bond lengths. Cu is bonded in a 12-coordinate geometry to ten Mg atoms. Si is bonded in a 12-coordinate geometry to ten Mg atoms.

36 MATERIALS SCIENCE↗

Materials Data on Mg14CuSi by Materials Project

Mg14CuSi crystallizes in the orthorhombic Amm2 space group. The structure is three-dimensional. there are seven inequivalent Mg sites. In the first Mg site, Mg is bonded to twelve Mg atoms to form a mixture of edge, face, and corner-sharing MgMg12 cuboctahedra. There are a spread of Mg–Mg bond distances ranging from 3.06–3.26 Å. In the second Mg site, Mg is bonded to twelve Mg atoms to form a mixture of edge, face, and corner-sharing MgMg12 cuboctahedra. There are a spread of Mg–Mg bond distances ranging from 3.07–3.26 Å. In the third Mg site, Mg is bonded to eight Mg, two equivalent Cu, and two equivalent Si atoms to form distorted MgMg8Cu2Si2 cuboctahedra that share corners with eighteen MgMg12 cuboctahedra, edges with ten MgMg8Cu2Si2 cuboctahedra, and faces with eight MgMg8Cu2Si2 cuboctahedra. There are a spread of Mg–Mg bond distances ranging from 3.02–3.11 Å. There are one shorter (3.02 Å) and one longer (3.16 Å) Mg–Cu bond lengths. There are one shorter (2.99 Å) and one longer (3.19 Å) Mg–Si bond lengths. In the fourth Mg site, Mg is bonded to twelve Mg atoms to form MgMg12 cuboctahedra that share corners with ten MgMg8Cu2Si2 cuboctahedra, edges with fourteen MgMg12 cuboctahedra, and faces with twelve MgMg12 cuboctahedra. There are a spread of Mg–Mg bond distances ranging from 3.11–3.29 Å. In the fifth Mg site, Mg is bonded in a 12-coordinate geometry to eight Mg, one Cu, and one Si atom. There are a spread of Mg–Mg bond distances ranging from 3.04–3.15 Å. The Mg–Cu bond length is 2.94 Å. The Mg–Si bond length is 2.96 Å. In the sixth Mg site, Mg is bonded to eleven Mg and one Cu atom to form distorted MgMg11Cu cuboctahedra that share corners with ten MgMg11Cu cuboctahedra, edges with twelve MgMg12 cuboctahedra, and faces with twelve MgMg12 cuboctahedra. Both Mg–Mg bond lengths are 3.11 Å. The Mg–Cu bond length is 3.06 Å. In the seventh Mg site, Mg is bonded to eleven Mg and one Si atom to form distorted MgMg11Si cuboctahedra that share corners with ten MgMg11Cu cuboctahedra, edges with twelve MgMg12 cuboctahedra, and faces with twelve MgMg12 cuboctahedra. The Mg–Si bond length is 3.06 Å. Cu is bonded in a 12-coordinate geometry to ten Mg atoms. Si is bonded in a 12-coordinate geometry to ten Mg atoms.

36 MATERIALS SCIENCE↗

Materials Data on Mg2CuSi3 by Materials Project

Mg2CuSi3 crystallizes in the trigonal R-3m space group. The structure is three-dimensional. Mg is bonded in a 12-coordinate geometry to four equivalent Mg, three equivalent Cu, and nine equivalent Si atoms. There are one shorter (2.95 Å) and three longer (3.21 Å) Mg–Mg bond lengths. All Mg–Cu bond lengths are 3.11 Å. There are three shorter (2.84 Å) and six longer (3.05 Å) Mg–Si bond lengths. Cu is bonded to six equivalent Mg and six equivalent Si atoms to form CuMg6Si6 cuboctahedra that share corners with six equivalent CuMg6Si6 cuboctahedra, corners with twelve equivalent SiMg6Cu2Si4 cuboctahedra, edges with six equivalent CuMg6Si6 cuboctahedra, and faces with eighteen equivalent SiMg6Cu2Si4 cuboctahedra. All Cu–Si bond lengths are 2.47 Å. Si is bonded to six equivalent Mg, two equivalent Cu, and four equivalent Si atoms to form SiMg6Cu2Si4 cuboctahedra that share corners with four equivalent CuMg6Si6 cuboctahedra, corners with fourteen equivalent SiMg6Cu2Si4 cuboctahedra, edges with six equivalent SiMg6Cu2Si4 cuboctahedra, faces with six equivalent CuMg6Si6 cuboctahedra, and faces with twelve equivalent SiMg6Cu2Si4 cuboctahedra. All Si–Si bond lengths are 2.67 Å.

36 MATERIALS SCIENCE↗

Materials Data on Mg6CuSi by Materials Project

Mg6CuSi crystallizes in the orthorhombic Amm2 space group. The structure is three-dimensional. there are seven inequivalent Mg sites. In the first Mg site, Mg is bonded to eight Mg, two equivalent Cu, and two equivalent Si atoms to form distorted MgMg8Cu2Si2 cuboctahedra that share corners with two equivalent CuMg10 cuboctahedra, corners with two equivalent SiMg10 cuboctahedra, corners with fourteen MgMg8Cu2Si2 cuboctahedra, edges with two equivalent SiMg10 cuboctahedra, edges with three equivalent CuMg10 cuboctahedra, edges with twelve MgMg8Cu2Si2 cuboctahedra, a faceface with one CuMg10 cuboctahedra, faces with two equivalent SiMg10 cuboctahedra, and faces with sixteen MgMg8Cu2Si2 cuboctahedra. There are a spread of Mg–Mg bond distances ranging from 2.96–3.10 Å. There are one shorter (3.01 Å) and one longer (3.05 Å) Mg–Cu bond lengths. Both Mg–Si bond lengths are 3.01 Å. In the second Mg site, Mg is bonded to eight Mg, two equivalent Cu, and two equivalent Si atoms to form distorted MgMg8Cu2Si2 cuboctahedra that share corners with two equivalent CuMg10 cuboctahedra, corners with two equivalent SiMg10 cuboctahedra, corners with fourteen MgMg8Cu2Si2 cuboctahedra, edges with two equivalent SiMg10 cuboctahedra, edges with three equivalent CuMg10 cuboctahedra, edges with twelve MgMg10Cu2 cuboctahedra, a faceface with one CuMg10 cuboctahedra, faces with two equivalent SiMg10 cuboctahedra, and faces with sixteen MgMg8Cu2Si2 cuboctahedra. There are a spread of Mg–Mg bond distances ranging from 3.01–3.10 Å. There are one shorter (3.01 Å) and one longer (3.05 Å) Mg–Cu bond lengths. Both Mg–Si bond lengths are 3.01 Å. In the third Mg site, Mg is bonded to ten Mg and two equivalent Cu atoms to form distorted MgMg10Cu2 cuboctahedra that share corners with four equivalent CuMg10 cuboctahedra, corners with fourteen MgMg8Cu2Si2 cuboctahedra, edges with two equivalent CuMg10 cuboctahedra, edges with sixteen MgMg8Cu2Si2 cuboctahedra, faces with two equivalent CuMg10 cuboctahedra, faces with six equivalent SiMg10 cuboctahedra, and faces with twelve MgMg8Cu2Si2 cuboctahedra. There are a spread of Mg–Mg bond distances ranging from 3.01–3.04 Å. Both Mg–Cu bond lengths are 3.01 Å. In the fourth Mg site, Mg is bonded to eight Mg, two equivalent Cu, and two equivalent Si atoms to form distorted MgMg8Cu2Si2 cuboctahedra that share corners with two equivalent CuMg10 cuboctahedra, corners with two equivalent SiMg10 cuboctahedra, corners with fourteen MgMg8Cu2Si2 cuboctahedra, edges with two equivalent CuMg10 cuboctahedra, edges with three equivalent SiMg10 cuboctahedra, edges with twelve MgMg10Cu2 cuboctahedra, a faceface with one SiMg10 cuboctahedra, faces with two equivalent CuMg10 cuboctahedra, and faces with sixteen MgMg8Cu2Si2 cuboctahedra. There are a spread of Mg–Mg bond distances ranging from 2.90–3.13 Å. Both Mg–Cu bond lengths are 2.97 Å. There are one shorter (2.94 Å) and one longer (3.12 Å) Mg–Si bond lengths. In the fifth Mg site, Mg is bonded to eight Mg, two equivalent Cu, and two equivalent Si atoms to form distorted MgMg8Cu2Si2 cuboctahedra that share corners with two equivalent CuMg10 cuboctahedra, corners with two equivalent SiMg10 cuboctahedra, corners with fourteen MgMg8Cu2Si2 cuboctahedra, edges with two equivalent CuMg10 cuboctahedra, edges with three equivalent SiMg10 cuboctahedra, edges with twelve MgMg8Cu2Si2 cuboctahedra, a faceface with one SiMg10 cuboctahedra, faces with two equivalent CuMg10 cuboctahedra, and faces with sixteen MgMg8Cu2Si2 cuboctahedra. There are one shorter (3.00 Å) and one longer (3.06 Å) Mg–Mg bond lengths. Both Mg–Cu bond lengths are 2.97 Å. There are one shorter (2.94 Å) and one longer (3.12 Å) Mg–Si bond lengths. In the sixth Mg site, Mg is bonded to ten Mg and two equivalent Si atoms to form distorted MgMg10Si2 cuboctahedra that share corners with four equivalent SiMg10 cuboctahedra, corners with fourteen MgMg8Cu2Si2 cuboctahedra, edges with two equivalent SiMg10 cuboctahedra, edges with sixteen MgMg8Cu2Si2 cuboctahedra, faces with two equivalent SiMg10 cuboctahedra, faces with six equivalent CuMg10 cuboctahedra, and faces with twelve MgMg8Cu2Si2 cuboctahedra. Both Mg–Si bond lengths are 3.01 Å. In the seventh Mg site, Mg is bonded to eight Mg, two equivalent Cu, and two equivalent Si atoms to form distorted MgMg8Cu2Si2 cuboctahedra that share corners with two equivalent CuMg10 cuboctahedra, corners with two equivalent SiMg10 cuboctahedra, corners with fourteen MgMg8Cu2Si2 cuboctahedra, edges with two equivalent SiMg10 cuboctahedra, edges with three equivalent CuMg10 cuboctahedra, edges with twelve MgMg8Cu2Si2 cuboctahedra, a faceface with one CuMg10 cuboctahedra, faces with two equivalent SiMg10 cuboctahedra, and faces with sixteen MgMg8Cu2Si2 cuboctahedra. There are a spread of Mg–Mg bond distances ranging from 2.96–3.10 Å. There are one shorter (3.01 Å) and one longer (3.05 Å) Mg–Cu bond lengths. Both Mg–Si bond lengths are 3.01 Å. Cu is bonded to ten Mg atoms to form distorted CuMg10 cuboctahedra that share corners with six equivalent CuMg10 cuboctahedra, corners with twelve MgMg8Cu2Si2 cuboctahedra, edges with two equivalent CuMg10 cuboctahedra, edges with four equivalent SiMg10 cuboctahedra, edges with twelve MgMg8Cu2Si2 cuboctahedra, faces with two equivalent SiMg10 cuboctahedra, and faces with fourteen MgMg8Cu2Si2 cuboctahedra. Si is bonded to ten Mg atoms to form distorted SiMg10 cuboctahedra that share corners with six equivalent SiMg10 cuboctahedra, corners with twelve MgMg8Cu2Si2 cuboctahedra, edges with two equivalent SiMg10 cuboctahedra, edges with four equivalent CuMg10 cuboctahedra, edges with twelve MgMg8Cu2Si2 cuboctahedra, faces with two equivalent CuMg10 cuboctahedra, and faces with fourteen MgMg8Cu2Si2 cuboctahedra.

36 MATERIALS SCIENCE↗