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In-plane thermal conductivity and the applicability of the Wiedemann–Franz law in dilute AlCu thin films

The Wiedemann–Franz (WF) law correlates heat and charge transport in metals. However, the validity of this correlation remains an open-ended question, especially in the context of inelastic scattering at room temperature. To address this gap in knowledge, we perform independent measurements of the in-plane thermal and electrical conductivities across four AlCu (0.5% Cu) films [thickness (⁠h⁠) ≈ 174, 98, 53, and 24 nm] using optical pump–probe metrologies and four-point probe techniques, respectively. For in-plane thermal conductivity measurements, we utilize time-domain thermoreflectance, in both concentric and beam-offset configurations, and the time-resolved magneto-optic Kerr effect. Our results show that the WF law overpredicts the thermal conductivity by at least ∼10% in all films, thus demonstrating modest deviations in predicted thermal conductivity when applying the WF law to dilute AlCu films. Using infrared variable angle spectroscopic ellipsometry, we demonstrate increased electron scattering rates in the thinnest film (⁠⁠h⁠ ≈ 24 nm), indicating electron-boundary scattering drives the reduction in in-plane thermal conductivity. Furthermore, this is generally an elastic scattering process, which is supported by our thermal conductivity measurements and analysis.

Electrical conductivity↗

Materials Data on AlCu by Materials Project

CuAl crystallizes in the monoclinic C2/m space group. The structure is three-dimensional. there are three inequivalent Cu sites. In the first Cu site, Cu is bonded in a 6-coordinate geometry to four Cu and six Al atoms. There are two shorter (2.56 Å) and two longer (2.57 Å) Cu–Cu bond lengths. There are four shorter (2.51 Å) and two longer (2.62 Å) Cu–Al bond lengths. In the second Cu site, Cu is bonded in a 11-coordinate geometry to four Cu and seven Al atoms. There are two shorter (2.64 Å) and one longer (2.66 Å) Cu–Cu bond lengths. There are a spread of Cu–Al bond distances ranging from 2.40–2.79 Å. In the third Cu site, Cu is bonded in a 11-coordinate geometry to four Cu and seven Al atoms. There are a spread of Cu–Al bond distances ranging from 2.52–2.68 Å. There are three inequivalent Al sites. In the first Al site, Al is bonded in a 6-coordinate geometry to six Cu atoms. In the second Al site, Al is bonded in a 6-coordinate geometry to six Cu atoms. In the third Al site, Al is bonded in a 8-coordinate geometry to eight Cu atoms.

36 MATERIALS SCIENCE↗

Materials Data on AlCu by Materials Project

CuAl is Tetraauricupride structured and crystallizes in the cubic Pm-3m space group. The structure is three-dimensional. Cu is bonded in a body-centered cubic geometry to eight equivalent Al atoms. All Cu–Al bond lengths are 2.60 Å. Al is bonded in a body-centered cubic geometry to eight equivalent Cu atoms.

36 MATERIALS SCIENCE↗

Materials Data on Tb(AlCu)6 by Materials Project

Tb(CuAl)6 crystallizes in the orthorhombic Immm space group. The structure is three-dimensional. Tb is bonded in a 12-coordinate geometry to twelve Cu and eight Al atoms. There are four shorter (3.20 Å) and eight longer (3.30 Å) Tb–Cu bond lengths. There are a spread of Tb–Al bond distances ranging from 2.97–3.10 Å. There are two inequivalent Cu sites. In the first Cu site, Cu is bonded to two equivalent Tb, four Cu, and six Al atoms to form a mixture of distorted edge, face, and corner-sharing CuTb2Al6Cu4 cuboctahedra. There are two shorter (2.52 Å) and two longer (2.54 Å) Cu–Cu bond lengths. There are a spread of Cu–Al bond distances ranging from 2.52–2.65 Å. In the second Cu site, Cu is bonded in a 12-coordinate geometry to two equivalent Tb, four equivalent Cu, and six Al atoms. There are a spread of Cu–Al bond distances ranging from 2.64–2.74 Å. There are three inequivalent Al sites. In the first Al site, Al is bonded in a 10-coordinate geometry to one Tb, six Cu, and three Al atoms. There are one shorter (2.62 Å) and two longer (2.83 Å) Al–Al bond lengths. In the second Al site, Al is bonded in a 8-coordinate geometry to one Tb, six Cu, and three Al atoms. There are one shorter (2.63 Å) and two longer (2.88 Å) Al–Al bond lengths. In the third Al site, Al is bonded in a 12-coordinate geometry to two equivalent Tb, six Cu, and four Al atoms.

36 MATERIALS SCIENCE↗

Materials Data on AlCu(WO4)2 by Materials Project

Computed materials data using density functional theory calculations. These calculations determine the electronic structure of bulk materials by solving approximations to the Schrodinger equation. For more information, see https://materialsproject.org/docs/calculations

36 MATERIALS SCIENCE↗

Materials Data on Yb(AlCu)6 by Materials Project

Yb(CuAl)6 crystallizes in the orthorhombic Immm space group. The structure is three-dimensional. Yb is bonded in a 12-coordinate geometry to twelve Cu and eight Al atoms. There are four shorter (3.19 Å) and eight longer (3.31 Å) Yb–Cu bond lengths. There are a spread of Yb–Al bond distances ranging from 2.97–3.10 Å. There are two inequivalent Cu sites. In the first Cu site, Cu is bonded to two equivalent Yb, four Cu, and six Al atoms to form a mixture of distorted corner, edge, and face-sharing CuYb2Al6Cu4 cuboctahedra. All Cu–Cu bond lengths are 2.53 Å. There are a spread of Cu–Al bond distances ranging from 2.52–2.65 Å. In the second Cu site, Cu is bonded to two equivalent Yb, four equivalent Cu, and six Al atoms to form a mixture of distorted corner, edge, and face-sharing CuYb2Al6Cu4 cuboctahedra. There are a spread of Cu–Al bond distances ranging from 2.65–2.73 Å. There are three inequivalent Al sites. In the first Al site, Al is bonded in a 10-coordinate geometry to one Yb, six Cu, and three Al atoms. There are one shorter (2.61 Å) and two longer (2.83 Å) Al–Al bond lengths. In the second Al site, Al is bonded in a 8-coordinate geometry to one Yb, six Cu, and three Al atoms. There are one shorter (2.64 Å) and two longer (2.88 Å) Al–Al bond lengths. In the third Al site, Al is bonded in a 12-coordinate geometry to two equivalent Yb, six Cu, and four Al atoms.

36 MATERIALS SCIENCE↗

Materials Data on Y(AlCu)6 by Materials Project

Y(CuAl)6 crystallizes in the orthorhombic Immm space group. The structure is three-dimensional. Y is bonded in a 12-coordinate geometry to twelve Cu and eight Al atoms. There are four shorter (3.21 Å) and eight longer (3.31 Å) Y–Cu bond lengths. There are a spread of Y–Al bond distances ranging from 2.97–3.10 Å. There are two inequivalent Cu sites. In the first Cu site, Cu is bonded in a 12-coordinate geometry to two equivalent Y, four Cu, and six Al atoms. There are two shorter (2.52 Å) and two longer (2.54 Å) Cu–Cu bond lengths. There are a spread of Cu–Al bond distances ranging from 2.53–2.65 Å. In the second Cu site, Cu is bonded to two equivalent Y, four equivalent Cu, and six Al atoms to form a mixture of distorted edge, face, and corner-sharing CuY2Al6Cu4 cuboctahedra. There are a spread of Cu–Al bond distances ranging from 2.64–2.74 Å. There are three inequivalent Al sites. In the first Al site, Al is bonded in a 10-coordinate geometry to one Y, six Cu, and three Al atoms. There are one shorter (2.62 Å) and two longer (2.84 Å) Al–Al bond lengths. In the second Al site, Al is bonded in a 8-coordinate geometry to one Y, six Cu, and three Al atoms. There are one shorter (2.64 Å) and two longer (2.90 Å) Al–Al bond lengths. In the third Al site, Al is bonded in a 12-coordinate geometry to two equivalent Y, six Cu, and four Al atoms.

36 MATERIALS SCIENCE↗

Materials Data on Tm(AlCu)6 by Materials Project

Tm(CuAl)6 crystallizes in the orthorhombic Immm space group. The structure is three-dimensional. Tm is bonded in a 12-coordinate geometry to twelve Cu and eight Al atoms. There are four shorter (3.19 Å) and eight longer (3.29 Å) Tm–Cu bond lengths. There are a spread of Tm–Al bond distances ranging from 2.95–3.08 Å. There are two inequivalent Cu sites. In the first Cu site, Cu is bonded in a 12-coordinate geometry to two equivalent Tm, four Cu, and six Al atoms. There are two shorter (2.51 Å) and two longer (2.53 Å) Cu–Cu bond lengths. There are a spread of Cu–Al bond distances ranging from 2.51–2.63 Å. In the second Cu site, Cu is bonded in a 12-coordinate geometry to two equivalent Tm, four equivalent Cu, and six Al atoms. There are a spread of Cu–Al bond distances ranging from 2.61–2.73 Å. There are three inequivalent Al sites. In the first Al site, Al is bonded in a 10-coordinate geometry to one Tm, six Cu, and three Al atoms. There are one shorter (2.62 Å) and two longer (2.83 Å) Al–Al bond lengths. In the second Al site, Al is bonded in a 8-coordinate geometry to one Tm, six Cu, and three Al atoms. There are one shorter (2.64 Å) and two longer (2.89 Å) Al–Al bond lengths. In the third Al site, Al is bonded in a 12-coordinate geometry to two equivalent Tm, six Cu, and four Al atoms.

36 MATERIALS SCIENCE↗

Materials Data on U(AlCu)6 by Materials Project

UCu6Al6 crystallizes in the orthorhombic Fmmm space group. The structure is three-dimensional. U is bonded in a 4-coordinate geometry to eight Cu and twelve Al atoms. There are four shorter (3.04 Å) and four longer (3.31 Å) U–Cu bond lengths. There are eight shorter (3.23 Å) and four longer (3.36 Å) U–Al bond lengths. There are two inequivalent Cu sites. In the first Cu site, Cu is bonded in a 12-coordinate geometry to two equivalent U, four equivalent Cu, and four equivalent Al atoms. All Cu–Cu bond lengths are 2.70 Å. All Cu–Al bond lengths are 2.43 Å. In the second Cu site, Cu is bonded in a 10-coordinate geometry to one U, three Cu, and six Al atoms. The Cu–Cu bond length is 2.64 Å. There are a spread of Cu–Al bond distances ranging from 2.62–2.73 Å. There are two inequivalent Al sites. In the first Al site, Al is bonded in a 12-coordinate geometry to two equivalent U, four equivalent Cu, and six Al atoms. There are two shorter (2.51 Å) and four longer (2.61 Å) Al–Al bond lengths. In the second Al site, Al is bonded in a 12-coordinate geometry to two equivalent U, six Cu, and four Al atoms. There are one shorter (2.76 Å) and one longer (3.00 Å) Al–Al bond lengths.

36 MATERIALS SCIENCE↗

Materials Data on Gd(AlCu)6 by Materials Project

Gd(CuAl)6 crystallizes in the orthorhombic Immm space group. The structure is three-dimensional. Gd is bonded in a 12-coordinate geometry to twelve Cu and eight Al atoms. There are four shorter (3.22 Å) and eight longer (3.31 Å) Gd–Cu bond lengths. There are a spread of Gd–Al bond distances ranging from 2.98–3.10 Å. There are two inequivalent Cu sites. In the first Cu site, Cu is bonded in a 12-coordinate geometry to two equivalent Gd, four Cu, and six Al atoms. There are two shorter (2.53 Å) and two longer (2.54 Å) Cu–Cu bond lengths. There are a spread of Cu–Al bond distances ranging from 2.53–2.66 Å. In the second Cu site, Cu is bonded to two equivalent Gd, four equivalent Cu, and six Al atoms to form a mixture of distorted corner, edge, and face-sharing CuGd2Al6Cu4 cuboctahedra. There are a spread of Cu–Al bond distances ranging from 2.65–2.74 Å. There are three inequivalent Al sites. In the first Al site, Al is bonded in a 10-coordinate geometry to one Gd, six Cu, and three Al atoms. There are one shorter (2.63 Å) and two longer (2.84 Å) Al–Al bond lengths. In the second Al site, Al is bonded in a 8-coordinate geometry to one Gd, six Cu, and three Al atoms. There are one shorter (2.64 Å) and two longer (2.90 Å) Al–Al bond lengths. In the third Al site, Al is bonded in a 12-coordinate geometry to two equivalent Gd, six Cu, and four Al atoms.

36 MATERIALS SCIENCE↗

Materials Data on Lu(AlCu)6 by Materials Project

Lu(CuAl)6 crystallizes in the orthorhombic Immm space group. The structure is three-dimensional. Lu is bonded in a 12-coordinate geometry to twelve Cu and eight Al atoms. There are four shorter (3.19 Å) and eight longer (3.29 Å) Lu–Cu bond lengths. There are a spread of Lu–Al bond distances ranging from 2.95–3.08 Å. There are two inequivalent Cu sites. In the first Cu site, Cu is bonded in a 12-coordinate geometry to two equivalent Lu, four Cu, and six Al atoms. There are two shorter (2.51 Å) and two longer (2.53 Å) Cu–Cu bond lengths. There are a spread of Cu–Al bond distances ranging from 2.52–2.63 Å. In the second Cu site, Cu is bonded in a 12-coordinate geometry to two equivalent Lu, four equivalent Cu, and six Al atoms. There are a spread of Cu–Al bond distances ranging from 2.60–2.73 Å. There are three inequivalent Al sites. In the first Al site, Al is bonded in a 10-coordinate geometry to one Lu, six Cu, and three Al atoms. There are one shorter (2.63 Å) and two longer (2.83 Å) Al–Al bond lengths. In the second Al site, Al is bonded in a 8-coordinate geometry to one Lu, six Cu, and one Al atom. The Al–Al bond length is 2.64 Å. In the third Al site, Al is bonded in a 12-coordinate geometry to two equivalent Lu, six Cu, and two equivalent Al atoms.

36 MATERIALS SCIENCE↗

Using θ' interfaces as templates for planar L1 2 precipitation in AlCuMnZr alloys

Controlled Mn and Zr additions to Al-Cu alloys have allowed for the improved retention of mechanical properties after extended 350°C exposures by stabilizing the main strengthening θ' (Al 2 Cu) phase. Ultimately, θ'/L1 2 (Al 3 Zr) co-precipitate formation stabilizes θ' most effectively; however, Zr diffuses sluggishly and has low solubility in aluminum castings. Increasing the Zr segregation rate would allow for faster and more effective θ'/L1 2 co-precipitation. It is demonstrated that the Zr segregation rate is faster when the Zr matrix content is higher. A much higher Zr matrix content was achieved by rapid cooling during additive manufacturing (AM) that produces θ'/L1 2 co-precipitation faster, which is shown by scanning transmission electron microscopy and atom probe tomography experiments. It was also found that Zr continuously segregates to θ' interfaces up to the most aggressive heat treatment studied such that planar L1 2 precipitates remain after the metastable θ' dissolves. In this manner, we demonstrate that θ' coherent interfaces serve as perfect templates to form stable planar L1 2 precipitates that can provide strength at higher temperatures than traditional θ' strengthened AlCu alloys. This work introduces an alloy design strategy that uses metastable precipitates to quickly nucleate and grow co-precipitates with a desired geometry that contain slow diffusing elements. These ideas can be applied to engineer more heat resistant alloys by taking advantage of high solute matrix contents enabled by rapid cooling during additive manufacturing.

36 MATERIALS SCIENCE↗