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Matrix effects in ion-induced emission as observed in Ne collisions with Cu-Mg and Cu-Al alloys

Ion induced Auger electron emission is used to study the surfaces of Al, Mg, Cu - 10 at. % Al, Cu - 19.6 at. % Al, and Cu - 7.4 at. % Mg. A neon (Ne) ion beam whose energy is varied from 0.5 to 3 keV is directed at the surface. Excitation of the lighter Ne occurs by the promotion mechanism of Barat and Lichten in asymmetric collisions with Al or Mg atoms. Two principal Auger peaks are observed in the Ne spectrum: one at 22 eV and one at 25 eV. Strong matrix effects are observed in the alloys as a function of energy in which the population of the second peak is greatly enhanced relative to the first over the pure materials. For the pure material over this energy range this ratio is 1.0. For the alloys it can rise to the electronic structure of alloys and to other surface tools such as secondary ion mass spectroscopy.

Ferrante, J.↗

Analytical gradient-based optimization of CALPHAD model parameters

The calibration of CALPHAD (CALculation of PHAse Diagrams) models involves the solution of a very challenging high-dimensional multiobjective optimization problem. Traditional approaches to parameter fitting predominantly rely on gradient-free methods, which while robust, are computationally inefficient and often scale poorly with model complexity. In this work, we introduce and demonstrate a generalizable framework for analytic gradient-based optimization of the parameters of the CALPHAD model enabled by the recently formalized Jansson derivative technique. This method allows for efficient evaluation of gradients of thermodynamic properties at equilibrium with respect to model parameters, even in the presence of arbitrarily complex internal degrees of freedom. Leveraging these semi-analytic gradients, we employ the conjugate gradient (CG) method to optimize thermodynamic model parameters for four binary alloy systems: Cu-Mg, Fe-Ni, Cr-Ni, and Cr-Fe. Across all systems, CG achieves comparable or superior optimality relative to Bayesian ensemble Markov Chain Monte Carlo (MCMC) with improvements in computational efficiency ranging from one to three orders of magnitude. Furthermore, our results establish a new paradigm for CALPHAD assessments in which high fidelity data-rich model calibration becomes tractable using deterministic gradient-informed algorithms.

CALPHAD↗

Materials Data on MgCu2 by Materials Project

MgCu2 is Cubic Laves structured and crystallizes in the cubic Fd-3m space group. The structure is three-dimensional. Mg is bonded in a 12-coordinate geometry to twelve equivalent Cu atoms. All Mg–Cu bond lengths are 2.91 Å. Cu is bonded to six equivalent Mg and six equivalent Cu atoms to form a mixture of face, edge, and corner-sharing CuMg6Cu6 cuboctahedra. All Cu–Cu bond lengths are 2.48 Å.

36 MATERIALS SCIENCE↗

Materials Data on Mg2Cu by Materials Project

Mg2Cu is Khatyrkite-like structured and crystallizes in the orthorhombic Fddd space group. The structure is three-dimensional. there are two inequivalent Mg sites. In the first Mg site, Mg is bonded in a 4-coordinate geometry to four equivalent Cu atoms. There are two shorter (2.72 Å) and two longer (2.74 Å) Mg–Cu bond lengths. In the second Mg site, Mg is bonded in a 4-coordinate geometry to four equivalent Cu atoms. There are two shorter (2.72 Å) and two longer (2.76 Å) Mg–Cu bond lengths. Cu is bonded in a 10-coordinate geometry to eight Mg and two equivalent Cu atoms. Both Cu–Cu bond lengths are 2.61 Å.

36 MATERIALS SCIENCE↗

Materials Data on Mg2Cu by Materials Project

Mg2Cu is Khatyrkite structured and crystallizes in the orthorhombic Ibam space group. The structure is three-dimensional. Mg is bonded in a 4-coordinate geometry to four equivalent Cu atoms. All Mg–Cu bond lengths are 2.75 Å. Cu is bonded in a 10-coordinate geometry to eight equivalent Mg and two equivalent Cu atoms. Both Cu–Cu bond lengths are 2.62 Å.

36 MATERIALS SCIENCE↗

Materials Data on MgCu by Materials Project

MgCu is Tetraauricupride structured and crystallizes in the orthorhombic Pmma space group. The structure is three-dimensional. Mg is bonded in a body-centered cubic geometry to eight equivalent Cu atoms. There are a spread of Mg–Cu bond distances ranging from 2.69–2.77 Å. Cu is bonded in a body-centered cubic geometry to eight equivalent Mg atoms.

36 MATERIALS SCIENCE↗

Materials Data on Mg3Cu by Materials Project

MgMg2Cu crystallizes in the orthorhombic Imm2 space group. The structure is two-dimensional and consists of two MgMg2Cu sheets oriented in the (0, 0, 1) direction. there are two inequivalent Mg sites. In the first Mg site, Mg is bonded in a 2-coordinate geometry to two equivalent Cu atoms. Both Mg–Cu bond lengths are 2.68 Å. In the second Mg site, Mg is bonded in a 4-coordinate geometry to four equivalent Cu atoms. There are two shorter (2.83 Å) and two longer (2.98 Å) Mg–Cu bond lengths. Cu is bonded in a distorted body-centered cubic geometry to eight Mg atoms.

36 MATERIALS SCIENCE↗

Materials Data on MgCu3 by Materials Project

MgCu3 is Uranium Silicide-like structured and crystallizes in the tetragonal I4/mmm space group. The structure is three-dimensional. Mg is bonded to twelve Cu atoms to form MgCu12 cuboctahedra that share corners with four equivalent MgCu12 cuboctahedra, corners with eight equivalent CuMg4Cu8 cuboctahedra, edges with eight equivalent MgCu12 cuboctahedra, edges with sixteen equivalent CuMg4Cu8 cuboctahedra, faces with four equivalent MgCu12 cuboctahedra, and faces with fourteen CuMg4Cu8 cuboctahedra. There are four shorter (2.64 Å) and eight longer (2.67 Å) Mg–Cu bond lengths. There are two inequivalent Cu sites. In the first Cu site, Cu is bonded to four equivalent Mg and eight equivalent Cu atoms to form distorted CuMg4Cu8 cuboctahedra that share corners with four equivalent CuMg4Cu8 cuboctahedra, corners with eight equivalent MgCu12 cuboctahedra, edges with twenty-four CuMg4Cu8 cuboctahedra, faces with six equivalent MgCu12 cuboctahedra, and faces with twelve CuMg4Cu8 cuboctahedra. All Cu–Cu bond lengths are 2.67 Å. In the second Cu site, Cu is bonded to four equivalent Mg and eight Cu atoms to form distorted CuMg4Cu8 cuboctahedra that share corners with twelve equivalent CuMg4Cu8 cuboctahedra, edges with eight equivalent MgCu12 cuboctahedra, edges with sixteen CuMg4Cu8 cuboctahedra, faces with four equivalent MgCu12 cuboctahedra, and faces with fourteen CuMg4Cu8 cuboctahedra. All Cu–Cu bond lengths are 2.64 Å.

36 MATERIALS SCIENCE↗

Materials Data on Mg5Cu by Materials Project

Mg5Cu crystallizes in the hexagonal P-62m space group. The structure is three-dimensional. there are two inequivalent Mg sites. In the first Mg site, Mg is bonded to nine Mg and three equivalent Cu atoms to form distorted MgMg9Cu3 cuboctahedra that share corners with nine equivalent MgMg9Cu3 cuboctahedra, corners with nine equivalent CuMg12 cuboctahedra, edges with eighteen MgMg9Cu3 cuboctahedra, faces with three equivalent CuMg12 cuboctahedra, and faces with seventeen MgMg9Cu3 cuboctahedra. There are six shorter (3.04 Å) and three longer (3.07 Å) Mg–Mg bond lengths. All Mg–Cu bond lengths are 3.07 Å. In the second Mg site, Mg is bonded to ten Mg and two equivalent Cu atoms to form distorted MgMg10Cu2 cuboctahedra that share corners with eighteen equivalent MgMg10Cu2 cuboctahedra, edges with four equivalent CuMg12 cuboctahedra, edges with fourteen MgMg9Cu3 cuboctahedra, faces with four equivalent CuMg12 cuboctahedra, and faces with sixteen MgMg9Cu3 cuboctahedra. There are two shorter (2.91 Å) and four longer (3.15 Å) Mg–Mg bond lengths. Both Mg–Cu bond lengths are 2.96 Å. Cu is bonded to twelve Mg atoms to form CuMg12 cuboctahedra that share corners with eighteen equivalent MgMg9Cu3 cuboctahedra, edges with six equivalent CuMg12 cuboctahedra, edges with twelve equivalent MgMg10Cu2 cuboctahedra, faces with two equivalent CuMg12 cuboctahedra, and faces with eighteen MgMg9Cu3 cuboctahedra.

36 MATERIALS SCIENCE↗