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DOE OSTI2024

Robust Solar Receivers Using MAX Phase Materials

This work was supported by the U.S. Department of Energy’s Office of Energy Efficiency and Renewable Energy under the Solar Energy Technologies Office Award Number 35928. The objective of the proposed effort was to develop and optimize additive manufacturing technologies for low-cost fabrication of high-temperature receivers using MAX phase-based materials (Ti 3 SiC 2 and Ti 3 AlC 2 ). MAX phase materials are a group of ternary metal carbides and nitrides where M stands for an early transition metal element, A is a group 13–16 element, and X is C and/or N. In Phase 1, the binder jetting additive manufacturing process was used to synthesize and characterize the Ti 3 SiC 2 MAX phase material. The typical process involved first producing a TiC preform using binder jetting followed by infiltration of the preform with silicon melt to form Ti 3 SiC 2 in situ. The reaction-infiltrated samples showed formation of MAX phase in the sample core; however, the surface showed cracking. Various process conditions—cooling rates, hold times, Si proportion, etc.—were varied to minimize the surface cracking. The fabricated MAX phase core was characterized by microstructure analysis and evaluations of mechanical properties such as hardness and thermal shock. In Phase 2, the focus included fabrication of Ti 3 SiC 2 MAX phase materials by spark plasma sintering (SPS) and synthesis of Ti 3 AlC 2 MAX phase materials by the Al melt infiltration process. It is expected that Al infiltration will not cause sample cracking, since Al does not expand during solidification. In addition, other processing approaches were investigated to fabricate the MAX phase materials, such as SPS with a graphite bedding approach for producing short-length Ti 3 AlC 2 MAX phase tubes for demonstration of prototypical Concentrating Solar Power receiver tubes. Fabricated samples underwent thermo-mechanical testing to validate the materials for the solar receiver application at temperatures >1000°C. In Phase 3, the effort focused on the development and optimization of the Ti-Al-C MAX phase composite material using the Al melt infiltration approach. We started with optimization of precursor powders and making preform structures by either pressing them in a die or using the binder jetting additive manufacturing process followed by Al melt infiltration. In addition, we investigated the formation of preform structures by cold isostatic pressing followed by Al melt infiltration for making Ti-Al-C MAX phase composite. Thermo-mechanical characterizations, such as creep, strength, and thermal shock, were conducted to establish the structures’ performance.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Development of Ti 3 SiC 2 MAX phase tubular structures for solar receiver applications

Solar receiver tubes are key components of concentrating solar-thermal power (CSP) systems that harvest solar energy. For better efficiency, the Gen3 CSP receivers, which collect heat into a heat transfer fluid, require a temperature exceeding 700 °C during operation and need to perform under extreme conditions of high temperature and high thermal stress. Operators are seeking CSP designs using new high-temperature structural materials with high thermal conductivity and high creep resistance to achieve a design life of 30 years and thus help recover the plant capital cost sooner. MAX phase materials, which consist of an early transition metal element, an A-group element, and carbon or nitrogen, are expected to exhibit high creep resistance as well as high fracture toughness. Here, in this paper, we describe fabricating both (1) dense Ti 3 SiC 2 MAX phase disks and (2) short-length tubes using field-assisted sintering technology (FAST). First, the disk samples that we fabricated are fully dense and contain ≈90 % Ti 3 SiC 2 MAX phase materials and ≈10 % TiC phase materials. We determined a flexure strength of 519 ± 32 MPa by conducting a four-point bending test at room temperature with rectangular bar samples of ≈100 % density. The thermal conductivity of the Ti 3 SiC 2 MAX phase samples, measured by light flashing analysis, decreases linearly from a value of 41 W . m -1 . K -1 at room temperature to a value of 36 W . m -1 . K -1 at 650 °C. A solar reflectance measurement of the Ti 3 SiC 2 MAX phase revealed that, temperature increases from 400 to 1400 °C, thermal emittance increases from 0.39 to 0.49, while selectivity decreases from 1.8 to 1.4, respectively. Whereas the surface oxidized MAX phase samples after 100 h exposure to air at 1000 °C exhibit that of SiC. Next, we discuss fabrication of the crack-free Ti 3 SiC 2 MAX phase tubular structures accomplished by using FAST processing in graphite bedding. A Ti 3 SiC 2 MAX phase content of > 95 % with traceable ≈3% remaining TiC phase and ≈15 % porosity were demonstrated after high-temperature annealing. An average fracture strength of ≈250 MPa was determined with Ti 3 SiC 2 MAX phase tubes of ≈85 % density by diametral compression testing at room temperature. Our work demonstrated that using FAST processing to produce Ti 3 SiC 2 MAX phase tubular structures for CSP receiver applications is a viable approach.

14 SOLAR ENERGY↗

DOE OSTI2026

Quaternary i-MAX Phases (Mo 2/3 RE 1/3 ) 2 AlC (RE: Dy, Tb, Er): Experimental Characterization and First-Principles Insights into their Fundamental Properties

Rare earth (RE)-based materials have unique electronic, magnetic, and optical properties, leading to the recent discovery of atomically layered solids with the chemical formula (M' 2/3 RE 1/3 ) 2 AlC, which have since garnered significant attention in the scientific community. This study aims to synthesize, characterize, and investigate the structural and thermal stability of the RE i-MAX phases. We prepared i-MAX phases using molybdenum (Mo) as M′ and RE elements as Dy, Tb, and Er, namely (Mo 2/3 Dy 1/3 ) 2 AlC, (Mo 2/3 Tb 1/3 ) 2 AlC, and (Mo 2/3 Er 1/3 ) 2 AlC. Structural characterization through x-ray diffraction (XRD) and Raman spectroscopy confirms the formation of the RE-based i-MAX phase, along with the presence of minor impurity phases in the alloys. Thermogravimetric analysis (TGA) conducted up to 1000°C under ambient conditions reveals that the i-MAX phases remain thermally stable up to approximately 450°C, beyond which oxidation leads to a noticeable weight gain in all samples. Differential scanning calorimetry (DSC) measurements during heating and cooling cycles show endothermic and exothermic peaks for (Mo 2/3 Dy 1/3 ) 2 AlC i-MAX in the 410–420°C range, indicating a temperature-induced minor atomic arrangement. In contrast, these peaks are absent in the Tb- and Er-based i-MAX phases. These findings offer valuable insights into the thermal behavior and stability of these i-MAX phases under thermal stress, contributing to a deeper understanding of their unique properties. Furthermore, first-principles density functional theory (DFT) calculations were performed to investigate the electronic and optical properties of the i-MAX phases. The results reveal their metallic nature, with pronounced contributions from Mo and RE elements near the Fermi level and within the conduction band.

Rare earth↗

DOE OSTI2022

A theoretical investigation of the effect of Ga alloying on thermodynamic stability, electronic-structure, and oxidation resistance of Ti 2 AlC MAX phase

We present a systematic investigation of thermodynamic stability, phase-reaction, and chemical activity of Al containing disordered Ti 2 (Al-Ga)C MAX phases using machine-learning driven high-throughput framework to understand the oxidation resistance behavior with increasing temperature and exposure to static oxygen. The A-site (at Al) disordering of Ti 2 AlC with Ga shows significant change in the chemical activity of Al with increasing temperature and exposure to static oxygen, which is expected to enable surface segregation of Al, thereby, the formation of Al 2 O 3 and improved oxidation resistance. We performed in-depth convex hull analysis of ternary Ti-Al-C, Ti-Ga-C, and Ti-Al-Ga-C based MAX phase, and provide detailed contribution arising from electronic, chemical and vibrational entropies. The thermodynamic analysis shows change in the Gibbs formation enthalpy (ΔG form ) at higher temperatures, which implies an interplay of temperature-dependent enthalpy and entropic contributions in oxidation resistance Ga doped Ti 2 AlC MAX phases. A detailed electronic structure and chemical bonding analysis using crystal orbital Hamilton population method reveal the origin of change in phases stability and in oxidation resistance in disorder Ti2(Al 1-x Ga x )C MAX phases. Our electronic structure analysis correlate well with the change in oxidation resistance of Ga doped MAX phases. We believe our study provides a useful guideline to understand to role of alloying on electronic, thermodynamic, and oxidation related mechanisms of bulk MAX phases, which can work as a precursor to understand oxidation behavior of twodimensional MAX phases, i.e., MXenes (transition metal carbides, carbonitrides and nitrides).

36 MATERIALS SCIENCE↗

DOE OSTI2024

Structural and Morphological Characteristics of Rare Earth Element-based MAX Phase and MXene

There has been a tremendous effort for the synthesis of crystalline MAX phases—a family of transition metal carbides and nitrides with a chemical formula of Mn+1AXn, where M is an early transition metal, A belongs to groups XIII – XVI in the periodic table, X is either C or N, and n can be in between 1 and 3. Furthermore, these materials have shown thermal and electrical conductance and have low density and high stiffness which open broad aspects of practical applications. Recently double transition metal MAX phases (M’ 2/3 M’’ 1/3 ) 2 AX - out-of-plane ordered, labeled as o-MAX and in-plane ordered, labeled as i-MAX, were reported. However, there are few reports on the synthesis and characterization of i-MAX and the corresponding MXenes. In this work, we synthesized Molybdenum-based rare earth containing i-MAX phase using arc melt technique. We then removed “A” element of i-MAX phase by acid treatment and sonication which resulted in two-dimensional (2D) transition metal carbides called MXenes. These MXenes offer high conductivity, hydrophilicity, magnetism, good dispersion ability in solvents, mechanical stability, and structural diversity with at least 100 stoichiometric MXene compositions and are recognized as multifunctional materials.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2022

Accelerated radiation tolerance testing of Ti-based MAX phases

MAX phases have recently attracted significant attention for potential nuclear applications due to their novel properties such as unique hexagonal-compact nanolayered crystal structure, high-machinability due to lower hardness levels compared to conventional ceramics, and high-chemical inertness. In order for MAX phases to be used in nuclear reactors, two aspects deserve detailed investigations: (i) their phase stability at high-temperatures and (ii) microstructural defect formation and recovery induced by energetic particle irradiation. To date, degradation mechanisms of MAX phases at high-temperatures and following irradiation are largely unexplored fields of research. This work focuses on the evaluation of two Ti-based MAX phases – Ti 2 AlC and Ti 3 SiC 2 – within the context of extreme environments. To accomplish this, a one-of-a-kind comparison between neutron irradiations, performed over a decade of research at the High Flux Isotope Reactor (HFIR), and heavy-ion irradiations, carried out in situ in a Transmission Electron Microscope (TEM) at the MIAMI-2 facility, has been conducted. The results show Ti-based MAX phases are prone to accelerated decomposition under the conditions investigated. This questions the hypothesis that MAX phases exhibit high phase stability, especially when used in future nuclear energy systems where energetic particle irradiation is a dominating degradation mechanism.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Computational Investigation of MAX as Intercalation Host for Rechargeable Aluminum‐Ion Battery

Abstract Layered carbides and their analogs with MAX phase (general formula AM n+1 X n ) have emerged as promising candidates for energy storage and conversion applications. One frontier for energy storage is using MAX as an Al‐ion intercalation electrode. Given that many MAXs have Al as the A sites, the structure can potentially serve as a stable host for Al intercalation. Here in this work, 425 ternary MAX Al‐ion battery electrodes are computationally enumerated. Specifically, first principal phase diagram calculations are performed on the combinatorial space of 17 types of typical transition metals, five types of anions (C, N, B, Si, and P), three types of stoichiometries (n = 1, 2, and 3) and two types of layered stackings (α and β). Among all the ternary MAX materials, 44 candidates show reasonable synthetic accessibility, and six with extraordinary performance are predicted to be promising Al‐ion battery electrodes. With the phase stability, and electrochemical performance (average voltage, theoretical capacity, energy density, and Al diffusion barrier), the work provides a comprehensive computational assessment of the great opportunities behind MAX‐based Al‐ion batteries.

Chemistry↗

DOE OSTI2024

Porous Ti 3 AlC 2 MAX phase enables efficient synthesis of Ti 3 C 2 T x MXene

Abstract MXenes, a large family of two‐dimensional carbides and/or nitrides, are among the most studied materials worldwide due to their great diversity of structures and compositions. Their unique properties find use in several applications. Typically, they are manufactured by selective wet‐chemical etching of layered MAX phase ceramics, which are produced nowadays primarily for MXene synthesis. However, the synthesis of MAX phases has not been changed since the time of their use in structural and high‐temperature applications, and it has not been optimized for MXene manufacturing. The main purpose of this study is to develop a porous Ti 3 AlC 2 MAX phase that can be easily ground into individual grains without time‐consuming, harsh, and tedious crushing and milling steps. Moreover, we also demonstrate the synthesis of highly porous Ti 3 AlC 2 from an inexpensive titanium sponge instead of a highly pure titanium powder and explain the mechanisms of reaction sintering and formation of porous MAX phase. MXene obtained from this MAX phase, Ti 3 C 2 Tx, shows larger flake size and higher electrical conductivity in thin films, compared to the materials produced from the costly fine titanium powder. The proposed approach may apply to the synthesis of other MAX phases as well.

Materials Science↗

DOE OSTI2025

Current Advances in i‐MAX Phases and their Two Dimensional Derivative i‐MXenes: Challenges and Opportunities (Adv. Electron. Mater. 21/2025)

The discovery of quaternary (M′ 2/3 M′′ 1/3 ) 2 AX phases has introduced newly ordered i-MAX phases in the MAX phase community. These atomically layered solids display in-plane chemical ordering of M′ and M′′, featuring a frustrated triangular lattice overlaid on an M′ honeycomb arrangement and an A Kagomé lattice. This unique structure gives rise to novel electronic and magnetic properties, paving the way for diverse applications and the creation of new MXenes. Both experimental and theoretical research have confirmed that these i-MAX phases can be chemically exfoliated into single- or multilayered and vacancy-ordered 2D transition metal carbides, known as i-MXenes. These 2D i-MXenes exhibit intriguing optical, electrochemical, piezoelectric, and magnetic properties, which are decidedly reliant on the surface functional groups (-F, -OH, -O). This review encompasses all available theoretical and experimental studies on i-MAX and i-MXenes, with a focus on their fundamental properties, organized in multiple sections. Along with the experimental investigation, significant attention is also directed toward theoretical predictions of potential i-MAX phases and i-MXenes, including their structural, vibrational, electronic, optical, magnetic, mechanical, piezoelectric, and electrochemical properties. This article provides a comprehensive understanding of vital properties of these materials by providing a review of foundational literature with existing challenges, limitations, and future perspectives.

electrochemical, electronic↗

DOE OSTI2021

Theoretical predictive screening of noble-metal-containing M 3 AuC 2 (M = Ti, V, and Cr) MAX phases

Using first-principles density functional theory (DFT), the ground state physical properties of the newly synthesized noble-metal-containing Ti 3 AuC 2 MAX phase have been investigated. The effect of transition-element Ti replacement (V and Cr) on physical properties, including structural, elastic, electronic, thermal, and optical are presented. The optimized lattice parameters of Ti 3 AuC 2 MAX phase are in good agreement with the experimental values and decrease when we replace Ti with V and then Cr. The magnetic properties of M 3 AuC 2 are predicted by using generalized gradient approximation (GGA) incorporating onsite electron correlation parameter (Hubbard U parameter) within DFT. Out of three studied MAX phases, V 3 AuC 2 and Cr 3 AuC 2 phases exhibit magnetism. The thermodynamical stability of M 3 AuC 2 (M = Ti, V, and Cr) phases is discussed by the formation enthalpy with respect to their most competing phases. The electronic structure reveals that these phases have metallic nature and are electrically anisotropic. The M-element replacement has an effect on the bonding properties of M 3 AuC 2 . The bonding between M-C is in the order of Cr 3 AuC 2 > V 3 AuC 2 > Ti 3 AuC 2 according to their peak positions and heights of density of states in the occupied site, which is also confirmed from the charge density distribution. The elastic properties indicate that M 3 AuC 2 phases are ductile, machinable, less stiff, and better resistant to thermal shock and are elastically anisotropic. To understand the properties of M 3 AuC 2 for the extreme environment, we employed a quasi-harmonic Debye model at the pressure and temperature range of 0–50 GPa and 0–1600 K, respectively. Additionally, we evaluated thermal conductivity and melting temperature to further understand the potential of these MAX phases in coating applications at elevated temperature. In relation to optical properties, these MAX phases have a reasonable absorption coefficient in the visible as well as in the ultra-violet regions. The reflectivity of M 3 AuC 2 phases is polarization dependent and of 45 % against the visible region, which reveals its potential as coating material to minimize solar heating.

312 MAX phases↗

DOE OSTI2024

Synthesis, microstructure and micro-mechanical characterization of metal (Nb, Ti) – MAX phase (Ti 2 AlC) nanolaminates

We utilize elevated temperature physical vapor deposition (PVD) techniques to design metal/MAX multilayered nanocomposite thin films with alternating nanoscale metallic (Nb, Ti) and MAX phase (Ti 2 AlC) layer thicknesses. These metal/MAX nanolaminate architectures attempt to exploit a unique hierarchical topology – as interfaces between the layers are expected to be in direct competition with the internal interfaces within the MAX layers, to drive their tunable macroscopic mechanical behavior. Two metal/MAX nanolaminates – Nb/Ti 2 AlC and Ti/Ti 2 AlC – were deposited. The Nb/Ti 2 AlC metal/MAX system showed highly diffused layer interfaces with distinct Ti – rich and Nb–Al – rich layers, with the presence of MAX phase alongside TiC and other Ti–Al and Nb–Al intermetallic phases. The Nb/Ti 2 AlC system possessed a layered architecture, though the MAX phases were not found to be continuously present in each alternating layer. The second Ti/Ti 2 AlC system showed a non-lamellar nanocomposite microstructure and the formation of mixed Ti n+1 AlC n phases (a mix of n = 1, 2), and no indication of layering. Diffusion occurring between the metal/MAX layers in both cases, likely due to the elevated temperatures during the deposition process, is speculated as the likely cause of these resultant microstructures. The mechanical properties of both systems were evaluated using micromechanical (nanoindentation and micro-pillar compression) techniques, which demonstrated high strengths for both systems (Nb system: yield and instability strengths of 4.88 ± 0.1 GPa and 5.57 ± 0.03 GPa, Ti system: yield and instability strength of 5.61 ± 0.28 GPa and 6.21 ± 0.25 GPa). In conclusion, this work highlights the promising mechanical properties of metal/MAX multilayered depositions and summarizes the challenges in PVD synthesis of metal/MAX multilayered nanolaminates.

MAX phase↗

DOE OSTI2025

Tribological behavior of spark plasma sintered Ti 3 SiC 2 MAX phase composites

Ti₃SiC₂ MAX phases are considered promising candidates for tribological applications; but, their low hardness (5-6 GPa) can lead to increased abrasive wear and higher wear rates. This study investigates the effect of incorporating hard SiC particles on microstructure, mechanical, and tribological behavior of Ti₃SiC₂-SiC-based MAX phase composites prepared using spark plasma sintering at 1400 °C, 40 MPa, 15-minute holding time. Phase and microstructural characterization of composites confirmed the formation of Ti₃SiC₂ MAX phase (90%) along with TiC as a minor phase (10%). For Ti₃SiC₂-SiC, homogeneous distribution of SiC grains within Ti₃SiC₂ matrix resulted in increased hardness from ~11.6 GPa to ~14.8 GPa; however, the flexural strength decreased from ~615 MPa to ~597 MPa due to coefficient of thermal expansion mismatch. Tribological behavior of Ti₃SiC₂-SiC MAX phase composites was assessed using unidirectional sliding ball-on-flat tests with a 52100 steel ball at different loads and a constant speed of 0.05 m/s. SiC reinforced composites exhibited a decreased friction coefficient from 0.39 to 0.29 and wear rates comparable to Ti₃SiC₂ (7-10×10⁻³ mm³/N·m). SEM and EDS analysis of the worn surfaces indicated material transfer from the steel ball counter body and its oxidation due to frictional heating, at lower loads (2N and 5N), whereas at higher load (10N), fracture of the transfer layer dominated, with the presence of microcracks, delamination, grain pull-outs, and wear debris. Improved mechanical properties and good adhesion of SiC with Ti₃SiC₂ matrix resulted in reduced microcracks and grain pull-outs, making Ti₃SiC₂-SiC/Steel tribo-pair more suitable for tribological applications.

36 MATERIALS SCIENCE↗

DOE OSTI2026

2D in-Plane Ordered MXene Nanosheets Derived from (Mo 2/3 Er 1/3 ) 2 AlC Rare-Earth i-MAX for Energy Storage Applications

MXenes have become one of the most versatile families of two-dimensional (2D) materials due to their high conductivity, hydrophilicity, and remarkable electrochemical performance. This has stimulated intense efforts to design and synthesize MXenes, including structurally unique in-plane ordered 2D MXenes called i-MXenes. Here, we have synthesized the quaternary rare earth (RE)-based i-MAX phase (Mo 2/3 Er 1/3 ) 2 AlC using an arc melting method, and the corresponding 2D i-MXene was then obtained through a LiF/HCl soft etching process. Literature studies have shown that Al and the RE element are etched out during the etching process, leading to the formation of pure vacancy-ordered Mo1.33C 2D i-MXene. However, our investigation reveals that upon exposure to a fluorine solution, the i-MAX phase forms RE fluoride impurities, which are challenging to remove through HCl−DI water washing and persist in the final product, resulting in impure Mo 1.33 C@Er i-MXene. These results were confirmed by various characterizations such as X-ray diffraction, Raman spectroscopy, X-ray photoelectron spectroscopy, and scanning transmission electron microscopy. Although the Mo 1.33 C@Er electrode showed a 24-fold increase in specific capacitance compared to its parent i-MAX phase, it still exhibited a high charge-transfer resistance arising from the insulating nature of RE fluoride byproducts, which adversely influence the overall capacitance behavior of the synthesized 2D Mo 1.33 C@Er i-MXenes. This study contributes to identifying pathways for the preparation of pure 2D i-MXenes from RE-based i-MAX phases and developing improved synthesis methods. With additional process optimization, the 2D i-MXene holds a strong potential for electrochemical energy storage applications. Additionally, the electronic structures of Mo 1.33 C were theoretically studied using first-principles density functional theory calculations, which revealed that pristine Mo 1.33 C is metallic, and this metallic nature is preserved even with −O, −F, and mixed functionalization.

chemical structure↗

DOE OSTI2022

Modeling the non-Schmid crystallographic slip in MAX phases

We present a crystal plasticity constitutive relation for the description of experimentally observed non-Schmid crystallographic slip in a class of ternary carbides and nitrides commonly referred to as MAX phases. In the constitutive relation, we assume that the evolution of the slip system strength in MAX phases has two components – a classical component that depends on the Taylor cumulative shear strain and a non-Schmid component that depends on the stress normal to the slip plane. The non-Schmid crystal plasticity constitutive relation is then used to carry out finite element simulations of micropillar compression of single crystals of two MAX phases, Ti 2 AlC and Ti 3 AlC 2 . The finite element simulations not only quantitatively predict the stress – strain response of a wide range of crystallographic orientations of the micropillars but also rationalize the non-uniform deformation and the deformed shape of the micropillars observed in the experiments for the two materials. As a result, parametric studies are also carried out to quantify the role of the non-Schmid effect and understand the effects of key experimental parameters on the stress – strain response of the micropillars of the two MAX phases.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Investigating a novel magnetic MAX phase nitride and its (001)-surfaces

We report magnetic MAX phases including their surfaces exhibit promising functional properties for magneto-electronic devices and self-monitoring smart coatings. By employing an integrated ab-initio approach, here we investigate a new member of the MAX phase, Mn 2 AuN. This compound satisfies the chemical, mechanical and dynamical stability criteria, leading to a possibility of its synthesis, and exhibits electronic and elastic anisotropy. The identified ferromagnetic configuration (with high Curie temperature) is the most energetically favorable among the five different spin configurations i.e., non-magnetic, ferromagnetic, and three anti-ferromagnetic. From the coatings perspective, the surface properties of Mn 2 AuN(001) terminations are investigated considering the four possible surface termination models. Remarkably, the magnetism does not get vanished even after cleaving the bulk unit cell into the (001)-surfaces. While evaluating the surface energetics in different chemical potentials, the N-001 terminated surface comes out to be the most stable termination contrasting with carbide MAX phases and is the only termination that exhibits the magnetic characteristics.

36 MATERIALS SCIENCE↗

DOE OSTI2023

On relaxations of the max k -cut problem formulations

Here, a tight continuous relaxation is a crucial factor in solving mixed integer formulations of many NP-hard combinatorial optimization problems. The (weighted) max k-cut problem is a fundamental combinatorial optimization problem with multiple notorious mixed integer optimization formulations. In this paper, we explore four existing mixed integer optimization formulations of the max k-cut problem. Specifically, we show that the continuous relaxation of a binary quadratic optimization formulation of the problem is: (i) stronger than the continuous relaxation of two mixed integer linear optimization formulations and (ii) at least as strong as the continuous relaxation of a mixed integer semidefinite optimization formulation. We also conduct a set of experiments on multiple sets of instances of the max k-cut problem using state-of-the-art solvers that empirically confirm the theoretical results in item (i). Furthermore, these numerical results illustrate the advances in the efficiency of global non-convex quadratic optimization solvers and more general mixed integer nonlinear optimization solvers. As a result, these solvers provide a promising option to solve combinatorial optimization problems. Our codes and data are available on GitHub.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

MAX-Phase Partial Optical Properties

The optical and electrical properties of MAX-phase materials have been thoroughly studied in the past. We present here a new technique to determine and study the partial contributions to the optical properties. Following the same methodology as the decomposition of the density of states to the partial density of states, we have decomposed the optical properties into the partial optical properties. Using this technique the differences of elemental and layer resolved optical properties are displayed for both the 211 and 312 phase of TiSiC and TiAlC MAX-phase materials.

Weigand, Alysse↗

DOE OSTI2024

Elemental and layer based analysis of optical properties: A new technique applied to four MAX-phases

Here we present here a novel technique to calculate partial contributions to the optical properties by atoms, elements, and layers. Following the same methodology as the calculation of the partial density of states from the density of states, we have decomposed the optical properties into the partial optical properties. Using this technique the differences of elemental resolved optical properties as well as layer-resolved optical properties are displayed for both the 211 and 312 phases of TiSiC and TiAlC MAX-phase materials.

36 MATERIALS SCIENCE↗