MAX phases: Bridging the gap between metals and ceramics Figure 1. Scanning electron microscopy of the fractured surface in Ti2AlC after dynamic testing of at a strain rate of 2400 s–1 showing typical laminated nature and deformation of individual grains by kinking.

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MAX phases: Bridging the gap between metals and ceramics By Miladin Radovic and Michel W. Barsoum

(Credit: Credit: Radovic and Benitez; TAMU.)

T

The MAX phases are a new and exciting class of carbides and nitrides that bridge the gap between properties typical of metals and ceramics, while offering fundamentally new directions in tuning the structure and properties of ceramics for emerging applications.

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he term “MAX phases” was coined in the late 1990s and applies to a family of 60+ ternary carbides and nitrides that share a layered structure as illustrated in Figures 1 and 2. They are so called because of their chemical formula: Mn+1AXn —where n = 1, 2, or 3, where M is an early transition metal, A is an A-group element (specifically, the subset of elements 13–16), and X is carbon and/or nitrogen, Figure 2.1 Nowotny and coworkers2, 3 discovered most of these phases in powder form roughly 40 years ago. However, Barsoum and El-Raghy’s4 report in 1996 on the synthesis of phase-pure bulk Ti3SiC2 samples and their unusual combination of properties catalyzed renewed interest in them. Since then, research on the MAX phases has exploded. According to ISI, to date around 1,200 papers have been published on one MAX phase alone, Ti3SiC2, with roughly half of those published in the past six years. www.ceramics.org | American Ceramic Society Bulletin, Vol. 92, No. 3

Crystal structure and atomic bonding in the MAX phases

The MAX phases are layered hexagonal crystal structures (space group P63/mmc) with two formula units per unit cell, as illustrated in Figure 2, for structures with n equal 1 to 3. The unit cells consist of M6X-octahedra with the X-atoms filling the octahedral sites between the M-atoms, which are identical to those found in the rock salt structure of the MX binaries. The octahedra alternate with layers of pure A-elements located at the centers of trigonal prisms that are slightly larger, and thus more accommodating of the larger A-atoms. When n = 1, the A-layers are separated by two M-layers (Figure 2(a)). When n = 2, they are separated by three layers (M3AX2 in Figure 2(b)). When n = 3, they are separated by four layers (M3AX2 in Figure 2(c)). MAX phases with more

(Credit: Credit: Radovic; TAMU.)

The growing interest results from the unusual, often unique, properties of the MAX phases. Like their corresponding binary carbides and nitrides (MX), the MAX phases are elastically stiff, good thermal and electrical conductors, resistant to chemical attack, and have relatively low thermal expansion coefficients.1 Mechanically, however, they cannot be more different. They are relatively soft and most are readily machinable, thermal shock resistant and damage tolerant. Moreover, some are fatigue, creep, and oxidation resistant. At room temperature, they can be compressed to stresses as high as 1 GPa and fully recover on removal of the load, while dissipating approximately 25 percent of the mechanical energy.6 At higher temperatures, they undergo a brittle-to-plastic transition (BPT), above which they are quite plastic even in tension.5 This article gives an overview of the salient properties of the MAX phases and of the status of our current understanding. Some of their potential applications also are highlighted. For a thorough review of the large body of work on MAX phases, the reader is referred to a recently published book1 and a number of excellent review articles.7–15 Figure 2. Unit cells of the Mn+1AXn phases for (a) n = 1 or M2AX, (b) n = 2 or M3AX2, and (c) n = 3 or M4AX3 phases, and (d) M, A, and X elements that form the MAX phases.

complex stacking sequences, such as M5AX4, M6AX5, and M7AX6 also have been reported.8,16 In addition to the “pure” MAX phases that contain one of each of the M, A, and X elements highlighted in Figure 2(d), the number of possible solid solutions is quite large. Solid solutions have been processed and characterized with substitution on1 • M sites, e.g., (Nb,Zr)2AlC, (Ti,V)2AlC, (Ti,Nb)2AlC, (Ti,Cr)2AlC, (Ti,Hf)2InC, and (Ti,V)2SC; • A-sites, e.g., Ti3(Si,Ge)C2, and Ti3(Sn,Al)C2; and • X-sites,17 e.g., Ti2Al(C,N) and Ti3Al(C,N)2.

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Interestingly, some of solid solutions exist even when one of the end members does not. The number of MAX phases and their solid solutions continues to expand. The discovery of new phases has advanced significantly through the combination of experimental and theoretical density functional theory (DFT) approaches.1,18–20 For example, ab-initio studies recently extended the family of the MAX phases to compounds with magnetic properties that contain later transition-metal substitutions on the M sites, such as (Cr,Mn)2AlC.21 A large body of work devoted to DFT calculations of the electronic structures and chemical bonding in the 21

(a)

(b) Temperature (K)

Temperature (K)

Figure 3. Temperature dependence of (a) electrical conductivity31 and (b) thermal conductivity of select MAX phases.32

MAX phases22-28 shows that • Similar to the MX phases, MAX phase bonding is a combination of metallic, covalent, and ionic bonds; • The M and X atoms form strong directional covalent bonds in the M-X layers that are comparable to those in the MX binaries;22, 27, 28 • M–d–M–d metallic bonding dominates the electronic density of states at the Fermi level, N(EF); and • In most MAX phases, the M–A bonds are relatively weaker than the M–X bonds. Given the similarities between some aspects of the atomic bonding in the MX and MAX phases it is not surprising they share many common attributes and properties, such as metal-like electrical conductivities, high stiffness values, thermal stability, and low thermal expansion coefficients.

(a)

(b)

(Credit: Sandvik Materials Technology, Sweden.)

Physical properties

Figure 4. (a) Ti2AlC-based heating element resistively heated to 1,450°C in air. (b) Micrograph of the Al2O3 oxide layer after 10,000 thermal cycles up to 1,350°C showing no spallation or cracking of the oxide layer.33 22

Most of the MAX phases are excellent electrical conductors, with electrical resistivities that mostly fall in the narrow range of 0.2–0.7 µΩ·m at room temperature.1,10 Like other metallic conductors, their resistivities increase with increasing temperatures (Figure 3(a). Ti3SiC2 and Ti3AlC2 conduct better than titanium metal. Even more interesting and intriguing, many of the MAX phases appear to be compensated conductors, wherein the concentrations of electrons and holes are roughly equal, but their mobilities are about

(Credit: Adapted from Ref. 31, 32.)

Resistivity (µΩ·m)

Thermal conductivity (W/m·K)

MAX phases: Bridging the gap between metals and ceramics equal, too.10 Several MAX phases, most notably Ti3SiC2, have very low thermoelectric or Seebeck coefficients.10,29 Solids with essentially zero thermopower can, in principle, serve as reference materials in thermoelectric measurements, for example, as leads to measure the absolute thermopower of other solids. The optical properties of the MAX phases are dominated by delocalized electrons.30 Magnetically, most of them are Pauli paramagnets, wherein the susceptibility is, again, determined by the delocalized electrons and, thus, is neither very high, nor temperature dependent.31 Thermally, the MAX phases share much in common with their MX counterparts, that is, they are good thermal conductors because they are good electrical conductors. At room temperatures their thermal conductivities (Figure 3(b)) fall in the 12–60 W/ (m·K) range.1,10 The coefficients of thermal expansion (CTE) of the MAX phases fall in the 5–10 µK–1 range and are relatively low as expected for refractory solids.15 The exceptions are some chromium-containing phases with CTEs in the 12–14 µK–1 range. At high temperatures, the MAX phases do not melt congruently but decompose peritectically to A-rich liquids and Mn+1Xn carbides or nitrides. Thermal decomposition occurs by the loss of the A element and the formation of higher n-containing MAX phases and/or MX. Some MAX phase, such as Ti3SiC2, are quite refractory with decomposition temperatures above 2,300°C.1 Because of their excellent electrical, thermal and high-temperature mechanical properties, some MAX phases currently are being considered for structural and nonstructural high-temperature applications. Their oxidation resistance, however, determines their usefulness in air. In most cases, MAX phases oxidize according to Eq (1). Mn+1AXn+bO2= (n+1)MOx/n+1+AOy+XnO2b-x-y (1) Consequently, their oxidation resis-

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(a)

(c)

Mechanical Properties

Despite similarities between the physical properties of the MX and MAX phases, the differences between their mechanical properties is striking. The MX phases are some of the hardest solids known. They are brittle, nonmachinable, damage intolerant, and susceptible to thermal shock. In sharp contradistinction, the MAX phases are exceedingly damage tolerant and thermal shock resistant, and most are readily machinable. This stark difference in behavior comes down to two words: mobile dislocations. At this time is it fairly well established that basal plane dislocations (BPD)—and only BPDs— are abundant, mobile, and able to multiply in the MAX phases at ambient temperatures.34 However, because the dislocations are constrained to the basal planes, the number of slip systems is fewer than the five needed for polycrystalline ductility. Therefore, the MAX phases occupy an interesting middle ground between metals and ceramics, in that they are pseudoductile under confined deformations or high temperatures, but are brittle at room temperature, especially in tension and thin form.

(b)

(Credit: Barsoum;Drexel University.)

tance depends on nature of the oxides that form. The most oxidation-resistant MAX phase is Ti2AlC, because it forms a stable and protective Al2O3 layer that can withstand thermal cycling up to 1,350°C for 10,000 cycles without spallation or cracking (Figure 4).33 The oxidation resistance of Cr2AlC also is superb because it also forms a protective Al2O3 layer, however, the oxide spalls off during thermal cycling. Elastically, the MAX phases are quite stiff, with near-isotropic room temperature Young’s and shear moduli in the 178–362 GPa and 80–142 GPa ranges, respectively.7, 14 Because the densities of some of the MAX phases are as low as 4–5 g/cm3, their specific stiffness values can be quite high. For example, the specific stiffness of Ti3SiC2 is comparable to Si3N4 and roughly three times that of titanium metal.

Figure 5. Transmission electron microscopy of (a) dislocation wall consisting of basal plane dislocations and (b) area containing kink band in Ti3SiC2 after compression at room temperature.35 (c) Schematic of the formation of incipient kink band, mobile dislocation walls kink bands, and delaminations. Red grains are “hard” grains, and blue grains are “soft” grains with the basal planes favorably oriented for easy slip.6

The BPDs arrange themselves either in walls (that is, high- or low-angle grain boundaries (Figure 5(a)), in arrays or dislocation pileups (not shown) parallel to the basal planes. Confining the dislocations to the basal planes, in turn, results in an important micromechanism that is quite ubiquitous in the MAX phases at all lengths scales, viz., kink band (KB) formation (Figures 1 and 5(b)6, 9). When the MAX phases are loaded, initially the “soft” grains— those with basal planes favorably oriented for easy slip (blue grains in Figure 3(c))—deform and, in turn, cause the “hard” grains (red grains in Figure 5(c)), to develop incipient kink bands (IKB). The latter are coaxial dislocation loops that, as long as their ends are not sundered, are spontaneously and fully reversible. With further increase in applied load, if the polycrystal does not fail by shear band formation or fracture, the IKBs result in mobile dislocation walls (MDW) and ultimately

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permanent kink bands (Figure 3(c)). At higher temperatures, the grain boundaries are soft and the IKBs devolve into MDWs and KBs that lead to delamination at the individual grain level and considerable plasticity. Although the MAX phases are quite stiff, they respond to cyclic loading, whether compression6 or tension5, with spontaneous, fully reversible, strainrate-independent hysteretic stress-strain loops (Figure 6(a). The shape and areas of these loops depend strongly on grain size (Figure 6(a) but weakly on the number of cycles. In other words, they are quite fatigue resistant. It follows that a significant portion of the mechanical energy—about 25 percent at 1 GPa in the case of Ti3SiC2—dissipates during each cycle.6 At this time, IKBs (Figure 5(c)) that form during loading and annihilate during unloading are believed to account for this nonlinear elastic (or hysteretic) effect. Above the BPT temperature, the 23

MAX phases: Bridging the gap between metals and ceramics 2–8 GPa. They are thus softer than most structural ceramics, but harder than most metals.1, 9 The room temperature fracture toughness (KIc) values—that range from 5 to almost 20 MPa·m1/2— are quite respectable when compared with other monolithic ceramics. The MAX phases also exhibit R-curve behavior, i.e., KIc increases with increasing crack length. For examEngineering strain Strain ple, for coarse-grained Ti3SiC2, KIc increases from Figure 6. (a) Typical cyclic compressive stress–strain curves for Ti3SiC2 with two grain sizes. The loops 8.5 to 11 MPa·m1/2, with overlap after one and one hundred cycles.6 (b) Engineering stress–strain curves for 2-mm cubes of highly oriented samples of Ti3SiC2. The inset cube shows a schematic sample with the chevron texture increasing crack size.37 35 and the orientation of the basal planes in individual grains depicted by thin lines. The high values of KIc and R-curve behavior result from the formaas ideal plastic solids (Figure 6(b)) stress-strain loops are open and strain tion of plastically deformable bridging even at room temperature, with strain rate dependent but become smaller ligaments (Figures 7(a) and (b)) and that exceeds 10 percent.35 By contrast, with increasing cycles, that is, cycling the crack-arresting properties of kink when the slip planes are parallel to the hardening takes place. The practical boundaries. The latter two mechanisms applied load (loaded along the x-axis implication of these phenomena for are unique to the MAX phases. in inset of Figure 6(b)) and deformastructural applications cannot be overThus far, Ti3SiC2 is the only MAX tion by ordinary dislocation glide is estimated because the MAX phases phase on which cyclic fatigue studsuppressed, the sample yields at higher can dissipate a large portion of harmful ies have been conducted. The studies stresses by KB formation. In this case, structural vibrations or acoustic loads, show that fatigue crack growth threshconsiderable strain softening occurs even at high temperatures. olds were comparatively higher than because the kink bands rotate basal The room-temperature ultimate those for typical ceramics and some compressive strengths of polycrystalline planes in such a way as to induce shear metals (e.g., 300-M alloy steel).37,38 band formation.35 MAX phases range from 300 MPa to 2 At 1,200°C, which is above the BPT, GPa and depend strongly on composithe crack-growth rate versus stress Softer than structural ceramics tion and grain size. Like typical ceramintensity curves show three distinctive Unlike their MX counterparts, the ics, their room-temperature flexural and regions emerging under the same condiMAX phases are relatively soft and tensile strengths are lower than their tions, which suggests delamination or exceptionally damage tolerant. The compressive strength.1,7,14 For example, grain-boundary decohesion as possible Vickers hardness values of polycrystalthe compressive and tensile strengths mechanisms. line MAX phases fall in the range of of Ti3SiC2, with 5-µm grains, are 1,050 All MAX phases tested to date go MPa and 300 MPa, respectively. At room temperature, they fail in a brittle manner. Nevertheless, they fail gracefully—samples do not shatter but, rather, fail along planes inclined 30°–40° relative to compression axis. The stress–strain response of highly oriented (textured) microstructures loaded in compression is quite different from polycrystalline behavior, because (b) the former exhibit strong plastic anisot- (a) ropy. For example, when the basal planes are oriented such that slip occurs Figure 7. SEM images of fatigue cracks in Ti3SiC2. The images also show bridging ligaments, which plastically deform as a function of crack propagation. Arrow along the basal plane (along the z-axis denotes direction of crack propagation.36, 37 in inset of Figure 6(b)), they behave (b)

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(Credit: Barsoum; Sci. Mater.)

(Credit: Barsoum; JACERS.)

(Credit: Adapted from Barsoum, et. al., Ref. 6, 35.)

Engineering stress (MPa)

Stress (MPa)

(a)

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(Credit: Sandvik Materials Technology, Sweden.)

(Credit: Barsoum; Wiley.)

Retained flexural strength (MPa)

Stress (MPa)

through a BPT. The (a) (b) BPT temperature varies from phase to phase, but for many of them tested so far falls between 1,000°C and 1,100°C. Below BPT, the ultimate strengths of the MAX phases depend weakly on temperature and deformation rate.1,5 Above BPT, their stress–strain response depends strongly on temperature and, more importantly, deformaTemperature (k [log t (h)+20]3 10–3) Quench temperature (°C) tion rate. More speFigure 8. (a) Creep properties of select metallic, intermetallic alloys, and Ti3SiC2 plotted as stress-to-rupture cifically, when loaded versus the Larson–Miller parameter. The solid black line represents compression results, and the dashed above their BPT tem1 7 peratures at high defor- line, tension results. (b) Postquench flexural strength versus quench temperature of select MAX phases. mation rates, they fail in from temperatures as high as 1,200°C patented, and widely used. For exama brittle manner. However, when loaded ple, Sandvik Materials Technology into ambient-temperature water (see slowly, they can be plastically deformed (Hallstahammar, Sweden) has manuFigure 8(b)). at 1,200°C in air—to strains greater factured Ti3SiC2 and Ti2AlC powders Lastly, arguably the most characthan 25 percent even in tension—before and parts since the late 1990s under its teristic trait of the MAX phases and 5 failing in a graceful manner. Because KIc MAXthal brand (Figure 9(b)). what truly sets them apart from other 39 drops above the BPT temperature, we MAX phases in any form usually are structural ceramics or high-temperature can categorically rule out the activation fabricated from elemental powders and/ alloys is the ease with which they can 37 of additional slip systems. A sufficient or binary carbides, and, thus, their price be machined (Figure 9(a)). The MAX condition needed to explain the BPT is is determined mostly by the price of phases can be readily machined with the onset of a temperature-dependent those powders. Currently, Sandvik sells regular high-speed tool steels or even grain-boundary decohesion-strength, Ti3SiC2 and Ti2AlC powders at around manually with a hacksaw. delamination strength, or both. $500 per kg. This price is significantly Although the MAX phases are higher than the price of Al2O3, SiC, Potential applications considered good candidate materiand Si3N4 powders used to make other Before discussing potential applicaals for high-temperature applications, structural and high-temperature ceramtions, availability and cost have to be there are only a few published reports ics. However, pressureless sintering in put in perspective. There are many on their creep response. The few that inert atmospheres can yield fully dense methods for processing the MAX phasexist for Ti3SiC2 and Ti2AlC suggest MAX phase parts without using sinteres as bulk materials, powders, porous that creep is independent of grain size, ing aids. More importantly, fully dense foams, coatings, and thin films.1,8,14 resulting from dislocation creep togethMAX phases are readily machined to Some of the methods are quite mature, er with significant accumulation of voids and microcracks.40 Nevertheless, (a) (b) creep resistance of the MAX phases is quite good when compared with other known creep-resistant materials (Figure 8(a)), and they offer great promise for future improvements. Another important property of the MAX phases is their exceptional thermal shock resistance. Unlike typical ceramics, the MAX phases not only do not shatter after quenching, and, Figure 9. (a) A MAX phase billet machined by a lathe. (b) Ti2AlC and Ti3SiC2 powders in some cases, their residual flexural and parts fabricated by Sandvik Heating Technology, Sweden, and commercially availstrengths increase even after quenching able under the trade name MAXthal 211 and MAXthal 312.

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MAX phases: Bridging the gap between metals and ceramics very high tolerances, which should render the cost of final parts competitive compared with other structural ceramics. Furthermore, the price of powders should drop as demand increases. The development of reaction synthesis methods from less-expensive precursor powders, such as TiO2 instead of pure titanium and TiC would constitute a major breakthrough. Given the remarkable set of properties that the MAX phases exhibit, especially their high-temperature stability, thermal shock resistance, damage tolerance, good machinability, and the exceptional oxidation resistance of some of them, it is not surprising that they were first targeted for high-temperature applications. The most promising MAX phase for high temperature applications is Ti2AlC because of the relatively low cost of raw materials needed, low density, superb oxidation resistance (that is immune to thermal cycling), and crack-healing capabilities,41 among others. This combination of properties together with good electrical conductivity led Kanthal to evaluate heating elements made from Ti2AlC. (Figure 5(a)). The company also tested MAX phases for gas burner nozzles and industrial die inserts. Other evaluated applications—such as hightemperature foil bearings, glove and condom molds, tooling for dry drilling of concrete (3-ONE-2, LLC), and nonstick cookware—took advantage of low friction and good wear resistance of the MAX phases and their composites.1 Besides high-temperature applications, there may be electrical applications. For example, the first commercial application of Ti3SiC2 was as sputtering targets for electrical contact deposition (Impact Coatings, Sweden). They also were investigated for electrochemical chlorine production electrodes.42

The way forward

Our understanding of the structure and properties of the MAX phases has come a long way in less than two decades. Typically, it takes between 10 and 20 years from “discovery” to appli-

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cations.43 The recent intense interest in the MAX phases indicates that applications are forthcoming. This is important—applications keep a research field vital. The understanding we have achieved to date not withstanding, there remain outstanding scientific questions to answer and technological hurdles to overcome. Questions under exploration by more than a dozen research groups around the world include • Can we extend the number of known MAX phases to M, A, and X elements not shown in Figure 2(c)? • What are the effects of the lattice defects on thermal and electrical properties? (As well as the related question of non-stoichiometry and its effect on properties?) • To what extent can properties be tailored by solid solutions or by controlling the microstructure? • Why are they so thermal shock resistant? • What determines their critical resolved shear stresses? • Can they be processed using more affordable precursors? • What benefits can be gained by combining the MAX phases with metals44 or ceramics in composite materials?

Acknowledgments

This work was partially funded by grants from the NSF (DMR-0503711) and the ARO (W911NF-07-1-0628 and W911NF-11-1-0525) to Drexel University and grants from the AFOSR (FA9550-09-1-0686) and NSF (CMMI1233792) to Texas A&M University.

About authors

Miladin Radovic is associate professor at the Department of Mechanical Engineering and Materials Science and Engineering Program at Texas A&M University, College Station, Texas. Michel W. Barsoum is distinguished professor, Department of Materials Science and Engineering, Drexel University, Philadelphia, Pa. Contact: [email protected] or barsoumw@ drexel.edu.

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