max phases: bridging the gap between metals and ceramics

www.ceramics.org | American Ceramic Society Bulletin, Vol. 92, No. 320

MAX phases: Bridging the gap between metals and ceramics

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

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T 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 (specifi-cally, 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 combina-tion 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.

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.

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 individu-al grains by kinking.

21American Ceramic Society Bulletin, Vol. 92, No. 3 | www.ceramics.org

The growing interest results from the unusual, often unique, properties of the MAX phases. Like their correspond-ing binary carbides and nitrides (MX), the MAX phases are elastically stiff, good thermal and electrical conduc-tors, 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 resis-tant. 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 under-standing. Some of their potential appli-cations also are highlighted. For a thor-ough 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

Crystal structure and atomic bonding in the MAX phases

The MAX phases are layered hex-agonal 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

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 solu-tions have been processed and charac-terized 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.

Interestingly, some of solid solu-tions 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 experi-mental and theoretical density func-tional theory (DFT) approaches.1,18–20 For example, ab-initio studies recently extended the family of the MAX phases to compounds with magnetic proper-ties 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

Figure 2. Unit cells of the Mn+1AX

n 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.

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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 domi-nates 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 surpris-ing they share many common attributes and properties, such as metal-like elec-trical conductivities, high stiffness val-ues, thermal stability, and low thermal expansion coefficients.

Physical properties Most of the MAX phases are excel-

lent electrical conductors, with electri-cal 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 concentra-tions of electrons and holes are roughly equal, but their mobilities are about

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 abso-lute 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 conductivi-ties (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 refrac-tory 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 forma-tion 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 mechan-ical properties, some MAX phases currently are being considered for structural and nonstructural high-tem-perature applications. Their oxidation resistance, however, determines their usefulness in air. In most cases, MAX phases oxidize according to Eq (1).

Consequently, their oxidation resis-

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

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Figure 4. (a) Ti2AlC-based heating ele-ment 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 crack-ing of the oxide layer.33

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Mn+1AXn+bO2= (n+1)MOx/n+1+AOy+XnO2b-x-y (1)

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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 spe-cific 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.

Mechanical PropertiesDespite similarities between the

physical properties of the MX and MAX phases, the differences between their mechanical properties is strik-ing. 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 ther-mal shock resistant, and most are read-ily machinable. This stark difference in behavior comes down to two words: mobile dislocations.

At this time is it fairly well estab-lished that basal plane dislocations (BPD)—and only BPDs— are abun-dant, mobile, and able to multiply in the MAX phases at ambient tem-peratures.34 However, because the dislocations are constrained to the basal planes, the number of slip sys-tems is fewer than the five needed for polycrystalline ductility. Therefore, the MAX phases occupy an interest-ing 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.

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 micro-mechanism 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 ori-ented 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 disloca-tion 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 dis-location walls (MDW) and ultimately

permanent kink bands (Figure 3(c)). At higher temperatures, the grain boundar-ies are soft and the IKBs devolve into MDWs and KBs that lead to delamina-tion 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, strain-rate-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 fol-lows that a significant portion of the mechanical energy—about 25 percent at 1 GPa in the case of Ti3SiC2—dis-sipates 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

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 dis-location 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

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stress-strain loops are open and strain rate dependent but become smaller with increasing cycles, that is, cycling hardening takes place. The practical implication of these phenomena for structural applications cannot be over-estimated because the MAX phases can dissipate a large portion of harmful structural vibrations or acoustic loads, even at high temperatures.

The room-temperature ultimate compressive strengths of polycrystalline MAX phases range from 300 MPa to 2 GPa and depend strongly on composi-tion and grain size. Like typical ceram-ics, their room-temperature flexural and tensile strengths are lower than their compressive strength.1,7,14 For example, the compressive and tensile strengths of Ti3SiC2, with 5-µm grains, are 1,050 MPa and 300 MPa, respectively. At room temperature, they fail in a brittle manner. Nevertheless, they fail grace-fully—samples do not shatter but, rath-er, 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 the former exhibit strong plastic anisot-ropy. For example, when the basal planes are oriented such that slip occurs along the basal plane (along the z-axis in inset of Figure 6(b)), they behave

as ideal plastic solids (Figure 6(b)) even at room temperature, with strain that exceeds 10 percent.35 By contrast, when the slip planes are parallel to the applied load (loaded along the x-axis in inset of Figure 6(b)) and deforma-tion by ordinary dislocation glide is suppressed, the sample yields at higher stresses by KB formation. In this case, considerable strain softening occurs because the kink bands rotate basal planes in such a way as to induce shear band formation.35

Softer than structural ceramicsUnlike their MX counterparts, the

MAX phases are relatively soft and exceptionally damage tolerant. The Vickers hardness values of polycrystal-line MAX phases fall in the range of

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 exam-ple, for coarse-grained Ti3SiC2, KIc increases from 8.5 to 11 MPa·m1/2, with increasing crack size.37 The high values of KIc and

R-curve behavior result from the forma-tion of plastically deformable bridging ligaments (Figures 7(a) and (b)) and the crack-arresting properties of kink boundaries. The latter two mechanisms are unique to the MAX phases.

Thus far, Ti3SiC2 is the only MAX phase on which cyclic fatigue stud-ies have been conducted. The studies show that fatigue crack growth thresh-olds were comparatively higher than those for typical ceramics and some metals (e.g., 300-M alloy steel).37,38 At 1,200°C, which is above the BPT, the crack-growth rate versus stress intensity curves show three distinctive regions emerging under the same condi-tions, which suggests delamination or grain-boundary decohesion as possible mechanisms.

All MAX phases tested to date go

Figure 6. (a) Typical cyclic compressive stress–strain curves for Ti3SiC2 with two grain sizes. The loops 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 and the orientation of the basal planes in individual grains depicted by thin lines.35

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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 denotes direction of crack propagation.36, 37

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through a BPT. The 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 ulti-mate 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, deforma-tion rate. More spe-cifically, when loaded above their BPT tem-peratures at high defor-mation rates, they fail in a brittle manner. However, when loaded slowly, they can be plastically deformed at 1,200°C in air—to strains greater than 25 percent even in tension—before failing in a graceful manner.5 Because KIc drops above the BPT temperature,39 we can categorically rule out the activation of additional slip systems.37 A sufficient condition needed to explain the BPT is the onset of a temperature-dependent grain-boundary decohesion-strength, delamination strength, or both.

Although the MAX phases are considered good candidate materi-als for high-temperature applications, there are only a few published reports on their creep response. The few that exist for Ti3SiC2 and Ti2AlC suggest that creep is independent of grain size, resulting from dislocation creep togeth-er with significant accumulation of voids and microcracks.40 Nevertheless, 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 ther-mal shock resistance. Unlike typical ceramics, the MAX phases not only do not shatter after quenching, and, in some cases, their residual flexural strengths increase even after quenching

from temperatures as high as 1,200°C into ambient-temperature water (see Figure 8(b)).

Lastly, arguably the most charac-teristic trait of the MAX phases and what truly sets them apart from other structural ceramics or high-temperature alloys is the ease with which they can be machined (Figure 9(a)). The MAX phases can be readily machined with regular high-speed tool steels or even manually with a hacksaw.

Potential applications Before discussing potential applica-

tions, availability and cost have to be put in perspective. There are many methods for processing the MAX phas-es as bulk materials, powders, porous foams, coatings, and thin films.1,8,14 Some of the methods are quite mature,

patented, and widely used. For exam-ple, Sandvik Materials Technology (Hallstahammar, Sweden) has manu-factured Ti3SiC2 and Ti2AlC powders and parts since the late 1990s under its MAXthal brand (Figure 9(b)).

MAX phases in any form usually are fabricated from elemental powders and/or binary carbides, and, thus, their price is determined mostly by the price of those powders. Currently, Sandvik sells Ti3SiC2 and Ti2AlC powders at around $500 per kg. This price is significantly higher than the price of Al2O3, SiC, and Si3N4 powders used to make other structural and high-temperature ceram-ics. However, pressureless sintering in inert atmospheres can yield fully dense MAX phase parts without using sinter-ing aids. More importantly, fully dense MAX phases are readily machined to

Figure 8. (a) Creep properties of select metallic, intermetallic alloys, and Ti3SiC2 plotted as stress-to-rupture versus the Larson–Miller parameter. The solid black line represents compression results, and the dashed line, tension results.1 (b) Postquench flexural strength versus quench temperature of select MAX phases.7

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Figure 9. (a) A MAX phase billet machined by a lathe. (b) Ti2AlC and Ti3SiC2 powders and parts fabricated by Sandvik Heating Technology, Sweden, and commercially avail-able under the trade name MAXthal 211 and MAXthal 312.

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very high tolerances, which should ren-der the cost of final parts competitive compared with other structural ceram-ics. 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 prop-erties that the MAX phases exhibit, especially their high-temperature stabil-ity, 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-tem-perature applications. The most promis-ing 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 capabili-ties,41 among others. This combina-tion 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 high-temperature foil bearings, glove and condom molds, tooling for dry drilling of concrete (3-ONE-2, LLC), and non-stick cookware—took advantage of low friction and good wear resistance of the MAX phases and their composites.1

Besides high-temperature applica-tions, there may be electrical applica-tions. For example, the first commercial application of Ti3SiC2 was as sputter-ing targets for electrical contact deposi-tion (Impact Coatings, Sweden). They also were investigated for electrochemi-cal chlorine production electrodes.42

The way forwardOur 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-

cations.43 The recent intense interest in the MAX phases indicates that applica-tions are forthcoming. This is impor-tant—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 prop-erties? (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 control-ling 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 met-als44 or ceramics in composite materials?

AcknowledgmentsThis 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 (CMMI-1233792) to Texas A&M University.

About authorsMiladin Radovic is associate profes-

sor 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 [email protected].

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