Cover Page

Table of Contents

Related Titles

Title Page




Chapter 1: Introduction

1.1 Introduction

1.2 History of the MAX Phases


Chapter 2: Structure, Bonding, and Defects

2.1 Introduction

2.2 Atom Coordinates, Stacking Sequences, and Polymorphic Transformations

2.3 Lattice Parameters, Bond Lengths, and Interlayer Thicknesses

2.4 Theoretical Considerations

2.5 To Be or Not to Be

2.6 Distortion of Octahedra and Trigonal Prisms

2.7 Solid Solutions

2.8 Defects

2.9 Summary and Conclusions

2.A Appendix Bond Distances and Distortions in the M3AX2 and M4AX3 Phases


Chapter 3: Elastic Properties, Raman and Infrared Spectroscopy

3.1 Introduction

3.2 Elastic Constants

3.3 Young's Moduli and Shear Moduli

3.4 Poisson's Ratios

3.5 Bulk Moduli

3.9 Infrared Spectroscopy

3.10 Summary and Conclusions


Chapter 4: Thermal Properties

4.1 Introduction

4.2 Thermal Conductivities

4.3 Atomic Displacement Parameters

4.4 Heat Capacities

4.5 Thermal Expansion

4.6 Thermal Stability

4.7 Summary and Conclusions

4.A Appendix


Chapter 5: Electronic, Optical, and Magnetic Properties

5.1 Introduction

5.2 Electrical Resistivities, Hall Coefficients, and Magnetoresistances

5.3 Seebeck Coefficients, Θ

5.4 Optical Properties

5.5 Magnetic Properties

5.6 Superconducting Properties

5.7 Summary and Conclusions


Chapter 6: Oxidation and Reactivity with Other Gases

6.1 Introduction

6.2 Ti3SiC2

6.3 Tin+1AlXn

6.4 Solid Solutions between Ti3AlC2 and Ti3SiC2

6.5 Cr2AlC

6.6 Nb2AlC and (Ti0.5,Nb0.5)2AlC

6.7 Ti2SC

6.8 V2AlC and (Ti0.5,V0.5)2AlC

6.9 Ti3GeC2 and Ti3(Si,Ge)C2

6.10 Ta2AlC

6.11 Ti2SnC, Nb2SnC, and Hf2SnC

6.12 Ti2InC, Zr2InC, (Ti0.5,Hf0.5)2InC, and (Ti0.5,Zr0.5)2InC

6.13 Sulfur Dioxide, SO2

6.14 Anhydrous Hydrofluoric, HF, Gas

6.15 Chlorine Gas

6.16 Summary and Conclusions

6.A Appendix Oxidation of Tin+1AlXn When Alumina Does Not Form a Protective Layer


Chapter 7: Chemical Reactivity

7.1 Introduction

7.2 Diffusivity of the M and A Atoms

7.3 Reactions with Si, C, Metals, and Intermetallics

7.4 Reactions with Molten Salts

7.5 Reactions with Common Acids and Bases

7.6 Summary and Conclusions

7.A Appendix


Chapter 8: Dislocations, Kinking Nonlinear Elasticity, and Damping

8.1 Introduction

8.2 Dislocations and Their Arrangements

8.3 Kink Band Formation in Crystalline Solids

8.4 Incipient Kink Bands

8.5 Microscale Model for Kinking Nonlinear Elasticity

8.6 Experimental Verification of the IKB Model

8.7 Effect of Porosity

8.8 Experimental Evidence for IKBs

8.9 Why Microcracking Cannot Explain Kinking Nonlinear Elasticity

8.10 The Preisach–Mayergoyz Model

8.11 Damping

8.12 Nonlinear Dynamic Effects

8.13 Summary and Conclusions


Chapter 9: Mechanical Properties: Ambient Temperature

9.1 Introduction

9.2 Response of Quasi-Single Crystals to Compressive Loads

9.3 Response of Polycrystalline Samples to Compressive Stresses

9.4 Response of Polycrystalline Samples to Shear Stresses

9.5 Response of Polycrystalline Samples to Flexure Stresses

9.6 Response of Polycrystalline Samples to Tensile Stresses

9.7 Hardness

9.8 Fracture Toughness and R-Curve Behavior

9.9 Fatigue Resistance

9.10 Damage Tolerance

9.11 Micromechanisms Responsible for High K1c, R-Curve Behavior, and Fatigue Response

9.12 Thermal Sock Resistance

9.13 Strain Rate Effects

9.14 Solid Solution Hardening and Softening

9.15 Machinability

9.16 Summary and Conclusions


Chapter 10: Mechanical Properties: High Temperatures

10.1 Introduction

10.2 Plastic Anisotropy, Internal Stresses, and Deformation Mechanisms

10.3 Creep

10.4 Response to Other Stress States

10.5 Summary and Conclusions


Chapter 11: Epilogue

11.1 Outstanding Scientific Questions

11.2 MAX Phase Potential Applications

11.3 Forming Processes and Sintering

11.4 Outstanding Technological Issues

11.5 Some Final Comments



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Title Page

Dedicated to my wonderful wife, close confidant, and best friend, Patricia.


The MAX phases are a fascinating class of layered solids that are relatively young. Interest in these 50+ phases has increased recently because they combine an unusual and very often unique combination of properties. For example, some are stiff and light and yet are readily machinable. Some are oxidation and creep resistant while also being metallic conductors and exceptionally thermal shock resistant. At this time, there are a number of good review articles on the MAX phases. However, the articles either focus on a few MAX phases, most notably Ti3SiC2, Ti3AlC2, Ti2AlC, and Cr2AlC, or try to tackle the entire subject in which much per force has to be glossed over. Said otherwise, there is no comprehensive compact monograph that renders these phases justice.

In this book, I attempt to summarize and explain, from both an experimental and a theoretical viewpoint, all the features that are necessary to understand the properties of these new materials. The book covers elastic, electrical, thermal, chemical, and mechanical properties in different temperature regimes. As much as possible, I tried to emphasize the physics.

One of the joys of working with the MAX phases is the ease by which one can change chemistry, while keeping the structure the same. As I anticipated many years ago, this has proven to be a real boon; I have a hunch, with no data to back me up, that the progress the MAX phase community has made in understanding their properties, in the past decade or so, can be traced directly to this feature. The range of experimental and theoretical techniques currently available has also indubitably made a big difference. In today's world, like much else, we have Science on steroids. We are quickly reaching the point – if we have not it already – at which the rate of data generation far exceeds our capability to make sense of them. In this book, I tried to buck the tide and make sense of what we currently know. The reader of this book will quickly realize from the sheer volume of data tabulated and plotted that this was not a trivial task. I do believe, however, that to truly understand properties and what influences them, one needs, every now and then, to step backward and make out the forest from the trees.

As shown in this book, this systemic approach, while tedious, is quite gratifying and edifying. For example, one of the leitmotivs of this book is the idea that above a certain concentration of valence electrons per unit volume, nval, the MAX phases are somehow destabilized. While plotting one set of properties versus nval does not necessarily make a compelling case, but when this destabilization is repeated and recognized in several different properties, the idea becomes harder to dismiss. Another important idea of this book is that we can roughly subdivide the MAX phases into four categories: (i) those with exceptionally low c-parameters, such as Ti2SC; (ii) those with large atoms, such as Sn, Hf, Zr; (iii) those in between but with low nval values; and (iv) those in between, but with high nval values that are relatively unstable, such as some of the Cr-containing MAX phases. Hopefully, this idea comes across.

The other joy of working with the MAX phases is their two-dimensional nature, especially when it comes to mechanical properties. The fact that dislocations are, for the most part, confined to 2D and that the orientation of the basal planes on which these dislocations glide are in many cases readily determined from optical microscope micrographs has rendered understanding their mechanical response rather straightforward. In solid-state physics, the pedagogy is well established; first you solve the one-dimensional problem, move on to the 2D, and then, and only then, generalize to the most complicated 3D situation. In dealing with the deformation of solids, however, the hapless metallurgy or materials science undergraduate is immediately asked to deal with more than five independent slip systems, a daunting task that certainly biased me toward ceramics, where I thought I would be safe. That I can now talk somewhat intelligently about dislocations is, in my case, not a mark of any intellectual prowess, but rather a reflection of the simplicity of the problem at hand. Basically, dislocations in the MAX phases, and in the much larger class of solids that we identified as kinking nonlinear elastic (KNE), appear either in dislocation pileups (DPs) and/or dislocation walls normal to the pileups or arrays. Confining the dislocations to 2D also helped us identify a new micromechanism in solids, namely, incipient kink bands (IKBs). As discussed in Chapters 8 and 9, IKBs are the yin to the yang of DPs. IKBs absorb significant amounts of energy at low strains; DPs result in large strains, but little stored energy. It follows that Nature's first line of defense in the case of KNE solids is to nucleate IKBs.

By bringing together, in a unified, self-contained manner, all the information on MAX phases hitherto only found scattered in the journal literature, I hope to help move the field along to the next stage. I have also tried to critically assess the now voluminous literature. The number of papers in the field has increased recently and the task of anybody attempting to review this body of work is becoming daunting. In 2000, when I wrote an early review article on the subject, the situation was significantly easier.

In addition to outlining the contents of this book, it is important to stress what it is not about and what it does not cover. This book is geared to understand the physics of the MAX and hence the synthesis of these phases is not discussed. Thin films are for the most part not covered. A recent review has done this topic justice. When thin films are discussed, it is only to make an important point for which the information is lacking in bulk solids. Composites of MAX phases with other compounds and second phases are also mostly not discussed, except in instances where comparing the properties of the composites with the pure bulk materials sheds light on the properties of the latter, which is the main focus of this book.

A perusal of the figures in this book will quickly establish that most of the figures originate from papers we wrote. This does not imply that other work is less important. It simply reflects the fact that the information was more easily accessible. In many cases, results and data have been grouped/replotted and in that case having access to the raw data is invaluable and time saving. I have assiduously tried to assign credit where credit is due. It follows that to the best of my abilities, I carefully combed the literature to make sure that when new information on the behavior of the MAX phases was reported, the original paper was cited. The record is out there and I tried my best. If at any time, such attribution is incorrect or lacking, I sincerely apologize and please contact me and I will try to set the record straight in any future editions of this book or any papers I write.

This book is divided into 11 chapters. The first chapter is an introductory chapter where the history of the MAX phases is outlined. Chapter 2 reviews the atomic structures and bonding commonalties and trends in these phases. This chapter also summarizes ab initio or density functional theory (DFT) calculations that, for the most part, capture the essence of the bonding in these solids. Chapter 3 deals with their elastic properties, both experimental and those calculated from DFT. Chapter 4 summarizes the thermal properties, including thermal expansion, conductivity heat capacities, atomic displacement parameters, and stability. Chapter 5 deals with the electrical transport, including conductivity, and Hall and Seebeck coefficient measurements. Their optical and magnetic properties are also touched upon.

Chapter 6 deals with the reactivity of the MAX phases with oxygen and other gases. The reactivities of the MAX phases with solids and liquids, including molten metals and common acids and bases, are reviewed in Chapter 7.

Chapters 8–10 deal with the mechanical properties. Chapter 8 deals with kinking nonlinear elasticity and damping. How the MAX phases respond to stresses – compressive, shear, tensile, and so on – at ambient temperature are discussed in Chapter 9. Chapter 10 deals with their response to stresses at elevated temperatures, including creep. Chapter 11 summarizes some of the outstanding scientific issues and outlines some of the potential applications and what needs to be done, research-wise, for these solids to be more widely used.

The quality and quantity of the papers one publishes in academia depend critically on the quality, resourcefulness, imagination, and hardwork of one's students. I would thus like to sincerely thank all my students who have worked with me on the MAX phases over the past 15 or so years. In rough chronological order, they are: T. El-Raghy, D. Brodkin, M. Radovic, S. Chakraborty, A. Procopio, J. Travaglini, L. H. Ho-Duc, I. Salama, P. Finkel, A. Murugaiah, T. Zhen, A. Ganguly, E. Hoffman, S. Gupta, S. Basu, A. Zhou, S. Amini, T. Scabarosi, J. Lloyd, I. Albaryak, C. J. Spencer, M. Shamma, N. Lane, D. Tallman, B. Anasori, M. Naguib, G. Bentzel, and J. Halim. It was a distinct pleasure to work with each and every one of them. Their productivity and contributions to the field cannot be overemphasized.

The number of postdocs that worked with me over the years is not as numerous as my students, but their input and insights were as important and appreciated. In chronological order, I would like to thank L. Farber, N. Tzenov, D. Filimonov, J. Córdoba, and V. Presser. I also had the distinct pleasure of working with a few visiting scholars who spent some time with me at Drexel. I would thus like to thank Drs. Z.-M. Sun, O. Yeheskel, V. Jovic, T. Cabioch, and E. Caspi.

I like to collaborate and I have sought out collaborators in many countries and on many continents. In that vein, I would like to profusely thank the following colleagues and friends with whom I have worked with over the years on the MAX phases and from whom I learned quite a bit. I am greatly indebted to G. Hug, M. Jaouen, L. Thilly, S. Dubois, M. Le Flem, J.-L. Béchade, and J. Fontaine in France; J. Hettinger and S. Lofland at the Rowan University; L. Hultman, M. Magnuson, P. Eklund, J. Rosen, J. Lu, and R. Ahuja in Sweden; and J. Schneider in Germany.

Much of this work would not have been possible without funding. The ceramics program of the Division of Materials Research of the National Science Foundation funded much of the early MAX phase work. I would like to especially thank Drs. L. Madsen and L. Schioler for their support. The Army Research Office has also funded our MAX phase work over the years. Here I am indebted to Drs. D. Stepp and S. Mathaudhu who have supported, and are still supporting, the work we are doing.

I would also like to acknowledge the support of the Swedish Foundation for Strategic Research (SSF) and the Linkoping University for funding my numerous visits to Linkoping since 2008. Prof. Lars Hultman must get the lion's share of the credit for arranging this very fruitful collaboration that is still ongoing. I would also like to thank the University of Poitiers, Poitiers, France, for hosting me for a few extended visits over the years. I would especially like to thank Profs. M. Jaouen and T. Cabioch for arranging the visits and their wonderful hospitality.

I would also be remiss if I did not acknowledge the many very fruitful discussions I have had over the years with my colleagues in the Department of Materials Science and Engineering at the Drexel University. Special thanks are due to R. Doherty, Y. Gogotsi. S. Tyagi, A. Zavaliangos, J. Spanier, G. Friedman, A. Kontsos, A. Zavaliangos, and S. Kalidindi.

I have coauthored papers with a large number of colleagues in many corners of the world. This list (again somewhat chronologically) includes Drs. M. Amer, M. Gamarnik, E. H. Kisi, J. A. Crossley, S. Myhra, L. Ogbuji, S. Wiederhorn, R. O. Ritchie, H.-I. Yoo, H. Seifert, F. Aldinger, J. Th. M. De Hosson, H. Drulis, M. Drulis, B. Manoun, J. Fontaine, J. Schuster, S. K. Saxena, D. Jurgens, M. Uhrmacher, P. Schaaf, B. Yang, D. Brown, S. Vogel, B. Clausen, X. He, and Y. Bai. I am indebted to all of them for the excellent papers we published together.

Chapter 1


1.1 Introduction

The Mn+1AXn, or MAX, phases are layered, hexagonal, early transition-metal carbides and nitrides, where n = 1, 2, or 3 “M” is an early transition metal, “A” is an A-group (mostly groups 13 and 14) element, and “X” is C and/or N. In every case, near-close-packed M layers are interleaved with layers of pure group-A element with the X atoms filling the octahedral sites between the former (Figure 1.1a–c). The M6X octahedra are edge-sharing and are identical to those found in the rock salt structure. The A-group elements are located at the center of trigonal prisms that are larger than the octahedral sites and thus better able to accommodate the larger A atoms. The main difference between the structures with various n values (Figure 1.1a–c) is in the number of M layers separating the A layers: in the M2AX, or 211, phases, there are two; in the M3AX2, or 312, phases there are three; and in the M4AX3, or 413, phases, there are four. As discussed in more detail in later chapters, this layering is crucial and fundamental to understanding MAX-phase properties in general, and their mechanical properties in particular. Currently, the MAX phases number over 60 (Figure 1.2) with new ones, especially 413s and solid solutions, still being discovered.

Figure 1.1 Atomic structures of (a) 211, (b) 312, and (c) 413 phases, with emphasis on the edge-sharing nature of the MX6 octahedra.


Figure 1.2 List of known MAX phases and elements of the periodic table that react to form them.


Most of the MAX phases are 211 phases, some are 312s, and the rest are 413s. The M group elements include Ti, V, Cr, Zr, Nb, Mo, Hf, and Ta. The A elements include Al, Si, P, S, Ga, Ge, As, Cd, In, Sn, Tl, and Pb. The X elements are either C and/or N.

Thermally, elastically, and electrically, the MAX phases share many of the advantageous attributes of their respective binary metal carbides or nitrides: they are elastically stiff, and electrically and thermally conductive. Mechanically, however, they cannot be more different: they are readily machinable – remarkably a simple hack-saw will do (Figure 1.3) – relatively soft, resistant to thermal shock, and unusually damage-tolerant. They are the only polycrystalline solids that deform by a combination of kink and shear band formation, together with the delaminations of individual grains. Dislocations multiply and are mobile at room temperature, glide exclusively on the basal planes, and are overwhelmingly arranged either in arrays or kink boundaries. They combine ease of machinability with excellent mechanical properties, especially at temperatures >1000 °C. Some, such as Ti3SiC2 and Ti4AlN3, combine mechanical anisotropy with thermal properties that are surprisingly isotropic.

Figure 1.3 One of the hallmarks of the MAX phases is the ease with which they can be machined with (a) a manual hack-saw and (b) lathe.


As discussed in this book, this unusual combination of properties is traceable to their layered structure, the mostly metallic – with covalent and ionic contributions – nature of the MX bonds that are exceptionally strong, together with M–A bonds that are relatively weak, especially in shear. The best characterized ternaries to date are Ti3SiC2, Ti3AlC2, and Ti2AlC. We currently know their compressive and flexural strengths and their temperature dependencies, in addition to their hardness, oxidation resistance, fracture toughness and R-curve behavior, and tribological properties. Additionally, their electrical conductivities, Hall and Seebeck coefficients, heat capacities (both at low and high temperatures), elastic properties and their temperature dependencies, thermal expansions, and thermal conductivities have been quantified.

1.2 History of the MAX Phases

The MAX phases have two histories. The first spans the time they were discovered in the early and mid-1960s to roughly the mid-1990s, when, for the most part, they were ignored. The second is that of the last 15 years or so, when interest in these phases has exploded. Table 2.2 lists the first paper in which each of the MAX phases was first reported.

1.2.1 History Before 1995

Roughly 40 years ago, Nowotny published a review article (Nowotny, 1970) summarizing some of the work that he and his coworkers had carried out during the 1960s on the syntheses of a large number of carbides and nitrides. It was an impressive accomplishment; during that decade, his group discovered over 100 new carbides and nitrides. Amongst them were more than 30 Hägg phases which are of specific interest to this work. These phases, also called H-phases – but apparently not after Hägg (Eklund et al., 2010) – had the M2AX chemistry (Figures 1.1a and 1.2).

The history of the H-phases, henceforth referred to as 211s, before 1997 is short. Surprisingly, from the time of their discovery until our first report (Barsoum, Brodkin, and El-Raghy, 1997) – and apart from four Russian papers in the mid-1970s (Ivchenko and Kosolapova, (1975, 1976); Ivchenko et al., 1976a,b) in which it was claimed that 90–92% dense compacts of Ti2AlC and Ti2AlN were synthesized – they were totally ignored. The early Russian results have to be interpreted with caution as their reported microhardness values of ≈21–24 GPa are difficult to reconcile with the actual values, which range from 3 to 4 GPa. Some magnetic permeability measurements on Ti2AlC and Cr2AlC were also reported in 1966 (Reiffenstein, Nowotny, and Benesovsky, 1966).

In 1967, Nowotny's group discovered the first two 312 phases, Ti3SiC2 (Jeitschko and Nowotny, 1967) and Ti3GeC2 (Wolfsgruber, Nowotny, and Benesovsky, 1967), both of which are structurally related to the H-phases in that M3X2 layers now separate the A layers (Figure 1.1b). It was not until the early 1990s, however, that Pietzka and Schuster, the latter a student of Nowotny's, added Ti3AlC2 to the list (Pietzka and Schuster, (1994, 1996)).

The history of Ti3SiC2 is slightly more involved. The first hint that Ti3SiC2 was atypical came as early as 1972, when Nickl, Schweitzer, and Luxenberg (1972) working on single crystals grown by chemical vapor deposition (CVD) showed that Ti3SiC2 was anomalously soft for a transition-metal carbide. The hardness was also anisotropic, with the hardness normal to the basal planes being roughly three times that parallel to them. When the authors used a solid-state reaction route, the resulting material was no longer “soft.” In 1987, Goto and Hirai (1987) confirmed the results of Nickl et al. A number of other studies on CVD-grown films also exist (Fakih et al., 2006; Pickering, Lackey, and Crain, 2000; Racault, Langlais, and Naslain, 1994; Racault et al., 1994).

The fabrication of single-phase, bulk, dense samples of Ti3SiC2 proved to be more elusive, however. Attempts to synthesize them in bulk always resulted in samples containing, in most cases, TiC, and sometimes SiC, as ancillary, unwanted phases (Lis et al., 1993; Morgiel, Lis, and Pampuch, 1996; Pampuch and Lis, 1995; Pampuch et al., 1989). Consequently, before our breakthrough in synthesis (Barsoum and El-Raghy, 1996), little was known about Ti3SiC2, and much of what was known has since been shown to be incorrect. For example, despite a sentence buried in one of Nowotny's papers claiming Ti3SiC2 does not melt but dissociates at 1700 °C into TiC and a liquid (Nowotny and Windisch, 1973), the erroneous information that it has a melting point of over 3000 °C is still being disseminated by some.

Furthermore, and before our work, many of the Ti3SiC2 samples fabricated in bulk form were unstable above ≈1450 °C (Pampuch et al., 1989; Racault, Langlais, and Naslain, 1994). It is now established that Ti3SiC2, if pure, is thermally stable to at least 1700 °C in inert atmospheres (Chapter 4). Another important misconception that tempered the enthusiasm for Ti3SiC2 was, again, the erroneous belief that its oxidation resistance above 1200 °C was poor (Okano, Yano, and Iseki, 1993; Racault, Langlais, and Naslain, 1994; Tong et al., 1995).

Despite the aforementioned pitfalls, Pampuch, Lis, and coworkers (Lis et al., 1993; Morgiel, Lis, and Pampuch, 1996; Pampuch, 1999; Pampuch and Lis, 1995; Pampuch et al., 1989) came closest to fabricating pure bulk samples; their best samples were ≈80–90 vol% pure (balance TiC). Nevertheless, using these samples they were the first to show that Ti3SiC2 was elastically quite stiff, with Young's and shear moduli of 326 and 135 GPa, respectively, and yet machinable (Lis et al., 1993). They also confirmed its relative softness (Vickers hardness of 6 GPa) and noted that the high stiffness-to-hardness ratio was more in line with ductile metals than ceramics, and labeled it a “ductile” ceramic. Apart from these properties, and a report that the thermal expansion of Ti3SiC2 was 9.2 × 10−6 K−1 (Iseki, Yano, and Chung, 1990), no other properties were known.

For the sake of completeness, it should be noted that reference to Ti3SiC2 in the literature occurs in another context. This phase was sometimes found at Ti/SiC interfaces annealed at high temperatures (Iseki, Yano, and Chung, 1990; Morozumi et al., 1985; Wakelkamp, Loo, and Metselaar, 1991). Ti3SiC2 was also encountered when Ti was used as a braze material to bond SiC to itself, in SiC-Ti-reinforced metal matrix composites, or as potential electrodes in SiC-based semiconductor devices (Goesmann, Wenzel, and Schmid-Fetzer, 1998).

The history of the 413 compounds before 1999 is the shortest: they had not been discovered!

1.2.2 History Since 1995

In 1996, we made use of a reactive hot pressing (HPing), process termed transient plastic phase processing (Barsoum and Houng, 1993) to fabricate, in one step, starting with TiH2, SiC, and graphite, fully dense predominantly single-phase samples of Ti3SiC2. Significantly, the processing temperature (1600 °C) was, at that time, considered to be above the decomposition temperature of this phase. Armed with these samples, we started characterizing the phase and were truly surprised by the combination of properties observed, so much so, that our enthusiasm carried over into the title of our paper: “Synthesis and Characterization of a Remarkable Ceramic: Ti3SiC2.”

The compound we made was a better electrical and thermal conductor than either Ti or TiC. It was relatively soft and most readily machinable, despite having a Young's modulus of 320 GPa and a density comparable to that of Ti. It was oxidation resistant at least up to 1400 °C in air. It was so resistant to thermal shocks that quenching in water from 1400 °C actually slightly increased its flexural strength compared to unquenched samples. That, by itself, was remarkable enough. Lastly, scanning electron microscopy (SEM) and optical microscopy (OM) images left little doubt as to its layered nature. When in 1997 (El-Raghy et al., 1997) we further showed that its fracture toughness was >6 MPa m1/2 and that it was exceedingly damage tolerant, the unique combination of properties of this compound became apparent. As we have argued over the years, what renders the MAX phases remarkable is not any one property per se, but a combination of properties.

Once this unique combination of properties was recognized, and it was realized that Ti3SiC2 was first cousin to a large family of ternaries, viz. the 211 or H-phases, the next logical step was to fabricate and characterize some of the latter. In 1997 (Barsoum, Brodkin, and El-Raghy, 1997), we published a paper in which we showed that Ti2AlC and Ti2AlN, Ti2GeC and Ti3GeC2 – not surprisingly – had properties that were quite similar to those of Ti3SiC2. In that paper, we also reported the fabrication of V2AlC, Nb2AlC, and Ta2AlC and showed them to be machinable as well. In the same year (Barsoum, Yaroschuck, and Tyagi, 1997), we published a paper on the fabrication and characterization of Ti2SnC, Zr2SnC, Nb2SnC, and Hf2SnC and showed them to also possess property combinations that were similar to those of other MAX phases.

From this body of work, we established beyond any doubt that we were dealing with a large family of layered compounds that all had some features in common: machinability – the true hallmark of these compounds and what, to date, distinguishes them from all other structural ceramics and other ternary and quaternary ceramics – damage tolerance, relatively low thermal expansion coefficients, and good thermal and electrical conductivities. We also showed that these compounds did not melt congruently, but peritectically decomposed into an A-rich liquid and the transition-metal carbide or nitride (Barsoum, Yaroschuck, and Tyagi, 1997).

In 1997, we published the first detailed study of the oxidation of a MAX phase, namely, Ti3SiC2 and showed that the oxidation kinetics were parabolic at least up to 10 h and that the oxidation occurred by the inward diffusion of oxygen and the simultaneous outward diffusion of Ti.

In 1998 and 1999, we showed by transmission electron microscopy (TEM) that dislocations multiplied and were mobile at room temperature (Barsoum et al., 1999a; Farber et al., 1998; Farber, Levin, and Barsoum, 1999). In 1999, (Barsoum and El-Raghy, 1999) we showed that, when the grains were very large and oriented, Ti3SiC2 cubes were ductile when compressed at room temperature and that the deformation occurred by the formation of kink bands in individual grains as well as shear bands across entire samples.

In 1999, we became interested in the MAX phases in the Ti–Al–N system. During our literature search, we came across a paper that claimed the existence of Ti3AlN2. When we compared the c lattice parameters reported for that phase – 23 Å – to those of its ostensibly isostructural first cousin Ti3AlC2 – whose c lattice parameter is closer to 18 Å – we wrote a comment (Barsoum and Schuster, 1998) making the case that the reported structure could simply not be a 312 structure. A year later, we showed by high-resolution transmission electron microscopy (HRTEM) that the phase reported as Ti3AlN2 was in fact Ti4AlN3 (Barsoum et al., 1999b). In the latter phase, four layers of Ti are N are separated by layers of Al (Figure 1.3c).

This was an important discovery, not because it was necessarily a new phase but because it opened the door to a mini gold rush. In the past five years, the following 413 phases have been discovered: Ta4AlC3 (Manoun et al., 2006), V4AlC3 (Hu et al., 2008), and Ti4GaC3 (Etzkorn et al., 2009). At this time, there is no reason to believe that their number will not increase, especially in terms of solid solutions, an area that is quite ripe for new discoveries.

With the discovery of the 413 phases, it became apparent that we were dealing with a family of ternary layered compounds with the general formula Mn+1AXn. During the past 15 years, we and many others have shown that these phases represent a new class of solids that can be best described as thermodynamically stable nanolaminates. It has long been predicted, and our results fully confirm, that nanoscale solids, especially laminates, should exhibit unusual and exceptional mechanical properties. Full-scale exploitation of this idea, however, had been hindered by two fundamental problems. The first had to do with the cost of manufacturing bulk samples; making large parts by molecular beam epitaxy, for instance, is not commercially viable. The second problem is more fundamental; even if fabricated, such fine-scale assemblages would not be thermodynamically stable and as such would be of limited use at elevated temperatures. It follows that the exceptional thermal stability of the dissimilar atomic layers in the MAX phases is truly extraordinary. And it is thus only logical that many of the remarkable properties of the MAX phases, such as their mechanical properties at ambient and elevated temperatures and the ease with which they can be machined, can be directly traceable to their layered nature.

The second powerful idea to emerge in the last couple of decades in the materials science community is that of biomimetics, wherein Nature's splendid designs that had evolved over millions of years would be imitated. For example, abalone shell (Figure 1.4b), mainly comprising a brittle calcium carbonate, is quite tough. This toughness arises from a submicrometer polymer film that lies between the calcium carbonate layers. The microstructural similarities between the fractured surfaces of abalone shell, for example, and those of the Mn+1AXn phases are noteworthy (Figure 1.4). The layering in abalone, however, is on a much coarser scale. Another fundamental distinction is that Nature optimized the properties of abalone for room-temperature use. Heating an abalone shell to a couple of hundred degrees destroys the polymer and thereby its toughness. Wood is another example, where, again, there is a marked resemblance to the MAX phases (see e.g. Figure 9.24b).

Figure 1.4 Typical SEM images of tortuous paths a crack takes in (a) a Ti3SiC2 grain and (b) an abalone shell (Barsoum and El-Raghy, 2001). Note that the two images are of quite different magnifications.

(Source: Abalone micrograph courtesy of D. E. Morse, University of California, Santa Barbara.)


Since 1996, when our first paper on Ti3SiC2 was published, the MAX-phase community has embarked on an ambitious program of synthesizing and characterizing as many of the MAX phases as possible. To date, most of the MAX phases have been fabricated, and at least preliminarily characterized. There are numerous research groups exploring various facets and applications of the MAX phases in Europe, Japan, China, India, South Korea, other South Asian countries, Australia, and South America. This book attempts to summarize this global effort.

Probably, the best indicator as to how dynamic and fecund MAX phase research is globally, is to refer to Figure 1.5a,b, in which the number of papers published and the number of citations garnered when Ti3SiC2 is entered as the keyword in Thomas Reuters (formerly ISI) Web of Knowledge data base is plotted as a function of time, starting from 1993. Similar trends are found when the keywords chosen are Ti3AlC2 or Ti2AlC. As noted above, today the research and interest in the MAX phases have exploded.

Figure 1.5 (a) Number of papers published and (b) number of citations each year as a function of time starting in 1992, when Ti3SiC2 is entered as the keyword, according to the Web of Science.

(Source: Thomson Reuters.)


In brief, and despite the relatively short time since these compounds have been identified as having unusual and sometime unique properties, we have come a long way in understanding their physical, mechanical, and chemical properties. In this book, I try to summarize this understanding. This book is divided into 11 chapters. Chapter 2 reviews the atomic structures and bonding commonalties and trends in these phases. This chapter also summarizes ab initio calculations that, for the most part, capture the essence of the bonding in these solids. Chapter 3 deals with their elastic properties, both experimental and those calculated from density functional theory (DFT). Chapter 4 summarizes the thermal properties, including thermal expansion, conductivity, heat capacity and stability. Chapter 5 deals with the electrical transport, including conductivity, as well as Hall and Seebeck coefficient measurements. Their optical and magnetic properties are also touched upon. Chapter 6 deals with the reactivity of the MAX phases with oxygen and other gases. The reactivities of the MAX phases with solids and liquids, including molten metals and common acids and bases, are reviewed in Chapter 7.

Chapters 8–10 deal with the mechanical properties. Chapter 8 deals with kinking nonlinear elasticity and damping. How the MAX phases respond to stresses – compressive, shear, tensile, and so on – at ambient temperature is discussed in Chapter 9. Chapter 10 deals with their response to stresses at elevated temperatures, including creep. The final chapter outlines some of the outstanding scientific issues and potential applications, in addition to what needs to be done researchwise for these solids to be more widely used.

A number of review articles have been published on various aspects of the MAX phases over the years. In 2000, I published the first review on the MAX phases (Barsoum, 2000). In 2004, the first entry on the MAX phases in the Encyclopedia of Materials Science and Technology appeared (Barsoum and Radovic, 2004), followed 2 years later by a review, in the same publication, of their physical properties (Barsoum, 2006). A review on Cr2AlC appeared in 2007 (Lin, Zhou, and Li, 2007). In 2009, Zhang et al. reviewed Ti3SiC2 (Zhang, Bao, and Zhou, 2009); in 2010, Eklund et al. published a review on the processing and properties of MAX-phase thin films (Eklund et al., 2010). In the same year, Wang and Zhou reviewed Ti2AlC and Ti3AlC2 (Wang and Zhou, 2010). In 2010, I published a general review (Barsoum, 2010). A third entry in the Encyclopedia of Materials Science and Engineering on kinking nonlinear elasticity – first discovered in the MAX phases (Chapter 8) – was published (Barsoum and Basu, 2010). More recently, Barsoum and Radovic reviewed their mechanical and elastic properties (Barsoum and Radovic, 2011). Sun published a general review in the same year (Sun, 2011).

1.2.3 Discovery of the MAX Phases

Lastly, a book on the MAX phases would surely be incomplete without the story of how they were discovered, and how they acquired their name. The details of how we stumbled on the MAX phases can be found elsewhere (Barsoum and El-Raghy, 2001). In short, like many such discoveries, it was by pure luck. However, as they say, providence every now and then rewards the well prepared. In retrospect, it was our processing breakthrough (Barsoum and Houng, 1993) – a few years before our 1996 paper – that ultimately paved the way to the discovery.

As for how they got their name – that was also due to the twists and turns of fate. Nowotny and coworkers discovered these phases and referred to them as either the H-phases or the M2BX phases (Nowotny, 1970). Being new to the field, we followed the pioneer's lead and also referred to these phases as M2BX. The title of our first progress report on these phases was “A Progress Report on Ti3SiC2, Ti3GeC2, and the H-Phases, M2BX” (Barsoum and El-Raghy, 1997). This paper was written before the 413 phases were discovered so the full richness of the family was still not apparent.

A few years later, however, we realized that in the 1980s the International Union of Pure and Applied Chemistry had scrambled the periodic table. In the new periodic table, the A elements became B, and the B elements became A. And that is how MAX was born. Since then, the periodic table has been modified yet again. In the latest version, chemists eschew letters altogether and simply number the periodic table columns from 1 to 18. In this latest, and probably final, tinkering with this foundation of chemistry and materials science, the A-group elements of the MAX phases now belong to groups 13–16.

Once the change was made from M2BX to M2AX, I knew immediately that the latter would, most likely, be perceived as a “Madison Avenue” type branding effort that in turn would cast disparaging shadows on the discovery. In my first major review article, I tried to buck the tide and made sure that the title referred to the Mn+1AXn phases and not MAX (Barsoum, 2000). But when, a year later, American Scientist, a mass circulation magazine for people interested in science, came calling (Barsoum and El-Raghy, 2001) – and despite my objections – there was no talking the editor into using the clumsy Mn+1AXn phases instead of MAX. That was the point of no return. Over the years, some have tried to change the name; one proposal was to change the “M” to a “T”. Needless to add, that proposal did not catch on especially in America.

In retrospect, I believe this happy accident is most appropriate for a discovery that was made by chance, and that, in some respects, the MAX phases do indeed live up to their name.

The MAX phases are truly a fascinating family of compounds. The fact that one can readily change chemistry while keeping the structure fixed has allowed us to quickly understand what affects many of the more important properties. From a scientific point of view, the fact that dislocations are confined to two dimensions has also shed important light on the motion of dislocations and their interactions with dislocation arrays.

It is my sincere hope that this book will inspire the next generation of MAX-phase researchers to take these phases to the next level and to develop as many applications as possible. The future looks bright indeed.


Barsoum, M.W. (2000) The Mn+1AXn phases: a new class of solids; thermodynamically stable nanolaminates. Prog. Solid State Chem., 28, 201–281.

Barsoum, M.W. (2006) Physical properties of the MAX phases, in Encyclopedia of Materials Science and Technology (eds K.H.J. Buschow, R.W. Cahn, M.C. Flemings, E.J. Kramer, S. Mahajan, and P. Veyssiere), Elsevier, Amsterdam.

Barsoum, M.W. (2010) The MAX phases and their properties, in Ceramics Science and Technology, Properties, Vol. 2 (eds R.R. Riedel and I.-W. Chen), Wiley-VCH Verlag GmbH.

Barsoum, M.W. and Basu, S. (2010) in Encyclopedia of Materials Science and Technology (eds K.H.J. Buschow, R.W. Cahn, M.C. Flemings, B. Ilschner, E.J. Kramer, S. Mahajan, and P. Veyssiere), Elsevier, Amsterdam.

Barsoum, M.W., Brodkin, D., and El-Raghy, T. (1997) Layered machinable ceramics for high temperature applications. Scr. Met. Mater., 36, 535–541.

Barsoum, M.W., Yaroschuck, B.G., and Tyagi, S. (1997) Fabrication and characterization of M2SnC (M = Ti, Zr, Hf and Nb). Scr. Mater., 37, 1583–1591.

Barsoum, M.W. and El-Raghy, T. (1996) Synthesis and characterization of a remarkable ceramic: Ti3SiC2. J. Am. Ceram. Soc., 79, 1953–1956.

Barsoum, M.W. and El-Raghy, T. (1997) A progress report on Ti3SiC2, Ti3GeC2 and the H-phases, M2BX. J. Mater. Synth. Process., 5, 197–216.

Barsoum, M.W. and El-Raghy, T. (1999) Room temperature ductile carbides. Metall. Mater. Trans., 30A, 363–369.

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Barsoum, M.W., Farber, L., Levin, I., Procopio, A., El-Raghy, T., and Berner, A. (1999b) High-resolution transmission electron microscopy of Ti4AlN3, or Ti3Al2N2 revisited. J. Am. Ceram. Soc., 82, 2545–2547.

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Barsoum, M.W. and Radovic, M. (2004) Mechanical properties of the MAX phases, in Encyclopedia of Materials Science and Technology (eds K.H.J. Buschow, R.W. Cahn, M.C. Flemings, E.J. Kramer, S. Mahajan, and P. Veyssiere), Elsevier, Amsterdam.

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