American Journal of Modern Physics
Volume 4, Issue 2, March 2015, Pages: 75-91

Study on Structural, Electronic, Optical and Mechanical Properties of MAX Phase Compounds and Applications Review Article

Md. Atikur Rahman*, Md. Zahidur Rahaman

Department of Physics, Pabna University of Science and Technology, Pabna-6600, Bangladesh

Email address:

(Md. Atikur Rahman)

To cite this article:

Md. Atikur Rahman, Md. Zahidur Rahaman. Study on Structural, Electronic, Optical and Mechanical Properties of MAX Phase Compounds and Applications Review Article. American Journal of Modern Physics. Vol. 4, No. 2, 2015, pp. 75-91. doi: 10.11648/j.ajmp.20150402.15

Abstract: The term "MAX phase" refers to a very interesting and important class of layered ternary transition-metal carbides and nitrides with a novel combination of both metal and ceramic-like properties that have made these materials highly regarded candidates for numerous technological and engineering applications. A relatively new class of transition metal layered compounds Mn+1AXn, (MAX phases) where M is an early transition metal, A is a group A element most likely Al, and X is C or N with n = 1, 2, 3………..Due to their unique structural arrangements and directional bonding, these ternary compounds possess some very outstanding mechanical and chemical properties such as damage-resistance, oxidation resistance, excellent thermal and electric conductivity, machinability, and fully reversible dislocation-based deformation. These properties can be explored in the search for new phases and their composites to meet the performance goals of advanced materials with applications in fossil energy conversion technology. Systematic and detailed computational studies on MAX phase compounds can provide fundamental understanding of the key characteristics that lead to these desirable properties and to the discovery of other new and better alloys.In this paper, we review on structural, electronic, optical and mechanical properties of around 50 MAX phase compounds and their applications. From the comparative study on the result of these compounds we think that this paper will enable to researcher to explore and predict new MAX phases and new composite alloys with better physical properties as advanced materials for various applications at extreme conditions.

Keywords: MAX Phase Compounds, Electronic, Optical and Mechanical Properties, Applications

1. Introduction

Metallic materials are typically characterized by being thermally and electrically conductive, plastically deformable at room temperature, readily machinable, thermal shock resistant, damage tolerant, relatively soft, etc. On the other hand, ceramics are generally characterized by high elastic moduli, good high temperature mechanical properties, good oxidation and corrosion resistance, etc. The relatively recent discovery of a family of new materials, namely the MAX phases [1] (also termed in some publications ‘metallic ceramics’ [2]) has provided materials that possess a useful combination of both metallic and ceramic characteristics. Recently, the interest in nanolaminated ternary Mn+1AXn (denoted 211, 312 and 413, where n=1, 2 and 3, respectively) carbides and nitrides, so-called MAX-phases, has grown significantly. МАХ phases are a family of ternary layered compounds with the formal stoichiometry Mn+1AXn (n = 1, 2, 3. …), where М is the transition d metal; А is the p element (e.g., Si, Ge, Al, S, Sn, etc.); X is carbon or nitrogen. 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. First reports on the synthesis of МАХ phases were presented in the works by Novotnoi et al. [3-7] performed in the 60’s of the last century. Intensive studies of the physicochemical properties of МАХ phases, started in the middle of the 1990’s, led to the conclusion that they were a unique class of layered materials combining chemical, physical, electrical, and mechanical properties inherent to both metals and ceramics [8]. Thus, similarly to metals, МАХ phases have good heat and electric conductivity and at the same time, like ceramics, they are refractory, oxidation and corrosion resistant and have low density. These properties can be explored in the search for new phases and their composites that have potential to meet the performance goals for materials to be used in the next generation of fossil energy power systems at a significantly reduced cost. МАХ phases are at present of increased interest as promising materials for polyfunctional high-temperature ceramics, protective coatings, sensors, and electrical contacts for catalysis. The current stage of the experimental studies of МАХ phases is marked by the development of synthesis methods for these compounds, including in film and nanocrystalline states, and also by the discovery of new phases [9-11]. For example, by the magnetron deposition method new phases of Ti4SiC3 and Ti4GeC3 (in the film state) along with a few others [11] have fairly recently been synthesized [12, 13]. Note that at present the family consists of 60 compounds [11] involving many d and p elements as components (Fig. 1). Moreover, detailed investigations of the functional properties of МАХ phases (in particular, doping and non-stoichiometry effects, polymorphism, tribological, mechanical, and newly found [14, 15] superconducting properties, etc.) as well as further searches for the promising technological use of these materials are being conducted [11].

Fig. 1. Periodic table of elements forming nanolaminates of the general composition Mn+1AXn (n= 1, 2, 3 ….), where M is a transition d metal, A is a pelement (Si, Al, S, Sn, etc), and X is carbon or nitrogen.

There are more than 70 known phases of MAX compounds and this number is rapidly growing. A list of MAX phase compounds are shown in Table 1.

Table 1. A list of the MAX phases known to date, in both bulk and thin film form.

211 Phases 312 Phases 413 Phases
Ti2CdC, Sc2InC, Ti2AlC, Ti2GaC, Ti2InC, Ti2TlC, V2AlC, Ti3AlC2, Ti4AlN3,
Cr2GaC, Ti2AlN, Ti2GaN, Ti2InN, V2GaC, V2GaN, Cr2GaN, V3AlC2, V4AlC3,
Ti2PbC, V2GeC, Cr2AlC, Cr2GeC, Ti2GeC, Ti2SnC, V2PC, Ti3SiC2, Ti4GaC3,
Zr2TlC, Nb2AlC, Nb2GaC, Nb2InC, V2AsC, Ti2SC, Zr2InC, Ti3GeC2, Ti4SiC3,
Zr2PbC, Nb2SnC, Nb2PC,Mo2GaC, Zr2InN, Zr2TlN, Zr2SnC, Ti3SnC2, Ti4GeC3,
Nb2AsC, Zr2SC, Nb2SC, Hf2InC, Hf2TlC, Ta2AlC, Ta2GaC, Ta3AlC2 Nb4AlC3,
Hf2SnC, Hf2PbC, Hf2SnN, Hf2SC   Ta4AlC3

Fig. 2. Crystal structure of 211, 312, 413, 514 phases of M=Ta, A=Al and X=C.

In this article, we review the electronic structure and mechanical properties of MAX phase compounds which have been done using first-principles methods. Some of them are: Ti3AC2 (A = Al, Si, Ge), Ti2AC (A = Al, Ga, In, Si, Ge, Sn, P, As, S), Ti2AlN, M2AlC (M = V, Nb, Cr), Tan+1AlCn (n = 1 to 4), Hf2TlC, Hf2SnC, Hf2PbC, Hf2SnN and Hf2SC (see Table 1).Most of them are Ti-containing phases, since they are the most common in MAX phases. They are chosen for a wide representation and for studying specific trends. The first 12 vary only by the A element and involve three (3 1 2) phases and the nine (2 1 1) phases. In addition to carbides, one example of nitride, Ti2AlN is also included. This is followed by three other (2 1 1) phases, (V, Nb, Cr)2AlC where the transition metal M have different d-electron configurations. The Ta-Al-C group is chosen to study the effect of the number of MX layers (see Fig.2). The calculated results include: band structures, total and partial density of states, effective atomic charges, quantitative bond order values, interband optical conductivities, elastic coefficients, bulk modulus, shear modulus, Young’s modulus, and Poisson’s ratio. By systematically analyzing these results and in comparison with available experimental data, several important features on structural stability, interatomic bonding and optical conductivities are identified. These results enable us to build a data base to facilitate the search for new MAX phases and new composite alloys with the potential of having better physical properties as advanced materials.

The publication of papers on the MAX phases has shown an almost exponential increase in the past decade. The existence of further MAX phases has been reported or proposed. In addition to surveying this activity, the synthesis of MAX phases in the forms of bulk, films and powders is reviewed, together with their physical, mechanical and corrosion/oxidation properties. Recent research and development has revealed potential for the practical application of the MAX phases (particularly using the pressureless sintering and physical vapour deposition coating routes) as well as of MAX based composites. The challenges for the immediate future are to explore further and characterize the MAX phases reported to date and to make further progress in facilitating their industrial application.

2. Early History of MAX Phase Compounds

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. The ternary compound, Ti3SiC2, was first synthesized and fully characterized by Dr. Michel Barsoum's research group at Drexel University in the 1990s. A year later they showed that this compound was but one of over sixty phases,[16] most discovered and produced in powder form in the 1960s by H. Nowotny and coworkers [17]. In 1999 they discovered Ti4AlN3 and realized that they were dealing with a much larger family of solids that all behaved similarly. Since 1996, when the first paper was published on the subject, tremendous progress has been made in understanding the properties of these phases and the 1996 article [18] has been cited over 650 times [19].

3. Crystal Structures of MAX Phase Compounds

Fig. 2.1. Unit cells of (a) 211, (b) 312 and (c) 413 phases. The c parameters are depicted by vertical dashed lines. dx denotes the thickness- from atom center to center of the Mn+1Xn layers; dα that of A layers. It follows that that for the 211 phases c= 2 dα + 2 dx. Also shown are the various z values (see Table 2).

Fig. 3. Schematics of (1120) planes in (a) M2AX, (b) α-M3AX2, (c) β-M3AX2, (d) α-M4AX3, (e) β-M4AX3 and (f) γ- M4AX3. Note that it is only in the α-M3AX2 structure that the A atoms lie on top of each other.

MAX-phase crystals have a hexagonal symmetry in space group P63/mmc. For the 211 structure, there are three inequivalent atoms; in the 312, there are four, and in the 413, there are five. The coordinates and internal parameters ZM of all the atoms are listed in Table 2 for the various polymorphs. For the 211 phases, there is only one polymorph (Figure 3a). In the 312 case there are two, α and β, shown in Figures 3b and c, respectively. For the 413 phases, there are three polymorphs, viz. α, β, and γ, shown in Figures 3d, e and f, respectively. The density (D) and lattice parameters (a, c) of MAX phase compounds are listed in Table 3 [22-35].

Table 2. Sites and idealized coordinates of the Mn+1AXn phases for n = 1-3. Also listed are the currently known polymorphs. The fifth column lists the canonical positions.

Atoms Chemistry/archetypical phase ZM Range Notes and reference
  M2AX / Ti2SC - Kudielka and Rohde (1960)
  Wyckoff x y Zi (canonical) - -
A 2d 1/3 2/3 ¾ -  
M 4f 2/3 1/3 1/12 (0.083) 0.07-0.1 ZM in Figure 2.1a
X 2a 0 0 0 -  
α-M3AX2/Ti3SiC2 Jeitschko and Nowotny (1967)
A 2b 0 0 4/16 - -
Ml 4f 1/3 2/3 2/16 (0.125) 0.131- 0.138 ZM1 in Figure 2.1b
MII 2a 0 0 0 - -
X l 4f 2/3 1/3 1/16 (0.0625) 0.0722 ZC in Figure 2.1b
β-M3AX2/Ti3SiC2 Farber et al. (1999)
A 2d 1/3 2/3 4/16 - Should be quite similar in
Ml 4f 1/3 2.3 2/16 (0.125) 0.1355 Properties to α-M3AX2
MII 2a 0 0 0 -  
X l 4f 2/3 1/3 1/16 (0.0625) 0.072  
α-M4AX3/Ti4AlN3 Barsoum et al. (1999c) and Rawn et al. (2000)
A 2c 1/3 2/3 5/20 - -
Ml 4e 0 0 3/20 (0.15) 0.155-0.158 ZM1 in Figure 2.1c
MII 4f 1/3 2/3 1/20 (0.05) 0.052-0.055 ZM2 in Figure 2.1c
X l 2a 0 0 0 - -
XII 4f 2/3 1/3 2/20 0.103-0.109 ZC in Figure 2.1c
β-M4AX3/Ta4AlC3 Eklund et al. (2007)
A 2c 1/3 2/3 5/20 - -
Ml 4e 1/3 2/3 12/20 (0.6) 0.658 -
MII 4f 1/3 2/3 1/20 0.055 Eklund et al. (2007)
X l 2a 0 0 0 - -
XII 4e 2/3 1/3 2/20 0.103 -
γ-M4AX3/Ta4GaC3 Etzkorn et al. (2009)
A 2c 1/3 2/3 5/20 - -
Ml 4e 0 0 3/20 (0.15) 0.156 -
MII 4f 1/3 2/3 1/20 0.056 Etzkorn et al. (2009) and He et al. (2011)
X l 2a 0 0 0 - -
XII 4f 2/3 1/3 2/20 0.1065 -

Table 3. Density and lattice parameters of 77 Max phase compounds.

No. Compounds Density D, ( Mgm-3) Lattice parameters a, c(Å)
211 Phases
1 Sc2AlC 2.99 3.280, 15.373
2 Sc2GaC 3.93 3.253, 15.813
3 Sc2InC 4.72 3.272, 16.452
4 Sc2TlC 6.60 3.281, 16.530
5 Ti2AlC 4.11 3.051, 13.637
6 Ti2AlN 4.31 2.989, 13.614
7 Ti2SiC 4.35 3.052, 12.873
8 Ti2PC 4.56 3.191, 11.457
9 Ti2SC 4.62 3.216, 11.22
10 Ti2GaC 5.53 3.07, 13.52
11 Ti2GaN 5.75 3.00, 13.3
12 Ti2GeC 5.30 3.07, 12.93
13 Ti2AsC 5.71 3.209, 11.925
14 Ti2CdC 9.71 3.1, 14.41
15 Ti2InC 6.30 3.134, 14.077
16 Ti2InN 6.54 3.07, 13.97
17 Ti2SnC 6.10 3.163, 13.679
18 Ti2TlC 8.63 3.15, 13.98
19 Ti2PbC 8.55 3.20, 13.81
20 V2AlC 4.07 3.1, 13.83
21 V2SiC 5.20 2.955, 11.983
22 V2PC 5.38 3.077, 10.91
23 V2GaC 6.39 2.93, 12.84
24 V2GaN 5.94 3.00, 13.3
25 V2GeC 6.49 3.00, 12.25
26 V2AsC 6.63 3.11, 11.3
27 Cr2AlC 5.21 2.863, 12.814
28 Cr2GaC 6.81 2.88, 12.61
29 Cr2GaN 6.82 2.875, 12.77
30 Cr2GeC 6.88 2.95, 12.08
31 Zr2AlC 5.78 3.2104, 14.2460
32 Zr2AlN 5.83 3.2155, 14.2134
33 Zr2SC 6.20 3.40, 12.13
34 Zr2InC 7.1 3.34, 14.91
35 Zr2InN 7.53 3.27, 14.83
36 Zr2SnC 6.9 3.3576, 14.57
37 Zr2TlC 9.17 3.36, 14.78
38 Zr2TlN 9.60 3.3, 14.71
39 Zr2PbC 8.2 3.38, 14.66
40 Nb2AlC 6.50 3.10, 13.8
41 Nb2PC 7.09 3.28, 11.5
42 Nb2SC0.4 7.01 3.27, 11.4
43 Nb2SCx - -
44 Nb2GaC 7.73 3.13, 13.56
45 Nb2InC 8.3 3.17, 14.37
46 Nb2SnC 8.3 3.214, 13.802
47 Nb2AsC 8.025 3.31, 11.9
48 Mo2GaC 8.79 3.01, 13.18
49 Hf2AlC 10.23 3.2121, 14.3830
50 Hf2AlN 10.92 3.1380, 14.1872
51 Hf2SC 11.36 3.36, 11.99
52 Hf2InC 11.24 3.309, 14.723
53 Hf2SnC 11.2 3.320, 14.388
54 Hf2SnN 7.72 3.31, 14.3
55 Hf2TlC 13.65 3.32, 14.62
56 Hf2PbC 11.5 3.55, 14.46
57 Ta2AlC 11.46 3.079, 13.860
58 Ta2GaC 13.05 3.10, 13.57
312 Phases
1 Ti3SiC2 4.52 3.0665, 17.671
2 Ti3AlC2 4.2 3.065, 18.487
3 Ti3GeC2 5.22 3.07, 17.76
4 Ti3SnC2 5.99 3.1366, 18.650
5 V3SiC2 5.27 2.915, 17.535
6 (V0.5Cr0.05)3AlC2 5.31 2.892, 17.73
7 Nb3SiC2 7.22 3.13, 17.94
8 Ta3AlC2 12.43 3.0930, 19.159
413 Phases
1 Ti4AlN3 4.58 2.988, 23.372
2 Ti4SiC3 4.65 3.05, 22.67
3 Ti4GeC3 - -, 22.7
4 V4AlC3 5.24 2.931, 22.719
5 Nb4AlC3 6.97 3.123, 24.109
6 α-Nb4SiC3 - 3.1819, 22.9877
7 Ta4AlC3 13.18 3.092, 23.708
8 Ti4GaC3 5.17 3.0690, 23.440
514 Phase
1 Ti5SiC4 4.81 3.04, 27.24
615 Phase
1 Ta6AlC5 13.69 3.078, 34.681
716 Phase
1 Ti7SnC6 4.80 3.2, 4.1

Fig. 4. Calculated DOS and atom-resolved PDOS of 20 MAX phase compounds.

Fig. 5. Optical conductivities of 20 MAX phase compounds. Blue (red) curve show the planer (axial direction).

4. Comparative Study on Electronic, Optical and Mechanical Properties of MAX Phase Compounds

4.1. Electronic and Optical Properties

The electronic structure and optical conductivities of the MAX phases were calculated using the first-principles orthogonalized linear combination of atomic orbitals (OLCAO) method which is based on the local density approximation (LDA) of density functional theory [58-59]. This method has been demonstrated to be highly accurate and efficient when dealing with materials with complex structures for both crystalline [60-66] and non-crystalline systems [67-71]. Details of the electronic structure and optical conductivity of 20 MAX phase compounds were reported using OLCAO in reference [20].In this review article we studied only some selected results. Fig. 4 shows the total density of states (TDOS) and atom-resolved partial density of states (PDOS) of the 20 MAX phases compounds. The local feature of the total density of states (TDOS) curve around the Fermi-level (Ef) is a reasonable indicator of the intrinsic stability of a crystal. A local minimum at Ef implies higher structural stability because it signifies a barrier for electrons below the Ef(E< 0 eV) to move into unoccupied empty states (E> 0 eV); whereas a local maximum at Ef is usually a sign of structural instability. This semi-quantitative criterion works reasonably well for the results of Fig.1. Ti2InC, Ti2SC, and Cr2AlC have a local minimum at Ef, suggesting a higher level of stability. Ti2PC, Ti2AsC, and Ta5AlC4 show a peak in the TDOS at Ef. These facts correlate quite well with the observation that the first group of MAX phases are easier to synthesize whereas those in the second group are not [20]. The calculated optical conductivities in the 20 MAX phase compounds for frequency range between 0 and 10 eV are shown in Fig. 5. The spectra are resolved into two components, one is the planar (a-b plane) component and the other is the axial (c-direction) component, or σ1, planar and σ1, axial for short. The number indicated in each plot is the anisotropy ratio, or the averaged (σ1, planar/σ1,axial) ratio over all the data points. From these plots, several interesting observations can be made [20]. Most of the MAX phases have the maximum optical conductivities around 5 eV and several phases show sharp peak structures with considerable anisotropy especially in the Ta series. The optical conductivity may be related to the electric conductivity in MAX phases if intra-band contribution at the frequency near 0.0 eV can be accounted for. It is conceivable that the anisotropy in optical conductivity in the low energy range could also imply that there may be similar trends in the electrical conductivity. The optical anisotropy in the low energy range of the calculation is quite low for the majority of the 20 phases which correlates well with the low anisotropy in the measured electrical conductivities. A notable exception is Nb2AlC. Indeed, experiments by T. H. Scabarozi et al. [21] showed that Nb2AlC has a significantly larger anisotropy in its electrical conductivity than other MAX-phase compounds.

4.2. Mechanical and Elastic Properties

Elastic constants are very important material parameters. Evident and direct application of elastic constants is in the evaluation of elastic strains or energies in materials under stresses of various origins: external, internal and thermal [75]. The elastic constants can also provide information on the stability, stiffness, brittleness, ductility, and anisotropy of a material and propagation of elastic waves and normal mode oscillations. Moreover, knowledge of the values of elastic constants is crucial for a sound understanding of the mechanical properties of the relevant material. The most important parameters for estimating mechanical properties of materials are bulk modulus (B), shear modulus (G), Young’s modulus (E) and Poisson’s ratio (ν). In this section we have studied about these properties. Elastic deformation in crystalline solids is a fully reversible and nondissipative process. For hexagonal symmetry, there are five independent elastic constants; they are C11, C12, C13, C33, and C44. To date, the nonavailability of large MAX single crystals has made it difficult to experimentally determine their elastic constants. What can be used until such measurements are available, however, are the results of ab initio calculations. In this article all the mechanical properties and elastic constant of MAX phases compounds are summarized and reviewed. All the properties are calculated by using density functional theory (DFT). The bulk moduli Bv and Young’s moduli Ev are calculated by using equations 1 and 2. Also the shear moduli Gv and Poisson’s ratio ν are calculated by using equations 3 & 4.The calculated results for these moduli are listed in table 4.





The Poisson’s ratio (S) defined as the ratio of transverse strain to the longitudinal strain is used to reflect the stability of the material against shear and provides information about the nature of the bonding forces. It takes value: -1 <ν <1/2. No real material is known to have a negative value of ν. So this inequality can be replaced with 0 < ν < 1/2. Bigger the Poisson’s ratio betters the plasticity. The calculated result of the Poisson’s ratio shown in table 4 indicates that the max phase compound is of good plasticity. The ν = 0.25 and ν = 0.5 are the lower limit and upper limit for central forces in solids, respectively. The obtained value of Poisson’s ratio of Ta2GaN, Cr2GeC and α-Ta4AlC3 are larger than the lower limit value, which indicates that the interatomic forces of those compounds are central forces. The bulk modulus is usually assumed to be a measure of resist deformation capacity upon applied pressure [76]. The larger the value of bulk modulus is, the stronger capacity of the resist deformation is. From figure 6 we can make a clear idea about the ability to resist deformation of Max phases. Similarly, the shear moduli are a measure of resist reversible deformation by shear stress [76]. The larger the value is, the stronger capacity of the resist shear deformation is. From Figure 6 we can make a clear idea about this. Furthermore, Young’s modulus is defined as the ratio between stress and strain, and it also provided a measure of stiffness of the solid materials. The larger the value is, the stiffer the material is. The calculated result shows that the stiffness of β -Ta4AlC3 is the largest among all Max phases which we studied.

The elastic parameters as presented in Tables 4 allow us to make the following conclusions.

(i) The Cij constants for all MAX phases are positive and satisfy the generalized criteria in Ref. [72] for mechanically stable crystals: C44>0, C11>|C12|, and (C11+C12) C33>2C213.

(ii) Among the MAX phases, α-Ta4AlC3 is the phase with the largest bulk modulus (~266 GPa), while Ti2CdC has the smallest Bv ~115.66 GPa. We have also seen that β -Ta4AlC3 has maximum Young’s modulus (~404) GPa whereTi2CdC and Zr2PbC have the smallest Ev ~174 GPa.

(iii) The Young’s modulus is defined as the ratio between stress and strain and is used to provide a measure of stiffness, i.e., the larger the value of Ev, the stiffer the material. In our case β -Ta4AlC3> α-V4AlC3> V2PC > α-Ta4AlC3> Ti4AlN3> α-Nb4AlC3> Cr2AlC > Ti3GeC2> Ti4GeC3> Hf2SC > Nb2PC > Ta4GaC3> V2GaC > V2AlC …………….. Hf2PbC > Ti2PbC > Zr2PbC (see details in Table 5).The maximum and minimum shear moduli are obtained in Ti4AlN3 and Zr2PbC. The ascending to descending values of bulk modulus (Bv), Young’s modulus (Ev), shear modulus (Gv) and Possion’s ratio of all the MAX phases compounds are shown in details in Table 5.

(iv) Poisson’s ratios for most of the MAX phases are around 0.2 (Table 4), which is lower than the 0.3 of Ti and most metals, and closer to the 0.19 of near-stoichiometric TiC. According to Pugh’s criteria [73], a material should behave in a ductile manner if G/B<0.5, otherwise it should be brittle. In our case, all the compounds have G/B< 0.5, (Table 5) therefore all the MAX phases compounds show ductile behavior.


Table 4. Summary of 50 MAX phase compounds, elastic constants Cij determined from ab-initio calculations. Also the values of Bv, Ev, Gv, and ν are listed calculated using Equations 1, 2, 3 & 4 respectively.

Compounds C11 C12 C13 C33 C44 Bv Ev Gv ν Ref.
        413 Phases            
Ti4AlN3 420 73 70 380 128 182.88 359 153 0.172 36
Ti4GeC3 381 96 95 349 148 187.00 341 143 0.195 37
α-Ta4AlC3 437 158 197 416 165 266.00 364 143 0.272 38
β -Ta4AlC3 509 143 156 440 147 263.11 404 162 0.244 39
Ta4GaC3 389 84 78 323 131 175.66 332 140 0.185 40
α-V4AlC3 435 121 105 384 168 212.88 384 160 0.199 39
α-Nb4AlC3 413 124 135 328 161 215.77 353 144 0.227 39
        312 Phases            
Ti3SiC2 365 125 120 375 122 203.88 307 123 0.248 42
Ti3GeC2 355 143 80 404 172 191.11 345 144 0.198 43
Ti3AlC2 361 75 70 299 124 161.22 321 132 0.178 44
Ti3SnC2 346 92 84 313 123 169.44 300 124 0.205 41
        211 Phases            
Ti2AlN 342 56 96 283 123 162.55 300 126 0.192 36
Ti2AlC 301 59 55 278 113 135.33 272 117 0.164 45
Ti2SnC 260 78 70 254 93 134.44 226 93 0.218 54
Ti2GeC 279 99 95 283 125 157.66 257 105 0.227 48
Ti2GaC 314 66 59 272 122 140.88 283 121 0.166 49
Ti2SC 315 98 99 362 161 176.00 310 127 0.209 46
Ti2CdC 258 68 46 205 33 115.66 174 69.6 0.249 53
Ti2InC 288 62 53 248 88 128.88 241 102 0.186 53
Ti2InN 229 56 106 248 92 138.00 208 83.3 0.248 54
Ti2PbC 235 90 53 211 66 119.22 182 73.2 0.245 54
V2AlC 346 71 106 314 151 174.66 324 136 0.190 51
V2GeC 282 121 95 259 160 160.55 277 114 0.212 47
V2GaC 343 67 124 312 157 180.88 326 136 0.199 49
V2GaN 281 71 142 293 128 173.88 263 106 0.246 54
V2AsC 334 109 157 321 170 203.88 318 128 0.240 57
V2PC 376 113 168 386 204 226.22 376 154 0.222 54
Cr2AlC 384 79 107 382 147 192.88 351 146 0.197 52
Cr2GeC 315 99 146 354 89 196.22 249 96.7 0.288 47
Cr2GaC 312 81 139 325 128 185.22 283 114 0.244 54
Mo2GaC 294 98 107 289 127 166.77 257 111 0.227 54
Nb2AlC 310 90 118 289 139 173.44 285 116 0.226 54
Nb2GaC 309 80 138 262 126 176.88 270 108 0.246 54
Nb2SnC 341 106 169 321 183 210.11 314 134 0.237 56
Nb2InC 291 76 108 267 102 159.22 247 99.4 0.241 54
Nb2AsC 334 104 169 331 167 209.22 317 127 0.247 57
Nb2PC 369 113 171 316 170 218.22 333 134 0.245 54
Hf2SC 344 116 138 369 175 204.55 336 137 0.226 50
Hf2SnC 318 96 99 301 123 169.44 280 114 0.225 55
Hf2SnN 240 62 103 236 92 139.11 211 84.5 0.247 54
Hf2InC 284 69 65 243 91 134.33 238 98.7 0.204 57
Hf2PbC 241 77 70 222 69 126.44 191 81 0.236 54
Ta2AlC 334 114 130 322 148 193.11 303 122 0.239 54
Ta2GaC 335 106 137 315 137 193.88 294 118 0.247 54
Ta2GaN 333 187 150 364 141 222.66 277 107 0.292 54
Zr2SnC 279 92 97 272 111 155.77 252 104 0.226 48
Zr2SC 326 103 119 351 160 187.22 318 130 0.218 50
Zr2InC 251 62 58 215 73 119.22 204 84 0.214 54
Zr2InN 241 71 89 223 85 133.66 203 81.4 0.246 54
Zr2PbC 219 70 67 206 68 116.88 174 71.4 0.246 54

Fig. 6. Bulk moduli (Bv), shear moduli (Gv) and Young’s moduli (Ev) of 50 Max Phases.

Table 5. Ascending to descending values of bulk modulus (Bv), Young’s modulus (Ev), shear modulus (Gv) and Possion’s ratio of all the MAX phase compounds.

Compounds Bv Compounds Ev Compounds Gv Compounds ν
α-Ta4AlC3 266 β -Ta4AlC3 404 β -Ta4AlC3 162 Ta2GaN 0.292
β -Ta4AlC3 263.11 α-V4AlC3 384 α-V4AlC3 160 Cr2GeC 0.288
V2PC 226.22 V2PC 376 V2PC 154 α-Ta4AlC3 0.272
Ta2GaN 222.66 α-Ta4AlC3 364 Ti4AlN3 153 Ti2CdC 0.249
Nb2PC 218.22 Ti4AlN3 359 Cr2AlC 146 Ti3SiC2 0.248
α-Nb4AlC3 215.77 α-Nb4AlC3 353 α-Nb4AlC3 144 Ti2InN 0.248
α-V4AlC3 212.88 Cr2AlC 351 Ti3GeC2 144 Nb2AsC 0.247
Nb2SnC 210.11 Ti3GeC2 345 Ti4GeC3 143 Hf2SnN 0.247
Nb2AsC 209.22 Ti4GeC3 341 α-Ta4AlC3 143 Ta2GaC 0.247
Hf2SC 204.55 Hf2SC 336 Ta4GaC3 140 V2GaN 0.246
Ti3SiC2 203.88 Nb2PC 333 Hf2SC 137 Nb2GaC 0.246
V2AsC 203.88 Ta4GaC3 332 V2AlC 136 Zr2InN 0.246
Cr2GeC 196.22 V2GaC 326 V2GaC 136 Zr2PbC 0.246
Ta2GaC 193.88 V2AlC 324 Nb2SnC 134 Ti2PbC 0.245
Ta2AlC 193.11 Ti3AlC2 321 Nb2PC 134 Nb2PC 0.245
Cr2AlC 192.88 V2AsC 318 Ti3AlC2 132 β -Ta4AlC3 0.244
Ti3GeC2 191.11 Zr2SC 318 Zr2SC 130 Cr2GaC 0.244
Zr2SC 187.22 Nb2AsC 317 V2AsC 128 Nb2InC 0.241
Ti4GeC3 187 Nb2SnC 314 Ti2SC 127 V2AsC 0.24
Cr2GaC 185.22 Ti2SC 310 Nb2AsC 127 Ta2AlC 0.239
Ti4AlN3 182.88 Ti3SiC2 307 Ti2AlN 126 Nb2SnC 0.237
V2GaC 180.88 Ta2AlC 303 Ti3SnC2 124 Hf2PbC 0.236
Nb2GaC 176.88 Ti3SnC2 300 Ti3SiC2 123 α-Nb4AlC3 0.227
Ti2SC 176 Ti2AlN 300 Ta2AlC 122 Ti2GeC 0.227
Ta4GaC3 175.66 Ta2GaC 294 Ti2GaC 121 Mo2GaC 0.227
V2AlC 174.66 Nb2AlC 285 Ta2GaC 118 Nb2AlC 0.226
V2GaN 173.88 Ti2GaC 283 Ti2AlC 117 Hf2SC 0.226
Nb2AlC 173.44 Cr2GaC 283 Nb2AlC 116 Zr2SnC 0.226
Ti3SnC2 169.44 Hf2SnC 280 V2GeC 114 Hf2SnC 0.225
Hf2SnC 169.44 V2GeC 277 Cr2GaC 114 V2PC 0.222
Mo2GaC 166.77 Ta2GaN 277 Hf2SnC 114 Ti2SnC 0.218
Ti2AlN 162.55 Ti2AlC 272 Mo2GaC 111 Zr2SC 0.218
Ti3AlC2 161.22 Nb2GaC 270 Nb2GaC 108 Zr2InC 0.214
V2GeC 160.55 V2GaN 263 Ta2GaN 107 V2GeC 0.212
Nb2InC 159.22 Ti2GeC 257 V2GaN 106 Ti2SC 0.209
Ti2GeC 157.66 Mo2GaC 257 Ti2GeC 105 Ti3SnC2 0.205
Zr2SnC 155.77 Zr2SnC 252 Zr2SnC 104 Hf2InC 0.204
Ti2GaC 140.88 Cr2GeC 249 Ti2InC 102 α-V4AlC3 0.199
Hf2SnN 139.11 Nb2InC 247 Nb2InC 99.4 V2GaC 0.199
Ti2InN 138 Ti2InC 241 Hf2InC 98.7 Ti3GeC2 0.198
Ti2AlC 135.33 Hf2InC 238 Cr2GeC 96.7 Cr2AlC 0.197
Ti2SnC 134.44 Ti2SnC 226 Ti2SnC 93 Ti4GeC3 0.195
Hf2InC 134.33 Hf2SnN 211 Hf2SnN 84.5 Ti2AlN 0.192
Zr2InN 133.66 Ti2InN 208 Zr2InC 84 V2AlC 0.19
Ti2InC 128.88 Zr2InC 204 Ti2InN 83.3 Ti2InC 0.186
Hf2PbC 126.44 Zr2InN 203 Zr2InN 81.4 Ta4GaC3 0.185
Ti2PbC 119.22 Hf2PbC 191 Hf2PbC 81 Ti3AlC2 0.178
Zr2InC 119.22 Ti2PbC 182 Ti2PbC 73.2 Ti4AlN3 0.172
Zr2PbC 116.88 Ti2CdC 174 Zr2PbC 71.4 Ti2GaC 0.166
Ti2CdC 115.66 Zr2PbC 174 Ti2CdC 69.6 Ti2AlC 0.164

5. MAX Phase Potential Applications

The MAX phases have been proposed for numerous applications, some of which are discussed briefly below. The purpose of this section is mostly to show the rich potential for applications and the range of industries that the MAX phases could in principle impact.

5.1. Replacement for Graphite at High Temperatures

Graphite is an important high-temperature material used extensively in many industries. For example, graphite is used as connectors, heaters, furnace linings, shields, rigid insulation, curved heating elements, and fasteners in vacuum furnaces. Graphite is also the material of choice for the hot pressing of diamond-cutting tools and other materials, for the construction industry. In general, some of the MAX phases such as Ti2AlC have several advantages over graphite such as better wear and oxidation resistance. The ease by which Ti2AlC can be machined to high tolerances is also an important consideration. The high strengths, moduli, and thermal conductivities of the MAX phases are also positive attributes. Figure 7 shows examples of MAX phase inserts that were actually tested in industrial dies and performed quite well.


Fig. 7. (a, b) MAX-based insets that were tested in industrial dies at elevated temperatures. (Courtesy of 3-ONE-2, LLC.).

5.2. Heating Elements

Fig. 8. Example of Ti2AlC-based heating element resistively heated to 1450 0C in air (Courtesy of Kanthal).

In the late 1990s, Kanthal Corp. licensed the MAX technology from Drexel University. Given that one of Kanthal’s core businesses is heating elements, it was not surprising that MAX phase heating elements were one of the first applications targeted by the Swedish company. The heating element shown in figure 8 was heated up to 1350 0C and cooled down to room temperature for 10 000 cycles (Sundberg et al., 2004). The resistance of the element was found to be very stable and the protective oxide that formed was quite adherent and protective. This heating element is quite versatile and can be used up to 1400 0C in air, argon, hydrogen, or vacuum.

5.3. High-Temperature Foil Bearings and Other Tribological Applications

A project funded by the Office of Navy Research led to the successful development of MAX based materials for foil bearings, having low friction and wear from room temperature to 823 K. Figure 9 shows a Ta2AlC/Ag shaft and a superalloy foil after testing for 10 000 cycles in a rig. The shaft was rotated at 50 000 rev min-1[329]. Honeywell Inc. was further developing this concept.


Fig. 9. (a) Ta2AlC/Ag composite cylinder mounted on a shaft after 10000 stop–start cycles in a rig test and (b) picture of superalloy foil after rig testing [74].

5.4. Gas Burner Nozzles

Fig. 10. Pictures of Ti2AlC and steel nozzles used in gas burners. The testing conditions that heavily corroded the steel nozzles did not appear to affect the MAX-based one.

Owing to its excellent high-temperature properties and because it forms a protective alumina layer, Ti2AlC-based MAX phases can be used in gas burning applications where traditional metallic alloys show limited service life (See Fig. 10). The same MAX compound can also replace metallic alloys to increase the burner process temperatures up to 1400 0C. Note that, in contrast to traditional ceramics, joining problems to existing equipment are easily overcome as MAX nozzles can be readily threaded and thus can directly replace metallic nozzles.

5.5. Tooling for Dry Drilling of Concrete

In the early 2000s, 3-ONE-2 (a small company Dr. T. El-Raghy) and Hilti developed tooling for the dry drilling of concrete, consisting of diamonds in MAX 312 (Ti3SiC2) segments, which were then brazed to steel. The performance of the MAX phase segments was reported to be far superior to that of current diamond/Co segments (Fig. 11 a,b). With further improvements in design to overcome the problem of smearing of concrete powders due to high temperatures and the inadequate toughness of the segments, this material may be close to market.

Fig. 11. Pictures of, (a) steel hollow cylinder to which diamond/Ti3SiC2 inserts were brazed, after dry drilling of concrete, (b) same as (a), but where the diamonds were embedded in a Co matrix; and (c) higher magnification of insert after dry drilling. (Courtesy 3-ONE-2.).

5.6. Glove and Condom Formers and Nonstick Cookware

Ansell Healthcare and Drexel University signed a research agreement for developing gloves and condom formers to make latex products. The work resulted in the development of the slip casting technology for manufacturing large, thin-walled complex parts (see Fig. 12 a–c) and a patent. In 2007, a patent was issued (El-Raghy and Lyons, 2007) for the use of the MAX phases and their coatings as durable, stick and stain and thermal shock resistant, dishwasher safe, cookware, cutlery, and other cooking utensils.

Fig. 12. Picture of (a) large, hollow, slip cast Ti3SiC2 glove former; (b) and (c) same as (a), but showing thin walls possible; and (d) complex solid and hollow slip cast parts starting with Maxthal powders. (Courtesy 3-ONE-2.).

5.7. Application in the Nuclear Industry

There are some of the MAX phases compounds, most notably Ti3AlC2 and Ti3SiC2, are quite resistant to radiation damage (Le Flem et al., 2010; Liu et al., 2010; Napp´e et al., 2009; Whittle et al., 2010). There is also a growing body of evidence that dynamic recovery may be occurring at temperatures of 700 0C or lower. In a post-Fukushima world, it is imperative to build some accident tolerance to the Zircaloy tubes that hold the nuclear fuel. The simplest is to spray a thin coating of Ti2AlC or Ti3AlC2 onto the Zircaloy tubes. If the coatings are thin enough and are designed in such a way that in the presence of oxygen they form a thin cohesive and adhesive alumina layer, then it is possible to protect the Zircaloy tubes in the case of accident due to loss of coolant. The challenge, however, is to thermally spray the Ti2AlC such that it does not lose its ability to form thin alumina layers. The current text on the topic shows that after high-velocity oxy-fuel, HVOF, spraying of Ti2AlC, heating in air results in the formation of titania instead of alumina (Frodelius et al., 2008; Sonestedt et al., 2010a,b). The fact that Ti3SiC2 does not react with molten Pb and or Pb–Bi alloys (Barnes, Dietz Rago, and Leibowitz, 2008; Heinzel, M¨uller, and Weisenburger, 2009; Utili et al., 2011) renders it a good material to be used for containing molten Pb or Pb–Bi alloys in nuclear reactors. In a recent paper, Sienicki et al. (2011) suggested that Ti3SiC2 could be used in an improved natural circulation Pb-cooled small modular fast reactor.

5.8. Ignition Devices and Electrical Contacts

Some of the MAX phases are used as the conductive element in spark plugs and other such ignition devices (Walker, 2010).One of the first applications for Ti3SiC2 was by a small Swedish company, Impact Coatings, as sputtering targets for the deposition of electrical contacts. Although the company now uses other cheaper targets, this early application is significant. Currently, others are sputter depositing Cr2AlC thin films on steels and turbineblades (e.g. Hajas et al., 2011). In some cases, MAX phase targets are used. On the basis of the growing worldwide interest in the MAX phases, it is reasonable to assume that a market for sputter targets should emerge soon. Owing to their good electrical conductivity and tribological properties, in addition to the acceptable mechanical properties, MAX phases such as Ti3SiC2 and Ti3AlC2 have been shown to perform better than carbon based pantographs for electric trains. Currently, a few leading projects are running in China, aiming for application on the high speed railway under construction.

5.9. Electrical Contact for SiC-based Devices

Presently, SiC-based devices are under development for use in electronic devicesthat are subjected to high temperatures and/or corrosive environments. Siliconcarbide’s material properties (large band-gap, high-thermal conductivity, extremely high-melting and decomposition temperatures, excellent mechanical properties, and exceptional chemical stability) are far superior to those of Si and render it suitable for operation in hostile environments. Because its band gap is nearly three times larger than that of Si, it is possible to use SiC as a semiconductor, for example, to temperatures as high as 1000 0C because of its low intrinsic carrier concentrations and operation within the dopant-controlled saturation regime required for semiconducting devices. One of the challenges of this technology isto find a material to use as an electrical contact that does not react with SiC at elevated temperatures and results in low contact resistances. In 2003, a patent was issued (Tuller, Spears, and Mlcak, 2003) for the use of Ti3SiC2 as an electrical contact for SiC electronic components. The major advantage of Ti3SiC2 is that it is in thermodynamic equilibrium with SiC. This would in turn allow the SiC devices to be operated in high-temperature environments without the contact material reacting with the SiC, and deteriorating the performance of the device. Some sensor applications are based on SiC field effect transistors that exploit the wide band gap of SiC and its chemical inertness. In such applications, there is also need a compatible inert electrode material such as Ti3SiC2.

5.10. Forming Processes and Sintering

One of the crucial advantages of working with the MAX phases is that they can be pressureless sintered to full density by heating green performs in inert atmospheres such as argon. The first report in the open literature for the pressureless sintering of a MAX phase to full density can be found in a patent that issued in 2002 (El-Raghy et al., 2002). The first paper published in 2004 (Murugaiah et al., 2004) not only on the pressureless sintering of Ti3SiC2 but also on its tape casting, a process that, not surprisingly, led to orienting the flaky prereacted hexagonal grains. In this paper, it was shown that the simplest method to producing highly oriented microstructures was to gently shake or tap the dies containing the prereacted Kanthal powders prior to sintering. The first paper published on the pressureless sintering in 2006 (Zhou et al., 2006). In general, the fact that the MAX phases can be sintered to full density, without the application of pressure is an important attribute that greatly enhances their chances for commercialization. The methods for forming the green bodies are quite varied. They range from slip casting, to produce complex, thin wall shapes (e.g., Figure 11), extrusion to form tubes (Figure 9), cold pressing to form simple shapes (Figure 7) and cold isostatic pressing to metal injection molding. It is significance noting that the inherent ductility of the MAX phases help to forming green bodies without help of any binder. Spark plasma sintering (SPS) is also emerging as a viable method to fabricate and densify the MAX phases (Cui et al., 2012; Hu et al., 2009, 2011b; Zhang et al., 2003). Currently there is little work, however, comparing the high-temperature properties of samples made by SPS with those made by reactive hot pressing or pressureless sintered commercial powders.

In addition to the applications mentioned above, a number of other potential applications have been found. These include: electrodes, exhaust gas filters for automobiles, free-cutting elements, microelectronics, biomaterials, damping materials (high stiffness and up to high temperatures), corrosion resistant materials, surface coatings, defense applications, such as armor, nuclear applications, low dimensional materials, and substrates for CVD diamond.

6. Conclusion

The MAX phases have attracted considerable attention and are garnering new devotees because they have a quite unusual combination of properties. The fact that their chemistries can be altered while keeping the structure the same allows for relatively rapid understanding. The emergence of possibly magnetic MAX phases is an exciting development that would greatly enhance their potential applications. On the mechanical side, the fact that dislocations are confined to 2D is proving invaluable in elucidating the deformation behavior of layered solids in general, and ones that are also conductive in particular. The most urgent issue in MAX phase research is to develop viable commercial applications for these materials. With the preliminary and potential application fields discussed above, market penetration by MAX phase materials will create more stimuli to carry out more research and development on this family of layered metallic ceramics. Research on MAX phases is currently funded by agencies, science foundations and defense industries in the USA, China, Europe and Australia. However, funding for research on MAX phases from governmental agencies in Japan is almost zero. The likelihood of the Japanese government funding such research remains small until a clear market scenario is available.

Another important issue is the search for new MAX phases. First, to better understand the MAX phases themselves, both those known to exist and those theoretically predicted to be thermodynamically and mechanically stable. To do so, thorough experimental investigations into the properties are needed. The second priority is to discover more MAX phases. It is encouraging that in the past few years many MAX phases, particularly 413 and 312 phases, have been discovered. More 312 or 211 MAX phases, plus their solid solutions, which are numerous, are awaiting exploration. In this review paper we have studied most of the MAX phase compounds, their different properties and applications in different sectors. We hope that the researches described in this overview will be helpful for the discovery of new MAX phase compound and their practical and possible applications in modern technology in near future.


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