physical properties of max phases

Physical Properties of the MAX Phases

1. Introduction

The layered ternary carbides and nitrides with the general formula MIl+IAXIl , where n= 1,2, or 3, M is an early transition metal, A is an A-group element (mostly IlIA or IVA), and X is either C or N, represent a new class of solids (Barsoum 2000, Barsoum and EI-Raghy 200Ia). These phases are layered, with MIl+1XIl layers interleaved with pure A-group el~

ment layers) (Fig. I). The hexagonal MIl+IAXIl umt cells~space group P63lmmc~have two formula units per unit cell. There are roughly 50 ~2~X phases (Nowotny 1970); three M3AX2: T13SIC2 (Jeitschko and Nowotny 1967), Ti3GeC2 (Wolfsgruber et al. 1967), and Ti3AIC2 (Pietzka and Schuster, 1996); and one M4AX3, Ti3AIN4 (Barsoum et at. 1999, Rawn et al. 2000).

The M lI+1AXlI phases combine an unusual, and sometimes unique, set of properties (Barsoum 2000). Like their corresponding binary carbides and nitrides, they are elastically stiff, good thermal and electrical conductors, resistant to chemical attack and have relatively low thermal expansion coefficients. Mechanically, however, they cannot be more different. They are relatively soft (1-5 GPa) and most readily machinable, thermal shock resistant, and damage tolerant (Barsoum and EI-Raghy 1996, Barsoum and Radovic 2004). Moreover, some are fatigue- and creep- and oxidation-resistant. At higher temperatures, they go through a ductile-to-brittle transition. At room temperature, they can be compressed to stresses as high as 1GPa and fully recover upon removal of the load, while dissipating 25% of mechanical energy (Barsoum et al. 2003) (see Mechanical Properties of the MAX Phases (Barsoum and Radovic 2004) for the mechanical properties of MAX).

This article summarizes our current understanding of the physical properties of bulk MIl+IAXIl phases. It does not discuss recent MAX-based thin-film work (Palmquist et al. 2002, Molina-Aldareguia et al. 2003, Wilhelmsson et al. 2004), to list a few. This article is divided into five sections and reviews their structure and bonding (including theoretical) characteristics, summarizes their elastic properties, and reviews their electrical and thermal properties.

2. Structure and Bonding

The unit cells of the 211, 312, and 413 phases are shown in Figs. l(a), l(b), and l(c), respectively. In each case, almost close-packed M-Iayers are interleaved with layers of pure group A-element, with the X-atoms filling the octahedral sites between the

I ~

M-layers

~ a

A-layers

I~c c

(a) (b) (c)

Figure 1 Schematic of (a) M2AX, (b) M3AX2, and (c) M4AX3

unit cells.

former. The M6X octahedra are identical to those found in the rock salt structure of the corresponding binary MX carbides. The A-group elements a~e located at the centers of trigonal prisms that are slightly larger, and thus better able to accommodate the larger A-atoms, than the octahedral sites. In the 211's there are two layers of M separating the Alayer~, in the 312's, three, and in the 413's there are four.

The MIl+IAXIl phases known to date are listed in Table I, together with their lattice parameters and theoretical densities. The A-group elements are mostly IlIA and IVA. All but four compounds are 211's, by far the most prevalent stru.cture: Al is the most versatile A-group element With eight compounds, including nitrides, 312's, and t?e sole 413 phase. Ga forms the most 211 phases, Wlt~ 9.. ..

Given the close chemical and structural slmIlanties of the MAX and MX phases, much can be learned about the former from what is known about the latter. Like the MX compounds (Cottrell 1995, Pierson 1996), it is useful to consider the ternaries to be interstitial compounds in which the A- and X-atoms fill the interstitial sites between the M-atoms. In such a scheme, the c-parameter of the 211 phases, comprising four M-Iayers per unit cell, should be :::::: 4 times the a-parameter, for a cia ratio of::::::4, ~s ob~erv~d (Table 1). Similar arguments. for the .312 s, With SIX M-Iayers per unit cell, predict a ratIO. of ::::::: 6, and the 413's a ratio of ::::::8. The actual cia ratIOs are,


Table 1 Summary of all M"+lAX" phases, their lattice parameters and theoretical densities known to date.

lIB IlIA IVA VA VIA

Al Si P S ThAIC, 4.11 (3.04, 13.60) ThSC, 4.62 (3.216.

11.22) VzAIC, 4.82 (2.914, 13.19) VzPC, 5.38 ZrzSC, 6.20 (3.40,

(3.077, 10.91) 12.13) CrzAIC, 5.24 (2.86, 12.8) Ti3SiCz, 4.52 NbzPC, 7.09 NbzSCo.4 (3.27,11.4)

(3.0665, 17.671) (3.28. 11.5) NbzAIC, 6.50 (3.10, 13.8) HfzSC (3.36, 11.99) TazAIC, 11.82 (3.07. 13.8) ThAIN, 4.31 (2.989. 13.614) ThAICz, 4.5 (3.075, 18.578) Ti~IN3' 4.76 (2.988, 23.372)

Zn Ga Ge As ThGaC, 5.53 (3.07. 13.52) ThGeC, 5.68

(3.07, 12.93) VzGaC, 6.39 (2.93, 12.84) VzGeC, 6.49 (3.00, VzAsC, 6.63 (3.11, Se

12.25) 11.3) CrzGaC, 6.81 (2.88, 12.61) NbzGaC, 7.73 (3.13, 13.56) MozGaC, 8.79 (3.01, 13.18) CrzGeC, 6.88

(2.95, 12.08) TazGaC, 13.05 (3.10, 13.57) NbzAsC, 8.025

(3.31, 11.9) TizGaN, 5.75 (3.00, 13.3) Ti3GeCZ' 5.55

(3.087,17.76) CrzGaN, 6.82 (2.875, 12.77) VzGaN, 5.94 (3.00, 13.3)

Cd In Sn SczInC TizSnC, 6.36

(3.163, 13.679) TizCdC 9.71 TizInC, 6.2 (3.13. 14.06)

(3.1, 14.41) ZrzInC, 7.1 (3.34, 14.91) ZrzSnC, 7.16 Sb Te

(3.3576, 14.57) NbzInC, 8.3 (3.17,14.73) NbzSnC, 8.4

(3.241, 13.802) HfzInC, 11.57 (3.30, 14.73) HfzSnC, 11.8

(3.320, 14.388) TizInN, 6.54 (3.07, 13.97) HfzSnN, 7.72

(3.31, 14.3) ZrzInN, 7.53 (3.27, 14.83)

TI Pb Bi ThTIC, 8.63 (3.15, 13.98) TizPbC, 8.55

(3.20. 13.81) ZrzTIC, 9.17 (3.36, 14.78) ZrzPbC, 9.2 (3.38,

14.66) HfzTIC, 13.65 (3.32, 14.62) HfzPbC, 12.13

(3.55, 14.46) ZrzTIN, 9.60 (3.3, 14.71)

The theoretical density (Mg m -3) is in bold letters. The a· and c·lattice parameters (A) are in brackets. Adapted from Nowotny H 1970 Struktuchemie Einiger Verbindungen der Ubergangsmetalle mit den elementen C. Si. Ge. Sn. Prog. Solid State Chem. 2,27.

2


respectively, ~ 5.8 to 6 and 7.8, supporting the notion of interstitial compounds.

With the exception of the Cr2AC phases, an excellent correlation exists between the a-lattice parameters of the MAX phases and the M-M distances in the corresponding MX binaries (Barsoum 2000). Why the three Cr-containing MAX phases do not fit the pattern is unclear at this time, but may be related to the fact that Cr is the only transition metal listed in Table 1 that does not crystallize in the rock salt structure.

In addition to the list shown in Table 1, the number of possible solid-solution permutations and combinations is obviously quite large; roughly a quarter of the periodic table could, in principle, come into play. It is possible to form solid solutions on the M-sites, the A-sites, and the X-sites and combinations thereof. A continuous series of solid solutions, Ti2AICo.8 _ xN", where .\'=0 to ~0.8, occurs at 1490°C (Pietzka and Schuster 1996). The ternaries Ti3GeC2 and Ti3SiC2 form a complete range of solid solutions (Ganguly et al. 2004). Amongst the solid solutions that form on the M-sites are: (Ti,VhSC (Nowotny et al. 1982); (Nb,ZrhAIC, (Ti,VhAIC, (Ti,NbhAIC, (Ti,CrhAIC, (Ti,TahAIC, (V,NbhAIC, (V,TahAIC, and (V, CrhAIC (Schuster et al. 1980, Salama et al. 2002); and (Ti, Hf)2InC (Barsoum et al. 2002a).

Lastly. it is important to note that currently there is quite a bit of effort in theoretical modeling of the MAX phases (Medvedeva et al. 1998, Sun and Zhou 1999, Holm et al. 2001, Hug and Frie 2002, Hug et al., Sun et al. 2004). The following conclusions of the theoretical work are noteworthy: (i) the M-X bonds are comparable to those in the MX binaries (Medvedeva et al. 1998), (ii) the density of states at the Fermi level, N(EF}-as in some MX binaries but notably not TiCis substantial, (iii) there is strong overlap between the p-orbitals of A- and the d-orbitals of the M-atoms, (iv) the electronic states at the Fermi level are mostly d-d

M-orbitals (Medvedeva et al. 1998), and (v) there is a net transfer of charge from the A-group element to the X-atoms, at least in the M2AIC phases (Hug et al. 2005). As discussed in the sections that follow, many of these conclusions have been supported by experimental results. Furthermore, recent ab initio work has been quite successful in calculating the elastic properties of some MAX phases (Sun et al. 2004) as well as the Raman active vibrational modes (Spanier et al. 2005).

3. Elastic Properties

The MAX phases are elastically quite stiff (Table 2). This is particularly true for the 312 and 413 phases. Given that the densities of some of these solids are

3relatively low, ~4.5 gcm- , their specific stiffnesses are considerable. For example, the specific stiffness of Ti3SiC2 is comparable to Si3N4 and roughly three times that of Ti, a metal prized for that property. Poisson's ratios for all compounds hover around 0.2, which is lower than that of Ti (0.3), and more in line with stoichiometric TiC (~0.19). Not surprisingly, given the larger fraction of M--X bonds in the 312's and 413's as compared to the 211's, the latter are less stiff. For example, at 161 GPa, the bulk modulus of Ti2AIN is significantly lower than the 216 GPa of Ti4AIN3. Increasing the atomic number of the Agroup element also results in lattice-softening. For example, at 178 GPa, 216GPa, and 237GPa the Young's moduli of Zr2SnC, Nb2SnC, and Hf2SnC (EI-Raghy et al. 2000), respectively, are all lower than any of the AI-containing ternaries (Table 2).

In stark contrast to other layered solids such as graphite, BN, and mica, and despite their huge plastic anisotropies (Barsoum and Radovic 2004), the anisotropies in their elastic properties are quite mild. For example, C33 and CII for Ti3SiC2 (Holm et al.

Table 2 Young's, E, shear, G, and bulk B. moduli of the select MAX phases and near-stoichimetric TiC. Also listed are the theoretical densities.

Theo. density G E Jf' Bb N(EF )

Solid (gcm-3) (GPa) (GPa) v (GPa) (GPa) 8 D 8l; (l/eV unit cell)

Ti2AIC 4.1 118 277 0.19 144 186c 732 672d 4.9d

V2AIC 4.81 116 235 0.20 152 20l c 696 625d 7.5d

Cr2AIC 5.24 102 245 0.20 138 166c 644 589d 14.5d

Nb2AIC 6.34 117 286 0.21 165 208c 577 NA 5.1 e

Ti3SiC2 4.52 139 339 0.2 190 206 715-780 715h 5 Ti3GeC2 5.02 142 340 0.19 169 179 725 670 5Af

Ti3AIC2 4.2 124 297 0.2 165 226 758 764e 3.8 f

Ti~IN3 4.7 127 310 0.22 185 216 762 779h 6.9g

TiCo.96 4.93 205 ~500 0.19 272 940g 845h 0.1--0.5g

The Poisson ratio. v. 8D calculated from Vm (column 8) and 8D calculated from low-temperature heat capacity measurements (column 9) are listed. The density of states at the Fermi level is listed in the last column. a Calculated from E and G assuming elastic isotropy. bDirectiy measured in a diamond anvil celL c Manoun et al. (in press). d Drulis et al. (submitted). e Lofland et al. (2004). fFinkel et al. (2004). g Finkel (2003). h Ho et al. (1999).

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2001) and some M2AIC phases (Sun et al. 2004) are almost equal. Similarly, the compressibilities along aand c-directions are comparable for most MAX phases measured to date (Onodera et af. 1999, Manoun et al. 2004a, 2004b, 2005).

Another important measure of the stiffness of a solid is its Debye temperature, (}D, which can be estimated assuming

(h) (3~bNAV) 1/3eD = - I'm (I)k B 4rrMw

where b, ~, and M w are the density. number of atoms per formula unit, and its molecular weight, respectively. is the mean velocity of sound in the solids ]1m

defined as

3] 1/3I'm = 3(1',1'1)

[21'3 + 1'3 (2)

1 ,

where VI and I's are the longitudinal and shear velocities, respectively. Column 8 in Table 2 lists (}D values calculated from Eqn. (l). In general, the Debye temperatures are quite high and more in line with stiff light ceramics such as Ab03 and Si3N4 than with metals. The values are also in good agreement with those calculated from low-temperature heat-capacity measurements (column 9, Table 2). Table 2 also lists the elastic properties of near-stoichiometric TiC for companson.

The AI-containing MAX phases and ThSiC2 have another useful attribute: their stiffnesses are not a strong function of temperature. For example, at 1273 K the shear modulus of Ti3AIC2 is ~ 88% of its room temperature value (Finkel et af. 2000). In that respect, their resemblance to the MX binaries is notable.

Figure 2 compares the measured shear and Young's moduli of select MAX phases to those predicted from ab initio calculations. With a few exceptions, like Cr2AlC and Ta2AlC, the agreement has to be considered quite good, considering that the calculations are 0 K calculations and assume perfect crystals (Holm et al. 2001, Sun et af. 2004); in reality neither condition is met.

Another clue to the nature of the bonding is Raman spectroscopy. The Raman modes for these compounds have been deciphered (Spanier et al. 2005) and they show that there are essentially two types of vibrations: low-energy (for the most part <300cm- l

) shear modes (along the a-direction) involving the A- and M-atoms, and higher-energy modes involving vibrations along the c-axis. The low-energy shear modes are not unlike the ones observed in graphite and other layered solids, that have been labeled rigid-layer modes (Zallen et al. 1971, Zallen and Slade 1974). These modes are a manifestation of the weakness of the M-A bonds in shear relative to the M-X bonds. That said, it

400

Cr2AIC Ti,Sio .,Young's moduli 350

Ti4 A1N? Ti2AIC .

~ 0.. 300 V2AIC~g o

o Ti 3GeC 2 Nb2AIC

S "3

" 250 0 6 .~ 200Vi - V2AIC ;)" "@ 150 .~ 0)...

Bulk moduli O.l 0

100 ~

50

o "-'--'-'--'--'--'--'-'--'-~L.L.>..-'-'-"""""-L..L..L.L.J.-'--'-""""""-'--'-""""""'L.L.>..""""'W

o 50 100 150 200 250 300 350 400 Experimental elastic moduli (GPa)

Figure 2 Summary of experimentally determined and theoretically calculated bulk (red squares) and Young's moduli (blue circles) of select MAX phases.

is incorrect to conclude from this statement that any of the bonds in the MAX phases are weak.

4. Electronic Transport

One of the characteristics of the MAX is their metallike resistivity, P, that increases linearly with increasing temperature. Figure 3(a) plots the temperature dependence of P-Po, where Po is the residual resistivity at 0 K. (The curves are shifted slightly in the ydirection for clarity). Table 3 lists the actual room temperature resistivities, PRT.

Both theoretical and experimental results strongly suggest that the electronic properties of the MAX phases are dominated by the d-d M-orbitals (Medvedeva et af. 1998, Lofland et al. 2004, Hug et al. 2005) and that these properties are, in turn, comparable to those of their respective transition metals. Before discussing the former, it is useful to briefly summarize what is known about the latter. The resistivities of transition metals are proportional to the density of states at the Fermi level, N(EF ) (Mott and Jones 1936, Ashcroft and Mermin 1976). Accordingly, the electron mobilities at 0 K, flo, should be inversely proportional to N(EF ). The quality of the crystal as measured by the residual resistivity ratio, RRR (PRT/ Po), is also important. Thus, a correlation between flo and (RRR - l)/N(Ep ) should exist and is indeed experimentally verified (Fig. 3(b». Similarly, dp/dT should also scale with N(EF ) and the electron/ phonon coupling factor (Hettinger et af. 2005). That

4

0.05 /""0

I

I '" >

N 0.04

Ti2AIC

• §

~ :0 0

0.Q3

R2 > 0.95 S I:: 0 0.02 b () <U

~ 0.01


0.7

0.6

0.5

/""0

E 0.4c:

3 0

Q.. 0.3I Q..

0.2

0.1

0 0 50 100 150 200 250 300

(a) Temperature (K)

0.06

.-- Ti4AIN3 O ......L...L-L...L-J--L-J--L-.l.....L......................L..J....L..J....l--L-.L-L..L-L.............lo....I...J

1.5 (b)

o 0.5 1

(RRR - I)/N(EF )

Figure 3 (a) Temperature dependence of p - Po for select MAX phases. (b) functional dependence of electronic charge mobilities at 4 K on RRR and the density of states at the Fermi level. N(EF ) (Hettinger et al. 2005).

it does can be seen by comparing the slopes of the lines shown in Fig. 3(a) with the N(EF ) values listed in Table 3.

To fully understand electronic transport in a solid, the density of charge carriers as well as their mobilities should be known. Typically, Hall coefficient, RH , measurements are used to measure the concentrations and sign of the majority charge carriers. With that information, the mobility is determined from the conductivity values. The MAX phases, however. are unlike most other metallic conductors in

that their Hall and Seebeck coefficients are quite small-in some cases vanishingly small-and are a weak function of temperature (Barsoum et af. 2000d, Y00 et al. 2000, Finkel et al. 2003, Finkel et al. 2004, Hettinger et al. 2005). Furthermore, the magnetoresistance (l1p/ p = [p(H) - p(H = 0)/p(H = 0)]), where H is the applied magnetic field intensity, is positive, parabolic, and nonsaturating.

These results are of crucial importance because they imply that the MAX phases are compensated conductors and a two-band conduction model is operative. In the low-field limit of the two-band model, the following applies:

I (j = - = e(nJ1n + PJ1p) (3)

p

I1p = cJ.Ji2 = J1nJ1p np(Pn + pp)2 B2 (4) Po (J1nn+ppp)2

(p;p - J1~n) RH = 0 (5)

e(ppp + Pnn)

where B is the magnetic field. There are thus four unknowns: the concentration of electrons and holes, 11, p, and their mobilities Iln and J1p, respectively. Given the small RH and Seebeck coefficient values. it is reasonable to assume that n ~ p in most cases. With that assumption, it is possible to solve for the four unknowns; the results are listed in Table 3.

Based on these results and those shown in Fig. 3, the following points pertaining to all MAX phases, except Ti4AlN3, are salient:

(i) Most of the room temperature resistivities of the MAX phases fall in the relatively narrow range of 0.2--0.7l!Q m. This is also true of other MAX phases not listed in Table 3 (Barsoum 2000). The resistivities of solid solution compositions, however, can be significantly higher.

(ii) For the most part, n ~ p and Iln ~ Ill'" The densities of electronic carriers fall in the relatively

1027 3narrow range of I to 3 X m . Note nand pare not related to N(Ep ).

(iii) At 4 K, the less defective samples, as measured by the RRR, have higher mobilities. The 4 K mobilities are also inversely proportional to N(Ep ).

(iv) dp/dT is proportional to N(Ep ).

The ternary Ti4AlN3 is somewhat unique in that its resistivity is more in line with semimetals than metals. The reason for this state of affairs is not clear at this time, but is most probably related to the fact that the sample tested was not stoichiometric, but closer to Ti4AlN2 .9 . The high defect concentration leads to a significantly reduced mobility (Table 3).

Solid solutions also result in reduced mobilities, but not equally. Substitutions on the A-sites appear to have little effect on resistivity (Finkel et al. 2004); substitutions on the M-sites, however, have a much more dramatic effect (Barsoum et al. 2002b).

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Table 3 Summary of room temperature resistivity results, mobilities of electronic carriers, and their densitites.

300K mobilities (m2 y- 1s-l) Carrier density (1027m-3)

Compound P (].lOrn) Pn Pp 11 P References

Ti3SiC2 0.22 0.005 0.006 2.5 2.5 Ti3Sio.5Geo.5C2 0.27 :::::0.005 :::::0.005 2 2 Finkel et al. (2004) Ti3GeC2 0.26 0.009 0.008 1.5 1.5

Ti3AIC2 0.39 0.0046--0.0042 0.0054---().003 1.5-1.6 1.5-2 Ti~IN3 2.61 0.00034 7 Finkel et al. (2003)

Ti2AIC 0.36 0.0090 0.0082 1.0 1.0 Y2AIC 0.26 0.0046 0.0039 2.7 2.7 Hettinger et al. (2005) Cr2AIC 0.74 0.0034 0.0036 1.2 1.2 Nb2AIC 0.39 0.0038 0.0031 2.7 2.7

TiCo.95 1-1.6 0.0012-0.0017 0.24---() .4 Barsoum et at. (2000d)

Substitutions on the X-sites have an effect that is only observed if the concentration of defects, presumably vacancies and displaced atoms, in the end-members are low.

5. Thermal Properties

5.1 Thermal Conductivities

Before discussing the thermal conductivities of the MAX phases, it is instructive to briefly review the theory of thermal conductivity in solids. The thermal conductivity, Kth, is given as

Kth = K e + Kph (6)

where h'e and Kph are, respectively, the electronic and phonon contributions to Kth. K e can be estimated from the Wiedemann-Franz law, that is,

LoT K e =- (7)

P

where Lg is the classic Lorenz number, 2.45 x \0- W Q K2. Using the electrical reslstlVlty values (Table 3) and their temperature-dependencies (not shown), it is straightforward to calculate Ke from Eqn. (7) and, Kph from Eqn. (6).

The temperature dependencies of the MAX phase K'S are plotted in Fig. 4(a); the corresponding phonon contributions are shown in Fig. 4(b). The room temperature results are listed in Table 4, together with the corresponding parameters for near-stoichiometric TiC", TiN", and NbC" for comparison. From these results, it is reasonable to conclude the following:

(i) All MAX phases are essentially good thermal conductors because they are good electrical conductors.

6

(ii) For the non AI-containing MAX phases, Kph« Ke (Table 4).

(iii) The AI-containing MAX phases are decent phonon conductors (Fig. 4(b)). The best phonon conductors at room temperature are Ti3AIC2 and Y2AIC; the worst is Nb2AIC.

(iv) MAX-phase solid solutions totally suppress Kph. This is true of substitutions on the A-sites (Fig. 4(b)). Along the same lines, at all temperatures, and similar to their MX counterparts (Williams 1971), the more Kph is suppressed, the more defective the samples. For example, in the M2AIC phases, a correlation exists between the quality of the crystal, as measured by RRR, and Kph (Hettinger et al. 2005).

Stiff, lightweight solids with high Debye temperatures are typically good phonon conductors. Given the rigidity of some of MAX phases, for example, ThSiC2, the fact that phonon conductivity is suppressed is somewhat surprising. As discussed in more detail elsewhere (Barsoum 2000), this result can be attributed to the scattering efficiency of the A-group atoms that tend to play the role of a "rattier" in these structures. Rattlers are atoms that vibrate about their equilibrium position more than other atoms (Keppens et al. 1998, Sales et al. 1999). Analysis of high-temperature (up to 1200°C) neutron diffraction spectra has shown that Si is indeed a rattler in Ti3SiC2 (Barsoum et al. 1999b, Barsoum 2000).

The situation for Al is more ambiguous. The results for Ti4AIN3, over the same temperature range, have shown that while the vibrational amplitudes of the Al atoms are greater than those of Ti or N (Barsoum et al. 2000e), the differences are not as large as in the case of Si. It thus appears that Al is


50

,.~ 40 ~ E

~ f' 30 > u = "0 <= o u 20

(;j

E v..c::... 10

50 100 150 200 250 300 (a) Temperature (K)

35

30 ~,. ~

25E

~ C :§ 20 u = "0 <= 150 u <= 0 <= 0 10..c:: c..

5

0 0 50 150100 200 250 300

(b) Temperature (K)

Figure 4 Temperature dependence of thermal conductivities of select MAX phases: (a) total thermal conductivity and (b) phonon contribution to total thermal conductivities. The data points and their corresponding MAX phase are color coded to match each other.

better bound, and thus less of a rattler, in the MIl+1AIC, ternaries, which partially explains why Kph

is not negligible in these compounds. Probably, the most convincing evidence for this hypothesis is to compare Kph for the isostructural compounds, Ti3SiC2 and Ti3AIC2. Based on the RRR values that are higher for Ti3SiC2, and the peak heights of the curves shown in Fig. 4(b), it is reasonable to conclude

that the Ti3SiC2 sample tested had less defects than Ti3AIC:> And yet at room temperature, Kph for the former is ~ 5 times smaller than for the latter (Fig. 4(b». Given the similarities of their elastic properties, and almost identical molecular weights and Debye temperatures (Table 2), it is obvious that Si is a much more potent phonon scatterer than AI.

In general, beyond AI, increasing the atomic number of the A-group element results in significant phonon scattering (e.g., compare ThInC with Ti2AIC in Table 4).

5.2 Thermal Expansion

The thermal expansion coefficients, TECs, of the MAX phases fall in the narrow range of 8 to lOx 10-6 K- 1 (Table 5). A correlation exists between the TECs of the ternaries and the corresponding MX binaries (Barsoum 2000, EI-Raghy et al. 2000). For example, the TECs of the Hf-containing MAX phases are lower than those containing Ti, which in turn are lower than Cr2AIC. For comparison, the TECs of HfC. TiC, and CrlC~ are 6.6 x 10-6 K-1, 7.4 X 10-6 K-I, and 10.5 x 10-6 K-I, respectively (Pierson 1996). Somewhat surprisingly, given their plastic anisotropy, the anisotropies in their thermal expansions (Barsoum 2000) and compressibilities (Onodera et al. 1999, Manoun et al. 2004a, 2004b, 2005) are relatively mild.

5.3 Thermal Stability

The MIl+1AXIl ternaries do not melt but decompose peritectically according to the following reaction:

(8)

The decomposition temperatures vary over a wide range; from ~ 850°C for Cr2GaN (Farber and Barsoum 1999) to above 2300 cC for Ti3SiC2 (Du et al. 2000). The decomposition temperatures of the Sncontaining ternaries range from 1200 °C to 1400 °C (EI-Raghy et al. 2000). It is important to note that the decomposition temperature is a function of many variables, the most important of which is oxygen contamination and/or other impurities (Tzenov et al. 2000).

5.4 Chemical Reactivit.v and Oxidation Resistance

The Mn+IXIl layers are chemically quite stable. By comparison, the A-group layers are relatively weakly bound and are thus the most reactive species. For example, heating Ti3SiC2 in a C-rich atmosphere results in the loss of Si and the formation of TiC, (EI-Raghy and Barsoum 1998). When the same compound is placed in molten cryolite (Barsoum et al. 1999a) or molten Al (EI-Raghy et at. 2001) essentially

7


Table 4 Summary of room temperature thermal conductivity (WmK-- 1

) results for a number of ternary carbides, nearstoichiometric TiC" and NbCx '

Compound Kth Ke References

Ti3SiC2 34 33 (97%) 40

TbGeC2 38 38 (100%) Ti3AIC2 40 21 (52%) Ti,AIN2.9 12 2.8 (23%) ThAIC 33 20.5 (62%)

46 20 (43%) V2AIC 48 29 (61 %) Cr2AIC 23 9 (39%) Nb2AIC 29 19 (66%)

23 23 (100%) TiNbAlC 16.6 9.4 (56%) Nb2SnC 17.5 17.5 (100%) Ti2InC ~26.5 26.5 (100%) TiHfInC ~20 20 (100%) Hf2InC ~26.5 26.5 (100%) TiC 33.5 12 (36%) TiCo.96 14.4 7.35 (50%) NbC, 14c 21 a

a Lo<2.45 x 1O-8 WQKc .

Table 5

~ 1 (3%)

19 (42%) 9.2 (77%) 12.5 (38%) 26 (57%) 19 (39%) 14 (61 %) 10 (34%)

7.2 (43%)

21.5 (64%) 7.05 (50%)

Barsoum et al. (1999) Finkel et al. (2004) Finkel et al. (2004) Finkel et al. unpublished Barsoum et al. (2000c) Hettinger et al. (2005) Barsoum et al. (2000a) Hettinger et al. (2005)

Barsoum et at. (2002b)

Barsoum et al. (2000b) Barsoum et at. (2002a)

Taylor (1961) Lengauer et al. (1995) Pierson (1996)

Summary of dilatometric thermal expansion values for select MAX phases ( x 106 K -1).

Compound TCE Compound TCE Compound TCE

Ti2AlC 8.8 Ti2AlN 8.2 Ti2AINo.5Co.s 8 Ti3SiC2 9.1 Ti3AlC2 9.0 Ti4AlN2.9 9.7 Ti3Al(C,Nh 7.0 Ti3(Sios,Geo.s)C2 9.3 Cr2AlC 12.0 Ti2SnC 10 Zr2SnC 8.3 Nb2SnC 7.8 Hf2SnC 8.1 Zr2PbC 8.2 HfzPbC 8.3 NbzAlC 7.5 (Nbos,Tio.shAlC 8.5 TizInC 9.5 (Tio.s,Hfo.shlnC 8.6 Hf2InC 7.6

The uncertainity for most values is ±O.2.

the same reaction occurs: the Si escapes and TiCx forms. In some cases, for example, Ti2InC, vacuum at elevated temperatures is sufficient to result in the loss of the A-group element and the formation of TiC, (Barsoum et al. 2002a).

Given their excellent high-temperature mechanical properties (Barsoum and Radovic 2004), some of the MAX phases are being considered candidates for a number of high-temperature applications, both structural and nonstructural. Since air is to be used, however, their oxidation resistance is of paramount importance. Early reports on Ti3SiC3 suggested it was oxidation-resistant to temperatures as high as 1400 °C (Barsoum et at. 1997). At this time, however, it appears that the highest temperature at which

ThSiC3 can be used continuously in air is ~ 900°C (Barsoum et al. 2003).

The most promising MAX phase to date, however, with superb oxidation resistance is Ti2AIC (Sundberg et al. 2004). After 10 000 cycles from 1350 °C to room temperature, a thin, adherent protective 15 /-lm Ab03 layer was found. The formation of Al20 3 is the key to high-temperature oxidation protection. It is worth noting that the formation of Ab03 is another example of the reactivity of the A-group element vis-a-vis the Mn+lX" blocks. Note that alumina forms despite the fact that the Al concentration is half that of Ti, another reactive metal. Wang and Zhou (2003) also reported the formation of alumina layers in Ti3AIC2, where the Al concentration is one third that of Ti.

8


In general, the oxidation of the MAX phases occurs according to the following reaction:

Mll+lAXn + b02 = (n + 1)MOx / n+1 + AO,. + nX02h- x - y

For example, the oxidation of Ti3SiC2 results in the formation of an outer pure rutile, Ti02, layer and an inner rutile and Si02 layer. Even in the case of Till+1AIC, the formation of a continuous alumina layer is a function of the purity of the samples. Impure samples or those with high contents of TiC tend to form Ah03 and rutile, rather than a pure layer of Ah03 (Barsoum 2001, Barsoum et al. 2001), Ti2InC forms Ti02 and In203, the Sn-containing ternaries, Sn02, etc. (Chakraborty et al. 2003).

6. Concluding Remarks

Some of the physical properties of the MAX phases, such as thermal expansion, elastic properties, and thermal conductivity, have much in common with their respective MX binaries. Their electronic structure and transport, however, are more akin to those of the transition metals themselves.

The unique combination of properties possessed by the MAX phases---ease of machinability, low friction, thermal and structural stability, good thermal and electrical conductivities-render them attractive for many applications such as rotating electrical contacts and bearings, heating elements, nozzles, heat exchangers, tools for die pressing, among many others. Many of these applications are currently being field-tested and are at various stages of development.

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physical properties of max phases

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