MAX phases: Bridging the gap between metals and ceramics
Figure 1. Scanning electron microscopy of the fractured surface
in Ti2AlC after dynamic testing of at a strain rate of 2400 s–1
showing typical laminated nature and deformation of individual grains by kinking.
bulletin
cover story
MAX phases: Bridging
the gap between metals
and ceramics
By Miladin Radovic and Michel W. Barsoum
(Credit: Credit: Radovic and Benitez; TAMU.)
T
The MAX phases are a new and exciting class of carbides
and nitrides that bridge the gap between properties typical
of metals and ceramics, while offering fundamentally new
directions in tuning the structure and properties of ceramics
for emerging applications.
20
he term “MAX phases” was coined
in the late 1990s and applies to a
family of 60+ ternary carbides and nitrides
that share a layered structure as illustrated in
Figures 1 and 2. They are so called because
of their chemical formula: Mn+1AXn —where
n = 1, 2, or 3, where M is an early transition
metal, A is an A-group element (specifically, the subset of elements 13–16), and X is
carbon and/or nitrogen, Figure 2.1 Nowotny
and coworkers2, 3 discovered most of these
phases in powder form roughly 40 years ago.
However, Barsoum and El-Raghy’s4 report
in 1996 on the synthesis of phase-pure bulk
Ti3SiC2 samples and their unusual combination of properties catalyzed renewed interest
in them. Since then, research on the MAX
phases has exploded. According to ISI, to
date around 1,200 papers have been published
on one MAX phase alone, Ti3SiC2, with
roughly half of those published in the past six
years.
www.ceramics.org | American Ceramic Society Bulletin, Vol. 92, No. 3
Crystal structure and atomic
bonding in the MAX phases
The MAX phases are layered hexagonal crystal structures (space group
P63/mmc) with two formula units per
unit cell, as illustrated in Figure 2, for
structures with n equal 1 to 3. The
unit cells consist of M6X-octahedra
with the X-atoms filling the octahedral
sites between the M-atoms, which are
identical to those found in the rock
salt structure of the MX binaries. The
octahedra alternate with layers of pure
A-elements located at the centers of
trigonal prisms that are slightly larger,
and thus more accommodating of
the larger A-atoms. When n = 1, the
A-layers are separated by two M-layers
(Figure 2(a)). When n = 2, they are
separated by three layers (M3AX2 in
Figure 2(b)). When n = 3, they are
separated by four layers (M3AX2 in
Figure 2(c)). MAX phases with more
(Credit: Credit: Radovic; TAMU.)
The growing interest results from the
unusual, often unique, properties of the
MAX phases. Like their corresponding binary carbides and nitrides (MX),
the MAX phases are elastically stiff,
good thermal and electrical conductors, resistant to chemical attack, and
have relatively low thermal expansion
coefficients.1 Mechanically, however,
they cannot be more different. They
are relatively soft and most are readily
machinable, thermal shock resistant
and damage tolerant. Moreover, some
are fatigue, creep, and oxidation resistant. At room temperature, they can be
compressed to stresses as high as 1 GPa
and fully recover on removal of the
load, while dissipating approximately
25 percent of the mechanical energy.6
At higher temperatures, they undergo
a brittle-to-plastic transition (BPT),
above which they are quite plastic even
in tension.5
This article gives an overview of the
salient properties of the MAX phases
and of the status of our current understanding. Some of their potential applications also are highlighted. For a thorough review of the large body of work
on MAX phases, the reader is referred
to a recently published book1 and a
number of excellent review articles.7–15
Figure 2. Unit cells of the Mn+1AXn phases for (a) n = 1 or M2AX, (b) n = 2 or
M3AX2, and (c) n = 3 or M4AX3 phases, and (d) M, A, and X elements that form
the MAX phases.
complex stacking sequences, such as
M5AX4, M6AX5, and M7AX6 also have
been reported.8,16
In addition to the “pure” MAX
phases that contain one of each of the
M, A, and X elements highlighted in
Figure 2(d), the number of possible
solid solutions is quite large. Solid solutions have been processed and characterized with substitution on1
• M sites, e.g., (Nb,Zr)2AlC,
(Ti,V)2AlC, (Ti,Nb)2AlC,
(Ti,Cr)2AlC, (Ti,Hf)2InC, and
(Ti,V)2SC;
• A-sites, e.g., Ti3(Si,Ge)C2, and
Ti3(Sn,Al)C2; and
• X-sites,17 e.g., Ti2Al(C,N) and
Ti3Al(C,N)2.
American Ceramic Society Bulletin, Vol. 92, No. 3 | www.ceramics.org
Interestingly, some of solid solutions exist even when one of the end
members does not. The number of
MAX phases and their solid solutions
continues to expand. The discovery of
new phases has advanced significantly
through the combination of experimental and theoretical density functional theory (DFT) approaches.1,18–20
For example, ab-initio studies recently
extended the family of the MAX phases
to compounds with magnetic properties that contain later transition-metal
substitutions on the M sites, such as
(Cr,Mn)2AlC.21
A large body of work devoted to
DFT calculations of the electronic
structures and chemical bonding in the
21
(a)
(b)
Temperature (K)
Temperature (K)
Figure 3. Temperature dependence of (a) electrical conductivity31 and (b) thermal
conductivity of select MAX phases.32
MAX phases22-28 shows that
• Similar to the MX phases, MAX
phase bonding is a combination of
metallic, covalent, and ionic bonds;
• The M and X atoms form strong
directional covalent bonds in the M-X
layers that are comparable to those in
the MX binaries;22, 27, 28
• M–d–M–d metallic bonding dominates the electronic density of states at
the Fermi level, N(EF); and
• In most MAX phases, the M–A
bonds are relatively weaker than the
M–X bonds.
Given the similarities between some
aspects of the atomic bonding in the
MX and MAX phases it is not surprising they share many common attributes
and properties, such as metal-like electrical conductivities, high stiffness values, thermal stability, and low thermal
expansion coefficients.
(a)
(b)
(Credit: Sandvik Materials Technology, Sweden.)
Physical properties
Figure 4. (a) Ti2AlC-based heating element resistively heated to 1,450°C in
air. (b) Micrograph of the Al2O3 oxide
layer after 10,000 thermal cycles up to
1,350°C showing no spallation or cracking of the oxide layer.33
22
Most of the MAX phases are excellent electrical conductors, with electrical resistivities that mostly fall in the
narrow range of 0.2–0.7 µΩ·m at room
temperature.1,10 Like other metallic
conductors, their resistivities increase
with increasing temperatures (Figure
3(a). Ti3SiC2 and Ti3AlC2 conduct
better than titanium metal. Even more
interesting and intriguing, many of the
MAX phases appear to be compensated
conductors, wherein the concentrations of electrons and holes are roughly
equal, but their mobilities are about
(Credit: Adapted from Ref. 31, 32.)
Resistivity (µΩ·m)
Thermal conductivity (W/m·K)
MAX phases: Bridging the gap between metals and ceramics
equal, too.10
Several MAX phases, most notably
Ti3SiC2, have very low thermoelectric
or Seebeck coefficients.10,29 Solids with
essentially zero thermopower can, in
principle, serve as reference materials
in thermoelectric measurements, for
example, as leads to measure the absolute thermopower of other solids.
The optical properties of the MAX
phases are dominated by delocalized
electrons.30 Magnetically, most of them
are Pauli paramagnets, wherein the
susceptibility is, again, determined by
the delocalized electrons and, thus,
is neither very high, nor temperature
dependent.31
Thermally, the MAX phases share
much in common with their MX
counterparts, that is, they are good
thermal conductors because they are
good electrical conductors. At room
temperatures their thermal conductivities (Figure 3(b)) fall in the 12–60 W/
(m·K) range.1,10 The coefficients of
thermal expansion (CTE) of the MAX
phases fall in the 5–10 µK–1 range and
are relatively low as expected for refractory solids.15 The exceptions are some
chromium-containing phases with
CTEs in the 12–14 µK–1 range.
At high temperatures, the MAX
phases do not melt congruently but
decompose peritectically to A-rich
liquids and Mn+1Xn carbides or nitrides.
Thermal decomposition occurs by the
loss of the A element and the formation of higher n-containing MAX
phases and/or MX. Some MAX phase,
such as Ti3SiC2, are quite refractory
with decomposition temperatures above
2,300°C.1
Because of their excellent electrical,
thermal and high-temperature mechanical properties, some MAX phases
currently are being considered for
structural and nonstructural high-temperature applications. Their oxidation
resistance, however, determines their
usefulness in air. In most cases, MAX
phases oxidize according to Eq (1).
Mn+1AXn+bO2=
(n+1)MOx/n+1+AOy+XnO2b-x-y(1)
Consequently, their oxidation resis-
www.ceramics.org | American Ceramic Society Bulletin, Vol. 92, No. 3
(a)
(c)
Mechanical Properties
Despite similarities between the
physical properties of the MX and
MAX phases, the differences between
their mechanical properties is striking. The MX phases are some of the
hardest solids known. They are brittle,
nonmachinable, damage intolerant, and
susceptible to thermal shock. In sharp
contradistinction, the MAX phases are
exceedingly damage tolerant and thermal shock resistant, and most are readily machinable. This stark difference
in behavior comes down to two words:
mobile dislocations.
At this time is it fairly well established that basal plane dislocations
(BPD)—and only BPDs— are abundant, mobile, and able to multiply
in the MAX phases at ambient temperatures.34 However, because the
dislocations are constrained to the
basal planes, the number of slip systems is fewer than the five needed for
polycrystalline ductility. Therefore,
the MAX phases occupy an interesting middle ground between metals and
ceramics, in that they are pseudoductile
under confined deformations or high
temperatures, but are brittle at room
temperature, especially in tension and
thin form.
(b)
(Credit: Barsoum;Drexel University.)
tance depends on nature of the oxides
that form. The most oxidation-resistant
MAX phase is Ti2AlC, because it forms
a stable and protective Al2O3 layer
that can withstand thermal cycling up
to 1,350°C for 10,000 cycles without
spallation or cracking (Figure 4).33 The
oxidation resistance of Cr2AlC also is
superb because it also forms a protective
Al2O3 layer, however, the oxide spalls
off during thermal cycling.
Elastically, the MAX phases are
quite stiff, with near-isotropic room
temperature Young’s and shear moduli
in the 178–362 GPa and 80–142 GPa
ranges, respectively.7, 14 Because the
densities of some of the MAX phases
are as low as 4–5 g/cm3, their specific stiffness values can be quite high.
For example, the specific stiffness of
Ti3SiC2 is comparable to Si3N4 and
roughly three times that of titanium
metal.
Figure 5. Transmission electron microscopy of (a) dislocation wall consisting of basal
plane dislocations and (b) area containing kink band in Ti3SiC2 after compression at
room temperature.35 (c) Schematic of the formation of incipient kink band, mobile dislocation walls kink bands, and delaminations. Red grains are “hard” grains, and blue
grains are “soft” grains with the basal planes favorably oriented for easy slip.6
The BPDs arrange themselves either
in walls (that is, high- or low-angle
grain boundaries (Figure 5(a)), in arrays
or dislocation pileups (not shown)
parallel to the basal planes. Confining
the dislocations to the basal planes, in
turn, results in an important micromechanism that is quite ubiquitous in
the MAX phases at all lengths scales,
viz., kink band (KB) formation (Figures
1 and 5(b)6, 9). When the MAX phases
are loaded, initially the “soft” grains—
those with basal planes favorably oriented for easy slip (blue grains in Figure
3(c))—deform and, in turn, cause
the “hard” grains (red grains in Figure
5(c)), to develop incipient kink bands
(IKB). The latter are coaxial dislocation loops that, as long as their ends are
not sundered, are spontaneously and
fully reversible. With further increase
in applied load, if the polycrystal does
not fail by shear band formation or
fracture, the IKBs result in mobile dislocation walls (MDW) and ultimately
American Ceramic Society Bulletin, Vol. 92, No. 3 | www.ceramics.org
permanent kink bands (Figure 3(c)). At
higher temperatures, the grain boundaries are soft and the IKBs devolve into
MDWs and KBs that lead to delamination at the individual grain level and
considerable plasticity.
Although the MAX phases are quite
stiff, they respond to cyclic loading,
whether compression6 or tension5, with
spontaneous, fully reversible, strainrate-independent hysteretic stress-strain
loops (Figure 6(a). The shape and
areas of these loops depend strongly on
grain size (Figure 6(a) but weakly on
the number of cycles. In other words,
they are quite fatigue resistant. It follows that a significant portion of the
mechanical energy—about 25 percent
at 1 GPa in the case of Ti3SiC2—dissipates during each cycle.6 At this
time, IKBs (Figure 5(c)) that form
during loading and annihilate during
unloading are believed to account for
this nonlinear elastic (or hysteretic)
effect. Above the BPT temperature, the
23
MAX phases: Bridging the gap between metals and ceramics
2–8 GPa. They are thus
softer than most structural
ceramics, but harder than
most metals.1, 9
The room temperature
fracture toughness (KIc)
values—that range from 5
to almost 20 MPa·m1/2—
are quite respectable when
compared with other
monolithic ceramics. The
MAX phases also exhibit
R-curve behavior, i.e., KIc
increases with increasing
crack length. For examEngineering strain
Strain
ple, for coarse-grained
Ti3SiC2, KIc increases from
Figure 6. (a) Typical cyclic compressive stress–strain curves for Ti3SiC2 with two grain sizes. The loops
8.5 to 11 MPa·m1/2, with
overlap after one and one hundred cycles.6 (b) Engineering stress–strain curves for 2-mm cubes of
highly oriented samples of Ti3SiC2. The inset cube shows a schematic sample with the chevron texture
increasing crack size.37
35
and the orientation of the basal planes in individual grains depicted by thin lines.
The high values of KIc and
R-curve behavior result from the formaas ideal plastic solids (Figure 6(b))
stress-strain loops are open and strain
tion of plastically deformable bridging
even at room temperature, with strain
rate dependent but become smaller
ligaments (Figures 7(a) and (b)) and
that exceeds 10 percent.35 By contrast,
with increasing cycles, that is, cycling
the crack-arresting properties of kink
when the slip planes are parallel to the
hardening takes place. The practical
boundaries. The latter two mechanisms
applied load (loaded along the x-axis
implication of these phenomena for
are unique to the MAX phases.
in inset of Figure 6(b)) and deformastructural applications cannot be overThus far, Ti3SiC2 is the only MAX
tion by ordinary dislocation glide is
estimated because the MAX phases
phase on which cyclic fatigue studsuppressed, the sample yields at higher
can dissipate a large portion of harmful
ies have been conducted. The studies
stresses by KB formation. In this case,
structural vibrations or acoustic loads,
show that fatigue crack growth threshconsiderable strain softening occurs
even at high temperatures.
olds were comparatively higher than
because the kink bands rotate basal
The room-temperature ultimate
those for typical ceramics and some
compressive strengths of polycrystalline planes in such a way as to induce shear
metals (e.g., 300-M alloy steel).37,38
band formation.35
MAX phases range from 300 MPa to 2
At 1,200°C, which is above the BPT,
GPa and depend strongly on composithe crack-growth rate versus stress
Softer than structural ceramics
tion and grain size. Like typical ceramintensity curves show three distinctive
Unlike their MX counterparts, the
ics, their room-temperature flexural and
regions emerging under the same condiMAX phases are relatively soft and
tensile strengths are lower than their
tions, which suggests delamination or
exceptionally damage tolerant. The
compressive strength.1,7,14 For example,
grain-boundary decohesion as possible
Vickers hardness values of polycrystalthe compressive and tensile strengths
mechanisms.
line MAX phases fall in the range of
of Ti3SiC2, with 5-µm grains, are 1,050
All MAX phases tested to date go
MPa and 300 MPa, respectively. At
room temperature, they fail in a brittle
manner. Nevertheless, they fail gracefully—samples do not shatter but, rather, fail along planes inclined 30°–40°
relative to compression axis.
The stress–strain response of highly
oriented (textured) microstructures
loaded in compression is quite different
from polycrystalline behavior, because
(b)
the former exhibit strong plastic anisot- (a)
ropy. For example, when the basal
planes are oriented such that slip occurs Figure 7. SEM images of fatigue cracks in Ti3SiC2. The images also show bridging
ligaments, which plastically deform as a function of crack propagation. Arrow
along the basal plane (along the z-axis
denotes direction of crack propagation.36, 37
in inset of Figure 6(b)), they behave
(b)
24
(Credit: Barsoum; Sci. Mater.)
(Credit: Barsoum; JACERS.)
(Credit: Adapted from Barsoum, et. al., Ref. 6, 35.)
Engineering stress (MPa)
Stress (MPa)
(a)
www.ceramics.org | American Ceramic Society Bulletin, Vol. 92, No. 3
American Ceramic Society Bulletin, Vol. 92, No. 3 | www.ceramics.org
(Credit: Sandvik Materials Technology, Sweden.)
(Credit: Barsoum; Wiley.)
Retained flexural strength (MPa)
Stress (MPa)
through a BPT. The
(a)
(b)
BPT temperature varies
from phase to phase, but
for many of them tested
so far falls between
1,000°C and 1,100°C.
Below BPT, the ultimate strengths of the
MAX phases depend
weakly on temperature
and deformation rate.1,5
Above BPT, their
stress–strain response
depends strongly on
temperature and, more
importantly, deformaTemperature (k [log t (h)+20]3 10–3)
Quench temperature (°C)
tion rate. More speFigure 8. (a) Creep properties of select metallic, intermetallic alloys, and Ti3SiC2 plotted as stress-to-rupture
cifically, when loaded
versus the Larson–Miller parameter. The solid black line represents compression results, and the dashed
above their BPT tem1
7
peratures at high defor- line, tension results. (b) Postquench flexural strength versus quench temperature of select MAX phases.
mation rates, they fail in
from temperatures as high as 1,200°C
patented, and widely used. For exama brittle manner. However, when loaded
ple, Sandvik Materials Technology
into ambient-temperature water (see
slowly, they can be plastically deformed
(Hallstahammar, Sweden) has manuFigure 8(b)).
at 1,200°C in air—to strains greater
factured Ti3SiC2 and Ti2AlC powders
Lastly,
arguably
the
most
characthan 25 percent even in tension—before
and parts since the late 1990s under its
teristic
trait
of
the
MAX
phases
and
5
failing in a graceful manner. Because KIc
MAXthal brand (Figure 9(b)).
what
truly
sets
them
apart
from
other
39
drops above the BPT temperature, we
MAX phases in any form usually are
structural
ceramics
or
high-temperature
can categorically rule out the activation
fabricated from elemental powders and/
alloys
is
the
ease
with
which
they
can
37
of additional slip systems. A sufficient
or binary carbides, and, thus, their price
be machined (Figure 9(a)). The MAX
condition needed to explain the BPT is
is determined mostly by the price of
phases
can
be
readily
machined
with
the onset of a temperature-dependent
those powders. Currently, Sandvik sells
regular
high-speed
tool
steels
or
even
grain-boundary decohesion-strength,
Ti3SiC2 and Ti2AlC powders at around
manually
with
a
hacksaw.
delamination strength, or both.
$500 per kg. This price is significantly
Although the MAX phases are
higher than the price of Al2O3, SiC,
Potential
applications
considered good candidate materiand Si3N4 powders used to make other
Before discussing potential applicaals for high-temperature applications,
structural and high-temperature ceramtions, availability and cost have to be
there are only a few published reports
ics. However, pressureless sintering in
put in perspective. There are many
on their creep response. The few that
inert atmospheres can yield fully dense
methods for processing the MAX phasexist for Ti3SiC2 and Ti2AlC suggest
MAX phase parts without using sinteres as bulk materials, powders, porous
that creep is independent of grain size,
ing aids. More importantly, fully dense
foams, coatings, and thin films.1,8,14
resulting from dislocation creep togethMAX phases are readily machined to
Some of the methods are quite mature,
er with significant accumulation of
voids and microcracks.40 Nevertheless,
(a)
(b)
creep resistance of the MAX phases is
quite good when compared with other
known creep-resistant materials (Figure
8(a)), and they offer great promise for
future improvements.
Another important property of the
MAX phases is their exceptional thermal shock resistance. Unlike typical
ceramics, the MAX phases not only
do not shatter after quenching, and,
Figure 9. (a) A MAX phase billet machined by a lathe. (b) Ti2AlC and Ti3SiC2 powders
in some cases, their residual flexural
and parts fabricated by Sandvik Heating Technology, Sweden, and commercially availstrengths increase even after quenching able under the trade name MAXthal 211 and MAXthal 312.
25
MAX phases: Bridging the gap between metals and ceramics
very high tolerances, which should render the cost of final parts competitive
compared with other structural ceramics. Furthermore, the price of powders
should drop as demand increases. The
development of reaction synthesis
methods from less-expensive precursor
powders, such as TiO2 instead of pure
titanium and TiC would constitute a
major breakthrough.
Given the remarkable set of properties that the MAX phases exhibit,
especially their high-temperature stability, thermal shock resistance, damage
tolerance, good machinability, and
the exceptional oxidation resistance of
some of them, it is not surprising that
they were first targeted for high-temperature applications. The most promising MAX phase for high temperature
applications is Ti2AlC because of the
relatively low cost of raw materials
needed, low density, superb oxidation
resistance (that is immune to thermal
cycling), and crack-healing capabilities,41 among others. This combination of properties together with good
electrical conductivity led Kanthal to
evaluate heating elements made from
Ti2AlC. (Figure 5(a)). The company
also tested MAX phases for gas burner
nozzles and industrial die inserts. Other
evaluated applications—such as hightemperature foil bearings, glove and
condom molds, tooling for dry drilling
of concrete (3-ONE-2, LLC), and nonstick cookware—took advantage of low
friction and good wear resistance of the
MAX phases and their composites.1
Besides high-temperature applications, there may be electrical applications. For example, the first commercial
application of Ti3SiC2 was as sputtering targets for electrical contact deposition (Impact Coatings, Sweden). They
also were investigated for electrochemical chlorine production electrodes.42
The way forward
Our understanding of the structure
and properties of the MAX phases
has come a long way in less than two
decades. Typically, it takes between 10
and 20 years from “discovery” to appli-
26
cations.43 The recent intense interest in
the MAX phases indicates that applications are forthcoming. This is important—applications keep a research field
vital.
The understanding we have achieved
to date not withstanding, there remain
outstanding scientific questions to
answer and technological hurdles to
overcome. Questions under exploration
by more than a dozen research groups
around the world include
• Can we extend the number of
known MAX phases to M, A, and X
elements not shown in Figure 2(c)?
• What are the effects of the lattice
defects on thermal and electrical properties? (As well as the related question
of non-stoichiometry and its effect on
properties?)
• To what extent can properties be
tailored by solid solutions or by controlling the microstructure?
• Why are they so thermal shock
resistant?
• What determines their critical
resolved shear stresses?
• Can they be processed using more
affordable precursors?
• What benefits can be gained by
combining the MAX phases with metals44 or ceramics in composite materials?
Acknowledgments
This work was partially funded by
grants from the NSF (DMR-0503711)
and the ARO (W911NF-07-1-0628
and W911NF-11-1-0525) to Drexel
University and grants from the AFOSR
(FA9550-09-1-0686) and NSF (CMMI1233792) to Texas A&M University.
About authors
Miladin Radovic is associate professor at the Department of Mechanical
Engineering and Materials Science and
Engineering Program at Texas A&M
University, College Station, Texas.
Michel W. Barsoum is distinguished
professor, Department of Materials
Science and Engineering, Drexel
University, Philadelphia, Pa. Contact:
mradovic@tamu.edu or barsoumw@
drexel.edu.
References:
M.W. Barsoum, MAX Phases: Properties
of Machinable Carbides and Nitrides. Wiley
VCH, 2013.
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N.J. Lane, M. Naguib, J. Lu, L. Hultman,
and M.W. Barsoum, “Structure of a new
bulk Ti5Al2C3 MAX phase produced by the
topotactic transformation of Ti2AlC,” J.
Eur. Ceram. Soc., 32 [Sep.] 3485–91 (2012).
16
T. Cabioch, P. Eklund, V. Mauchamp,
and M Jaouen, “Structural investigation of
substoichiometry and solid solution effects
in Ti2Al(Cx,N1−x)y” compounds. J Eur Ceram
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M. Dahlqvist, B. Alling, and J. Rosen,
“Stability trends of MAX phases from first
principles,” Phys. Rev. B, 81 [June] 104110
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18
T. Ouisse and D. Chaussende,
“Application of an axial next-nearestneighbor Ising model to the description of
Mn+1AXn phases,” Phys. Rev. B, 85 [Mar.]
(2012).
19
P. Eklund, M. Dahlqvist, O. Tengstrand, L.
Hultman, J. Lu, N. Nedfors, U. Jansson, and
J. Rosén, “Discovery of the ternary nanolaminated compound Nb2GeC by a systematic theoretical–experimental approach,”
Phys. Rev. Lett., 109 [July] 035502 (2012).
20
M. Dahlqvist, B. Alling, I. A. Abrikosov,
and J. Rosen, “Magnetic nanoscale laminates with tunable exchange coupling from
first principles,” Phys. Rev. B, 84 [Dec.]
220403 (2011).
21
N.I. Medvedeva, D.L. Novikov, A.L.
Ivanovsky, M.V. Kuznetsov, and A.J.
Freeman, “Electronic properties of Ti3SiC2based solid solutions,” Phys. Rev. B, 58
[Dec.] 16042–50 (1998).
22
G. Hug and E. Fries, “Full-potential electronic structure of Ti2AlC and Ti2AlN,”
Phys. Rev. B, 65 [Mar.] 113104 (2002).
23
G. Hug, M. Jaouen, and M.W. Barsoum,
“XAS, EELS, and full-potential augmented
plane wave study of the electronic structures
of Ti2AlC, Ti2AlN, Nb2AlC, and
(Ti 0.5,Nb0.5)2AlC,” Phys. Rev. B, 71, 24105
(2005).
24
Z.M. Sun and Y.C. Zhou, “Ab initio calculation of Ti3SiC2,” Phys. Rev. B, 60, 1441
(1999).
25
Z. Sun, R. Ahuja, S. Li, and J.M.
Schneider, “Structure and bulk modulus of
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M2AlC (M=Ti, V, and Cr) Appl Phys Lett,
83, 899 (2003).
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J.P. Palmquist, S. Li, P.O.A. Persson, J.
Emmerlich, O. Wilhelmsson, H. Hogberg,
M.I. Katsnelson, B. Johansson, R. Ahuja, O.
Eriksson, et. al. “M(n+1)AX(n) phases in the
Ti-Si-C system studied by thin-film synthesis and ab initio calculations,” Phys. Rev. B,
70, 165401 (2004).
Z.M. Sun, S. Li, R. Ahuja, and J.M.
Schneider, “Calculated elastic properties of
M2AlC (M = Ti, V, Cr, Nb, and Ta),” Solid
State Commun., 129 [Feb.] 589–92 (2004).
28
H.I. Yoo, M.W. Barsoum, and T. El-Raghy,
“Ti3SiC2: A material with negligible thermopower over an extended temperature
range,” Nature, 407, 581–2 (2000).
29
30
S. Li, R. Ahuja, M.W. Barsoum, P. Jena,
and B. Johansson, “Optical properties of
Ti3SiC2 and Ti4AlN3,” Appl. Phys. Lett., 92,
221907 (2008).
31
P. Finkel, M.W. Barsoum, J.D. Hettinger,
S.E. Lofland, and H.I. Yoo, “Lowtemperature transport properties of nanolaminates Ti3AlC2 and Ti4AlN3,” Phys. Rev.
B, 67, 235108 (2003).
J.D. Hettinger, S.E. Lofland, P. Finkel, J.
Palma, K. Harrell, S. Gupta, A. Ganguly, T.
El-Raghy, and M.W. Barsoum, “Electrical
transpot, thermal transport and elastic
properties of M2AlC (M = Ti, Cr, Nb
and V) phases,” Phys. Rev. B, 72, 115120
(2005).
32
33
M. Sundberg, G. Malmqvist, A.
Magnusson, and T. El-Raghy, “Aluminaforming high-temperature silicides and carbides,” Ceram. Int., 30, 1899–904 (2004).
L. Farber, I. Levin, and M.W. Barsoum,
“High-resolution transmission electron
microscopy study of a low-angle boundary in
plastically deformed Ti3SiC2,” Philos. Mag.
Lett., 79 [Apr.] 163–70 (1999).
34
35
M.W. Barsoum and T. El-Raghy, “Roomtemperature ductile carbides,” Metall. Mater.
Trans. A, 30, 363–69 (1999).
36
D. Chen, K. Shirato, M.W. Barsoum,
T. El-Raghy, and R.O. Ritchie, “Cyclic
fatigue-crack growth and fracture properties
in Ti3SiC2 ceramics at elevated temperatures,” J. Am. Ceram. Soc., 84 [12] 2914–20
(2001).
C.J. Gilbert, D.R. Bloyer, M.W. Barsoum,
T. El-Raghy, A.P. Tomasia and R.O. Ritchie,
“Fatigue-crack growth and fracture properties of coarse and fine-grained Ti3SiC2,” Scr.
Mater., 42 [Apr.] 761–67 (2000).
37
propagation behavior of Ti3SiC2 synthesized
by pulse discharge sintering (PDS) technique,” Scri. Mater., 49, 87–92 (2003).
D. Chen, K. Shirato, M.W. Barsoum, T.
El-Raghy, and R.O. Ritchie, “Cyclic fatiguecrack growth and fracture properties in
Ti3SiC2 ceramics at elevated temperatures,”
J. Am. Ceram. Soc., 84, 2914 (2001).
39
M. Radovic, M.W. Barsoum, T. El-Raghy,
and S. Wiederhorn, “Tensile creep of finegrained (3–5 μm) Ti3SiC2 in the 1000–1200
degrees C temperature range,” Acta Mater.,
49 [Nov.] 4103–12 (2001).
40
G.M. Song, Y.T. Pei, W.G. Sloof, S.B. Li,
J.T.M. De Hosson, and S. van der Zwaag,
“Oxidation-induced crack healing in
Ti3AlC2 ceramics,” Scr. Mater., 58, 13–16
(2008).
41
V.D. Jovic and M.W. Barsoum,
“Electrolytic cell and electrodes for use in
electrochemical processes,” US Pat. No.
7,001,494.
42
Materials Genome Initiative for Global
Competitiveness, National Science and
Technology Council, Washington, DC,
2011.
43
W.J. Wang, V. Gauthier-Brunet, G.P. Bei,
J. Bonneville, A. Joulain, and S. Dubios,
“Powder metallurgy processing and compressive properties of Ti3AlC2/Al composites,”
Mater. Sci. Eng. A, 530, 168 (2011). n
44
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