論文

先進セラミックス研究センター年報（2016）. Vol. 5, 1‑11

Structural Basis for the Anisotropic Thermal Expansion of Aluminum
Titanate, Al2TiO5, at Elevated Temperatures
Alexandra Doncieux*, Keisuke Ninomiya, Nobuo Ishizawa, Toshitaka Ota and Marc Huger*
Advanced Ceramics Research Center, Nagoya Institute of Technology,
10-6-29, Asahigaoka, Tajimi, Gifu 507-0071, JAPAN*ENSCI, Centre Européen de la Céramique, 12, rue Atlantis,
87068 Limoges Cedex, FRANCE
Evolution of the undoped and Mg-doped Al2TiO5 crystal structures at elevated temperatures up to ~1300 K was investigated by
the single-crystal X-ray diffraction technique. The compounds crystallize in the pseudobrookite-type [4c]M1[8f]M22O5 structurewith the space group Cmcm, containing crystallographically independent M1 site at the Wyckoff position of 4c and M2 site at 8f
for the metal atoms. The structural formula was found to be [4c][Al0.615(3)Ti0.385(3)][8f][Al0.693(2)Ti0.307(2)]2O5 for the undoped Al2TiO5 and[4c][Al0.616(9)Ti0.384(9)][8f][Al0.562(4)Ti0.373(4)Mg0.065(10)]2O5 for the Mg-doped one from the population analysis of the metal atoms. The

mean thermal expansion coefficients were approximately ­3.8 × 10­6 along the a-axis, 11.0 × 10­6 along the b-axis and 20.0 ×
10­6 along the c-axis. During heating, the tunnels running along the c-axis in the structure change shape gradually with acharacteristic buckling deformation of the chevron-shaped pillars composed of metal-oxygen bonds, resulting in an expansion of
the tunnel along all directions perpendicular to the a-axis and the associated Poisson contraction along the a-axis. The large
anisotropy in thermal expansion of the compounds, especially the negative thermal expansion along the a-axis, was thus
explained from atomistic point of view.
Keywords: Al2TiO5, Mg-doped Al2TiO5, high-temperature structures, anisotropic thermal expansion, Poisson deformation

1. Introduction

2. Experimental

Crystals of aluminum titanate (tieilite) Al2TiO5 adopt
an Fe2TiO5 pseudobrookite-type structure [1, 2]. Sinteredceramics of Al 2TiO 5 and related ones are known to
exhibit a low thermal expansion, which is an important
property for the thermal shock resistant materials for theindustrial applications [3–7]. The relationship between
the macroscopic thermal expansion behaviour and themicroscopic evolution of atomic arrangement in the
structure, however, has not been well clarified since thepioneering work by Morosin and Lynch in 1972 [8]. The
present study thus aims to afford structural information
at elevated temperatures through the in-situ singlecrystal X-ray diffraction experiments in order toestablish the structural basis for the anisotropic thermal
expansion in Al2TiO5. The Al2TiO5 ceramics are usuallysynthesized with cation dopants such as Mg, since thepure compound possesses a eutectoid decomposition
temperature around 1553 K [3, 9], and isthermodynamically unstable at room temperature. The
present study, therefore, also involves the hightemperature experiments on the Mg-doped Al2TiO5 anddiscusses the effect of Mg-doping on the structural
evolution.

The undoped Al 2 TiO 5 sintered sample (AT) was
synthesized by pressing the spray-drying ceramic
powders (TM-20P, Marusu Co., Ltd.) in a mold and thensintering the material at 1873­1923 K for 16 h. The Mgdoped Al2TiO5 sintered sample (ATM) was prepared by
the coauthors ʼ group in France [10], by sintering a
mixture of Al2O3, TiO2 and MgO powders in a molar
ratio of 0.406:0.525:0.069 at 1873 K for 2 h. The molar
ratio corresponds to 85.5 mol% Al2TiO5 + 14.5 mol%
MgTi2O5. Compositions of crystals were analyzed by theelectron backscattering diffraction (EBSD) techniqueusing JSM-7001FF scanning electron microscope(JEOL, Co., Ltd.). Chemical impurities of Si, Fe and Ca
were detected in both samples but their amounts were
negligibly small for the quantitative analysis.
Determination of the Mg content in ATM is detailed in
Section 3.2.
Diffraction experiments were carried out using asingle-crystal X-ray diffraction apparatus (Mo Kα) witha two-dimensional charge-coupled device detector(Bruker Smart Apex II). The temperature of the crystal
was controlled in a hot nitrogen gas stream using acrystal heater attached to the diffractometer. The sample―1―Structural Basis for the Anisotropic Thermal Expansion of Aluminum Titanate, Al2TiO5, at Elevated Temperatures

Table 1. Summary of structure refinements of the undoped

Al2TiO5 (sample ATh_11).
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Figure 1 . Octahedral drawing of the pseudobrookite-type

M11M22O5 structure viewed along the c-axis.

determination were then carried out at 322, 631, 943 and1254 K in the 2θ range up to 100 , taking approximately
9 h at each temperature.
Similar diffraction experiments were carried out forATM. A fragment was chosen from the ATM sinteredsample and ground into a sphere of approximately 90
μm in diameter (sample name: ATMh_19). The hightemperature experiments were executed at 296, 373,
580, 787, 995 and 1254 K during heating, and 995, 787,
580, 373 and 296 K during cooling, in this sequence.
After this first run, the second run was executed at 296,
631, 995 and 1306 K during heating, and at 631 (1st),631 (2nd), 373 (1st), 373 (2nd) and 296 K duringcooling. These heating and cooling processes in the tworuns were named as heat 1, cool 1, heat 2 and cool 2,
respectively. The two runs and the doubled experiments
at 631 and 373 K in the cooling process of the second
run were necessary to examine the hysteresis of thethermal expansion behavior of the a-axis in ATM, as
described in Section 3.3. Structure determination of theATMh_19 sample was also carried out at eachtemperature, but most experiments were done in a rapid
way within 3 h in the range 2θ < 60°for the primary
purpose of the determination of unit cell dimensions.
Therefore, the data qualities of ATMh_19 were slightly
inferior to those of ATh_11.
All the frame data were processed by SAINT [11].
The absorption correction was carried out using
SADABS [12]. Structures were solved by SUPERFLIP[13] and refined by Jana2006 [14]. Structures werevisualized by DIAMOND [15] and VESTA [16]. Fullstructure data about ATh_11 and ATMh_19 are available
as supplementary information in the format of thecrystallographic information file (CIF).

temperature was calibrated using a cubic polynomial.
A rectangular fragment (sample name: ATh_11) waschosen from AT and used for the high-temperatureexperiments. The fragment was surrounded by six welldeveloped faces; (0 0 ±1), (0 ±1 0) and (±1 0 0) in
terms of the orthorhombic Cmcm lattice, with the longest
edge of ~250 μm along the a-axis. Unit cell dimensions
were measured at 10 different temperatures between 322
and 1254 K during heating and cooling processes,
respectively. Intensity data collections for structure―2―

Alexandra Doncieux, Keisuke Ninomiya, Nobuo Ishizawa, Toshitaka Ota and Marc Huger

The chemical composition of the Mg-doped Al2TiO5
becomes, accordingly, Al 1.74(4)Ti 1.13(2)Mg 0.13(2)O 5. The
Al 2 O 3 :TiO 2 :MgO molar ratio in this composition
corresponds to 0.408:0.531:0.061, which was very close
to the ratio of 0.406:0.525:0.069 of the powder mixture
before sintering, as stated in Section 2 . Since thechemical impurities were found to be negligibly small
by the EDS analysis, a stoichiometric composition of
Al2TiO5 was assumed for the undoped Al2TiO5 crystal(AT).
It is known that that Al3+, Ti4+ and Mg2+ can occupy
M1 and M2 sites in the formula [4c]M11[8f]M22O5 [8].
Therefore, the general structural formula can be writtenas[4c][Ala1Tit1Mgm1]1[8f][Ala2Tit2Mgm2]2O5,
where a1, t1, m1 are the population variables of Al, Ti
and Mg at M1, respectively, and a2, t2 and m2 are thoseat M2. Assuming that M1 and M2 sites are fully
occupied:
a1 + t1 + m1 = 1(1)
a2 + t2 + m2 = 1(2)
From the comparison between the structural andchemical formulae,
a1 + 2 a2 = 2 ­ 2x
(3)
t1 + 2 t2 = 1 + x(4)m 1 + 2 m2 = x(5)These five equations (1)–(5), among which any four
are independent, have six population variables, a1, a2,
t1, t2, m1 and m2. Therefore, the structural formula canbe expressed using any two variables, for example, m2(the Mg population at M2) and t2 (the Ti population atM2), as[4c][Al­2x+2t2+2m2Ti1+x­2t2Mgx­2m2]1[8f][Al1­t2­m2Tit2Mgm2]2O5.
Since x = 0, i.e., m1 = m2 = 0, in the undoped Al2TiO5,
the structural formula can be written as a function of asingle population variable,[4c][Al2t2 Ti1­2t2]1[8f][Al1­t2Tit2]2O5.
In the least-squares structural refinements of the Mgdoped Al2TiO5 (ATM), the population of Mg at M1 site
(i.e. m 1) became always slightly negative at all thetemperatures. Accordingly, m1 was fixed at zero, and m2
was constrained at x /2 = 0.065(10) in the further
refinements. The structural formula of ATM was writtenas,[4c][Al­x+2t 2 Ti1+x­2t2]1[8f][Al1­t 2­x/2Tit2 Mgx/2]2O5.
The final structural compositions were determined byaveraging the values determined at all temperatures, as[4c][Al0.615(3)Ti0.385(3)][8f][Al0.693(2)Ti0.307(2)]2O5
for the undoped Al2TiO5 (AT), andFigure 2. Distribution of metal atoms at the M1 (4c) and M2(8 f ) sites in the undoped Al 2TiO 5 at 322 K and Mg-doped
Al2TiO5 at RT. Two pie charts are drawn for M2 in accord withthe ratio in number of the M1 and M2 sites. The ionic radii of
Al3+, Ti4+ and Mg2+ in six-ford coordination with oxygens areshown at the bottom.

3. Results and discussion
3.1 Refinements of X-ray diffraction data

The structure of pseudobrookite-type M3O5 has two
crystallographically independent metal atom sites, M1
and M2, which are located, respectively, at the 4c and 8f
Wy c k o ff p o s i t i o n s o f t h e s p a c e g r o u p C m c m .
Conventionally, the metal atoms are described to be
surrounded by six oxygens forming rather deformed
octahedra, as shown in Fig. 1. The results of structurerefinements of the sample ATh_11 at 322, 631, 943 and1254 K during heating are summarized in Table 1.
3.2 Crystal chemical formula

A sample was selected from the fragments of Mgdoped Al 2 TiO 5 ceramics (ATM), and its chemicalcomposition was investigated on twelve different points/
areas by the EBSD/EDS analysis.
When x MgO is doped to Al 2TiO 5, the compoundshould have a chemical formula Al 2­2xTi 1+xMg xO 5 inorder to satisfy the electrically neutral condition under
the assumptions:i) The Al, Ti, Mg and O atoms take the formaloxidation states of +3, +4, +2 and ­2, respectively.
ii) The lattice is perfect, having neither interstitialatoms nor lattice vacancies.
The EBSD/EDS analysis on ATM indicated that themole fraction of xMgO is 0.13(2), where the number inparentheses indicates the estimated standard uncertainty.
―3―

Structural Basis for the Anisotropic Thermal Expansion of Aluminum Titanate, Al2TiO5, at Elevated Temperatures[4c][Al0.616(9)Ti0.384(9)][8f][Al0.562(4)Ti0.373(4)Mg0.065(10)]2O5
for the Mg-doped Al2TiO5 (ATM).
The distribution of metal atoms at the M1 and M2
sites is illustrated in Fig. 2. An important tendency isthat a relatively-large [17] and low-valent Mg2+ stays
away from the M1 site and goes to the M2 site
preferentially. The reason why the Mg dopant prefers theM2 site is discussed in Sections 3.5 and 3.6.
Recent single-crystal X-ray diffraction study [18]reported the structural composition of the melt-quenched
Al2TiO5 as[4c][Al0.626(7)Ti0.374(7)]1[8f][Al0.687(3)Ti0.313(3)]2O5.
The populations of Al/Ti at M1 and M2 agreed withthose in the present sample (AT) with excellent
precisions. On the other hand, Skala et al. [9] carriedout a high-temperature neutron and X-ray powder
diffraction study on Al 2 TiO 5 and reported thecomposition as

3.3 Cell dimensions

Changes in the unit cell dimensions with temperatureare shown in Fig. 4. The data points obtained from theAT sample showed a good coincidence at eachtemperature, irrelevant to the heating or coolingprocesses. Thermal expansion of the unit cell dimensions(Å) of AT can be approximated using a second orderpolynomial as a function of temperature T (K);a = 3.5958(5) ­ 0.204(13)×10­4 T + 0.64(8)×10­8 T 2,
b = 9.4100(15) + 0.82(4)×10­4 T + 1.7(2)×10­8 T 2,
c = 9.6059(17) + 1.41(5)×10­4 T + 3.8(3)×10­8 T 2.
Morosin & Lynch [8] reported the mean thermal
expansion coefficients (MTECs) of Al2TiO5 as ­1.4×10­6,
9.8×10­6, and 20.6×10­6 along the a-, b- and c-axes,
respectively, based on their single-crystal X-ray
diff raction experiments at RT and 873 K. The
corresponding MTEC values in the present study,
calculated from the above polynomials at 293 and 873 K,
are ­3.8×10­6, 11.0×10­6, and 20.0×10­6 along the a-,b- and c-axes, respectively. The agreements between
these values in the two studies seem fine, considering thepotential impurities and lattice defects in crystals.
The Mg-doped Al2TiO5 (ATM) had a slightly larger
unit cell dimensions compared with AT, mainly due to[Al0.588(3)Ti0.412(3)]1[8f][Al0.712(4)Ti0.288(3)]2O5,
which is slightly different from the results of the two
single-crystal studies aforementioned.
Skala et al. [9] also reported that the Al/Ti ratio at M1
and M2 in Al2TiO5 changes with temperature suggesting
a possible metal atom exchange over the two sites athigh temperatures. Temperature dependence of the Al
population at M1 and M2 in AT and ATM used in thepresent study is shown in Fig. 3. The population of Al
at M1 tended to increase marginally during heating, andvice versa at M2. However, the exchange population
was much smaller and less significant in the present
study compared with the literature [9].
[4c]the size effect of cations as shown in Fig. 2. In addition,a curious behavior was found in the temperaturedependence in the cooling process of the first run, as
shown in Fig. 4 (a); the a-length showed significantly
small values during cooling compared with those during
heating. This stands in contrast against the otherobservations in which the heating/cooling process

Figure 3. Aluminum population at (a) M1 and (b) M2 sites in the pseudobrookite-type [4c]M11[8f]M22O5 structure. The open circles

connected by black polyline are data obtained from the undoped Al2TiO5 during heating. The other scattered marks are those obtained
from the Mg-doped Al2TiO5 during the first heating/cooling and the second heating/cooling processes. The relationship between thecolour marks and processes is shown in the legend.
―4―Alexandra Doncieux, Keisuke Ninomiya, Nobuo Ishizawa, Toshitaka Ota and Marc Huger

Figure 4. Changes in the unit cell dimensions with temperature; (a) a-length, (b) b-length, (c) c-length, and (d) unit cell volume. The

open circles connected by polyline are data obtained from the undoped Al2TiO5 during heating (red) and cooling (blue). The otherscattered marks are those obtained from the Mg-doped Al2TiO5 during the first heating/cooling and the second heating/coolingprocesses. The relationship between the colour marks and processes is shown in the legend.

dependency was almost undetectable. It should be noted,
however, that a similar hysteresis in thermal expansionof the a-length has been observed in MgTi2O5 by theneutron powder diffraction [19] (the original unit cell
vectors are converted to fit into the present study),
although this phenomenon remains inexplicable.

elevated temperatures, as detailed in Sections 3.5 and
3.6.
3.5 M‒O Distances

Changes in the M–O interatomic distances withtemperature are shown in Fig. 7. The metal atoms at theM1 and M2 sites are surrounded by six oxygens withfour short (1.8~1.9 Å) and two long (~2.1 Å) M–O
distances. The most conspicuous temperature change in
the M1–O distance is that the longer two M1–O bonds
become much longer at elevated temperatures whereas
the four short M1–O bonds stay at almost the samelengths throughout the temperature range between RT
and ~1300 K. This suggests a gradual decrease inoxygen coordination number of M1 from six toward
four at elevated temperatures. The displacement arrowsof M1 and O1 atoms during heating, as shown in Fig. 6,
also indicate a tendency of tetrahedralization(M1O12O22) during heating. It is noted that the decrease

3.4 Atomic coordinates

Changes in atomic coordinates with temperature areshown in Fig. 5. As listed in Table 1, the refinable
positional parameters of the Cmcm pseudobrookite-type
structure are limited to the y-coordinates of M1, M2, O1,
O2 and O3 atoms and the z-coordinates of M2, O2 andO3 atoms. Among these parameters, the y-coordinates of
M1 and O1 showed the most conspicuous temperaturechange. The directions of these changes during heating
are shown in Fig. 6 by arrows. The changes in the
y-coordinates of M1 and O1 are closely related to thetetrahedralization of the M1 coordination polyhedron at―5―Structural Basis for the Anisotropic Thermal Expansion of Aluminum Titanate, Al2TiO5, at Elevated Temperatures

Figure 5. Temperature changes in the y-coordinates of (a) M1 (M1y), (b) M2 (M2y), (c) O1 (O1y), (d) O2 (O2y) and (e) O3 (O3y),and the z-coordinates of (f) M2 (M2z), (g) O2 (O2z) and (h) O3 (O3z). The open circles connected by polyline are data obtained fromthe undoped Al2TiO5 during heating. The other scattered marks are those obtained from the Mg-doped Al2TiO5 during the first heating/cooling and the second heating/cooling processes. The relationship between the colour marks and processes is shown in the legend.

presence of such short M2–M2 distance is the reason
why the low-valent Mg2+ compared with Al3+ and Ti4+
prefers M2 in ATM with the formula,[4c][Al0.616(9)Ti0.384(9)] [8f][Al0.562(4)Ti0.373(4)Mg0.065(10)]2O5,
to reduce the electrostatic repulsion between the M2 pairat the 8f sites. This short M2–M2 interatomic distancealso plays an important role in the thermal expansion of
the compound, which is discussed in Section 3.7.
Finally, it should be stressed that no strange thing
happened such that any M–O bonds became shorter atelevated temperatures. All the M–O bonds are elongatedduring heating though the degrees of elongation are
different with each other. This is of course a naturalin coordination number of M1 in pseudobrookite-type
structure is actually evidenced in MgTi2O5 at ~1623 K[19]. A rapid increase in the two long M-O bonds is also
observed for M2. However, it is noted that one M2–O2
short bond (~1.9 Å) also shows an increasing tendency
during heating similar to the two long M2–O bonds,
which is slightly different from the case for M1.
The tetrahedral drawing of the pseudobrookite-type
structure is illustrated in Fig. 8, where the long M1–O
and M2–O bonds (> 2 Å; dashed lines in Fig. 6) areneglected. Note that a pair of M2 atoms forms the edgesharing tetrahedra with a very short M2–M2 interatomic
distance of ~2.8 Å, as indicated by the yellow line. The―6―

Alexandra Doncieux, Keisuke Ninomiya, Nobuo Ishizawa, Toshitaka Ota and Marc Huger
Figure 6. The room-temperature structure of the

Figure 8. Tetrahedral drawing of the pseudobrookite-type

pseudobrookite-type M11M22O5 (Al2TiO5) projected along a

structure, neglecting two long M–O bonds (dashed lines in Fig.

direction close to the a-axis. The thermal ellipsoids are drawn6) from the MO6 octahedra. The very short M2–M2 interatomic

at 90% probability level. The shorter ( ≤ 2 Å) and longer (> 2

distance of ~2.8 Å between the edge-sharing M2O4 tetrahedraÅ) M – O bonds are drawn by solid and dashed lines,

is shown by the yellow line.

respectively. The arrows attached to M1 and O1 indicate thedirection of displacements of these atoms during heating.

tendency in most crystals, but it could be rather
surprising if we recall once again that the length of thea-axis of this compound becomes short (!) at elevatedtemperatures. This can be explained from the Poisson
effect on the tunnel deformation in the structure, which
is detailed in Section 3.8.

3.6 Comparison of MO6 octahedra

Four geometrical indices, the mean M–O interatomic
distance (MD) in Å, the octahedral volume (OV) in Å3,
the quadratic elongation (QE) with no dimension, andthe angle variance (AV) in square degree, are taken into
consideration for comparison. The latter two indices aredefined by Robinson et al. [20]: the quadratic elongation

Figure 7. Temperature changes in the (a) M1–O and (b) the M2–O interatomic distances. The open circles connected by polyline aredata obtained from the undoped Al2TiO5 during heating. The other scattered marks are those obtained from the Mg-doped Al2TiO5during the first heating/cooling and the second heating/cooling processes. The relationship between the colour marks and processes isshown in the legend.
―7―

Structural Basis for the Anisotropic Thermal Expansion of Aluminum Titanate, Al2TiO5, at Elevated Temperatures(QE) is a measure to evaluate the distribution of M–O
distances (if all bonds have the same length, then QE =1), the angle variance (AV) is a measure to evaluate the
distribution of O–M–O angles (if all angles are the same,then AV = 0). Temperature changes in these four indices
are shown in Fig. 9. The main differences between the
M1O6 and M2O6 octahedra are as follows.
・The mean M1–O distance is larger than the mean
M2–O while the octahedral volume of M1O 6 issmaller than that of M2O6 in both AT and ATM.
This is somewhat confusing, and should be treatedcarefully.
・ The quadratic elongation shows that the M–O
distances in M1O6 octahedron are rather scatteredcompared with M2O6 in both AT and ATM.
・ The angle variance suggests that the M1O 6
octahedra are largely deformed compared withM2O6 octahedra in both AT and ATM.

The geometrical features of the octahedral
deformation are basically similar in AT and ATM.
3.7 M‒M Distances

Changes in the M–M distance between the nearby M
atoms with temperature are shown in Fig. 10. The six
M–M interatomic distances from the shortest increase as
a function of temperature. As mentioned already, the M2
site has a very short M2–M2 interatomic distance of~2.8 Å, making a clear difference between the second
coordination shells around M1 and M2. The presence ofsuch short M2–M2 distance also prevents thetetrahedralization of coordination polyhedron at M2 incontrast with M1 at elevated temperatures.
3.8 Negative thermal expansion

From atomistic point of view, the anisotropic thermal
expansion property of Al 2 TiO 5 arises from the

Figure 9. Temperature changes in the four geometrical indices to characterize the M1O6 and M2O6 octahedra; (a) mean M–O

interatomic distance, (b) octahedral volume, (c) quadratic elongation, and (d) angle variance. The open circles connected by polyline
are data obtained from the undoped Al2TiO5 during heating. The other scattered marks are those obtained from the Mg-doped Al2TiO5during the first heating/cooling and the second heating/cooling processes. The relationship between the colour marks and processes isshown in the legend.
―8―Alexandra Doncieux, Keisuke Ninomiya, Nobuo Ishizawa, Toshitaka Ota and Marc Huger

Figure 10. Temperature changes in the six M–M distances from the shortest around (a) M1 and (b) M2. The open circles connected bypolyline are data obtained from the undoped Al2TiO5 during heating. The other scattered marks are those obtained from the Mg-doped
Al2TiO5 during the first heating/cooling and the second heating/cooling processes. The relationship between the colour marks andprocesses is shown in the legend.

around the center of the unit cell and walled by M2 andO2 with capping O3. The latter cage contains an M24
rectangle, as indicated by dashed black lines in the
figure. The M24 rectangle consists of two M2 pairs
having the shortest M2–M2 distance of ~2.8 Å and theother two pairs having the distance corresponding to thea-length of ~3.6 Å.
Temperature evolution of the chevron angles of theM1–O1–M1 and M2–O3–M2 pillars in the tunnel are
shown in Fig. 12. All the chevron angles of the pillars
in the tunnel belong to either one of the two. These
angles decrease monotonically with increasing
temperature. This is a typical indicator how the pillars of
the tunnel buckle, and the tunnel clearance along thedeformation of a tunnel-like cavity running along thec-axis, which has not been pointed out in the literature to
our knowledge. As shown in Fig. 11 (a), the tunnel has
a flat ceiling and floor composed of M and O atoms at x
= ±1/2, with a clearance, i.e., height of the tunnel,
corresponding to the a-length. The side walls of thetunnel are composed of the M–O–M or O–M–O pillars
with a chevron shape, buckling outside toward directions
perpendicular to the a-axis.
The view along a direction close to the a-axis in Fig.
11 (b) indicates that the two types of cages alternate in
the tunnel along the c-axis; i) irregularly shaped cage
located around 0 < z < 1/2 and walled by M1, M2, O1,
O2 and O3, and ii) pseudo-tetragonal cage located

Figure 11. A structural tunnel running in the pseudobrookite-type M11M22O5 structure, viewed along a direction close to (a) the c-axis

and (b) the a-axis. The chevron angles about O1 in the M1–O1–M1 pillar and that about O3 in the M2–O3–M2 pillar are shown by
round arrows in (a).
―9―Structural Basis for the Anisotropic Thermal Expansion of Aluminum Titanate, Al2TiO5, at Elevated Temperatures

Figure 12. Temperature dependence of the M1–O1–M1 (left-axis) and M2–O3–M2 (right-axis) angles of the chevron-shaped
pillars of the tunnel in Al2TiO5. The open circles connected bypolyline are data obtained from the undoped Al2TiO5 during
heating. The other scattered marks are those obtained from Mgdoped Al2TiO5 during the first heating/cooling and the second
heating/cooling processes. The relationship between the colour
marks and processes is shown in the legend.

a-axis becomes small during heating. It should be
reminded that the M1–O1 and M2–O3 bonds
constituting the pillars stay almost unchanged in length(actually, very mildly elongated) during heating (Fig. 7).
A schematic illustration of the deformation of tunnel
in Al2TiO5 at elevated temperatures is shown in Fig. 13,
where the unit cell dimensions are exaggerated for view
purpose in the high-temperature structure while thefractional coordinates and the anisotropic displacement

parameters are taken exactly from the data at 1254 K.
All the M–O bonds are elongated during heating in orderto mitigate the electrostatic repulsion of electron clouds
between the nearby atom pairs, in association with theenhanced atomic thermal vibration. As a result, thetunnel expands primarily along the c-axis and secondly
along the b-axis by the elongation of the M–O bonds onthe ceiling and floor of the tunnel. This tendency isstrengthened by the repulsion between the M2 pair on(100), facing each other with the shortest M2–M2
distance of ~2.8 Å in the center cage (Fig. 11 (b)). The
structural evolution takes place minimally under the
restriction of the space group symmetry. The larger
expansion of the c-length rather than the b-length is ofcourse a result of all-atom displacements, but would beconceivable since the tunnels run in parallel along thec-axis.
When the tunnel expands toward all directions
perpendicular to the a-axis, it contracts along theirnormal, i.e., the a-axis, by the Poisson effect [21]. From
the atomistic point of view, the contraction occurs by thepillar buckling; extrusion of atoms at the middle of thechevron-shaped pillars toward outside of the tunnel.
From the macroscopic point of view, on the other hand,the phenomenon manifests itself in the contraction of thesubstance along the a-axis. It should be once recalledthat this atomistic deformation occurs compatibly withthe elongation of ʻallʼ M–O bond-lengths during heating.
4. Conclusion

Al2TiO5 and related compounds are known to show aFigure 13. Schematic diagram to show changes in the shape of the tunnel in Al2TiO5 with temperature. Deformation directions during

heating are shown by black arrows.
― 10 ―

Alexandra Doncieux, Keisuke Ninomiya, Nobuo Ishizawa, Toshitaka Ota and Marc Huger

large anisotropy in their thermal expansion properties. In
the present study, the structural basis for this anisotropy
has been explained through the in-situ single-crystal
X-ray diffraction experiments carried out in thetemperature range up to ~1300 K. The structure contains
tunnels running along the c-axis, which change shape
gradually with increasing temperature. The change inthe shape of tunnel has two features; one is a buckling
deformation of the chevron-shaped pillars composed ofmetal–oxygen bonds in association with the expansionof the tunnel along all directions perpendicular to thea-axis, and the other is the associated Poisson
contraction along the a-axis. The former expansion is
not isotropic on all directions perpendicular to the a-axis,
but anisotropic due to a complexity in atomic
arrangement constituting the tunnel. The overall
atomistic deformation results in the negative
macroscopic mean thermal expansion coefficients ofapproximately ­ 3.8 ×10 ­6 along the a-axis, and, in
contrast, positive and relatively large values ofapproximately 11.0×10­6 along the b-axis and 20.0×
10­6 along the c-axis.
The population analysis of the metal atom sites of M1
at 4c and M2 at 8f in the space group Cmcm revealed
that the structural formula of the undoped Al2TiO5 canbe written as[4c][Al0.615(3)Ti0.385(3)][8f][Al0.693(2)Ti0.307(2)]2O5,
and that of the Mg-doped one is[4c][Al0.616(9)Ti0.384(9)][8f][Al0.562(4)Ti0.373(4)Mg0.065(10)]2O5.
The site preference of metal atoms with different
oxidation states and different ionic sizes is rather
complicated but can be essentially explained from theiradaptability to the geometry of coordination polyhedra
around M1 and M2, and the electrostatic repulsion
between the M2–M2 pair separated by a very shortdistance of ~2.8 Å.
A hysteresis in the negative thermal expansion of thea-length was observed for the Mg-doped Al2TiO5 sample
in the first heating/cooling processes, which was
detected neither in the second heating/cooling processes
in the same sample nor in the undoped Al2TiO5 sample.
Considering that a similar hysteresis has been reported
in the literature, however, it indicates a presence ofconcealed phenomenon intrinsic to this substance, while
the details are left for future study.

Center, Nagoya Institute of Technology, for the electronbackscattering diffraction and the energy dispersive
X-ray spectroscopy analyses.
References[1] L. Pauling, Z. Kristallogr., 73 (1930) 97.
[2] A.E. Austin, C.M. Schwartz, Acta Crystallographica, 6(1953) 812-813.
[3] E. Kato, K. Daimon, J. Takahashi, J. Am. Ceram. Soc., 63(1980) 355-356.
[4] Y. Ohya, Z. Nakagawa, K. Hamano, J. Am. Ceram. Soc.,
70 (1987) C-184-C-186.
[5] K. Daimon, J. Ceram. Soc. Jpn., 98 (1990) 365-369.
[6] C. Babelot, A. Guignard, M. Huger, C. Gault, T. Chotard, T.
Ota, N. Adachi, Journal of Materials Science, 46 (2011)
1211-1219.
[7] Y. Ohya, S. Yamamoto, T. Ban, M. Tanaka, S. Kitaoka, J.
Eur. Ceram. Soc., 37 (2017) 1673-1680.
[8] B. Morosin, R.W. Lynch, Acta Crystallogr. Sect. B, 28(1972) 1040-1046.
[9] R.D. Skala, D. Li, I.M. Low, J. Eur. Ceram. Soc., 29 (2009)67-75.
[10] A. Gallet-Doncieux, P. Michaud, M. Huger, T. Chotard, N.
Ishizawa, T. Ota, Proceedings of the Unified International
Technical Conference on Refractories (UNITECR 2011),
Kyoto, (2011) 3211.
[11] Bruker, SAINT and Smart Apex II, Bruker AXS Inc.,
Madison, Wiskonsin, USA., (2007).
[12] Bruker, SADABS, TWINABS. Bruker AXS Inc., Madison,
Wisconsin, USA. (2001).
[13] L. Palatinus, G. Chapuis, J. Appl. Crystallogr., 40 (2007)
786-790.
[14] V. Pet㶣í㶜ek, M. Dušek, L. Palatinus, Z. Kristallogr., 229(2014) 345.
[15] K. Brandenburg, H. Putz, Crystal Impact GbR, Postfach
1251, D-53002 Bonn, Germany, Version 4.3 (2016).
[16] K. Momma, F. Izumi, J. Appl. Crystallogr., 44 (2011)
1272-1276.
[17] R.D. Shannon, C.T. Prewitt, Acta Crystallogr., B25 (1969)
925-946.
[18] S.T. Norberg, N. Ishizawa, S. Hoffmann, M. Yoshimura,Acta Crystallogr. Sect. E, 61 (2005) i160-i162.
[19] A.R. Lennie, K.S. Knight, C.M.B. Henderson, Am.
Mineral., 92 (2007) 1165-1180.
[20] K. Robinson, G.V. Gibbs, P.H. Ribbe, Science, 172 (1971)
567-570.
[21] S.D. Poisson, Ann. Chim. Phys., 36 (1827) 384-387.

5. Acknowledgement

We are grateful to the staff members, especiallyHisashi Hibino, of the Advanced Ceramics Research― 11 ―