JOURNAL OF APPLIED PHYSICS 114, 083520 (2013)
Atomic-scale mechanism for pressure-induced amorphization of b-eucryptite
Badri Narayanan,1 Ivar E. Reimanis,1 and Cristian V. Ciobanu2,a)
1
Department of Metallurgical and Materials Engineering, Colorado School of Mines, Golden,
Colorado 80401, USA
2
Department of Mechanical Engineering and Materials Science Program, Colorado School of Mines,
Golden, Colorado 80401, USA
(Received 21 June 2013; accepted 13 August 2013; published online 29 August 2013)
We present here a reactive force field based metadynamics study of pressure-induced amorphization
in b-eucryptite, a lithium aluminum silicate that exhibits negative thermal expansion, i.e.,
volumetric contraction upon heating. From our simulations, we found that b-eucryptite amorphizes
under a moderate applied pressure of 3 GPa. A careful inspection of the amorphous phase showed
that it contains AlO3, AlO4, AlO5, and SiO4 polyhedra, indicating clear short-range order. We have
also identified the atomic-scale processes responsible for the amorphization of b-eucryptite. These
processes are (a) tilting and distortion of tetrahedra centered at Al/Si, (b) change in atomic
coordination around Al, and (c) disordering of Li atoms with the formation of Li-Li, Li-O, and
Li-O-Li linkages. We discuss our results in the context of a possible general link between negative
thermal expansion, radiation tolerance, and pressure-induced amorphization in flexible network
C 2013 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4819452]
structures. V
I. INTRODUCTION
Pressure-induced amorphization (PIA) in crystalline solids has been studied extensively over the past few decades
due to its commercial importance, such as in large-scale production of bulk glassy materials via grinding, ball milling,
and compression.1–6 PIA was first observed in ice;1 later,
numerous spectroscopic experiments and theoretical calculations have evidenced that PIA occurs in a wide variety of
crystals including pure elements (e.g., Si,7 Ge (Ref. 8)) and
compounds (e.g., oxides,9–11 silicates,2 tungstates,12–14 and
others).15–17 Recently, polyhedral network structures that exhibit negative thermal expansion (NTE) have drawn interest
because they undergo PIA at moderate pressures.6,12–14,18,19
More importantly, from a fundamental perspective, NTE and
PIA could both originate from the flexible nature of the
structural framework of the crystals.14,20
The hexagonal b-eucryptite, LiAlSiO4, with an anisotropic coefficient of thermal expansion (aa ¼ 7.26 106 K1
normal to crystallographic c-axis, ac ¼ 16:35 106 K1
parallel to c-axis)21 typifies the behavior of NTE materials. It
exhibits a slight volumetric contraction with increasing temperature over a wide temperature range (300 K–1400 K);21
this provides exceptional thermal shock resistance to beucryptite, making it suitable for a variety of applications
such as heat exchangers, telescopic mirror blanks, and highprecision optical devices.21–23 b-eucryptite is also known for
its one-dimensional Li ion conduction24–27 and for its radiation tolerance,28–30 which could lead to applications in Li-ion
batteries and nuclear breeder reactors. Owing to its technological relevance, b-eucryptite constitutes a suitable prototype
material for expanding our fundamental understanding of the
connection between NTE and PIA.
a)
Author to whom correspondence should be addressed. Electronic mail:
cciobanu@mines.edu
0021-8979/2013/114(8)/083520/9/$30.00
The crystal structure of b-eucryptite has hexagonal symmetry (space group P64 22) and can be thought of as a stuffed
derivative of b-quartz.21,31–37 It is composed of a network of
corner-linked SiO4 and AlO4 tetrahedra with significant
voids in between, voids in which lithium atoms reside forming channels parallel to the c-axis [Fig. 1]. Similar to other
NTE materials,12–14 the anomalous thermal behavior of beucryptite has been attributed to two processes (a) rotation
and distortion of the tetrahedral units (i.e., AlO4, SiO4) and
(b) spatial disordering of Li atoms.21,38–40 Interestingly, our
recent molecular dynamics (MD) simulations showed that
these same processes, along with changes in coordination
around Al/Si atoms enable b-eucryptite to retain its longrange crystalline order upon exposure to radiation.30
Furthermore, most of the Si atoms that lose their tetrahedral
O-coordination in the radiation-damaged structure were
found to recover upon thermal annealing.30 This finding suggests that the structural connection between NTE and PIA in
flexible network structures possibly extends to other phenomena, such as radiation tolerance.
In their recent high-pressure X-ray diffraction (XRD)
experiments, Zhang et al. found that b-eucryptite begins to
FIG. 1. Crystal structure of hexagonal ordered b-eucryptite projected (a)
along the c axis, and (b) along the a1 axis. The structure is composed of a
framework of corner-sharing AlO4 (gray) and SiO4 (orange) tetrahedra, with
Li atoms (purple) existing in channels parallel to the c axis. The black lines
outline the unit cell containing 12 formula units of LiAlSiO4 (84 atoms).
114, 083520-1
C 2013 AIP Publishing LLC
V
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083520-2
Narayanan, Reimanis, and Ciobanu
amorphize at pressures of 3–5 GPa via reconstructive transformations with significant changes in atomic coordinations,18,41 and suggested that PIA in b-eucryptite is possibly
assisted by mechanical instability and kinetic hindrance of
equilibrium phase transformations owing to reduced atomic
mobility at 300 K.18 Furthermore, recent nano-indentation
studies have revealed that the pressure-induced transition in
b-eucryptite is associated with an activation volume similar
to that of SiO4 and AlO4 tetrahedra.42,43 However, the
atomic-scale mechanisms that govern PIA in b-eucryptite
and the detailed structural characteristics of the amorphous
phase are still unclear.
To gain a better understanding of PIA in b-eucryptite,
we turn to atomistic simulations. The most commonly used
technique to understand the response of crystalline solids to
applied pressure is constant pressure MD simulation based
on classical force fields.17,44–46 Most of the pressure-induced
phase transitions are associated with energy barriers that are
significantly higher than thermal energy; it is highly unlikely
that such high barriers can be surmounted in MD simulations
within practical timescales at the experimentally observed
transition pressures.47–49 To circumvent this time-scale problem, we employ metadynamics simulations47,50,51 in which
structural transitions under pressure are explored by sampling a history dependent free-energy surface in the space of
a few relevant order parameters called collective variables
(CVs).47,50,51 Since this method does not require elevated
temperatures or pressures to accelerate the phase transition,
it can identify the lowest energy transition pathways.48
Metadynamics has been extensively used to study phase
transitions,48,52–55 e.g., Si,51,53 SiO2,52 and CdSe.48 More relevant to the present study, metadynamics has been used to
successfully determine the atomic-scale mechanisms responsible for reconstructive phase transition from anhydrous LiABW zeolite to c-eucryptite.54
In this article, we focus on examining PIA in beucryptite close to the experimentally known transition pressure18,41 using metadynamics coupled with MD simulations
based on a reactive force field. Our analysis of the structural
evolution showed that b-eucryptite undergoes PIA at an
applied pressure of 3 GPa. We have characterized the
obtained amorphous phase and found that it possesses significant short-range order while lacking crystalline long-range
order. Our structural analysis also indicates that there is a pronounced change in the O-coordination around Al atoms,
change which leads to the formation of AlO3 and AlO5 polyhedra that share edges with the SiO4 tetrahedra. Furthermore,
we have identified the mechanisms associated with the lowest
energy pathway for PIA in b-eucryptite, which are (a) tilting
and distortion of AlO4/SiO4 tetrahedra, (b) changes in atomic
coordination around Al resulting in the formation AlOx polyhedra (x ¼ 3 or 5), and (c) spatial disordering of Li atoms
forming new Li-Li, Li-O bonds, and Li-O-Li bridges.
The remainder of this article is organized as follows. In
Sec. II, we briefly describe the computational methodology
that we adopted to study the response of b-eucryptite to
applied pressure. The results concerning the detection of the
phase transition and the structural characterization of the
newly formed amorphous phase are described in detail in
J. Appl. Phys. 114, 083520 (2013)
Sec. III. We discuss these results to identify the mechanism
for PIA in b-eucryptite in Sec. IV, and draw comparisons
with the atomic scale processes that are known to occur in beucryptite in response to temperature changes and radiation
exposure. Finally, we summarize our results and highlight
the main conclusions in Sec. V.
II. METHODOLOGY
A. Solid-state phase transition by metadynamics
We have employed the metadynamics technique developed by Martonak and co-workers47,51 to explore structural
phase transitions in b-eucryptite under applied pressure.47,50,51
This approach involves a systematic exploration of the Gibbs
free energy surface in a space of the CVs to search for new
local minima. The CVs are chosen to be the periodicity vectors of the computation supercell, a, b, and c arranged in the
form of a matrix h ¼ (a b c), whose columns hold the supercell vectors. To simplify the analysis, h is constrained to be an
upper triangular matrix.47 The CVs are evolved in a steepestdescent manner via51
hnþ1 ¼ hn þ dh
/n
;
j/n j
(1)
where hn are the CVs at metadynamics
step n, dh is the step
n
size in the CV space, and j//n j gives the direction of the driving force /n at the nth metadynamics step. This driving force
is derived from a history-dependent Gibbs potential Gðhn Þ as
/n ¼ @Gðhn Þ
;
@hn
(2)
where Gðhn Þ is the sum of the thermodynamic free energy
Gt ðhn Þ and an artificial potential Gg ðhn Þ created by a superposition of gaussians centered at every hm accessed prior to
step n. Gg ðhn Þ can be written as
!
2
XY
½hnij hm
ij n
W exp Gg ðh Þ ¼
;
(3)
2dh2
m<n i;j
where the quantities W and dh are the height and width of
gaussians, respectively. The term Gg ðhn Þ prohibits the system
from revisiting previously explored configurations by filling
up the initial well of the Gibbs free energy, and in turn,
drives the system out of a local minimum. From Eq. (2), it is
clear that /n is the sum of two components (a) thermodynamic force Ft ðhn Þ ¼ @Gt ðhn Þ=@hn , and (b) gaussian force
Fg ðhn Þ ¼ @Gg ðhn Þ=@hn which can be easily derived from
Eq. (3). The ij element of Ft ðhn Þ can be expressed in terms
of average internal pressure tensor pn at step n and applied
pressure p as47
½Ft ðhn Þij ¼
@Gt ðhn Þ
¼ V n ½ðhn Þ1 ðpn pÞji ;
@hij
(4)
where Vn is the volume of the computational supercell at the
nth step given by V n ¼ detðhn Þ. pn is evaluated by equilibrating the configuration at the nth step in a relatively short conventional MD run with the supercell shape fixed at hn .
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083520-3
Narayanan, Reimanis, and Ciobanu
In practice, the metadynamics algorithm as outlined in
Eqs. (1)–(4) is implemented in two stages. The evolution
starts from an equilibrium configuration at the desired temperature T and pressure p. In the first stage, the evolution of
the CVs is determined by both thermodynamic and gaussian
driving forces. This continues until the accumulation of
Gg ðhn Þ pushes the system into the basin of attraction of a new
phase, i.e., new local minimum. Physically, this occurs via
the progressive deformation of the initial structure, which
eventually leads to a structural transition. Once such a transition is detected, the simulation proceeds to the second stage,
wherein the gaussian contribution to /n is turned off and the
system is driven towards the new local minimum by the thermodynamic force alone. In this second stage, the metadynamics simulation is equivalent to standard constant-pressure MD
in which the supercell vectors are allowed to vary.
B. Computational details
The interactions between Li, Al, Si, and O atoms were
modeled by a general bond-order dependent reactive force
field (ReaxFF)56,57 that has been found to describe well the
formation and dissociation of bonds. In the ReaxFF formalism, the total energy of the system contains contributions
from several connectivity-dependent interactions; all these
short-range interactions are functions of bond orders that are
derived from the instantaneous interatomic distances.56,57
Additionally, the long-range contributions (i.e., van der
Waals and Coulomb) are computed for every pair of atoms
regardless of their coordination. The redistribution of atomic
charges is evaluated at every step using a charge equilibration scheme.58 This approach enables ReaxFF to describe
metallic, ionic, and covalent systems equally well.56,57,59–64
ReaxFF has been employed successfully to study numerous
ceramic systems, e.g., surface reactions in Si/SiO2,57,65 Al/
Al2O3 (Ref. 59), and ZnO,60 phase transitions in BaTiO3,66
and defect structure in yttria-stabilized zirconia.67 In this
work, we employed the ReaxFF parameters developed
recently for lithium aluminum silicates.64 This parameter set
has been shown to reproduce the empirically observed order
of stability of various eucryptite polymorphs, and describes
well the structural, thermodynamic, and elastic properties of
several bulk phases of silicates, aluminates, and oxides.64
For our metadynamics simulations, we used a computational supercell made up of one unit cell of hexagonal
b-eucryptite containing 84 atoms (12 formula units of
LiAlSiO4) with the lattice parameters predicted by ReaxFF
under ambient conditions; we used larger systems as well
(up to 672 atoms), and reached the same conclusions.
Periodic boundary conditions were employed to simulate
bulk samples. All MD simulations were performed using the
classical MD simulation package LAMMPS68 with a timestep of 0.5 fs. Before starting the metadynamics, we equilibrated the initial structure at 3 GPa and 300 K using constant
pressure MD in the NPT ensemble for 1 ns. This equilibrated
atomic configuration (at 3 GPa and 300 K) was used as a
starting structure for the metadynamics at the desired hydrostatic pressure p ¼ 3 GPa. The metadynamics parameters
were set as W ¼ 4.5 eV and dh ¼ 1 Å in accordance to the
J. Appl. Phys. 114, 083520 (2013)
guidelines provided by Refs. 47 and 51. At each metadynamics step n, the configuration was equilibrated at constant hn
using MD simulations in NVT ensemble for 25 ps; pn was
obtained by averaging the microscopic virial tensor over the
last 10 ps of this run.
III. RESULTS
A. Phase transition
The onset of a structural transition in a metadynamics
simulation can be identified by monitoring the relative orientation of thermodynamic (Ft ) and gaussian (Fg ) driving
forces.51 Initially, when the structure is near a local energy
minimum (i.e., while a well is being filled up by gaussians)
these two forces act along nearly opposite directions. On
passing the saddle point, Ft and Fg become almost parallel.
This sudden change in the relative orientation of Ft and Fg at
the transition point manifests itself as a spike in the indicator
Ft Fg =ðjFt jjFg j).51 Figure 2(a) shows the evolution of
this indicator during the metadynamics simulation of beucryptite at 3 GPa and 300 K. As expected, in the beginning,
the value of Ft Fg =ðjFt jjFg j) remained negative. At step
n ¼ 58, however, a sudden jump to positive value was
observed [Fig. 2(a)], which indicates transition to a new
basin in the free energy landscape. Beyond this step, the
gaussians were switched off (W ¼ 0) to allow the system to
relax towards the new local energy minimum driven by Ft
alone.
A more intuitive indicator signaling a solid-state phase
transition is the structure factor S, which provides the signature for a given spatial arrangement of atoms in a periodic
lattice.47 The structure factor Shkl for a specific crystallographic plane with Miller indices (hkl) in a computational
supercell containing N atoms can be evaluated as69
FIG. 2. Evolution of (a) relative orientation of forces Ft and Fg , and (b)
structure factor during the metadynamics simulation of b-eucryptite under
hydrostatic pressure of 3 GPa at 300 K. A spike in the relative orientation of
Ft and Fg indicates structural transition at step 58.
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083520-4
Narayanan, Reimanis, and Ciobanu
Shkl ¼
N
X
fj e2piðhxj þkyj þlzj Þ ;
J. Appl. Phys. 114, 083520 (2013)
(5)
j
where fj is the X-ray atomic scattering factor for atom j
located at fractional coordinates (xj ; yj ; zj ). The values of fj
for Li, Al, Si, and O atom types were obtained from Ref. 69.
Equation (5) shows that Shkl is a complex number; the square
of its magnitude, jShkl j2 is directly related to the intensity of
XRD peaks arising from (hkl) planes. Hence, jShkl j2 provides
a convenient parameter to monitor structural changes associated with (hkl) planes.
Using Eq. (5), we computed the jShkl j2 values corresponding to three planes—(200), (202), and (224) for structures
obtained at each metastep [Fig. 2(b)]. These three planes were
specifically chosen because they contribute to the most intense
peaks in the XRD pattern of hexagonal b-eucryptite.70
Initially, at step 0, wherein the structure is hexagonal (bphase), the computed jShkl j2 values for these planes were found
to be high [Fig. 2(b)] as expected; furthermore, the order of
their magnitudes was consistent with XRD experiments.70
At step 9, a sudden drop in the jShkl j2 values for (202)
and (224) planes was observed [Fig. 2(b)]. By direct visualization, we observed that until step 9 the structures consisted
of a framework of corner sharing AlO4 and SiO4 tetrahedra.
However, at step 9, the O-coordination around few Al deviates from four, resulting in the formation of AlO5 and AlO3
polyhedra. Consequently, this change in O-coordination
around Al disrupts the periodicity of (202) and (224) planes
which leads to a significant drop in the corresponding jShkl j2
values. To determine whether a phase transition takes place at
step 9, we switched off the gaussians and continued the metadynamics run with Ft alone. This caused the supercell to
revert to the original b-eucryptite structure with associated
increase in the values of jShkl j2 values indicating that no phase
change occurred at step 9. Upon continuation of the metadynamics with active gaussians beyond step 9, the jShkl j2 values
continue to decrease gradually [Fig. 2(b)] to very low values
at step 58. These low values of jShkl j2 change negligibly after
step 58 even upon setting W ¼ 0.
As mentioned in Sec. II, the initial structure for the metadynamics (i.e., at step 0) was obtained by equilibrating
b-eucryptite at 3 GPa and 300 K using conventional variablecell MD for 1 ns. At the end of this isobaric-isothermal MD
run, the structure remains hexagonal as shown by the supercell lengths (a ¼ b ¼ 10.62 Å, c ¼ 11.36 Å) and angles (a ¼ b
¼ 90, c ¼ 120). The supercell densifies to a volume that is
2.5% smaller than that corresponding to ambient conditions. To escape the free energy minimum corresponding
to the b-phase and explore other structures, we performed
metadynamics using a history-dependent potential with
W ¼ 4.5 eV and dh ¼ 1 Å. We monitored the supercell lengths
and angles at every step during this run and have plotted their
evolution in Figure 3. It is interesting to note that at step 9,
there is a marked decrease in c [Fig. 3(a)], while the cell
angles a and b begin to deviate from 90. This behavior is
consistent with the formation of AlO5 and AlO3 polyhedra,
which were observed by direct visualization. Beyond step 58
(at which the gaussians were switched off), the supercell
lengths and angles did not revert to the original values. Instead,
FIG. 3. Evolution of structural parameters of the computational supercell (a)
edge lengths, namely, a, b, c, and (b) angles, namely, a, b, and c during
metadynamics. The portion of the run in which the gaussians are turned on
(i.e., up to step 58) is shown as the shaded region, while the gaussians are
switched off (i.e., W ¼ 0) in the unshaded region.
they fluctuate around new cell parameters of a ¼ 10.03 Å,
b ¼ 9.63 Å, c ¼ 11.82 Å, a ¼ 70.5, b ¼ 86.9, and c ¼ 116.8
and the structure appears triclinic. This indicates that an energy
barrier has been overcome and the hexagonal b-phase has
transformed into a new phase. We used a smaller dh (0.1 Å) after the gaussians were switched off in order to better pinpoint
the new values of the cell parameters.
To assess the stability of this newly found phase, we performed variable-cell constant pressure MD simulation (at
3 GPa and 300 K) on this structure for 1 ns. During this run,
the structure changed negligibly, indicating that the new
phase obtained from metadynamics resides at a new local
energy minimum. The enthalpy of this new phase is 2.7 eV/
formula unit lower than the enthalpy of b-eucryptite.
We also computed the XRD spectrum for b-eucryptite
and the new phase obtained by metadynamics to provide further evidence for phase transition [Fig. 4]. These spectra
FIG. 4. Simulated XRD spectra for b-eucryptite (black) and the new phase
(red) obtained at P ¼ 3 GPa and T ¼ 300 K. The loss of well-defined peaks in
the XRD spectrum of the new phase indicates that it is amorphous.
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083520-5
Narayanan, Reimanis, and Ciobanu
were calculated using FullProf package71 with a Cu-Ka
beam of wavelength 1.54 Å. The computed XRD spectrum
for b-eucryptite (black line) was found to be in excellent
agreement with experiments.70 For the sake of convenience,
we have only shown the indices for the three most intense
peaks [Fig. 4], namely, (202), (224), and (200) in decreasing
order of intensity. These three peaks disappear in the new
phase (red line) at 3 GPa consistent with our structure factor
calculations [Figs. 4 and 2(b)], clearly indicating a phase
transition. Furthermore, the XRD for the new phase lacks
well-defined peaks suggesting that it could be amorphous.
B. Structural characterization of the new phase
To better understand the atomic configuration in the
newly formed phase, we analyzed the pressure induced
changes in the spatial ordering using radial distribution functions (RDF) for Al-O, Si-O, Li-O, and Li-Li pairs [Fig. 5].
The corresponding RDF for b-eucryptite under ambient conditions is also shown in Fig. 5 for comparison. In the newly
obtained phase at 3 GPa, the first peak of the RDF for Al-O
pair (r ¼ 1.75 Å) broadens slightly and reduces in intensity as
compared to that of the perfect b-eucryptite [Fig. 5(a)]. The
peak corresponding to the next-nearest neighbor (r ¼ 4.1 Å)
was found to be very broad, while the higher order peaks are
non-existent [Fig. 5(a)]. Similar signs of structural disordering, i.e., broadening of the first RDF peak accompanied by
disappearance of higher order peaks, have been observed
during amorphization of SiC,72 b-crystobalite,73 and aquartz.74 The RDF for Si-O, Li-O, and Li-Li pairs [Figs.
5(b)–5(d)] show features similar to Al-O [Fig. 5(a)], indicating loss of long-range order under pressure. This further evidences that the new phase obtained from our metadynamics
simulation at 3 GPa is amorphous.
Interestingly, the RDF for Li-O and Li-Li pairs exhibit
an additional feature [Figs. 5(c) and 5(d)]. The nearestneighbor peaks for the Li-O and Li-Li pairs shift to significantly smaller distances in the high-pressure phase as compared to b-eucryptite under ambient conditions. For Li-O
pairs, the first peak shifts from 2 Å in b-eucryptite to
1.7 Å in the new phase, which is close to the typical Li-O
bond length, 1.61 Å. Similarly, the nearest-neighbor Li
FIG. 5. Radial distribution functions of (a) Al–O, (b) Si–O, (c) Li–O, and
(d) Li–Li pairs in b-eucryptite (black) and in the new phase (red) obtained
under a hydrostatic pressure of 3 GPa at 300 K. In the new phase, the long
range ordering is absent indicating amorphization.
J. Appl. Phys. 114, 083520 (2013)
pairs in the high-pressure phase were found to be 2.6 Å
apart, which is closer to the Li-Li bond length (3.04 Å) in
metallic Li-bcc than to the Li-Li spacing in b-eucryptite
(3.8 Å). Evidently, new Li-O and Li-Li bonds are formed
under pressure; these bonds were also previously observed in
the amorphous phase obtained via indentation of b-eucryptite.64 The structure of b-eucryptite, as aforementioned, consists of a framework of corner sharing AlO4 and SiO4
tetrahedra with vast open spaces between them. The Li
atoms occupy these open spaces without forming any bonds
with tetrahedra and other Li atoms as indicated by smallest
Li-O (2 Å) and Li-Li (3.8 Å) separations in the b-phase [Fig.
5]. However, under pressure, the Li atoms move freely
owing to the open spaces resulting in the formation of Li-Li
and Li-O bonds. Consistent with our RDF calculations, we
have also observed Li-O-Li trimers in the high-pressure
phase by direct visualization.
A detailed analysis of the high-pressure phase in terms
of the deformation of the quasi-rigid structural units, namely,
AlO4 and SiO4 tetrahedra is crucial to gain significant
insights into the atomic scale mechanisms that occur in beucryptite under applied pressure. To accomplish this, we
characterized the relative arrangement of atoms in the highpressure phase by computing the distribution of angles
between different bonds. Figure 6 shows the angle distribution functions g for the angles defined in Fig. 6(a). In beucryptite, every Al and Si is surrounded by four O atoms in
a tetrahedral coordination; however, the tetrahedra centered
FIG. 6. Angle distribution functions g for the angles defined in panel (a).
The g functions for (b) O–Si–O, (c) O–Al–O, (d) Al–O–Si, (e) O–Si–Al, and
(f) O–Al–Si angles in b-eucryptite (black) and new phase obtained at
P ¼ 3 GPa and T ¼ 300 K are shown here.
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083520-6
Narayanan, Reimanis, and Ciobanu
at Al/Si are slightly irregular owing to small differences in
the cation-oxygen bond lengths within a given tetrahedron.21,37 This irregularity manifests itself as split peaks in
angle distribution functions of O-Al-O (107, 112) and OSi-O (98, 111). Upon application of pressure, the g function for O-Si-O angle reduces in intensity and broadens
significantly, with its maximum at 109 indicating that the
SiO4 tetrahedra distort considerably without affecting the tetrahedral O-coordination. On the other hand, the O-Al-O
peak for the high-pressure phase is extremely broad, signaling the formation of over- and under-coordinated AlOx polyhedra. Such broadening of g functions along with change in
O-coordination around cations has been previously observed
during amorphization of a-berylinite.15,17 This provides further confirmation that the new phase obtained at 3 GPa and
room temperature is amorphous.
The bridge angle Al-O-Si and the torsional angles O-SiAl, O-Al-Si define the orientation of the AlO4 and SiO4 tetrahedral structural units relative to each other. In b-eucryptite,
the distribution of Al-O-Si angle shows a sharp peak centered at 146 indicating crystalline order [Fig. 6(d)]. Under
an applied pressure, the g function for the Al-O-Si angle
does not have well-defined peaks, which indicates that the
new phase lacks long-range order. This also shows that the
AlO4 and SiO4 units significantly tilt relative to each other.
Such tilting of the polyhedral structural units have been
reported to be associated with amorphization of other framework materials like SiO2, AlPO4, and LiKSO4.17 The distribution of the torsional angles O-Si-Al and O-Al-Si showed
an interesting response to applied pressure [Figs. 6(e) and
6(f)]. They were found to spread out and reduce in intensity
at higher angles under applied pressure providing further evidence for tetrahedral tilting. Additionally, the low angle
peak at 20 in the g functions for O-Si-Al and O-Al-Si that
was present in b-eucryptite is completely lost in the new
phase obtained at 3 GPa [Figs. 6(e) and 6(f)]. This loss of the
low angle peaks is due to the formation of under/over-coordinated AlOx polyhedra.
In order to provide a qualitative assessment of the extent
of deformation of AlO4 and SiO4 tetrahedra in the amorphous
phase obtained at 3 GPa, we determined the number of Aland Si-centered polyhedra with different O-coordinations
[Fig. 7]. Initially, in the computational supercell containing
the b-eucryptite structure, all the Al and Si atoms (100%) are
tetrahedrally coordinated by O atoms. Under applied pressure, the O-coordination around 41.7% of Al atoms deviates
from 4. Around a quarter of the Al atoms form AlO5 polyhedra, 16.7% form AlO3 polyhedra, while the remaining
58.3% of Al atoms remain tetrahedrally coordinated. The
number of SiO4 tetrahedra, on the other hand, remains unaffected by pressure.
IV. DISCUSSION
Although, strictly speaking, our calculations with periodic boundary conditions predict a triclinic system for the
high-pressure phase, information from the structure factor
[Fig. 2(b)], radial and angular distribution functions (Figs. 5
and 6), and simulated XRD spectrum (Fig. 4) unambiguously
J. Appl. Phys. 114, 083520 (2013)
FIG. 7. Comparison of the number of AlOx and SiOx polyhedra of different
O-coordinations (i.e., different values of x) in b-eucryptite under ambient
conditions and the new phase obtained at 3 GPa and 300 K.
indicate that the new phase is amorphous. This finding is
consistent with the previous in situ XRD experiments.18,41
Structural characterization revealed that the amorphous
phase is composed of AlO3, AlO4, AlO5, and SiO4 structural
units; thus, it possesses significant short range order despite
lacking long-range crystalline order. Such short range order
is known to be preserved upon amorphization of other framework ceramics like SiO2,17,74,75 AlPO4,15,16 ZrW2O8 (Ref.
14), and others.12,13,20 The structural changes that accompany amorphization of b-eucryptite consists of (a) tilting of
AlO4 and SiO4 tetrahedra, (b) deviation of O-coordination
around some Al atoms away from 4, and (c) disordering
of Li atoms with concomitant formation of new Li-O and
Li-Li bonds. In the following paragraph, we focus on
the atomic scale mechanism governing the amorphization of
b-eucryptite under applied pressure [refer to Fig. 8].
In the initial configuration [Fig. 8(a)], the structure is
composed of a network of corner-linked tetrahedra centered
on Al and Si atoms. The Li atoms are present in the spaces
between these tetrahedra without being bonded to them. In
the first few metadynamics steps, these tetrahedra tilt relative
to each other, and at the same time, the spatial array of Li
atoms becomes disordered—refer, for example, to the snapshot taken at step 2 [Fig. 8(b)]. The disordering of the Li
atoms results in the formation of Li–Li and Li–O bonds.
Some of the Al-O bonds experience stretching, which leads
to the gradual distortion of the associated AlO4 tetrahedra.
As seen at step 9 [Fig. 8(c)], the tetrahedral tilting along with
stretching of Al-O bonds causes the O-coordination around a
few Al atoms to change, resulting in the formation of AlO3
and AlO5 polyhedra. This change in O-coordination around
Al atoms is consistent with the sudden drop in the structure
factors corresponding to (202) and (224) planes [Fig. 2(b)] at
step 9. As the metadynamics algorithm proceeds, the number
of off-coordinated Al atoms gradually increases to 25% at
the transition point, i.e., step 58 [Fig. 8(d)]. After the transition, the distortion of the AlO4 tetrahedra into other polyhedra continues to increase [Figs. 8(e) and 8(f)] until 41.7%
of Al atoms are centers of under/over-coordinated polyhedra
in the amorphous phase at equilibrium [Fig. 8(f)]. On the
other hand, the SiO4 tetrahedra remain intact during the
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083520-7
Narayanan, Reimanis, and Ciobanu
J. Appl. Phys. 114, 083520 (2013)
FIG. 8. Atomic scale mechanism of
amorphization of (a) b-eucryptite under
a hydrostatic pressure of 3 GPa at 300 K.
The amorphization proceeds via relative
tilting of SiO4 (orange) and AlO4 (gray)
[panel (b)] that eventually leads to
change in O coordination around Al
resulting in AlO3 (pink) and AlO5 polyhedra [panel (c)–(h)]. Significant disordering of Li (purple) is observed
resulting in the formation of Li–O (blue)
bonds. For the sake of clarity, computational supercell (outlined by black lines)
is replicated along the three supercell
vectors.
entire metadynamics run. In fact, in the final amorphous
phase, the lengths of the Si–O bonds are nearly identical to
the average Si-O bond length in b-eucryptite under ambient
conditions (1.6 Å). This finding supports the hypothesis of
Zhang et al. that in b-eucryptite, the SiO4 tetrahedra will not
deform under applied pressures up to 17 GPa.18
A close inspection of the amorphous phase [Fig. 8(f)]
reveals that the newly formed AlO5 polyhedra share edges
with the SiO4 tetrahedra. The formation of edge-sharing polyhedra results in a drastic decrease in the open spaces available in the structure, causing densification. Indeed, the
amorphous phase obtained under pressure was found to be
19.4% denser than b-eucryptite. Each of the nearly planar
AlO3 polyhedra shares two of its corners with either SiO4/
AlO4 tetrahedra or AlO5 polyhedra, while the third O corner
is bonded to a Li atom. Furthermore, 83% of the Li atoms
are bonded to either O or other Li atoms; often these Li
atoms were found to be involved in Li-O-Li triatomic clusters. The remaining 17% of Li stays unbound and is therefore mobile.
In essence, the atomic scale processes responsible for
amorphization of b-eucryptite are (a) tilting of AlO4 and SiO4
tetrahedra relative to each other that eventually results in the
formation of AlO3 and AlO5 polyhedra while keeping the
SiO4 intact, and (b) disordering of Li atoms with the formation of (new) Li-Li and Li-O bonds. This behavior is similar
to several other ceramic oxides that possess a framework
structure with corner-sharing polyhedra;12–17 the principal
reason for the PIA of all these compounds was reported to be
polyhedral tilting with concomitant change in O-coordination
around cation(s). For instance, SiO2, LiKSO4, and AlPO4
under applied pressures (10–15 GPa) undergo crystalline-toamorphous transition when the inter-polyhedral bridge angle
reduces to 124, consequently increasing oxygen coordination around some cations.17 Of particular interest is berylinite
(AlPO4), which is made up of a network of corner-sharing
AlO4 and PO4 tetrahedra. Similar to b-eucryptite, the AlO4
tetrahedra of berylinite deform to the point of changing the
oxygen coordination around Al.15,17 The other type of tetrahedra, namely, SiO4 (in b-eucryptite) and PO4 (in berylinite)
remain intact. This behavior can be attributed to the higher
strength of Si-O and P-O bonds as compared with the Al-O
bonds, as suggested by the larger Al-O bond length (1.6 Å for
Si-O, 1.52 Å for P-O,45 1.75 Å for Al-O). The rigidity difference between the Si-O bonds in SiO4 and Al-O bonds in
AlO4 tetrahedra manifests itself in another structural transition, Li-ABW zeolite ! c-eucryptite, which occurs solely via
dissociation and reformation of certain Al-O bonds.54
It is interesting to note that b-eucryptite transforms into
an amorphous phase at moderate pressures 3 GPa similar to
other flexible network oxide structures exhibiting NTE.12–14
Using high-pressure spectroscopic studies on ZrW2O8,
Perottoni and da Jornada illustrated that both NTE and PIA
can be attributed to the rotation of the ZrO6 and WO4 polyhedra. Our previous density functional theory studies,40 along
with other calculations38,39 and XRD experiments21 showed
that the negative coefficient of thermal expansion of beucryptite is a consequence of tetrahedral tilting and progressive Li-disordering. As shown by Fig. 8, these same atomic
scale processes occur during the crystalline-to-amorphous
transition in b-eucryptite under applied pressure of 3 GPa.
The tetrahedral tilting that arises due to the natural flexibility
of the network of corner-sharing AlO4 and SiO4 acts as the
driving force for NTE and as the way to accommodate the
applied pressure during amorphization; the major difference
is the extent of tilting, which is much larger during the
amorphization under pressure.
Apart from temperature changes and applied pressure, it
has been previously reported that tetrahedral tilting, change
in O-coordination around cations, and disordering of Li
atoms occur when b-eucryptite is exposed to neutron radiation.30 Upon exposure to radiation, the O-coordination
around both Al and Si atoms deviates from the value of 4.
When the damaged b-eucryptite is annealed, most of the
SiO3 polyhedra were found to heal, i.e., the Si atoms belonging to these SiO3 polyhedra revert to their tetrahedral Ocoordination via a mechanism involving tilting of SiO3 and
AlO5 polyhedra. The AlO5 polyhedra, although vital for the
structural repair of SiO3, do not heal.30 In contrast, under
applied pressure, we found that only the AlO4 tetrahedra
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083520-8
Narayanan, Reimanis, and Ciobanu
deform, while SiO4 tetrahedra remain intact [Figs. 7 and 8].
Thus, the three apparently disconnected phenomena exhibited by b-eucryptite, namely, negative thermal expansion,
radiation tolerance, and amorphization under moderate pressures are all related to the inherent flexible nature of the network of corner-sharing AlO4 and SiO4 tetrahedra.
V. CONCLUSIONS
In summary, we have performed metadynamics simulations using a reactive force field to examine the structural
changes that occur in b-eucryptite under hydrostatic compression. From these simulations, we found that under an
applied pressure of 3 GPa b-eucryptite loses its long-range
order resulting in an amorphous phase that is 19.4% denser
than b-eucryptite. We characterized the structure of this
amorphous phase and found that several AlO4 tetrahedra
present in b-eucryptite deform appreciably under pressure
and turn into either AlO3 or AlO5 polyhedra. The SiO4 tetrahedra, on the other hand, remain unperturbed. The AlO5 polyhedra share edges with SiO4 while SiO3 were found to
share two of its corners with any of the other polyhedra
(AlO4, AlO5, or SiO4) with the third O attached to a Li. The
formation of polyhedra centered at Al with off-tetrahedral
coordination causes densification via formation of edgesharing AlO5 and SiO4 polyhedra and disruption of longrange order. In addition, the Li atoms disorder considerably
and form new Li-Li and Li-O bonds.
Our metadynamics simulations also revealed the lowest
energy atomic scale pathways followed by PIA in beucryptite at 3 GPa and 300 K. The dominant mechanism responsible for PIA in b-eucryptite was found to be the tilting
and distortion of AlO4 and SiO4 tetrahedra that eventually
causes change in O-coordination around Al. Furthermore, a
comparison of this underlying mechanism for PIA with those
that are known to occur in response to thermal and radiation
environments in b-eucryptite indicate that NTE, PIA and
radiation tolerance have common origin in the flexible
framework of AlO4 and SiO4 tetrahedra.
ACKNOWLEDGMENTS
This research work was performed with support from
the Department of Energy’s Office of Basic Energy Sciences
through Grant No. DE-FG02-07ER46397, and from the
National Science Foundation through Grant No. CMMI0846858. Supercomputer time was provided by the Golden
Energy Computing Organization at Colorado School of
Mines.
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