Journal of The Electrochemical Society, 152 共6兲 H84-H93 共2005兲
H84
0013-4651/2005/152共6兲/H84/10/$7.00 © The Electrochemical Society, Inc.
Theoretical Investigation of Structure and Stability of
Reidinger Defects in Barium Magnesium Aluminate
K. C. Mishra*,z
OSRAM-SYLVANIA Development Incorporated, Central Research, Beverly, Massachusetts 01915, USA
An atomistic simulation method has been used to study the equilibrated geometry, defect structure, and phase mixing of barium
magnesium aluminate 共BAM兲 and related compounds. The calculated lattice energies are used to study the stability of defect
structures in the ␤-alumina lattice, particularly in the presence of excess alumina in the starting materials. It is shown that excess
alumina in the starting compounds could lead to the formation of Reidinger defects in BAM. The calculated structural modification
of the lattice due to a Reidinger defect is in excellent agreement with the experimental results. These defects are responsible for
generation of F+ and F-type color centers by 共vacuum兲 ultraviolet radiation and bombardment of energetic particles from the
discharge. BAM could be made resistant to the formation of color centers by adhering to a strictly stoichiometric formulation of
this phosphor.
© 2005 The Electrochemical Society. 关DOI: 10.1149/1.1914759兴 All rights reserved.
Manuscript submitted October 19, 2004; revised manuscript received December 17, 2004. Available electronically May 5, 2005.
Barium magnesium aluminate 共BaMgAl10O17兲 activated by divalent europium ions is a blue-emitting phosphor. This phosphor is
popularly known as BAM in lighting applications. It is used as a
blue-emitting phosphor in triband phosphor coatings in low-pressure
Hg-discharge lamps. Unlike the other components of triband phosphors, namely, the red-emitting yttrium oxide phosphor activated by
trivalent europium, and the green-emitting lanthanum phosphate
phosphor activated by terbium, BAM is relatively unstable during
high-temperature processing 共⬃400°C兲 of certain fluorescent lamps
in an oxidizing environment.1,2 Similar processing conditions are
also encountered in plasma display panel applications with similar
results. BAM also tends to degrade faster during the lamp life under
high loading conditions,a leading to “unacceptable” color shifts during the lamp life. The last few years have seen intense activities in
the luminescent community toward developing an understanding of
the nature of the thermal degradation process. It is believed that the
thermal degradation of BAM results from the oxidation of europium
ions.3 However, similar efforts to understand the nature of the degradation process during the lamp life are still lacking. This paper
presents the results of a theoretical investigation of the structure and
origin of defects that could contribute to the generation of color
centers during the lamp life.
One of the reasons for phosphor degradation in the lamp environment is the generation and growth of color centers in phosphors
due to lamp operation. Inside the fluorescent lamps, the phosphors
exist in a very harsh environment of an arc discharge. During the
lamp operation, the surfaces of microcrystalline phosphor particles
are continuously subjected to bombardment of energetic electrons,
ions, and neutral atoms and irradiation by vacuum ultraviolet 共VUV兲
photons. The color centers are induced by these discharge-related
processes.
The lamp phosphors are usually made from complex inorganic
hosts. The color center literature is sparse on the investigation of
such systems. The haloapatite phosphors are the only class of lamp
phosphors that have been extensively studied for color centers. For a
brief review, see Ref. 4. Similar studies for the triband phosphors are
lacking because of their robust performance in conventional fluorescent lamps. The instability of BAM was noticed only when this
phosphor was applied to phosphor coatings in the highly loaded,
* Electrochemical Society Active Member.
z
a
E-mail: [email protected]
The phenomenon of degradation of BAM during lamp life is well known in the lamp
community. Many lamp-related causes have been identified. For example, see C. R.
Ronda, V. W. Weiler, A. Johnene, J. A. F. Peak, and W. M. P. Van Kemenade, U.S. Pat.
5, 811, 154 共1998兲 for a discussion on the role of mercury adsorption in the degradation
process. M. Raukas has shown that the nature of degradation of BAM during lamp life
can be simulated by irradiating the phosphor with 193 nm laser radiation. This observation calls for a proper understanding of the role of color centers in the degradation
process.
electrodeless, fluorescent lamps and in VUV lamps, e.g., Xe*2 discharge.
An understanding of the color centers in a crystalline solid requires reliable information on the crystal structure and the distribution of occupied Wyckoff sites of the host lattice. BAM crystallizes
in the ␤-alumina structure.5 The distribution of various ions in this
structure is discussed later in detail. In the following discussions,
arabic numerals within parentheses indicate the site occupancy of an
ion in conformity with the X-ray diffraction 共XRD兲 studies.
Fortunately, the color centers in other hexaaluminates with similar ␤-alumina structures have been extensively studied.6,7 Based on
their optical absorption characteristics, one could identify three specific color centers of interest from the lamp maintenance perspective: two electron centers F and F+, and a hole center V. The first two
correspond to electrons trapped at an oxygen vacancy, and the third,
to a hole trapped at an oxygen site adjacent to an Mg2+ ion substituting for an Al3+ ion. Both the electron centers are UV-absorbing
color centers. The absorption bands associated with the F and F+
centers peak at 4.20 and 4.76 eV, respectively. They could compete
with the divalent europium ions for 254 nm photons from the Hg
discharge. The V center absorbs near 2.60 eV and could contribute
to the loss of visible radiation.
The electron centers are known to originate from the Reidinger
defects.6,7 The Reidinger defects are intrinsic to barium hexaaluminate in phase I 共Ba.75Al11O17.25, BAL兲,8 but in other hexaaluminates,
they appear as isolated, extrinsic defects.b The primary constituent
of a Reidinger defect is an oxygen ion, OR, trapped at a 6h site in the
intermediate plane with ideal internal coordinates being
共5/6,2/3,1/4兲. This site is referred to as an mO site and is indicated
by a shaded sphere in Fig. 1. Subsequent generation of vacancies at
these sites is responsible for the creation of electron centers.
The Reidinger defect leads to a complex rearrangement of the
local structure surrounding the interstitial OR atom. In Fig. 1, the
local distortions induced by a Reidinger defect in BAL near the
intermediate plane in the adjacent spinel blocks have been shown
schematically in contrast to a regular half-cell. In the defect halfcell, the barium ion is missing and an oxygen ion occupies an mO
site. The presence of OR in the intermediate plane creates two Frenkel defects involving Al 共1兲 ions in the spinel block 共Fig. 1兲. These
aluminum ions are located in the spinel blocks, vertically above and
below the OR ions along a direction parallel to the hexagonal c axis.
They relax toward the interstitial OR ion through the layer of O 共2兲
and O 共4兲 ions to almost the level of Al 共3兲 ions. The spin resonance
b
+1
The Reidinger defects are known to exist in M1+x
Al11O17+x/2 in the ␤-alumina structure, where M+1 represents monovalent ions like Na+,K+, and Li+. In these systems,
there are no cationic vacancies in the intermediate plane as in phase I of Ba
␤-aluminate.
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Journal of The Electrochemical Society, 152 共6兲 H84-H93 共2005兲
Figure 1. Schematic representation of two kinds of half-unit cells in presence of Reidinger defects. The large empty sphere, the solid large sphere,
and the shaded large sphere represent oxygen ions at the 2c site, barium ions
at the 2d 共BR兲 site, and oxygen ion 共OR兲 associated with the Reidinger defect
at the interstitial 6h 共mO兲 site. The small spheres represent aluminum ions.
The solid ones correspond to aluminum ions in tetrahedral coordination and
the empty ones to ions in octahedral coordination. The mechanism of formation of the Reidinger defect with an interstitial oxygen ion is presented in the
half-cell on the right. The displacement of an aluminum ion toward the
intermediate plane is indicated by an arrow.
studies of the F+ centers suggest that this distortion locks the Al 共1兲
ions to their new positions, even after a vacancy is created at the OR
site.7,9-11 The Reidinger defects could possibly lead to the generation
of several color centers in the following manner. First, a lattice
defect is created at the OR site, possibly displacing the oxygen ion to
an interstitial, metastable site. Then, the vacancy at the OR site captures one or two electrons, generating either an F+ or an F center.
The oxygen ion at the interstitial site could then move to an adjacent
mO site, inducing the formation of a new Reidinger defect. This is
plausible because the mO sites are present in triplicate around a
Beevers-Ross 共BR site兲, a 2d site normally occupied by a large
cation in the ␤-alumina lattice.5 Additionally, triple Reidinger defects exist in phase II of Ba-rich barium hexaaluminate.12
The F+ centers have been observed in nonstoichiometric
␤-alumina compounds having Reidinger defects. These defects are
formed for overall charge compensation of the lattice due to excess
cations. If the charge compensation can be achieved without incorporating oxygen ions into the lattice, then the material has no such
defects. Stoichiometric Na+␤-alumina, which contains no Reidinger
defects, is known to be resistant to the generation of color centers.11
Nonstoichiometric Na+␤⬙-alumina, charge compensated by divalent
ions at the aluminum sites, are not known to develop the color
centers. Thus, one would expect that BAM with stoichiometric input
would not be susceptible to generation of color centers. However,
recent measurements by Raukas13 demonstrate their existence in
BAM, even with stoichiometric input. To improve the performance
of BAM, it is crucial to properly understand the factors that lead to
formation of the Reidinger defects.
Unlike the materials crystallizing in the magnetoplumbite structure, the anion close packing 共including large cations兲 of the
␤-alumina structure is not complete.14 For the close packing to be
complete, four anion sites 共per half-unit cell兲 in the intermediate
plane should be occupied. In the ␤-alumina structure, one Ba ion
occupies a 2d 共BR兲 site, and the oxygen ions a 2c site. Considering
the barium ion as a large ion, ideal close packing would have required occupancy of three mO sites surrounding the BR site by large
H85
ions. The incompleteness of the anion close packing in the
␤-alumina structure allows accommodation of large ions like barium
in the intermediate plane. At the same time, the relatively open
structure in the intermediate plane in the ␤-alumina structure is the
source of all the structural defects in BAM.
This paper attempts to understand two aspects of the Reidinger
defects. The first relates to the relaxation of the crystal structure
surrounding the OR site. The second aspect involves the energetics
of formation of the Reidinger defects. Both aspects have been studied using an atomistic simulation approach. Using the appropriate
thermodynamic potentials calculated by this approach, the generation and variation of concentration of the Reidinger defects with
initial conditions of synthesis have been studied.
BAM is usually synthesized by solid-state reaction at ⬃1500°C.
The ingredients 共starting materials兲 are thoroughly mixed and then
held at a constant temperature to attain equilibrium by diffusion.
When the chemical equilibrium is finally obtained, one expects the
synthesis of the desired compound to be complete in accordance
with the phase diagram for the chemical components of the mixture.
The quality of the mechanical mixture of the chemical components,
the thermal history, ambient conditions, and other relevant factors
dictate the quality of equilibrium obtained and, therefore, the quality
of the final products. Fluctuations in the concentration of the reactants either due to deliberate manipulation of the starting mixtures or
loss of material during synthesis could lead to an undesirable level
of defect concentration. In this context, the atomistic simulation
methods provide an excellent tool for predicting the nature of the
final product given the contents of the input materials and the thermal history using the calculated thermodynamic potentials for the
optimized structures of the reactants and products.
In the next section, the simulation method, as implemented in the
computer codes “Shell,” has been described. The details of the
theory of Shell are given in Ref. 15. Results from the atomistic
simulation are then discussed, including the validation of the approach from a study of simple binary systems. Two distinct scenarios of formation of the Redinger defects in BAM are discussed.
In the final section, conclusions based on the present calculations are
presented.
Simulation Method
Interaction potential.— The simulation method employed in this
work is based on the Born model of ionic solids.16 Any ionic solid is
assumed to be a collection of point ions moving in the combined
field of pairwise interaction potentials. These potentials have an attractive part, which is a sum of the Madelung and van der Waals
potentials, and a repulsive component arising from the overlap of
electronic clouds surrounding each ion. The repulsive component
reflects the effect of Pauli repulsion, and prevents the collapse of the
lattice structure from the long-range attractive, electrostatic potential. It is usually modeled in simple analytical forms, such as the
Morse potential, Born-Mayer potential, and inverse potential.
We have used in this work the Buckingham function, which combines the short-range overlap potential in an exponential form and
the van der Waals potential as an inverse potential
Vij = Aije−共rij/␳ij兲 − Cij
1
rij6
关1兴
where rij represents the distance between ions i and j. The parameters A,␳, and C describing the pairwise potentials for various ion
combinations in various chemical environments are available from
the literature. Additionally, the polarization of the solid is included
by using the shell model originally proposed by Dick and
Overhauser.17 In this model, each ion is assumed to consist of a
massive core and a “massless” shell, the total charge on the ion
being partitioned between the shell and core. The shell and core of a
given ion are connected by a “massless” spring with a spring constant, k.
There are several conceptual issues concerning the calculation of
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H86
Journal of The Electrochemical Society, 152 共6兲 H84-H93 共2005兲
cohesive energy of solids and other structural thermodynamical
properties based on the classical Born model. They have been discussed extensively in the literature.18 First, the concept of additive
two-body potentials is only approximate. Early quantum mechanical
calculations for the cohesive energy of solids have shown that much
of the cohesive energy cannot be described by the two-body
potentials.19 Second, the validity of the concept of separation of the
motion of the nuclei from that of the electrons rests on the validity
of the Born-Oppenheimer approximation. For most ionic solids with
large optical gaps, the Born-Oppenheimer approximation is a very
good approximation at low temperatures. But, with increasing temperature, most solids tend to be conducting, and the forbidden energy gap decreases rapidly. Thus, at a high temperature, one expects
the Born-Oppenheimer approximation to break down. Therefore, describing the high-temperature behavior of solids using potential parameters based on structural properties at room temperature may not
be a valid approach. Third, there are many different sets of pairwise
potential parameters available in the literature.20 The difficulties in
choosing appropriate pairwise potentials are apparent when one
chooses to use this classical approach for predicting properties of
complex systems. In this work, we addressed this issue by comparing various material properties of constituent binary oxides of BAM,
namely aluminum oxide, barium oxide, and magnesium oxide, using
various potential parameters. It is shown that the structural properties of interest in this work do not vary significantly with the choice
of parameters. This is discussed in detail in the Results and Discussion section. Despite these apparent drawbacks, atomistic simulation
methods of solids have led to many interesting results. For a complex system such as BAM, this method provides a fast computational approach for studying equilibrated structural properties. When
used carefully with a proper appreciation of the complexity of the
system, this classical approach provides reasonable explanations of
the observed structural properties and predictions of novel properties
of the material.
Lattice dynamics approach for atomistic simulation of solids.—
In this work, atomistic simulations of BAM and its defect structure
were performed using the computational codes Shell.15 The scope of
Shell extends beyond the static energy calculation and optimization
of crystal structures at absolute zero temperature. The code implements a lattice dynamics approach for calculating the temperature
dependence of the thermodynamic properties of solids. It provides a
powerful alternative to molecular dynamics and Monte Carlo simulation of solids. Some of the interesting features of the lattice dynamics simulations of solids are discussed in the following section.
Shell implements the lattice dynamics formalism within a quasiharmonic approximation. The equation of state thus generated is
correct to the first order in anharmonicity. The free energy of the
crystal is assumed to depend on the vibrational motion of nuclei in
the harmonic potential generated by the superposition of pairwise
potentials. The effect of anharmonicity of the crystal potential derives from the change in mode frequencies as a function of coordinates and temperature. This approach provides a powerful, robust
alternative to molecular dynamics and Monte Carlo simulation of
solids.15,21-23 It is particularly relevant below the Debye temperature
when the quantum mechanical effects cannot be excluded.
Shell is designed for optimization of the periodic crystal structures. Because our main focus is on understanding the nature of the
defect structure of BAM and related thermodynamic properties, we
used Shell within the framework of supercell approximation of imperfect solids24 in preference to the Mott-Littleton embedded cluster
approach.25 In this approximation, point defects are assumed to be
distributed periodically throughout the bulk, but the corresponding
unit cells are significantly larger than the unit cells of the ideal
lattice. With a random distribution of point defects within a unit cell,
the supercell approach provides a powerful tool for simulation of the
defect structure of a material.
Structural input and optimization scheme.— A periodic crystal structure is defined by a lattice and a basis of atoms. External
strain can deform the shape of the lattice, which is described
by the external coordinates, ␧ext. The internal coordinates, ␧int,
define the positions of the basis of atoms within a unit cell.
The optimization process involves minimization of a suitably chosen
thermodynamic potential with respect to these coordinates.
The positions of the particles including core and shell in a macroscopically strained coordinate system are given by
␣
rix
=
兺 共␦
␥
␣␥
+ e␣␥兲共x␥ + ␳i␥兲
关2兴
where the Greek superscripts are Cartesian indices 1…3, x is a
lattice vector of the unconstrained lattice, and ␦␣␥ represents the
Kronecker delta. Components of the tensor, e␣␥, describe the state
and orientation of the strain. ␳␥i describes the ␥ component of the
internal coordinate for particle i within a unit cell. The Voigt macroscopic strain coordinates ␧␭ are the components of the six-element
vector
冢 冣
关3兴
兺ua = 兺uA
关4兴
e11
e22
e33
␧=
e23 + e32
e13 + e31
e12 + e21
The internal coordinates ␳i␣ are given in dimensionless units from
the XRD measurements
␳i␣ =
t ␣
i t
t
t t␣
i
t
where the matrix At␣ describes the metric obtained from the lattice
vector at. It is helpful to use the internal symmetry to reduce the
number of internal coordinates. When optimizing a crystal without
any external stress, the lattice vectors describe the external coordinates. The variables uti are expressed in terms of symmetric internal
coordinates wm
uit = git +
兺w
t
mgm,i
关5兴
m
where gti is a fixed vector for a given particle i, and the directions
gtm,i are determined by symmetry. The geometry of a crystal is then
determined by optimizing the appropriate free energy with respect to
the lattice vectors and internal coordinates wm. Using wm reduces
significantly the number of independent variables and preserves the
symmetry of the crystal. The significance of wm is obvious from a
consideration of input coordinates for atoms occupying 6h sites in
the space group, P63 /mmc. For example, the coordinate of an atom
occupying a site with coordinates 共x, 2x, z兲 can be written as
关x共1, 2,0兲 + z共0, 0, 1兲兴. The entire set of coordinates describing
atoms at the 6h site can be described by a suitable choice of direction gtm,i which will be held fixed during the minimization procedure and two variables x and z. Here x and z represent the internal
coordinates wm. Thus, using x and z as internal coordinate variables
not only preserves the overall symmetry of the crystal structure but
also reduces the number of independent variables in the present case
from 18 to 2.
At a finite temperature under an applied pressure P0. the stable
structure of a periodic lattice can be obtained by minimizing the
Gibbs free energy G
G = U − TS + P0V = F + P0V = ␾stat + Fvib + P0V
关6兴
where U is the internal energy, S is the entropy, and F is the Helmholtz free energy. F has two parts: ␾stat is the static 共lattice兲 energy,
and Fvib is the vibrational contribution to the Helmholtz energy. The
stable configuration corresponds to that vector in the parameter
space which satisfies the condition
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Journal of The Electrochemical Society, 152 共6兲 H84-H93 共2005兲
H87
Table I. Interatomic potential parameters. A„eV…, C „eV · Å6… and ␳ „Å… are defined in the text. K„eV/Å2… is the spring constant between
oxygen shell and core. The numbers in parentheses provide appropriate constant for tetrahedral coordination.
a. Source: See text footnote c.
Function
Atom type
Atom type
A
C
k
␳
O
O
O
O
O
Al
O
O
22,764
1460.3
-
27.879
-
74.92
0.149
0.29912
-
Atom type
Atom type
A
C
k
␳
O
O
O
O
O
Al
O
O
9547.46
1725.2
-
32
-
54.8
0.21916
0.28971
-
Atom type
Atom type
A
C
k
␳
O
O
O
O
O
O
O
Al
Mg
Ba
O
O
22,764
1474.40 共1334.31兲
821.60 共710.50兲
931.70
-
17.890
-
27.29
0.149
0.30059
0.32420
0.39490
-
Short
Short
Inverse
Spring
b. Source: Grimes 共Ref. 28兲
Function
Short
Short
Inverse
Spring
c. Source: Park and Cormack 共Ref. 26,27兲
Function
Short
Short
Short
Short
Inverse
Spring
d. Distribution of charges on oxygen
Source
Cormack
Catlow
Grimes
冉 冊
⳵G
⳵ ␧A
=0
␧⬘
关7兴
where ␧⬘ corresponds to all other coordinates other than A. The
algorithm that implements the optimization condition 共Eq. 7兲 in
Shell is discussed in detail in Ref. 15.
In addition to optimization with respect to all coordinates, Shell
also determines the optimal geometry at two levels of approximations: the zero static internal stress approximation 共ZSISA兲 and constant internal strain parameter 共CISPA兲 conditions. The condition for
full optimization is
冉 冊 冉 冊
⳵G
⳵G
=
=0
⳵ ␧lext ␧⬘
⳵ ␧int
k ␧⬘
The equilibrium condition in ZSISA is given by
关8兴
冉 冊 冉 冊
⳵G
⳵ Gstat
=
=0
关9兴
⳵ ␧lext ␧⬘
⳵ ␧ext
k
␧⬘
Because the number of external coordinates never exceeds 6, this
approximation for large unit cells is considerably faster. In CISPA, a
set of internal coordinates is found by full minimization of the static
energy
冉 冊 冉 冊
⳵ Gstat
⳵ Gstat
=
=0
关10兴
⳵ ␧lext ␧⬘
⳵ ␧int
k
␧⬘
These internal coordinates are then held constant during subsequent
optimization with respect to the external coordinates. BAM being a
very complex system, we have confined the entire defect-related
calculations to minimization with respect to the static energy, also
referred to as the lattice energy. This approach has been used in the
past to study the lattice structure of barium and lanthanum
hexaaluminates.26,27 Here we have extended this approach to more
complex defect structures with very interesting results.
Oxygen 共shell兲
Oxygen 共core兲
−2.207
−2.869
−2.8
0.207
0.869
0.8
Results and Discussion
Validation of potential parameters.— Alumina was used as a
test case for validating the approach described earlier. In Tables I,
different sets of potential parameters for pairwise interaction of aluminum and oxygen ionsc 28 for simulating aluminum oxides are
listed along with those used for studying hexaaluminates.d Although
the variation in the values of the interatomic potential parameters is
significant, these parameters yield a nearly identical functional dependence of the potential on interatomic distance. In Table I, the
pairwise potentials used by Park and Cormack are listed.26,27 The
suitability of these potentials has been established for studying the
structural and thermodynamic properties of hexaaluminates.26,27
Note that the potential parameters are different for octahedral and
tetrahedral coordinations of the aluminum and magnesium ions
Table II lists the calculated values of the lattice energy, lattice
parameters, and elastic constants of ␣-alumina. The lattice energy is
the same as the static lattice energy, ␾stat. The structural parameters
have been calculated by minimizing the static energy with respect to
the lattice constants and dimensionless parameters, u in Eq. 4. The
full lattice dynamics formalism of Shell has not been utilized, i.e.,
contributions from the vibrational motion of the nuclei are not included. This is not a very serious approximation, as we found from
calculations on BAM. It has also been shown by Gillan that this is
often a good approximation at higher temperatures because the
change in internal energy is, to the first order, equal to the difference
between enthalpy 共zero pressure兲 and 0 K internal energy.29 The
entropy effects on the structural stability are not serious. Finally, the
c
The potential parameters used by Catlow and his collaborators are taken from the web
site: http://www.ri.ac.uk/potentials
d
The potential parameters used by Park and Cormack in Ref. 26 and 27. They are almost
the same as those in Ref. 30.
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Journal of The Electrochemical Society, 152 共6兲 H84-H93 共2005兲
H88
Table II. Comparison of structural data of Al2O3 using potential parameters from Catlow library (text footnote c) and Grimes (Ref. 28).
Experimental values are taken from Table II of Ref. 30.
Structural data
Units
Lattice energy
a
c
u1
u2
c11
c12
c13
c14
c33
c44
c66
eV
Å
Å
共units of a兲
共units of a兲
1011 dyn/cm2
1011 dyn/cm2
1011 dyn/cm2
1011 dyn/cm2
1011 dyn/cm2
1011 dyn/cm2
1011 dyn/cm2
Experiment
−160.4
4.7628
13.0032
0.352
0.306
49.49
16.36
11.09
−2.35
49.80
14.74
16.67
Grimes 共Shell兲
Grimes
4.812
12.734
0.357
0.291
69.58
32.22
22.56
−4.69
57.44
15.95
18.69
structural parameters calculated by Shell are compared with those
by the earlier workers using a similar lattice energy minimization
procedure. This comparison provides a check for the reliability of
the Shell algorithm.
Alumina is one of the binary oxide components of BAM. Corundum, ␣-alumina, crystallizes in the hexagonal space group, R3̄c
共167兲. The aluminum and oxygen atoms occupy the 12c and 18e
Wyckoff positions, respectively. Two lattice constants, a and c, and
two u parameters completely describe the lattice and the coordinates
of the aluminum and oxygen ions. Two sets of potential parameters
were utilized for studying the stable alumina structure. They lead to
lattice properties that are in good agreement with each other and
also with the experimental values. We have also indicated results
from Shell using these parameters, which compare well with those
calculated by Catlow et al.30 and Grimes.28 Similar results were also
obtained for MgO and BaO. These calculations provide justification
for using the parameters listed in Table I for investigating the structural properties of BAM.
Optimization of BAM structure: Distribution of the Mg sites at
Al(2).—The interatomic potential parameters listed in Table I are
used here for further investigation of structural properties of BAM
and point defects in this lattice. Occasionally, results from other
variations of interatomic potentials are used to establish the adequacy of those used by Park and Cormack. 共See footnoted.兲
In this section, we report three different aspects of our structural
investigation of BAM: the distribution of Mg ions at Al共2兲 sites,
optimized structure of BAM with Mg atoms at the most stable site,
and temperature dependence of thermodynamic potentials of BAM.
The crystal structure of BAM has been investigated using single
crystal5 and powder samples. 共Several recent papers are based on
powder diffraction.兲31,32 BAM crystallizes in the ␤-alumina structure in the hexagonal space group, P63 /mmc. The crystal structure
of BAM is related to the ␤-alumina structure of Na Al11O17. The
hexaaluminates in ␤-alumina, magnetoplumbite, and related phases
exhibit layer structures, consisting of intermediate layers containing
Ba ions and spinel blocks stacking alternately along the c direction.
The structure of BAM can be better appreciated if we consider Na
␤-alumina as the parent structure and BAM as a derived system in
which the Na ions are replaced by Ba ions, accompanied by charge
compensation with Mg ions at Al sites. Because each unit cell contains two formula units and, therefore, two barium ions, there are
two magnesium ions distributed among the aluminum sites. The
XRD pattern for BAM is often analyzed assuming a random distribution of the magnesium ions at the aluminum ion sites in the spinel
block.
The aluminum ions occupy three different Wyckoff sites in the
␤-alumina structure: 12k 关Al共1兲兴, 4f 关Al共2兲兴, 4f 关Al共3兲兴, and 2a
关Al共4兲兴. The aluminum ions at the 12k and 2a sites are octahedrally
coordinated, and those at the 4f sites are tetrahedrally coordinated.
−161.10
4.811
12.732
0.359
0.297
69.60
32.23
22.58
−4.68
57.43
15.96
18.68
Catlow et al.
−160.21
13.2
42.96
15.48
12.72
−2.99
50.23
16.66
13.70
Catlow 共Shell兲
−160.56
4.7792
12.5638
0.359
0.294
64.82
29.69
20.63
−4.53
50.49
15.36
15.36
Clearly, unless the Mg ions occupy the 2a sites, they must be randomly distributed over the available aluminum sites to retain the
same space group symmetry.
Based on modeling27 and qualitative arguments,31 the magnesium ions are believed to occupy the Al共2兲 sites. But there are four
Al共2兲 sites:
Site 1 1/3 1/3 z
Site 2 2/3 1/3 z + 1/2
Site 3 2/3 1/3 −z
Site 4 1/3 2/3 −z + 1/2 with z = .024. The question is then if
there is a preference for any particular combination of sites on the
basis of lattice energies.
Lattice energies, ␾stat, for Mg atom pairs for combinations of
sites 共1,2兲, 共1,3兲, 共1,4兲, 共2,4兲, 共2,3兲, and 共3,4兲 are calculated using
two sets of potentials differing only in aluminum-oxygen interatomic potentials 共Table III兲. One set of potentials is from Lewis and
Catlow33 used earlier for calculations involving alumina. 共These parameters are listed in the web site of footnotec.兲 The potential parameters in this set differ slightly from those used by Park and
Cormack,26,27 but provide a better agreement with the observed cohesive energy for alumina. The Gibbs energies for occupancy of
these sites by Mg atoms were probed using two sets of potentials.
Except for the occupancies of site combinations 共1,3兲 and 共2,4兲, the
occupancies of all other site combinations are energetically favorable. At 300 K, ⌬G corresponding to the chemical reaction
5Al2O3 + MgO + BaO → BaMgAl10O17
关11兴
is ⬃−6 eV. This suggests first the stability of the BAM lattice structure, and second that the magnesium ions are distributed randomly
in the lattice. However, the magnesium ions avoid occupancy of
Table III. Comparison of lattice energies of BaMgAl10O17 with
Mg atoms distributed over different Al(2) sites. The change in
lattice energy, ⌬E, corresponds to E„BaMgAl10O17…
− E„MgO… + E„BaO… + E„5Al2O3….
Compound
BaO
MgO
5Al2O3 共Catlow and Lewis兲
BaO + MgO + Al2O3
BAM: Mg共1,2兲/共3,4兲
BAM: Mg共1,3兲/共2,4兲
BAM: Mg共1,4兲/共2,3兲
5Al2O3
BAM: Mg共1,3兲/共2,4兲
BAM: Mg共1,2兲/Mg共3,4兲
Lattice energy
共kJ/mol兲
⌬E 共kJ/mol兲
⌬E 共eV兲
−3020.746
−3902.216
−77359.052
−84282.014
−84862.051
−84222.552
−84853.434
−76602.247
−83361.845
−83985.761
−580.037
59.462
−571.420
163.365
−460.552
−6.01
0.62
−5.92
1.69
−4.77
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Journal of The Electrochemical Society, 152 共6兲 H84-H93 共2005兲
H89
Table IV. Variation of thermodynamic potentials of BAM with temperature.
a. Temp. 300 K, a = 5.701 Å, c = 22.475 Å
␾stat 共kJ/mol兲
−3902.086
−3019.721
−76601.424
−83523.424
−83985.154
−461.73 共−4.78 eV兲
Compound
MgO
BaO
5Al2O3
MgO + BaO + 5Al2O3
BAM
⌬
U 共kJ/mol兲
−3883.146
−3003.278
−76336.908
−83223.332
−83682.693
−459.3605 共−4.75 eV兲
G 共kJ/mol兲
−3892.378
−3022.064
−76420.948
−83335.388
−83795.572
−460.183 共−4.77 eV兲
U 共kJ/mol兲
−3823.340
−2940.478
−75640.557
−82404.376
−82872.840
−468.463 共−4.85 eV兲
G 共kJ/mol兲
−3985.484
−3157.681
−77404.675
−84547.839
−85004.392
−456.552 共−4.73 eV兲
U 共kJ/mol兲
−3794.135
−2908.218
−75324.956
−82027.309
−82507.608
−480.299 共−4.98 eV兲
G 共kJ/mol兲
−4043.819
−3234.670
−78040.109
−85318.598
−85769.775
−451.177 共−4.67 eV兲
b. Temp. 1500 K, a = 5.728 Å, c = 22.582 Å
␾stat 共kJ/mol兲
−3898.951
−3015.583
−76592.791
−83507.326
−83976.536
−469.211 共−4.86 eV兲
Compound
MgO
BaO
5Al2O3
MgO + BaO + 5Al2O3
BAM
⌬
c. Temp. 2000 K, a = 5.741 Å, c = 22.639 Å
␾stat 共kJ/mol兲
−3894.458
−3008.179
−76584.636
−83487.274
−83968.192
−480.918 共−4.98 eV兲
Compound
MgO
BaO
5Al2O3
MgO + BaO + 5Al2O3
BAM
⌬
sites where they are close to each other within the same spinel block
as for the occupancy of sites 共1,3兲/共2,4兲. This is expected if one
considers BAM as a derivative of Na ␤-alumina, in which Ba atoms
at the Na sites are charge compensated by the Mg atoms occupying
Al sites. The Mg atoms at the Al sites are negatively charged with
respect to the rest of the lattice, and thus, clustering of the Mg atoms
is prevented by mutual electrostatic repulsion. Additionally, calculations performed with the potential used by Park and Cormack26,27
show the same trend, although the magnitude of change in the lattice
energy is slightly lower 共⬃−4.8 eV兲. In the subsequent calculations
of BAM, we have used the minimum energy configuration with the
Mg ions at the site 共1,2兲.
We also investigated the stability of BAM and the variation of
static energy ␾stat internal energy U, and Gibbs energy G at 300,
1500, and 2000 K. The results of these calculations are listed in
Table IV, and the optimized geometry at 300 K is given in Table V.
Table IV also gives lattice parameters a and c at the corresponding
temperatures.
There are several reasons for studying the variation of thermodynamic potential with temperature. In the subsequent calculations,
we focus our attention on the stability of defect structures with respect to composition of the starting mixtures and ideal BAM. Be-
cause BAM is synthesized at fixed temperature and pressure, the
correct potential is the Gibbs energy. A chemical reaction at constant
temperature and pressure moves forward, if it minimizes the corresponding Gibbs energies, i.e., the change in Gibbs energies is negative. Second, the optimized structure also refers to a minimum Gibbs
energy configuration. But the calculation of Gibbs energy for a complex system such as BAM can be very time consuming. The supercell calculations for defect structures could be both time consuming
and unstable. Thus, it is essential to determine if optimization of the
static energy could lead reliably to the observed equilibrated structures. It is clear from Table IV that the changes in static energy,
internal energy, and Gibbs energy are nearly equal. The optimized
geometries calculated by minimization of the Gibbs energy are almost the same as those obtained by minimization of the static energy.
Table V gives the optimized structure by minimization of the
static energies. It is assumed that the magnesium atoms occupy aluminum ion sites 共1,2兲. For comparison, the structural data for BAM
from the XRD measurements are also given in Table V. The agreement between the observed5,31 and calculated structures is excellent.
Table V. Comparison of structural parameters of BAM calculated by Shell with experimental ones (Ref. 5 and 31) Lattice constants: a
= 5.628 Å (expt.), 5.701 Å (theory); c = 22.658 Å (expt.), 22.475 Å (theory).
Atom
Wyckoff site
x 共expt.兲
y 共expt.兲
z 共expt.兲
x 共theory兲
y 共theory兲
z 共theory兲
Ba
Al共1兲
Al共2兲
Al共3兲
Al共4兲
O共1兲
O共2兲
O共3兲
O共4兲
O共5兲
2d
12k
4f
4f
2a
12k
12k
4f
4e
2c
2/3
0.8343
1/3
1/3
0
0.1534
0.5042
2/3
0
1/3
1/3
0.6686
2/3
2/3
0
0.3068
0.0084
1/3
0
2/3
1/4
0.10544
0.0240
0.017416
0
0.05152
0.14799
0.05901
0.14437
1/4
2/3
0.8325
1/3
1/3
0
0.1541
0.5002
2/3
0
1/3
1/3
0.6650
2/3
2/3
0
0.3082
0.0047
1/3
0
2/3
1/4
0.10459
0.0248
0.17391
0
0.05128
0.1461
0.059263
0.13843
1/4
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Journal of The Electrochemical Society, 152 共6兲 H84-H93 共2005兲
H90
Table VI. Lattice energies for BaO, MgO, Al2O3, and the model
compound Ba2Al22O35.
Lattice energy 共kJ/mol兲
Model compound
BaO
MgO
Al2O3
Ba2Al22O35
−3020.746
−3902.216
−15320.450
−175351.032
Local structure of oxygen interstitials in intermediate plane.— It
was discussed earlier how the color centers play an important role in
the performance of a phosphor in fluorescent lamps. They have high
oscillator strengths, and thus, the presence of color centers in a ppm
range could provide strong absorption centers. Two electron centers
共F and F+兲 and a hole center have been observed in Ba ␤-alumina
phase I and M+-aluminates upon irradiation by X-ray and ␥-ray
irradiations, and to a lesser degree by VUV/UV radiation. Only two
of these color centers, a hole center, OI⬘, and an electron center, F+,
are identified to be paramagnetic in nature by electron spin resonance and electron-nuclear double resonance measurements.6,8-10,34
The 11 line hyperfine pattern with a sequence of peaks in the intensity ratio of 1:2:3:4:5:6:5:4:3:2:1 for the F+ center suggests that this
center is located between two equivalent Al nuclei with I = 5/2.34
The hyperfine structure results from the interaction of an unpaired
electron with the two symmetrical Al ions. This center is associated
with an anion vacancy, namely an oxygen vacancy in ␤-alumina.
The question is then which oxygen atom is responsible for generation of this center.
The oxygen atoms in the spinel block are coordinated either to
four or three aluminum ions. There are only two oxygen atoms in
phase I of Ba ␤-alumina that are coordinated to two aluminum ions:
the bridging oxygen atom in the intermediate plane O 共5兲, and the
interstitial oxygen ion OR located at a mid-oxygen site. These oxygen ions generate the Reidinger defects.
O共5兲 is the bridging atom between the spinel blocks in all
␤-alumina structures. It is located in the intermediate plane and is
coordinated to two symmetrical aluminum ions, Al共3兲. The Reidinger defect appears in barium hexaaluminates phases I and II in
the ␤-alumina structure. 共For more details, see Ref. 26 and 31 and
references cited.兲 This defect is associated with a highly reconstructed site with an oxygen atom, OR, located in the intermediate
plane and bonded to two tetrahedrally coordinated aluminum atoms.
Thus, the F+ center is associated with either the vacancy of O 共5兲 or
OR. The F+ centers are rare in stoichiometric Na+-␤-alumina or
nonstoichiometric Na+-␤⬙-alumina, where the charge compensation
is due to divalent ions in the spinel block. However, both these
systems contain bridging oxygen atoms, O 共5兲. Therefore, the F+
centers could be formed only at the Reidinger defects.
The structural information of Reidinger defects has been obtained by modeling and diffraction measurements. There are two
simple questions of fundamental significance to the synthesis of
BAM: First, what are the sources of the the oxygen interstitials in
BAM? Second, will such interstitials induce the Reidinger defects?
Oxygen interstitials could be formed in two circumstances. The
first case is when the two magnesium ions are replaced by two
aluminum ions. These two substitutional point defects could be
charge compensated by one oxygen ion. This oxygen ion could be
trapped in the intermediate plane. Second, a solid solution of BAL
and BAM is formed due to excess alumina in the starting mixture.35
The situation of excess alumina is realized by deliberate addition of
alumina over stoichiometry or the loss of MgO 共and BaO兲 during
synthesis. We have investigated both scenarios leading to formation
of oxygen interstitials in the following sections.
Formation of AlMg-AlMg-Ol defect structure.—This complex defect
structure, which results from substituting aluminum ions for two
magnesium ions in BAM, is simulated by calculating the lattice
energy of a model compound, Ba2Al22O35. This compound can be
considered as resulting from a chemical reaction
2BaO + 11Al2O3 → Ba2Al22O35
关12兴
If the change in the Gibbs energy 共⬃⌬G兲 is negative for this reaction, the reaction can go forward. The final product in Reaction 12 is
equivalent to BAM with two magnesium ions being replaced by two
aluminum ions.
The lattice energies for BaO, MgO, Al2O3, and Ba2Al22O35 are
summarized in Table VI. The change in the Gibbs energy is approximated by the change in lattice energy of the reactants and the products. The change in Gibbs energy, ⌬G, for Reaction 12 is
−146.97029 kJ/mol 共−1.52 eV兲. Thus, if magnesium oxide is lost
during solid-state synthesis, there would be a tendency to form
BaAl22O35. In other words, Reaction 12 could lead to incorporation
of oxygen defects in BAM.
Next we consider the stability of oxygen defects with respect to
BAM by studying the chemical reaction
Ba2Mg2Al20O34 + Al2O3 → Ba2Al22O35 + 2MgO
关13兴
This reaction describes alumina being dissolved in BAM accompanied by precipitation of MgO. The change in Gibbs energy is positive for this reaction and is equal to 136.5070 kJ/mol 共1.414 eV兲. At
a synthesis temperature of 2000 K for BAM, this could lead to
⬃270 ppm oxygen defects in the lattice. At this concentration, color
centers generated at oxygen defect sites could affect the performance of BAM.
Next, we examine the structural details of the model compounds
to determine if these oxygen centers are structurally similar to the
Reidinger defects. We do not have any structural data for such defects, so we compare the calculated structural parameters with those
Table VII. Optimized structural parameters (Å) for Ba2Al22O35. Experimental data are from Ref. 31.
Structural parameters
x
0.3801
0.8211
0.8464
Bond length
Al1RO4
Al1RO2共x2兲
Al1ROR
1.73
1.74
1.76
Lattice parameters
a
c
Experiment 共structural data for Ba-hexaaluminate, Phase I兲
Theory
Atoms
Ba
Al1R
OR
5.6894
22.2497
y
0.1539
0.6710
0.6918
z
0.25
0.1711
0.25
x
2/3
0.84176
0.87303
y
1/3
0.68352
0.74606
z
0.25
0.17709
0.25
1.73
1.77
1.68
5.588412
22.72626
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Journal of The Electrochemical Society, 152 共6兲 H84-H93 共2005兲
Table VIII. Lattice vectors in Å.
Material
BAL
BAM
a 共theory兲
c 共theory兲
a 共expt.兲
c 共expt.兲
5.65262
5.69161
22.48881
22.44138
5.588412
5.62534
22.72626
22.65751
Table IX. Coordinates of Al and OR ions of the Reidinger defect.
The subscript R is used to describe the interstitial oxygen atom in
the conduction plane. The coordinates are given in terms of lattice vectors.
Ion x 共theory兲 y 共theory兲 z 共theory兲 x 共expt.兲 y 共expt.兲 z 共expt.兲
O
Al
0.89799
0.86683
0.73665
0.68862
0.25
0.17734
0.87303
0.84176
0.74606
0.68352
0.25
0.17709
Table X. AlAO bond lengths (in Å) of the Reidinger defect.
Bond
Al-OR
AlO4
AlO2 共x2兲
H91
ton or an energetic ion from the discharge removes this oxygen atom
from the lattice, the associated oxygen vacancy could capture one or
two electrons, forming F+- or F- type color centers, respectively.
The local geometry of a Reidinger defect has been determined
using the XRD technique.31,37,38 The calculated structural parameters reported in Tables VIII-X are in excellent agreement with the
experimental ones.31 In Table VIII, we have shown the lattice parameters for BAM and BAL. The lattice constant a decreases from
5.63 Å in BAM to 5.59 Å in BAL and c increases from 22.66 Å to
22.73 Å. The theoretical values of these parameters for BAM and
BAL show the same trend. The calculated positions of OR and Al共1兲
ions associated with the Reidinger defect are in good agreement
with the experimental ones. The experimental values of Al-O bond
lengths for this defect are satisfactorily reproduced by theory. The
good agreement of experimentally observed structural parameters
with those calculated by theory justifies the goodness of the twobody potentials used in this work and the structural model of BAL
and that of Reidinger defects.
To study the stability of BAL, the lattice energy of BAL is compared with those of alumina and barium oxide in relation to the
chemical reaction
Length 共theory兲
Length 共expt.兲
3BaO + 22Al2O3 Ba3Al44O69
1.651
1.746
1.767
1.684
1.734
1.770
The change in the lattice energy is −1882.92 kJ/mol 共−19.51 eV兲,
indicating that this reaction would lead to formation of BAL. The
stability of BAL with respect to BAM is examined by investigating
the lattice energies of materials involved in the chemical reaction
for barium hexaaluminate in phase I 共Ba.75Al11O17.25兲 共see Table
VII兲, in which the presence of the Reidinger defects has been
established.31
The calculated parameters reveal some interesting details about
the interstitial oxygen ions.
1. Oxygen interstitials are located at the mO sites near the large
cation site.
2. In phase I of Ba-hexaaluminate, the large cation is actually
missing near the oxygen interstitial. In the present case, the Ba ion
moves to an mO site to allow the structural relaxation around the
impurity ion. This is the first theoretical evidence of a cation occupying an mO site in the BAM lattice.3,36
3. Al共1兲 atoms above and below the interstitial oxygen ion move
toward the intermediate plane to form a “Reidinger defect.” The
coordination of the aluminum atoms changes from an octahedral to
a tetrahedral configuration similar to those of the Reidinger defects.
4. The Al-O bond lengths for this reconstructed defect compare
reasonably well with those for a Reidinger defect in ideal phase I
共Table VII兲.
These results suggest the possibility of formation of the Reidinger defects in BAM at a ppm level when the starting materials
have excess alumina or are deficient in MgO. Most importantly, it
suggests that the energetically favorable configuration surrounding
an interstitial oxygen ion is very similar to a Reidinger defect. We
also examined several other plausible mechanisms to incorporate an
interstitial oxygen ion, but they require substantially high energy for
their formation and are unlikely to be formed.
Stability of BAM-BAL solid solution.—The role of Reidinger defects, as the most likely precursors of color centers in BAM, was
discussed earlier. The Reidinger defects are intrinsic to barium
hexaaluminate in phase I, Ba.75Al11O17.25 共BAL兲. The chemical
composition of BAL and the available sites in the ␤-alumina structure in which BAL crystallizes imply that one of every four halfcells would have a vacancy at the site of a barium ion and an extra
oxygen atom at the mid-oxygen site adjacent to this vacancy. These
defect half-cells are randomly distributed throughout the crystal. The
interstitial oxygen ion, near a barium ion vacancy and occupying a
mid-oxygen site, generates the Reidinger defect. When a VUV pho-
关14兴
2Ba2Mg2Al20O34 + 2Al2O3 Ba3Al44O69 + BaO + 4MgO
关15兴
This hypothetical chemical reaction provides the theoretical basis to
determine if excess alumina would induce generation of BAL. The
change in lattice energy in this reaction proceeding from left to right
is −40.713 kJ/mol 共−0.42 eV兲, and thus, it favors formation of
BAL when the input mixture for BAM contains excess alumina.
Reaction 15 also suggests that BaO and MgO would leave the BAM
lattice to accommodate BAL. Based on lattice energies calculated
for various oxides in this study, the error in lattice energies in Reaction 15 is estimated to be less than ±0.5%. The relatively small
change in lattice energy should also be considered from the perspective of forming solid solution BAM and BAL. BAM has already
been shown to be very stable with respect to BaO, Al2O3, and MgO,
and So is BAL 共Reaction 14兲. Thus, we expect only a small change
in lattice energy between the reactants and products. Additionally,
the entropic contribution to the change in Gibbs energy at the high
solid-state synthesis temperature is also expected to favor the forward reaction.
The significance of this reaction is evident when one examines
the phase diagram of BAM39 with recent modifications suggested by
Diaz et al. 共Fig. 2兲.35 The chemical composition of the reactants in
Reaction 15 corresponds to a point on BAM and the alumina join
close to BAM. Using the phase diagram in Fig. 2, one would conclude that this composition in equilibrium would lead to two separate phases of BAM and alumina. However, the lattice energy calculation for Reaction 15 suggests that the chemical reaction favors
phase separation of BAL, BaO, and MgO. Thus, our calculations
and the original phase diagram are not compatible. Two simple
modifications of the phase diagram would make it compatible with
our calculations and, most importantly, with some recent experimental results regarding the solubility of alumina in BAM. There is
probably another stable point in the phase field of BAM, alumina,
and BAL which splits the phase field near BAM. This was suggested
by Diaz et al.35 based on a study of color shift of BAM with excess
alumina and XRD results indicating absence of alumina up to a
certain amount of excess alumina in the starting materials for BAM.
The revised phase field due to point P is indicated by the dashed
lines. The other alternative is that the phase field characterized by
BAM, BAL, alumina, and spinel-alumina solid solution can be di-
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H92
Journal of The Electrochemical Society, 152 共6兲 H84-H93 共2005兲
Figure 2. Phase diagram of BaO, Al2O3, and MgO. The dashed lines are
recommended changes in the phase field near BAM by Diaz et al.35 BAL-I is
the same as BAL discussed in the text. BAL-II is the barium-rich phase of
barium hexaaluminate, Ba2.33Al21.33O34.33. BAM-S is the solid solution join
of BAL and BAM. BAM-II and BAM-IIS are Mg-rich phases of BAM. For
more details, see Ref. 39.
vided into two regions by a BAL and spinel join instead of a BAM
and alumina join. In either case, the BAM and alumina mixture in
Reaction 15 leads to two phases: a solid solution of BAM and BAL,
and a solid solution of alumina and spinel. This requires that the
following equation should allow solutions for x,y, and z
2共Ba2Mg2Al20O34 + Al2O3兲
xBa3Al44O69 + yBa2Mg2Al20O34
+ z共MgAl2O4 + 2.07Al2O3兲
关16兴
The spinel and alumina contents on the right side of Reaction 16
correspond to the solid solution limit of spinel and alumina in the
phase diagram. Reaction 16 leads to values of x,y, and z of 0.12,
1.81, and 0.37, respectively, corresponding to a mixture of BAL,
BAM, and a solid solution of spinel alumina in the ratio of 5:79:16.
Because BAM and BAL have a continuous solid solution range at
this range, BAM and BAL would appear as a solid solution if the
reaction is favored energetically.
To establish if the chemical reaction hypothesized in Reaction 16
would lead to a solid solution of BAM and BAL, one needs the
lattice energy for the spinel in addition to those of BAM, BAL, and
alumina. Therefore, the structural and thermodynamic properties of
spinel were calculated. The pair potentials for Mg, Al, and O ions
are the same as those used in our earlier calculations involving
BAM. The lattice energy for the spinel was calculated assuming a
face-centered cubic structure. The magnesium and aluminum ions
are assumed to occupy special Wyckoff positions 8a and 16d. The
oxygen atoms occupy the Wyckoff site 32e. For a complete specification of all the coordinates, this site requires specification of a
parameter u in addition to the lattice constant a. Thus, the lattice
energy was optimized with respect to the lattice parameters a and u.
The optimized values of the lattice constant a and the structural
parameter u are 8.1002 Å and 0.38951, respectively. These values
compare well with the experimentally observed values of a and u of
8.0625 Å and 0.38672 from XRD40 and 8.08 Å and 0.387 from
neutron diffraction measurements.41
Using the calculated lattice energy for the optimized structure,
the change in lattice energy for the chemical reaction Al2O3
+ MgO MgAl2O4 is −142.47763 kJ/mol 共−1.47607兲. It is in reasonable agreement with the observed value of −0.38 eV.42 The over-
estimation is partly due to the choice of separate potentials for aluminum and magnesium ions in octahedral and tetrahedral
coordinations used in this work. As indicated by Park and
Cormack,27 this is essential for a proper description of the lattice
structures where the aluminum ions occupy both the octahedral and
tetrahedral sites, as in BAM.
Using the lattice energy calculated by spinel, BAM, BAL, and
alumina, one could determine if the reaction of BAM and alumina
共Reaction 15兲 would result in BAL, BAM, and a solid solution of
spinel and alumina. Using the corresponding lattice energies, the
change in lattice energy is −114.89 kJ/mol. This suggests that the
presence of alumina would drive the aforementioned chemical reaction forward. Because BAM and BAL form a continuous solid solution range, the resulting product would contain two phases: a solid
solution of BAM and BAL, and a solid solution of spinel and alumina.
Clearly, from the earlier discussion, a solid solution of BAM and
BAL would be formed if alumina were present in the composition of
the starting materials in excess of stoichiometry. It could happen in
two different ways: deliberate addition of alumina to the starting
compounds in excess of stoichiometry or loss of MgO and BaO
during synthesis. In either case, excess alumina in the input mixture
of materials would lead to a solid solution of BAM and BAL. BAL
would introduce the Reidinger defects, which in turn would generate
color centers during lamp life. Thus, the best way to control color
centers is to search for synthesis procedures to generate stoichiometric BAM. The other alternative is to search for phosphor treatments that could prevent creation of oxygen vacancies by VUV
radiation from the discharge.
Conclusions
The main objective of this study is to determine mechanisms of
degradation of BAM during lamp life. Based on earlier works on
color centers in ␤-alumina, it was hypothesized that the Reidinger
defects are precursors of the electron centers, F and F+. Based on
this hypothesis, plausible different scenarios that could lead to formation of these centers were explored using atomistic simulation
methods. Two scenarios are interesting from the perspective of
phosphor synthesis. Both involve the presence of excess alumina. In
one case, two aluminum ions substitute for two magnesium ions and
incorporate an oxygen atom at an mO site. This would lead to a
reconstruction of the site around the oxygen atom at the mO site,
leading eventually to a Reidinger defect and the displacement of a
Ba ion from the BR site to a nearby mO site. Two magnesium ions
precipitate out of the lattice. This could lead to formation of a Reidinger defect near a Ba site. The other case involves a solid solution
of BAL and BAM. It is also induced by excess alumina, but differs
from the previous case in that a Reidinger defect is created near a Ba
vacancy and Ba and Mg ions leave the lattice. This solid solution is
thermodynamically more stable than the first scenario and is more
likely to form if excess alumina is present in the starting mixture or
if the starting mixture is deficient in both MgO and BaO. The loss of
MgO and possibly BaO could occur during the synthesis of phosphor in hydrogen atmosphere. This loss could result in the enhancement of alumina in the starting material. Raukas observed color
center absorption bands in a stoichiometric formulation of BAM
共see footnotea兲. One of the plausible explanations for this observation is the loss of Mg ions during the synthesis process. Bheemineni
and Readey43 have observed that the rate of evaporation of MgO is
inversely proportional to the water vapor content of the reducing
hydrogen gas and directly proportional to the square root of the gas
velocity. Probably one could use wet hydrogen during the synthesis
process and optimize its flow rate to reduce the vaporization rate of
MgO while reducing trivalent europium ions.
Acknowledgments
I am grateful to Professor N. Allan for a copy of Shell and
associated codes for analysis of the results from Shell. Special ac-
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Journal of The Electrochemical Society, 152 共6兲 H84-H93 共2005兲
knowledgments are due to Professor K. H. Johnson, Dr. J. Lister, E.
Dale, and Dr. M. Raukas for many helpful discussions and suggestions.
OSRAM-SYLVANIA Incorporated assisted in meeting the publication
costs of this article.
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