Pressure effects on phase equilibria and solid solubility ...
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Pressure effects on phase equilibria and solid solubility in MgO-Y2O3nanocompositesE. K. Akdoğan, İ. Şavklιyιldιz, B. Berke, Z. Zhong, L. Wang et al. Citation: J. Appl. Phys. 111, 053506 (2012); doi: 10.1063/1.3691219 View online: http://dx.doi.org/10.1063/1.3691219 View Table of Contents: http://jap.aip.org/resource/1/JAPIAU/v111/i5 Published by the AIP Publishing LLC. Additional information on J. Appl. Phys.Journal Homepage: http://jap.aip.org/ Journal Information: http://jap.aip.org/about/about_the_journal Top downloads: http://jap.aip.org/features/most_downloaded Information for Authors: http://jap.aip.org/authors
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Pressure effects on phase equilibria and solid solubility in MgO-Y2O3
nanocomposites
E. K. Akdogan,1,a) _I. S� avkliyildiz,1 B. Berke,1 Z. Zhong,2 L. Wang,3 D. Weidner,3
M. C. Croft,4 and T. Tsakalakos1
1Department of Materials Science and Engineering, Rutgers University, Piscataway, New Jersey 08854, USA2National Synchrotron Light Source, Brookhaven National Laboratory, Upton, New York 11973, USA3Mineral Physics Institute, Stony Brook University, Stony Brook, New York 11794, USA4Department of Physics and Astronomy, Rutgers University, Piscataway, New Jersey 08854, USA
(Received 5 October 2011; accepted 1 February 2012; published online 5 March 2012)
We study the temperature and pressure dependence of phase evolution in the 0.5MgO-0.5Y2O3
nanocomposite system using a diamond anvil apparatus in conjunction with in situ synchrotron
energy dispersive x-ray diffraction at 7 GPa hydrostatic pressure. At (298 K, 7.0 GPa), structural
transformations in the Y2O3 phase are observed, giving rise to the co-existence of its cubic,
hexagonal, and monoclinic polymorphs together with cubic MgO. An increase in temperature to
1273 K causes the crystallinity of the Y2O3 hexagonal and monoclinic phases to increase.
Isothermal and isobaric hold at (1273 K, 7.0 GPa) for 60 min results in yttrium dissolution in cubic
MgO, causing �1.0% expansive volumetric lattice strain despite the large differences in the ionic
radii of the cations. Cooling the nanocomposite to (298 K, 0 GPa) after a 60 min soak yields four
phase co-existence among cubic MgO and cubic, hexagonal, and monoclinic Y2O3. The residual
MgO unit cell volume expansion is 0.69% at 298 K, indicating solid solution formation at room
temperature despite large differences in the ionic radii of Mg2þ and Y3þ. The macroscopic
shrinkage due to densification is 3% by volume. Thermodynamic considerations suggest that the
relative molar partial volume of Y3þ in MgO is a negative quantity, indicating that the partial
molar volume of Y3þ in the solid solution is smaller than its molar volume in the pure state. Aging
of the nanocomposites for 240 h does not change the observed 4 phase co-existence. We propose a
crystallographic model in which the observed volumetric expansion of the MgO unit cell is
primarily attributed to two hydrostatic expansive strain components accompanying solid solution
formation: (i) Coulomb repulsion among O2� ions in the immediate vicinity of Mg2þ vacancies,
and (ii) misfit strain due to differences in ionic radii upon Y3þ substitution on Mg2þ sites. VC 2012American Institute of Physics. [http://dx.doi.org/10.1063/1.3691219]
I. INTRODUCTION
The physics of solids under high pressure is one of the
fields of high activity in condensed matter research,1 while
the high pressure processing of polycrystalline optical materi-
als is of utmost interest when the challenge is to obtain micro-
structures with a grain size<100 nm. One such a drive in
condensed matter stems from the need to obtain cost-effective
polycrystalline solids with both outstanding optical properties
and high mechanical strength.2 However, such challenges in
solid state research require that one consider the effects of
high pressure (and temperature, whenever applicable) on the
phase composition in multiphase systems. Here, we report on
the effects of high pressure on the phase evolution in the
MgO-Y2O3 (MY) nanocomposite system. The optical trans-
mittance of the MY system in the mid-IR range is interesting,
making it a potential replacement for single crystal Al2O3.2
Cubic MgO is stable over a very a wide pressure range
and has been used as a high pressure standard for many dec-
ades, thanks to its very reliably measured equation of
state.3–7 In addition, it is a prototype ionic oxide that has
been extensively studied as a prototype system for ab initiocalculations.1 Y2O3 is a rare earth sesquioxide and is known
to exhibit two polymorphic phase transitions at 298 K with
increasing pressure: (i) cubic (Ia-3) ! monoclinic (C2/m)
at 13 GPa, and (ii) monoclinic (C2/m) ! hexagonal
(P-3m1) at 24.5 GPa.8–11 The sequence of the mentioned
polymorphic transitions is not reversible upon the release
of pressure, and only the hexagonal (P-3m1)! monoclinic
(C2/m) transition is observed.10 The physical properties of
Y2O3 under pressure are well documented,11–14 and
processing-structure relationships also have been studied in
powders with particle sizes of �500 nm.15 In pure or doped
form, Y2O3 has many applications, among which optical
applications are the front-runners.16,17
Although much is known about MgO and Y2O3, in situstudies of the high pressure effects in MY nanocomposites in
which the starting mechanical mixture comprises �100 nm
particles are extremely scarce.18 In such nanocomposite sys-
tems, a much higher reactivity in each phase is expected
because of the very high specific surface area, resulting in a
large excess surface free energy.19–22 In this study, we exam-
ine the consequences of changing the thermokinetic state of
the nanocomposite system at high temperature and pressure.
It is shown that one is able to obtain physicochemical
a)Author to whom correspondence should be addressed. Electronic mail:
0021-8979/2012/111(5)/053506/7/$30.00 VC 2012 American Institute of Physics111, 053506-1
JOURNAL OF APPLIED PHYSICS 111, 053506 (2012)
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properties that are otherwise not achievable under ambient
conditions in this binary system.
This article is organized as follows: In Sec. II, we pro-
vide a concise description of the experiment conducted at
high temperature and pressure and describe the thermal cycle
used in this study. The experimental results are presented in
Sec. III and discussed within the framework of phase
equilibria in a multicomponent and multiphase system. The
theoretical considerations are presented in Sec. IV, in which
the discussion is centered on the pressure dependence of ac-
tivity in solution thermodynamics; defect chemistry in
oxides; and elastic strains arising from ionic misfit, electro-
striction, thermal expansion mismatch, and differences in
bulk moduli.
II. EXPERIMENTAL
A diamond anvil apparatus was used in conjunction with
high energy polychromatic x-ray radiation with photon ener-
gies reaching up to 100 keV at the X17-B2 beamline of the
National Synchrotron Light Source in Brookhaven National
Laboratory. The Bragg angle was kept constant at 2h¼ 6.62�
in the experiment reported herein.23,24 High purity commer-
cial MgO and Y2O3 powder (average particle size¼ 100 nm),
which was homogenously mixed in a 50:50 ratio by weight,
was placed into a specialty sample holder. The details of the
experimental method used in this study can be found
elsewhere.23,24
Pressure calibration was accomplished by using the
MgO phase of the nanocomposite as the pressure standard.25
The pressure at which the experiment was conducted is
7.0 GPa. The state of stress to which the nanocomposite was
subjected was hydrostatic throughout the entire cycle.23,24
Fig. 1 is a schematic showing the thermal cycle used in this
study, which consists of the following steps: (i) isothermal
compression to 7 GPa at 298 K (process A! B), (ii) isobaric
heating to 1273 K under 7 GPa applied hydrostatic pressure
(process B! C), (iii) isothermal and isobaric soak at 1273 K
and 7 GPa for 60 min (process C! D, the thermokinetic seg-
ment of the cycle), (iv) isobaric cooling to 298 K under
7 GPa applied hydrostatic pressure (process D! E), and (v)
isothermal decompression to ambient pressure (1 atm) at
298 K (process E ! F). Diffraction data were collected at
each point (A-F), and over 20 scans were taken during the
60 min period for the thermokinetic study (process C ! D).
The macroscopic linear dimensional change of the sample
was monitored using x-ray tomographic images (see Refs. 23
and 24), from which the macroscopic linear and volumetric
strains were evaluated (a.k.a. the sintering shrinkage).
III. EXPERIMENTAL RESULTS
The evolution of phases in the MY nanocomposite sys-
tem is shown in Fig. 2. At (298 K, 0 GPa), the thermody-
namic system is a typical mechanical mixture of cubic MgO
and Y2O3 with Fm–3 m and Ia-3 cell symmetries,
respectively [see Fig. 2(a)]. One observes a four phase co-
existence consisting of hexagonal and monoclinic Y2O3
phases of P-3m1 and of C2/m symmetry, respectively, and
the previously mentioned cubic phases of MgO and Y2O3
when the thermodynamic state of the MY system is changed
to (298 K, 7.0 GPa) [See Fig. 2(b)].26 Heating the system
with a heating rate�100 K/min to (1273 K, 7.0 GPa) did not
change the number of phases observed at (298 K, 7.0 GPa),
as can be verified from Fig. 2(c). However, the change of
state to (1273 K, 7.0 GPa) resulted in sharper Bragg reflec-
tions in all phases, which is indicative of increased crystal-
linity for each phase involved in the system. One also
observes an increase in the hexagonal and monoclinic
phases’ volume fractions, as can be verified from the hexago-
nal (011) and (100) and monoclinic (711), (020), (313), and
(–113) reflections of Y2O3 [see Fig. 2(c)]. The MY system
was then subjected to an isothermal and isobaric hold at
(1273 K, 7.0 GPa) for 60 min, during which the diffraction
spectrum was sampled at approximately 3 min intervals (see
Fig. S1 in the supplemental material).51 No additional phases
were observed during or at the end of the 60 min long iso-
thermal and isobaric hold. Furthermore, no change in the rel-
ative intensity of each phase was observed (see Fig. S1).51 In
other words, the four–phase co-existence remained unal-
tered, indicating that the observed phase transformation was
complete to the observed extent once the state of the system
was changed from (298 K, 0 GPa) to (300 K, 7.0 GPa). Figure
2(d) shows the diffraction pattern of the MY system at
(1273 K, 7.0 GPa) after the 60 min hold; one can observe that
the four-phase co-existence has no time dependence
whatsoever. When the temperature is reduced to 298 K via
the use of a cooling rate greater than 150 K/min under iso-
baric conditions at 7.0 GPa, the phase composition of the
MY system remains the same [see Fig. 2(e)]. Figure 2(f)
depicts the x-ray spectrum of the MY composite after com-
plete decompression; no changes in the number of phases are
seen. Thus, the phases present at (1273 K, 7.0 GPa, t¼ 0 min)
and (298 K, 0 GPa, t¼ 60 min) are identical. Therefore, one
is led to conclude that there is a four-phase stabilization in
the MY nanocomposite system after the thermodynamic
cycle used in this study.
Per the Gibbs phase rule (Fþ P¼Cþ 2, with F¼ degrees
of freedom, P¼ number of phases, and C¼ number of
FIG. 1. (Color online) The thermal cycle used in this study, con-
sisting of five segments. The segment C ! D is the thermoki-
netic study.
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components),22 a four phase equilibrium should define a sin-
gular point in the P-T-x (x¼ composition) space of a given bi-
nary system, because P¼ 4 and C¼ 2, for which F¼ 0.20 The
results reported herein indicate that the observed four phase
co-existence remains unaltered when the temperature is arbi-
trarily changed from 298 K to 1293 K, which should otherwise
induce the appearance of new phases or the disappearance of
old phases in principle.20 Furthermore, we aged the sample
for a period of 240 h and measured its energy-dispersive x-ray
diffraction spectrum under ambient conditions at X17-B1
beamline with photon energies up to 200 keV (see Fig. 3). No
changes in phase were observed. Thus, we conclude that the
observed four phase equilibrium is metastable but does not
show any phase reversal under ambient conditions. (In Fig. 3,
the peaks marked as Mullite and BN are reflections originat-
ing from the sample holder and do not pertain to the MgO-
FIG. 2. (Color online) Synchrotron energy dispersive x-ray diffraction spectrum showing the evolution of phases in the MgO-Y2O3 nanocomposite system: (a)
(298 K, 0 GPa, t¼ 0 min), (b) (298 K, 7.0 GPa, t¼ 0 min), (c) (1273 K, 7.0 GPa, t¼ 0 min), (d) (1273 K, 5.5 GPa, t¼ 120 min), (e) (300 K, 7.0 GPa, t¼ 120),
and (f) (300 K, 0 GPa, t¼ 120 min).
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Y2O3 nanocomposite systems considered herein. These peaks
appear because of the diffraction optics at the X17-B1
beamline.)
In Fig. 4, the macroscopic longitudinal strain of the com-
posite system, which was obtained from x-ray tomographic
images, is shown as a function of time during the 60 min iso-
thermal and isobaric hold at (1273 K, 7 GPa). The observed
longitudinal strain (also known as linear shrinkage) is �1.1%,
which corresponds to a volumetric shrinkage of �3.3% per
the binomial approximation.19 This shrinkage is simply due to
the densification of the MY nanocomposite. We also meas-
ured the lattice parameters during the aforementioned isother-
mal and isobaric 60 min soak. No discernable changes in the
lattice parameters of the Y2O3 phases were observed during
the soak, whereas a systematic variation in the lattice parame-
ter of MgO was measured, from which the unit cell volume
was computed as a function of time as shown in Fig. 5. We
observed a �1% volumetric expansion of the MgO unit cell
during the (1273 K, 7.0 GPa, t¼ 0 min) ! (1273 K, 7.0 GPa,
t¼ 60 min) thermokinetic change of state. Because this
change of state was accomplished under isothermal and iso-
baric conditions, the observed changes in the MgO cell
dimensions cannot be attributed to thermal expansion due to a
temperature difference DT or to volumetric changes due to a
pressure difference DP. Thus, we attribute the observed
change in the cubic MgO unit cell volume to the dissolution
of Y3þ in the cubic cell of MgO in accordance with Vegard’s
law.27 We also conclude that the dissolution of Mg2þ in all
phases of Y2O3 is negligibly small, because we have seen no
discernable changes in the appertaining lattice parameters,
although a minute amount of Mg2þ in Y2O3 cannot be com-
pletely ruled out in accordance with the theory of solutions.20
We also have compared the cubic MgO lattice parameters for
the (298 K, 0 GPa, t¼ 0 min) ! (298 K, 0 GPa, t¼ 60 min)
change in state, i.e., the initial and final states. The observed
volumetric change in the cubic MgO unit cell volume is
0.69%, which indicates that a large fraction of Y3þ remains in
the MgO unit cell upon its return to 298 K and complete
decompression. Based on the preceding discussion, one is led
to conclude that the application of 7.0 GPa and the thermal
activation at 1273 K forces Y3þ into the face centered cubic
unit cell of MgO. What is most peculiar is that solid solubility
takes place despite a substantial difference in the ionic radii
(66 pm for Mg2þ versus 89 pm for Y3þ),28 as evidenced by
the �1.0% unit cell expansion of MgO at (1273 K, 7.0 GPa,
t¼ 60 min), which is actually why there is no solid solubility
under ambient conditions (1 atm) for all temperatures below
the melting point.29 Moreover, at (298 K, 0 GPa, t¼ 60 min),
the unit cell expansion is still 0.69%, indicating that a meta-
stable solid solution is stabilized at room temperature without
quenching from 1273 K.
The empirical observations of this study suggest that the
applied pressure has a profound effect on the solid solubility
relations in the MY nanocomposite system. However, the
effect of the initial particle size (100 nm for both MgO and
FIG. 3. (Color online) Synchrotron energy dispersive x-ray diffraction spec-
trum of MgO-Y2O3 composite after 240 h showing no changes in phases
present in the nanocomposites after aging. The peaks marked as Mullite and
BN are reflections originating from the sample holder and are not related to
the MgO-Y2O3 nanocomposite systems considered herein. These peaks
appear because of the different diffraction optics at the X17-B1 beamline as
compared to the X17-B2 beamline.
FIG. 4. (Color online) Variation of the longitudinal macroscopic strain as a
function of time under isothermal and isobaric conditions at 1273 K and
7.0 GPa. The overall volumetric shrinkage is 3.3% over a period of 60 min.
FIG. 5. (Color online) Variation of the MgO cubic unit cell volume as a
function of time under isothermal and isobaric conditions at 1273 K and
7.0 GPa. The overall volumetric expansion is a colossal �1% and is attrib-
uted to Y3þ dissolution in MgO under the applied pressure.
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Y2O3) cannot be ruled out because the chemical potential of
a given species in a particle is inversely proportional to the
particle radius according to the Gibbs-Thomson effect: the
smaller the particle, the higher the surface curvature, and the
higher the chemical potential of a given species.19,20
Although the pressure induced polymorphic cubic ! mono-
clinic and monoclinic ! hexagonal phase transitions in
Y2O3 (particle size> 1 lm) take place at 13 and 24.5 GPa at
298 K, respectively,10 the results obtained in this study show
that all three polymorphs of Y2O3 are observed at 7 GPa in
MY nanocomposites. One does not expect the presence of
MgO to affect the polymorphic transitions in Y2O3 due to
the limited availability of thermal activation at 298 K needed
for chemical interactions. Thus, we are led to conclude that
the initial particle size (�100 nm) does have a profound
effect on the phase transition characteristics of Y2O3 in MY
nanocomposites following a self-consistent line of reasoning
based on the principles of thermodynamics of surfaces.30,31
However, the conclusion presented herein should be consid-
ered as a postulate, because a particle size dependent study
in the<100 nm range is highly elusive. This is so because of
the difficulties pertaining to the synthesis of highly crystal-
line and monodisperse oxide nanocrystals in the<100 nm
size range with systematically varying particle size.
IV. THEORETICAL CONSIDERATIONS ANDDISCUSSION
As per the thermodynamics of solutions, the relative
partial molar Gibbs free energy of mixing of a given species
i in a solution (D �Gmi ) is given by19,20
D �Gmi ¼ NAkBTlnðaiÞ; (1)
where NA is Avogadro’s number, kB is Boltzmann’s con-
stant, T is the absolute temperature, and ai is the chemical
activity of species i in the solution of interest (here, i is Y2O3
with MgO as the matrix). The pressure and temperature de-
pendence of D �Gmi is expressed in its most general form as19
D �Gmi ¼ D �V
mi dP� D�S
mi dT; (2)
where D �Vmi and D�S
mi are the relative partial molar volume
and entropy of mixing, respectively. The isothermal pressure
dependence of D �Gmi follows from Eq. (2) as19
@D �Gmi
@P
� �T
¼ D �Vmi : (3)
The following integral equation can be obtained by combin-
ing Eqs. (1)–(3):19,20,22
ðai@P
ai@Po
@lnðaiÞ ¼1
NAkBT
� �ðP
Po
D �Vmi @P; (4)
which, once integrated, gives the functional for the pressure
dependence of ai as
aiðPÞ ¼ expPD �V
mi
NAkBT
� �; (5)
where Po¼ 1 atm and DP ¼ P� Po with P� Po, for which
DP ffi P in this study. Here, we assume D �Vmi 6¼ f ðPÞ for sim-
plicity, without any loss of generality or rigor.
One should note that under ambient conditions (298 K,
Po¼ 1 atm), the Y2O3 solubility in MgO (Ref. 29) is known
to be null, which means ai(Po)¼ 1. Because one observes an
expansion of the MgO unit cell due to the solubility of Y2O3
(as Y3þ) upon the 60 min soak at (1273 K, P¼ 7.0 GPa), one
now requires ai(P)< 1 at (1273 K, 7.0 GPa, t¼ 60 min) and
(298 K, 0 GPa, t¼ 60 min).20 As DP¼P � Po with P � Po
here [see Eq. (5)], and assuming that D �Vmi is not a function of
pressure to a first approximation, we conclude that D �Vmi < 0,
which suggests �Vi < Voi , because by definition
D �Vmi ¼ �Vi � �V
oi ,19,20 in which �Vi is the partial molar volume
of Y2O3 in MgO and Voi is the molar volume of pure
Y2O3.19,20 It follows from the foregoing analysis that the
molar volume of Y2O3 is smaller when dissolved in the cubic
MgO host than in its pure form.19,20
If one considers the close packed face centered cubic
structure of MgO, no Y3þ incorporation into interstitial sites
is expected.32,33 As such, the only option with which one is
left is Y3þ substitution at empty Mg2þ sites in MgO that
were created by thermal vacancy formation for all T> 0 K,
thereby forming a substitutional solid solution.18–22 Under
such circumstances, electrostatic charge compensation has to
take place via additional Mg2þ vacancy creation, because
each Y3þ brings an extra electron into the unit cell (i.e., do-
nor doping).34–38 Thus, the defect formula should read
ðMg2þ1�ð3x=2Þ;Y
3þx ;VMg
x=2ÞO; (6)
where x is the mole fraction of Y3þ in the unit cell and VMg
designates Mg2þ vacancies created due to donor doping with
Y3þ to preserve charge neutrality.37–39 In what follows, we
elaborate on the origins of the observed volumetric expan-
sion in the MgO unit cell.
Figure 6 is a schematic depicting the (100) surface of
MgO (the unit cell is face centered cubic) in which the
defect structure represented by Eq. (6) is also shown.
According to Eq. (6), charge compensation takes place via
the creation of one Mg2þ vacancy for every two Y3þ in
solid solution (see Fig. 6, where two Mg2þ vacancies for
four Y3þ donor dopants are shown for clarity). Fundamen-
tal electrostatic considerations suggest that the introduction
of Mg2þ vacancies for charge compensation alters the
(electrostatic) interactions among O2� ions as exemplified
in Fig. 6 by the a1�a4 oxygen quartets, in which the central
Mg2þ is missing due to Y3þ substitution. As such, the
attractive interaction between Mg2þ�O2� is absent in the
a1�a4 O2� quartets. Most importantly the Debye screen-
ing40 is absent in all of the O2��Mg2þ�O2� segments
along all three principal directions ([100], [010], and [001])
whenever there is a Mg2þ vacancy. As a consequence, the
a1�a4 O2� quartets need to volumetrically expand due to
O2��O2� repulsion per Coulomb’s law.41 To such
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O2��O2� repulsion there correspond local electric fields in
the a1�a4 O2� quartets, as jq~EðrÞj ¼ j~FðrÞj per the laws of
electromagnetism (q¼ electrical charge).41 The local elec-
tric field (~EðrÞ) is the thermodynamic driving force of the
expansive volumetric strain (uh) wherein the ~EðrÞ : uh cou-
pling is due to electrostriction, the most fundamental elec-
tromechanical coupling in all insulators.42 The ð~EðrÞ : uhÞcoupling can be represented as uh ¼ Qhe2
11j~Ej2
(Qh > 0
¼ hydrostatic electrostriction coefficient and e11¼permittivity).43–46 It follows from the defect structure and
related electrostatic considerations that one can expect the
expansion of the MgO unit cell upon Y3þ dissolution.
Another contributor to the observed volumetric strain in the
MgO unit cell should be the purely elastic volumetric misfit
strain (uoh) caused by substituting the larger Y3þ for the
smaller Mg2þ (66 pm for Mg2þ versus 89 pm for Y3þ),
which deforms the surrounding octahedron (see Fig. 6).28
Based on the foregoing discussion, we have the two
strains uh and uoh, the origins of which we inferred from the
isothermal and isobaric hold at (1273 K, 7 GPa). During the
isothermal and isobaric hold, the MY nanocomposite also
undergoes densification, resulting in 3% volumetric shrink-
age (see Fig. 4). Therefore, additional elastic strain contri-
butions need to be considered during the isothermal and
isobaric hold, such as strain due to differential sintering
(uds), strain due to thermal expansion coefficient (a) mis-
match (uDa), and strain (uDK) due to mismatch in the bulk
moduli (K). Differential sintering of a multiphase particulate
system is known to take place when the particle sizes of
each phase are markedly different.47,48 This is so because
the thermodynamic driving force for densification is chiefly
determined by the excess surface free energy, which scales
inversely with the particle size.47,48 Both phases in the MY
system used in this study are comprised of �100 nm par-
ticles, leading us to conclude that the uds contribution to the
overall observed strain uh is negligible. However, there is
appreciable contrast between the linear thermal expansion
coefficients of MgO and cubic Y2O3 at �1273 K—
16.0 10�6 K�1 versus 8.1 10�6 K�1, respectively (we
assume aMgO> aY2O3 for all polymorphs).13,47 Because the
expansion coefficient of MgO is much larger than that of
Y2O3, the MgO phase would be under compression based
on thermal expansion considerations alone. Thus, we con-
clude that the observed volumetric expansion in the MgO
unit cell occurs despite the compressive contribution to the
strain from the thermal expansion coefficient mismatch. The
KMgO and KY2O3 are 146.6 and 149.5 GPa at 298 K, respec-
tively. Although the bulk modulus mismatch is only �2% at
298 K, it increases to �15% at 1273 K with KMgO¼ 149.5
and KY2O3¼ 132.5 GPa because the dK=dT values for MgO
and Y2O3 are �31.5 and �17.0 MPa/�C, respectively (also
see the comment regarding monoclinic and hexagonal
phases of Y2O3 in Ref. 49). Therefore, it is plausible to pre-
sume that the differences in the bulk moduli between the
phases should make a tensile contribution to the state of
stress on the MgO phase. In light of the foregoing discus-
sion, we postulate that the observed volumetric strain in
MgO has four components (strains are additive50) as uRh ¼
uoh þ uh þ uDa þ uDK with ðuo
h þ uhÞ > ðuDa þ uDKÞ.
V. CONCLUDING REMARKS
We have shown that high pressure has a profound
impact on phase composition in nanocomposite systems, so
much so that solid solubility relationships can be signifi-
cantly altered as exemplified in the MgO-Y2O3 linear dielec-
tric system. The high pressure response of this binary system
indicates that the conventional wisdom in the context of solid
solubility in oxides needs to be revisited, as one is able to
induce solid solubility despite the large difference in the
ionic radii of the cations. Moreover, we have shown that fi-
nite solid solubility and phase assemblages obtained at high
pressures and temperatures can be retained at room tempera-
ture and under ambient pressure.
We have shown that multiphase co-existence under am-
bient conditions is due to the suppression of the conventional
reversible phase transitions in Y2O3, which is attributed to
the small particle size (�100 nm). The retention of appreci-
able Y2O3 solubility in MgO at 298 K and 1 atm is attributed
to kinetic stabilization of the metastable state formed at
(1273 K, 7 GPa).
ACKNOWLEDGMENTS
The authors wish to express their gratitude for the finan-
cial support provided by the Office of Naval Research
(ONR) under Contract No. N00014-10-1-042. The authors
wish to thank Dr. L. Kabacoff of the ONR for his valuable
technical feedback and support of this project. This research
was partially supported by COMPRES, the Consortium for
Materials Properties Research in Earth Sciences, under NSF
Cooperative Agreement No. EAR 06-49658. This research
was carried out in part at the NSLS, which is supported by
the U.S. Department of Energy, Division of Material Scien-
ces and Division of Chemical Sciences, under Contract No.
DE-AC02-76CH00016.
FIG. 6. (Color online) Schematic showing the proposed defect model upon
the dissolution of Y3þ into the cubic MgO structure, where it occupies Mg2þ
sites with charge compensation via Mg2þ vacancies (€).
053506-6 Akdogan et al. J. Appl. Phys. 111, 053506 (2012)
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