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:

eka@rci.rutgers.edu.

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.

053506-2 Akdogan et al. J. Appl. Phys. 111, 053506 (2012)

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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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