Size dependence of the pressure-induced γ to α structural phase transition in iron oxide

nanocrystals

This article has been downloaded from IOPscience. Please scroll down to see the full text article.

2005 Nanotechnology 16 2813

(http://iopscience.iop.org/0957-4484/16/12/013)

Download details:

IP Address: 129.93.16.3

The article was downloaded on 12/09/2013 at 19:02

Please note that terms and conditions apply.

View the table of contents for this issue, or go to the journal homepage for more

Home Search Collections Journals About Contact us My IOPscience

INSTITUTE OF PHYSICS PUBLISHING NANOTECHNOLOGY

Nanotechnology 16 (2005) 2813–2818 doi:10.1088/0957-4484/16/12/013

Size dependence of the pressure-inducedγ to α structural phase transition in ironoxide nanocrystalsS M Clark1, S G Prilliman2, C K Erdonmez2 and A P Alivisatos2,3

1 Advanced Light Source, Lawrence Berkeley National Laboratory, MS6R2100, Berkeley,CA 94720, USA2 Department of Chemistry, University of California, Berkeley, CA 94720, USA3 Materials Science Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720,USA

Received 11 July 2005, in final form 15 September 2005Published 11 October 2005Online at stacks.iop.org/Nano/16/2813

AbstractThe size trend for the pressure-induced γ -Fe2O3 (maghemite) to α-Fe2O3(haematite) structural phase transition in nanocrystals has been observed.The transition pressure was found to increase with decreasing nanocrystalsize: 7 nm nanocrystals transformed at 27 ± 2 GPa, 5 nm ones at34 ± 3 GPa and 3 nm ones at 37 ± 2 GPa. Annealing of a bulk sample ofγ -Fe2O3 was found to reduce the transition pressure from 35 ± 2 to24 ± 2 GPa. The bulk modulus was determined as 262 ± 6 GPa for 7 nmnanocrystals of γ -Fe2O3, which is significantly higher than the value of190 ± 6 GPa that we measured for bulk samples. For α-Fe2O3, the bulkmoduli for 7 nm nanocrystals (336 ± 5) and the bulk (300 ± 30) were foundto be almost the same within error. The bulk modulus for the γ phase wasfound to decrease with decreasing particle size between 10 and 3.2 nmparticle size. Values for the ambient pressure molar volume were foundwithin 1% to be: 33.0 cm3 mol−1 for bulk γ -Fe2O3; 32.8 cm3 mol−1 for7 nm diameter γ -Fe2O3 nanocrystals; 30.7 cm3 mol−1 for bulk α-Fe2O3;and 30.6 cm3 mol−1 for α-Fe2O3 nanocrystals.

1. Introduction

The properties of nanoscale materials can be quite differentfrom those of the bulk [1]. Some properties have beenfound to vary continuously with particle size, the most wellknown example being the reduction in melting temperatureat smaller sizes [2]. This reduction is driven by the factthat the liquid generally has a lower surface energy than thesolid, and this is observed almost universally. For sometime now we have been interested in determining whetherthere is a comparable trend with size in pressure-inducedsolid–solid transformations to denser structures. The earliest,and still most comprehensive, study of a pressure-inducedphase transition used highly monodisperse nanocrystals ofCdSe [3, 4] and demonstrated an increase of transitionpressure with decreasing nanocrystal size. An increase intransition pressure was also reported in a large number ofsubsequent studies, including those of the anatase form of

TiO2 [5–7], the rutile form of TiO2 [8], ZrO2 [9], PbS [10, 11],ZnS [12, 13], Si [14], ZnO [15], GaAs [16], WO3 [17] andCoFe2O4 [18]. This increase in transition pressure may arisefor both kinetic and thermodynamic reasons. In nanocrystalsthe surface atoms form a significant percentage of the totalnumber of atoms. These relatively high energy surfacesmake the denser phase less thermodynamically stable thanthat in the bulk. Also, nanocrystals, particularly those madein solvents at high temperature, lack the internal defects thatserve as nucleation points for structural phase transitions [19]increasing the kinetic barrier to transition. For these reasons wenormally expect observed transition pressures to increase withdecreasing nanocrystal size. However, there is one case, thepressure-induced transition fromγ -Fe2O3 toα-Fe2O3 [20–22],where early evidence has suggested that the pressure fora solid–solid transition is in fact reduced with decreasingnanocrystal size. The study of Jiang et al [20] found atransition pressure of 27 GPa for 9 nm nanocrystals, the Zhao

0957-4484/05/122813+06$30.00 © 2005 IOP Publishing Ltd Printed in the UK 2813

S M Clark et al

et al study [21] found a value of 25–30 GPa for 10 nmnanocrystals and the Wang and Saxena study [22] founda transition pressure of 26.6 GPa for 25 nm nanocrystals.This compares with reported values of 35 GPa for bulkmaterial [20, 22]. The study of Wang and Saxena [22] went onto study the α-Fe2O3 to perovskite structure transition at higherpressure and found no difference in transition pressure fromthat for bulk material. One significant difficulty arises fromthe fact that transitions that involve a large volume changeusually exhibit significant hysteresis, so it can be difficult todistinguish between kinetically controlled observations and thethermodynamic transition points. Examples where this hasbeen an issue include SnO2 [23], α-Fe [24] and CeO2 [25].A further study on the iron oxide system, using an extendedrange of nanocrystal sizes below 9 nm, may prove helpful indetermining whether there is a decrease in transition pressurewith decreasing nanocrystal size. Here, we present the resultsof a study of the transition pressure of the γ -Fe2O3 to α-Fe2O3

transition upon application of pressure in well defined, isolatednanocrystals, dispersed in a soft matrix (not a polycrystallinepowder) for a range of nanocrystal sizes and for bulk material.Combining our data with the literature data allows us tomore definitively establish a trend with size, not only for thetransition pressure, but also for the bulk modulus.

2. Experimental section

2.1. Synthesis and characterization of γ -Fe2O3 nanocrystals

Samples of γ -Fe2O3 nanocrystals were synthesized by avariation of a method published previously [26]. Briefly,cupferrone, an oxygen terminated bidentate chelating agent,was complexed with Fe3+ in aqueous solution. The productwas purified, dried and dissolved in hexadecylamine underargon. When the solution was heated to approximately 200 ◦C,iron cupferronate was decomposed, producing γ -Fe2O3

nanocrystals. Samples were maintained at 270 ◦C for 5–40 min, during which time the particles grew in size.By quenching the reaction at different times, nanocrystalsof 3.2, 5.7 and 7.2 nm average diameter were obtained.The final washed particles retained a monolayer coating ofhexadecylamine, making them soluble in non-polar solvents.Samples used in this study were evaluated by transmissionelectron microscopy (TEM) and x-ray diffraction analysis [26].Approximately 100 nanocrystals were counted in TEM forsizing. Each nanocrystal was roughly spherical and composedof a single-crystalline domain as seen from comparison of theTEM sizing to that obtained by a Scherrer analysis of the x-raydiffraction line broadening [27]. The size distributions for eachsample were ±15% (2σ of the mean particle size from TEM).Bulk γ -Fe2O3 powder (99.9%) was purchased from AldrichInc. This was divided into three aliquots. The first was leftas delivered, the second was annealed for five days and thethird was annealed for two months. Annealing was conductedat 140 ◦C under vacuum, well below the ∼300 ◦C necessaryto nucleate α-Fe2O3. Phase purity was confirmed by ambientpressure x-ray diffraction. High pressure measurements weremade on all three samples.

2.2. High pressure diffraction measurements

High pressures were generated using a diamond anvil cell(DAC), type WCME, supplied by Diacell Products Ltd.Diamonds with 300 µm culet diameter were used withspring steel gaskets with 150 µm holes. Nanocrystalswere redissolved in ethylcyclohexane and bulk samples weredispersed in the same solvent. The pressure was measuredusing the ruby fluorescence method [28]. Each sample waspressurized up to 40 GPa in 2–5 GPa pressure increments.X-ray powder diffraction patterns were collected at eachpressure. These data were collected on beamline 7.3.3 atthe Advanced Light Source, Lawrence Berkeley NationalLaboratory, Berkeley, CA. This beamline is optimized forDAC studies using angle-dispersive diffraction [29, 30]. Thesynchrotron beam was focused to a size of 50 µm×120 µm atthe sample. The optimal wavelength for these measurementson this beamline was found to be 1.117 Å, which wasused throughout. Two-dimensional diffraction patterns werecollected using a Mar345 imaging plate detector system (MarResearch, Evanston, IL). Diffraction patterns were taken, withexposure times of 25 min, at regular intervals of approximatelyone every 50 min in order to minimize kinetic effects. Thesample-to-detector distance was calibrated using LaB6 andAl2O3 as diffraction standards. The system accuracy wasfound to be approximately 0.01◦ in 2θ , or 0.001 Å in d-spacing.Two-dimensional diffraction patterns were radially integratedusing the program Fit2D [31], to obtain one-dimensionalpatterns. Voigt peak shape functions were fitted to thesepatterns in order to determine diffraction peak positions andwidths. All measurements were made at room temperature.

3. Results and discussion

3.1. Determination of the transition pressure

Figure 1 shows selected diffraction patterns at a number ofpressures for the briefly annealed bulk γ -Fe2O3 sample (a)and for 7.2 nm γ -Fe2O3 nanocrystals (b). The peaks of thenanocrystal samples are Debye–Scherrer broadened relativeto the bulk as expected [27]. For both nanocrystal and bulksamples, only the γ phase was present at low pressures. Aspressure was increased, peaks associated with the α phasebegan to appear. Finally, at even higher pressures, pureα phase was obtained. When quenched to atmosphericpressure, both bulk and nanocrystal samples retained the α

structure. The peak widths of the narrowest peaks of thebulk samples increased from 0.3◦ to 0.5◦ across the transition.The peak widths of both α-Fe2O3 nanocrystals and γ -Fe2O3

nanocrystals were found to be about 1.0◦ throughout themeasurements.

Because some peaks were less intense and broader in theα phase, it was difficult to accurately determine the phasepercentages at a given pressure. Following the method ofJiang et al [20], we quantified the transition progress byplotting the ratio of the integral intensities of the γ -Fe2O3

(311) and γ -Fe2O3 (220) diffraction peaks as a function ofpressure. The γ -Fe2O3 (311) coincides closely with theα-Fe2O3 (110), while the γ -Fe2O3 (220) has no coincidentpeak in the α-Fe2O3 pattern. As the transition proceeds,the I 220/I 311 ratio increases from its pure γ -Fe2O3 value of

2814

Size dependence of the pressure-induced γ to α structural phase transition in iron oxide nanocrystals

Figure 1. X-ray diffraction patterns of bulk γ -Fe2O3 annealed for five days (a) and 7.2 nm diameter nanocrystalline γ -Fe2O3 (b), at variouspressures as noted on the figure. The two lowest patterns show each sample entirely in the γ phase. Peaks labelled with diamonds are (inorder, left to right), the γ (220), (311), (400), (422) and (511). As pressure is increased, α peaks appear, until at the highest pressure only αis present. Upon recovery to ambient pressure (topmost patterns), the samples retain the α structure. Labelled with asterisks are (left toright), α (102), (104), (110), (113), (024) and (116). Other small peaks in these patterns are due to diffraction from the ruby chips used as afluorescence pressure calibrant.

approximately 3.0. The result of this analysis is presentedin figure 2(a) for nanocrystal samples with diameters of 3.2,4.9 and 7.2 nm. We observe that for decreasing nanocrystaldiameters, the rise in the I 220/I 311 ratio is shifted to higherpressures. This allows us to graphically estimate transitionpressures of 27 ± 2 GPa for 7.2 nm diameter nanocrystals,34±3 GPa for 4.9 nm ones and 37±2 GPa for 3.2 nm ones. Theestimated transition pressures are taken for when the I 220/I 311

ratio reaches 10. For bulk samples (figure 2(b)) the observedtransition pressure decreases with increasing annealing time.The unannealed sample transformed at 32±2 GPa, the sampleannealed for five days transformed at 25±2 GPa and the sampleannealed for two months transformed at 24 ± 2 GPa.

These data show that the transition pressure for theγ -Fe2O3 to α-Fe2O3 phase transition for nanocrystal samplesincreases as the nanocrystal size decreases for nanocrystals inthe range 3.2–7.2 nm. The transition pressure of 27 ± 2 GPathat we have determined for the 7.2 nm diameter nanocrystalsis, within error, the same as the values of 27 GPa determinedby Jiang et al [20] for 9 nm diameter nanocrystals, 26.6 GPadetermined by Wang and Saxena [22] for 25 nm nanocrystalsand 24 ± 2 GPa determined for our annealed bulk sample(figure 4). It is seen that the transition pressure increaseswith decreasing particle size and scales about linearly withthe surface to volume ratio.

The variation of the transition pressure for the bulk samplewith annealing time is not surprising. Maghemite has acation deficient spinel structure which may be represented asFe8[Fe40/3[ ]8/3]O32 where [ ] denotes a vacancy. Eight Fe3+

atoms occupy tetrahedral sites while the remainder occupyoctahedral sites. The vacancies may be ordered or disorderedor partially occupied by impurity atoms. This allows acertain amount of variability of the crystal structure andmicrostructure depending on sample preparation and history.This is manifested in, for example, the thermal transition fromγ -Fe2O3 to α-Fe2O3 that has been found to depend strongly onsample preparation [32]. The important point is that annealing

Figure 2. The ratio of the integrated intensities of theγ (311)/γ (220) which increases as the transition to α proceeds. Thecolloidal nanocrystals (a) studied here demonstrate a strongdependence of transition pressure on size. A wide range oftransition pressures can be obtained for the bulk (b) depending onhow well the sample has been annealed. The ‘partially annealedsample’ was annealed for five days and the ‘annealed sample’ wasannealed for two months.

the bulk γ sample reduced the transition pressure to a limitingvalue similar to that found for nanocrystals larger than 7 nm.

The increased transition pressure could be due to a numberof reasons which are difficult to unravel due to the possibleconvolution of both thermodynamic and kinetic effects. For

2815

S M Clark et al

Table 1. Transition pressures determined for different nanocrystalsizes.

Nanocrystal size Transition pressure(nm) (GPa) Reference

3.2 37 ± 2 This study4.9 34 ± 3 This study7.2 27 ± 2 This study9 27 [20]10 25–30 [21]25 26.6 [22]Annealed 24 ± 2 This studybulk sample

Table 2. Bulk moduli and molar volume at ambient pressureobtained by fitting the Birch equation to our data.

Bulk modulus Molar vol. at ambient pressureSample (GPa) (cm3 mol−1)

Bulk γ -Fe2O3 190 ± 6 33.0 ± 0.27 nm γ -Fe2O3 262 ± 6 32.8 ± 0.2Bulk α-Fe2O3 300 ± 30 30.7 ± 0.37 nm α-Fe2O3 336 ± 5 30.6 ± 0.1

example, it could be due to an increased Gibbs free energy ofthe α phase. The surface energies of the analogous Al2O3

system have been extensively studied with the result thatthe γ phase is more stable than the α phase for surfaceareas greater than 125 m2 g−1 [33]. Also, it has beenshown that activation energy depends on nanocrystal sizefor nanocrystalline titania [34]. Maghemite and haematitealso exhibit complex magnetic properties which have strongparticle size dependences [35]. Whatever the underlyingreason, the results presented here do establish the correct sizedependent trend.

3.2. Determination of the bulk moduli and ambient pressurevolumes

In addition to transition pressures, we determined from ourdata bulk moduli and ambient pressure volumes for bulkγ -Fe2O3, bulk α-Fe2O3 formed by the phase transition frombulk γ -Fe2O3, 7 nm nanocrystals of γ -Fe2O3 and α-Fe2O3

nanocrystals formed by the phase transition from 7 nmnanocrystals of γ -Fe2O3 (table 1). The unit cell volume asa function of pressure for nanocrystals (open symbols) andthe bulk (filled symbols) is shown for γ -Fe2O3 (triangles) andα-Fe2O3 (squares) in figure 3. The values in table 1 wereobtained by fitting the first-order Birch equation [36],

P(V ) = 3B0

2

[(V0

V

) 73

−(

V0

V

) 53

],

to our data with the pressure derivative of the bulk modulus setto a value of 4 after Jiang et al [20]. The Birch equation fits arealso shown graphically in figure 3. For fitting purposes, onlydata from diffraction patterns clearly showing a single phasewere used in order to avoid errors due to overlapping γ -Fe2O3

and α-Fe2O3 peaks. Volumes for bulk α-Fe2O3 formed fromthe variously annealed bulk γ -Fe2O3 samples were found to beindistinguishable. Therefore, these volumes were combinedbefore determining the values in table 2. The percentage

28

28.5

29

29.5

30

30.5

31

31.5

32

32.5

33

0 5 10 15 20 25 30 35

Pressure (GPa)

Vo

lum

e (c

c/m

ol)

Figure 3. The volume as a function of pressure for the bulk (filledtriangles, γ ; filled squares, α) and nanocrystals (open triangles, γ ;open squares α). A strong departure from the P–V curves wasobserved only for nanocrystals of the γ phase at pressures above10 GPa.

volume change at the mid-point of the transition was foundto be about 10%.

The value that we determined for the bulk modulus of bulkγ -Fe2O3, 190 ± 6 GPa, agrees within error with the value of203 ± 10 GPa found by Jiang et al [20]. The value of the bulkmodulus that we found for γ -Fe2O3 nanocrystals, 262±6 GPa,is significantly lower than the values of 305±15 GPa found byJiang et al [20] and 375±9 GPa found by Zhao et al [21]. Dueto the wide peak widths and low intensity of the diffractionprofiles from very small nanocrystals, we were unable todetermine a reliable bulk modulus from our 3.2 or 4.9 nmdiameter samples. When we combine all of our nanocrystaldata together we obtain a bulk modulus of 211±15 GPa whichwe can use as an indication of the relative change in bulkmodulus with particle size. All of these values are shown infigure 5. The bulk modulus clearly decreases with decreasingnanocrystal size. This decrease in the bulk modulus, orsoftening of the material, is not easily explained in terms ofsurface energy or kinetic effects. A more plausible explanationof the softening of bulk in comparison with 10 nm nanocrystalscan be given by noting that maghemite produced by thermaloxidation of magnetite is known to possess ordering of cationvacancies within a tetragonal supercell for large (>200 nm)particles and exhibit the absence of this type of ordering of

2816

Size dependence of the pressure-induced γ to α structural phase transition in iron oxide nanocrystals

20

22

24

26

28

30

32

34

36

38

40

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

1/(nano crystal radius) (nm-1)

Tran

sitio

n P

ress

ure

(GP

a)

Figure 4. Variation of transition pressure as a function of surface to volume ratio for γ -Fe2O3. The diamonds are our data, the square isfrom Jiang et al [20], the triangle is from Zhao et al [21] and the circle is from Wang and Saxena [22]. The line is a guide for the eye.

100

150

200

250

300

350

400

0 2 4 6 8 10 12

Particle size (nm)

Bu

lk m

od

ulu

s (G

Pa)

Figure 5. Variation of bulk modulus with nanocrystal size for γ -Fe2O3. Diamonds are our data, the square is from Jiang et al [20] and thetriangle is from Zhao et al [21].

vacancies in fine particles (<100 nm) [37]. Such a loss of ordermay explain the increase in bulk modulus going from the bulkto nanocrystals. Enhanced bulk modulus in nanocrystals hasbeen observed before, for example in ZnS [37], and attributedto increase of the disorder.

The value that we found for the ambient pressuremolar volume of γ -Fe2O3, 33.0 cm3 mol−1, is the same,within error, as the value of 32.9 cm3 mol−1 found both byJiang et al [20] and Haul and Schoon [38]. The valuesthat we determined for the bulk moduli of both bulk andnanocrystalline α-Fe2O3 are higher than those previouslyreported. Our value of 299 ± 30 GPa for bulk α-Fe2O3 islarger than the value of 205 ± 5 GPa determined by Jiang et al[20], 231 ± 10 GPa determined by Sato and Akimoto [39],225 ± 4 GPa determined by Finger and Hazen [40], 258 ±6 GPa determined by Rozenburg et al [41] and 206 ± 5 GPadetermined by Liu et al [42]. The bulk modulus of bulkα-Fe2O3 does seem to be very sensitive to the pressure

transmitting medium and the degree of hydrostaticity [42].Alternatively, the large variation of the compressibility andtransition behaviour has also been attributed to impuritiesand crystallization history [40]. Other properties of α-Fe2O3

have also been found to depend on the method of samplepreparation [43]. So it may be that our method of preparingthe bulk α-Fe2O3 sample, by pressure-induced transformationfrom bulk γ -Fe2O3, may lead to a sample with a higher bulkmodulus. The value that we determined for the ambientpressure molar volume of bulk α-Fe2O3, 30.7 ± 0.3 agrees,within experimental error, with values of 30.3–30.4 cm3 mol−1

determined previously [20, 40, 41, 43].

4. Conclusions

The transition pressure for the γ -Fe2O3 to α-Fe2O3 phasetransition on increasing pressure was found to increasewith decreasing nanocrystal size. The bulk modulus

2817

S M Clark et al

of nanocrystalline γ -Fe2O3 was found to decrease withdecreasing particle size between 3 and 7 nm particle size.

Acknowledgments

We would like to thank Rich Celestre, Alastair Macdowell andEdward Domining for help on beamline 7.2.2. and RaymondJeanloz for helpful discussions. We would like to thankJ Rockenberger and J Kwong for help with making the samples.The Advanced Light Source is supported by the Director,Office of Science, Office of Basic Energy Sciences, MaterialsSciences Division, of the US Department of Energy underContract No DE-AC03-76SF00098 at Lawrence BerkeleyNational Laboratory.

References

[1] Alivisatos A P et al 1998 Adv. Mater. 10 297[2] Buffat P and Borel J P 1976 Phys. Rev. A 13 2287[3] Tolbert S H and Alivisatos A P 1994 Science 265 373[4] Tolbert S H and Alivisatos A P 1995 J. Chem. Phys. 102 4642[5] Swarmy V, Dubrovinsky L S, Dubrovinskaia N A,

Simionovici A S, Drakopoulos M, Dmitriev V andWeber H-P 2003 Solid State Commun. 125 111

[6] Wang Z and Saxena S K 2001 Solid State Commun. 118 75[7] Wang Z, Saxena S K, Pischedda V, Liermann H P and Zha C S

2001 J. Phys.: Condens. Matter 31 8317[8] Staun Olsen J, Gerward L and Jiang J Z 2002 High Pressure

Res. 22 385[9] Kawasaki S, Yamanaka T, Kune S and Ashida T 1990 Solid

State Commun. 76 527[10] Qadri S B, Yang J, Ratna B R and Skelton E F 1996 Appl.

Phys. Lett. 69 2205[11] Jiang J Z, Gerward L, Secco R, Frost D, Olsen J S and

Truckenbrodt J 2000 J. Appl. Phys. 87 2658[12] Jiang J Z, Gerward L, Frost D, Secco R, Peyronneau J and

Olsen J S 1999 J. Appl. Phys. 86 66088[13] Ji Y, Guo L, Xu H, Liu J, Li X, Li Y, Wu Z and Simon P 2003

Phys. Status Solidi a 198 210[14] Tolbert S H, Herhold A B, Brus L E and Alivisatos A P 1996

Phys. Rev. Lett. 76 4384[15] Jiang J Z, Olsen J S, Gerward L, Frost D, Rubie D and

Peyronneau J 2000 Europhys. Lett. 50 48[16] Jiang J Z, Staun Olsen J, Gerward L and Steenstrup S 2002

High Pressure Res. 22 395

[17] Boulova M and Lucazeau G 2002 J. Solid State Chem. 167 425[18] Wu Z, Bao Z, Cao L, Liu C, Li Q, Xie S and Zou B 2003

J. Appl. Phys. 93 9983[19] Jacobs K, Zaziski D, Scher E C, Herhold A B and

Alivisatos A P 2001 Science 293 1803[20] Jiang J Z, Staun Olsen J, Gerward L and Morup S 1998

Europhys. Lett. 44 620[21] Zhao J, Guo L, Liu J, Yang Y, Chen R and Zhou L 2000

Chin. Phys. Lett. 17 126[22] Wang Z and Saxena S K 2002 Solid State Commun. 123 195[23] Jiang J Z, Gerward L and Olsen J S 2001 Scr. Mater. 44 1983[24] Jiang J Z, Staun Olsen J and Gerward L 2001 Mater. Trans. 42

1571[25] Wang Z, Saxena S K, Pischedda V, Liermann H P and Zha C S

2001 Phys. Rev. B 64 012102[26] Rockenberger J, Scher E C and Alivisatos A P 1999 J. Am.

Chem. Soc. 121 11595[27] Guinier A 1963 X-ray Diffraction in Crystals, Imperfect

Crystals and Amorphous Bodies (New York: Dover)[28] Eremets M 1996 High Pressure Experimental Methods

(Oxford: Oxford University Press)[29] Shimomura O, Takemura K, Fujihisa H, Fujii Y, Oshishi Y,

Kikegawa T, Amemiya T and Matsushita T 1992 Rev. Sci.Instrum. 63 967

[30] Nelmes R J, Hatton P D, McMahon M I, Piltz R O, Crain J,Cernik R J and Bushnell-Wye G 1992 Rev. Sci. Instrum. 631039

[31] Hammersley A P, Svensson S O, Hanfland M, Fitch A N andHausermann D 1996 High Pressure Res. 14 235

[32] Gillot B, Nouaim H, Mathieu F and Rousset A 1991Min. Chem. Phys. 28 389

[33] McHale J M, Auroux A, Perrotta A J and Navrotsky A 1997Science 277 788

[34] Zhang H Z and Banfield J F 2005 Chem. Mater. 17 3421[35] Ganguly B, Huggins F E, Rao K R P and Huffman G P 1993

J. Catal. 142 552[36] Birch F 1938 J. Appl. Phys. 9 279[37] Gilbert B, Huang F, Zhang H, Waychunas G A and Banfield J F

2004 Science 305 651[38] Haul R and Schoon Th 1939 Z. Phys. Chem. 44 216[39] Sato Y and Akimoto S 1979 J. Appl. Phys. 50 5285[40] Finger L W and Hazen R M 1980 J. Appl. Phys. 51 5362[41] Rozenberg G Kh, Dubrovinsky L S, Pasternak M P, Naaman O,

Le Bihan T and Ahuja R 2002 Phys. Rev. B 65 064112[42] Liu H, Caldwell W A, Benedetti L R, Panero W and Jeanloz R

2003 Phys. Chem. Miner. 30 582[43] Maslen E N, Streltsov V A, Streltsova N R and Ishizawa N

1994 Acta Crystallogr. B 50 435

2818