Matvei Zinkevicha, Francisco Miguel Moralesa, Heiko Nitschea, Martin Ahrensb,Manfred Rühlea, Fritz Aldingera

a Max-Planck-Institut für Metallforschung, Stuttgart, Germanyb Max-Planck-Institut für Festkörperforschung, Stuttgart, Germany

Microstructural and thermodynamic studyof c-Ga2O3

The metastable nanocrystalline c form of gallium oxide hasbeen prepared and its microstructure and thermochemistryhave been studied for the first time by employing X-rayand electron diffraction, high-resolution transmission elec-tron microscopy, adiabatic and differential scanning calorim-etry. The randomly oriented crystallites of maximum 5 nmin size have been observed. The sponge-like morphologyof c-Ga2O3 particles may explain the high specific surfacearea, previously reported for this material. The defectspinel-type structure of c-Ga2O3 is similar to that of c andg-Al2O3. Up to 5.7 wt.% of water can be stored in c-Ga2O3

and subsequently released at elevated temperatures. Dryc-Ga2O3 specifically absorbs atmospheric water at roomtemperature. The transformation of c-Ga2O3 into stableb-Ga2O3 occurs in two steps. In the range 650 –800 K,c0-Ga2O3 is formed in the course of a reversible higher-or-der phase transition. The latter irreversibly transforms intob-form above 873 K. The enthalpy of this exothermictransformation is determined as – 19.3 C 0.4 kJ & mol – 1.The coefficients of the Gibbs energy equation for c andc0-Ga2O3 have been assessed.

Keywords: Ga2O3; Metastable nanocrystals; HRTEM; Mi-crostructure; Thermodynamics

1. Introduction

Gallium (III) oxide (Ga2O3, gallia) has been reported toform five modifications: (, b, c, d, and e [1– 5]. However,b-Ga2O3 is the only stable crystalline modification [4, 5],whereas all other polymorphs are metastable and transforminto the b-form at sufficiently high temperatures. Thec-Ga2O3 polymorph is of particular interest because of itshigh surface area, which opens the possibility of using thismaterial as an efficient catalyst [6]. In fact, the unique cata-lytic activity of gallium-containing microporous materialsin such processes as cyclization of hydrocarbons, methanolconversion, or NO reduction has been observed [7 – 10].The structure of c-Ga2O3 is considered to be very similarto that of c-Al2O3 [4– 6]. Since the latter is an extremelyimportant nanosized material, extensive literature exists onthe preparation, characterization, properties, and applica-tions of c-Al2O3 [11]. In contrast, there is a lack of reportson c-Ga2O3. Böhm [12] first described the preparation ofthis gallia polymorph from gallium hydroxide, which hasbeen quickly dried. According to Roy and co-workers [4],

c-Ga2O3 prepared by this method transforms into b-modifi-cation at 650 or 300 °C in dry and wet conditions, respec-tively. Pohl [13] reported the precipitation of cubicc-Ga2O3 with a defect spinel structure by heating metallicgallium with an organic solution at 150 °C for several days.Recently, it has been shown [6] that c-Ga2O3 can success-fully be prepared by calcination (at 500 °C) of gallia gel ob-tained by adding ammonia to an ethanolic solution of gal-lium nitrate. The X-ray diffraction pattern exhibited verybroad lines – a feature, which is typical for all nanocrystal-line materials. Some physical properties of c-Ga2O3 (sur-face area, porosity, infrared spectra) have also been studied[6]. The present paper is focused on microstructure, thermalstability, and thermodynamics of c-Ga

2O3, which have not

been addressed in previous works.

2. Experimental

To prepare c-Ga2O3 a method described in Ref. [6] wasadopted. About 10 g of high-purity Ga(NO3)3 · xH2O(Strem Chemicals) was dissolved in 150 ml ethanol. Con-centrated HNO3 (10 ml) was added to suppress the hydroly-sis. White gel was precipitated upon adding of concentratedaqueous ammonia (25 vol.%) diluted with ethanol(50 vol.%). The precipitate was filtered, thoroughly washedwith ethanol, dried at 75 °C for 10 h, and then calcined at500 °C for 3 h in air.

Chemical analysis was carried out to determine the watercontent by carrier-gas hot extraction technique (Water-Car-bon-Analyzer; Model CWA 5003, Fisher-Rosemount, Ha-nau). In addition, water desorption was monitored by ther-mogravimetric and differential thermal analysis with Ar asa carrier gas and a heating/cooling rate of 10 K & min – 1

(TG/DTA; Model STA 449C, NETZSCH-GerätebauGmbH, Selb, Germany), which was coupled to a mass-spectrometer (MS; Model GAM 200, IPI – In Process In-struments, Bremen, Germany). The X-ray diffraction pat-tern of the powder sample (XRD; Model D-5000 Theta/Theta, Siemens AG, Karlsruhe, Germany) was recordedwith CuK(-radiation, a 2H step width of 0.02°, and acounting time of 20 s. For quantitative refinement of theatom positions and occupancies, full-profile Rietveld re-finement of the X-ray diffraction pattern was carried outusing TOPAS software. The microstructure was studied bytransmission electron microscopy (TEM) techniques, hold-ing the c-gallia powder on a Cu-grid with square holes.Prior to deposition the powder was dispersed in pure etha-

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nol to produce a suspension. Conventional TEM and se-lected area electron diffraction (SAED) experiments werecarried out in a JEOL 2000FX electron microscope. En-ergy-filtered SAED patterns were registered in a ZeissEM 912 OMEGA microscope while a JEOL 4000EX wasused to perform high-resolution transmission electron mi-croscopy (HRTEM). To study particle size distribution andto carry out image filtering by fast Fourier transform (FFT)the software DigitalMicrographTM was used. Electron dif-fraction patterns based on the dynamical theory were calcu-lated by EMS software (P.H. Jouneau and Pierre Stadel-mann, EPFL, Lausanne) while crystal structures werecalculated and modeled using the software DiamondTM.

The enthalpy and heat capacity of c-Ga2O3 were studiedby differential scanning calorimetry (DSC; Models Pyris1, Perkin-Elmer Instruments, Norwalk, USA, between 323and 873 K and MHTC96, SETARAM S.A., Caluire,France, between 373 and 1373 K) calibrated with In, Pb,Zn, and Li2SO4 standards. The low-temperature specificheat of c-Ga2O3 between 11 and 300 K was measured bymeans of a home-made high-precision calorimeter applyingNernst’s quasi-adiabatic step heating method [14, 15]. Thesample holder was a 0.1 mm thick sapphire disc supportingthe heater (evaporated stainless steel, ~ 2 kX) and a com-mercially calibrated resistance thermometer (depending onthe range of temperature either CERNOX or Pt100). The1.3 g sample was sealed in an evacuated DURAN glass am-poule, which was cemented to the sample holder using aweighed amount of Apiezon-N grease. The contributionsof glass, grease, and sapphire disc to the specific heat weresubtracted to obtain the net sample values.

3. Results and discussion

3.1. Crystal structure and chemical properties

The observed, calculated, and difference X-ray diffractionpatterns of c-Ga2O3 are shown in Fig. 1. Very broad peaksindicate a very small crystallite size. Using the Scherrer for-mula, an apparent crystallite size of 5 nm is calculated.Structural parameters of c-Ga2O3 determined by the Riet-veld refinement are given in Table 1. To get the same totalnumber of Ga-ions, as required by the stoichiometry, huge

isotropic displacement parameters (B) for Ga-ions have tobe assumed. The corresponding value for oxygen has beenadopted from the neutron diffraction study of c-Al2O3

[16]. Furthermore, some Ga – O distances appear to be tooshort, if the corresponding ionic radii [17] are taken into ac-count. Although this can probably be tolerated, since theGa-sites are only partially occupied, in view of the exten-sive reflection overlapping, the value listed in Table 1should be considered as preliminary. It is also possible that,as in the case of c-Al2O3 [18], the XRD powder pattern ofc-Ga2O3 exhibits anomalous reflection broadening, whichcannot be well accounted for by a single profile function.The best fit has been obtained with the use of the Pearson-VII function. It is believed that more accurate structure de-termination of c-Ga2O3 is possible by using neutrons orsynchrotron radiation. Nevertheless, noticeable differencesbetween the crystal structures of c-Ga2O3 and c-Al2O3 [16,18] have been mentioned. Both structures can be derivedfrom the spinel prototype (MgAl2O4) by incorporation ofcations on special Wyckoff sites, which are unoccupied inthe spinel structure. All cation sites, which are actuallyinterstices in the close-packed array of oxygen ions, arethen filled incompletely to maintain electroneutrality. Forc-Al2O3 additional sites 32e or 16c of the cubic space groupFd3m have been proposed [16, 18], both structure modelsresult in very similar calculated diffraction patterns. How-ever, they do not work for c-Ga2O3, for which a reasonablefit of the XRD pattern could only be obtained assumingthe partial occupation of the 48f site (Table 1). Accordingto Zhou and Snyder [18], the presence of tetrahedrally coor-dinated Al3+ on this site is characteristic for g-Al2O3, so thatthe material obtained in this work can also be calledg-Ga2O3 (note that g- and c-Al2O3 give very similar XRDpatterns).c-Ga2O3 specifically absorbs atmospheric water at room

temperature. The water content in the sample is determinedas 5.7 C 0.3 wt.%. The absence of any other absorbates isconfirmed by recording the mass spectrum during heatingof the specimen up to 873 K. The desorption of H2O beganjust above 373 K and manifested itself through the weightloss and the endothermic effect on the DTA curve. Themaximum desorption rate was achieved at 403 K. Whenthe sample is cooled down to room temperature under Ar at-mosphere and then immediately heated again, no changes

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Fig. 1. Observed (dots), calculated (line), and difference (bottom)X-ray diffraction patterns of c-Ga2O3. Vertical bars correspond to thecalculated positions of diffraction maxima.

Table 1. Structural parameters of c-Ga2O3 for space group Fd3m,a = 0.8238(6) nm. Figures of merit [19]: Rp = 10.9, Rwp = 14.9,Bragg factor (RB): 1.87, goodness of fit (GOF): 2.469.

Site x y z B (nm2) Occupancy

Ga (8a) 0.125 0.125 0.125 0.105 0.797Ga (16d) 0.500 0.500 0.500 0.105 0.569Ga (48f) 0.919 0.125 0.125 0.105 0.122O (32e) 0.250 0.250 0.250 0.010 1.000

Core geometries (distances in nm, angles in deg) around Ga-ions

Ga (8a) – O 1.780 (43)Ga (16d) – O 2.062 (63)Ga (48f) – O 1.602 (23) 2.01 (23)

O – Ga (8a) – O 109.5O – Ga (16d) – O 89.9 90.1 180.0O – Ga (48f) – O 92.9 106.8 130.3

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on TG, DTA, and MS curves are observed. However, keep-ing the sample in air at room temperature results in wateruptake from the atmosphere even within short time. Itseems that c-Ga2O3 behaves as a sponge, where water canbe stored and subsequently released. Similar behaviour isknown for c-Al2O3 [20]. The latter is believed to absorbwater in a reactive way, so that an etching of the materialoccurs by stoichiometric Al2O3 units. The proposed mech-anism of water storage, which is probably responsible forthe remarkable catalytic properties, can only be realized ifc-Al2O3 exists over a range of hydrogen content and therules of valence must be satisfied throughout this range[20]. From the crystallographic point of view the formulaof c-alumina can be expressed as H3mAl2 – mO3, while thecommonly used notation to represent the water content isAl2O3 & nH2O, where 04 n4 0.6 and m = 2n/(n + 3). EveryH-atom associates more closely with one of the nearest-neighbour O atoms forming an OH-type bond. The upperlimit of the H-content in the spinel structure, n = 0.6 [20]is consistent with the composition of c-gallia, Ga2O3 & nH2O(n = 0.63 C 0.03) determined in this work. The presence ofhydrogen, of course, cannot be taken into account in theRietveld refinement of the XRD pattern.

3.2. Morphology and particle size

Because of the low synthesis temperature, the c-Ga2O3 par-ticles show a foam-like, spongy texture, random shapes,and a high range of both sizes (from nano to microscale)and apparent thickness (denoted by changes in contrastacross one individual particle). It is such a morphology thatappears to be the origin of the high specific surface area ofc-Ga2O3. It should be noted that the considered larger parti-cles, at least for some cases, seem to be formed by aggrega-tion of smaller particles. A statistical analysis was carriedout with respect to the distribution of the sizes of particles.The particles are shown in the digitized bright fieldplan-view images of Fig. 2. The selected magnification

(3 3000) allows the detection of particles above a linearlimit of detection of around 50 nm, which is low enough toresolve the smallest present particles. 1553 particles wereanalysed. Considering the area, the mean size is around0.9 lm2, the smallest particle is 1760 nm2 and the biggestis 58 lm2, the standard deviation being ± 3.5 lm2 and thestandard error ± 0.09 lm2. Figure 3 shows the histogram ofthe particle size distribution. It is evident that the vast ma-jority of particles is small. This is evident for not only thewhole range studied, but even for the “magnified” region,where particles smaller than 0.3 lm2 are taken into account.

3.3. Microstructure observed by electron diffraction andHRTEM

Selected area electron diffraction (SAED) patterns were re-gistered from the c-Ga2O3 particles at different exposuretimes. The SAED patterns show five well-defined ringsrelated with five diffracting families of lattice planes. Fig-ure 4a shows an energy-filtered SAED pattern where thediffraction rings are labeled from 1 to 5, following the orderfrom small to large g-vector. The image contrast is invertedfor a better visualization of the rings. Such rings are typicalin polycrystalline samples with a large amount of randomlymisoriented and fine (nanocrystalline) grains. Figure 4bshows a conventional SAED pattern and the correspondingaveraged line intensity profile, where the brighter features(rings) are reflected as maxima in the intensity (uppercurve). The lower curve shows the standard deviation ofthe intensity values. After careful indexing of these reflec-tions in conventional SAED patterns, considering the latticespacing of stable and metastable phases of Ga and O, it isconcluded that each of these rings is associated with the me-tastable c-Ga2O3 defect spinel structure with a latticeparameter of a = 0.8238 nm as calculated from the XRDpattern. The ring labeled “1” is a {113}-type reflectionof this compound, with an interplanar spacing of0.2484 ± 0.0048 nm; ring “2” corresponds to a spacing of0.2051 ± 0.0025 nm, associated to {004} planes; ring 3 cor-responds to 0.1458 ± 0.0026 nm, associated to {044}planes; ring “4” corresponds to 0.1060 ± 0.0025 nm, asso-ciated to {535} or {317} reflections, while ring “5” wasmeasured as 0.0829 ± 0.0025 nm associated to {557} or{717} planes of this gallium oxide structure.

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Fig. 2. BF-TEM micrographs of particles distribution used for the sta-tistical study of sizes.

Fig. 3. Histogram about particle sizes of c-Ga2O3 in Fig. 2. Insetshows the “magnified” region, where particles smaller than 0.3 lm2

are taken into account.

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The c-gallia structure was also tested by HRTEM. The in-set in Fig. 5 is a bright-field TEM image of the particle fromwhich the HRTEM micrograph was taken. The magnifiedimage shows a region, where three types of planes are visi-ble: {022}, {113}, and {004}. It can be seen that individualcrystallites are around 5 nm in size, thus confirming the

XRD result. Moreover, it is evident that each particle inFig. 2 consists of a cluster of gallia nanocrystals. In orderto identify these crystals, FFT of specific areas helped to ex-tract the interplanar spacings in the high-resolution images.FFT of HRTEM micrographs taken from silicon single-crystals was used as reference. These measured parametersare listed for every nanocrystal in Table 2 and agree withaverage lattice spacings calculated by XRD, also presentedin this table for comparison. Figure 6 shows two examplesof HRTEM images taken from c-Ga2O3 nanocrystals in dif-ferent regions. For each image, the corresponding FFT pat-tern and a Fourier-filtered image are shown. The Fourier-filtered images contain only the periodic information, thusreducing noise. The fringes displayed in Fig. 6a are {022}planes while in Fig. 6b a couple of {113} planes are visible.The images in Fig. 7 show (a) an HRTEM micrograph of ac-Ga2O3 grain, (b) the corresponding FFT pattern and (c)the respective Fourier filtered image for the same picture.From the analysis of the bright spots in the FFT, it is con-cluded that {111}, {113}, {022}, and {004} reflectionscontribute to the experimental image and that the crystal isoriented parallel to the <110> direction. Indeed, the FFTpattern (b) and the calculated SAED pattern for thec-Ga2O3 structure for the <110> zone axis (d) are similar.In the calculated SAED pattern, only reflections appearingin the FFT pattern (b) are labeled. Finally, Fig. 7e showsthe calculated structure of c-gallia in [110] projection,where bright spheres represent gallium cations and darksperes are associated to oxygen anions. Oxygen ions are re-presented as smaller spheres, even though they have a largerion radius, because they do not contribute in the formationof the HRTEM image to a great extent. In fact, a correlationbetween the filtered image (c) and the model (e) is evident.

3.4. Thermal stability and thermodynamics

Like c-Al2O3, c-Ga2O3 is a metastable phase. Both struc-tures exist in the nanocrystalline state. In support of thisstatement, attempts to obtain larger crystals of c-Ga2O3 bythermal annealing in air at 923 K have failed. After 10 h ofsuch treatment, no changes on the X-ray diffraction patternhave been found, while additional 10 h annealing resultedin appearance of reflections corresponding to b-Ga2O3. Fig-ure 8 shows the DSC trace of the c-Ga2O3 sample, whichhas been held at 373 K for 1.5 h to remove the absorbed

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Fig. 4. (a) Energy-filtered and (b) conventional SAED of c-Ga2O3with identified reflections.

Fig. 5. HRTEM micrograph registered from the border of one powderparticle (inset) where some interplanar spacings related with c-Ga2O3grains are clearly detected and labelled.

Table 2. Interplanar distances extracted from the HRTEM imageof nanocrystals in Fig. 5.

c-Ga2O3

planesXRD spacing (nm) Measured by HRTEM

(± 0.0050 nm)

{004} 0.2060 A 0.2046B 0.2040C 0.2071

{113} 0.2484 A 0.2470B 0.2491C 0.2494D 0.2504E 0.2483

{022} 0.2913 A 0.2912B 0.2922C 0.2919D 0.2935

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water. The onset of an exothermic event is found at876 C 5 K. Visual inspection of the sample heated to1373 K at room temperature revealed a volume shrinkageof about 50 % and XRD analysis showed the presence ofonly b-Ga2O3. Hence, the observed exothermic effect hasto be associated with the transformation into b-gallia. Theonset temperature of 876 K is relatively low compared to1373 K reported for Al2O3 [21] indicating that incorpora-tion of larger Ga-ions leads to severe distortion of the spi-nel-type structure. To evaluate the enthalpy of transforma-tion, the peak area has been calculated by numericalintegration. The baseline has been defined by interpolationbetween 873 and 1223 K using the third-order polynomialfunction, which fits both the DSC curve of c-Ga2O3 in therange 573 – 873 K and that of the transformed sample above1223 K (Fig. 8). From three independent measurements, theenthalpy of the c! b transformation in Ga2O3 of– 19.3 C 0.4 kJ & mol – 1 has been determined. This value isof the same order as the enthalpy of c! ( transformationin Al2O3, which is reported as – 26.8 C 0.4 kJ & mol – 1 at1470 K [22] and – 21.4 C 2 kJ & mol – 1 at 978 K [23].

Results of the heat capacity measurements for c-galliaare given in Fig. 9. Data acquired below room temperature(crosses) refer to Ga2O3 & 0.63 H2O. Since no anomaly isobserved around 273 K, it can be concluded that no molecu-lar water was present in the sample. To estimate the specificheat of dry c-Ga2O3, the tabulated heat capacity of ice in the

range 20– 273 K [24] was approximated by the third-orderpolynomial, while below 20 K the T3-approximation wasused. This function was assumed to represent the excesscontribution to the heat capacity of the sample due to thechemisorbed H2O and subtracted from the experimentalCP-values. The result is represented by the solid curve inFig. 9. The filled circles, which almost coincide with thiscurve stand for the heat capacity of b-Ga2O3 [25]. Thus, be-low 230 K, the heat capacity of dry c-Ga2O3 and b-Ga2O3 isnearly the same. Measurements above room temperaturewere performed under Ar-flow at atmospheric pressure.Therefore, a very large heat capacity due to the desorptionof water has been recorded in the first run (dashed curve inFig. 9). When the sample was cooled down and immedi-ately heated again, very reproducible heat capacity valueswere obtained (open circles in Fig. 9), which continue thelow-temperature curve of dry c-Ga2O3. Its heat capacity issmaller compared to b-Ga2O3 (dotted curve). It can be seenthat between 650 and 800 K there is an anomalous increaseof heat capacity with an inflection point around 730 K.Such an “S”-shaped heat capacity curve may be an indica-tion of rearrangement in the crystal structure of c-Ga2O3

before the transition to the stable b-form occurs. It is, how-ever, neither a first-order nor a second-order phase transi-tion, otherwise a singularity of the heat capacity curve

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Fig. 6. (a) HRTEM micrograph registered from two c-Ga2O3 nano-crystals and (b) corresponding FFT patterns and filtered images.

Fig. 7. (a) HRTEM micrograph registered from one c-Ga2O3 nano-crystal and (b) related FFT pattern, (c) Fourier filtered image, (d) cal-culated SAED and (e) calculated crystal structure.

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would appear. In support of this conclusion, no latent heatcan be associated with this transformation (Fig. 8). Similarobservations have been made for c-Al2O3. The latter trans-forms into corundum through the intermediate formationof d- and h-Al2O3 (transition aluminas), whereas no thermaleffects on DTA curves have been detected [18]. In a morerecent in-situ X-ray and neutron diffraction study [26], anew phase, which has been designated as c0-Al2O3 wasfound in place of d-Al2O3, and evidence for a higher-orderof c! c0 phase transformation was obtained. For c-Ga2O3,no detailed investigation of the transformation pathway onheating has been reported. Thus, the present study providesfirst evidence that c-Ga2O3 does not transform directly intob-Ga2O3. Because of the difficulties in the Rietveld refine-ment of XRD pattern of c-Ga2O3 even at room temperature(see above) no attempt has been made in this work to deter-mine the crystal structure of this high-temperature form,which is denoted as c0-Ga2O3. Its heat capacity is largerthan that of b-Ga2O3. The c! c0 transition in Ga2O3 is re-versible: when the sample is cooled down, the “S”-shapedheat capacity curve shown in Fig. 9 is exactly reproduced.

Thermodynamic functions for c-Ga2O3 and c0-Ga2O3

have been evaluated separately. The heat capacity is usuallyfitted by the equation:

CP(T) = – c – 2dT – 2eT–2 (1)

The enthalpy, entropy, and Gibbs energy are then repre-sented as follows [27]:

H(T) = a – cT – dT 2 + 2eT – 1 (2)

S(T) = – b – c – c ln(T) – 2dT + eT – 2 (3)

G(T) = a + bT + cT ln(T) + dT 2 + eT–1 (4)

where a, b, c, d, and e are adjustable coefficients and T is theabsolute temperature (K). They are listed in Table 3 to-gether with the corresponding parameters for b-Ga2O3

[28]. An expression for the heat capacity of dry c-Ga2O3

has been obtained by the non-linear least-squares fit to theexperimental points between 200 and 570 K, where the cor-rection for water content was applied below 300 K (seeabove). For c0-Ga2O3, the measured heat capacity curveabove 815 K is extrapolated to lower temperatures by mod-ifying the coefficients c and d in the heat capacity equationfor b-Ga2O3 [28], assuming that CP(c0) = CP(b) at 298 K.The obtained curve is shown in Fig. 9 (dash-dot). Thestandard entropy of c0-Ga2O3 at 298 K equals then that ofb-Ga2O3 (°S298 = 84.79 J & mol – 1 & K – 1). The standardentropy of dry c-Ga2O3 (°S298 = 73.40 J & mol – 1 & K – 1) iscalculated by the numerical integration under the curveCP/T vs. T according to the third law of thermodynamics.From these data, the coefficient b has been calculated ac-cording to Eq. (3). The coefficient a for c0-Ga2O3 has beenevaluated using Eq. (2) and the value of DH(c0 ! b) deter-mined by DSC. Since c0-Ga2O3 is metastable, the transfor-mation temperature is a function of heating rate, crystallitesize, atmosphere, etc. According to Fig. 8 it occurs between873 and 1223 K. For a quantitative calculation, the differ-ence in heat capacity of c0 and b-Ga2O3 over this tempera-ture range is taken into account. To determine the coeffi-cient a for c-Ga2O3, its enthalpy at 570 K is calculatedusing the experimental heat capacity values between 570and 815 K and the enthalpy of c0-Ga2O3 at 815 K.

From Eq. (3) it is evident that the entropy of c0-Ga2O3 islarger compared to b-Ga2O3. The higher entropy indicatesa highly disordered state of the former phase. Extrapolation

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Fig. 8. Example of DSC curve for c-Ga2O3. Dotted line represents theinterpolated baseline.

Fig. 9. Heat capacity of gallia polymorphs. Solid circles representlow-temperature data for b-Ga2O3 [25], dotted and dash-dot curvesshow the high-temperature heat capacity of b-Ga2O3 and c0-Ga2O3, re-spectively, both fitted to Eq. (1).

Table 3. Coefficients of Gibbs energy equation G(T) = a + bT + cT ln(T) + dT 2 + eT – 1 (in J & mol – 1) for three gallia polymorphs.

Phase a b c d e Tmin – Tmax (K)

c-Ga2O3 – 1 096 219 563.7468 – 93.4942 – 0.00846346490 529 558 298 – 570c0-Ga2O3 – 1 111 417 666.6405 – 109.2020 – 0.01330000000 1 080 114 298 – 3000b-Ga2O3 – 1 127 917 684.8332 – 112.3935 – 0.00796268819 1 080 114 298 – 3000

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of the Gibbs energy shows that c0-Ga2O3 would becomestable at 2505 K against the transformation into b-Ga2O3.The corresponding temperature for c and (-Al2O3 is2427 K. The stability of both phases is only hypothetical,in fact, liquid or gas are thermodynamically stable at suchhigh temperatures.

4. Summary

The metastable nanocrystalline c-form of gallium oxide hasbeen prepared and characterized by X-ray and electron dif-fraction, high-resolution transmission electron microscopy,adiabatic and differential scanning calorimetry. The ob-served sponge-like morphology of c-Ga2O3 particles ismost likely the origin of the high specific surface area ofthis material, while the size of individual crystallites doesnot exceed 5 nm. These nanocrystals are randomly ori-ented, so that rings appear in selected area electron diffrac-tion patterns instead of spots. Using the Rietveld refinementtechnique, preliminary parameters of the crystal structure ofc-Ga2O3 have been obtained. Like c-alumina, c-gallia crys-tallizes in a defect spinel-type structure. Both phases are,however, not fully isomorphous since different sites of thecubic space group Fd3m become partially occupied in addi-tion to those of the spinel prototype. Several interplanar dis-tances, which are characteristic for c-Ga2O3 have been mea-sured by HRTEM and the conformity of the micrographswith the proposed structure model has been demonstratedusing FFT image filtering.

At room temperature, water is present in c-gallia in vary-ing amounts. Its actual chemical formula can be written asGa2O3 & nH2O (0 4 n 4 0.63). Increasing temperature re-sults in water desorption beginning at 373 K. Dry c-Ga2O3

is very hygroscopic and behaves like c-Al2O3. Heating thesample above 873 K results in irreversible exothermictransformation into stable b-Ga2O3. The enthalpy of thistransformation is determined as – 19.3 C 0.4 kJ & mol – 1.Heat capacity measurements revealed a reversible higher-order phase transition in the range 650 – 800 K, which indi-cates a two-steps transformation pathway: c-Ga2O3)c0-Ga2O3) b-Ga2O3. The coefficients of Gibbs energyequation for c and c0-Ga2O3 have been assessed.

The authors wish to express their thanks to Albrecht Meyer, GerhardKaiser, Ewald Schmitt, Kersten Hahn, and Maria Sycha from Max-Planck-Institute Stuttgart, for technical assistance.

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(Received June 24, 2004; accepted July 7, 2004)

Correspondence address

Dr. Matvei ZinkevichMax-Planck-Institut für MetallforschungPulvermetallurgisches LaboratoriumHeisenbergstraße 3D-70569 StuttgartGermanyTel.: +49 711 68 93 105Fax: +49 711 68 93 131E-mail: zinkevich@mf.mpg.dewww: http://aldix.mpi-stuttgart.mpg.de/zinkevit/home_mz.html

M. Zinkevich et al.: Microstructural and thermodynamic study of c-Ga2O3

762 Z. Metallkd. 95 (2004) 9

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