Thermodynamic properties of MgGa2O4 and phase relations in the system Mg-Ga-O

Accepted Manuscript Thermodynamic properties of MgGa2O4 and phase relations in the system Mg-Ga-O K.T. Jacob, Shivesh Sivakumar PII:

S0925-8388(18)33821-0

DOI:

10.1016/j.jallcom.2018.10.147

Reference:

JALCOM 47965

To appear in:

Journal of Alloys and Compounds

Received Date: 26 June 2018 Revised Date:

11 October 2018

Accepted Date: 12 October 2018

Please cite this article as: K.T. Jacob, S. Sivakumar, Thermodynamic properties of MgGa2O4 and phase relations in the system Mg-Ga-O, Journal of Alloys and Compounds (2018), doi: https://doi.org/10.1016/ j.jallcom.2018.10.147. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

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Thermodynamic properties of MgGa2O4 and phase

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relations in the system MgMg-GaGa-O K.T. Jacob*, Shivesh Sivakumar

Avenue,, Department of Materials engineering, Indian Institute of Science, C.V. Raman Avenue

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560012.. Bengaluru, Karnataka, India – 560012

Kallarackel Thomas Jacob – E-mail address: [email protected]; [email protected]; [email protected]

Shivesh Sivakumar

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Contact number: +91 80 2293 2494; + 91 98454 79865 – E-mail address: [email protected]

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* corresponding author

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Contact number: +91 78240 52227

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Abstract Materials based on MgGa2O4 find use in microwave dielectrics, optoelectronics, spintronics and solid electrolytes for high-temperature fuel cells. For designing optimum processing

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conditions and evaluating interactions with other materials and environments,

thermodynamic data and appropriate phase diagrams are required. As part of a larger systematic study on spinels with functional applications, thermodynamic properties of MgGa2O4 are determined in the temperature range from 875 to 1325 K using an

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electrochemical cell incorporating yttria-stabilized zirconia as the solid electrolyte. The Gibbs energy of formation of MgGa2O4 from its constituent binary oxides MgO with halite

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D C±135F/J mol-1 = – structure and β-Ga2O3 with monoclinic structure is obtained: ∆ABCDEF

39868 – 8.742 CT/KF. The heat capacity of MgGa2O4 in the temperature range from 310 to 1200 K is measured by DSC. Both positive and negative deviations from Neumann-Kopp rule are seen in different temperature ranges. Derived from these measurements are the standard enthalpy of formation and standard entropy of MgGa2O4 at 298.15 K. The isothermal section of the phase diagram of the system Mg-Ga-O and oxygen potential-

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composition diagram at 1200 K are computed from thermodynamic data. Keywords

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Heat capacity, Gibbs energy of formation, Enthalpy, Entropy, Oxygen potential diagram,

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Magnesium gallate

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1. Introduction Sintered MgGa2O4 ceramics exhibit excellent microwave dielectric properties [1]. The spinel compound is a wide bandgap transparent semiconductor, with an optical bandgap of

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4.9 eV at room temperature, suitable for electronic and optoelectronic applications [2]. Since both Ga and trivalent lanthanide CLn3+F ions have similar electronegativity and size, MgGa2O4 is a suitable host material for phosphors. Trivalent Pr and Eu ions incorporated in MgGa2O4 produce strong monochromatic emission in blue-green CPrF and red CEuF bands

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because of efficient electron energy transfer from the spinel host to the 4f sublevel of the lanthanide ions [3]. When transition metal ions are introduced into the spinel lattice,

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photoluminescence caused by d-d transitions and/or charge-transfer excitation is observed. Nipan et al. [4] have suggested that MgCFe0.8Ga0.2FO4 is a semiconductor with spin-oriented carriers suitable for spintronic applications.

Complex oxide perovskite La1-xSrxGa1-yMgyO3-δ CLSGMF, which belongs to the quaternary oxide system La2O3-SrO-Ga2O3-MgO, is a solid electrolyte with application in high-

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temperature fuel cells [5]. It has higher oxygen ion conductivity than yttria-doped zirconia CY2O3FZrO2 electrolyte currently used in solid oxide fuel cells CSOFCF. To understand phase relations in the quaternary system and to analyze reactions between LSGM and electrode materials, it is necessary to know thermodynamic properties and phase diagrams of

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constituent binaries. Although the phase relations in the pseudo-binary system MgO-Ga2O3 have been delineated in the temperature range from 1300 to 1673 K [6], thermodynamic

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properties of the only inter-oxide compound MgGa2O4 are not well established. Heat capacity CSTD F of MgGa2O4 was first measured by Wilkerson et al. [7] in the temperature range from 298 to 673 K with standard deviation of 6%. More recently Kondrat’eva et al. [8] have measured heat capacity more accurately in the temperature range from 7 to 1200 K. Adiabatic calorimetry was used in the range from 7 to 347 K and DSC from 322 to 1200 K. Although low-temperature adiabatic calorimetry is generally considered to be the gold standard for obtaining reliable data on standard entropy, the extent of residual entropy in the inverse spinel MgGa2O4 cannot be assessed by calorimetry. Enthalpy of formation of

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MgGa2O4 from component binary oxides has been measured by Navrotsky and Kleppa [9] using oxide-melt solution calorimetry as –40.2C±1.2F kJ mol-1 at 970 K. From a massspectrometric study of vaporization from a MgO-Ga2O3 sample containing 40 mol% Ga2O3, activity of Ga2O3 was obtained at 1750 K [10]. The composition falls in the two-phase field

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containing MgO+MgGa2O4. The Gibbs energy of formation of MgGa2O4 at 1750 K can be derived from this study with appropriate corrections for solid solubility of Ga2O3 in MgO. The spinel phase is non-stoichiometric at high temperatures. At 1673 K spinel phase

extends from 42.1 to 50.7 mol % MgO [6]. With reducing temperature, homogeneity range

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narrows down considerably. At 1300 K, the spinel phase extends from 47.4 to 50.3 mol % MgO [6]. Solubility of Ga2O3 in MgO decreases rapidly with temperature, from 12.7 mol %

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at 1873 K to 4.7 mol % at 1673 K [11]; the solubility is negligible below T <1400 K. In this study, electrochemical measurements are carried out in the temperature range from 875 to 1325 K for determining the Gibbs energy of formation of MgGa2O4. Electrochemical technique is more accurate than other methods for measurement of Gibbs energy. From measurements over an extended temperature range, enthalpy and entropy of formation at

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an average temperature are derived. To compute enthalpy of formation and standard entropy of MgGa2O4 at 298.15 K, variation of heat capacity with temperature should be known. Hence, differential scanning calorimetry CDSCF is employed to measure heat capacity in the temperature range from 310 to 1200 K. Comparing standard entropy

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obtained from high-temperature Gibbs energy measurement with that from adiabatic

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calorimetry can shed light on residual entropy of the inverse spinel at 0 K. 2. Experimental methods

2.1 Sample preparation

MgO C99.95% pureF and Ga2O3 C99.99% pureF are obtained from Alfa-Aesar. The oxides are heated in dry air for ~87 ks at 1373 K before use. The ternary oxide MgGa2O4 is prepared by direct solid-state reaction between MgO and Ga2O3 at 1473 K in air. Fine powders of MgO and Ga2O3, each of 99.99% purity, are first dehydrated by heating under flowing Ar 4

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gas at 773 K and then mixed and ground together in stoichiometric ratio using an agate mortar and pestle. The mixture is pelletized using a steel die at 100 MPa pressure. The pellets are first calcined at 1473 K for ~30 ks. The pellets after cooling are reground and repelletized for heat treatment at 1523 K for an additional 20 ks. The pellet is then crushed

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and ground to fine powder. The product is pure cubic MgGa2O4 with lattice parameter a = 0.8286 nm obtained using XRD. The average particle size of the powder determined using SEM is ~2 µm. Chemical analysis using inductively coupled plasma atomic emission

spectroscopy CICP-AESF confirmed the Ga/Mg molar ratio as 2.011C±0.009F. Before use in

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DSC and electrochemical measurement, the MgGa2O4 sample is homogenized at 1100 K for ~30 ks. The measuring electrode is prepared by mixing Ga+MgGa2O4+MgO in equimolar

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ratio. In the reference electrode, Ga+Ga2O3 is taken in equimolar ratio. β-Ga2O3 used in this study has monoclinic structure Cspace group C2/mF with lattice parameters a = 1.2216, b = 0.3038, c = 0.5802 nm and β = 103.83o. In β-Ga2O3, oxygen octahedra do not share faces unlike in the case of α-Ga2O3 in which both faces and edges are shared. To study cation non-stoichiometry of the spinel MgGa2O4, two pelletized samples, one

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containing an equimolar mixture of MgO and MgGa2O4 and the other an equimolar mixture of MgGa2O4 and β-Ga2O3, are equilibrated in air at 1300 K for ~300 ks. After quenching, the samples are analyzed by EDX. No detectable MgO is present in β-Ga2O3 grains in contact with MgGa2O4. The MgO grains adjacent to MgGa2O4 contained 0.52C±0.19F mol % Ga2O3.

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The spinel phase in contact with MgO contained 50.1C±0.2F % MgO. The spinel phase in contact with β-Ga2O3 contained 48.6C±0.2F % MgO. The compositions are averages of at

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least eight measurements. The width of the spinel phase field at 1300 K is 1.5 mol % MgO; non-stoichiometry is mainly on the Ga2O3 side. The non-stoichiometry is expected to be considerably less at lower temperatures. The oxygen nonstoichiometry of the spinel sample equilibrated at 1300 K in air is investigated by measuring mass loss on hydrogen reduction at 1073 K for 3.6 ks. The products identified after reduction are MgO and Ga. The excess oxygen δ in MgGa2O4+δ was found to be 0.013C±0.02F.

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2.2 Heat capacity measurement

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A heat-flux differential scanning calorimeter CDSCF, used earlier for measurements on Rh2O3 [12], RuO2 and OsO2 [13], GaN [14], is used to measure the heat capacity of

Φstoichiometric MgGa2O4 in the temperature range from 310 to 1200 K in dry air. Dry air is obtained by passing synthetic air C\] ^ = 0.21F from a cylinder through drying columns

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filled with silica gel and magnesium perchlorate. Platinum crucibles are used to hold the sample and reference material Cα-Al2O3F. The mass of the sample is 42.23 mg. The mass of reference material is similar. NIST synthetic sapphire CSRM 720F with corundum structure

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is used as the reference material. The alumina powder is dehydrated by vacuum treatment at 1200 K before use. The temperature calibration is done using phase transition temperatures of reference materials; anhydrous potassium nitrate CT Tr = 400.85 KF, silver sulfate CT Tr = 703.15 KF and lithium sulfate CT Tr = 851.43 KF. The DSC is operated in the step heating mode to increase accuracy. The classical three-step procedure was followed.

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In the first step, heat flow rate CΦoF with empty crucibles in the sample and reference side is measured. In the second step, the α-Al2O3 is placed in the sample crucible with empty crucible on the reference side and the corresponding heat flow rate is measured CΦrF. In the third step, α-Al2O3 in the sample crucible is replaced by MgGa2O4 and the heat flow rate

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is determined CΦsF. The ratio CΦs -ΦoF/CΦr -Φo F is used to compute heat capacity during heating at a constant rate C0.0333 K/sF over small temperature steps C10 KF with

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isothermal dwell time of 0.9 ks. Prior to measurements on MgGa2O4, heat capacity of copper using corundum crucibles was measured under Ar atmosphere. Based on measurements on copper, combined error Csystematic and randomF in heat capacity is estimated to be ~0.8% of the measured value.

2.3 Measurement of Gibbs energy of formation at high temperature A solid-state cell is designed to directly measure the Gibbs energy of formation of MgGa2O4 from its component binary oxides. The cell can be represented as: 6

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W, Ga + MgGa2O4 + MgO // CY2O3F ZrO2 // β-Ga2O3 + Ga, W The cell is written such that the right hand electrode is positive. Yttria-stabilized zirconia CY2O3F ZrO2 is selected as the solid electrolyte because oxygen potential boundary for the onset of electronic conduction in this material is lower than that for calcia and magnesia-

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doped zirconia. A schematic of the apparatus used for high-temperature emf

measurements is shown in Fig. 1. The solid-state cell is enclosed inside a vertical alumina tube flushed with pre-purified Ar gas flowing at 8.3 ml s-1. The measuring electrode,

consisting of an equimolar mixture of Ga+MgO+MgGa2O4, is placed in a MgO crucible. The

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crucible is supported on an inverted closed-end alumina tube enclosing the Pt/Pt-13%Rh thermocouple. The yttria-stabilized zirconia CYSZF solid electrolyte in the form of an

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impervious tube closed at one end is used to contain reference electrode consisting of an equimolar mixture of Ga+β-Ga2O3. The solid electrolyte tube is inserted into the measuring electrode mixture in the MgO crucible. Tungsten wire is used as an electrical lead to liquid Ga at each electrode. A narrow alumina tube is used to insulate the tungsten lead to liquid Ga inside the solid-electrolyte tube. Argon gas is passed through this narrow tube to flush the reference electrode. A perforated MgO cover is placed over both electrode mixtures to

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minimize the escape of Ga as Ga2O at high temperatures. This gas specie CGa2OF is invariably present at high temperatures over mixtures of Ga and oxides containing Ga. The design of the apparatus provides for isolation of the gas phase over reference and measuring electrodes; the solid electrolyte tube provides the barrier. This is necessary to

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prevent transport of oxygen from one electrode to the other via the gas phase.

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The outer alumina tube is closed at both ends with gas-tight brass fittings with inlets/outlets for gas and electrical leads. The outer alumina tube is placed inside a vertical resistance furnace such that the electrodes are maintained in the constant temperature zone C±1 KF of the furnace. The temperature of the furnace is controlled to ±1 K. A cylindrical stainless steel sheath, placed around the outer alumina tube enclosing the cell, is earthed to minimize induced emf on cell leads from furnace windings. Emf of the cell is measured using a high-impedance C>1012 ohmsF digital voltmeter with an accuracy of 0.01 mV. The thermal reversibility of the cell is verified by temperature cycling: 7

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the same emf is registered when temperature is approached from higher and lower ends. Electrochemical reversibility of the cell is checked through microcoulometric titration, wherein a small current of magnitude ~50 µA is passed through the cell in each direction. The open-circuit emf is measured with time after each titration. The emf is found to return

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to the steady state value prior to titration, after successive displacements from equilibrium in opposite directions. Varying the flow rate of the inert gas in the range 5 to 12 ml s-1

through the alumina tube enclosing the cell had no effect on the emf. At the end of each experiment, the electrodes are examined by optical microscopy, XRD and SEM. No change

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in phase composition of the electrodes caused by high temperature exposure is detected.

3. Results and discussion

3.1 Heat capacity of MgGa2O4

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The YSZ solid electrolyte retained its fully stabilized cubic structure during the experiment.

Displayed in Fig. 2 is the measured heat capacity of MgGa2O4 as a function of temperature.

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The data are well fitted by a standard empirical equation involving four terms: STD C±0.101F/J mol-1 K-1 = 175.206 + C3.53x10-3FCT/KF + C5.284x10-8FCT/KF2 4.19x106CT/KF-2

…C1F

The uncertainty estimate corresponds to 95% confidence interval C2σF and reflects random

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errors in measurement. Significantly higher are possible systematic errors C±1 J mol-1K-1F. Equation C1F extrapolated to 298.15 K gives a value of 129.36 J mol-1 K-1. Heat capacity of

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MgGa2O4 measured by Wilkerson et al. [7] is also displayed in Fig. 2 for comparison with values obtained in this study. The results of Wilkerson et al. [7] are systematically lower, but within their stated uncertainty of 6%. There is good agreement between this study and Kondrat’eva et al. [8] at 298.15 K with a difference of only 0.05 J mol-1K-1. But the difference progressively increases with temperature. At 1200 K, the difference is 4.5 J mol-1K-1. The heat capacity difference ΔSTD between ternary oxide MgGa2O4 and its constituent binary oxides MgO and β-Ga2O3 is shown as a function of temperature in Fig. 3. Although the Neumann-Kopp rule is approximately obeyed near room temperature, there are significant

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positive deviations at moderately elevated temperatures and negative deviations at higher temperatures. ΔSTD exhibits a maximum at 450 K and then decreases continuously with increasing temperature. The complex behavior of ΔSTD is related to change in cation distribution and anion position parameter of the inverse spinel with temperature and

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consequent vibrational changes.

The molar heat content of MgGa2O4 can be obtained by integrating the heat capacity; d

CHT - H298.15F / J mol-1 = c^ef.ghC STD FdT

C2F

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= 175.206CT/KF + 1.765x10-3CT/KF2 + 1.761x10-8CT/KF3 + C4.19x106FCT/KF-1 – 66448

d

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The molar entropy increment of MgGa2O4 can be obtained from the equation: CST - S298.15F / J mol-1 K-1 = c^ef.ghC STD /T FdT

= 175.206 lnCT/KF + 3.53x10-3CT/KF + 2.642x10-8CT/KF2 + C2.095x106FCT/KF-2 – 1022.874

…C3F

The calculated values for molar heat content and molar entropy are given in Table 1 at

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regular intervals of temperature.

3.2 Thermodynamic properties of MgGa2O4

The measured emf CEF of the solid-state electrochemical cell is displayed in Fig. 4 as a

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function of temperature in the range from 875 to 1325 K. The emf is found to increase linearly with temperature. The following linear relation is obtained by least-squares

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regression analysis:

E C+0.224F/mV = 68.867 + 0.015CT/KF

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The uncertainty estimate corresponds to 95% confidence interval C2σF. The uncertainty estimates for y-intercept and slope are ±0.213 and ±1.92x10-4 respectively. The electrochemical reaction at the right-hand electrode of the cell is, β-Ga2O3 + 6e- → 2Ga ClF + 3O2-

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At the left-hand electrode the corresponding reaction is: 2Ga ClF + 3O2- + MgO → MgGa2O4 + 6e-

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The virtual cell reaction is the sum of reactions occurring at the anode and cathode: β-Ga2O3 + MgO → MgGa2O4

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The reversible emf of the cell relates to the Gibbs energy of formation of MgGa2O4 from its component binary oxides by the Nernst equation:

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D CMgGa^ Oj F = –nFE = –39868 – 8.742 CT/KF ∆A D C±135F/ J mol-1 = ∆ABCDEF

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where n = 6 is the number of electrons involved in the electrode reactions, F = 96485.33 C D CMgGa^ Oj F is the Gibbs energy of formation of mol-1 is the Faraday constant and ∆ABCDEF

essentially stoichiometric MgGa2O4 from its constituent binary oxides. From equation C8F

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the Gibbs energy of formation of MgGa2O4 from binary oxides at 1750 K is obtained as 55167C±190F J mol-1. This compares well with the value of -55481 J mol-1 derived from

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mass-spectrometric measurement of the activity of Ga2O3 C0.024F at 1750 K by KuncewiczKupczyk [10] in the two-phase region MgGa2O4+MgO. Although activity of MgO was assumed to be unity by Kuncewicz-Kupczyk [10] in the two-phase region, solubility of Ga2O3 in MgO at 1750 K is 0.08 mol %. In calculating the Gibbs energy of formation from the measurement of Kuncewicz-Kupczyk [10], the activity of MgO is estimated as 0.92

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D CMgGa^ Oj F = RklnC0.024x0.92F = −55481 J molmg . following Raoult’s law. Thus, ∆ABCDEF

The second-law enthalpy and entropy of formation of MgGa2O4 from component oxides at a D CMgGa^ Oj FC±0.13F/ mean temperature of 1100 K are obtained from equation C8F: ∆nBCDEF

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D CMgGa^ Oj F C+0.114F/J mol-1 K-1 = 8.742. The enthalpy of kJ mol-1 = –39.868 and ∆oBCDEF

formation from oxides obtained in this study agrees well with the calorimetric value of – 40.2C±1.2F kJ mol-1 reported by Navrotsky and Kleppa [9] at 970 K. The positive entropy of

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formation is related to the configurational entropy arising from the mixing of Ga and Mg ions on the tetrahedral CtF and octahedral CoF sites of the spinel. For the ideal inverse spinel CGaFt[Mg,Ga]oO4 structure stable at low temperatures, the entropy of mixing assuming completely random distribution on each site is -11.53 J mol-1 K-1. At high temperatures, the spinel will move away from the strictly inverse composition towards the random composition. Structural measurements by Schmalzried [6] indicate that the cation distribution at 1100 K can be represented as CMg0.07Ga0.93Ft[Mg0.93Ga1.07]oO4. The ideal

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configurational contribution to the entropy of the spinel corresponding to this distribution is calculated as ∆S CM = -R[C0.07lnC0.07F+0.93lnC0.93FF+2C0.465lnC0.465F+0.535lnC0.535FF] = 13.58 J mol-1 K-1. Jacob and Alcock [15] have suggested that entropy of formation of cubic spinels

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from component binary oxides with rock-salt and corundum structures can be expressed as -7.25 + ∆SCM, where ∆SCM is the configurational contribution to the entropy of the spinel. This correlation holds well for spinel compounds that do not contain transition metal ions exhibiting Jahn-Teller distortion. The correlation predicts an entropy of formation of

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MgGa2O4 from MgO and α-Ga2O3 with corundum structure as 6.33C±2F J mol-1 K-1. The entropy of transformation of β-Ga2O3 to α-Ga2O3 has been estimated as 2.3C±0.8F J mol-1 K-1

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[16]. Combining the value for entropy of formation from the correlation with the estimate for the entropy of transformation of Ga2O3, one obtains entropy of formation of the spinel MgGa2O4 from MgO and β-Ga2O3 as 8.63C±2.2F J mol-1 K-1, in good agreement with the measured value.

The enthalpy and entropy of formation of MgGa2O4 from oxides at 298.15 K can be

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calculated from STD values measured in this study in combination with data for MgO and βGa2O3 from the thermodynamic data compilation of Pankratz [17].

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D D CMgGa^ Oj F C±0.5F/kJ mol-1 = ∆nBCDEF,ggpp CMgGa^ Oj F – ∑CH1100 – H298.15F ∆nBCDEF,^ef.gh

= –39.868 – 1.309 = –41.177

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where ∑Cnggpp − n^ef.gh F is a short notation for Cnggpp − n^ef.gh Frstuv ]w – Cnggpp −

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n^ef.gh Frs] – Cnggpp − n^ef.gh Ftuv ]x . Similarly, at 298.15 K, D D CMgGa^ Oj F C±0.5F/J mol-1 K-1 = ∆oBCDEF,ggpp CMgGa^ Oj F – ∑CS1100-S298.15F ∆oBCDEF,^ef.gh

= 8.742 – 2.612 = 6.13

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where ∑Coggpp − o^ef.gh F is a short notation for Coggpp − o^ef.gh Frstuv]w – Coggpp − o^ef.gh Frs] – Coggpp − o^ef.gh Ftuv ]x . The standard entropy of MgGa2O4 at 298.15 K can be obtained using the relation, D D D D CMgGa^ Oj F C±1.5F/J mol-1K-1 = o^ef.gh CMgOF+ ∆oBCDEF o^ef.gh CGa^ Oy F + o^ef.gh CMgGa^ Oj F

= 26.945+ 84.98 + 6.13 = 118.055

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This value is significantly higher than the value of 110.83C±0.24F J mol-1K-1 obtained by Kondrat’eva et al. [8] from low-temperature heat capacity measurements using adiabatic calorimetry. This difference of 7.225C±1.5F J mol-1K-1 can be attributed to the residual entropy of the inverse spinel MgGa2O4 at 0 K. MgGa2O4 is an inverse spinel at low

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temperatures. Both Ga and Mg are present in the octahedral sites giving rise to

configurational entropy of mixing on the octahedral site. On cooling, gradual onset of shortrange order is expected without a significant signature in heat capacity spectrum. However, an ordering reaction would be clearly manifested in the plot of heat capacity versus

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temperature. Measurements of Kondrat’eva et al. [8] do not show any evidence of an

ordering reaction at low temperatures. Hence, residual configurational entropy is expected

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at 0 K. The residual entropy of 7.225C±1.5F J mol-1K-1 for cubic MgGa2O4 identified in this study is similar to that found in inverse spinel Zn2TiO4 with cubic structure, 7.95C±2.51F J mol-1K-1 [18].

The standard enthalpy of formation of MgGa2O4 from elements at 298.15 K can be computed by combining the formation enthalpy from binary oxides with data on the binary

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oxides. For the formation reaction, Mg + 2Ga + 2O2 → MgGa2O4

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D ∆nBD CMgGa^ Oj F C±1.5F/kJ mol-1 = ∆nBD CGa^ Oy F + ∆nBD CMgOF + ∆nBCDEF CMgGa^ Oj F

C13F

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= –1089.09 – 601.492 – 41.177 = –1731.759

This compares with an estimated value of -1719.2C±4.2F kJ mol-1 for enthalpy of formation given by Glushko [19] and cited by Kodrat’eva et al. [8]. More reliable is the calorimetric

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data from Navrotsky and Kleppa [9] on enthalpy of formation from oxides which is in good accord with the result of this study. Thermodynamic data table for MgGa2O4 developed in this study, listing important properties at regular intervals of temperature in the range from 298.15 to 1800 K, is presented in Table 1. The enthalpy of formation shows discontinuity at temperatures corresponding to melting and boiling of elements Ga and Mg. The Gibbs energy of formation exhibits a change in slope C∆oBD F at these temperatures. Data beyond 1200 K is based on extrapolated heat capacity data using the polynomial equation C1F. Hence, the 12

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calculated Gibbs energy of formation at 1800 K is associated with an uncertainty of ±3 kJ mol-1. Nevertheless, the good agreement between the calculated Gibbs energy of formation and the mass-spectrometric measurements of Kuncewicz-Kupczyk [10] at 1750 K discussed earlier is encouraging. MgGa2O4 at the measuring electrode, defined by the reaction,

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The oxygen potential corresponding to three-phase equilibrium involving Ga, MgO and

Gibbs energy of formation of Ga2O3 from Pankratz [17]. D ∆ABCgjF C±897F/ J molmg =−1135439 + 323.6Ck⁄KF

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MgO + 2Ga + 3z2O2 → MgGa2O4 C14F can be obtained by combining data for reaction C7F obtained in this study with standard

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D = –756959 + 215.85CT/KF ∆|]rv C+897F/ J mol-1 = Rkln}\] ^ ~ = C2z3F∆ABCgjF

C15F C16F

The Gibbs energy of formation of Ga2O3 in the temperature range from 800 to 1300 K from Pankratz [14] used in the above calculation can be represented by the linear relation: ∆ABD C+887F/J mol-1 = –1095571 + 332.52CT/KF

C17F

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The oxygen partial pressures corresponding to the three-phase equilibrium CGa+MgO+MgGa2O4F measured in this study and two-phase equilibrium CGa+Ga2O3F defining the reference electrode are compared in Fig. 5 with the low oxygen pressure boundary for predominant ionic conduction Cσion=100σeF in yttria-stabilized zirconia

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electrolyte. Experimental data on conduction boundary C[20-23]F at high temperatures is extended to lower temperatures for comparison [24]. It is clear that the low oxygen partial pressures associated with reference and measuring electrodes are well within the ionic

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conduction domain of the electrolyte and Nernst law is valid under the experimental conditions used in this study.

3.3 Binary system Mg-Ga: Excess Gibbs energy and chemical potentials In order to compute the ternary phase diagram for the system Mg-Ga-O, data on the binary Mg-Ga is required. Meng et al. [25] have reviewed the literature on thermodynamic properties and phase diagram of the binary system Mg-Ga. They suggested the Redlich 13

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Kister model for excess Gibbs energy of mixing C∆A  F of liquid phase of the Ga-Mg system. At 1200 K, ∆A  / J molmg = €rs €tu [–26046 + 563C€tu - €rsF + 5249C€tu - €rsF2 ]

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In this expression, Xi represents mole fraction of component i. The corresponding partial

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excess Gibbs energies or chemical potentials of Mg and Ga are given by the equations; ^  ∆A‚ / J molmg = €ƒ„ [–26046 + 563CXGa – 3XMgF + 5249CXGa – 5XMgFCXGa – XMgF]

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 ^ / J molmg = €‚ [–26046 + 563C3XGa – XMgF + 5249C5XGa – XMgFCXGa – XMgF] ∆Aƒ„

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The partial excess Gibbs energy of a component i and its chemical potential in the liquid are

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related by the equation:

C21F

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∆µi =∆Gi =RT lnCXiF + ∆A…

3.4 Isothermal section of phase diagram of the system Mg-Ga-O

The ternary phase diagram of the system Mg-Ga-O can be computed from thermodynamic data on MgGa2O4 obtained in this study, thermodynamic properties of the alloy Mg-Ga [25], Gibbs energies of formation of the binary oxides [17] and binary phase diagrams [26]. Each

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three-phase region is bounded by three narrow two-phase regions, represented by solid lines. Tie-lines in the two-phase region are displayed by dash lines. Along the binary Mg-O, only MgO with rock-salt structure is observed. Along the binary Ga-O, only β-Ga2O3 with

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monoclinic structure is stable. β-Ga2O3 is isomorphous with θ-Al2O3 and contains two crystallographically nonequivalent gallium positions. MgGa2O4 with structure close to that of an inverse spinel is the only ternary phase [6]. The computed isothermal section of the

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ternary phase diagram for the system Mg-Ga-O at 1200 K is displayed in Fig. 5. At this temperature, the liquid phase CMg-Ga alloyF is stable over the entire range of composition [26]. All the alloy phases are in equilibrium with MgO. There are two 3-phase fields involving metal Ga: Ga+MgO+MgGa2O4 and Ga+Ga2O3+MgGa2O4. There are two 3-phase fields involving O2 gas: O2+MgO+MgGa2O4 and O2+Ga2O3+MgGa2O4. The maximum solubility of oxygen in liquid Ga in equilibrium with Ga2O3 at 1200 K is 0.013 at. % O [27]. Oxygen solubility in alloys in equilibrium with MgO is expected to be significantly lower.

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3.5 Oxygen potential-composition diagram

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The oxygen potential-composition diagram for a ternary system at constant temperature is 3-dimensional, with composition represented on a Gibbs triangle in the X-Y plane and oxygen potential plotted along the Z-direction. It is difficult to read temperatures and

compositions precisely from 3-D projections. Hence, it is useful to reduce the diagram to

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two dimensions by defining an amended composition parameter ‡tu /C‡rs +‡tu F, where ‡… represents number of moles of component i. This parameter represents the cationic or

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metallic fraction in a stable phase. In the 2-D oxygen potential – composition diagram, oxygen potential is plotted against the modified composition parameter. Because oxygen is not included in the amended composition parameter, oxygen non-stoichiometry of oxide phases and oxygen solubility in alloys cannot be represented in the 2-D diagram. The diagram is in one sense akin to isothermal Gibbs triangle representation of ternary phase relations in systems of the type Mg-Ga-O, where the alloy compositions are displayed on

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the base of the triangle and oxygen concentration at the apex. The Gibbs triangle representation shows the evolution of phases with increasing oxygen concentration starting with the binary alloy system Mg-Ga. The 2-D oxygen potential diagram shows the

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evolution of phases with increasing oxygen chemical potential over the alloy. The oxygen potential diagram for the system Mg-Ga-O at 1200 K, calculated from results

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obtained in this study and auxiliary data from the literature [17, 25] is shown in Fig. 5. At the lowest oxygen potentials only alloy phases corresponding to the binary Mg-Ga are present. As the oxygen potential is increased, pure Mg gets oxidized first, followed by Mg from the alloy. The oxygen potential defining reaction involving the equilibrium between the Mg-Ga alloy and MgO is: Mg + 1z2O2 → MgO

(22)

D ∆|ˆ ^ = 2(∆AB,rs] – ∆µMg)

(23)

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Oxidation of pure Mg occurs at -939.91 kJ mol-1 at 1200 K. With increasing oxygen potential magnesium in Mg1-xGax gets oxidized progressively. Thus, the two-phase field involving MgO+Mg1-xGax extends over a range of oxygen potentials. For a fixed oxygen potential, the composition of the alloy in equilibrium with MgO is uniquely defined. The oxygen potential

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increases exponentially as the Mg is depleted from the alloy. At the higher oxygen potentials corresponding to this two-phase equilibrium, essentially pure Ga is in equilibrium with MgO.

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Further increase in oxygen potential results in the formation of the spinel compound

MgGa2O4 from Ga and MgO. In a ternary system, when three condensed phases co-exist at a

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fixed pressure and temperature, the system is invariant. Therefore, each three-phase equilibrium is associated with a constant oxygen potential, represented on the diagram by a horizontal line. This oxygen potential C–497.807±2.3 kJ mol-1F which prevailed at the measuring electrode of the solid-state cell at 1200 K, is given by equation C16F. Above this oxygen potential, there are two two-phase fields, MgO+MgGa2O4 and Ga+MgGa2O4, which

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extend over a range of oxygen potentials.

An increase in oxygen potential to –464.597C±2F kJ mol-1 at 1200 K, results in the oxidation horizontal.

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4. Conclusions

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of Ga to Ga2O3 and generation of an additional two-phase field Ga2O3+MgGa2O4 above the

The standard Gibbs energy of formation of stoichiometric MgGa2O4 from its constituent binary oxides was determined with high accuracy using a solid-state electrochemical D technique in the temperature range from 875 to 1325 K: ∆ABCDEF C±135F/J mol-1 = –39868 –

8.742 CT/KF. Increasing relative stability of the compound with temperature originates from the mixing of cations on two non-equivalent crystallographic sites of the spinel. The Gibbs energy of formation when extrapolated, agrees well that derived from mass-

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spectrometric determination of the activity of Ga2O3 in the two-phase mixture CMgGa2O4+MgOF at 1750 K [10] after a suitable correction for activity of MgO. Measured using DSC is the heat capacity of MgGa2O4 in the temperature range from 310 to

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1200 K. Within experimental error, the heat capacity of MgGa2O4 at room temperature is an additive sum of heat capacities of MgO and β-Ga2O3. With increase in temperature, positive deviations from Neumann-Kopp rule are seen. The deviations reach a maximum and then decrease to negative values. The complex behavior of the heat capacity is related to

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changes in cation distribution and oxygen position parameter of the spinel with

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temperature.

The second-law enthalpy of formation of MgGa2O4 obtained in this study is in good agreement with oxide-melt solution calorimetry of Navrotsky and Kleppa [9]. The standard enthalpy of formation from elements and standard entropy of MgGa2O4 at 298.15 K are estimated as –1731.76C±1.5F kJ mol-1 and 118.06C±1.5F J mol-1 K-1 respectively. By combining the results of this study with low-temperature adiabatic calorimetric

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measurements of Kondrat’eva et al. [8], the residual entropy of cubic MgGa2O4 can be estimated as 7.225C±1.5F J mol-1K-1. The phase relations in the system Mg-Ga-O are computed. An isothermal section of the ternary system and oxygen potential-composition

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diagram at 1200 K are presented.

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Acknowledgements

K T Jacob thanks the National Academy of Sciences, India, for the award of NASI – Senior Scientist Platinum Jubilee Fellowship. This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

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[10] W. Kuncewicz-Kupczyk, Investigation of the thermodynamic properties of the

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gallium oxide systems with the group IIA oxides and lanthanum oxide at high temperatures, Ph.D. Thesis, Wroclaw University of Technology C2002F. [11] G. Katz, S. Kachi, R. Roy, Gallium ion diffusion in magnesium oxide, Jpn. J. Appl. Phys. 8 C1969F 429–435. doi:10.1143/JJAP.8.429.

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[12] K.T. Jacob, T. Uda, T. H. Okabe, Y. Waseda, The standard enthalpy and entropy of formation of Rh2O3 - A third-law optimization, High Temp. Mater. Process. 19 C2000F 11–16. doi:10.1515/HTMP.2000.19.1.11

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ruthenium dioxide and osmium dioxide, J. Am. Ceram. Soc. 83 C2000F 1745–1752.

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[14] K.T. Jacob, S. Singh, Y. Waseda, Refinement of thermodynamic data on GaN, J. Mater. Res. 22 C2007F 3475–3483. doi:10.1557/JMR.2007.0441. [15] K.T. Jacob, C.B. Alcock, The oxygen potential of the systems Fe+FeCr2O4+Cr2O3 and Fe+FeV2O4+V2O3 in the temperature range 750–1600oC, Metall. Trans. B. 6 C1975F 215–221. doi:10.1007/BF02913562.

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[21] M. Sasabe, M. Miyashita, J.Z. Hua, H. Senoo, Determination of a partial electronic conduction parameter of solid electrolytes for an oxygen sensor by using AC two terminals method, Tetsu-to-Hagane. 77 C1991F 790–797. doi:10.2355/tetsutohagane1955.77.6_790. [22] D.A.J. Swinkels, Rapid determination of electronic conductivity limits of solid 19

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electrolytes, J. Electrochem. Soc. 117 C1970F 1267–1268. doi:10.1149/1.2407286 . [23] M. Iwase, E. Ichise, M. Takeuchi, T. Yamasaki, Measurements of the parameter, ˆm , for the determinations of mixed ionic and n-type electronic conduction in doi.org/10.2320/matertrans1960.25.43.

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commercial zirconia electrolytes, Trans. JIM. 25 C1984F 43–52. [24] C. Shekhar, Studies on thermodynamics and phase equilibria of selected oxide systems, Ph.D. Thesis, Indian Institute of Science, Bangalore, India C2011F.

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system, Trans. Nonferrous Met. Soc. China. 20 C2010F 450–457. doi:10.1016/S10036326C09F60161-8.

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[26] A.A. Nayeb-Hashemi, J.B. Clark, The Ga-Mg Cgallium-magnesiumF system, Bull. Alloy Phase Diagrams. 6 C1985F 434–439. doi:10.1007/BF02869505. [27] C.B. Alcock, K.T. Jacob, Solubility and activity of oxygen in liquid gallium and galliumcopper alloys, J. Less Common Met. 53 C1977F 211–222. doi:10.1016/0022-

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5088C77F90106-0.

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Table 1: Thermodynamic properties of MgGa2O4 ∆nBD

∆ABD

CJ mol-1 K-1F

CkJ mol-1F

CkJ mol-1F

-1731.759

-1610.606

-1731.778

-1609.855

-1731.773

-1608.659

-1742.953

-1608.659

159.431

-1742.814

-1565.605

29.976

194.168

-1741.409

-1521.45

165.71

46.295

223.907

-1739.542

-1477.615

700

169.16

63.049

249.728

-1737.524

-1434.113

800

171.5

80.089

272.478

-1735.496

-1358.928

900

173.26

97.331

292.785

-1733.521

-1347.951

922**

173.54

101.146

296.973

-1733.1

-1338.715

922**

173.54

101.146

296.973

-1742.049

-1338.715

1000

174.62

114.725

311.111

-1740.566

-1304.498

1100

175.71

132.242

327.805

-1738.731

-1260.989

1200

176.59

149.857

323.132

-1736.998

-1217.649

1300

177.41

167.557

357.313

-1735.332

-1174.397

1363***

177.92

178.75

365.723

-1734.336

-1147.282

1363***

177.92

178.75

365.723

-1860.903

-1147.298

178.11

185.333

370.498

-1859.736

-1127.994

178.76

203.176

382.818

-1856.566

-1075.861

179.35

221.082

394.381

-1853.393

-1023.926

1700

179.9

239.045

405.277

-1850.203

-972.188

1800

180.44

257.062

415.581

-1847.005

-920.632

CKF

CJ mol-1 K-1F

298.15

129.36

0

118.055

300

129.88

0.24

118.857

302.9*

130.69

0.65

120.11

302.9*

130.69

0.65

120.11

400

150.5

14.392

500

160.23

600

1500 1600

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1400

CkJ mol-1F

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STD

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oD

D nD − n^ef.gh

T

* Melting point of Ga [14]; ** Melting point of Mg [14]; *** Boiling point of Mg [14]

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Figure captions Fig. 1 Schematic of the experimental apparatus for emf measurement.

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Fig. 2 Variation of heat capacity of MgGa2O4 with temperature obtained in this study. Data of Wilkerson et al. [7] and Kondrat’eva et al. [8] are shown for comparison.

Fig. 3 Deviation of ∆STD CMgGa2O4F from Neumann-Kopp rule as a function of temperature. Fig. 4 Variation of reversible emf of solid-state electrochemical cell with temperature.

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Fig. 5 Electrolytic domain boundary for yttria-stabilized zirconia [20-24] in comparison with oxygen potentials prevailing at the electrodes in this study.

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Fig. 6 Isothermal section of phase diagram of Mg-Ga-O system at 1200 K, where the boundaries of three-phase regions are shown by solid lines and tie-lines in the two-phase region are displayed by dash lines.

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Fig. 7 Oxygen potential-composition diagram for the system Ga-Mg-O at 1200 K.

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Highlights • First measurement of Gibbs energy of formation of MgGa2O4 over a temperature range. • Residual entropy of cubic MgGa2O4 is estimated as 7.225(±1.5) J mol-1K-1. • Computation of isothermal section of phase diagram of the system Mg-Ga-O. • Computation of oxygen potential-composition diagram of the system Mg-Ga-O. • MgGa2O4 has potential as transparent semiconducting oxide and microwave dielectric.

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