Thermodynamic Study of the Vaporization ofCerium OrthophosphateBY M. GUIDO, G. BALDUCCI,* G. DE MARIA AND G. GIGLIIstituto di Chimica Fisica, Universith di Roma,CittA Universitaria-00185 Rome, ItalyReceived 27th November, 1975The high temperature Knudsen cell mass spectrometric technique has been used to study theFrom the second- and third-law analyses of the equilibrium reaction : CeP04(s) = CeOz(g) + vaporization behaviour of solid cerium orthophosphate over the temperature range 1700-1 850 K.PO,(g), the following standard heat of formation of &PO&) has been derived :AHZg8,f [CeP04(s)] = - 1898.5k31.5 kJ mol-l.These results are discussed and compared with those obtained by other authors for other LnP04compounds.Rare earth orthophosphates form an interesting class of compounds for whichevaluations of thermodynamic data of value, e.g., in determining the best conditionsin chemical transport processes,'.have been very limited ; few such data areavailable in standard compilations. Rat'kovskii et aZ.3-5 carried out mass spectro-metric studies of the thermal dissociation of LaPO, and other orthophosphates ofthe yttrium group adopting the same decomposition scheme as that for AlP04,5 forall the compounds studied. Other thermodynamic data available refer to themeasurements of the enthalpies and heat capacities of solid lanthanum, neodymiumand yttrium orthophosphates, as reported by Tsagareishvili et aL6 However, nosuch data are available for CePO, ; vaporization behaviour under equilibriumconditions is reported in this paper.EXPERIMENTALThe vaporization mode of cerium orthophosphate was investigated by the Knudseneffusion mass-spectrometric technique.A Nuclyde Analysis Associated magnetic massspectrometer coupled with a conventional Knudsen cell source was used. Details of theexperimental apparatus and procedure are as described previ~usly.~ *Preliminary vaporization experiments carried out using different Knudsen cells to selectthe crucible material showed that noticeable interaction of the sample with the containeroccurred when using tantalum, tungsten and molybdenum metal crucibles, while reproducibleevaporation conditions were achieved when using an alumina-lined tungsten crucible whichwas subsequently used throughout this work.The Knudsen effusion orifice was 1 mm indiameter and 1.2 mm in length.A sample of powdered anhydrous CeP04 (99.9 % pure from Schilling BHS), checked byX-ray analysis was loaded into the cell together with 2mg of high purity silver metal ascalibrating substance. The cell was heated by radiation and electron bombardment froma tungsten strip. The electron bombardment power regulating system limited temperaturefluctuations to < & 5°C at 1700°C. Temperatures were measured w i t h a k d s andNorthrupoptical pyrometer, periodically checked against a tungsten ribbon standard lamp calibratedby N.B.S. by sighting into a blackbody hole drilled in the bottom of the cell. Temperature12122 VAPORIZATION OFreadings were corrected for window and prism transmission. At an average temperatureof 1300 K, where no detectable vaporization of the sample occurred, the silver was quanti-tatively vaporized in order to obtain the instrument calibration constant.The temperaturewas then raised gradually and the vaporization of the sample was followed for a period ofabout 15 h over the temperature range 1700-1 850 K. The vaporization was then interruptedby rapidly lowering the cell temperature and a portion of the residue sample was checkedby X-ray analysis. Subsequently, the remaining sample was submitted to a second seriesof vaporization measurements for an overall period of about 50 h using the same crucible,and with the same procedure. The residue was again examined by X-ray diffraction (seethe following section).RESULTSIDENTIFICATION OF IONSIn the course of the vaporization experiments, ions at mfq corresponding to P408+,P40T, P406+, P 3 0 t , P30:, P:, PO,’, P;, PO+, P+, O,*, as well as the cerium con-taining species CeO,’, CeOf, and Ce+ were observed in the mass spectra.Of these ions, only CeO;, CeO+, Ce+, PO,’ and PO+, with a shutter profilesimilar to that of Ag+, and also 0,’ with a shutter profile less than 100 %, but narrowand symmetrical, were considered as originating from species effusing from theKnudsen cell.In any case, the intensity of the discarded ions was low enough notto affect the results. The appearance potentials (A.P.) for CeO:, PO:, PO+ and0; were measured to be 9.8 _+ 0.5, 11.7 _+ 0.5, 9.1 _+ 0.5 and 12.1 0.5 eV, respectively,in accord with published values ;9-11 these ions were identified as parent ions.Onlywith PO+ ion did the ionization efficiency curve exhibit a break which indicated thatthe primary ionization was not the only process responsible for the formation ofthis ion. The energy of the observed secondary onset (13.920.5 eV) is consistentwith the dissociative ionization of PO2. Given that &PO;) is the portion of the ionintensity measured at mass 47 due to the fragmentation of PO2, the ratio I(PO&)/I(P0;) in the actual experimental conditions was evaluated to be 0.625 at 98 eV,and the ion intensities measured for PO+ and PO: ions were corrected accordingly.The ions CeO+ and Ce+, [with A.P. of about 13 eV and 20 eV respectively, and forwhich the intensity ratios Z(CeO+)/I(CeO,’) and I(Ce+)/Z(CeO,’) were temperatureindependent and equal to 0.25 and 0.131 were identified as fragment ions from CeO,.The measured CeO; ion intensity was corrected accordingly.X-RAY RESULTSDebye-Scherrer X-ray diffraction patterns of the initial samples and the residuestaken at different stages of the vaporization were made by two different laboratories.In all cases the patterns presented no lines other than those corresponding to themonoclinic structure of the monazite type CeP04.12 The only detectable differencebetween the patterns taken on the initial samples and on the thermally treated residueswas an increased crystallinity shown by sharper diffraction lines.THERMODYNAMICSThe ion intensities of the parent species measured at 98 eV and corrected, whennecessary, for the fragmentation contributions, were converted into the correspondingpartial pressures by use of the well-known relation :8 Pi = Ii+T/Scya,.The instru-mental sensitivity constant, S, was determined, as previously mentioned, through asilver calibration experiment and subsequently through an internal calibrationprocedure * based on the study of the equilibrium reaction (1) as described later inthe text. The electron multiplier efficiency, 7, was assumed for each ion to bM. GUIDO, G . BALDUCCI, G. DE MARIA AND G. GIGLI 123proportional to the inverse of the square root of its mass. The ionizing electronenergies used corresponded in all cases to the maximum of the ionization efficiencycurves of the relative ions; thus the molecular ionization cross sections, cr, werederived from the maximum values of the atomic cross sections given by Mann l3according to a procedure outlined e1~ewhere.l~ The resulting values are : 15.26,7.09, 6.74 and 3.13 for CeO,, PO2, PO and 02, respectively.Values of the partialpressures calculated at various temperatures over the range 1600-1 850 K indicatedfair reproducibility in the case of POz and CeOz as well as for the equilibrium constantof the dissociation reactionbut the partial pressures of PO(g) and 02(g) varied somewhat erratically, dependingon the vaporization conditions.To ascertain that satisfactory equilibrium conditions were attained at least in thegaseous phase, reaction (1) has been studied, especially in the initial part of theexperiment.No direct heat of reaction (1) has been reported previously. However,a value of = 254f 12 k J mol-1 for this reaction is derived by combiningliterature data for AH;,at[PO,(g)] l5 and for D;98(02) l6 and D;98(PO).16 Ourdata have been evaluated by two independent procedures, the so called ‘‘ second-law ”method based on the well known equationand the so called “ third-law ” method, or absolute entropy method, based on theequation :The necessary heat-content functions, (H; - Hig8), and free energy functions,(G$-H,”g8)/T, for PO(g) and O,(g) were taken as reported JANAF Tables,16 andfor PO,(g) the values reported by JANAF Tables l6 were corrected for the vibrationalcontribution as proposed by Drowart et aZ.15The least-square equation representing the temperature dependence of Kp forreaction (1) is :PO,(g) = PO(g) + +02(g) (1)AH298 = -R d In Kp/d(l/n+x(H;- H2098)reactants-~(H~-H2098)~roductsAH2098 = -RT Kp f Tx(Gg -.Hi9 S)/Treactants - Tx(G$ - &9 8)/Tproduets*log Kp(l), atm = (4.165&0.66)-(1.275&0.115) 104/T (2)TABLE 1 ,-THIRD-LAW CALCULATIONS FOR EQUILIBRIUM REACTION (I) :POz(g) = PO(g)++Oz(g)T/K -logm(Kp/atm*) AHi9,/kJ mol-11767 3.01 233.51850 2.76 235.61805 2.87 233.71715 3.205 233.11770 3.06 235.61817 2.895 236.11802 2.815 23 1.41752 3.155 236.41715 3.33 237.21757 3.045 233.41787 3 .OO 235.81757 3.075 234.41730 3.24 236.3average 234.8+ 1.7Note : The quantity A(G~!-HJ,,)/T for reaction (1) is practically constant over the temperaturerange and equal to -74.538 (J K-l mol-I)124 VAPORIZATION OF &Po4where the quoted errors are the standard deviations on the slope and intercept.Thesecond-law heat of reaction (1) is derived to be = 243.1 k22.2 k J mol-f.The individual third-law AHZ98 values corresponding to the experimental points arereported in table 1. These values do not exhibit any temperature trend and theaverage value, AH& = 234.8 & 1.7 k J mol-l, agrees with the second-law resultwithin the reported uncertainties. This was taken as an indication of the internalconsistency of our data. Moreover, the average value between our second- andthird-law results compares well with the aforementioned heat of reaction (1) derivedfrom literature data, so indicating that equilibrium conditions were actually establishedin the vapour phase.Therefore, the value AH2098 = 244f 10 kJ mol-', the averagebetween our value and the literature value, has been selected as the heat of reaction(1) and then used to establish an internal calibration of the instrument. Also, itenabled us to derive the standard heat of formation of PO,(g): AH&8[Po2(g)] =-253.1 & 12.1 kJ mol-l.The temperature dependences of PO,(g) and CeOz(g) partial pressures arerepresented by the least-squares equations :(3)(4)log P(P02), atm = (8.855 k0.25) - (2.6985 0.0435) 104/Tlog P(CeO,), atm = (8.865 kO.47) - (2.841 k0.084) 104/Twhere the associated errors are standard deviations.As long as solid CeP0, at unit activity is present in the Knudsen cell, the reaction(5) CeP04(s) = Ce02(g) + P02(g)can be utilized to derive the standard heat of formatioil of cerium orthophosphate.It is known that natural monazite (orthophosphate of cerium with other lanthaniderare earth elements as constituents) has a stable monoclinic structure.SyntheticCePO, has been found to be dimorphic, with an hexagonal form which transformsat about 500°C into the monazite monoclinic form stable at high temperature.17The transformation is reported to be monotropic and sluggish. As in our experi-ments we found that the initial CePO, samples and the vaporization residues werein the monoclinic form, we assumed that the gas phase we studied was the decom-position product of the monazite type CeP04.With this in mind we derived theheat of reaction (5) by both the aforementioned second-law and third-law procedures.The necessary thermodynamic functions for CePO,(s) were calculated by estimatingthe heat capacity between 298 K and the temperatures of interest through an inter-polation of the experimental C, values reported for LaPO,(s) and NdPO,(s)according to the relation :[C,(Ce) - C,(La)l/l_C,(Nd) - C,Wl =[C,(CePO,) - C,(LaPO,)l/EC,(NdPo,) - Cp(LaP04)I,where the necessary heat capacities for the rare earth elements were taken fromHultgren.18 The standard entropy of CePO,(s) was evaluated to be S;98 =131.25 J K-1 mol-l following the procedure proposed by Tananaev et al. by assumingthat Sg98[CeP04(s)] = *Sg98[Ce,O3(s)] + +S&[P401O(s)].The entropies forCe,O,(s) and P~O~O(S) were taken from the literature.". * l *For CeO,(g), the thermodynamic functions were calculated using the recentresults of Gabelnick et aL2' for the apex angle (146") and for the symmetric andasymmetric frequencies o1 = 75.7 mm-1 and o3 = 73.7 mni-l, while an estimatedbending frequency o2 = 12.0mm-l was assumed, the same value as that used forTh02(g).23 The internuclear distance r(Ce-0) was estimated as 187 prn by com-parison with the ThO(g) and Tho&) molecules.23 By analogy with Tho&), thM. GUIDO, G. BALDUCCI, G . DE MARIA A N D G . GIGLI 125electronic contribution was assumed to be zero. The thermodynamic functions forCe02(g) and CePO,(s) calculated with the above assumptions, are reported in table 3.TABLE 2.-THIRD-LAW CALCULATIONS FOR REACTION (5) :CeP04(s) = CeOz(g)+ PO&)- T/K17171767185017701792181718021752(logio(Kp/atmz)14.5513.62512.18513.5613.1713.0614.0012.805-NGT - Hj: 9 ,)IT) AH;,,371.35 1115.93 70.345 1115.3368.65 1113.63 70.28 5 11 14.9369.845 11 14.8369.32 1116.5369.63 5 1116.6370.64 1118.91.6/J K-1 mol-1 jk J mol-1average 1 1 1 5.8298.15 00,OOO 278.140 000.000 131.2521600 75.228 324.155 1 92.1 71 244.1361700 77.990 326.917 209.849 251.5211800 83.759 329.557 227.8 82 258.6551900 89.533 332.088 246.291 265.5792000 95.3 12 334.5 19 265.056 272.316Third-law calculations for reaction (5) are summarized in table 2.The averagethird-law AH&8 = 1115.8f 1.6 kJ inol-l agrees with the second law AH2098 =1125.1 f 18.4 kJ mol-l resulting from combination of eqn (3) and (4). Therefore,the average value AH;98 = 1120.5 & 18.4 kJ mol-’ was selected as the best valuededucible from our data. The error term corresponds to an estimated standarddeviation equal to that associated with the second-law result. An average value of= 565&21 kJ mol-’ for the standard heat of vaporization of CeO,(s) toCeO,(g), selected from published data 9 p 24 was combined with the standard heat offormation,25 AH;98,f[Ce02(~)] = 1090.3 f 1.3 kJ mol-1 and other thermodynamicdata 26 for CeO,(s), to give a standard heat of formation of CeO,(g) : AH&8,r[CeO,(g)] = -525f21 kJ mol-l.By combining this value with the aforementionedAHz98,f[Po2(g)] and with the selected value for the heat of reaction (5), the followingstandard heat of formation is obtained for CeP04(s) : AH;98,f[CeP04(~)] = - 1898.5k31.5 kJ mol-l.DISCUSSIONThe establishment of equilibrium in the vapours effusing from the Knudsen cellhas been proved by the study of reaction (1). The reproducibility of the PO&) andCe02(g) partial pressures measured in different runs indicates that equilibrium ornear-equilibrium conditions were also reached between the solid phase and the vapourphase. In these conditions the observed non-reproducibility of the partial pressuresof PO(g) and O,(g) could be explained by admitting, e.g., that they originate from th126 VAPORIZATION OF cePo4thermal dissociation of PO, rather than from the evaporation from the sample, andthat a slow interaction occurs between the oxygen and the container.The measured partial pressures of Ce02(g) are reproducible, but somewhat lowerthan required for congruent vaporization.This suggests an enrichment of the samplein cerium and oxygen. A comparison of the CeO,(g) partial pressures here measuredwith those measured by previous authors ’ 9 24 over CeO,,(s) indicates the formationof a cerium oxide phase possibly of the CeO, composition which vaporizes at nearlyunit activity. The relatively small quantity of the sample vaporized from the initialmass may account for the failure to observe the formation of this compound byX-ray analysis.According to the experimental results obtained we are led to conclude that thevaporization of that CePO, crystal modification which is stable in the temperaturerange covered by the measurements could properly be described by the followingreactions : CeP04(s) = CeO,(g) + P02(g) ; [Ce02,J, = CeO,(g) ; and PO,(g) =PO(g)++O,(g), where x is zero or close to zero and a, the activity, is close to unity.Although a definite direct experimental proof that the solid CePO, phase is themonazite monoclinic phase cannot yet be given(no X-ray analyses at high temperatureshave been made) on the basis of the arguments given previously in the text, andconsidering the thermal history of the sample (at the end of each vaporization run thecell temperature was quickly lowered from 1850 K to room temperature), it seems thatfew doubts exist that the solid phase we studied was actually monoclinic.In anyevent, for the purpose of deriving the heat of formation of CePO,(s) through thereaction (9, the uncertainties in the thermodynamic functions should cover theuncertainties in the CeP0, crystal modification actually present at the temperaturesof the experiments and, therefore, the standard heat of formation we reported forthe monazite type CePO, should be reliable within the quoted error.Rat’kovskii et aZ.3-5 have studied the vaporization behaviour of LaPO, and ofother orthophosphates of the lanthanide elements (excluding cerium) using a similarapproach over a similar temperature range to that described here.From theirresults they concluded that rare earth orthophosphates decompose according to thescheme : 2 LnP04(s) = Ln203(s)+2P02(g)+$0,(g). However it seems to us thatthis scheme is not sufficiently supported by the experimental facts. The only partialpressure measured was that of PO,@. The absence of PO(g) from the vapour and,consequently, the ratio of the partial pressure of PO(g) to that of 02(g) as it appearsin the proposed reaction scheme was inferred from having attributed the recordedPO+ ion intensity entirely as due to the fragmentation of P02(g). However theirreported I(PO~)/I(PO~) intensity ratio (about 5 ) is very high compared with thevalue we found, and corresponds to a ratio of the fragmentation cross section to theprimary ionization cross section which is itself unusually high compared with thevalues found in the mass spectrometry of high temperatures molecules with high bondstrength such as that of the P-0 bond in PO2.On the other hand, the A.P. theyfound for the PO+ ion (12.1 k0.5 eV) is somewhat higher than the value we found(9.1 eV) and the value reported by Drowart et aZ.15 (9.5 eV), but rather too low toaccount for the dissociative ionization of PO,(g) to PO+ (the rupture of a OP-0bond requires about 5eV). Therefore, the composition of the gaseous product ofthe decomposition reaction of the lanthanide orthophosphates as reported byRat’kovskii et aZ.3-5 seems questionable. The presence of the Ln203 solid phase asdecomposition product, particularly at unit activity, appears reasonable as a workinghypothesis in default of any experimental information. Were this hypothesis correctin the case of the LnP0, compounds studied by the above authors, we would concludethat the decomposition reaction for GPO, differs from that of the other lanthanidM.GUIDO, G . BALDUCCI, G. DE MARIA AND G. GIGLI 127orthophosphates studied ; this difference could be attributed to the availability of ahigher oxidation state for cerium.The authors are indebted to Dr. G. De Angelis and Dr. P. L. Cignini for theThis work has been supported by the Consiglio Nazionale delle Ricerche throughX-ray analyses.the Centro di Studio per la Termodinamica Chimica alle Alte Temperature.H. Schaefer, V. P. Orlovskii and M. Wiemeyer, 2. anorg. Chem., 1972,390,13.V. P.Orlovskii, Kh. Kurbakov, B. S. Khalikov, V. I. Bugakov and I. V. Tananaev, Izvest.Akad. Nauk S.S.S.R., Neorg. 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