The solid state phase transformation of potassium sulfate
aa r X i v : . [ c ond - m a t . m t r l - s c i ] J a n The solid state phase transformation ofpotassium sulfate
S. Bin Anooz a , R. Bertram b and D. Klimm b , ∗ a Physics Department, Faculty of Science, Hadhramout University of Science &Technology, Mukalla 50511, Republic of Yemen b Institute for Crystal Growth, Max-Born-Str. 2, 12489 Berlin, Germany
Abstract
Potassium sulfate single crystals that are grown from aqueous solutions lose uponthe first heating up to 1% of mass that is assumed to be water. This mass lossoccurs in the vicinity of the PT from orthorhombic to hexagonal K SO . Only inthe first heating run of K SO that has not yet released water, pretransitional ther-mal effects can be observed in the DTA curve. If K SO crystals are grown fromsolutions containing 4 wt.% Cd, Cu, or Fe, only Cu or Fe can be incorporated signif-icantly with concentrations of several 0.1%. The phase transformation temperaturemeasured for such solid solutions depends on the heating rate. For pure K SO , thephase transformation temperature is independent on heating rate 581 . ◦ C and theenthalpy of transformation is (5 . ± .
2) kJ/mol.
Key words:
A. dielectrics, B. crystal growth, D. phase transitions
PACS:
Potassium sulfate K SO belongs at room temperature T = 25 ◦ C to the or-thorhombic system and has four formula units per D h = P nma (olivinetype) unit cell, with lattice parameters a = 7 .
476 ˚A, b = 10 .
071 ˚A, and c = 5 .
763 ˚A [1]. The substance transforms upon heating at T t ≈ ◦ C intoa hexagonal structure D h = P /mmc with a = 5 .
92 ˚A and c = 8 .
182 ˚A(measured at 640 ◦ C) where the oxygen positions of the SO − tetrahedra are ∗ corresponding author Email addresses: s [email protected] (S. Bin Anooz), [email protected] (R. Bertram), [email protected] (D. Klimm).
Preprint submitted to Solid State Commun. 6 December 2006 nly partially occupied [2]. In the following, the hexagonal high T phase willbe called α -K SO and the orthorhombic phase will be called β -K SO . Un-fortunately, the opposite denomination is sometimes used in the literature [2].An analogous phase transformation (PT) to a α -K SO type phase at high T is shown by other K SO -family crystals (e.g. Na SO , LiKSO , K CrO , andK SeO ), in spite of structural differences at lower T [3,4]. Another PT of sec-ond order at 56 K was derived from the temperature dependence of the latticeparameters. The crystal symmetry of this low-temperature phase ( γ -K SO )is assumed to be monoclinic [5].Other authors observed the α − β transformation of K SO at 592 ◦ C or 612 ◦ C,respectively [6,7], but these investigations were performed with mixtures in-stead of pure K SO . Electrical conductivity measurements on single crystalshave been carried out by Choi et al. [8], the transition temperature rangeextends to 3 K and transition occurs at 586 . ◦ C on heating and 581 . ◦ C oncooling, with a thermal hysteresis of 5.4 K. Chen et al. performed electricalcomplex impedance measurements on K SO single crystals [9]. The T depen-dence of electrical conductivity and dielectric constant revealed an anomalyaround 587 ◦ C which was attributed to the transformation to α -K SO . Tem-perature dependence of Raman spectra of K SO was measured from 27 to900 ◦ C [10]. A remarkable change of the Raman frequencies is not observedthrough the phase transition temperature T t .Choi et al. [8] observed for a heating rate of 1 K/min that most of the samplescrack near 500 ± ◦ C showing an abrupt drop in electrical conductivity. Inthe heating process, elastic distortions, caused by the rotational disorder ofsulfate ions, may be produced inside the crystal. Hence it is suggested that theoccurrence of cracks around 500 ◦ C is further minor evidence for the existenceof a pretransitional region in advance of the structural transition. Diosa et al.[11] reported recently a deviation from the Arrhenius behavior of the complexdielectric permittivity of polycristalline K SO in the temperature range 538 − ◦ C, which is attributed to the onset of disordering of SO − tetrahedra anda ‘pretransition’ phenomenon as discussed by Choi et al. [8]. Diosa et al. [11]did not comment on the remarkable difference between the dc-conductivity vs. T curve obtained during heating of fresh material in comparison to subsequentheating/cooling runs (Fig. 1 of their paper).The theoretical entropy change calculated from Boltzman’s relation gives ∆ S t = 5 .
77 J/(mol K), provided that the configuration of the SO − tetra-hedron in α -K SO has two orientational possibilities. The observed entropychange, ∆ S t = 5 .
02 J/(mol K), agrees well with the calculation and the crys-tal structure of α -K SO appears reasonable in respect of the entropy change[12].In literature one can observe differences in the reported data about high T SO crystal. Therefore we report here more detailedmeasurements of the PT using thermogravimetry (TG) and differential ther-mal analysis (DTA) techniques. Special emphasis is placed on the influenceof water traces in the crystals grown from aqueous solution on pretransitionphenomena. The investigation of doping effects with Cu , Fe , or Cd insmall concentrations on the measured phase transition is another target ofthis article. Transparent and colorless crystals with well-defined edges (length up to 15 mm)were obtained by the slow evaporation method of saturated aqueous K SO solution. K SO doped with Cu , Fe , or Cd was grown by the samemethod from solutions containing 4 wt% of the corresponding transition metalsulfate. Potassium sulfate usually crystallized in prismatic crystals, the ~b -axiswas found along the long axis of the prism and the ~c -axis was along one edgeof the quasi-triangular basal plane.ICP-OES measurements compare the intensity of spectral lines obtained fromthe sample with the intensity of lines from calibrated standards. After care-ful calibration, main components as well as trace impurities down to 1 ppmcan be measured quantitatively with high precision. For the present study, an“IRIS Intrepid HR Duo” (Thermo Elemental, USA) was used. The precisionis ≈
3% relative standard deviation (R.S.D.) for concentrations above back-ground equivalent concentration (BEC). For the undoped K SO crystals onlyimpurities on the ppm level could be found. The doped crystals contained thefollowing concentrations of the dopant (in weight-%): Cu : = 0.192%, Fe = 0.076%, Cd = 0.014%.X-ray measurement were performed with a single crystal powder diffractome-ter (Seifert URD6) using Cu K α radiation. The K β line was suppressed with athin Ni filter, whereas the Cu K α –K α double peak structure was deconvo-luted by using the Rachinger correction [13]. The measurements were swappedfrom 10 ◦ ≤ θ ≤ ◦ with a step width of ∆ θ = 0 . ◦ and a scanning speedof about 0 . ◦ /sec.Thermal analysis was performed with a NETZSCH STA 449C “Jupiter”.A DTA sample carrier with each 2 series connected Pt90Rh10/Pt thermo-couples for sample ( ≈
10 mg) and reference was used with Al O cruciblesthat were covered by a lid. All measurements were performed in flowingargon (99.999% purity, 30 ml/min). No calibration files were used for themeasurements, as separate calibration measurements under identical condi-tions were performed with melting zinc ( T f = 419 . ◦ C, ∆ H f = 7322 J/mol)3nd with the first solid PT of barium carbonate BaCO ( T t = 805 . ◦ C, ∆ H t = 18828 J/mol). These calibration values were taken from the Fact-Sage 5.3. database [14] were for the α − β transformation of K SO one canfind T t = 582 . ◦ C, ∆ H t = 8954 J/mol. For the measurements heating/coolingrates from ±
20 K/min down to ± T during a DTA measurement is determined near the refer-ence and the DTA signal is the difference between the sample temperature and T , hence an exothermal effect in the sample leads to a positive DTA signal.If a sudden heat pulse is produced in the sample the signal DTA( t ) ( t – time)rises quickly to a maximum (peak, time t ) and drops then exponentiallyDTA( t ) = k exp − ( t − t ) τ ! + k (1)where the constants k and k describe the peak height and the position ofthe basis line and the time constant τ describes the thermal relaxation rate ofthe signal [15]. It turned out, that the PT of the calibration substance BaCO showed strong supercooling (up to 50 K) if T was lowered during DTA runs,resulting in a sharp peak rise near T ≈ ◦ C. The dropping wing of the peakcould very good be fitted to an exponential function (1) giving τ = 49 s for thetime constant of the DTA set-up that will be used in the following discussion. The grown crystal of K SO was crushed and subjected to powder X-raydiffraction analysis. A powder X-ray diffraction pattern of undoped potassiumsulfate is shown in the top panel of Fig. 1. The diffraction peaks match verywell the reported values of the peaks for K SO crystal in the literature [1].The data were treated by XPowder computer software [16] and the calculatedlattice parameters are in good agreement with the reported values for undopedcrystal (Tab. 1). Table 1Comparison of measured cell parameters with literature data [1]. ( V – unit cellvolume) a [˚A] b [˚A] c [˚A] V [˚A ]this work 7.489 10.073 5.763 434.7PDF 01-070-1488 7.476 10.071 5.763 433.9 All K SO samples showed in the first heating run a mass loss in the orderof 0 . − .
9% that occurs together with the PT. It must be assumed that4 ig. 1. Top: X-ray diffraction spectrum of K SO crystal. Middle: Peak positionsand relative intensity of the spectrum. Bottom: PDF No. 01-070-1488 ( β -K SO )[1] traces of water are incorporated in the (formally anhydrous) crystal structureand that the structural changes upon the PT lead to the emanation. As thisprocess is connected with heat exchange, the DTA peak related with the PTis superimposed by this heat (solid DTA curve in Fig. 2). In the second and allsubsequent heating runs (dashed lines) no mass loss occurs and the PT peakoccurs without superimposed secondary effects. Only the first DTA heatingcurve, before the irreversible mass loss, showed a remarkable exothermal bentstarting near 400 ◦ C that is completely absent for all further DTA runs. Itshould be mentioned that Miyake [12] observed for
T > ◦ C precursorphenomena for K SO crystals being also crystallized from aqueous solutionthat might be related to traces of the solvent too.Arnold et al. [2] attributed precursor phenomena of the K SO PT to OH +3 ions that are incorporated in crystals grown at room temperature from aque-ous solution. In the T region from 300 to 500 ◦ C (573 to 773 K) these ionsbecome mobile and decay finally at the PT under emanation of water. Singlecrystals are usually destroyed by this process. Chen and Chen [17] reportedthat crystals of K SO burst into pieces as they were heated to 500 ◦ C andthey attributed this phenomena to the OH +3 ions which reported by Arnold et5 ig. 2. First and second DTA heating run of an undoped K SO crystal with10 K/min al [2]. It is well known that pure potassium hydrogen sulfate were 50% of theK + ions are replaced by H + , melts at ≈ ◦ C and decomposes upon furtherheating 2 KHSO − H O −→ K S O − SO −→ K SO (2)under mass loss to potassium sulfate [18]. The theoretical mass loss that canbe calculated for the first step of equation (2) is 6.6%. The mass loss that istypically observed upon the first heating of undoped K SO ( ≈ . of this value — thus indicating that a considerable amountof K + ions is substituted by H + (or OH +3 , respectively) in the K SO crystalgrown from aqueous solution. It should be remarked, however, that the presentmeasurements do not allow the determination, how water is contained in thecrystal: As OH +3 [2,17] or simply as molecule in K SO · x H O whith x ≈ . SO · n H O ( n – integer) is not knownunder the current conditions.Data for the PT of pure K SO and for K SO :Fe , K SO :Cu , K SO :Cd were determined by a DTA measurement with multiple heating/cooling cycleswith rates of ± ± ± ± ±
2, and ± were performed and analyzed identically. Depending onheating rate, the T error for the melting of Zn ranged from − . − . − µ Vs/J. For BaCO the T errorwas − . . . . + 1 K and the sensitivity was 358 − µ Vs/J.Typical original DTA heating and cooling curves around the PT peak areshown for K SO and for K SO :Fe in Fig. 3. T t can be obtained fromthe intersection of the extended basis line with the tangent at the inclinationpoint (extrapolated onset). It is remarkable that for pure K SO T t as obtainedfrom the heating or cooling run, respectively, does not differ considerably. Incontrast, the onset of the peak is lower in the heating curve and higher in6he cooling curve for K SO :Fe . This phenomenon will be discussed later inFig. 5. Fig. 3. DTA heating and cooling curves( ±
10 K/min) for pure K SO (full lines) andfor K SO :Fe (dashed lines)Fig. 4. Top: Uncorrected and corrected phase transformation temperature of pureK SO from this work as compared to the FactSage 5.3 database value [14]. Bottom:Enthalpy of the phase transformation ∆ H t = 5 . Fig. 4 shows that the uncorrected extrapolated onsets of the PT peak for allheating rates (squares) are nearly independent on the heating rate at 579 . ◦ C.The corrected values (circles) are obtained by adding the errors that were ob-tained from the interpolated Zn and BaCO calibration measurements and canbe extrapolated (for zero heating rate) to the PT temperature T t = 581 . ◦ C ofpure K SO . This value is by 1.5 K lower as literature data [14]. From the peakareas of the PT peaks one obtains with the sensitivity values (interpolatedbetween Zn and BaCO ) the enthalpy of the PT ∆ H t = (5 . ± .
2) kJ/mol.This value is smaller as the database value 8.954 kJ/mol [14] but larger than7easured by Miyake et al. [12] who obtained 4.28 kJ/mol. heating rate (K/min) T t ( ° C ) undopedCdCuFe Fig. 5. Uncorrected extrapolated onsets of the PT peak during heating (full symbols)and cooling runs (empty symbols) for all samples and heating/cooling rates from20 K/min down to 1 K/min
Fig. 5 collects extrapolated onsets that were obtained for all heating/coolingrates and for all samples. Uncorrected values had to be used for this compari-son, as a good correction could not be obtained for the cooling runs due to thesupercooling of the BaCO PT. Fortunately, this restriction does not influencethe trends that are obvious from this figure, as any possible correction wouldinfluence every measurement data identically. It turns out that the values forK SO and for K SO :Cd do not differ much, irrespective of the absoluterate. In contrast, for K SO :Cu and for K SO :Fe the onset temperaturesare found to depend on the heating/cooling rate if the rate exceeds 3 K/min.Actually it must be assumed that a rate dependence for lower rates is notobserved for heating/cooling rates below ˙ T ≈ ∆ T /τ where τ = 49 s is thetime constant of the DTA set-up and ∆ T = lim ˙ T → ∆ T is the temperaturedifference to be detected. If we assume ∆ T = 1 . T ≈ . T ≤ SO (for ˙ T = 10 K/min shown in Fig. 3, forall rates shown by circles in Fig. 5). It is not unexpected that the K SO :Cd crystals (squares in Fig. 5) showed almost the same behavior, as the Cd con-centration was found to be very small (0.014 ma%) and cannot influence re-markably the PT. The PT peak for all heating and cooling curves of thesesamples behaves like it should be expected for a first order phase transforma-tion of a pure substance. Neither precursor phenomena (except the release ofwater in the first heating run as described above) nor kinetic effects can be8bserved for these samples.The behavior is different for the samples that were doped by Fe (0.076 ma%,triangles up in Fig. 5) or Cu (0.192 ma%, triangles down in Fig. 5), respec-tively, where a remarkable influence of ˙ T on T t can be observed. The PT peakstarts at lower T upon heating and starts at higher T upon cooling. Thistemperature shift increases with the rate of temperature change and reachesalmost 10 K for K SO :Fe and 20 K/min. Such behavior is the opposite ofa normal hyteresis where one should expect just a delay of PT resulting in ahigher T t upon heating and a lower T t upon cooling. aba+b K SO T t dopant xx' Fig. 6. Thermodynamic model for the explanation of the rate dependence of T t Instead, Fig. 6 could possibly give an explanation of the observed phenomenaon a thermodynamic basis: As the PT between the α and β phases of K SO is a first order phase transformation, solid solutions cannot transform at onetemperature. Instead, a 2-phase region must separate the two 1-phase regions α -K SO and β -K SO ; in analogy to the lens-shaped liquid/solid region thatis typically for the melting of solid solutions. For high heating/cooling rates thephase boundaries limiting the 2-phase region are crossed close to the averagecomposition x of the solid solution. If the rate of T change is sufficientlyslow, segregation can take place if T approaches the phase boundary, leadingto a solid solution with lower concentration of the solute x ′ and some minoramounts of the pure solvent, or of some other intermediate phase, respectively.If the composition of the K SO solid solution is “wandering” along the phaseboundaries, T t approaches the equilibrium value of pure K SO . If this modelis true, the extrapolated onsets should for very high ˙ T converge to that T werethe limits of the 2-phase region intersects x . Unfortunately, such saturationcould not be observed under the current experimental conditions. The DTA results presented in this study confirm, that the PT between β - and α -K SO is of first order. Pretransition effects below T t could be attributedto water that is included in the crystals grown from aqueous solution. Hence,previous reports on such effects [8,11,12] should be handled with care as itis not completely clear whether the observed effects are really intrinsic in the9otassium sulfate (mobility of K + or SO − , respectively) or due to the mobilityof extrinsic species like OH +3 .The kinetic properties of the α ↔ β transformation that were observed forK SO :Cu and K SO :Fe cannot be explained by a simple kinetic modelbased on thermally activated processes, as such processes should shift the PTpeak for higher heating rate ˙ T to higher T , in contrast to the experimentalresults. Instead, a thermodynamic model is presented that can explain theobservations on the basis of an extented 2-phase region between the β -K SO and α -K SO SO based solid solutions. Acknowledgements
Awarding a scholarship from the “Germany Academic Exchange Service”(DAAD) for this work is gratefully acknowledged. The authors want to expresstheir gratitude to M. Schmidbauer (IKZ Berlin) for X-ray characterization.
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