J. Chem. Thermodynamics 62 (2013) 35–42

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J. Chem. Therm odyna mics

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Low temperature heat capacity study of FePO 4 and Fe3(P2O7)2

Quan Shi a, Liying Zhang b, Mark E. Schlesinger b, Juliana Boerio-Goates a, Brian F. Woodfield a,⇑a Department of Chemistry and Biochemistry, Brigham Young University, Provo, UT 84602, United States b Department of Materials Science and Engineering, Missouri University of Science and Technology, Rolla, MO 65409, United States

a r t i c l e i n f o

Article history:Received 8 February 2013 Accepted 24 February 2013 Available online 4 March 2013

Keywords:FePO4

Fe3(P2O7)2

Iron phosphates Heat capacity PPMS

0021-9614/$ - see front matter � 2013 Elsevier Ltd. Ahttp://dx.doi.org/10.1016/j.jct.2013.02.017

⇑ Corresponding author. Tel.: +1 801 422 2093; faxE-mail address: Brian_Woodfield@byu.edu (B.F. W

a b s t r a c t

The heat capacities of FePO 4 and Fe3(P2O7)2 have been measured using a Quantum Design Physical Prop- erty Measurement System (PPMS) over the temperature range from (2 to 300) K. The phase transit ion due to the Fe3+ magnetic ordering in FePO 4 has been determined to occur at T = 25.0 K, which agrees well with magnetic measurements reported in the literature. For Fe3(P2O7)2, a Schott ky anomaly and a four-peak phase transition have been found below 50 K. The thermodynamic functions, magnetic heat capacities,and magnetic entropies of these two compounds have been calculated based on curve fitting of the exper- imental heat capacity values. The standard molar entropy at T = 298.15 K has been obtained to be(122.21 ± 1.34) J � K�1 �mol�1 and (384.12 ± 4.23) J � K�1 �mol�1 for FePO 4 and Fe3(P2O7)2, respectively.

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1. Introduction

Iron phosphates have attracted considerable interest of soil sci- entists as well as material investigators due to their remarkable chemical, thermal, electrical and magnetic properties [1–5]. FePO 4is one of the most technologic ally popular iron phosphates used invarious fields such as catalysts [6,7], industrial coatings [8], tissue engineering [9], biosenso r fabrication [10], bio-abso rbable glass fi-bers [11], electrochemi stry [12–15], magnetic and optical materi- als [16–20]. Moreove r, exhibiting a theoretical capacity of143 mA � h � g�1 and an average discharge voltage of 2.7 V, FePO 4has been recently proposed as the next generation of positive- elec- trode material for lithium batteries due to its lower cost, safety,stability, low toxicity, and benign environmental properties inpractical applications [21,22].

Iron phosphat es have magnetic propertie s due to the unpaired 3d-electron s in the Fe3+ or Fe2+ ions. Brukner et al. performedMössbauer measureme nts on FePO 4 and found antiferromagneti cordering below T = 25 K [23], and later the magnetic susceptibility study by Beckmann et al. indicated an antiferromagneti c to para- magnetic transition appearing at a temperature near 25 K [24].More recently, magnetic susceptibility and ESR measurements byThomas et al. revealed that FePO 4 had an anisotropic antiferro mag- net transition with a Neel temperature of 21 K [25].

Heat capacity is an important thermodyna mic property of amaterial since it provides important information related to the compound structure, especiall y for these iron phosphat es with magnetic transitions at low temperature s. However, there are still

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no heat capacity data available for FePO 4 except for measurements from 1961 for FePO 4 � 2H2O where the magnetic transition was determined to be at or below 7.5 K [26].

Fe3(P2O7)2 is a mixed-valen ce iron diphosphate which is well known for its application in oxidative dehydrogen ation [27]. The unit cell of this compound contains four [Fe 3O12]16� clusters,where an [Fe 2+O6] trigonal prism shares opposite faces with two [Fe3+O6] octahedra, and these clusters are connected by bent P2O7 groups [28,29]. Ijjaali et al. studied the magnetic property ofFe3(P2O7)2 and showed it was antiferroma gnetic with a Neel tem- perature near 18 K, while the magnetic coupling s are probably fer- romagneti c inside the Fe3O12 clusters with an antiferroma gnetic arrangem ent between the clusters [28]. However , the heat capacity of Fe3(P2O7)2 has not been studied until now.

In the present study, we have measure d heat capacities of FePO 4and Fe3(P2O7)2 over the temperature range from (2 to 300) K using a PPMS calorimeter which employs a new technique of powdered sample heat capacity measureme nt developed recently in our lab- oratory [30,31]. The experimental heat capacity results have been fitted to a series of theoretical and polynomial functions, and the correspondi ng thermod ynamic functions have been calculated based on the fitted data. Addition ally, the thermodyna mic property in the transition region has been explored from the magnetic heat capacity, which has been calculated by subtracting the lattice con- tribution from the total heat capacity.

2. Experimen tal

The iron phosphat e samples were prepared from commercially available materials as follows where purity is as mass fraction:FePO4�xH2O (Alfa Aesar, 1.00), Fe2O3 (Alfa Aesar, 645 lm, P

FIGURE 1. Plot of the experimental, fitted and lattice heat capacities of FePO 4 as afunction of temperature over the temperature range from (2 to 300) K. The inset shows the data in the transition region.

36 Q. Shi et al. / J. Chem. Thermodynamics 62 (2013) 35–42

0.99), NH4H2PO4 (Alfa Aesar, 0.98), Fe3O4 (Fisher Chemical, P0.99)and Fe (Fisher Chemical , 0.99). The starting materials were mixed thoroughly and then heated in a sealed silica tube by controlling the atmosph ere, temperature and time of heating profile to obtain the different compounds. The phase purity of the products was confirmed by X-ray diffraction (Scintag XDS 2000). The experimen- tal details about sample preparation and characterizati on have been reported in our previous work [5]. The chemical purity ofthe samples was determined to be better than 0.99 on a metals ba- sis fraction using a Perkin–Elmer inductive ly coupled plasma opti- cal emission spectromete r (ICP-OES) Optima 4300 DV. The information for the samples used in this study is listed in table 1.

The heat capacity measure ments were performed using a Quan- tum Design PPMS in zero magnetic field with logarithmic spacing over the temperat ure range from (2 to 100) K, 10 K temperature intervals from (100 to 300) K and 0.1 K intervals in the tempera- ture region of a phase transition. The accuracy of heat capacity measureme nts on a high-purity copper pellet was found to bewithin ±0.6% from (20 to 300) K and ±2% below 22 K [30]. Heat capacities of powdered iron phosphates were measured using anew technique develope d in our recent work of powdered sample measureme nt with a PPMS calorimeter, which can achieve anaccuracy of ±1% and ±(2 to 5)% in the temperature range from (22 to 300) K and below 22 K, respectively , for both conducting and non-conductin g powdered samples [30]. The details of sample preparation and heat capacity experimental procedure can befound in our previous publications [30,31]. The sample mass used in the measurement is 14.82 mg for FePO 4 and 22.60 mg for Fe3(P2O7)2.

FIGURE 2. Plot of the experimental, fitted and lattice heat capacities of Fe3(P2O7)2

as a function of temperature over the temperature range from (2 to 300) K. The inset shows the data in the transition region.

3. Results

The experimental heat capacities measure d by the PPMS for FePO4 and Fe3(P2O7)2 samples are shown graphica lly in figures 1and 2, and listed in tables 2 and 3, respectively . It can be seen that the heat capacity of both compounds generally increases with tem- perature rising in the experimental range except in the magnetic phase transition region where a peak and a four-peak anomaly ap- pear in FePO 4 and Fe3(P2O7)2, respectively . The transition temper- ature for FePO 4 evaluated from the peak temperature in heat capacity curve in the transition region is 25.0 K, which agrees well with magnetic measure ments performed by Brukner et al. [23] andBeckmann et al. [24]. For Fe3(P2O7)2, the four-peak anomaly takes place within the temperature range from (18 to 28) K, which iscomparable to the report by Ijjaali et al. [28] that the transition isantiferroma gnetic with a Neel temperature near 18 K.

The experimental heat capacity values for these two com- pounds have been fitted to theoretical functions below T = 10 K, aseries of orthogonal polynomi al functions from (10 to 50) K [32],a combination of Debye and Einstein heat capacity functions above 50 K [33–35], and cubic spline polynomi als in the magnetic phase transition region [36]. The fitted data is shown in figures 1 and 2using solid lines for FePO 4 and Fe3(P2O7)2, respectivel y. The stan- dard thermod ynamic functions have been calculated at selected

TABLE 1Information of the samples used in this study.

Formula Source State Mass fraction purity

FePO 4�xH2O Alfa Aesar Powder 1.00 NH4H2PO4 Alfa Aesar Powder 0.98 Fe2O3 Fisher Powder 0.99 Fe3O4 Fisher Powder 0.99 Fe Fisher Powder 0.99 FePO 4 Synthesized in-house Powder >0.99 Fe3(P2O7)2 Synthesized in-house Powder >0.99

temperat ures from (0 to 300 K) based on the fitted heat capacity,and the results are listed in table 4 for FePO 4 and table 5 forFe3(P2O7)2. The standard molar entropies at T = 298.15 K have been determined to be (122.21 ± 1.34) J � K�1 �mol�1 and(384.12 ± 4.23) J � K�1 �mol�1 for FePO 4 and Fe3(P2O7)2,respectivel y.

4. Discussion

The heat capacity of a substance below about T = 10 K is gener- ally fit to theoretical functions, which may provide important informat ion about the lattice, electronic and magnetic propertie sof a material [37–39]. For FePO 4, due to the effect of the low tem- perature side of the magnetic transition, we could not fit the heat capacity data and obtain a meaningful fit until below 5 K. The the- oretical equation used has the form.

Cp;m ¼ cT þ B3T3 þ B5T5 þ BaswT3e�D=T ð1Þ

where the linear term represe nts the contribu tion from defects and oxyge n vacancies in the sample [40]; the odd-power s in tempera- ture are the harmonic lattice model for the lattice vibration

TABLE 2Molar heat capacit y at constant pressure for FePO 4 from T = (2 to 300) K. M = 150.8184 g �mol�1.a

T/K Cp,m/(J � K�1 �mol�1) T/K Cp,m/(J � K�1 �mol�1) T/K Cp,m/(J � K�1 �mol�1)

1.8860 0.040934 21.495 15.547 38.068 16.641 1.9970 0.047821 21.706 16.039 39.076 17.074 2.1807 0.061698 21.917 16.341 40.083 17.527 2.4757 0.091261 22.105 16.682 41.100 17.992 2.7361 0.12704 22.320 17.081 42.107 18.432 3.0283 0.18040 22.514 17.476 43.117 18.880 3.3600 0.26009 22.728 17.859 44.121 19.313 3.7522 0.38074 22.919 18.383 45.137 19.794 4.1870 0.54779 23.114 18.701 46.143 20.260 4.6592 0.76730 23.357 19.344 47.170 20.760 4.8449 0.86186 23.550 19.723 48.165 21.225 5.1803 1.0466 23.758 20.247 49.191 21.702 5.7699 1.3914 23.945 20.841 50.221 22.153 6.4139 1.8142 24.146 21.416 53.703 23.847 6.7975 2.0840 24.378 21.925 59.643 26.605 7.1319 2.3092 24.608 22.611 66.276 29.555 7.9331 2.8653 24.872 23.084 73.591 32.724 8.7700 3.4657 25.080 23.276 81.694 36.295 8.8320 3.5156 25.178 22.795 90.719 40.161 10.049 4.4033 25.399 21.443 100.73 44.094 11.149 5.2350 25.428 20.485 110.86 47.981 12.375 6.1894 25.618 18.256 120.94 51.730 12.937 6.6159 25.681 17.587 131.04 55.469 13.734 7.2602 25.716 17.263 141.13 58.974 14.434 7.7623 25.936 15.763 151.25 62.313 14.953 8.2940 25.991 15.493 161.40 65.707 15.432 8.7191 26.154 14.920 171.44 68.868 15.939 9.1811 26.411 14.371 181.60 71.845 16.432 9.6741 26.937 13.871 191.71 74.758 16.947 10.227 27.457 13.735 201.83 77.690 17.451 10.799 27.938 13.719 211.94 80.421 17.836 11.202 28.453 13.757 222.06 83.120 18.128 11.709 28.970 13.894 232.15 85.843 18.448 12.080 29.447 14.007 242.24 88.094 18.816 12.450 29.983 14.006 252.28 90.685 19.220 12.731 30.992 14.133 262.36 92.914 19.662 13.196 32.007 14.378 272.53 95.971 19.989 13.490 33.009 14.682 282.61 99.141 20.250 13.975 34.025 15.039 292.62 101.41 20.641 14.429 35.047 15.431 302.73 102.84 20.824 14.728 36.054 15.828 21.099 15.097 37.061 16.234

a The combined standard uncertainties [30] in the values of the heat capacities are determined to be ±(0.02 to 0.05) Cp,m for T/K < 22 and ±0.01 Cp,m for 22 < T/K < 300.

Q. Shi et al. / J. Chem. Thermodynamics 62 (2013) 35–42 37

contributio n [37,41]; the BaswT3e�D/T term describes the magnetic behavior in the heat capacity [39]. In the magnet ic expression, the BaswT3 is the typical dependenc e of heat capacity with temperatur efor anti-ferromag nets, and the expone ntial function of e�D/T repre-sents a gap of the spin-wave spectrum generated in an ordered magnet when anisotropy occurs [42,43]. This interpret ation isconsiste nt with the magnetic study from Thomas et al. where FePO 4was found to be an anisotro pic antiferr omagnet [25].

In the case of Fe3(P2O7)2, the low temperature values could not be fitted using equation (1) since a small bump exists around 8.5 Kin the heat capacity curve. To fit the data through the bump, wehave included a simple two-level Schottky function in equation (1), and thus the fitting function is rewritten with the form

Cp;m ¼ cT þ B3T3 þ B5T5 þ BaswT3e�D=T þ nRðh=TÞ62

� expðh=TÞ=ð1þ expðh=TÞÞ2 ð2Þ

where n, R and h represent the number of moles, the molar gas con- stant, and the level spacing in units of temperatur e, respective ly.The fitting paramete rs of Fe3(P2O7)2 as well as FePO 4 can be found in table 6.

It is worth noting that these two compounds as well as other iron phosphates studied in our previous work [44,45] have rela- tively large linear terms compared to the linear contribution of ele- mental iron [37]. As discussed in our previous work [44], this large

linear term is not related to the electronic contributi on but stems from a number of oxygen vacancies in the layered structure likely formed in these iron phosphates [28,46–48]. Additionally , the lay- ered structure makes it possible for these compounds to exhibit anisotropi c properties, which results in the formation of a gap inthe spin-wave spectrum. As for the Fe3(P2O7)2 in this study, we also found a Schottky anomaly existing below T = 15 K. This is likely due to uncorrelated spins in the lattice caused by defects in the lay- ered structure .

Another important property we can study on these two iron phosphat es is the magnetic heat capacity extracted by subtracting the lattice contribution from the total heat capacity. In our previ- ous studies, we found that a combination of one Debye and two Einstein functions may accurately estimate the lattice of iron phos- phates [44,45]. This fitting equation can be expressed by

Cp;m ¼ m � DðHD=TÞ þ n1 � EðHE;1=TÞ þ n2 � EðHE;2=TÞ ð3Þ

where D(HD/T), E(HE,1/T) and E(HE,2/T) are Debye, low and high temperat ure Einstein functions respective ly; m, n1, n2, HD, HE,1,HE,2 are adjustable paramete rs; and the sum of (m + n1 + n2) should be approximat ely equal to the number of atoms in the molecule.The Debye-Ein stein fitting paramete rs are listed in table 7. The use of a low temperatu re and high temperatur e Einstein functions

TABLE 3Molar heat capacity at constant pressure for Fe3(P2O7)2 from T = (2 to 300) K. M = 515.42 76 g �mol�1.a

T/K Cp,m/(J � K�1 �mol�1) T/K Cp,m/(J � K�1 �mol�1) T/K Cp,m/(J � K�1 �mol�1)

1.9079 0.21981 22.745 35.802 34.782 38.198 2.0531 0.28339 22.859 36.259 35.287 38.772 2.2365 0.37994 22.950 36.583 36.017 39.674 2.5252 0.57348 23.073 37.001 36.998 40.853 2.7880 0.78567 23.145 37.244 38.007 42.118 3.0810 1.0715 23.350 37.457 39.014 43.511 3.4209 1.4570 23.363 37.447 39.085 43.520 3.8452 1.9509 23.542 37.413 40.019 44.907 4.2515 2.4953 23.746 37.482 41.026 46.314 4.7315 3.1375 23.870 37.702 42.031 47.801 4.9037 3.3807 23.950 37.841 43.040 49.141 5.2520 3.8663 24.087 38.176 44.048 50.656 5.4469 4.1108 24.153 38.382 45.062 52.139 5.8458 4.6823 24.272 38.710 46.087 53.765 6.0519 4.9761 24.347 38.930 47.115 55.255 6.4917 5.6227 24.476 39.348 48.141 56.898 6.7459 5.9626 24.546 39.556 48.222 56.869 7.2326 6.6704 24.677 40.012 49.170 58.468 7.5163 7.1010 24.748 40.216 50.177 59.921 8.0523 7.8961 24.878 40.713 53.554 65.427 8.3760 8.4025 24.950 40.967 55.936 69.239 8.9502 9.0837 25.078 41.386 59.478 75.071 9.3412 9.4416 25.156 41.664 62.325 79.657 9.8482 10.125 25.280 42.045 66.061 85.829 9.9472 10.282 25.358 42.278 69.409 91.349 10.285 10.780 25.479 42.535 73.356 97.848 10.910 11.684 25.559 42.589 77.267 104.31 11.391 12.480 25.629 42.472 81.471 111.39 11.893 13.289 25.694 41.990 86.002 118.73 12.316 13.985 25.761 41.294 90.492 126.54 12.394 14.109 25.897 39.532 95.712 134.60 12.892 14.924 25.965 38.734 100.46 142.30 13.395 15.774 26.104 37.671 105.87 150.33 13.666 16.217 26.166 37.408 110.62 157.15 13.897 16.622 26.302 37.219 115.68 164.83 14.395 17.483 26.364 37.251 120.57 171.78 14.899 18.347 26.501 37.348 125.69 179.03 15.183 18.865 26.565 37.426 130.67 186.02 15.397 19.216 26.700 37.641 135.85 193.25 15.897 20.109 26.764 37.795 140.71 199.65 16.398 21.023 26.899 38.095 145.82 205.89 16.873 21.933 26.964 38.226 150.78 211.84 16.897 21.996 27.102 38.505 155.92 218.37 17.399 23.016 27.166 38.655 160.85 224.45 17.901 24.093 27.303 38.785 166.00 230.38 18.379 25.404 27.372 38.771 170.90 236.00 18.711 26.190 27.505 38.434 176.10 241.71 18.738 26.258 27.566 38.067 181.04 246.76 18.882 26.668 27.720 36.896 186.17 252.47 18.953 26.840 27.773 36.418 191.21 257.43 19.148 27.351 27.975 35.041 196.30 262.54 19.346 27.912 28.175 34.327 201.26 267.67 19.386 28.039 28.217 34.251 206.35 272.36 19.516 28.499 28.375 34.068 206.45 272.46 19.717 29.196 28.532 33.963 211.80 277.98 19.845 29.604 28.573 33.938 216.72 281.75 19.917 29.716 28.713 33.880 221.84 287.01 20.109 29.666 28.774 33.886 226.87 290.81 20.311 29.617 28.976 33.886 231.96 295.66 20.351 29.635 29.180 33.928 236.94 300.34 20.512 29.702 29.216 33.943 242.04 304.27 20.714 30.021 29.383 33.994 247.01 309.14 20.852 30.315 29.578 34.077 252.13 312.36 20.916 30.416 29.719 34.124 257.17 316.62 21.115 30.819 29.786 34.145 262.13 320.57 21.317 31.334 30.224 34.363 267.24 324.59 21.352 31.449 30.727 34.745 272.20 328.42 21.516 31.853 31.233 35.094 277.32 332.29 21.721 32.443 31.738 35.514 282.36 336.71 21.854 32.788 32.250 35.934 287.31 340.82 21.925 33.019 32.759 36.291 292.44 342.78 22.128 33.612 33.264 36.693 297.49 342.14 22.339 34.297 33.767 37.121 302.43 348.65 22.540 34.997 34.273 37.656

a The combined standard uncertainties [30] in the values of the heat capacities are determined to be ±(0.02 to 0.05) Cp,m for T/K < 22 and ±0.01 Cp,m for 22 < T/K < 300.

38 Q. Shi et al. / J. Chem. Thermodynamics 62 (2013) 35–42

TABLE 4Standard thermodynamic functions for FePO 4. U�m ¼ Dt

0S�m � Dt0H�m=T . M = 150.8184 g �mol�1.a

T/K C�p;m/(J � K�1 �mol�1) DT0S�m/(J � K�1 �mol�1) DT

0H�m/(kJ � K�1 �mol�1) /�m/(J � K�1 �mol�1)

0 0 0 0 01 0.0037825 0.0012525 9.3962E �07 3.1283E �042 0.040387 0.011572 1.7765E �05 0.0026899 3 0.18004 0.049701 1.1642E �04 0.010896 4 0.47659 0.13808 4.3068E �04 0.030409 5 0.93866 0.29113 0.0011252 0.066103 6 1.5392 0.51363 0.0023546 0.12119 7 2.2197 0.80154 0.0042311 0.19709 8 2.9132 1.1429 0.0067955 0.29350 9 3.6354 1.5276 0.010068 0.40888 10 4.3673 1.9484 0.014068 0.54152 11 5.1210 2.3997 0.018810 0.68971 12 5.8974 2.8785 0.024319 0.85198 13 6.6704 3.3810 0.030602 1.0271 14 7.4427 3.9042 0.037666 1.2138 15 8.3227 4.4460 0.045524 1.4111 16 9.2430 5.0124 0.054306 1.6183 17 10.282 5.6033 0.064057 1.8352 18 11.490 6.2235 0.074914 2.0616 19 12.581 6.8772 0.087010 2.2978 20 13.570 7.5455 0.10004 2.5434 25 23.115 11.493 0.18943 3.9161 30 14.017 14.261 0.26485 5.4326 35 15.412 16.506 0.33775 6.8556 40 17.521 18.698 0.41996 8.1990 45 19.757 20.890 0.51313 9.4873 50 22.038 23.089 0.61760 10.737 55 24.346 25.298 0.73355 11.961 60 26.663 27.516 0.86107 13.164 65 28.973 29.741 1.0002 14.354 70 31.256 31.972 1.1508 15.533 75 33.495 34.205 1.3127 16.703 80 35.673 36.437 1.4856 17.867 85 37.771 38.663 1.6692 19.025 90 39.895 40.881 1.8633 20.177 95 42.033 43.095 2.0682 21.325 100 44.107 45.304 2.2835 22.469 110 48.062 49.696 2.7446 24.745 120 51.773 54.038 3.2440 27.005 130 55.279 58.322 3.7794 29.250 140 58.625 62.542 4.3490 31.478 150 61.849 66.697 4.9515 33.688 160 64.983 70.789 5.5857 35.879 170 68.050 74.821 6.2509 38.051 180 71.061 78.796 6.9465 40.205 190 74.021 82.718 7.6720 42.339 200 76.933 86.589 8.4268 44.455 210 79.792 90.412 9.2104 46.553 220 82.593 94.189 10.022 48.632 230 85.331 97.921 10.862 50.694 240 88.001 101.61 11.729 52.739 250 90.597 105.25 12.622 54.767 260 93.114 108.86 13.540 56.778 270 95.551 112.42 14.484 58.773 273.15 96.301 113.53 14.786 59.398 280 97.904 115.93 15.451 60.752 290 100.17 119.41 16.442 62.715 298.15 101.96 122.21 17.265 64.303 300 102.35 122.84 17.454 64.662

a The combined uncertainties in the values of the fitted heat capacities are determined from the experimental and fitted uncertainties to be ±(0.022 to 0.051) Cp,m forT/K < 10,±0.012 Cp,m for 10 < T/K < 50 and ±0.011 Cp,m for 50 < T/K < 300.

Q. Shi et al. / J. Chem. Thermodynamics 62 (2013) 35–42 39

[49] can allow us to estimate the lattice of these iron phosphates properly in the entire experime ntal temperatur e region.

The estimated lattice heat capacities of FePO 4 and Fe3(P2O7)2 areshown respectively in figures 1 and 2 with dashed lines. The mag- netic heat capacity can be calculated from the difference between the lattice and the total heat capacity, and the results are presented in figure 3(a) for FePO 4 and figure 3(b) for Fe3(P2O7)2. Conse- quently, the entropy due to the magnetic ordering is determined by integrating the magnetic heat capacity divided by temperature (Cmag(K)/T) in the transition region.

The magnetic entropy of FePO 4 has been calculated to be(12.32 ± 0.14) J � K�1 �mol�1, which is only about 83% of the expected theoretical value of (1.79R) with S = 5/2. In reality, this discrepan cy is likely attributed to the thermal anomalie s we ob- served in the low temperature side of the transition during the measure ment. This interesting aspect can be seen in figure 4,where the unusuall y high and low data points are due to the incor- rect fit of relaxation curves during the heat capacity measurement.There appears to be a first-order transition appearing in this region so that the released latent heat gives rise to distorted relaxation

TABLE 5Standard thermodynamic functions for Fe3(P2O7)2. U

�

m ¼ DT0S�

m � DT0H

�

m/T. M = 515.4276 g�mol�1.a

T/K C�p;m/(J � K�1 �mol�1) DT0S�m/(J � K�1 �mol�1) DT

0H�m/(kJ � K�1 �mol�1) U�m/(J � K�1 �mol�1)

0 0 0 01 0.037235 0.012464 9.3412E �06 0.012455 2 0.28853 0.097840 1.4634E �04 0.024670 3 0.99012 0.32594 7.3215E �04 0.081890 4 2.1562 0.76413 2.2832E �03 0.193330 5 3.5120 1.3897 0.0051117 0.36736 6 4.9034 2.1515 0.0093112 0.59963 7 6.3316 3.0151 0.014932 0.88196 8 7.8287 3.9577 0.022007 1.2068 9 9.1193 4.9604 0.030534 1.5677 10 10.353 5.9795 0.040217 1.9578 11 11.834 7.0350 0.051303 2.3711 12 13.466 8.1347 0.063953 2.8053 13 15.106 9.2771 0.078237 3.2589 14 16.798 10.458 0.094183 3.7306 15 18.532 11.676 0.11185 4.2193 16 20.292 12.928 0.13125 4.7249 17 22.193 14.214 0.15248 5.2446 18 24.371 15.542 0.17572 5.7798 19 26.954 16.929 0.20138 6.3301 20 29.660 18.387 0.22982 6.8960 25 41.170 26.082 0.40339 9.9464 30 34.247 32.852 0.58835 13.240 35 38.441 38.418 0.76914 16.443 40 44.948 43.961 0.97708 19.534 45 52.129 49.666 1.2196 22.564 50 59.679 55.546 1.4990 25.566 55 67.536 61.600 1.8169 28.565 60 75.634 67.823 2.1747 31.578 65 83.910 74.202 2.5735 34.610 70 92.298 80.727 3.0140 37.670 75 100.74 87.383 3.4966 40.762 80 109.16 94.153 4.0214 43.886 85 117.50 101.02 4.5881 47.042 90 125.70 107.97 5.1961 50.236 95 133.69 114.98 5.8447 53.457 100 141.43 122.04 6.5325 56.715 110 157.30 136.27 8.0273 63.295 120 171.92 150.59 9.6743 69.971 130 185.57 164.90 11.462 76.731 140 198.49 179.13 13.383 83.537 150 210.84 193.25 15.430 90.383 160 222.71 207.23 17.599 97.236 170 234.16 221.08 19.883 104.12 180 245.21 234.78 22.280 111.00 190 255.88 248.33 24.786 117.88 200 266.16 261.71 27.397 124.73 210 276.05 274.94 30.108 131.57 220 285.53 288.00 32.916 138.38 230 294.61 300.90 35.817 145.17 240 303.29 313.62 38.807 151.92 250 311.56 326.17 41.882 158.64 260 319.43 338.55 45.037 165.33 270 326.92 350.74 48.269 171.97 273.15 329.20 354.55 49.303 174.05 280 334.02 362.76 51.574 178.57 290 340.77 374.60 54.948 185.12 298.15 346.00 384.12 57.747 190.44 300 347.16 386.26 58.388 191.63

a The combined uncertainties in the values of the fitted heat capacities are determined from the experimental and fitted uncertainties to be ±(0.022 to 0.051) Cp,m forT/K < 10, ±0.012 Cp,m for 10 < T/K < 50 and ±0.011 Cp,m for 50 < T/K < 300.

40 Q. Shi et al. / J. Chem. Thermodynamics 62 (2013) 35–42

curves which may generate incorrect heat capacities. However, the relaxation technique employed in the PPMS is not well suited atmeasuring first order transitions, and thus we were not able tomap out these anomalies using the present instrument. To calcu- late the thermodyna mic functions, we have deleted these ‘‘irrepro- ducible’’ heat capacity values in the data fitting procedure represented above. Therefore, we may conclude that the magnetic entropy of FePO 4 in this study is perhaps larger than (12.32 ± 0.14) J �mol�1 � K�1.

As for Fe3(P2O7)2, it is interesting that the four-peak transition is substantially different from that of FePO 4 as well as the other four iron phosphates in the previous studies [44,45]. This isprobably due to the unique molecular structure with Fe2+/Fe3+

mixed-va lence in this compound. It is worth noting that the Fe3(P2O7)2 sample was prepared from the mixture of FePO 4, Fe2-

P2O7 and Fe4(P2O7)3 [5,28], and the magnetic transition in Fe3(P2-

O7)2 may be related to the transition in those three iron phosphat es.

TABLE 6Fitting parameters of heat capacities of FePO 4 and Fe3(P2O7)2 at low temperatures.

Parameters FePO 4 Fe3(P2O7)2

c/(mJ �mol�1 � K�1) 13.211 26.613 B3/(mJ �mol�1 � K�4) 1.0431 22.099 B5/(mJ �mol�1 � K�6) �0.25886 �0.18953Basw/(mJ �mol�1 � K�4) 34.591 514.49 D/K 5.1096 44.965 n/mole 0.40689 h/K 17.266 Temperature region Below 5 K Below 15 K%RMS 0.29 1.24

TABLE 7Fitting parameters of the Debye and Einstein functions used in the lattice estimation from T = (0 to 300) K.

Parameters FePO 4 Fe3(P2O7)2

m/mole 2.8044 10.122 HD/K 682.54 592.31 n1/mole 1.3633 3.3500 HE,1/K 130.91 133.51 n2/mole 3.4512 7.4033 HE,2/K 1506.9 1197.1 %RMS 0.32 0.17

FIGURE 3. Plot of magnetic heat capacity of (a) FePO 4 and (b) Fe3(P2O7)2 calculated by subtracting the lattice contribution from the total heat capacity.

FIGURE 4. Plot of heat capacity of FePO 4 with thermal anomalies in the transition region.

FIGURE 5. Plot of heat capacity comparison of Fe3(P2O7)2, FePO 4, Fe2P2O7 [44] and Fe3(P2O7)2 [45].

Q. Shi et al. / J. Chem. Thermodynamics 62 (2013) 35–42 41

The comparison of heat capacitie s of Fe3(P2O7)2, FePO 4, Fe2P2O7

and Fe4(P2O7)3 is illustrated in figure 5. It can be seen from the plot

that Peak 1 is in the phase transition region of Fe2P2O7, suggesting this peak can be attributed to the Fe2+ ordering; Peak 3 and 4 are inthe transition region of FePO 4 and Fe4(P2O7)3, respectively , indicat- ing that these two peaks are likely related to Fe3+ ordering; Peak 2 islocated in the transition regions of both Fe2P2O7 and FePO 4, making it possible to consider this peak is due to the interaction between Fe2+ and Fe3+. This explanat ion is reasonable since the ratio ofFe3+/Fe2+ is 2 in the Fe3(P2O7)2 compound, however, the absence of detailed magnetic measurements in this region makes it difficultto have any further confirmation beyond the heat capacity data.

Neverthel ess, the magnetic entropy of Fe4(P2O7)3 has been cal- culated from the magnetic contribution to be (29.02 ± 0.32) J � K�1

�mol�1, which is only about 67% of the theoretical value of 5.19R (assuming 2 mol of Fe3+ with S = 5/2 and 1 mol of Fe2+ with S = 2).This suggests there are a large number of spins that are not corre- lated in the lattice. The entropy from the Schottky anomaly is only (2.34 ± 0.03) J � K�1 �mol�1 (using the fitting parameters in table 6),thus there are still a large fraction of the spins that are not ordering.

5. Conclusion s

In conclusio n, the heat capacities of FePO 4 and Fe3(P2O7)2 havebeen measured over the temperature range from (2 to 300) K using

42 Q. Shi et al. / J. Chem. Thermodynamics 62 (2013) 35–42

a Quantum Design PPMS calorimeter, and the standard thermody- namic functions have been derived from the fitted experi- mental values. The standard molar entropies at T = 298.15 Khave been calculated to be (122.21 ± 1.34) J � K�1 �mol�1 and(384.12 ± 4.23) J � K�1 �mol�1 for FePO 4 and Fe3(P2O7)2, respec- tively. The theoretical fitting of the heat capacity of FePO 4confirmed this compound to be an anisotropic antiferroma gnet.The four-peak magnetic transition in Fe3(P2O7)2 has been reason- ably interpreted by comparing the heat capacity of this compound with that of other iron phosphates .

Acknowled gments

This research is being performed using funding received from the DOE office Nuclear Energy’s Nuclear Energy University Pro- grams (USA) under contract numbered 88688 and project num- bered 09-800. We would like to thank Jacob Schliesser for his work on editing the manuscript.

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