Heat Capacity and Standard Thermodynamic Functions of NaGdTiO4

Article pubs.acs.org/jced

Heat Capacity and Standard Thermodynamic Functions of NaGdTiO4 and Na2Gd2Ti3O10 over the Range from (6 to 630) K Alexey V. Markin,*,† Anna M. Sankovich,†,‡ Natalia N. Smirnova,† and Irina A. Zvereva‡ †

Lobachevsky State University of Nizhni Novgorod, 23/5 Gagarin Avenue, 603950, Nizhni Novgorod, Russia St. Petersburg State University, 26 Universitetsky Avenue, Petrodvorets, 198504, St. Petersburg, Russia

‡

ABSTRACT: The heat capacities of layered perovskite-like oxides NaGdTiO4 and Na2Gd2Ti3O10 were measured by precision adiabatic vacuum calorimetry over the temperature range from T = (6 to 344) K and by differential scanning calorimetry over the temperature range from T = (320 to 630) K. The standard thermodynamic functions: molar heat capacity Cp,m ° , enthalpy H°(T) − H°(5), entropy S°(T) − S°(5), and Gibbs energy of the compounds were evaluated from the experimental heat capacity temperature dependences over the range from T = (5 to 630) K.

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Na 2CO3 + 3TiO2 + Gd 2O3 → Na 2Gd 2Ti3O10 + CO2

INTRODUCTION

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Layered perovskite-like oxides are the objects of close attention because they are one of the promising classes of ceramic materials. Compounds with this crystal structure exhibit remarkable physicochemical properties, such as very large magnetoresistance,1 multiferroism,2 high-temperature superconductivity,3 catalytic and photocatalytic activity,4−6 and ion exchange properties.7 The knowledge of thermophysical properties for these materials would facilitate their practical application in various branches of chemical engineering and electronics. Moreover, it would be valuable from the theoretical point of view. However, high-quality thermodynamic data available in the literature8−11 for this class of compounds are scarce. The purpose of the present paper is to report the results of calorimetric investigation of layered perovskite-like titanates NaGdTiO4 and Na2Gd2Ti3O10 over the temperature range from T = (6 to 630) K. These oxides belong to the Ruddlesden− Popper phases12 (Na,Gd)n+1TinO3n+1, where n is a number of perovskite layers. Interest in the above oxides is motivated by their use as catalysts for photoinduced reactions and precursors for synthesis of other layered compounds via ion exchange and topochemical routes.13

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The following reactants (Johnson Matthey) were used as the initial compounds: gadolinium oxide Gd2O3 (the content of the main component was 99.95 %) preliminarily calcined at T = 1173 K for 5 h in order to remove moisture, finely dispersed titanium oxide TiO2 (99.9 %) in the anatase modification, and sodium carbonate Na2CO3 (99.5 %). The reactants were carefully mixed in an agate mortar (on the basis of 40 min of grinding per gram of the initial mixture). The prepared batch mixture was pressed into pellets of 0.5 g in weight and 0.7 cm in diameter. The samples were sintered in a Nabertherm HTCT 01/16 high-temperature furnace in corundum crucibles at atmospheric pressure in air. The temperature conditions were controlled by a platinum− rhodium thermocouple. The isothermal conditions of heat treatment were ensured to be standard uncertainty for temperature u(T) = 1 K with the use of a TP-403 programmable temperature controller. NaGdTiO4 was synthesized at temperature T = 1073 K for 4 h, Na2Gd2Ti3O10, at T = 1273 K for 10 h. Characterization of the samples was provided by X-ray powder diffraction analysis and optical emission spectrometry analysis. Qualitative X-ray powder diffraction analysis of the samples was performed on a Rigaku MiniFlex II diffractometer (Cu Kα radiation). The XRD patterns (Figure 1) were recorded under the following conditions: 2θ = 5° to 60° at a step of 0.02° and a rate of 2° per min. The phase composition of the samples was determined using the ICDD PDF-2 Database. Optical emission spectrometer ICPE-9000 (Shimadzu, Japan) was used to determine qualitative composition of the samples. No significant

EXPERIMENTAL SECTION

Synthesis and Characterization of Layered Perovskitelike Oxides. The layered perovskite-like oxides NaGdTiO4 and Na2Gd2Ti3O10 were obtained according to the conventional ceramic technology14 through the reactions: Na 2CO3 + 2TiO2 + Gd 2O3 → 2NaGdTiO4 + CO2 © XXXX American Chemical Society

Received: January 14, 2015 Accepted: October 9, 2015

(1) A

DOI: 10.1021/acs.jced.5b00047 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

Figure 1. X-ray diffraction patterns of NaGdTiO4 (a) and Na2Gd2Ti3O10 (b). 2θ is a scattering angle.

Figure 3. Experimental molar heat capacity Cp,m of Na2Gd2Ti3O10 as a function of temperature.

Figure 2. Experimental molar heat capacity Cp,m of NaGdTiO4 as a function of temperature.

The crystal structures of NaGdTiO4 and Na2Gd2Ti3O10 are displayed in Figure 2 panels c and d, respectively. NaGdTiO4 belongs to the orthorhombic tetragonal system with the space group Pbcm (57) and the symmetry of Na2Gd2Ti3O10 is tetragonal I4/mmm (139). It can be seen that the crystal structures consist of single (NaGdTiO4) or triple (Na2Gd2Ti3O10)

impurities were detected, the sensitivity limit is 10−9 to 10−8. It is observed that all diffraction peaks match well with the standard data of NaGdTiO4 (ICDD PDF-2 No. 01-086-0830) or those of Na2Gd2Ti3O10 (ICDD PDF-2 No. 01-086-1372) in our experimental range. No impurity diffraction peaks were found. Table 1. Sample Information chemical name NaGdTiO4 Na2Gd2Ti3O10

source present work present work

state

mole fraction purity

powder

0.98

powder

0.98

analysis method X-ray fluorescence spectrometry, X-ray powder diffraction, optical emission spectrometry, thermogravimetric analysis X-ray fluorescence spectrometry, X-ray powder diffraction, optical emission spectrometry, thermogravimetric analysis B



Article

Table 2. Experimental Molar Heat Capacity Cp,m of Crystalline NaGdTiO4 (M = 292.10 g·mol−1)a T K

Cp,m −1

T −1

J·K ·mol

K

Cp,m −1

T −1

J·K ·mol

K

T

Cp,m −1

−1

J·K ·mol

K

Cp,m −1

J·K ·mol

T −1

K

series 1 6.81 6.98 7.18 7.38 7.58 7.78 7.98 8.17 8.37 8.56 8.75 8.94 9.13 9.32 9.51 9.71 9.89 10.08 10.35 10.70 11.05 11.40 11.76 12.12 12.49 12.86 13.24

1.52 1.45 1.42 1.41 1.37 1.37 1.35 1.38 1.33 1.33 1.34 1.36 1.38 1.38 1.39 1.39 1.35 1.38 1.39 1.39 1.39 1.42 1.44 1.50 1.53 1.55 1.57

80.89 83.89 86.41 88.93 91.45 93.98 96.51 99.05 101.59 104.12 106.67 109.21 111.76 114.31

53.93 56.40 58.39 60.35 62.32 64.24 66.14 67.93 69.81 71.60 73.34 75.05 76.80 78.47

13.62 14.00 14.38 14.76 15.15 15.52 15.92 16.31 16.71 17.11 17.51 17.92 18.33 18.74 19.17 19.59 20.01 20.85 22.13 23.43 24.77 26.13 27.52 28.93 30.36 31.82 33.30

1.59 1.61 1.64 1.70 1.74 1.81 1.90 1.95 2.05 2.17 2.24 2.36 2.50 2.67 2.76 2.86 3.095 3.434 4.020 4.694 5.427 6.260 7.200 8.195 9.286 10.43 11.59 series 2 157.85 103.0 160.41 104.2 162.98 105.4 165.54 106.6 168.11 107.7 170.67 108.8 173.24 110.0 175.80 111.3 178.36 112.2 180.93 113.2 183.49 114.4 186.05 115.5 188.60 116.6 191.16 117.5

34.79 36.29 37.81 39.34 40.89 42.45 44.02 45.60 47.19 48.79 50.40 52.02 53.64 55.27 56.91 58.55 60.20 61.85 63.50 65.16 66.82 68.49 70.16 72.24 74.73 77.23 79.74 234.70 237.26 239.82 242.39 244.95 247.51 250.08 252.64 255.21 257.77 260.33 262.89 265.45 268.01

12.79 14.04 15.37 16.74 18.06 19.50 20.95 22.45 23.92 25.45 27.01 28.57 30.04 31.51 33.04 34.55 36.04 37.52 39.02 40.72 41.92 43.51 45.10 46.90 49.06 51.29 53.31 133.9 134.7 135.7 136.5 137.4 138.2 139.1 139.8 140.7 141.4 142.2 143.0 143.7 144.5

116.86 119.41 121.98 124.53 127.09 129.65 132.21 134.77 137.33 139.90 142.46 145.03 147.59 150.15 152.72 155.28 316.05 319.33 322.61 325.88

80.11 81.69 83.34 84.90 86.43 87.87 89.41 90.90 92.37 93.76 95.16 96.47 97.84 99.20 100.5 101.7 158.3 159.2 160.3 161.4

193.72 196.28 198.84 201.40 203.95 206.51 209.07 211.63 214.19 216.75 219.31 221.87 224.44 227.00 229.56 232.13 329.14 332.40 335.65 338.89

320.1 325.1 330.1 335.1 343.1 348.1 351.3 355.1 360.1 365.1 370.1 375.1 380.1 385.1 390.1 395.1 400.1 405.1 410.1 415.1 420.1

160 161 163 164 168 169 170 172 173 175 176 178 179 180 182 183 184 185 185 186 187

425.1 430.1 435.1 440.1 443.8 450.1 455.1 460.1 465.1 470.1 475.1 480.1 485.1 490.1 495.1 500.1 505.1 510.1 515.1 520.1 525.1

Cp,m −1

T −1

J·K ·mol series 2 118.6 119.6 120.6 121.6 122.8 123.6 124.6 125.6 126.6 127.5 128.4 129.5 130.4 131.3 132.6 133.1 162.4 163.5 164.7 166.0 DSC 187 188 188 189 189 190 190 190 191 191 192 192 192 192 193 193 193 193 194 194 194

Cp,m −1

K

J·K ·mol−1

270.57 273.12 275.68 278.23 280.77 283.32 285.84 288.38 290.92 294.66 297.49 300.00 302.86 306.18 309.48 312.78 342.12 345.34

145.3 146.0 146.8 147.5 148.2 149.0 149.8 150.5 151.2 152.0 152.5 153.9 154.4 155.4 156.3 157.3 167.3 168.7

530.1 535.1 540.1 545.1 550.1 555.1 560.1 565.1 570.1 575.1 580.1 585.1 590.1 595.1 600.1 605.1 610.1 615.1 620.1 625.1 630.1

194 195 195 195 195 195 195 196 196 197 197 197 198 198 198 198 199 199 199 199 199

a The standard uncertainty for temperature u(T) = 0.01 K in the temperature range from T = (6 to 350) K, and u(T) = 0.5 K in the interval between T = (320 and 630) K. The relative standard uncertainty for heat capacity ur(Cp,m) = 0.02 in the temperature range from T = (6 to 15) K, ur(Cp,m) = 0.005 between T = (15 to 40) K, ur(Cp,m) = 0.002 in the temperature range from T = (40 to 350) K, and ur(Cp,m) = 0.02 over the range from T = (320 to 630) K.

According to the thermogravimetric (TG) analysis carried out by us, it was established that the samples were thermally stable in the studied temperature range (until T = 673 K). The information for the studied titanates is listed in Table 1. The molar masses of NaGdTiO4 and Na2Gd2Ti3O10 were calculated from the International Union of Pure and Applied Chemistry (IUPAC) table of atomic weights.15 Adiabatic Calorimetry. A BCT precision automatic adiabatic calorimeter (Termis, Moscow) was used to measure isobaric heat capacities (Cp,m) of NaGdTiO4 and Na2Gd2Ti3O10 over the temperature range of (6 to 350) K. The design and

perovskite-like slab layers stacked along the [001] direction which are separated by the rock-salt type double layers. The last are presented by (NaO) and (GdO) layers in the case of NaGdTiO4 and (NaO) layer for Na2Gd2Ti3O10. The chemical analysis of the investigated titanates was carried out on the energy dispersive X-ray fluorescence spectrometer EDX-900HS (Shimadzu, Japan). From the experimental data it was found that the ratio of elements Ti/Gd is equal to 0.98:1.02, and 2.99:2.01 for NaGdTiO4 and Na2Gd2Ti3O10, respectively. Additionally, the obtained results allow excluding nonstoichiometric oxygen in the studied samples. C



Article

Table 3. Experimental Molar Heat Capacity Cp,m of Crystalline Na2Gd2Ti3O10 (M = 664.07 g·mol−1)a T K

Cp,m −1

T −1

J·K ·mol

K

Cp,m −1

T −1

J·K ·mol

K

T

Cp,m −1

−1

J·K ·mol

Cp,m −1

T −1

K

J·K ·mol

112.32 114.88 117.44 120.01 122.59 125.16 127.74 130.31 132.89 135.46 138.04 140.62 143.20 145.78 148.37 292.17 294.79 297.41 300.01 303.06 306.49

172.2 176.3 180.2 184.2 188.1 192.0 195.7 199.4 203.1 206.7 210.3 213.8 217.3 220.6 223.9 354.6 356.2 357.9 359.8 361.7 363.8

182.08 184.67 187.27 189.87 192.47 195.06 197.66 200.26 202.87 205.49 208.10 210.71 213.32 215.93 218.54 309.92 313.33 316.75 320.16 323.58 326.99

320.3 325.3 330.3 335.3 340.3 345.3 350.3 355.3 360.3 365.3 370.3 375.3 380.3 385.3 390.3 395.3 400.3 405.3 410.3 415.3 420.3

375 378 380 383 386 388 391 395 397 400 403 404 406 407 408 409 411 411 412 412 413

425.3 430.3 435.3 440.3 445.3 450.3 455.3 460.3 465.3 470.3 475.3 480.3 485.3 490.3 495.3 500.3 505.3 510.3 515.3 520.3 525.3

K

series 1 5.36 5.56 5.78 5.99 6.20 6.41 6.60 6.79 6.99 7.18 7.36 7.55 7.73 7.91 8.09 8.27 8.45 8.63 8.81 8.98 9.16 9.33 9.50 9.67 9.84 10.02 10.27 10.59 68.43 70.10 81.46 84.37 86.89 89.41 91.94 94.48 97.02 99.56 102.11 104.65 107.21 109.76

2.20 2.09 1.96 1.85 1.69 1.57 1.52 1.53 1.44 1.41 1.38 1.36 1.33 1.38 1.36 1.34 1.35 1.31 1.34 1.37 1.37 1.32 1.37 1.40 1.47 1.48 1.42 1.48 94.41 97.88 119.0 124.7 129.3 133.8 138.2 142.6 147.1 151.4 155.8 160.0 164.1 168.2

10.91 11.23 11.53 11.86 12.20 12.54 12.89 13.24 13.60 13.96 14.32 14.68 15.06 15.43 15.81 16.19 16.58 16.97 17.35 17.75 18.15 18.56 18.97 19.39 19.81 20.63 21.89 23.20 72.19 74.69

1.50 1.52 1.62 1.67 1.73 1.85 1.95 2.05 2.17 2.28 2.49 2.67 2.84 2.98 3.24 3.49 3.76 4.04 4.26 4.56 4.88 5.31 5.62 5.98 6.31 7.250 8.595 10.12 101.9 106.7 series 2 150.95 227.2 153.54 230.3 156.13 233.6 158.72 236.7 161.31 239.7 163.92 242.6 166.51 245.5 169.10 248.4 171.70 251.3 174.29 254.0 176.88 256.9 179.48 259.6

24.53 25.89 27.28 28.70 30.14 31.60 33.07 34.57 36.08 37.61 39.16 40.71 42.28 43.85 45.44 47.04 48.65 50.27 51.89 53.52 55.16 56.80 58.45 60.10 61.76 63.42 65.09 66.75 77.19 79.71

11.90 13.76 15.85 18.07 20.52 22.94 25.59 28.21 30.88 33.70 36.60 39.57 42.56 45.69 48.89 52.01 55.29 58.63 61.81 65.10 68.18 71.45 74.83 78.20 81.39 84.61 87.97 91.38 111.5 116.1

221.16 223.77 226.39 229.01 231.63 234.25 236.88 239.50 242.13 244.76 247.42 250.05

299.5 301.8 304.0 306.9 308.9 310.7 312.8 315.0 317.4 319.6 321.8 323.8

Cp,m −1

T −1

J·K ·mol series 2 262.3 265.0 267.6 270.2 272.6 275.2 277.9 280.4 282.7 285.4 287.7 290.1 292.4 295.0 297.2 366.4 369.1 372.0 374.9 377.7 378.5 DSC 414 414 416 416 416 417 417 418 418 419 420 420 422 422 422 421 422 423 423 423 423

Cp,m −1

K

J·K ·mol−1

252.68 255.31 257.95 260.58 263.21 265.85 268.48 271.12 273.75 276.38 279.02 281.65 284.28 286.90 289.55 330.43 333.86 337.27 340.68 344.09

326.0 328.0 330.0 332.2 334.1 336.0 338.1 339.9 341.7 343.7 345.8 347.3 349.1 351.1 353.1 379.2 380.8 383.0 385.8 386.9

530.3 535.3 540.3 545.3 550.3 555.3 560.3 565.3 570.3 575.3 580.3 585.3 590.3 595.3 600.3 605.3 610.3 615.3 620.3 625.3 630.3

423 423 424 425 425 426 426 426 427 428 428 429 429 430 431 432 433 433 434 434 435

a The standard uncertainty for temperature u(T) = 0.01 K in the temperature range from T = (5 to 344) K, and u(T) = 0.5 K in the interval between T = (320 and 630) K. The relative standard uncertainty for heat capacity ur(Cp,m) = 0.02 in the temperature range from T = (6 to 15) K, ur(Cp,m) = 0.005 between T = (15 to 40) K, ur(Cp,m) = 0.002 in the temperature range from T = (40 to 350) K, and ur(Cp,m) = 0.02 over the range from T = (320 to 630) K.

operation of the calorimeter were described in detail earlier.16,17 The relative uncertainties in heat capacity measurements were ur(Cp,m) = 0.02 at T < 15 K, ur(Cp,m) = 0.005 over the temperature range of (15 to 40) K, and ur(Cp,m) = 0.002 between T = (40 to 350) K. The accuracy of the calorimeter was verified using standard reference samples (benzoic acid and α-Al2O3). A titanium calorimetric cell with a volume of 1.5 cm3 was loaded with a sample and then degassed in vacuum with a residual pressure of ∼5 Pa. Dry helium gas (at p = 4 kPa and room temperature) was introduced into the cell to facilitate heat transfer during the measurements. The sample masses used for

calorimetric measurements were 1.3814 g of NaGdTiO4 and 1.6506 g of Na2Gd2Ti3O10. An iron−rhodium resistance thermometer placed on the inner surface of the adiabatic shield was used for the temperature measurements in the calorimetric experiments. The temperature difference between the cell and the shield was determined by a differential copper−iron−chromel thermocouple. The sensitivity of the thermometric circuit was 10−3 K. After being assembled, the measuring system was cooled in a liquid nitrogen bath. If the measurements were performed below 80 K, a liquid helium bath was used. The samples were cooled to D



Article

Table 4. Smoothed Molar Heat Capacity and Thermodynamic Functions of Crystalline NaGdTiO4 (M = 292.10 g·mol−1) at Pressure p = 0.1 MPaa T K 5 10 15 20 25 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 260 270 280 290 298.15

[H°(T) − H°(5)]

Cp,m ° −1

−1

J·K ·mol

1.73 1.37 1.70 3.089 5.590 8.998 17.28 26.62 35.85 44.94 53.63 61.35 68.62 75.62 82.09 88.14 93.80 99.09 104.0 108.6 112.9 117.1 121.0 125.0 128.7 132.3 135.7 139.0 142.1 145.1 148.1 150.9 153.2

kJ·mol

−1

0 0.00720 0.0147 0.02660 0.04830 0.08350 0.2157 0.4328 0.7475 1.150 1.645 2.219 2.870 3.591 4.381 5.231 6.142 7.106 8.122 9.184 10.29 11.44 12.63 13.86 15.13 16.44 17.78 19.15 20.56 21.99 23.46 24.95 26.19

[S°(T) − S°(5)] −1

−1

J·K ·mol

0 1.00 1.62 2.284 3.2307 4.5153 8.2314 13.06 18.74 24.94 31.52 38.29 45.13 52.01 58.86 65.68 72.42 79.07 85.62 92.07 98.40 104.6 110.7 116.7 122.6 128.4 134.1 139.7 145.3 150.7 156.0 161.3 165.5

−Φm °b

T

−1

kJ·mol

K

0 0.00288 0.00957 0.01905 0.03246 0.05192 0.1136 0.2199 0.3772 0.5963 0.8771 1.227 1.643 2.130 2.683 3.307 3.996 4.755 5.578 6.468 7.419 8.435 9.511 10.65 11.84 13.10 14.41 15.78 17.21 18.69 20.22 21.81 23.14

300 310 320 330 340 350 360 370 380 390 400 410 420 430 440 450 460 470 480 490 500 510 520 530 540 550 560 570 580 590 600 610 620 630

[H°(T) − H°(5)]

Cp,m ° −1

J·K ·mol 153.7 156.5 159.5 162.7 166.2 170 173 176 179 182 184 185 186 188 189 190 190 191 192 192 193 193 194 194 195 195 195 196 197 198 198 199 199 200

−1

−1

kJ·mol 26.48 28.03 29.61 31.22 32.86 34.5 36.3 38.0 39.8 41.6 43.4 45.3 47.1 49.0 50.9 52.8 54.7 56.6 58.5 60.4 62.3 64.3 66.2 68.1 70.1 72.0 74.0 75.9 77.9 79.9 81.9 83.9 85.8 87.8

[S°(T) − S°(5)] −1

−1

J·K ·mol 166.4 171.5 176.5 181.5 186.4 191 196 201 206 210 215 219 224 228 233 237 241 245 249 253 257 261 265 268 272 276 279 283 286 289 293 296 299 302

−Φm °b kJ·mol−1 23.45 25.14 26.88 28.67 30.50 32.4 34.3 36.3 38.3 40.4 42.6 44.7 46.9 49.2 51.5 53.9 56.2 58.7 61.2 63.7 66.2 68.8 71.4 74.1 76.8 79.5 82.3 85.1 88.0 90.8 93.8 96.7 99.7 103

a Standard for temperature u(T) = 0.01 K in the temperature range from T = (5 to 344) K, and u(T) = 0.5 K in the interval between T = (320 and 630) K. The standard uncertainty for pressure u(p) = 10 kPa. Combined expanded uncertainties for the heat capacity Uc(Cp,m°) are 0.02, 0.005, 0.002, and 0.02; the combined expanded uncertainties Uc[H°(T) − H°(5)] are 0.022, 0.007, 0.005, and 0.022; Uc[S°(T) − S°(5)] are 0.023, 0.008, ° ] are 0.03, 0.01, 0.009, and 0.03 in the ranges 6 ≤ T/K ≤ 15, 15 ≤ T/K ≤ 40, 40 ≤ T/K ≤ 344, and 320 ≤ T/K ≤ 630, 0.006, and 0.023; Uc[Φm ° = [H°(T) − H°(5)] − T[S°(T) − S°(5)]. respectively, for 0.95 level of confidence (k ≈ 2). bΦm

the temperature of the measurement onset at a rate of 10−2 K·s−1. Then the samples were heated with a temperature step of (0.5 to 2) K at a rate of 10−2 K·s−1. Sample temperature was recorded after an equilibration period (temperature drift < 10−2 K·s−1, approximately 10 min per experimental point). The ratio of the sample heat capacity to the total (sample + cell) one was between 0.6 to 0.8. DSC and TG Analysis. Heat capacities of NaGdTiO4 and Na2Gd2Ti3O10 over the range of (320 to 630) K were measured in a DSC 204 F1 Phoenix differential scanning calorimeter (Netzsch Gerätebau, Germany) with use of a μ-sensor. The calorimeter was calibrated and tested against melting of n-heptane, adamantane, indium, tin, bismuth, and zinc. The heat capacity was determined by the “ratio method”, with sapphire used as a standard reference sample. The curves of heat capacities for both titanates were recorded three times at the repeated cooling and heating of each sample. The Cp,m values were reproduced within the limits of the experimental error of the method. The technique

for determining the Cp,m according to the data of DSC measurements is described in detail in a Netzsch Software Proteus and in refs 18 and 19. The relative standard uncertainty for heat capacities was ur(Cp,m) = 0.02. Measurements were carried out in argon atmosphere. Liquid nitrogen was used as a cryogen. The thermogravimetric analysis of NaGdTiO4 and Na2Gd2Ti3O10 over the range of (300 to 673) K was done using a TG 209 F1 Iris thermal microbalance (Netzsch Gerätebau, Germany). The thermal microbalance allows fixing the mass change within standard uncertainty u(m) = 10−5 g. The measurement was performed with a heating rate of 10 K·min−1 in argon atmosphere. The measuring technique of the TG analysis was standard, according to the Netzsch Software Proteus.

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RESULTS AND DISCUSSION Heat Capacity. Experimental heat capacity data for NaGdTiO4 and Na2Gd2Ti3O10 in the temperature range of (6 to 630) K are plotted in Figures 2 and 3, and given in Tables 2 and 3, E



Article

Table 5. Smoothed Molar Heat Capacity and Thermodynamic Functions of Crystalline Na2Gd2Ti3O10 (M = 664.07 g·mol−1) at Pressure p = 0.1 MPaa T K 5 10 15 20 25 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 260 270 280 290 298.15 300 310 320 330 340 350 360 370 380 390 400 410 420 430 440 450 460 470 480 490 500 510 520 530 540 550

[H°(T) − H°(5)]

Cp,m ° −1

−1

J·K ·mol

2.06 1.39 2.82 6.652 12.57 20.22 38.27 57.92 77.94 97.65 116.6 134.8 152.1 168.6 184.3 199.0 212.9 225.9 238.1 249.5 260.2 270.4 280.1 289.4 298.5 307.3 315.7 323.7 331.5 339.5 346.4 352.7 358.3 359.5 367.0 374.4 380.7 385.5 391.3 397 402 406 408 410 412 413 414 416 417 418 419 420 422 421 423 423 423 424 425

−1

kJ·mol

0 0.00820 0.0173 0.05230 0.08730 0.1893 0.4830 0.9893 1.619 2.594 3.569 4.915 6.262 7.947 9.631 11.62 13.61 15.87 18.12 20.62 23.11 25.81 28.52 31.41 34.30 37.38 40.45 43.69 46.92 50.31 53.71 57.24 60.11 60.76 64.43 68.10 71.91 75.71 79.63 83.5 87.5 91.6 95.6 99.7 104 108 112 116 120 125 129 133 137 141 146 150 154 158 163 F

[S°(T) − S°(5)] −1

J·K ·mol

−1

0 1.11 1.84 3.525 5.209 8.564 16.69 27.42 39.36 53.25 67.15 82.09 97.04 112.4 127.7 143.0 158.3 173.3 188.4 203.1 217.7 232.0 246.2 260.0 273.7 287.1 300.5 313.4 326.4 338.9 351.5 363.7 373.6 375.8 387.7 399.5 411.1 422.6 433.8 445 456 467 477 488 498 508 517 527 536 545 554 563 572 581 589 597 605 613 621

−Φm °b kJ·mol−1 0 0.00288 0.0103 0.01819 0.042923 0.06762 0.1845 0.3818 0.7429 1.134 1.803 2.473 3.442 4.412 5.689 6.966 8.549 10.13 12.02 13.90 16.08 18.26 20.72 23.18 25.92 28.66 31.66 34.67 37.93 41.20 44.71 48.23 51.27 51.99 55.75 59.74 63.74 67.96 72.19 76.6 81.1 85.8 90.5 95.3 100 105 110 116 121 126 132 137 143 149 155 161 167 173 179 DOI: 10.1021/acs.jced.5b00047 J. Chem. Eng. Data XXXX, XXX, XXX−XXX


Article

Table 5. continued T

Cp,m °

[H°(T) − H°(5)]

[S°(T) − S°(5)]

−Φm °b

K

J·K−1·mol−1

kJ·mol−1

J·K−1·mol−1

kJ·mol−1

560 570 580 590 600 610 620 630

426 427 428 429 431 432 434 435

167 171 175 180 184 188 193 197

629 636 643 651 658 665 672 679

185 191 198 204 211 218 224 231

a

Standard for temperature u(T) = 0.01 K in the temperature range from T = (5 to 344) K, and u(T) = 0.5 K in the interval between T = (320 and 630) K. The standard uncertainty for pressure u(p) = 10 kPa. Combined expanded uncertainties for the heat capacity Uc(Cp,m°) are 0.02, 0.005, 0.002, and 0.02; the combined expanded uncertainties Uc[H°(T) − H°(5)] are 0.022, 0.007, 0.005, and 0.022; Uc[S°(T) − S°(5)] are 0.023, 0.008, ° ] are 0.03, 0.01, 0.009, and 0.03 in the ranges 6 ≤ T/K ≤ 15, 15 ≤ T/K ≤ 40, 40 ≤ T/K ≤ 344, and 320 ≤ T/K ≤ 630, 0.006, and 0.023; Uc[Φm respectively, for 0.95 level of confidence (k ≈ 2). bΦ°m = [H°(T) − H°(5)] − T[S°(T) − S°(5)].

the curves of heat capacities with respect to T and ln T, respectively (Tables 4 and 5), and Φm ° was equal to [H°(T) − H°(5)] − T[S°(T) − S°(5)]. The calculation procedure was described in detail elsewhere.23

respectively. Heat capacities of the samples rise gradually with temperature increase over the main temperature interval. At the same time, heat capacities of both compounds were found to increase with a temperature decrease in the range of (6 to 8) K for NaGdTiO4 and (6 to 10) K for Na2Gd2Ti3O10 (insets in Figures 2 and 3). The experimental points of Cp,m were fitted using least-squares method in the temperature range of (20 to 630) K, and the polynomial equation of the temperature dependency of Cp,m was the following: k

Cp , m =

⎛ T ⎞n ⎟ 30 ⎠

∑ ai⎜⎝ n=0

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CONCLUSIONS This work reports heat capacities of crystalline layered perovskite-like oxides NaGdTiO4 and Na2Gd2Ti3O10 studied over the range of (6 to 630) K. Heat capacity measurements were performed by two different calorimetric methods: precise adiabatic vacuum calorimetry and differential scanning calorimetry. Heat capacity anomalies, which are likely to be associated with magnetic ordering, were observed below 8 K for NaGdTiO4 and below 10 K for Na2Gd2Ti3O10. The standard thermodynamic functions of both compounds over the range of (5 to 630) K were calculated.

(3)

,where ai are polynomial coefficients and k is the polynomial degree. The relative standard uncertainty for the heat capacities was ur(Cp,m) = 0.005 in the temperature range of (20 to 90) K, ur(Cp,m) = 0.0025 between T = (80 to 350) K, and ur(Cp,m) = 0.006 between T = (350 to 630) K. The low-temperature heat capacities of both complex oxides are found not to obey the Debye’s theory. Such anomalies observed in the heat capacity curves are likely to be descending branches for magnetic disorder−order phase transitions,9,20 which lie outside the measuring range of the calorimeter. To give the quantitative description for phase transitions under consideration, magnetic susceptibility measurements as well as heat capacity determined in an external magnetic field are required. However, according to the earlier heat capacity measurements for NaGdTiO4 in the range of (0.5 to 40) K,21 this compound shows a peak at T = 1.74 K originated from magnetic transition. The identical character of temperature dependencies of heat capacities of the two titanates over all studied ranges also points out the similarity of structure of both compounds. Thus, the heat capacity of two titanates reaches the saturation level at the same temperature T ≈ 400 K. The heat capacity of NaGdTiO4 and Na2Gd2Ti3O10 coincides within an experimental error of Cp,m measurements at T < 12 K, since a magnetic component22 provides the main contribution to the total heat capacity in this range. Standard Thermodynamic Functions. As stated above, the extrapolation of heat capacity down to T = 0 K was not performed. For this reason we cannot assume the residual entropy to be zero. Hence, we started to determine standard thermodynamic functions from 5 K. The calculations of H°(T) − H°(5) and S°(T) − S°(5) were made by numerical integration of

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AUTHOR INFORMATION

Corresponding Author

*Fax: +7 831 462 35 59. E-mail: [email protected]. Funding

This work was financially supported by the Russian Foundation for Basic Research (Contract No. 14-33-0676) and the Ministry of Education and Science of the Russian Federation (Contract No. 4.1275.2014/K). Adiabatic measurements were performed in Lobachevsky State University of Nizhni Novgorod. Powder X-ray study was carried out in the X-ray Diffraction Centre of St. Petersburg State University. DSC study was carried out in the Thermogravimetric and Calorimetric Research Centre of St. Petersburg State University. Notes

The authors declare no competing financial interest.

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Heat Capacity and Standard Thermodynamic Functions of NaGdTiO4

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