Heat Capacities of Natural Antlerite and Brochantite at Low Temperature

Article pubs.acs.org/jced

Heat Capacities of Natural Antlerite and Brochantite at Low Temperature Mira R. Bissengaliyeva,†,* Nuraly S. Bekturganov,‡ Daniil B. Gogol,† Shynar T. Taimassova,§ Temirgaly A. Koketai,§ and Michael A. Bespyatov⊥ †

Institute of Complex Development of Mineral Resources, Ippodromnaya Street 5, Karaganda, 100019, Kazakhstan National Scientific-Technological Holding “Parasat”, Republic Avenue 18, Astana, 010000, Kazakhstan § Academician E.A.Buketov Karaganda State University, Universitetskaya Street 28, Karaganda, 100028, Kazakhstan ⊥ Nikolaev Institute of Inorganic Chemistry, Siberian Branch of Russian Academy of Sciences, Akademik Lavrentiev Avenue 3, Novosibirsk, 630090, Russia ‡

S Supporting Information *

ABSTRACT: The investigation of a magnetic component of the heat capacity of natural samples of copper sulfates antlerite Cu3SO4(OH)4 in the temperature range below 40 K and brochantite Cu4SO4(OH)6 below 55 K has been carried out. A regular component of the heat capacity has been calculated from experimental data of adiabatic calorimetry. In the lowtemperature area of (0 to 55) K two peaks of magnetic heat capacity for brochantite have been registered. The contributions of anomalous component ΔStr into entropy of the minerals are (11 ± 3) J·mol−1·K−1 for antlerite and (5.3 ± 1.5) J·mol−1·K−1 for brochantite.

1. INTRODUCTION Natural copper hydroxosulfates antlerite Cu3SO4(OH)4 and brochantite Cu4SO4(OH)6 belong to the sulfate minerals of the oxidation zone of sulfide copper deposits. They are the components of hard-concentrated oxidized ores. Investigation of their physicochemical properties is of some interest for both modern mining industry and research of corrosion processes in copper-containing materials where antlerite and brochantite are intermediate products. The crystalline structure of brochantite is formed by double chains of copper−oxygen octahedrons aggregated into layers by sulfate tetrahedrons.1 The presence of transition metal atoms in the structure of brochantite adds magnetic properties to the mineral. The crystalline structure of antlerite characterized by the presence of triple chains of copper−oxygen octahedrons is described in a work of Hawthorne et al.2 In a number of studies3−6 it was determined that synthetic antlerite is a low-dimensional antiferromagnet, and at Néel temperature TN = 5.3 K it undergoes a phase transition from a low-dimensional state into 3D-state with a long-range magnetic order. This work presents the results of experimental research by the method of adiabatic calorimetry of the heat capacity of a natural antlerite over the temperature range of (4.47 to 324) K. On the basis of the experimental data main thermodynamic functions and a magnetic component of the heat capacity of antlerite have been calculated. In the present work also a contribution of magnetic component and thermodynamic parameters of © 2013 American Chemical Society

magnetic transformation for natural brochantite have been determined on the basis of experimental heat capacity data. The heat capacity and thermodynamic properties of a brochantite sample from the Udokan copper deposit were investigated in a previous work7 by the method of low-temperature adiabatic calorimetry. Hereinafter a brief description of this research is given. The size of crystals did not exceed 24 mm; the color of the mineral was deep emerald-green. The crystalchemical formula Cu3.98Al0.01Ca0.01[SO4]1.00(OH)6.01 calculated on the basis of the results of chemical analysis in Institute of Geology of Ore Deposits, Petrography, Mineralogy and Geochemistry RAS (IGEM RAS) is close to the theoretic one. Investigations of the low-temperature heat capacity of brochantite at (3.8 to 302) K were carried out by means of a vacuum adiabatic calorimeter with periodic input of heat. A weight quantity of brochantite was 3.69 g. A measurement error (according to the results of experiments with a standard substance an electrolytic copper annealed in vacuum) is estimated as 0.03 at T < 20 K, 0.015 at (20 to 60) K, and 0.006 at (100 to 300) K. The standard thermodynamic functions are: Cop298.15 = 328.3 ± 1.8 J·mol−1·K−1, So298.15 = 338.9 ± 5.4 J·mol−1·K−1, Ho298.15 − Ho0 = 53.2 ± 0.6 kJ·mol−1, ΔHof,298.15 = −2053.5 ± 14.9 kJ·mol−1, ΔGof,298.15 = −1683.1 ± 14.9 kJ·mol−1. The presence of a heat capacity anomaly in the area of (5.5 to 8.5) K has been established. Received: February 7, 2013 Accepted: October 8, 2013 Published: October 30, 2013 2904

dx.doi.org/10.1021/je400130b | J. Chem. Eng. Data 2013, 58, 2904−2912

Journal of Chemical & Engineering Data

Article

calculated for three cations is close to the theoretical one; therefore the calculation of thermodynamic properties of the studied mineral was based on its ideal formula Cu3SO4(OH)4. The X-ray phase analysis was carried out in the DRON2 diffractometer using the monochromatic Feα-radiation. The X-ray pattern (Figure 2) confirmed the crystallinity of the investigated sample and its adequacy to mineral antlerite (ASTM database, No. 7407). The results of infrared spectroscopy (Figure 3) obtained with a NICOLET 5700 FTIR (Thermo Electron Corporation) instrument in the Institute of Chemical Sciences named after Bekturov (Almaty) also coincide with the data published earlier.3,10,11 2.2. Calorimetric Measurements. Measurements of the antlerite heat capacity have been performed by the method of adiabatic calorimetry in a low-temperature thermophysical installation produced by CJSC “Termis” (Mendeleevo, Moscow region). The calorimeter uncertainty when measuring a standard sample of the heat capacity measure (copper of the grade OFC) does not exceed ± 0.0144 at 5 K, about ± 0.0023 at 40 K, and less than ± 0.0011 over the range of (80 to 300) K.12 The temperature is measured with an iron−rhodium resistance thermometer RIRT3 (R0 = 50 ohm) calibrated in the VNIIFTRI (National Research Institute for Physicotechnical and Radio Engineering Measurements) in accordance with ITS90. Thermal stability of the cryostate is within ± 0.2 mK near 0.6 K and within ± 2 mK at 300 K. A weighed portion of the sample of antlerite was 1.7307 g; the measurements were carried out in a titanium container (1 cm3 in volume) filled with heat-exchange helium and sealed with a gasket from indium foil. In mode of stage heating 275 experimental points of the specific heat capacity (Table 2) were obtained over the range of (4.47 to 324) K. A magnitude of a temperature stage was 0.2 K over the range of (4.47 to 6) K, 0.5 K at (6 to 10) K, 1 K at (10 to 20) K, 2 K over the interval of (20 to 70) K, and 3 K for the range of (70 to 324) K. The molar mass used when calculating the molar heat capacity was determined from the formula Cu3SO4(OH)4, and it is 354.7308 g·mol−1. The temperature dependence of the molar heat capacity of antlerite is presented in Figure 4. The experimental values of the heat capacity of antlerite over the range of (4.8 to 324) K were smoothed following the method of a spline-approximation13,14 by the third power polynomials of Cp = a0 + a1T + a2T2 + a3T3 form (Table S1 of the Supporting Information). The overlapping of the data span in the regions of the polynomial change was not fewer than 3 to 4 points. Extrapolation of the experimental data to absolute zero was carried out in accordance with the Debye law Cp = aT3. Linearization in coordinates CpT−1 versus T2 was carried out based on the data from the range of (4.4 to 4.8) K. The value of coefficient a is 6.8776 × 10−2 J·mol−1·K−4. Relative deviations of the experimental data on the heat capacity from the smoothed values and the corridor of uncertainty that includes 95 % values are given in Figure F1 of the Supporting Information. Values of entropy ΔT0 Som, enthalpy change ΔT0 Hom and thermodynamic potential Φom are obtained based on the calculated coefficients of the smoothing equations by integrating Cp(T) over the range of (0 to 320) K (Table 3). The standard values of thermodynamic functions of antlerite at T = 298.15 K are: Cop,m = 246.62 ± 0.26 J·mol−1·K−1, ΔT0 Som = 263.46 ± 0.47 J·mol−1·K−1, ΔT0 Hom = 40327 ± 46 J·mol−1.

The anomaly was presumably associated with magnetic transformations resulting in a phase transition with critical temperature of Ttr ≈ 6.3 K; these data are presented in Figure 1 in comparison with data from ref 8 of a synthetic sample of brochantite.

Figure 1. The heat capacity of brochantite in the phase transition area: open diamonds, natural mineral, ref 7; black squares, synthetic sample, ref 8.

It has been established that a synthetic brochantite is a lowdimensional antiferromagnet and at TN ≈ 7 K it undergoes the phase transition from the low-dimensional state into 3D-state with long-range magnetic order.8 Since values of temperatures TN and Ttr are close, then the observed anomaly in the heat capacity can be considered as a reflection of the alteration in the magnetic subsystem. Recently the results of thermodynamic investigations of synthesized basic copper sulfates including antlerite and brochantite were published.9 The heat capacity of the samples was measured by a relaxation calorimetry method. In the article the values of molar heat capacity, entropy and enthalpy change, Gibbs free energy, enthalpy of formation, and equilibrium constants are reported.

2. EXPERIMENTAL DETAILS 2.1. The Analysis of a Sample. A sample of natural antlerite (Zhezkazgan deposit, Central Kazakhstan) in the form of a finecrystalline powder of a light-green color from A.E. Fersman Mineralogical museum RAS (sample No. 57917) was used in the measurements. The monomineralic fraction of the sample was prepared by hand with using of a binocular microscope, Carl Zeiss, Stemi-2000C. A chemical analysis of antlerite (Table 1) Table 1. The Chemical Analysis of Antlerite

a

composition

chemical formula

mass fraction

analysis method

copper(II) oxide sulfur(III) oxide phosphorus(V) oxide water

CuO SO3 P2O5 H2O

0.668 0.226 0.003 0.107

EDXa TGb EDX TG

X-ray microanalysis. bThermogravimetry.

was performed by the X-ray spectrum method using a microprobe analyzer “Camebax SX-50” at the mineralogy chair of geology department of M.V. Lomonosov Moscow State University; the content of sulfur trioxide and water was determined according to the data of a thermal analysis on a derivatograph “Q-1500 D” (Hungary). The obtained chemical formula 2905



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Figure 2. X-ray diffractogram of the antlerite sample. The numbers in the figure corresponds to the interplanar distances d/Å.

Figure 3. The infrared spectrum of the antlerite sample.

3. DISCUSSION OF THE RESULTS The experimental heat capacity Cp in the temperature range from (0 to 40) K for antlerite and from (0 to 55) K for brochantite has two components: magnetic Cm and lattice CL, that is, Cp = CL + Cm. Above these temperatures according to the data on magnetic susceptibility,3,8 destruction of magnetic ordering occurs and only the lattice component contributes to the experimental heat capacity. To distinguish Cm it is necessary to calculate CL in the range from (0 to 40) K for antlerite and from (0 to 55) K for brochantite (assuming that Cp ≈ CV at low temperatures). For this purpose the experimental heat capacity was extrapolated according to the equation proposed in refs 15 and 16: ⎛ C L ⎞m ⎜1 − ⎟ = K ⎝ 3Rn ⎠ T3

CL

(1)

Figure 4. The experimental molar heat capacity of antlerite.

where T is temperature (K), CL is the lattice heat capacity (J·mol−1·K−1), n is the number of atoms in a molecule, K is the constant related to the Debye characteristic temperature (J·mol−1·K4), and m is an empirical coefficient. Taking the logarithm of both parts of the equation we obtain ⎛C ⎞ ⎛ C ⎞ ln⎜ L3 ⎟ = m ln⎜1 − L ⎟ + ln K ⎝T ⎠ ⎝ 3Rn ⎠

dependence. Correctness of the eq 2 has been verified by the authors in refs 15 and 16 using a great amount of experimental materials. The experimental heat capacity of antlerite and brochantite in coordinates ln(Cp/T3) versus ln(1 − Cp/(3Rn)) is given in Figure 5. It can be seen that the heat capacity is well described by the eq 2 in the temperature range of (40 to 80) K for antlerite and (55 to 100) K for brochantite. A systematic deviation from the linear dependence associated with the presence of the magnetic

(2)

In coordinates ln(Cp/T3) versu ln(1−Cp/3Rn) the heat capacity in a wide range of temperatures acquires an appearance of a linear 2906



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Table 2. The Experimental Values of the Specific Heat Capacity of Antleritea Cp/J·g−1·K−1

T/K Series 1 Series 1 4.3209b 4.5708 4.9442 5.2177 5.4958 5.8181 6.1472 6.5658 7.0992 7.6351 8.1591 8.6704 9.1719 9.6682 10.16 10.926 11.978 13.03 14.06 15.073 16.075 17.071 18.06 19.042 20.025 21.495 23.464

Series 2 17.795 18.778 19.76 21.224 23.179 25.153 27.122 29.089 31.061 33.034 35.009 36.985 38.96

0.013889 0.018787 0.024962 0.028724 0.027502 0.022367 0.020395 0.019158 0.018215 0.017543 0.017073 0.016733 0.016506 0.016344 0.016158 0.016159 0.01621 0.01649 0.01711 0.018021 0.018949 0.020064 0.021641 0.023222 0.024901 0.028157 0.032467

0.021206 0.022798 0.02444 0.027568 0.031733 0.036716 0.042261 0.048313 0.054549 0.060938 0.067525 0.074281 0.081593 Series 3

34.808 37.092 39.071 41.044 43.018 44.993 46.973 48.952 50.931 52.909 54.890b 56.878 58.869b 60.857 62.844 64.836 66.821 68.81 70.809 73.307 76.313 79.328 82.354

Series 2 4.2757b 4.4671 4.7508 4.9439 5.1091 5.2813 5.4611 5.6589 5.8637 6.0583 6.2978 6.5917 6.8889b 7.18 7.4595 7.7432 8.0239 8.3041 8.5853 8.8658 9.1436 9.4205 9.6964 9.9718 10.628 11.683 12.744 13.783 14.802 15.806 16.805

Cp/J·g−1·K−1

T/K

0.010909 0.017078 0.02072 0.025043 0.027194 0.029016 0.028275 0.024278 0.021823 0.020756 0.019858 0.018857 0.017362 0.018032 0.017658 0.017399 0.017136 0.016955 0.01679 0.016604 0.016465 0.016305 0.016204 0.016221 0.016195 0.016179 0.016378 0.016884 0.017717 0.018706 0.019664

0.066708 0.074788 0.08199 0.089174 0.096164 0.10329 0.11019 0.11715 0.12456 0.13245 0.13989 0.1457 0.15185 0.15985 0.16686 0.17338 0.1798 0.18617 0.19236 0.20057 0.21009 0.21945 0.22879 Series 4

79.149 82.874 85.917 88.965 92.019 95.083 98.16 101.24 104.33 107.42 110.53 113.64 116.76 119.89 123.02 126.17 129.34 132.5 135.67 138.84 142.03 145.22 2907

0.21847 0.22993 0.23909 0.2481 0.25703 0.26611 0.27479 0.28348 0.29226 0.30054 0.309 0.31737 0.3256 0.33396 0.34274 0.35079 0.35957 0.36732 0.37558 0.38449 0.39264 0.40069



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Table 2. continued T/K

Cp/J·g−1·K−1

T/K

0.40852 0.41662 0.42454 0.43172 0.43909 0.44649 0.45467 0.46129 0.46942 0.47636 0.48375 0.49072 0.49778 0.5046 0.51165 0.51885 0.52541 0.53196 0.53845 0.54465 0.55054 0.55707 0.56339 0.56974 0.57603 0.5823 0.58885 0.59454 0.60073 0.6062 0.61198 0.61753 0.62374 0.62953 0.63492 0.64011 0.64576 0.65085 0.65493 0.66063 0.66589 0.6706 0.67643 0.67997 0.6831 0.68721 0.69292 0.69775 0.70205 0.70622 0.70994 0.71389 0.71748 0.72116 0.72459 0.72777

97.528 100.62 103.71 106.81 109.92 113.05 116.17 119.31 122.46 125.61 128.76 131.93 135.11 138.3 141.49 144.68 147.87 151.08 153.75 155.89 158.03 160.17 162.32 164.47 166.62 168.77 170.92 173.08 175.23 177.4 179.56 181.72 183.88 186.04 188.2 190.37 192.53 194.69 196.86 199.04 201.21 203.39 205.57 207.76 209.94 212.16 214.35 216.54 218.74 220.93 223.12 225.3 227.48 229.65 231.82 233.99 236.16 238.32 240.47 242.63

Series 4 148.42 151.63 154.85 158.08 161.31 164.54 167.79 171.04 174.3 177.57 180.86 184.14 187.43 190.73 194.03 197.33 200.64 203.96 207.29 210.62 213.96 217.3 220.63 223.97 227.29 230.62 233.94 237.24 240.54 243.84 247.12 250.39 253.64 256.89 260.12 263.34 266.52 269.68 272.8b 275.92 278.99 282.03 284.97b 287.96 290.92 293.88b 296.81 299.68 302.54 305.37 308.18 310.97 313.74 316.5 319.23 321.95

Series 5

Series 5 87.611 91.375 94.444

Cp/J·g−1·K−1

0.24432 0.25498 0.26409 2908

0.27279 0.28148 0.29005 0.29859 0.30739 0.31577 0.32401 0.33283 0.34064 0.34894 0.35742 0.36579 0.37379 0.38289 0.39039 0.39834 0.40689 0.41483 0.42052 0.42569 0.431 0.43676 0.44096 0.44576 0.45057 0.45589 0.4607 0.46557 0.46995 0.47528 0.47905 0.48354 0.48911 0.49309 0.49865 0.50345 0.50698 0.51292 0.51763 0.52171 0.52465 0.53069 0.53467 0.53712 0.54272 0.54628 0.55103 0.55557 0.55966 0.56215 0.56598 0.57153 0.57498 0.58005 0.58444 0.58884 0.59233 0.5962 0.60059 0.60409



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Table 2. continued T/K

Cp/J·g−1·K−1

T/K

0.60743 0.61027 0.61443 0.61915 0.62314 0.62686 0.63045 0.63389 0.63721 0.64099 0.64286 0.64703 0.65123 0.65446 0.65802 0.65965 0.66412 0.66855 0.67112 0.67404

286.57 288.59 290.6 292.61 294.6 296.58 298.56 300.53 302.49 304.44 306.39 308.34 310.27 312.09 314.01 315.94 317.86 319.77 321.68 323.58

Series 5 244.78 246.91 249.05 251.18 253.31 255.43 257.55 259.67 261.78 263.89 265.99 268.1 270.18 272.26 274.34 276.41 278.48 280.47 282.51 284.55

Cp/J·g−1·K−1 Series 5 0.67737 0.68117 0.68406 0.68655 0.68956 0.69245 0.69533 0.69811 0.70114 0.70384 0.70645 0.70895 0.71144 0.71532 0.71668 0.71895 0.72145 0.72354 0.72609 0.72835

Uncertainties of temperature measurements are u(T) = ± 0.2 mK at 0.6 K and u(T) = ± 2 mK at 300 K; for heat capacity u(Cp) = ± 0.0409 T − 0.697 (level of confidence = 0.95). bPoints, which are not included into the set of data for smoothing.

a

Figure 5. Description of the heat capacity according to the eq 2: (a) antlerite, (b) brochantite. Black circles are the experimental data; a dashed line is the assumed behavior of the lattice component.

Figure 6. The heat capacity in the area of phase transition: (a) antlerite, (b) brochantite. Black circles are the experimental data; a dashed line is the lattice component of the heat capacity obtained by eq 1.

data on the lattice component CL are obtained, it is possible to calculate the magnetic component Cm from the difference between the experimental and lattice heat capacity. The contribution into the heat capacity associated with magnetic ordering is given in Figure 7. In Figure 7b it is seen that in the extracted magnetic component two peaks with maxima at temperatures T ≈ 6.3 K

contribution into the heat capacity is seen below these temperatures. An extension of the linear dependence in the area of low temperatures defines the regular lattice component by means of extrapolation. These values can be obtained both by the least-squares method and in a graphical form. A dashed line in Figure 6 denotes the regular lattice component calculated according to eq 1. When the 2909



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(Cu3 + Cu4) from the 1D to the 3D state). The authors of ref 8 also state that the behavior of magnetic susceptibility observed by them at temperatures below 40 K is typical for the formation of ferromagnetic clusters, which occur from ferromagnetic coupling of individual chains. The values of the regular lattice and magnetic heat capacity for antlerite and brochantite are given in Tables S2, S3, S4 and S5 of the Supporting Information. To calculate entropy of the distinguished magnetic component ΔS, it is necessary to obtain information on the behavior of Cm in the range from (4 to 0) K. Below TN antlerite and brochantite are known to behave as 3D-ordered antiferromagnets, correspondingly, thermal excitation of magnon near zero makes a contribution into the heat capacity proportional to T3. In Figure 8 it is seen that Cm ∼ T3 is indeed a good approximation for Cm at temperatures below 4 K: The experimental points presented in coordinates Cm vs T3 come on the straight line passing through the origin of coordinates. The values of magnetic heat capacity resulting from extrapolation from T = (4 to 0) K are also presented in Figure 7 (a dashed line). Entropy of the magnetic component of brochantite obtained in the result of integrating dependence Cm/T versus T in the range of (0 to 55) K is SM = 5.3 ± 1.5 J·mol−1·K−1. This value is rather close to theoretical value of R ln 2. In ref 8 the authors also estimated the entropy value slightly more than R ln 2 and noted that it is far from expected 4R ln 2. The possible explanation of this fact is that the copper chains in the brochantite structure undergo magnetic ordering as a comprehensive whole. The uncertainty of the SM entropy value is determined, first of all, by an extrapolation error of the lattice component in the range from (55 to 0) K. The entropy of magnetic component of antlerite, also having been determined by means of integration of the dependence Cm/T versus T over the range (0 to 40) K, is SM = 11 ± 3 J·mol−1·K−1. Uncertainty of the entropy SM value is due to an error of extrapolation of the lattice component from (40 to 0) K. In accordance with refs 3 and 4 a magnet structure of antlerite can be imagined in the form of triple chains of Cu2+, separated by sulfate groups. Magnetic moments of copper ions (with spin s = 1/2), belonging to the outer chains orientate themselves in ferromagnetic order inside the chain, and they orientate themselves in antiferromagnetic order between two outer chains, while antiferromagnetic ordering of magnetic moments of copper ions is observed along the central magnetic chain. In this respect, maximal value of magnetic entropy Smax M , connected with changing of ordering of magnetic moments of three copper atoms (s = 1/2) in Cu3(OH)4(SO4) must be equal to Smax M = 3R ln(2s + 1) = 17.2 J·mol−1·K−1. The value of magnetic entropy SM obtained by us significantly differs from the theoretical one (17.2 J·mol−1·K−1), but it is very close to value 2R ln 2 (11.5 J·mol−1·K−1). References 3 and 5 report that below 5.3 K, in transition from the 1D state to the 3D state, the spins of copper atoms in the central chain do not participate in stabilization of a long-range ordering. On the basis of the data of neutron spectroscopy3 the zero moment has been suggested, and this unusual magnetic behavior is associated with an idle-spin state. In Figure 9 the comparison of our heat capacity data for natural antlerite and brochantite with values for synthetic samples from ref 9 is presented. The authors of ref 9 used for fitting and component extraction the equation which included the lattice heat capacity polynomial, Schottky anomaly term, and magnetic contribution to Cp. Although the authors of ref 9 extracted the

Table 3. Thermodynamic Functions of Antlerite T K 4 4.5 5 6 7 8 9 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 260 270 273.15 280 290 298.15 300 310 320

ΔT0 Som

Cp,m J mol

−1

−1

K

4.402 6.267 9.138 7.452 6.491 6.095 5.868 5.750 6.341 8.850 12.91 18.13 24.00 30.19 36.59 43.07 49.46 55.63 61.62 67.43 73.06 78.53 83.89 89.13 94.27 99.30 109.1 118.6 128.1 137.4 146.3 154.8 162.9 170.9 178.5 185.9 192.8 199.5 206.1 212.7 218.9 225.1 231.1 232.9 236.7 242.2 246.6 ± 0.3 247.6 252.8 257.4

J mol

−1

K

−1

1.467 2.089 2.882 4.557 5.618 6.456 7.160 7.770 10.15 12.27 14.66 17.46 20.69 24.29 28.22 32.41 36.81 41.38 46.07 50.85 55.70 60.59 65.51 70.45 75.41 80.38 90.30 100.2 110.1 119.9 129.7 139.4 149.0 158.6 168.0 177.4 186.6 195.7 204.7 213.7 222.5 231.2 239.8 242.5 248.3 256.7 263.5 ± 0.5 265.0 273.2 281.3

ΔT0 Hom/T

Φom

−1

−1

J mol−1 K−1

1.100 1.567 2.166 3.328 3.834 4.139 4.343 4.488 4.952 5.573 6.614 8.083 9.932 12.07 14.44 16.98 19.64 22.39 25.18 27.99 30.81 33.62 36.42 39.20 41.97 44.71 50.12 55.43 60.66 65.81 70.88 75.86 80.74 85.53 90.23 94.83 99.33 103.7 108.0 112.3 116.4 120.5 124.5 125.7 128.4 132.2 135.3 ± 0.2 135.9 139.6 143.2

0.3668 0.5223 0.7167 1.228 1.783 2.317 2.817 3.282 5.195 6.696 8.044 9.373 10.75 12.22 13.77 15.43 17.17 18.99 20.90 22.87 24.89 26.97 29.09 31.25 33.45 35.67 40.18 44.77 49.42 54.10 58.82 63.55 68.30 73.05 77.80 82.54 87.28 92.00 96.71 101.4 106.1 110.7 115.3 116.8 119.9 124.5 128.2 ± 0.4 129.0 133.6 138.0

J mol

K

and T ≈ 18 K for brochantite are observed. In ref 8 the investigation of brochantite magnetic susceptibility in the temperature range from (2 to 300) K has been carried out. At temperatures 7 K and 18 K two anomalies are also noted in the curve of magnetic susceptibility.8 They are similar in shape, and the authors associate them with establishment of a long-range magnetic order at a temperature decrease (apparently it is a stepwise transition of coupled copper chains (Cu1 + Cu2) and 2910



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Figure 7. The contribution into the heat capacity associated with magnetic ordering: (a) antlerite, (b) brochantite. Black circles are experimental points; a dashed line represents the extrapolated values (Cm ∼ T3).

Figure 8. The experimental heat capacity at temperature below 8 K: (a) antlerite, (b) brochantite. A dashed line corresponds to Cm ∼ T3.

Figure 9. The comparison of heat capacity data measured by quasi-adiabatic and relaxation calorimetry for (a) antlerite and (b) brochantite. (a) Antlerite: open diamonds, experimental Cp, this paper; open squares, extracted magnetic contribution, this paper; black squares, experimental Cp, ref 8; gray circles, extracted magnetic contribution, ref 8; open circles, experimental Cp, ref 9; solid line, fitted data, ref 9. (b) Bronchantite: open diamonds, experimental Cp, ref 7; open circles, experimental Cp, ref 9; solid line, fitted data, ref 9.

4. CONCLUSIONS A regular lattice heat capacity and magnetic component of lowtemperature heat capacity of natural antlerite and brochantite have been determined as a result of the carried out experiments. The standard thermodynamic functions of antlerite have also been determined on the basis of the results of experimental measurements of the antlerite heat capacity. The presence of two maxima are seen in the temperature dependence of the magnetic component of the heat capacity of brochantite. This fact supports a gradual ordering of magnetic moments in brochantite from the 1D to the 3D state.

magnetic component of the heat capacity for antlerite and brochantite, they does not give the values of the entropy of magnetic transitions for these compounds. It can be seen from Figure 9 that values measured by relaxation calorimetry give less clear and sharp peaks at low temperatures than data obtained by quasi-adiabatic calorimetry. Also, two peaks in the magnetic heat capacity for brochantite are not observed in ref 9. In consideration of these facts, the extracted magnetic contribution to the heat capacity of antlerite and brochantite in ref 9 seems underestimated. 2911



Article

(9) Zittlau, A. H.; Shi, Q.; Boerio-Goates, J.; Woodfield, B. F.; Majzlan, J. Thermodynamics of the basic copper sulfates antlerite, posnjakite, and brochantite. Chem. Erde, Geochem. 2013, 73, 39−50. (10) Gadsden, J. A. Infrared Spectra of Minerals and Related Inorganic Compounds; Butterworths: London, 1975. (11) Martens, W.; Frost, R. L.; Kloprogge, J. T.; Williams, P. A. A Raman spectroscopic study of the basic copper sulfates-implications for copper corrosion and “bronze disease”. J. Raman Spectrosc. 2003, 34, 145−151. (12) Bissengaliyeva, M. R.; Gogol, D. B.; Taymasova, Sh. T.; Bekturganov, N. S. Measurement of heat capacity by adiabatic calorimetry and calculation of thermodynamic functions of standard substances: copper, benzoic acid, and heptane (for calibration of an adiabatic calorimeter). J. Chem. Eng. Data 2011, 56, 195−204. (13) Iorish, V. S.; Tolmach, P. I. The technique and program of lowtemperature heat capacity experimental data proceeding with using approximating spline. Zh. Fiz. Khim. 1986, 60, 2583−2587 In Russian. (14) Titov, V. A.; Chernyavskii, L. I.; Voronin, I. A.; Kornilov, A. N. On the spline approximation of low-temperature calorimetry data. Russ. J. Phys. Chem. A 2006, 80, 1025−1028. (15) Krestov, G. A.; Yatsimirsky, K. B. Thermodynamics characteristics of the compositions of cobalt (III) of chlorpentamine type. Zh. Neorg. Khim. 1961, 6, 2294−2303 In Russian. (16) Melia, T. P.; Merrifield, R. J. Thermal properties of transition metal compounds: Heat capacity, entropy, enthalpy, free energy and heat of fusion of the tris (acetylacetonato) complexes of scandium(III), vanadium(III), manganese(III), iron(III) and cobalt(III) and the vapour pressure of tris(acetylacetonato) iron(III)−IV. J. Inorg. Nucl. Chem. 1970, 32, 2573−2579.

The values of entropy of the magnetic phase transition in antlerite and brochantite have been determined. The value for brochantite (5.3 ± 1.5 J·mol−1·K−1) is close to the value of R ln 2. For antlerite the value of entropy (11 ± 3 J·mol−1·K−1) corresponds to 2R ln 2. These values are less than theoretical ones. In the case of brochantite this fact allows the supposition that copper chains undergoe the magnetic transformation as a whole. For antlerite it may be suggested that a cause of discrepancy between the obtained values of magnetic entropy SM and Smax M is connected with the idle-spin state phenomenon, and value SM ≈ 2R ln 2 points to the fact that two ions of copper (belonging to the side chains) in a molecule take part in magnetic ordering, while one ion of copper belonging to the central chain does not.

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ASSOCIATED CONTENT

S Supporting Information *

Polynomial coefficients of the antlerite heat capacity, regular lattice, and magnetic heat capacity for antlerite and brochantite, and deviations of the experimental values of antlerite heat capacity. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]; [email protected]. Notes

The authors declare no competing financial interest. Funding

This research was performed within the scientific Grant 0615/ GF-2 “Research of fundamental thermodynamic and thermochemical parameters of oxygen-containing natural compounds of non-ferrous metals” of the Science Committee of the Ministry of Education and Science of Republic of Kazakhstan.

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REFERENCES

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Heat Capacities of Natural Antlerite and Brochantite at Low Temperature

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