Low-temperature molar heat capacities and entropies of MnO2 (pyrolusite), Mn3O4 (hausmanite), and Mn2O3 (bixbyite)

Low-temperature molar heat capacities and entropies of MnO, (pyrolusite), Mn,O, (hausmanite), and Mn,O, (bixbyite) RICHARD

A. ROBIE

U.S. Geological

and BRUCE

Survqv. R&on,

S. HEMINGWAY

VA 22092, U.S.A.

[Received 10 May 1984; in revised-form

23 Ju1.y 1984)

Pyrolusite (MnO,), hausmanite (Mn,O,), and bixbyite (Mn,O,), are important ore minerals of manganese and accurate values for their thermodynamic properties are desirable to understand better the jp(O,), 7’) conditions of their formation. To provide accurate values for the entropies of these important manganese minerals, we have measured their heat capacities between approximately 5 and 380 K using a fully automatic adiabatically-shielded calorimeter. All three minerals are paramagnetic above 100 K and become antife~omagnetic or ferromagnetic at lower tem~ratures. This transition is expressed by a sharp h-type anomaly in q. m for each compound with Neel temperatures TN of (92.2*0.2), (43.1*0.2), and (79.45+0.05) K for MnO,, Mn,O,, and MnaOa, respectively. In addition, at T z 308 K, Mn,O, undergoes a crystallographic transition, from orthorhombic (at low temperatures) to cubic. A significant thermal effect is associated with this change. Hausmanite is ferrimagnetic below TN and in addition to the normal h-shape of the heat-capacity maxima in MnO, and Mn,O,, it has a second rounded maximum at 40.5 K. The origin of this subsidiary bump in the heat capacity is unknown but may be related to a similar “anomalous bump” in the curve of magnetization against temperature at about 39 K observed by Dwight and Menyuk.“’ At 298.15 K the standard molar entropies of MnO,, Mn304, and Mn,O,, are (52.75+0.07), (164.1+0.2), and (113.7kO.2) J.K-’ .moll’, respectively. Our value for Mn,O, is greater than that adopted in the National Bureau of Standards tables@) by 14 per cent.

1. rntr~~ction Accurate values for the thermodynamic properties of the manganese-ore minerals are necessary for understanding the conditions of temperature, pressure, and oxygen fugacity of their formation and for determining the most energy-efficient procedures for the extraction of manganese from the different types of ore. Equilibria between the different oxides of manganese, in particular

4Mn,O,(cr,

hausmanite)+

O,(g) = 6Mn,O,(cr,

bixbyite),

(1)

hausmanite)

12)

and 6“MnO”(cr,

manganosite) + O,(g) = 2Mn,O,(cr,

are frequently used as “buB’ers” to control the fugacity of oxygen in mineralogical equilibrium experiments (see for example Huebner).‘3’ 0021-9614/85/020165+

17 %02.00/O

$1 1985 Academic Press Inc. (London) Limited

166

R. A. ROBIE AND B. S. HEMINGWAY

Many of the earlier measurements of the heat capacities for manganese compounds extended down to only 50 K. As a consequence entropies obtained by extrapolating these values smoothly to T -+ 0 may be incorrect because of the occurrence of a paramagnet~c-to~antiferromagnetic transition at temperatures less than 50 K. The slopes of the equilibrium curves for (1) and (2) can be determined more precisely from the calorimetric entropies and heat capacities than they can from the measured temperature dependence of the equilibrium constants themselves. The heat capacity of MnO, (pyrolusite) has been measured previously by Kelley and Moorec4) between 53.5 and 294.7 K, and by Millar@’ from 72.5 to 293.8 K, and Moore’@ has measured {H;(T) - &,(298.15 IQ] up to 778 K. Kingc7) measured of MnzO, (bixbyite) between 54.4 and 296.2 I(, and Orr@’ has measured ;i;T)_H”(298 15 K)} up to 1350 K. The onl; previously published Ci, m measurements for Mn,O, are those of M~~lar(‘) between 72.2 and 305.4 K and the cnth~py-increment measurements of Southard and Moore”’ which extended up to 1769 K. Additionally Shornate has measured the molar enthalpies of formation of Mn,O, and MnO, by sulfuric-acid solution calorimetry. Because of the above-mentioned possibility for errors in the currently accepted values for the entropies of the manganese oxides and so as to reduce the uncertainties in the temperature dependence of the buffer reactions (1) and (2) (see figures 4 and 7 of Schaefer),“” we believe that C&, measurements on well characterized materials extending downwards to 5 K are highly desirable.

2. Experimental MATERIALS

Pyrolusite (MnO,) is tetragonal and has the same crystal structure as rutile. The sample used for our heat-capacity measurements was Baker Analyzed Reagent 8392. This material was in the form of spherical polycrystalline aggregates with diameters between 0.15 and 0.05 mm. X-Ray unit-cell parameters for this material are a = (0.4387 f 0.0005) and c = (0.2860 + 0.0002) nm. The sample mass was 89.268 g. Hausmanite (Mn,O,) is a distorted (tetragonal) spine1 up to 1445 K above which it inverts to a cubic modification. Our heat-capacity sample was prepared from Baker Analyzed Reagent 8392 MnO, by heating in a platinum-lined ceramic boat in air at 1273 K for 68 h and then cooling in air. Hausmanite is transparent and exhibits a deep red to orange-red color in transmitted light whereas MnO, and Mn,O, are opaque and MnO is emerald green. Thus optical examination is a very sensitive method for determining phase purity. Unit-cell parameters for our calorimetric sample were a = (0.5756+0.0005) and c = (0.9441 rt:O.O003) nm. The sample mass was 69.782 g. Mn,O, was prepared from Baker Analyzed Reagent 8392 MnO, heated at (1083 _+10) K for 66 h in a platinum crucible (in air) and quenched in liquid nitrogen. X-Ray and microscopic investigation indicated pure single-phase orthorhombic Mn,O,. Bixbyite is nominally cubic Mn,O,, but pure Mn,O, is

Si OF MnO,, Mn,O,, AND Mn,O,

167

172 12 Heater

Power SUPPlY HP 6115A

l---l-l d.v.m. HP 3456A

I

Scanner HP 3495A

I

I IEEE-488

Printing terminal HP 2635A

I

I

Bus

D-to-A converter HP 59303A

(704 Chart recorder HP 7123A

FIGURE 1. Block diagram of automatic data-acquisition system for low-tem~rature

caiorimetry.

cubic only above 308 K; below this temperature it readily inverts to the orthorhombic modification according to Geller and Espinosa.t12) The cubic form can be stabilized at tem~ratures below 308 K by the addition of small amounts of iron, as shown by Grant, Geller, Cape, and Espinosa.‘13) The sample was sieved and the fraction between 0.1 and 0.15 mm was saved for Ci, m measurements. The sample mass was 79.396 g. APPARATUS

AND MEASUREMENTS

Our heat-capacity measurements were made using a fully automatic dataacquisition system. The current version of this system is shown in figure 1. The system is under the control of, and all calculations are performed by, the Hewlett

R. A. ROBIE AND B. S. HEMINGWAY

168

TABLE 1. Experimental molar heat capacities of MnO, (pyrolusite). M = 86.9368 g. mol- r T E

6.00 8.59 9.62 10.60 11.74 13.06 14.50 16.10 17.86 19.80 21.96 24.38 27.08 30.10 33.50 37.30 41.55 46.32 51.18 55.91 60.66 65.30 69.51 73.19 76.65 79.97 83.22 86.42 89.51 92.41

c;.m J.K-'.mo]--~i

Series 1 0.005 0.027 0.035 0.047 0.063 0.084 0.115 0.161 0.230 0.325 0.463 0.662 0.944 1.343 1.895 2.651 3.597 4.807 6.170 7.650 9.331 11.12 12.89 14.59 16.37 18.31 20.60 23.80 29.83 41.39”

T

Gin

K

J.K-‘,moil’

95.61 99.16 102.18 104.87 107.84 110.98 114.12 117.28 120.43 123.58 126.72 129.86 132.98 136.12 139.23 142.34 145.45 148.55 151.64 154.73 157.81 160.89 163.96 167.02 170.08 173.13 176.17 179.20 85.03 86.79

21.95 22.61 22.11 22.14 22.4 1 22.84 23.37 23.93 24.54 25.13 25.79 26.44 27.17 27.78 28.43 29.16 29.78 30.48 31.16 31.84 32.49 33.12 33.74 34.37 35.06 35.54 36.18 36.84

Series 2 22.27 24.18

T

K 88.22 89.66 91.15 92.64 94.39 96.29 97.90 99.27 90.94 91.08 91.23 91.38 91.53 91.69 91.85 92.00 92.16 92.32 92.48 92.64 92.79 92.95 93.10 93.26 93.42 93.57 93.73 93.89 94.04 94.20

G.m

J.K-i.mol-i 26.39 29.94 37.72 43.42 32.87 25.09 23.25 22.56 Series 3 34.98 35.56 38.00 39.38 41.09 41.93 43.68 45.69 47.40 45.99 a 46.04 43.69 43.34 40.91 39.86 40.08 39.49 36.36 35.91 35.74 35.33 35.09

T

c;. m

T

q, m

K

J.K-i.moIl’

K

J.K-‘.mol-’

94.36 94.52 94.68 94.84 94.99 95.15 95.31 95.46 95.62 95.78 95.94 96.10 96.26 96.42 96.58 96.74 96.90 97.06 97.21 97.37 97.53

33.78 32.08 31.28 30.47 28.78 27.65 27.69 28.28 27.06 27.24 26.01 24.79 25.09 25.45 24.29 23.77 23.70 23.54 23.53 23.41 23.22

175.12 180.65 185.79 190.99 196.43 201.87 207.30 212.72 218.14

Series 4 36.02 37.13 38.13 39.12 40.14 41.07 42.06 43.07 43.94

223.55 228.96 234.37 239.78 245.18 250.56 255.94 261.30 266.65 271.98 277.30 282.61 287.92 293.21 298.50 303.77 309.03 314.28 31952 324.74 329.96 335.17 340.38 345.56 350.74 355.92 361.08 366.24 371.37 376.50

44.89 45.79 46.58 47.45 48.18 48.97 49.62 50.41 51.03 51.82 52.29 53.06 53.65 54.32 54.78 55.40 56.10 56.42 56.89 57.47 57.94 58.27 58.77 59.26 59.84 60.13 60.54 60.8 1 61.21 61.64

* Temperature rise straddled the maximum in C;. m

Packard 9825Ti computer. The digital voltmeter replaces the potentiometer, and the scanner replaces the selector switch of the older manually operated system described by Robie, Hemingway, and Wilson. (14) The digital voltmeter has a sensitivity of 100 nV for a 100 line-cycle integration period (i.e. 1.66 s), and has an accuracy of 0.~2 per cent fuli scale. Between 30 and 385 K the precision of a standard heat-capacity measurement, i.e. AT = 3 to 5 K, is between 0.05 and 0.02 per cent using a 1 mA current through the thermometer. Below 35 K the thermometer current is increased automatically to 3 mA, to compensate in part for the decreasing sensitivity of the platinum thermometer. At 10 K the precision of a measurement is 0.8 per cent for a temperature rise of 1 K. In the immediate t Use of trade names in this report is for descriptive purposes only does not constitute endorsement by the U.S. Geological Survey.

Sk OF MnO,, Mn,O,, AND Mn,O,

169

neighborhood of a lambda transition we reduce the temperature increases to about 0.2 K so as to map out the h-peak in as much detail as possible. This in turn reduces the precision of the Ci,, measurements to about 1 per cent.

3. Results Our experimental results are listed in chronological order of measurement in tables 1, 2, and 3 for MnO,, Mn,O,, and Mnz03, respectively. MnO, (pyrolusite) is paramagnetic above 92.2 K. Below this temperature (TN) the

TABLE 2. Ex~~m~atal

T K Series 1 5.65 0.110 6.25 0.167 6.81 a.244 7.36 0.249 8.26 0.400 0.551 9.09 0.834 10.06 11.22 1.190 12.48 1.631 13.93 2.258 15.50 3.039 17.21 4.004 19.24 5.205 6.657 21.42 23.85 8.472 26.52 10.84 29.46 14.16 32.68 19.35 28.28 35.22 36.69 37.69 38.49 39.23 39.89 40.42 40.94 41.41 41.84 42.26 42.66 43.09 43.74 44.54

Series 2 32.60 37.59 44.75 49.19 54.38 54.46 55.31 60.90 70.03 84.78 106.2 106.3 53.86 27.66

molar heat capacities of MnsO, (hausmanite), M = 228.8116 g.mol-*

c;,m J.K-r.mol-’

45.25 45.90 46.75 47.76 48.81 49.88

24.78 24.12 24.04 24.42 24.73 25.24

39.72 39.94 40.13 40.33 40.56 40.78 40.99 41.21 41.42 41.64 41.85 42.06 42.27 42.48 42.69 42.90 43.12 43.39

Series 3 53.76 55.42 55.55 55.45 54.38 54.59 56.51 58.33 60.89 65.22 70.48 77.07 87.12 99.26 111.9 118.4 121.4 119.7”

43.48 43.78 44.03 44.23 44.41 44.76 45.28 45.80 46.61

Series 4 75.67 49.16 36.38 31.22 28.41 26.12 25.96 24.24 24.06

y Large temperature drifts.

T

qhn

T

K

J.K-r.mol-’

K

47.67 48.72 49.79 50.88 51.96 53.05 56.34 61.77 67.36 73.27 79.24 85.19 91.11

24.20 24.62 25.09 25.61 26.12 26.88 29.19 32.96 37.06 41.50 45.93 SO.27 54.47

Series 6 b 69.74 38.63 74.63 42.35 46.06 79.62 84.88 49.80 90.79 54.00 96.66 58.15 102.52 62.15 108.34 66.15 114.12 69.81 119.83 73.56 f 25.48 77.15 131.09 80.66 136.65 83.89 142.15 86.97 147.61 90.04 153.02 92.77 158.37 95.72 163.67 98.52 168.93 101.0 174.14 103.5 179.30 106.1 184.43 108.3

cy+m J.K-‘.mol-’

189.53 194.58 199.61 204.59 209.55 214.54 219.57 224.57 229.57

110.4 112.3 114.3 116.2 lf8.3 120.0 121.8 123.5 125.1

234.47 239.28 244.14 249.07 253.92 258.78 263.62 268.43 273.23

Series 7 126.7 127.9 129.6 131.0 132.7 134.1 134.8 135.9 137.2

280.15 285.26 290.10 294.95 299.69 304.43 309.17 313.90 318.63 323.37 328.10 332.84 337.58 342.35

Series 8 138.7 139.9 140.9 141.9 142.8 143.9 145.1 145.8 146.7 147.3 148.5 149.3 149.7 150.4

b Series 5 deleted because of instrument failure.

T -L---..c; m

K

J.K-‘.mol-’

346.87 351.67 356.51 361.35 366.15 370.94 375.73 380.52

Series 9 151.3 152.0 152.4 152.8 153.8 154.7 155.1 155.8

Series 10 210.55 118.5 215.76 120.4 220.70 122.0 225.65 123.9 230.55 125.5 235.44 127.0 240.3 1 128.6 245.16 130.2 250.01 131.3 254.85 132.7 259.71 133.9 264.59 135.2 269.48 136.1 274.34 137.4 279.20 f38.6 284.04 139.5 288.88 140.6 293.70 141.9 298.52 142.9 303.34 143.8 308.15 144.7 312.96 145.6 317.77 146.6 147.5 322.59

170

R. A. ROBIE AND B. S. HEMINGWAY

Mn4” ions become antiferromagnetically ordered into a complex spiral arrangement as suggested by YoshimorP5) and confirmed by the powder neutrondiffraction studies of Gonzaio and COX’~~’ at 4.2 K. Our value for TN, 92.2 K, agrees well with that obtained by Gonzalo and Gox (16) from the temperature dependence

TABLE 3. Experimental molar heat capacities of Mn,O, (bixbyite). M = 157.8742 g+mol-’ T K

CP.* J.K-‘.mol-’

Series 1 300.60 110.1 303.58 110.9 307.54 110.4 312.74 105.4 316.82 103.4 Series 2 299.23 109.8 303.80 110.9 308.96 ’ 109.5 314.15 104.5 319.39 103.4 324.46 103.5 329.52 103.7 334.62 104.1 339.74 104.8 344.86 105.2 349.92 355.02 360.01 365.00

Series 3 105.9 106.3 106.7 107.4

Series 4 52.12 21.85 57.00 25.91 61.80 30.28 67.11 35.78 71.65 41.60 73.75 44.93 74.93 47.04 76.07 49.58 77.15 52.44 78.21 55.46 79.29 ’ 56.73 80.43 40.24 81.60 38.75 84.55 37.95 89.69 38.65 95.25 40.58 100.92 42.34

-

T K 106.68 112.44 118.15 123.82 129.44 135.03 140.58 146.09 151.57 157.01 162.45 167.83 173.20 178.56 183.93 189.29 194.63 199.96 205.28 210.61 215.95 221.28 226.64 232.00 237.36 242.73 248.07

CY.In J.K-‘.mol-’ 44.36 46.68 49.01 51.32 53.62 55.83 57.96 60.13 62.29 64.35 66.38 68.34 70.29 72.13 73.96 75.77 77.59 79.26 80.92 82.53 84.18 85.79 87.27 88.73 90.40 91.97 93.60

Series 5 203.19 80.27 208.63 81.92 213.81 83.54 219.03 85.10 224.38 86.68 229.71 88.09 235.01 89.66 240.30 91.27 245.59 92.86 250.89 94.37 256.18 95.82 261.46 97.39 266.73 98.86 271.98 loo.5

T K 277.21 282.43 287.66 292.88 298.09 301.55 302.92 303.89 304.83 305.77 306.71 307.65 308.59 309.53 310.47 311.42 312.35 313.28 314.22 315.15 318.20 323.33 328.43 333.54 338.64 343.76 348.86

CP.ttl J*K-i,rnol-* 102.1 103.9 105.9 107.8 109.5 110.7 110.0 110.6 110.8 111.4 111.6 109.8 109.8 109.5 108.3 106.1 105.1 105.8 105.2 lQ4.4 103.3 103.3 103.7 104.2 104.7 105.1 105.7

Series 6 76.46 50.38 76.75 51.57 77.00 52.10 77.24 52.67 77.78 53.99 78.31 55.75 78.58 56.90 78.85 57.40 79.12 59.42 79.38 60.04 79.67 49.16 79.98 43.22 80.25 41.03 80.49 40.07

a Temperature rise straddled the maximum in C;,,.

T K

c;. m J.K-i.mol-”

80.88 81.42 81.96 82.49 83.02

39.33 38.89 38.46 38.16 38.04

165.92 170.02 175.00 180.07 185.37

Series 7 67.65 69.14 70.91 72.65 74.44

84.45 78.40 78.67 78.92 79.17 79.44 79.72

Series 8 37.96 56.05 57.33 58.32 59.92 59.23 47.20

5.06 5.56 6.57 7.25 7.99 8.91 9.88 10.96 12.21 13.58 15.09 16.79 18.66 20.72 23.02 28.38 31.68 35.22 39.12 43.52

Series 9 0.086 0.129 0.214 0.322 0.411 0.562 0.747 0.985 1.285 1.648 2.090 2.621 3.267 4.046 4.992 7.552 9.160 11.05 13.35 15.97

T z

Gn J.K-‘.mol-‘f

48.42 53.82 Series 23.98 24.40 24.79 25.10 25.44 25.78 26.12 26.46 26.80 27.13

19.16 23.22 11 * 5.507 5.688 5.900 6.091 6.225 6.362 6.493 6.632 6.756 6.904

Series 12 79.26 60.30 79.72 48.53 80.20 41.29 80.70 39.59 81.18 39.06 81.69 38.67 82.22 38.29 82.75 38.09 83.28 38.03 83.81 38.01 Series 15 308.39 110.5 308.69 111.6 308.94 108.5 309.20 108.7 309.47 109.1 309.74 106.5 310.01 105.7 310.27 106.9 310.54 107.7 310.81 104.3 311.08 105.0 311.35 107.0 311.61 107.8 311.89 108.0

* Series 10, 13, 14, 16, and 17 not tabulated to conserve space.

Sm OF MnO,, Mn30,, AND Mn,O,

171

of the magnetic (100) and (001) reflections between 4.2 and 100 K, and from the heat-capacity values above 50 K of Kelley and Moore.f4) In figure 2 we show our measurements of the heat capacity of MnO, between 5 and 120 K. We have estimated the entropy associated with the ordering of the magnetic moments of the Mn4+ ions in MnO, using the co~esponding-states entropy approximation of Stout and Catalan0 u’) to estimate the lattice entropy. We used the C;,,, results of Dugdale, Morrison, and Patterson”@ and of Shornate for rutile (TiOJ to estimate the lattice heat capacity for MnO,. The resultant values for the magnetic contribution to the entropy of MnO, are shown in figure 3. Smag,,, approaches R In 4, at T/T, > 2.2, as would be expected for a first-transition-group ion with a spin quantum number of 3/2. Our heat-capa~ty measurements on hausmanite between 25 and 50 K are shown in figure 4. The most significant feature in the Ci, m curve of Mn,O, is a prominent lambda-peak near 43.1 IL From earlier measurements of the magnetization by Dwight and Menyuk’“’ and of the magnetic spin structure at low temperatures by Boucher, Buhl, and Perrin(20) we knew that Mn,O, becomes ferrimagnetic below about 43 K and thus we anticipated that it would exhibit a transition in Ci,, at low temperatures. The sharp transition at (43.lkO.2) K arises from the spin ordering which causes the ferrimagnetism of hausmanite.

FIGURE 2. Experimental molar heat capacities of pyrolusite (MnO,) between T -+ 0 and 120 K.

R. A. ROBIE AND B. S. HEMINGWAY

172

7-7-v -__--..---

__-

-----

R In 4

2

I

01 0 FIGURE 3. Magnetic entropy against temperature For MnO,.

In their neutron-diffraction studies, Boucher, Buhl, and Perrin(“’ examined the temperature variation of the intensities of neutron reflections associated with the spin ordering and noted an abrupt change at 33 K at which temperature the magnetic unit cell and the chemical unit cell became identical. Although we did not make detailed measurements between 30 and 40 K inspection of figure 4 suggest the possibility of a minor bump in Ci,, near 35 K which might correlate with the neutron observations. At 40.1 K our heat-capacity measurements show a clearly defined bump. Dwight and Menyuk”’ measured the magnetization of natural hausmanite crystals between 4.2 and 50 K in magnetic field strengths of 19.89, 79.58, and 795.8 kA. m-l applied along the easy direction. Their vaiues at 19.89 kA *m-r show “a pronounced bump just below the Curie point” and strongly suggest a common origin with the bump that we observe in C;,, at 40.1 K. The heat capacity of Mn,O,, figure 5, exhibits several interesting features. The sharp h-point at (79.45kO.05) K arises from the antiferromagnetic ordering of the magnetic moments of the Mn3+ ions below this temperature. This is shown in detail in figure 6. The broad change in Ci,, near (307,5f 1.0) K is most certainly associated with the orthorhombic-to-cubic transition discovered by Geller and Espinosa (12’ by powder X-ray measurements. This transition appears to be

Sp, OF MI-IO,, Mn,O,, AND Mn,O,

FIGURE 4. Experimental molar heat capacities of hausmanite (Mn,O,) 0, Series 1; A, series 2; t], series 3 and 4.

173

between 25 and 50 K.

continous with no enthalpy of transition. Our results in this region have a significantly larger scatter (+ 1.0 to 1.5 per cent) than can be attributed to the decrease in measurement precision caused by the small temperature-rises; this should be no more than 0.4 per cent. We suspect that the increased scatter is due to the finely divided nature of the Mn,O, sample. In the temperature range 23 to 27 K measurements were made at closely spaced intervals (series 11, table 3) to see if we could find evidence in Ci,, of the sharp change in magnetic susceptibility observed by Grant et uLo3) at 25 K. There is a very minor bump in CE;., in this temperature region as shown in figure 6, but nothing as dramatic as might have been anticipated from the magnitude and abruptness of the change in the susceptibility.

4. Therm~ynamic

properties

Our experimental heat capacities (corrected for curvature) were extrapolated to T -+ 0 using a plot of C;* m/'T against T2. These extrapolated values were combined with our experimental results and smoothed by computer fitting to give the thermodynamic functions C;, m, {%(T)-%(O)}; (K%(T)-Ki(O)}IT, and {G:(T)- ~~~O)~/T listed in table 4 for temperatures between 5 and 380 K. At

174

R. A. ROBIE AND B. S. HEMINGWAY

I 100

I

200 T/K FIGURE 5. Experimental molar heat capacity of Mn,O,

I

3On

i I)

between T-t 0 and 370 K.

298.15 K the standard molar entropies of MnO,, Mn,O,, and Mn,O, are (52.75 +0.07), (164.1+0.2), and (113.7-L-0.2) J * K-’ . mol-‘, respectively. Our C& values for MnzO, are systematically greater than those of King”’ by about 0.5 per cent. At 298.15 K King’s value for Sk(T) is (110.5+2.1) J-K-‘.mol-‘. This is smaller than our value by 3.2 J * K-i emol- ‘. Most of this difference (2.4 J. K-i . mol- ‘) arises from King’s estimate of (Sk(51 K)- S&(O)). The C;, m results of Kelley and Moore (4) for MnO, exceed our values at 80 K by 3 per cent and are 0.5 per cent less than ours at 250 K. Kelley and Moore’s value at 298.15 K, (53.14f0.41) J.K-‘*mol-‘, exceeds ours by 0.39 J-K-‘.mol-‘. Again most of the dif’Ierence between Kelley and Moore’s value and ours arises from their estimate of (Sk(50 K)-%(O)}, 2.5 J.K-‘.mol-‘, compared with our measured value of 2.0 J-K-‘amol-‘. Huebner and Sato(21’ have determined f(O,, T), where f denotes fugacity, for reaction (1) between 867 and 1225 K and for reaction (2) between 1044 and 1475 K using an electrochemical method. They have also summarized the results of a number of earlier studies’22-34) of these same equilibria using different techniques. More recently Schaefer”” has also studied reactions (1) and (2) electrochemically. With the exception of the results of Isihara and Kigoshi’22’ and Kim, Wilbert, and Marion,(29) the log,,(jj(O,, T)/kPa) results for both reactions (1) and (2) are in

SO,OF MnO,, Mn,O,, AND Mn,O,

FlGURE 6. Experimental molar heat capacity of Mn,O,

175

between T + 0 and 100 K.

reasonable agreement between 1000 and 1200 K although the slopes of the “equilibrium” curves vary widely. We wish to compare values for the molar Gibbs free energies of formation of these three manganese oxides~obtained from the above-mentioned equilibrium studies with values for Arc:(T) obtained from our new molar entropies for MnO,, Mn304, and Mn,O, and the carefully measured enthalpies of formation reported by Shornate for MnO, and Mn,O, based upon sulfuric-acid solution calorimetry. To evaluate the thermodynamic functions Cg, m, and Xi 9, (G:(T)- Hk(298.15 K)}/T at those temperatures for which the equilibrium f(0,) was determined, we have combined our Ci,,., measurements between 250 and 380 K (in the form of molar enthalpy increments) with the ~~~(T)-~~(298.~5 K)f values for MnO, between 406.7 and 777.9 K from Moore,“) with those of Orr@) on Mn,O, (397.3 to 1350.4 K), and with those of Southard and Moore”) on Mn,O, between 498.3 and 1768.1 K, The combined results were then fitted by least squares to polynomials constrained to agree with the values obtained with the lowtemperature calorimeter. The polynomials were differentiated to give the heatcapacity equation: C;,,/(J.K-“.mol-‘)

= u+~(~‘/K)+c(~‘/K)~+~(T/K)-~+~(T/K)-”~.

(3)

176

R. A. ROBIE

10 15 20 25 30 35 40 45 50

60 IO 80 90 100 110 120 130 140 1.50 160 170 180 190 200 210 220 230 240 250 260 270 280 290 300 310 320 330 340 350 360 370 273.15 298.15

TABLE

4. Molar

MnO,

(pyrolusite).

10 15 20 25 30

0.087 0.810 2.782 5.697 9.45 1 14.89

B. S. HEMINGWAY

thermodynamic

M = 86.9368

0.001

0.005 0.038 0.132 0.337 0.724 1.330 2.174 3.240 4.445 5.826 9.100 13.10 18.34 31.15 22.42 22.34 24.37 26.50 28.63 30.80 32.93 34.98 36.98 38.92 40.77 42.56 44.29 45.92 47.45 48.87 50.21 51.49 52.71 53.87 54.97 56.00 56.91 57.90 58.79 59.65 60.43 61.15 51.88 54.77 Mn,O,

5

AND

0.012 0.043 0.105 0.218 0.399 0.664 1.020 1.470 2.010 3.350 5.050 7.120 9.800 13.07 15.18 17.21 19.24 21.29 23.33 25.39 27.45

29.51 31.56 33.60 35.63 37.65 39.66 41.65 43.61 45.56 47.47 49.37 51.24 53.08 54.90 56.70 58.47 60.21 61.92 63.61 65.28 48.07 52.75 (hausmanite).

M = 228.8116 0.027 0.237 0.898 2.077 3.731 5.893

properties

g. mol-

1

0.000 0.009 0.032 0.080 0.166 0.306 0.509 0.783 1.120 1.520 2.500 3.720 5.200 7.160 9.530 10.68 11.73 12.79 13.84 14.90 15.96 17.02 18.07 19.12 20.16 21.18 22.19 23.19 24.17 25.13 26.07 26.98 27.88 28.76 29.61 30.45 31.26 32.06 32.83 33.58 34.32 35.03 27.27 29.46

O.OQO 0.003 0.011 0.025 0.052 0.093 0.155 0.240 0.351 0.490 0.850 1.320 1.910 2.630 3.530 4.504 5.479 6.459 7.445 8.436 9.432 10.43 11.43 12.44 13.45 14.45 15.46 16.47 17.48 18.48 19.49 20.49 21.49 22.48 23.47 24.46 25.44 26.41 27.38 28.34 29.30 30.25 20.80 23.29

g.mol-’ 0.020 0.180 0.685 I.555 2.740 4.273

0.007 0.057 0.213 0.522 0.991 1.620

Sm OF

MnO,,

Mn,O,,

TABLE

AND

Mn,O,

4-continued

T E 35 40 45 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 260 270 280 290 300 310 320 330 340 350 360 370 380 273.15 298.15

25.76 53.34 26.11 25.36 31.22 38.86 46.38 53.57 60.48 67.19 73.68 79.90 85.77 91.32 96.60 101.6 106.2 110.5 i 14.5 118.3 121.9 125.3 128.4 131.4 134.0 136.4 138.7 140.9 143.0 145.1 146.9 148.6 150.2 151.6 153.0 154.4 155.7 137.2 142.7 Mn,O,

5 10

15 20 2s 30 35 40 45 :: 60 65

0.090 0.781 2.070 3.710 6.000 8.280 10.95 13.87 16.90 20.26 24.21 28.59 33.49

8.875 13.94 21.59 24.22 29.30 34.68 40.36 46.25 52.25 58.33 64.46 70.60 76.74 82.85 88.91 94.92 100.9 106.7 112.5 118.2 123.8 129.3 134.7 140.0 145.2 150.3 155.3 160.2 165.0 169.7 174.3 178.9 183.4 187.7 192.0 196.2 200.4 151.9 164.1 (bixbyite).

M = 157.8742 0.028 0.257 0.799 1.616 2.682 3.970 5.450 7.100 8.900 10.86 12.97 15.26 17.74

6.445 10.42 16.46 17.31 19.08 21.36 24.02 26.91 29.92 33.01 36.13 39.26 42.37 45.45 48.48 51.46 54.38 57.22 59.99 62.68 65.29 67.83 70.29 72.67 74.98 77.21 79.37 81.45 83.47 85.42 87.32 89.15 90.92 92.64 94.29 95.90 97.46 77.90 83.10

2.430 3.518 5.127 6.909 10.21 13.32 16.34 19.34 22.33 25.32 28.33 31.35 34.37 37.40 40.43 43.46 46.48 49.50 52.50 55.50 58.47 61.43 64.37 67.29 70.18 73.05 75.90 78.72 81.52 84.29 87.03 89.75 92.43 95.09 97.73 100.3 102.9 73.95 81.00

g.moi-’ 0.02 I 0.194 0.590 1.162 1.893 2.760 3.740 4.080 5.990 7.250 8.610 10.09 11.69

0.007 0.063 0.209 0.454 0.789 1.210 1.710 2.280 2.910 3.610 4.360 5.170 6.040

178

R. A. ROBIE AND B. S. HEMINGWAY TABLE 4-continued

c;.,

T rc

%(n - %@I

J,K-‘-mot-’

J.K-*+mol-’

39.28 47.30 41.10 38.45 42.06 45.69 49.76 53.83 57.76 61.66 65.47 69.13 72.63 76.02 79.27 82.36 85.38 88.22 91.17 94.11 96.84 99.85 103.1 107.0 110.4 107.8 103.3 103.7 104.8 105.8 106.8 100.8 109.9

20.42 23.38 26.85 31.36 35.60 39.77 43.92 48.07 52.20 56.32 60.42 64.50 68.55 72.57 76.55 80.50 84.40 88.26 92.07 95.85 99.60 103.3 107.0 110.7 114.4 118.0 121.3 124.5 127.6 130.7 133.7 104.5 113.7

70 15 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 260 270 280 290 300 310 320 330 340 350 360 273.15 298.15

{H;(T)

- ~~(O)~~T

J.K-‘.mol-’

- {G:(7')

- ~~(O)~~T

J.K-‘.mof-*

--

13.45 15.42 17.82 20.09 22.11 24.09 26.05 28.03 30.02 32.00 33.97 35.93 37.88 39.79 41.69 43.55 45.38 47.19 48.96 SO.70 52.43 54.13 55.82 57.52 59.23 60.86 62.24 63.49 64.68 65.84 66.97 54.66 58.91

6.970 7.970 9.030 11.27 13.49 15.69 17.87 20.03 22.18 24.32 26.45 28.57 30.68 32.78 34.87 36.95 39.01 41.07 43.12 45.1s 47.17 49.18 51.18 53.17 55.15 57.12 59.07 61.01 62.92 64.81 66.68 49.81 54.78

For Mp,O, we first numerically integrated our C;,m values between 298.15 and 325 K to obtain {I~?:(325 K)-Hl(298.15 K)} = 2872 J smol-‘. We then subtracted this quantity from each of the 12 measurements of (Hm(T)- Hi(298.15 K)) of Orr@) to obtain values of (Pm{,(T)-HL(325 K)}. This procedure was necessary because of the orthorhombic-to”cubic transition at 308 K and because the desired representational polynomial could not accurately fit the steep curvature in the transition region. The resultant heat-capacity equations and their range of validity are: C~.,(MnO,)/(J.K-‘-moi-‘) C;+,(Mn,O,)/(J*K-’

= 290.41-0.14424(7’/K)+2.0119 +4.541 x 10~5{~/K)2-3786.7(~/K)-

x 106(7’/K)-2 ‘I’, (298 to 850 K), (4)

emol-‘) = 162.36+0.01211(7’/K)+ 1.046 x 106(T/K)-2 +3.462x 10-6(7-/K)2-1317.3(T/K)-1’2, (325 to 1400 K), (5)

Sp, OF MnO,, Mn,O,, AND Mn,O,

Ci, ,(Mn,O,)/(J.

K-’

*mol-‘)

= - 7.432 +O.O9487(‘7’/K)-6.712 + 3395.6( T/K)- lj2,

179 x 104(7’/K)- 2 (298 to 1400 K). (6)

For reaction (1) we calculated A,GD(l 100 K) from the equations given by Schaefer,“l) Charette and Flengas,‘33) Huebner and Sate,“” Hahn and Muan~23~ Hochgeschwender and Ingraham,‘34) Ingraham,f30) and Otto(26) to obtain an average value for A,G~(llOO K) of -(23.82 + 1.37) kJ. mol- l. We combined this value with our heat-capacity equations and entropies to calculate A,rm(298.15 K) = -(217.34+1.37) kJ.mol-’ for reaction (1). Our measured ArSm(298.15 K) for reaction (1) is -(179.4&U) J-K-‘*mol-’ and at 1100 K, A,S~(llOO K) = - (162.9 f 3.0) J. K - ’ * mol- ‘. Values of A$&( 1100 K) calculated from the slopes of experimental log,,(f(O,, T)/kPa) range from - 184.9 to - 140.9 J*K-’ ernol-‘. There is no direct calorimetric measurement of A,H*(298.15 K) for Mn,O,. The values listed in Robie et aE.‘35’ and in Wagman et u!.‘~’ were obtained from the equilibrium measurements of Otto(36’ for the reaction: 4MnO,(cr)

= 2Mn,O,(cr)

+ O,(g),

(7)

and the calorimetric value for ArHk(298.15 K) for MnO, measured by Shornate.“‘) For reaction (l), A,Hk(298.15 K) calculated from the tables of either Wagman et ~1.‘~) or of Robie et uJ.‘~~) yield - (203 + 14) kJ ’ mol- ‘. Reaction (2) is complicated by the non-stoichiometry of “MnO”. However, Alcock and Zadort3’) have shown from a third-law treatment of their results between 923 and 1273 K, for the reaction: Mn(cr) + $0,(g) = MnO(cr),

03)

that the calorimetric AfHL(298.15 K) of Southard and Shomate(38) and their thirdlaw value agree to within 550 J. mol- ‘. The slight variation with tem~rature of the calculated A,Hz(298.15 K) (750 Jemol-’ in 350 K) might be, as they suggested, due to a small error in the entropy of either MnO or Mn, or it might also be the consequence of the changing composition of the Mn,-,O phase with temperature. At 1300 K the composition of the “MnO” phase in equilibrium with stoichiometric Mn,O, is approximately MnOo.ss based on the measurements of Bransky and Tallan,‘3Q’ Picard and Gerdanian,(40) and Keller and Dieckmann.(41) Thus we believe it is safe to neglect the non-stoichiometry of MnO below 1300 K for reaction (2) certainly within the impr~ision of the “equilibrium” results, and that this assumption will not introduce significant error into the value of A,HL(298.15 K) derived below. For reaction (2) we calculated A,G~(llOO K) from the equations given by Huebner and Sate,(“) Schaefer,“‘) Charette and Flengas,‘j3) Blumenthal and Whitmore,(25) and Schwerdtfeger and Muan’32’ to obtain an average value of We combined this value with our AL\,Gm(llOO K) = -(202.75&4.00) kJ-mol-‘. measured molar entropies and heat capacities and values for O,(g) and MnO(cr) from Robie et a1.(35fto get A,HL(298.15 K) = -(458.96~4.~~ kJ*mol-‘. This may be compared with -(463.88f 3.60) kJ*mol- ’ calculated from the solutioncalorimetric results of Shornate”” and Southard and Shomate.‘38) The calorimetric and equilibrium results are thus in agreement well within their combined

R. A. ROBIE AND B. S. HEMINGWAY

180

TABLE 5. Standard molar Gibbs free em&es of formation of MnO, Mn,O,, MnO, and Mn,O, temperatures, (p" = lo5 Pa) A,Gy(kJ.mol-‘)

T/K “MIIO” 298.15 400 500 600 700 800 900 loo0 1100 1200 1300 1400

at high

- 362.90 & 0.50 -355.32 - 349.98 - 340.69 -333.44 - 326.22 -319.00 -311.75 -304.31 - 296.86 - 289.40 -281.89

MN, -

1282.46+ 1.00 1247.14 1213.98 1180.46 1147.83 1113.83 1080.63 1047.39 1013.68 -979.98 - 946.43 -912.84

MnO,

-466.17f0.44 -447.39 - 429.05 -410.86 - 392.78 - 314.19 - 356.89 -339.35

MM3

-882.06f0.84 - 855.89 -830.38 - 805.04 - 779.83 - 754.71 - 729.72 - 704.66 - 679.53 - 654.37 - 629.34 -604.35

uncertainties. The calorimetric AL\,S&(298.15 K) = - (235.2 k 2.6) J. K- ’ * mol- ’ and Ac\,Sm(liOO K) = -227.3 J. K-’ ‘mol-” with an estimated uncertainty (2s) of Tf4.0 J. K-r 1mol-‘. The A$&(1100 K) value for reaction (2) calculated from the cquiiibrjum measurements range from - 256.9 to - 221.3 J. K - ’ * moi- ‘. fn one of the two reaction schemes used by Shornate to determine A,Hg(298.15 K) of Mn,O, it was necessary to use a literature value for A,Hi(HI, aq, 298.15 K). Rand 142)has pointed out that, if the newer more accurate values listed in Wagman et ~1.‘~’ are used, Shomate’s value for AtHk(298.15 K) for Mn,O, becomes - 1383.45 kJ * mol- I. The molar enthalpy for formation of Mn,O, obtained by Shomate’s second method is not changed. The average of the two values becomes - 1385.45 kJ .mol-’ and the “calorimetric” values for A$k(298.15 K) for reactions (1) and (2) become -212.0 and -459.6 kJ . mol- ’ respectively, in very much better agreement with the values we calculated from the “average” of the equilibrium studies. From the above considerations of both the calorimetric and equilibrium studies we adopt A~~~(298.~5 K) = -(385.22-i:0.50), -(1384.5f 1.4), -(959.0* l.O), and -(520.0+0.7) kJ=mol-’ as the best values for MnO, Mn,O,, MnzOs, and MnO, respectively. These values, together with our entropy and heat-capacity values were used to calculate the A,Gz(T) values in table 5. For those who need an analytical expression for the manganese oxide buffers, the oxygen fugacity for reaction (1) can be expressed by log,,{f(O,)/kPa

= 10.655- 10709(T/K)-r,

(9)

to within 8 per cent between 800 and 1300 K, and for reaction (2) log,,(f(Oz)/kPa)

= 13.646-23345(7-/K)-‘,

to within 0.6 per cent for the temperature range 700 to 1400 K.

(10)

S; OF MnO,, Mn,O,, AND Mn,O,

181

We express our appreciation to our U.S. Geological Survey colleagues J. Stephen Huebner and Carl R. Thornber for their considerable help in preparing the samples, providing the X-ray results, and together with John L. Hass, Jr. for numerous very useful discussions concerning earlier equilibrium measurements. REFERENCES

I. Dwight, K.; Menyuk, N. Phys. Rev. 1960, 119, 1470. 2. Wagman, D. D.; Evans, W. H.; Parker, V. B.; Schumm, R. H.; Halow, I.; Bailey, S. M.; Churney, K. L.; Nuttall, R. L. Naf. Bur. Stds. Tables of Chemical Thermodynamic Properfie~~, J. Phys. Chem. Re$ Data 1982, 11, supplement 2. 3. Huebner, J. S. Research Techniques for High Pressure and Temperafure. Chap. 5. Ulmer, G. S.: editor. Springer-Verlag: New York. 1971. 4. Kelley, K. K.; Moore, G. E. J. Am. Chem. Sot. 1943, 65, 782. 5. Millar, R. W. /. Am. Chem. Sot. 1928, 50. 1875. 6. Moore, G. E. J. Am. Chem. Sot. 1943,65, 1398. 7. King, E. G. J. Am. Chem. Sue. 1954, 76, 3289. 8. Orr, R. L. .I. Am, Chem. Sot. 1954, 76, 857. 9. Southard, J. C.: Moore, G. E. J. Am. Chem. Sot. 1942, 64, 1769. IO. Shomate. C. H. J. Am. Chem. SW. 1943,65, 785. II. Schaefer, S. C. U.S. Bur. Mines Rep. &west. 8704, 1982. 12. Geller, S.; Espinosa, G. P. Whys.Rev. B 1970, I, 3763. 13. Grant. R. W.; Geller, S.; Cape, J. A.; Espinosa, G. P. Phys. Rev. 1968, 175, 686. 14. Robie, R. A.; Hemingway, B. S.; Wilson, W. H. J. Res. U.S. Geol. Survey 1976, 4, 631. 15. Yoshimori, A. J. Phys. Sot. Jpn 1959, 14. 807. 17. Gonzalo, J. A.; Cox, D. R. Sot. &I., Fis. y Quim. 1970, 66, 407. 17. Stout, J. W.; Catalano. E. J. Chem. Phys. 1955,23, 2013. 18. Dugdale, J. S.; Morrison, J. A.: Patterson, D. Proc. Roy. Sot. London A 1954, 224, 228. 19. Shomate, C. H. J. Am. Chem. Sot. 1947, 69, 218. 20. Boucher. B.; Buhl, R.; Perrin, M. J. Appl. Phys. 1971, 42, 1615. 21. Huebner. J. S.; Sato, M. Am. Mineral. 1970, 55, 934. 22. Isihara, T.; Kigoshi, A. Sendai Univ. Res. Inst. Sci. Repfs.. Ser. A. 1953,4-5, 172. 23. Hahn, W. C., Jr.; Muan, A. Am. J. Sci. IWO, 258, 66. 24. Klingsberg, C.: Roy, R. J. Am. Ceramic Sot. 1960, 43, 620. 35. Blumenthal, R. N.; Whitmore, D. H. J. Am. Ceramic Sot. 1961, 44, 508. 26. Otto, E. M. J. Elecfrochem. Sot. 1964, 11 I, 88. 27. Schmahl. N. G.; Stemmler, B. J. Elecfrochem. Sot. 1965, 112, 365. 28. Matsushima. T.: Thoburn. W. J. Can. J. Chem. 1965.43. 1723. 29. Kim, D. Q.; Wijbert. Y.; Marion, F. Compr. Rend. Sk. C 1966,262, 756. 30. fngraham, T. R. Can. Mef. @curt. 1966, 5, 109. 31. Shenouda, F.; Aziz, S. J. Appl. Chem. (London) 1967, 17,258. 32. Schwerdtfeger, K.; Muan, A. Trans. AIME 1967, 239, 1114. 33. Charette, G. G.; Flengas, S. N. J. Elecfrochem. Sot. 1968, 115, 796. 34. Hochgeschwender, K.; Ingraham, T. R. Can. Mef. Quart. 1967,6, 71. 35. Robie, R. A.; Hemingway, B. S.: Fisher, J. R. U.S. Geof. Survey Bull. 1452, 1979. 36. Otto, E. M. J. ~leefrochem. Sot. 1%5, 112, 367. 37. Alcock, C. B.; Zador, S. ~lectrochimjca Acta 1967, 12, 673. 38. Southard, J. C.; Shomate, C. H. J. Am. Chem. Sot. 1942, 64, 1770. 39. Bransky, I.; Talian, N. M. J. Elecfrochem. Sot. 1971, 118, 788. 40. Picard. C.: Gerdanian. P. J. Solid Sfate Chemisfrv 1974. 11. 190. 41. Keller, M.: Dieckmann, R. Trans. Jpn Inst. Met&s 1983, 24, 650. 42. Rand, M. H. unpublished results.