Enthalpy difference of hexagonal and rhombohedral graphite

Carbon

1964, Vol. 2, pp. 1-6.

Pergamon

Press Ltd.

ENTHALPY HEXAGONAL

Printed in Great Britain

DIFFERENCE

OF

AND RHOMBOHEDRAL H. P. BOEHM

Anorganisch-Chemisches

GRAPHITE

and R. W. COUGHLIN*

Institut

der CniversitBt,

Heidelberg,

German!

(Received 2 December 1963) Abstract-This paper describes an isothermal calorimeter which was used for measuring the heat of formation of potassium graphite, C,K. The observed heat of reaction was - 84.1&0.3 cal/gC using pure hexagonal graphite, but -88.1 kl.1 cal/gC using graphite containing 33 per cent rhombohedral modification. From these results one calculates that 0.14&0,04 kcal/g-atom is liberated upon transition of rhombohedral into hexagonal graphite. Only by mechanical treatment, such as grinding, can the rhombohedral modification be obtained. Estimation of the energy stored in the lattice defects produced by grinding leads to values significantly lower than those measured.

1. INTRODUCTION

from the hexagonal modification in this way, by the action of shear. Grinding graphite powder never produced more than 33 per cent rhombohedral form. After prolonged grinding, there would be random distribution of the layers, A, B and C and, in the limit, turbostratic graphite with complete disorientation which is evidenced by the disappearance of the (hkl) reflexions.

THE usual structure of graphite is the hexagonal modification with the carbon layers in the sequence ABAB . . . . It is a known fact, however, that graphite can occur in a rhombohedral modification(‘) with the layer sequence ABCABC . . . . This situation is analogous to the polymorphism displayed by certain metals which can assume either hexagonal or cubic close-packed lattices. A good example is cobalt. In both graphite modifications the interlayer spacing is the same; that is to say, that the spacing is equal within the accuracy of measurement. The two forms of graphite distinguish themselves in X-ray diffraction patterns through the (Ml) reflections, mainly (lOi’1) and (1121). The rhombohedral form of graphite has never been observed in the pure state. Naturally occurring, well crystallized graphite is almost exclusively pure hexagonal. Only by mechanical treatment, e.g. grinding, does the rhombohedral modification arise(2-4) as a consequence of translation or gliding of the layer planes. Implicit in this mechanical explanation is the assumption that the transition AB+AC takes place in a preferred direction.In other words, that direction is preferred which would exclude AAA . . . as a possible intermediate state. Figure 1 shows how the rhombohedral arises *Present Company,

address: Madison,

Esso Research New Jersey.

and

A_ -

B_ A e

-

----L

Moving

layers

BW A-----L / Rhombohed.

mod.‘\,

A_

A_

CW

BM

B_

CM

A_

A_

cm

B_ +---

Direction

of stress _f

FIG. 1. Mechanism of the formation of rhombohedral graphite from hexagonal by the influence of shearing forces.

Engineering 1

2

H. P. ROEHM

and R. W. COUGHLIN

Rhombohedral graphite appears to be unstable between 300°K and 3000°K. Interstitial compounds (e.g. potassium graphite, CsK; graphite hydrogen sulphate, C& HSO< . ZH,SO,; bromographite, CsBr) can be prepared from graphite having either rhombohedral or hexagonal stacking sequence. However, decomposition of these interstitial compounds always produced pure hexagonal graphite, irrespective of the original reactants. In most graphite interstitial compounds, the carbon layers immediately adjacent to the foreign atoms or ions assume identical positions (. . . AXA . . .), while the other carbon layers retain the originai mutual orientation.f5) Upon decomposition (by heating or reaction with water) it should be possible to obtain the stacking sequence AB or AC with equaI probability. The sequence i3&43 . . . is always produced, however. If graphite containing rhombohedral modification is heated to high temperatures, transition to the hexagonal modification starts at about 1400°C. In experiments using a finely powdered graphite it was found that the amount reconverted was dependent on temperature. This suggests that the activation energy for the conversion is a function of the layer size. At about 2700-3000°C rhombohedral graphite changed completely to hexagonal. It would be expected that the enthalpy difference between the two modifications would be very slight. A computation by ~o~IG~~A~N~~) gives about the same values for the energy of cubic and hexagonal close-packed lattices. The transition enthalpy of hexagonal a-Cobalt into cubic P-Cobalt has been reported as +6,(7) +60’*’ and +90(‘) Cal/g-atom. A somewhat lower value should be expected in the case of graphite which has a relatively larger separation of the layer planes, and therefore, smaller interlamellar binding energy. In graphite the bonding energy along the c axis has been estimated to be about 8 kcal/g-atom.(“) Other workers have estimated the stacking fault energy in graphite as about 0.6 ergjcm2.f”) Using these estimates one calculates an energy difference of the order of magnitude of 10F3 kcal/g-atom for rhombohedral graphite. This low value suggests that hexagonal and rhombohedral graphite should occur side by side nearly always. However, this has been observed practically never. When graphite single crystals contain some rhombohedral modification as they occur in nature,(12) there is always

reason to believe that the crystals experienced shearing stress in the parent rock after formation. Thus, there is reason to expect an energy difference greater than lop3 kcal/g-atom between the two modifications. Attempts to estimate the free-energy difference from the potentials of cells like graphite 1HSSO., 1C&HSOr . 2HzSOp or graphite 1H2S04 1PbO%, Pt gave no useful results. The potentials were not constant and seemed to depend very much on the graphite pretreatment. HENNIC observed similar behaviour.(‘s) Apparently the potential is affected by surface oxides. Experiments by HOPMANN@) support this explanation.

Although these experiments were unsuccessful, we nevertheless attempted to measure an enthalpy difference. Combustion of graphite to CO, with a heat of reaction of 90 kcal/g-atom did not appear to be suitable for detecting a small enthalpy difference. It seemed better to form an interstitial compound using, on the one hand, pure hesagonal graphite and on the other hand, a sample containing the greatest possible concentration of rhombohedral graphite. In the first experiments, graphite was oxidized to the hydrogen sulphate compound, using potassium dichromate in concentrated sulphuric acid. But the results were not fruitful. The reaction proceeded too slowly (the thermal effect persisted for about 2 hr); besides, it is seldom ever completely stoichiometric.(‘4) We measured about 1.0 kcal/ g-atom C, using hexagonal graphite. The reaction of graphite with liquid potassium to form C,K goes practically to completion and takes place almost instantaneously. It was therefore more suitable for the intended measurement. In order to measure, with great accuracy, the liberated heat in vacua and above the melting point of potassium (63*5”C), an isothermal calorimeter was constructed. This device operates according to the principle of Bunsen’s ice calorimeter. THOMAS(“) has successfully used such a calorimeter with naphthalene in the place of ice. We also used naphthalene; its melting point was appropriate: 80.1”C. 2. EXPERIMENTAL Figure 2 shows the construction of the calorimeter. The central reaction tube can be evacuated to 1O-5 mm Hg; it is surrounded by a jacket which contains naphtha-

lene floating on mercury. Care was exercised that no air was trapped in the naphthaiene jacket. A mercury

ENTHALPY

DIFFERESCE

OF

HEXAGONAL

AND

RHOSIBOHEDRAL

Constant temperature both (oil)

GRAPHI’I’F

r Mett ler Balance

Copper cylinder,

Naphthalene-

IOcm

I FIG. 2. Construction

of isothermal

delivery tube leads from the bottom of the jacket to the outside. The entire assembly is surrounded by a still larger outer jacket which normally serves as a thermal barrier. This jacket initially contained hot water while the calorimeter was being filled with molten naphthalene; during the experiments it held only air. The entire apparatus is blown in one piece using a glass similar to Pyrex. The calorimeter was immersed in a constant temperature (&O.OOS’C) oil bath with only the upper ends of reaction tube and delivery tube protruding above the oil surface. The system was kept warm between experiments as well. The mercury delivery tube is connected to a reservoir and to a capillary tube. The end of the tube is drawn to a fine point which dips below the surface of mercury in a cylindrical vessel. This vessel rests on the pan of a direct-reading balance having a sensitivity of 20-30 mg. The cylinder diameter is such that the rising and falling

.~ I

calorimeter.

of the mercury level is exactly compensated by the travel of the balance pan. Thus, the mercury level always remains at the same position with respect to the capillary. This eliminates errors due to capillary buoyancy. Before each measurement a sufficient amount of naphthalene was frozen on the outer wall of the reaction tube by blowing a stream of air inside. Then a thinwalled copper vessel, previously filled with pure potassium under vacuum was placed in the reaction tube. The small clearance between copper and glass was filled with silicone oil in order to obtain better heat transfer. The graphite samples were outgassed at elevated temperature under high vacuum in a thin-walled glass ampoule, then sealed-in under vacuum. The ampoule was fastened to a glass rod passing through a close-fitting glass sleeve into the reaction space. Rod and sleeve (KPG tubing of Schott u. Gen., Maim) formed a vacuum-tight seal when lubricated with silicone grease. An outer band on the rod prevented premature breaking

H. P. BOEHM

and R. W. COUGHLIN

Grophiie

:

AF spez. 99.90-99.95% Somple weight: 1.087g

C, 3000”

HT

17:oo

Time,

FIG. 3. Typical

determination,

TABLE 1. DESCRIPTION OF Graphite

Purity (% C)

hr

graph of balance reading vs. time.

THE

GRAPHITE SAMPLES

Rhombohedral modification (%I

Specific

Surface

fm”lg)

AF spezial

99.90-99.95

33

AF spezial, 3000”*

99.90-99.9s

0

5.6

99.95

0

about 0.01

99.7

3

about 0.01

Madagascar 540, soda+ *Heated

flakes

to 3OOO”C, cooled at about lO”C/hr.

of the ampoule by the action of atmospheric pressure. When in place the ampoule dipped into the liquid potassium. The reaction space wss evacuated and the thermostat temperature so adjusted that the rate of heat transfer from the calorimeter was as small as co&d be observed on the balance. When the steady state had been attained, the ampoule was broken on the top of a steel cone resting on the bottom of the copper vessel. The weight increase due to the delivery mercury, i.e. the heat transferred, was recorded as a function of time. Figure 3 shows the course of a typica measurement. First of all, the calorimeter was calibrated electrically. Direct current from a constant-voltage source was passed through a resistance in the reaction tube and the quantity of charge passed in a given time was measured with a silver coulometer. ‘This calibration indicated a heat equivalent of 18.33&0.12 Cal/g Hg. From data in the literature, one would calcuiate 18.28 Cal/g Hg using the following values: density of mercury at 8O”C= 13.40 gfcmg(‘Q heat of fusion of naphthalene= 35.6 cal/g,(17) volume increase of naphthalene upon fusion = 0.1456 cma/g@‘). The experimental value of 18.33 Cal/g Hg was used in the evaluation of the measurements.

8.2

+Purified with molten Naz COB.

3. RESULTS

Table 1 shows some of the information about the graphite we employed. As a graphite with a known rhombohedral modification content, we used a finely ground, very pure natural material which originated in the Passau district of Bavaria. Evaluation of X-ray diffraction patterns”) showed a concentration of 33&3 per cent rhombohedral modification. Some of the graphite was heated to about 3300°K in an industrial graphitizing furnace, then very slowly cooled. After this treatment the diffraction pattern showed the presence of hexagonal graphite only. In order to be sure that the particle size was of no consequence, two graphites in the form of large flakes were also evaluated. One graphite was pure hexagonal, the other contained 3 per cent of the rhombohedral form. The specific surface of the fine-particIe graphite was measured by the BET method (N, at -196”C, 16.2 11’ per N,

ENTHALPY TABLE

2.

DIFFERENCE

Reaction enthalpy AH

Hexagonal graphite: AF spezial, 3000”

84.2 Cal/g 83.6 84.0 84.0 84.1 (84.9)X 84.5

flakes

S40, soda

mean-84.1 33 l/o Rhombohedral AF spezial

f0.3

Cal/g C

hl.1

cdl/g C

graphite: 87.1 89.9 86.8 88.7 88.0 mean=88.1

*See

HEXAGONAL

HEAT OF FORMATIONOF C,K

Sample

Madagascar

OF

text.

molecule) ; in the case of the larger flakes it was estimated. Table 2 shows the results of the measurements. In the case of the graphite containing 3 per cent rhombohedral modification, 10 per cent of the heat-of-reaction difference between the other graphites was deducted from the experimental result. The value obtained in this way is what appears m the table. It agrees with the pure hexagonal samples. This is good evidence that the particle size had no influence on the heat of reaction. PRIMAK(‘~)determined the heat of reaction of graphite with potassium by measuring the temperature rise of the reaction products. He obtained 81&2 Cal/g after a correction (2 cal) for heat conduction. This is in good agreement with our value of 84.1 f0.3 cal/gC. From the heat-of-reaction measurements and the appropriate rhombohedral concentration one calculates a heat of transition from rhombohedral into hexagonal graphite of -12.O._t-3.4 Cal/g or -O.l44f0*041 kcal/g-atom. This value is unexpectedly high. What errors could have influenced the measurements? At 3300”K, graphite in thermal equilibrium contains noticeable quantities of vacancies in the carbon-layers. These vacancies are “frozen in” if the material is quenched quickly. However, our graphite cooled inside the industrial furnace at a

AND

RHOMBOHEDRAL

GRAPHITE

5

rate of about lO”C/hr. This treatment would have allowed most of the lattice defects to anneal out. Besides, the large flakes of natural graphite gave the same results. The finely ground graphite could, of course, contain additional lattice faults which would influence the heat of reaction, e.g. dislocations. On the other hand, estimates by HENNIC(“) and by SPENCE(“) of the energies contained in such defects (arising from cold working) are at least an order of magnitude lower than our results. Unfortunately, we cannot say how many lattice faults were present in our ground graphite. The broadening of the diffraction pattern lines indicates an average crystallite size of 15OOA in the c direction (2OOOA from (002) reflexion and 1000 a from (004) reflexion). Infinite size was indicated by the (1120) reflexion for the a direction (no broadening). In the heat-treated sample, no line broadening could be detected. Finally, the existence of broken bonds within the layers of the milled graphite should be considered. The estimated energy of a carbon-carbon bond in graphite layers is 108 kcal,mole.(“) If all the broken bonds recombined on formation of the potassium compound, one broken bond in every 750 would be necessary to account for the measured energy. Since a “broken” bond in an undistorted perfect layer is inconceivable, an extensive crumpling of the layers should have been evident with disruptions every 45 A4in a linear direction. On the contrary, the X-ray diagram showed no broadening of the (hk0) reflexions at all. It would be difficult to understand why rhombohedral graphite practically never is formed under natural conditions if the measured difference in heat of reaction were caused by the milling treatment only. It appears, therefore, at least provisionally, that the observed difference in heats of reaction can actually be ascribed to the difference between the enthalpies of hexagonal and rhombohedral graphite. Acknowledgement-This work was supported by the European Research Associates, Brussels. The authors would like to thank the Graphitwerke Kropfmiihl organization for providing the graphite samples; the firm Siemens-Plania, Meitingen, Germany for heat treatment of the samples; the U.S. Fulbright Commission for a fellowship for R.W.C. and Professor U.

HOFMANN for graciously providing

rhe facilities at the

H. P. BOEHM

6

and R. W. COUGHLIN

Institute of Inorganic Chemistry, Heidelberg. Gratitude is also extended to G. R. HENNIC and G. B. S~ENCE for helpful discussions. REFERENCES 1. LIPSON H. and STOKES A. R., Proc. Roy. Sot. (London) A181, 101 (1942). 2. BOEHM H. P. and HOFMANN U., 2. Anorg. Allg. Chem. 278, 58 (1955). 3. BACON G. E., Acta Cryst. 3, 320 (1950). 4. LAVES F. and BASKIN Y., 2. I-Gist. 107, 337 (1956). 5. RU~ORFF W., 2. Physik. Chem. (B) 45, 42 (1940); RUDORFF W. and SCHULZE E., Z. Anorg. Allg. Chem. 277, 156 (1954). 6. HONICMANNB., in preparation, cited by LUCK W., KLIER M. and WE~SLAU H., Naturwissenschuften 50, 485 (1963). 7. v. STEINWEHR H. and SCHULZE A., Physik. 2. 36, 307 (1935). 8. ARMSTRONGL. D. and GRAYSON-SMITHH., Can. r. Res. A 28, 51 (1950). 9. JAEGER F. M., ROSENBOHME. and ZUITHOFF A. J., Rec. Traa. Chim. 59, 831 (1940). 10. FEILCHENFELD H., J. Phys. Chem. 61, 1133 (1957).

11. BAKER C., CHOU Y. T. and KELLY A., Phil. Mug. 6, 1305 (1961); HEDLEY J. A. and ASHWORTHD. R., J. Nucl. Mat. 4, 70 (1961); DELAVICNETTEP. and AMELINCKX S., 3’. Nucl. Mat. 5, 17 (1962); SPENCE G. B., Proceedings of the Fifth Carbon Conference, Vol. II, p. 531. Pergamon Press, Oxford (1963). 12. JAGODZINSKIH., Acta Cryst. 2, 298 (1949); HOERNI J., Helv. Phys. Actu 23, 587 (1950). 13. HOFMANN U. and KBNIG E., Z. Anorg. Allg. Chem. 234, 326 (1937). 14. RUDORFF W. and HOFMANN U., Z. Anorg. Allg. Chem. 238, 1 (1938). 15. THOMAS A., Trans. Faraday Sot. 47, 569 (1951). 16. Handbook of Chemistry and Physics, (42nd ed.), p. 2144. The Chemical Rubber Publ. Co., Cleveland, Ohio (1960). 17. Handbook of Chemistrv and Phvsics. (42nd ed.). p. 2316.” The Chemical R&be; Publ. Cd.; Cleveland, Ohio (1960). 18. BLOCK H., 2. Phys. Chem. 78, 385 (1911). 19. QUARTERMANR. and PRIMAK W., r. Am. Chem. Sot. 74, 806 (1952). 20. HENNIG G., private communication. 21. SPENCE G. B., private communication.