No data available.
Please log in to see this content.
You have no subscription access to this content.
No metrics data to plot.
The attempt to load metrics for this article has failed.
The attempt to plot a graph for these metrics has failed.
Pyrolytic Graphites: Their Description as Semimetallic Molecular Solids
1.C. A. Klein, W. D. Straub, and R. J. Diefendorf, Phys. Rev. 125, 468 (1962).
2.C. A. Klein, Revs. Modern Phys. 34, 56 (1962).
3.L. C. F. Blackman, P. H. Dundas, and A. R. Ubbelohde, Proc. Roy. Soc. (London) A255, 293 (1960).
4.L. C. F. Blackman, J. F. Mathews, and A. R. Ubbelohde, Proc. Roy. Soc. (London) A256, 15 (1960)
4.and L. C. F. Blackman, J. F. Mathews, and A. R. Ubbelohde, A258, 329, 339 (1960). These three papers will be referred to as BMU I, BMU II, and BMU III, respectively., Proc. R. Soc. London, Ser. A
5.R. R. Haering and S. Mrozowski, Progress in Semiconductors (John Wiley & Sons, Inc., New York, 1960), Vol. V, p. 273.
6.G. R. Hennig, Proceedings of the Fourth Conference on Carbon (Pergamon Press, New York, 1960), p. 221.
7.R. O. Grisdale, A. C. Pfister, and W. van Roosbroeck, Bell System Tech. J. 30, 271 (1951).
8.D. E. Soule, Proceedings of the Fifth Conference on Carbon (Pergamon Press, New York, to be published), paper 73. References to papers presented at the Fifth Biennial Conference on Carbon are based on information contained in the program issued by The Pennsylvania State University, University Park, Pennsylvania, June 1961.
9.B. Bovarnick, Proceedings of the Fifth Conference on Carbon (Pergamon Press, New York, to be published), paper 18.
10.J. C. Bowman, J. A. Krumhansl, and J. T. Meers, Industrial Carbon and Graphite (Society of Chemical Industry, London, 1958), p. 52.
11.R. Bacon, J. Appl. Phys. 31, 283 (1960).
12.Pyrographite (PG), Pyrographalloy (PGA), and Pyrofiber (PF) are trade names for the deposits of pyrolytic graphite, the doped pyrolytic graphites, and the filaments of pyrolytic graphite manufactured by Raytheon Company. In the present context we make use of these abbreviations for the sake of convenience exclusively. Under no circumstances shall this be construed as an attempt to impose their adoption upon the scientific community.
13.A. R. Ubbelohde and F. A. Lewis, Graphite and its Crystal Compounds (Oxford University Press, London, 1960).
14.O. J. Guentert and S. Cvikevich, Proceedings of the Fifth Conference on Carbon (Pergamon Press, New York, to be published), paper 110.
15.D. E. Soule, Phys. Rev. 112, 698 (1958).
16.G. H. Kinchin, Proc. Roy. Soc. (London) A217, 9 (1953).
17.A. Pacault and A. Marchand, J. Chim. Phys. 57, 873 (1960).
18.A. R. G. Brown and W. Watt, Industrial Carbon and Graphite (Society of Chemical Industry, London, 1958), p. 86.
19.J. Pappis and S. L. Blum, J. Am. Ceram. Soc. 44, 592 (1961).
20.E. E. Loebner, Phys. Rev. 102, 46 (1956).
21.J. W. McClure and L. B. Smith, Proceedings of the Fifth Conference on Carbon (Pergamon Press, New York, to be published), paper 74.
22.D. F. Johnston in Appendix to W. N. Reynolds and P. R. Goggin, Phil. Mag. 5, 1049 (1960).
23.Note that we are implicitly assuming identical effective masses for all the holes and all the electrons involved in the chargetransport process; some justification for the use of parabolic bands will be given in Sec. III B.
24.C. A. Klein, Proceedings of the Fifth Conference on Carbon (Pergamon Press, New York, to be published), paper 71.
25.These two closely related structural parameters are believed to control the band‐population ratio; the electron‐hole mobility ratio should not be particularly sensitive to the state of crystalline perfection.
26.S. Mrozowski and A. Chaberski, Phys. Rev. 104, 74 (1956).
27.Experiments on a deposit annealed at 3600 °C (courtesy of R. J. Diefendorf), which exhibits strictly single‐crystalline electrical properties in the basal planes, indicate that is close 0.15 Ω‐cm at room temperature.
28.The room‐temperature coefficient of resistance is in close accordance with British data for a specimen (Table I in BMU III). This is noteworthy for two reasons: First, the British workers prepare their material by using a different method of deposition (A. R. Ubbelohde, private communication). Second, they do not copper‐plate their samples.
29.This will be established in Sec. II C.
30.D. E. Soule, Phys. Rev. 112, 708 (1958).
31.J. W. McClure, Phys. Rev. 112, 715 (1958).
32.D. E. Soule, Proceedings of the Fourth Conference on Carbon (Pergamon Press, New York, 1960), p. 183.
33.J. Maire and J. Mering, Proceedings of the Fourth Conference on Carbon (Pergamon Press, New York, 1960), p. 345.
34.C. R. Houska and B. E. Warren, J. Appl. Phys. 25, 1503 (1954).
35.E. R. Stover, Proceedings of the Fifth Conference on Carbon (Pergamon Press, New York, to be published), paper 17.
36.J. M. Reynolds, H. W. Hemstreet, and T. E. Leinhardt, Phys. Rev. 91, 1152 (1953).
37.Y. Uemura and M. Inoue, J. Phys. Soc. Japan 13, 382 (1958).
38.C. A. Klein and W. D. Straub, Phys. Rev. 123, 1581 (1961).
39.The “graphitized coke” values in Fig. 6 are as given by Eq. (15) with magnetoresistances taken from Table V of reference 16 and a factor of to correct for the random distribution of current‐flow directions.
40.O. J. Guentert and C. T. Prewitt, Bull. Am. Phys. Soc. 5, 187 (1960).
41.Because of their size and valence‐electron configuration, boron atoms are believed to generate “ideal” acceptor centers.
42.P. Albert and J. Parisot, Proceedings of the Third Conference on Carbon (Pergamon Press, New York, 1959), p. 467.
43.Two‐dimensional in the sense of Wallace [Phys. Rev. 71, 622 (1947)], which means that we are dealing with a zero‐gap system the bands touch at the corners of the Brillouin zone.
44.G. Hennig, J. Chem. Phys. 19, 922 (1951).
45.In their investigation of graphite crystal compounds these authors showed that Eq. (20b) may yield acceptable δ values directly from the ratio of the room‐temperature resistances before and after formation of the compound. Their procedure rests on the hypothesis that “because of the sandwich structure of the crystal compounds of graphite, intercalation of additive is not likely to affect scattering of electrons in the direction of the a axis to any large extent.” A priori, an approach on this basis must be ruled out in dealing with substitutional impurities.
46.This would be the case in the vicinity of the so‐called “inflection point” bearing in mind that Eq. (21) does not hold under such conditions.
47.We emphasize that this is in line with our basic assumption that defects and impurities would not seriously disturb the density‐of‐states situation.
48.Note that we are concerned with a degenerate two‐carrier system, and thus that a constant‐τ formalism should apply.
49.Lack of accuracy in the determination of the boron content (spectroscopic methods!) prevents us from establishing this beyond reasonable doubt.
50.I. B. Mason, Industrial Carbon and Graphite (Society of Chemical Industry, London, 1958), p. 60.
51.J. E. Hove, Phys. Rev. 100, 645 (1955).
52.Reference cited in footnote 43.
53.In the sense of McClure [Proceedings of the Fourth Conference on Carbon (Pergamon Press, New York, 1960), p. 177], namely, the analysis of cyclotron‐resonance data, of the de Haas‐van Alphen effect, and of the steady magnetic susceptibility of perfect graphite.
54.An improved boron‐content analysis of some recently investigated specimens suggests that the ionization efficiency might be significantly higher and rather close to 50%, in particular with graphitized PGA structures.
55.This statement rests on the belief that other fixed scatterers do not intervene; the good agreement with crystallite sizes deduced from x‐ray work (see Table I) is quite convincing in this respect.
56.J. T. McCartney and S. Ergun, Proceedings of the Third Conference on Carbon (Pergamon Press, New York, 1959), p. 223.
57.When (one‐carrier system), in accordance with the rule for degenerate semiconductors.
58.R. T. Bate and A. C. Beer, J. Appl. Phys. 32, 800 (1961).
59.Incidentally, it appears that preferred orientation and bulk density have no influence on the thermoelectric power; the Seebeck coefficient of bonded carbons and graphites reflects basal‐plane contributions originating from organized phases of the material with no or very little perturbation by intercrystallite potential barriers.
60.J. E. Hove, Proceedings of the First and Second Conferences on Carbon (The University of Buffalo, Buffalo, New York, 1956), p. 125.
61.W. W. Tyler and A. C. Wilson, Phys. Rev. 89, 870 (1953).
62.R. A. Smith, Semiconductors (Cambridge University Press, London, 1959).
63.Generally speaking, TEP characteristics exhibit little sensitivity to moderate variations in doping at these levels; judging from the presumed Fermi‐level position we suspect that the specimen considered in Fig. 10 actually contains much less boron than reported by the manufacturer.
64.We have no explanation to offer for this phenomenon beyond suggesting that it might originate from the pronounced influence of boron on the c‐direction conductivity (see Fig. 8) via the factor of the Mott and Jones expression for of metallic conductors; the linear temperature dependence, on the other hand, again points to a broad similarity of the responsible mechanisms in both directions.
65.L. Meyer, Z. Physik. Chem. B17, 385 (1932).
66.“Fiber structure” here refers to a highly orientated type of crystallite arrangement with most of the aromatic planes lying parallel to the filament axis.
67.X‐ray diffraction studies corroborate this inference: Pyrofibers mounted with their axis perpendicular to the x‐ray beam give rise to (002) reflections that remain perpendicular to the filament when it is rotated about its axis. The degree of preferred orientation can be readily appraised by recording the (002)‐peak intensity as a function of the angle between filament axis and normal to the plane delineated by the incident and diffracted beams. For further information the reader is referred to “Final Report on High Temperature Materials Development, Contract NOrd 19135 (FBM), Task 1: Pyrofibers,” Raytheon Company, 1960 (unpublished).
68.M. Hillert and N. Lange, Z. Krist. 111, 24 (1958).
69.We note that in this respect filaments grown by the decomposition of hydrocarbons differ from the whiskers investigated by Bacon (reference 11), which can be deliberately flattened by mechanical pressure.
70.The amorphous core represents less than 2% of the total volume and can be neglected if we are exclusively concerned with in‐plane transport phenomena.
71.In single crystals the magnetoresistance effect is negligible with H perpendicular to the c axis (reference 16).
72.The confrontation confirms Mrozowski’s suspicion “the alignment of the flakes throughout such a plate was not perfect.”
73.G. Wagoner, Phys. Rev. 118, 647 (1960).
74. remains roughly equal to the free electron value, namely (reference 73).
75.A. W. Smith and N. S. Rasor, Phys. Rev. 104, 885 (1956).
76.J. T. Meers, Proceedings of the Fifth Conference on Carbon (Pergamon Press, New York, to be published ), paper 16.
77.In dealing with PF structures of irregular shape such measurements have the added asset of being independent of the exact sample geometry, and thus, of providing reliable information on the crystalline perfection.
78.We assume, or course, that the poorly‐graphitized randomly orientated core (radius ) does not substantially contribute to
79.Note that ( and H in laboratory units) remains smaller than one over the whole temperature range.
80.The curious negative temperature coefficient of resistance at around 77 °K would thus have to he accounted for by a “premature” flattening out of the mobility curve as a result of sample damage generated—in Meer’s thesis—by poor handling.
81.Observations on the thermal expansion also point in this direction (J. Pappis, private communication).
82.In this respect graphite belongs to the class of molecular solids, as stated by H. A. Pohl in his preface to “ Proceedings of the Princeton University Conference on Semiconduction in Molecular Solids,” February 16–17, 1960 (unpublished).
83.J. Mering and J. Maire, J. Chim. Phys. 57, 803 (1960).
84.Incidentally, this is in harmony with some of Stover’s comments in a very different context (reference 35).
85.A. K. Dutta, Phys. Rev. 90, 187 (1953).
86.W. Primak and L. H. Fuchs, Phys. Rev. 95, 22 (1954).
Article metrics loading...
Full text loading...
Most read this month
Most cited this month