Changes of Probabilities P₁, P_ABA, _PABC with Heat Treatment of Carbons

Abstract

The probability of nearest neighbour layers having the graphite relation (P₁) and the probabilities of second neighbour layers being in the ABA sequence (P_ABA) and in the ABC sequence (P_ABC) were determined for the heat-treated samples of a petroleum coke, a thermal black and a channel black. The profiles of (10) and (11) diffraction lines were measured by using Ni-filtered Cu K_α radiation. A propotional counter furnished with a puls-heights analyser was used to cut off the white ray component. The observed profiles were corrected for instrumental broadening by the Stokes' method, for low absorption effect by the method of Keating and Warren, and for Lorentz polarization and scattering factors. An electronic computor was used for the corrections and also for the calculations of Fourier coefficients.
Observed values of P₁ and a₃ (=c_o/2) were very well represented by the Warren's relation, that is,
a₃=P₁·a₃+ (1-P₁) ·a'₃ (1)
where a₃= 3.354 and a'₃=3.44Å.
According to Maire and Mering,
P_n=gⁿ⁺¹ (2)
where P_n is the probabilty of n-th neighbour layers being ordered in the graphite relation and
a₃=g·a₃+ (1-g) ·a'_3·
They verified experimentally,
P₁=g² (3)
From Eq.(1), on the other hand, one can obtain,
P₁=g (4)
In the present experiment, Eq.(4) was verified. For P₂, however, the equivalent relation to Eq.(2) (P₂=g³) was obtained. In order to discuss on these relations in more detail, the further experimental works are needed.
The probabilities P_ABA and P_ABC were almost equal in the range of p₁≤0.8. Above that value of P₁, P_ABA increased rapidly, while P_ABC remained as unchanged at a value of 0.23 or P_ABC/P₁=0.3. The latter relation corresponds to a reported value (33%) for the concentration of rhombohedral modification in the well-pulverized natural graphite.