Disorder in Staging of Potassium Graphite: Fractional Stage 3/2 and Stage 7
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D.B. McWiHAN Bell Laboratories, Murray Hill, New Jersey 07974, USA ABSTRACT At high pressure KC8 undergoes a staging transition to a mixture of stages 1 and 3/2 at 15 kbar and stages 1 and 2 at 19 kbar. The width of the new peaks are not resolution limited but show a pronounced and non-monotonic variation with Q. This broadening is the result of a finite concentration of staging defects which can be simply modeled by stochastic disordering of an appropriately chosen two component layer sequence. This same analysis has also been used to explain deviations from the Bragg locations in KC84. INTRODUCTION Staging in layer intercalates refers to the formation of ordered periodic sequences of filled and empty gaps between adjacent host layers. This periodic sequence of graphite and intercalant layers can be described as a one dimensional crystal for scattering along the (OOL) direction. The scattering from one dimensional crystals has been described by Hendricks and Teller [1]. Their intensity equation provides for the selection of arbitrary scattering powers and phase shifts. The disorder in the crystal is determined by the statistical correlation between layers. The problem of solving this equation has been further simplfied by Kakinoki and Komura This analysis has been used recently by Johnston and Frysinger on [2]. Na 1/3(H 2 0) 1 .5TaS 2 [3]. MODEL AND PARAMETERS Our model contains two cells and each cell can contain any number of graphite and intercalant planes. We shall refer to the two cells as S1 and S2' The probability of any position being occupied by a cell of type Si is given by P. . where P . + P 2 = 1. These parameters fix the stoichiometry of the model. The statistical correlation between the layers is determined by a 2x2 matrix with elements Pij. These elements define the probability of a Sj cell following a Si cell. These four elements are subject to the restrictions: Pi Pii + Pj Pji = Pi and Pii + Pii = 1. We define the parameter X = PIP1 1 to determine the statistical correlation matrix given a fixed stoichoimetry, P X must be a positive number less than P1 and greater than (2P 1 -1). TIhis defines a triangle in (P 1 , X) space.
Hat. Res. Soc. Symp. Proc. Vol. 20 (1983)I
Elsevier Science Publishing Co., Inc.
40 Allowing P1 to approach 1 produces an interference pattern of ýtage S with increasing order. Approaching along the line of X = (P 1 ) causes the placement of the minority cells to occur randomly in the otherwise stage S1 crystal. Approaching the point (0.5, 0) in (PI' X) space models the formation of a well ordered stage whose stacking appears as $S12S1S2 etc. APPLICATION TO STAGE 3/2 (HIGH PRESSURE) Figures ia) and Ib) show the (OOL) scans of the two mixed stage regions of KC8 observed at 16 and 19 kbar respectively. The five new reflections in Fig. 1a) are indexed as L=1 through 5 with a repeat distance 13.61 A which we attribute to the fractional stage 3/2 (repeat sequence CMCCM, where C refers to a carbon layer and M an alkali layer). At higher pressure, Fig. Ib), the stage 3/2 refl
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