Stochastic model of staging in graphite intercalation compounds
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(Received 27 July 1987; accepted 16February 1988) A stochastic model is presented for staging transitions in graphite intercalation compounds. Three types of kinetic processes are introduced into the domain model of Daumas and Herold, and a one-dimensional Monte Carlo simulation is carried out within the framework of a singlecolumn model to study the time evolution of the system for a variety of cases of staging transitions. Results of Monte Carlo simulations from stage 3 to stage 2 after a sudden change of chemical potential show that the staging transition depends sensitively on the final value of the chemical potential/^, temperature of the system, and the kinetic coefficients. When/Zy is taken in a certain range in the phase diagram, the time evolution of the structure factor demonstrates the coexistence and no significant broadening of peaks corresponding to the initial and final stage states. For other values of/x/; it is observed that the staging transitions proceed via disordered states and in some cases the final states are also disordered. Similar results are obtained for staging transitions from stage 4 to stage 3. Simulations are also made for staging transitions in which the start is from stage 4 and suddenly// changes to a value in the stage-2 stable region. It is found that the system transforms either directly into a stage-2 state or into a metastable stage-3 state without showing evidence of further transition into a final stage-2 state, depending upon the values ofyty and kinetic coefficients. A discussion is presented on the possibility of observing an intermediate metastable stage-3 state during the transition from stage 4 to stage 2.
I. INTRODUCTION When layered materials are intercalated with atoms or molecules of different chemical species (intercalant), they form intercalation compounds in which some of the empty galleries of the host materials are filled by intercalants.' The intercalation process is usually accompanied with charge transfer between intercalants and host materials, which brings about significant modification of the electronic properties of the host materials, e.g., highly conductive compounds.2 In graphite intercalation compounds (GIC's), in particular, the intercalation processes are easily controlled by controlling the chemical potential of intercalants.3 It is for this reason that the physical and chemical properties of GIC's have attracted much interest over the past few decades, and a variety of structural phase transitions have been found that are associated with the ordering of the guest intercalant layers (I layers). 4 ' 5 One of the characteristic features of GIC's is that the I layers in the ordered state are arranged periodically along the c axis of the host graphite. This periodic sequence of I layers is best classified by the stage number n, which denotes the number of carbon layers sandwiched by adjacent two I layers. This phenomenon, called staging, is unique to GIC's and is the key feature in yielding a variety of structural and electronic properties of GIC'
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