Phase selection and transformation kinetics in KC 60 L. Gra ´ na ´ sy and S. Pekker Research Institute for Solid State Physics, H– 1525 Budapest, P.O.B. 49, Hungary O. Chauvet Institut des Materiaux de Nantes, Laboratoire de Physique Cristalline, F-44072 Nantes, Cedex 03, France L. Forro ´ Departement de Physique, E ´ cole Polytechnique Fe´derale de Lausanne, CH-1015 Lausanne, Switzerland ~Received 10 June 1996! Phase selection in the 205–500 K range and the kinetics of phase transformations are studied by differential scanning calorimetry in KC 60 . The long-time phase selection is compatible with the Gibbs free energies determined previously. The Avrami exponent ( n 5 1.9 6 0.1! found for polymerization is consistent with two-dimensional polymorphic growth at a fixed number of sites. In the 320–380 K temperature range, poly- merization is coupled with phase separation of a volume fraction ~0 to ; 40 %! increasing with temperature. Between ;380 and 440 K, the phase separation takes place by diffusion-controlled three-dimensional growth accompanied with heterogeneous nucleation approaching site saturation. @S0163-1829~96!06942-1# KC 60 has a rich phase diagram. At high temperatures a fcc rocksalt structure ~HT! containing freely rotating C 60 monomers is stable. 1,2 When it is cooled slowly ( ;1 K/min!, an orthorhombic structure containing covalently bonded charged polymer ~P! chain forms by @212# cycloaddition. 3,4 Heating the polymer, a mixture of C 60 and K 3 C 60 forms by phase separation on a few hundred Å scale ~PS state!, which recombines into the HT on further heating. 5 At cooling rates of ;1 K/s polymerization can be bypassed, and a metastable monoclinic phase containing singly bonded ~C 60 2 ) 2 dimers 6 ~D! appears. Heating the dimer, a transient cubic ~TC! structure develops that consists of locked ~or per- haps librating! C 60 ions. 7 Its structure may be either fcc or simple cubic depending on the degree of orientational order- ing. Heating the TC phase, a rotational transition similar to that in C 60 is observed resulting in an fcc structure. In RbC 60 , the lattice constant of the respective phase fits to the low-temperature extrapolation of HT which implies that this phase ~LHT! is the low-temperature continuation of HT. 8 Recently, we evaluated the Gibbs free energies and stabil- ity ranges of these phases from thermal data measured by differential scanning calorimetry ~DSC!. 9 The stable phases are the polymer below ;380 K, the PS state between ;380 K and 440 K, and the HT above @see Fig. 1~a!#. While the Gibbs free energies combined with kinetic effects fully account for the observed phase sequences, 9 the low- temperature stability of the polymer conflicts the phase dia- gram proposed by Poirier et al. 10 Their x-ray photoemission spectroscopy ~XPS! measurements, performed on vapor- deposited C 60 layers doped with K, indicate that the PS state is stable below 425 K. This finding is supported by recent electron spin resonance ~ESR! data on a powder sample by Robert et al. 11 which suggest that at 360 K phase separation takes place in the polymer on a 20-h time scale. To clarify this issue, the long-time phase selection and the kinetics of phase separation are investigated in this work. Powder samples were produced by coevaporating K and high-purity ~99.9%! C 60 . The phase transformations were studied by a Perkin-Elmer DSC-2 calorimeter. The investi- gations were performed on a nearly stoichiometric and an off-stoichiometric sample, containing unreacted C 60 of X C60 50.04 and 0.14, respectively, as evaluated from the thermal effect of the rotational transition at 267 K. The thermograms recorded after 1- and 20-h heat treat- ments are shown in Figs. 1~b! and 1~c!. They were obtained as follows. First, the sample was held at 500 K for 10 min to obtain the HT phase. Then, it was quenched to the tempera- ture of the heat treatment T ht at the highest cooling rate avail- able ( ;1 K/s, high enough to suppress both polymerization and phase separation!. After the heat treatment, the sample was further quenched to the starting temperature of the DSC measurement ~205 K!. Finally, the thermogram was recorded between 205 and 500 K at a heating rate of 20 K/min. As expected, the stable phases ~HT, PS, and P! or their mixtures appear after the heat treatments. Note that during the quench- ing to 205 K, the HT phase transforms into the dimer. Ac- cordingly, the DSC curves are weighted sums of those for the fully polymerized, phase separated, and dimerized states known from previous works, 5,9 which show the following phase transitions: P → PS → HT 5 @Fig. 1~b!, lowermost curve#, PS8 →PS→ HT ~Ref. 5!@Fig. 1~c!, T ht 5395 K; PS8 2PS below the rotational transition of C 60 #, and D → TC → LHT → P → HT @Fig. 1~b!, uppermost thermogram#. Before a detailed discussion, we note that ~i! the polymer ‘‘relaxes.’’ Upon heat treatment, the depolymerization peak at ;400 K becomes sharper, and shifts upwards, while the subsequent phase separation and recombination peaks be- come less pronounced ~cf. curves for 1 and 20 h at T ht 5350 K!. This indicates that the relaxed polymer is less willing to phase separate upon depolymerization than the unrelaxed one. ~ii! The PS state also evolves with time. On heat treatment, the temperature of the rotational transition of the C 60 regions ( ;255–260 K! shifts towards the bulk value PHYSICAL REVIEW B 1 NOVEMBER 1996-I VOLUME 54, NUMBER 17 54 0163-1829/96/54~17!/11865~4!/$10.00 11 865 © 1996 The American Physical Society