M C Valsakumar

Low temperature x-ray diffraction study of the phases of C70

Results of X-ray diffraction study at 300K, 77K and 10K are presented for C 70 powder prepared by both solution route and by crushing a collection of single crystals. For the sample prepared by solution route the room temperature hep phase is quenched and retained up to 10K. Small changes however are observed in the c/a ratio. For the sample prepared via single crystal route the intensities of the Bragg peaks are several orders of magnitude larger and the line widths considerably reduced enabling more accurate phase analysis to be carried out. At room temperature the sample is predominantly of rhombohedral phase with an admixture of fcc phase which is less than 6%. At 10K the structure is predominantly monoclinic with the fcc fraction becoming vanishingly small. Upon warming back, the structure reverts back to rhombohedral + fcc (∼ 6%) at 300K. The results observed suggest that the equilibrium structure at room temperature could be either rhombohedral or fcc depending on the microstructural defect state of the system and / or impurities in the system and also that the equilibrium structure at low temperature is monoclinic. The results also imply for the first time that there is a path in which the fcc phase transforms directly to monoclinic phase on cooling without the intermediary rhombohedral phase implying a simultaneous freezing of all orientations.

Diffraction from a quasi-crystalline chain

We present a general formalism for diffraction from a one-dimensional quasicrystal with arbitrary length scales and sequences. The notion of sub-quasi-lattices is introduced and the effect of different basis on different sites is studied. The relevance of this work for the study of vibrational and electronic spectra of the chain is discussed.

Signature of chaos in power spectrum

We investigate the nature of the numerically computed power spectral densityP(f, N, τ) of a discrete (sampling time interval,τ) and finite (length,N) scalar time series extracted from a continuous time chaotic dynamical system. We highlight howP(f, N, τ) differs from the true power spectrum and from the power spectrum of a general stochastic process. Non-zeroτ leads to aliasing;P(f, N, τ) decays at high frequencies as [πτ/sinπτf]2, which is an aliased form of the 1/f2 decay. This power law tail seems to be a characteristic feature of all continuous time dynamical systems, chaotic or otherwise. Also the tail vanishes in the limit ofN → ∞, implying that the true power spectral density must be band width limited. In striking contrast the power spectrum of a stochastic process is dominated by a term independent of the length of the time series at all frequencies.

SPECIFIC HEAT STUDY OF C60 SINGLE CRYSTALS

Abstract We present the results of measurements of specific heat between 77K and 300K on a collection of C60 single crystals, using quasi-adiabatic heat pulse calorimetry. In the temperature warming cycle the well known orientational transformation occurs at261.5 K, with a peak value of 16 J/gm.-K, both the temperature and magnitude being the highest reported. The transformation occurs at 260.4 K in the cooling cycle, the hysteresis being noticeable due to the extreme sharpness of the peak. Considerable excess specific heat, observed over the contribution due to intramolecular vibrations, is shown to arise from the molecular reorientations between two configurations, corresponding to a pentagonal or hexagonal face of a molecule facing the interhexagonal double bonds of the adjacent molecule. A hysteresis in Cp is also observed below 240K between the warming and cooling cycles, the termination of which at 100 K is identified with the orientational glass transition. Further, heat evolution is observed at many temperatures below 180 K. These features may indicate a complex orientational dynamics of the C60 molecules

Crystal structure of solid C70

Detailed analysis of the room temperature X-ray powder diffraction data of pure solid C70 is reported. C70 prepared by slow evaporation from toluene solution adopts an hcp structure (space groupP63/mmc) witha=10·53(1) A andc=17·24(1) A. C70 sublimed on to Si wafer adopts an fcc structure witha=14·89(1) A. The occurrence of both the hcp and fcc phases is rationalized in terms of cohesive energy calculations. Theoretical calculations of the diffraction pattern for the hcp structure, taking into account (a) orientational disorder amongst the molecules (b) presence of stacking faults and (c) a fraction of the sample to be amorphous/microcrystalline is seen to provide very good agreement with the experimental diffraction pattern.

Algebraic structure of Nambu mechanics

Abstracting from Nambu’s work [1] on the generalization of Hamiltonian mechanics, we obtain the concept of a classical Nambu algebra of type I (CNA-I). Consistency requirement of time evolution of the trilinear Nambu bracket leads to a new five point identity (FPI). Incorporating the FPI into CNA-I, we obtain a classical Nambu algebra of type II (CNA-II). Nambu’s algorithm for generalized classical mechanics turns out to be compatible with CNA-II. Tensor product composition of two CNA-I’s results in another CNA-I whereas that of two CNA-II’s does not. This implies that interacting systems cannot be consistently treated in Nambu’s framework. It is shown that the recent generalization of Nambu mechanics based on an arbitrary Lie group (instead of the particular case of the rotation group as in the case of Nambu’s original algorithm) suggested by Biyalinicki-Birula and Morrison [2], is compatible with CNA-I but not with CNA-II. Relaxation of the commutative and associative observable product by making it nonassociative so as to arrive at the quantum counterpart meets with serious difficulties from the view point of tensor product composition property. Thus neither CNA-I nor CNA-II have quantum counterparts. Implications of our results are discussed with special reference to existing work on Nambu mechanics in the literature.

Stochasticity, decoherence and an arrow of time from the discretization of time?

Certain intriguing consequences of the discreteness of time on the time evolution of dynamical systems are discussed. In the discrete-time classical mechanics proposed here, there is an arrow of time that follows from the fact that the replacement of the time derivative by the backward difference operator alone can preserve the non-negativity of the phase space density. It is seen that, even for free particles, all the degrees of freedom are correlated in principle. The forward evolution of functions of phase space variables by a finite number of time steps, in this discrete-time mechanics, depends on the entire continuous-time history in the interval [0, ∞]. In this sense, discrete time evolution is nonlocal in time from a continuous-time point of view. A corresponding quantum mechanical treatment is possible via the density matrix approach. The interference between nondegenerate quantum mechanical states decays exponentially. This decoherence is present, in principle, for all systems; however, it is of practical importance only in macroscopic systems, or in processes involving large energy changes.

Noise-induced jumps in two coupled Duffing oscillators

We consider two coupled Duffing oscillators with the coexistence of four attractors. Switching between the coexisting attractors by noises is investigated. Three types of noises such as Gaussian, amplitude dependent and dichotomous are used. We observed noise-induced extrinsic intermittency. Intermittent dynamics is characterized using power spectrum, average and relative residence times on each precoupled attractors and probability distribution of time interval between successive switchings. Variation of probability distribution of state variables in Poincare map is studied as a function of noise strength. The effect of various noises is compared. The occurrence of crisis-induced and type-I intermittencies are also presented.

Solid state effects during deuterium implantation into copper and titanium

Results of neutron counting experiments during deuterium implantation into titanium and copper are reported. Models for neutron yield have been developed by taking into account different solid state effects like energy degradation of incident ions, energy dependent d-d fusion cross section and diffusion of implanted deuterium possibly influenced by surface desorption and formation of metal deuterides. The asymptotic time dependence of the neutron yield during implantation has been compared with the experimental results. Using these results, solid state processes that might occur during deuterium implantation into these metals are inferred.

Diffusion controlled multiplicative process: typical versus average behaviour

We investigate the dynamics of the number of particles diffusing in a multiplicative medium. We show that the typical behaviour of the growth process is different from the average. We develop a new formalism to study the average growth process and extend it to the calculation of higher moments and finally of the probability distribution. We show that the fluctuations of the growth process increase exponentially with time. We describe the interesting features of the distribution.