Jean-Louis Colot

The freezing of hard spheres: The density functional theory revisited

We have analysed the recent theories of freezing and found that all results obtained hitherto are biased numerically by the early truncation of slowly converging series. As a result the local density of the solid is shown to become very negative in the interstitial regions. Therefore we have reconsidered the theory of freezing starting from formally exact equations, making three physical approximations and testing all numerical methods for the case of the freezing of hard spheres. A fluid-solid transition is found which is in fair agreement with the known computer experiments.

The freezing of hard disks and hyperspheres

Abstract A unified density functional theory for the freezing of hard rods, disks, spheres and hyperspheres is presented. The hard rod solid is shown to be unstable with respect to density changes (negative compressibility). The results for the hard disk and the hard sphere transition compare well with the computer simulations.

The freezing of hard spheres II: A search for structural (f.c.c.-h.c.p.) phase transitions

The recently proposed theory of freezing is reformulated entirely in real (direct lattice) space. This allows high precision calculations to be performed easily and also leads to a better understanding of the underlying freezing mechanism. When applied to the freezing of hard spheres into f.c.c. or h.c.p. lattices it is found that the free energy differences involved are extremely small. A differentiation between the compact structures will be possible only if the range of the true direct correlation function appreciably exceeds its Percus-Yevick value used here.

Theoretical structure factors for hard-core fluids

On the basis of a geometrical interpretation of the direct correlation function of a hard-core fluid the authors propose a general expression for it that is consistent with the known results for hard rods, hard discs and hard spheres and that is considerably simple than Leutheussers recent proposal (see J.Chem. Phys., vol.84, p.1050, 1986).

The hard-sphere glass: metastability versus density of random close packing

The density functional theory is applied to the freezing of the hard-sphere fluid into a dense-random-packed glass configuration. It is shown that the relative thermodynamic stability of the fluid, glass and crystal phases is completely determined by only two structural features: the number of nearest neighbours and the density of close packing.

Stability of the high-density hard-sphere solid in the density-functional theories of freezing

It is shown that the recently proposed density-functional theory of freezing predicts a thermodynamically stable hard-sphere solid up to the density of crystal close packing. The behaviour is contrasted with the unphysical remelting of the hard-sphere solid just after freezing found in an alternative theory. Some possible reasons for this discrepancy are pointed out.

APW bands and bonding in transition metal oxides, nitrides and carbides

To understand more fully the relationships between APW bands and covalent binding in these compounds, a model is constructed where bonds are formed of 2s and 2p anionic states extended towards neighbouring sites by means of six equivalent metallic orbitals. Valence bands are generated in the way similar to that of the bond orbital model for semiconductors. The model explains by the intermediary of electronegativity differences the correlation between cohesion energies and the valence bandwidths quoted by Slater (1974). Moreover in contrast to the tight-binding approximation, it confers only a secondary role to lattice spacing. This model emphasizes the importance, previously recognized by Ramqvist and Phillips, of the electronegativity differences in these compounds.

Critical indices in three dimensions

A modification of Wilsons epsilon -expansion scaling procedure is adapted to direct calculation in three dimensions. The parameter log r is replaced by (r- epsilon 2/-1) where r=tgamma (t=temperature) and all calculations are carried out directly at epsilon =1. Several conclusions are drawn: (i) Numerical agreement with the best known data for gamma and eta is excellent (1% in gamma and 10% in eta ) whereas the corresponding values are far less good in the epsilon -expansion where eta is off by a factor of more than two. (ii) The series appears to converge very well when corrections to the leading term are summed two by two. (iii) Extrapolations of the early orders of the epsilon -expansion to epsilon =1 are unjustified.

Heat capacity of two-dimensional O(n) spin systems by the Monte Carlo method

Monte Carlo estimates of the heat capacity of the two-dimensional O(n) spin systems with n=3, 4 and 5 are compared to the results given by the spherical model (n to infinity ). The values of the maxima of the heat capacity are approximately equal to 1/2n, when the temperature is 2n-1. The C/n against nT curves of the estimates come close to the curve of the spherical model for nT>or approximately=4.

Failure of length scaling in Wilson's ϵ expansion

Abstract We show that length scaling of the four-point scattering amplitude in Wilsons ϵ expansion is not consistent in the order of ϵ 3 . However, in conformity with conformal invariance at the critical point, momentum scaling in a given channel is consistent. This latter method permits us to calculate the dimension of the field φ 2 at the critical point without recourse to length scaling and one finds d φ 2 = d 2 − 1 ν to O (ϵ 2 ) as if length scaling were true. However, this does not imply Kadanoffs relation 2− α = νd which is predicted on length scaling. Indeed the above-mentioned inconsistency makes impossible the determination of α by these methods.