N.H. March

Small band-gap graphitic CBN layers

Abstract Electronic band structure computations for a perfect hexagonal layer of CBN have been performed via density functional theory using the local density approximation to the exchange-correlation potential. A small band gap of ∼0.2xa0eV is thereby obtained, with the band gap being offset away from the central Γ-point of the two-dimensional Brillouin zone. These results are rationalized in terms of a simple empirical Huckel model, for which simple structural criteria for a zero band gap are noted. Special attention is paid to the case with a minimum content of carbon, and some comparison is made to earlier band structures for two different geometrical layers of C 2 BN.

Weizsäcker inhomogeneity kinetic energy term for the inhomogeneous electron liquid characterising some 30 homonuclear diatomic molecules at equilibrium and insight into Teller’s theorem in Thomas–Fermi statistical theory

A natural orbital functional theory for non-relativistic quantum chemistry due to one of us [MP] is here utilised to calculate the von Weizsäcker inhomogeneity kinetic energy at the equilibrium bond length (Re) for some 30 homonuclear diatomic molecules. Tw/N2, where N is the total number of electrons in the molecule considered, behaves remarkably simply and tends to a value very near to 1/2 for the Ge2 molecule when N = 64. This is in spite of the irregular variation of Re with N, which is inputted here from the experiment. It is then proposed that the dissociation energy De should be a functional of Tw to be sought. A start is made via the power law proposed earlier by one of us [NHM].

Is the Hartree-Fock prediction that the chemical potential µ of non-relativistic neutral atoms is equal to minus the ionisation potential I sensitive to electron correlation?

Numerical estimates of the chemical (µ) and ionisation (I) potentials from natural orbital functional (NOF) theory of one of us are presented for neutral atoms ranging from H to Kr, and compared with the corresponding experimental ionisation energies. The semi-empirical treatment by Vela et al. relates µ approximately to the measured I. By a physical argument based on the concept of the Pauli potential, we thereby derive in the fully correlated ground states of atoms. The predicted vertical I by means of the extended Koopmans theorem is in good agreement with the corresponding experimental data. However, the NOF theory of µ lowers the experimental values considerably though oscillatory behaviour is again in evidence. This comparison has prompted us to reopen the Hartree-Fock prediction by Alonso and March that .

Crucial combinations of critical exponents for liquids–vapour and ferromagnetic second-order phase transitions

Four combinations of critical exponents pertaining to the Ising model are constructed which yield simply the dimensionality d. One of these, connecting γ and η, is shown to lead to an immediately useful estimates of the sum α + η in three dimensions, about which exponents controversy still exists. This sum in three dimensions is shown to be very near or equal to 1/8, a condition which Zhang’s predictions, for the exact solution of the 3D Ising model, satisfy with α = 0 and η = 1/8. But the pioneering work of Wilson based on renormalisation group theory gave the estimate η = 0.037, while the Perk advocates α = 0.1, without however, proceeding a proof. We therefore finally stress the current importance of further experimental measurements. The critical exponent δ may be the most favourable focus, to distinguish between Zhang’s prediction of 13/3 and a value around 4.8 following for d = 3 from Wilson’s value of η quoted above.

Fractal network dimension determining the relation between the strength of bulk metallic glasses and the glass transition temperature

[Ma et al., Nat. Mater. 8, 30 (2009)] have uncovered the fractal dimension Df=2.31 associated with the medium-range order in a variety of bulk metallic glasses, reflected in the first sharp diffraction peak q1 determined from neutron and x-ray measurements. Here, based on the proposal in this journal of [Yang et al., Appl. Phys. Lett. 88, 221911 (2006)], which related the strength σy of bulk metallic glasses to the glass transition temperature Tg, we show that the product q1Dfσy is linear in Tg.

Liquid-vapour critical point behaviour: especially crossover from two to three dimensions via a magnetic analogy

Motivation for this Letter comes from two experiments. The first, by Kim and Chan (Phys. Rev. Lett. 53, 170 (1984)), measured a two-dimensional (2D) liquid–vapour critical point exponent. The second studied, via the magnetism of ultrathin metal films, the crossover of the critical exponent β from 2D to 3D. Here, the analogy between magnetic behaviour near criticality and the corresponding liquid–vapour behaviour is first used to discuss the 2D–3D crossover in the latter case. Finally, the experimentally observed magnetic behaviour near criticality is considered for the ferromagnet CrBr3 to allow fingerprints of the 3D Ising Hamiltonian to be anticipated.

Changes in nonlinear potential scattering theory in electron gases brought about by reducing dimensionality

Recent work has shown the essential equivalence of stopping power, force-force correlation function, and phase-shift analysis for nonlinear potential scattering in a three-dimensional electron gas. In the present study, we first demonstrate that the above situation is markedly different when the scattering occurs from a localized potential in a two-dimensional (2D) electron gas. Only to second order in the potential do the three methods referred to above precisely agree. However, all these methods can still be applied in 2D, some fully nonlinear evaluation proving possible. The one-dimensional case is also discussed, albeit more briefly. Scattering from a two-center modeling of the localized potential is also calculated, but now only in the Born approximation, due to the added complication of a noncentral potential.

Lowest excitation energy in atoms in the adiabatic approximation related to the single-particle kinetic energy functional

Time-dependent density-functional theory (DFT) leads to a formally exact eigenvalue equation for determining excitation energies. In an adiabatic approximation, we have first calculated the lowest excitation energies for various neutral atoms and positively charged atomic ions, for comparison with experimental data. Then, to gain further insight, the time-dependent theory is reformulated by using the chemical potential equation of time-independent DFT. The central new quantity then appearing is a second functional derivative of the single-particle kinetic energy Ts. If chemical hardness can be treated as a correction to the term involving Ts, then further analytical progress is effected. Good numerical results testify to the usefulness of invoking the time-independent DFT within the present context.

Unconventional phase diagram for six heavy rare earth metals showing melting plus magnetic transitions versus the de Gennes factor

Melting temperatures Tm of six heavy rare earth metals are well established experimentally. Here, a close correlation is displayed between these values Tm and the de Gennes factor (ξ below), which is proportional to the product of (g − 1)2 with total angular momentum values J (J + 1). We thereby exhibit a tendency of a plot of Tm versus ξ−1 to saturate at the largest ξ, this corresponding to Gd of the six selected elements. Second, following Chikazumi’s book, it is stressed that the Néel temperatures TN of the remaining five metals display empirically a good linear correlation with . Finally, the monovacancy formation energy is briefly considered in relation to the thermal energy kBTm, the ratio Ev/kBTm being of order 10 in other known cases.

Proposed relationship between the exponents γ and η at liquid–vapour critical point via the dimensionality d

In earlier work, Ma [S.K. MA, Phys. Rev. Lett., 29, 1311 (1972)] has studied the critical exponents γ and η for charged and neutral Bose gases. Here we use the result of Ma, valid for general dimensionality d but only to O(m −1), where m is the number of components of the Bose field, to write a relation between γ(d) and η(d) to O(m −1). This then motivates, but now for the Ising model, a relationship between the critical exponents γ and η, via the dimensionality d. We finally demonstrate a connection between the two renormalisation group eigenvalues y t and y h , via the critical exponent δ with a dimensional dependence.