Table of contents

Lattice Hamiltonians with on-site interaction W have W = 0 solutions, that is, many-body singlet eigenstates without double occupation. In particular, W = 0 pairs give a clue to understand the pairing force in repulsive Hubbard models. These eigenstates are found in systems with high enough symmetry, like the square, hexagonal or triangular lattices. By a general theorem, we propose a systematic way to construct all the W = 0 pairs of a given Hamiltonian. We also introduce a canonical transformation to calculate the effective interaction between the particles of such pairs. In geometries appropriate for the CuO₂ planes of cuprate superconductors, armchair carbon nanotubes, or cobalt oxide planes, the dressed pair becomes a bound state in a physically relevant range of parameters. We also show that W = 0 pairs quantize the magnetic flux as superconducting pairs do. The pairing mechanism breaks down in the presence of strong distortions. The W = 0 pairs are also the building blocks for the antiferromagnetic ground state of the half-filled Hubbard model at weak coupling. Our analytical results for the 4 × 4 Hubbard square lattice, compared to available numerical data, demonstrate that the method, besides providing an intuitive grasp on pairing, also has quantitative predictive power. We also consider including phonon effects in this scenario. Preliminary calculations with small clusters indicate that vector phonons hinder pairing while half-breathing modes are synergic with the W = 0 pairing mechanism both at weak coupling and in the polaronic regime.

The cascaded parametric processes, i.e. optical parametric oscillation (OPO) and difference frequency generation (DFG), can be used to induce efficient CW mid-infrared radiation at 4–5 µm in a single optical superlattice obtained by aperiodically poling a ferroelectric crystal. The superlattice consists of basic building blocks modulated by a spatial function. We numerically solve the coupling equations considering pump depletion and mid-IR absorption and realize the optimal condition for the cascaded frequency-down-conversion processes. Simultaneously, it is seen that the output performance is enhanced by the cascaded parametric design compared to the standard OPO configuration.

Self-assembled and well aligned RuO₂ nanorods (NRs) have been grown on sapphire (SA) substrates via metal–organic chemical vapour deposition (MOCVD), using bis(ethylcyclopentadienyl)ruthenium as the source reagent. The surface morphology, structural, and spectroscopic properties of the as-deposited NRs were characterized using field-emission scanning electron microscopy (FESEM), transmission electron microscopy (TEM), selected-area electron diffractometry (SAD), x-ray diffraction (XRD), x-ray photoelectron spectroscopy (XPS), and micro-Raman spectroscopy. FESEM micrographs reveal that vertically aligned nanorods (NRs) were grown on SA(100), while the NRs on the SA(012) were grown with a tilt angle of from the normal to the substrates. TEM and SAD measurements showed that the RuO₂ NRs with square cross-section have the long axis directed along the [001] direction. The XRD results indicate that the RuO₂ NRs are (002) oriented on SA(100) and (101) oriented on SA(012) substrates. A strong substrate effect on the alignment of the RuO₂ NRs growth has been demonstrated and the probable mechanism for the formation of these NRs has been discussed. XP spectra show the coexistence of higher oxidation state of ruthenium in the as-grown RuO₂ NRs. Micro-Raman spectra show the red-shift and peak broadening of the RuO₂ signatures with respect to that of the bulk counterpart which may be indicative of a phonon confinement effect for these NRs.

Extended x-ray absorption fine structure studies were performed to follow the structural behaviour of FeSe₂ and FeSe/Fe₇Se₈ nanocrystalline phases produced from a mechanically alloyed Fe₂₅Se₇₅ mixture when exposed to high pressure. A phase transition from marcasite FeSe₂ to NiAs-type FeSe/Fe₇Se₈ was previously reported when the milling time was increased from 20 to 62 h; this study proposes to verify the possibility of inducing the same phase transition in high-pressure experiments using a diamond anvil cell.

U/Fe multilayers constitute a magnetic system in which the 3d magnetism of the Fe layers will be modified by hybridization with the U 5f electrons. This paper describes a programme of measurements of the magnetic behaviour of these systems beginning with the fabrication and thorough characterization of the samples. Metallic U/Fe multilayers were prepared by DC sputtering in a UHV chamber. A range of samples with measured U thicknesses, t_U, in the range 18–66 Å and Fe thicknesses, t_Fe, from 7 to 108 Å was fabricated. X-ray and neutron reflectivity measurements showed strong peaks indicating good layer structure and gave a determination of the bilayer thickness. X-ray diffraction analysis showed crystalline α-U and α-Fe for layer thicknesses greater than about 20 Å. The α-Fe is strongly textured with (110) planes in the layer plane. The Fe lattice parameter is larger for the case of thin layers, but approaches the bulk value of 2.866 Å at . Mössbauer spectra of α-Fe were obtained for ; a non-magnetic component of thickness  per layer is always present. The results from these different experimental techniques are combined to present a detailed description of these multilayer systems.

Well-defined U/Fe multilayers of varying layer thicknesses and bilayer repeat numbers were prepared by a dc magnetron sputtering method. Polarized neutron reflectometry, off-specular neutron diffraction and magnetic moment measurements were used to determine the physical properties of the multilayers leading to an evaluation of the magnetic moments associated with the U and Fe atoms. The multilayers exhibit ferromagnetic behaviour with the easy axis in the plane of the multilayer. The saturation magnetization was found to increase with increasing Fe-layer thickness and the magnetic moment averaged over the structured iron layers was below the bulk value of 2.2 μ_B/Fe atom. No anomalies were observed in the magnetization from 4.2 to 375 K in temperature-dependent scans at 0.005 and 0.1 T or in magnetic field scans from 0 to 7 T at 4.2 and 295 K. The hysteresis curves exhibited a small degree of perpendicular magnetic anisotropy. The Curie temperatures for the multilayers were determined from ac susceptibility measurements and were found to be less than the bulk Fe value of 1043 K.

A numerical simulation study of the density dependence (ρ = 2.2–4.0 g cm⁻³) of the high energy collective dynamics in vitreous silica at mesoscopic wavevectors (Q = 1–18 nm⁻¹) is reported. The dynamic structure factor, S(Q,ω), and the density of states, ρ(E), have been determined in the harmonic approximation via the system eigenvalues and the eigenvectors, in turn obtained by the direct diagonalization of the dynamical matrix. The BKS interaction potential employed is capable of reproducing the experimentally observed excess of states (boson peak), and its density dependence. The numerical simulation also indicates a strong density dependence of the transverse excitation dispersion relation, Ω_T(Q), at large Q. Specifically, Ω_T(Q) is found to flatten at high Q to a value that increases with increasing density. The parallel between the density dependent flattening of Ω_T(Q) and the density dependence of the boson peak suggests that the latter feature arises from the high Q portion of the transverse branch. This hypothesis is in line with both the interpretation by Elliott and co-workers (Taraskin et al 2001 Phys. Rev. Lett. 86 1255), who assign the boson peak to a phenomenon in glass reminiscent of the lowest energy Van Hove singularity in the companion crystal, and the Buchenau et al (1986 Phys. Rev. B 34 5665) assignment of the boson peak to the localized hindered rotation of SiO₂ tetrahedra.

We have studied how different growth conditions, namely, oxygen flow rate, annealing temperature and annealing time affect the diameter, aspect ratio and number density of CuO nanorods using scanning and transmission electron microscopy. CuO nanorods are synthesized by thermal annealing of thin copper foil. It is observed that while the diameter and number density of nanorods depend critically on the oxygen flow rate and annealing temperature, the aspect ratio and dispersion in diameter of nanorods can mostly be improved by thermal annealing for extended time periods. The growth mechanism of the nanorods is inferred from the evolution of observed microstructural changes. It is proposed that the growth of nanorods takes place from triangular shaped pyramids due to the relaxation of stress accumulated in oxide film during the process of oxidation and annealing.

The equilibrium geometries, phonon spectra, electronic structures and optical properties of the C_iO_i defect in bulk Si and Si_1−xGe_x systems are calculated using the ab initio plane wave density-functional method. We find that in a Ge-doped Si crystal it is more energetically favourable for the defect to stabilize in a configuration with no Ge atoms in the first sphere. Our calculations show that the vibrational properties of the defect in the Si_1−xGe_x alloy are similar to those in the pure Si bulk crystal and only one local vibrational mode is sensitive to the presence of the Ge substitutions. The effect of C, O, Si and Ge isotopes on the phonon spectra are also investigated and found to be in good agreement with available experimental data. It also follows from our calculations of the singlet–triplet splitting and a position of the gap state of the defect with respect to the top of the valence band that the optical energies of the C_iO_i defect are expected to increase due to Ge doping, which is in agreement with available experimental data.

Synthetic samples of the pyrochlores La₂Zr₂O₇ and La₂Hf₂O₇ were irradiated in situ in the intermediate voltage electron microscope (IVEM-Tandem Facility) at Argonne National Laboratory using 1.0 MeV Kr²⁺. Results of this study demonstrate that both pyrochlores pass through the crystalline–amorphous transformation albeit with significantly different critical amorphization dose curves. The critical dose values extrapolated to 0 K (D_c0) are 11 ± 3 × 10¹⁴ ions cm⁻² ( dpa) for La₂Zr₂O₇ and 5.5 ± 0.7 × 10¹⁴ ions cm⁻² ( dpa) for La₂Hf₂O₇. Non-linear least squares analysis of the dose–temperature curves gave values of the critical temperature (T_c) of 339 ± 49 K for La₂Zr₂O₇ and 563 ± 10 K for La₂Hf₂O₇. This analysis also gave values of the activation energy (E_a) for thermal recovery of damage of 0.02 ± 0.01 and 0.05 ± 0.01 eV for the zirconium pyrochlore and the hafnium pyrochlore, respectively. These results demonstrate that there is a major difference in the dose–temperature response dependent upon the nature of the B-site cation of these two pyrochlores. Results are discussed in terms of the pyrochlore structural parameters r_A/r_B and x(48f) as well as the stopping powers, displacement energies, and defect energies of the materials.

We investigate the ground state properties of the t–J model on a two-leg ladder with anisotropic couplings (t,α = J/t) along rungs and () along legs. We have implemented a cluster approach based on four-site plaquettes. In the strong asymmetric cases and the ground state energy is well described by plaquette clusters with charges Q = 2,4. The interaction between the clusters favours the condensation of plaquettes with maximal charge—a signal for phase separation. The dominance of Q = 2 plaquettes explains the emergence of tightly bound hole pairs. We have presented the numerical results from exact diagonalization to support our cluster approach.

A universal orthogonal tight-binding (TB) model is developed for transition metals, with special emphasis on spin-polarized self-consistent calculations. The parameters of the TB model are directly obtained from the ab initio bulk calculations within the linear muffin-tin orbital atomic sphere approximation method, without any fitting. With the environmental dependence of the Hamiltonian included in the localized structure constants, the TB model can be reliably applied to various situations, from periodic bulk structures to small clusters, for both pure metals and alloys. We have tested the model in spin-polarized calculations against ab initio results for small computational cell systems, and applied the model to study the spin and orbital magnetism of some large clusters.

We have performed systematic high-resolution angle-resolved photoemission spectroscopy (ARPES) on layered transition-metal dichalcogenides Nb_1−xTi_xXc₂ (Xc =  S, Se, Te) to study the mechanism of metal–semiconductor transition as a function of x and Xc. We found a pseudogap near E_F in the S- and Se-based compounds while a clear Fermi edge is observed in the Te-based compound. The existence of the pseudogap indicates the strong scattering of electrons by the random potential caused by substitution, which prevents formation of the charge density wave and at the same time decreases the metallic conductivity. The metallic character of Nb_1−xTi_xTe₂ is explained in terms of the relatively strong Te 5p–Nb 4d (Ti 3d) hybridization near E_F.

We present first-principles investigations of the structural and electronic properties of PPV in both the isolated chain and the crystalline state. The calculations are mainly based on the local density approximation within density functional theory. With this approach, we have determined the optimal structure and torsional conformation for an isolated one-dimensional polymer chain. The predicted structural and electronic properties of PPV are generally in good agreement with recent work. However, for the vinyl C = C double bond, there exists a relatively large difference (>0.03 Å) in bond length between experiment and theory, and we postulate that this arises from a bond alternation. In the crystalline state, we find that intrachain interactions are dominant, and that interchain effects play a secondary but significant role for some bands. Effective masses are calculated from the band structure, which are helpful for understanding the opto-electronic properties of the polymer, and in particular, allow us to calculate the exciton binding energy and radius.

An explicit expression for the quadratic density-response function of a many-electron system is obtained in the framework of the time-dependent density-functional theory, in terms of the linear and quadratic density-response functions of noninteracting Kohn–Sham electrons and functional derivatives of the time-dependent exchange–correlation potential. This is used to evaluate the quadratic stopping power of a homogeneous electron gas for slow ions, which is demonstrated to be equivalent to that obtained up to second order in the ion charge in the framework of a fully nonlinear scattering approach. Numerical calculations are reported, thereby exploring the range of validity of quadratic-response theory.

Quantum mechanical coupling and strain in two vertically arranged InP/InGaP quantum dots is studied as a function of the size of the dots and the spacer thickness. The strain distribution is determined by the continuum mechanical model, while the single-band effective-mass equation and the multiband theory are employed to compute the conduction and valence band energy levels, respectively. The exciton states are obtained from an exact diagonalization approach, and we also compute the oscillator strength for recombination. We found that the light holes are confined by strain to the spacer, which is the reason that the hole states exhibit coupling at much larger distances as compared with the electrons. At small d, the doublet structure of the hole energy levels arises as a consequence of the relocation of the light hole from the matrix to the regions located outside the stack, close to the dot–matrix interface. When d varies, the exciton ground state exhibits numerous anticrossings with other states, which are related to the changing spatial localization of the hole as a function of d. The oscillator strength of the exciton recombination is strongly reduced in a certain range of spacer thicknesses, which effectively turns a bright exciton state into a dark one. This effect is associated with anticrossings between exciton energy levels.

We estimate, using high-temperature series expansions, the transition temperatures of the spin , 1 and Heisenberg ferromagnet and antiferromagnet in three dimensions. The manner in which the difference between Curie and Néel temperatures vanishes with increasing spin quantum number is investigated.

We present ¹⁵¹Eu Mössbauer measurements on Eu₂BaNiO₅, where the Ni²⁺ form well separated S = 1 antiferromagnetic chains. The appearance of magnetic moments in this compound evidences a 'crossed bootstrap' polarization since neither the Eu³⁺ nor the Ni²⁺ will carry magnetic moments unless polarized by an exchange field coming from the other sublattice. We confirm that the Eu³⁺ ion carries a magnetic moment below 30 K implying that Ni²⁺ ordered moments also appear below this temperature. We measure the thermal dependence of the size of the Eu³⁺ moment and of the polarizing field produced by the Ni²⁺. Both show distributions which we link to the role of defects in the nickel chains. The measurements also provide the thermal dependence of the relative size of the Ni²⁺ moments. We compare the rare earth and nickel properties of Eu₂BaNiO₅ with those of isomorphous compounds.

The magnetic properties of PrMn_2−xCu_xSi₂ () were studied by field-cooled and zero-field-cooled magnetization measurements in the temperature range 5 K  K in low external fields (5 mT) and by magnetic-field-dependent magnetization measurements in fields up to 5.5 T. Substitution of Cu for Mn leads to a linear decrease in the lattice constant c and the unit cell volume V and a linear increase in the lattice constant a. Earlier neutron diffraction experiments showed that Pr does not order down to 1.6 K in PrMn₂Si₂ while the ferromagnetic Mn planes are ordered antiparallel along the c axis. With the increasing Cu content, the magnetization increases rapidly at low temperatures for the samples with . Cu substitution strongly changes the magnetic properties and leads to the magnetic ordering of the Pr sublattice. This is mainly deduced from the discussion of the values of the magnetic moments at low temperatures. Below the Curie temperatures T_C, the spins in the Mn sublattice are arranged parallel to the Pr sublattice. With increasing Cu, T_C(x) has a maximum value of 155 K at x = 0.6 and decreases for samples with .

Extensive magnetization measurements have been performed over wide ranges of temperature and magnetic field on polycrystalline Ni₇₅Al₂₅ samples 'prepared' in different states of site disorder and thoroughly characterized by x-ray diffraction (XRD), x-ray fluorescence and inductively coupled plasma optical emission spectroscopy. Detailed analysis of the magnetization (XRD) data permits an accurate determination of the spontaneous magnetization, M₀, zero-field differential susceptibility, χ₀, and spin wave stiffness, D₀, at 0 K, Curie temperature, T_C, density of states (DOS) at the Fermi level, N(E_F) (the atomic long-range order parameter, S, which is a direct measure of the site disorder present). The effect of site disorder on the ground-state as well as the finite-temperature magnetic properties of Ni₇₅Al₂₅ is clearly brought out by the observed variations of M₀, χ₀, D₀, T_C and N(E_F) with S. The main findings are as follows. Site disorder smears out the sharp features in the DOS curve near the Fermi level, E_F, reduces N(E_F) and thereby promotes both propagating transverse spin fluctuations (spin waves) and non-propagating zero-point as well as thermally excited spin fluctuations. The reduction in N(E_F), in turn, results in diminished (enhanced) values of M₀, D₀ and T_C(χ₀) with increased site disorder. Site disorder only affects the magnitude of the suppression of spin waves and thermally excited spin fluctuations by the magnetic field (H) but does not alter the functional form of the suppression with field. This functional dependence on field is for spin waves at low temperatures and slows down from a linear variation at intermediate temperatures to a variation at temperatures close to T_C for the thermally excited spin fluctuations. Another important observation is that all the physical quantities of interest such as M₀, χ₀, D₀, T_C and N(E_F) exhibit a sizable change in their magnitudes when point defects such as vacancies play an important role in enhancing the degree of site disorder.

The results of a detailed study of the magnetic properties of well-characterized polycrystalline Ni_pAl_100−p () alloys are presented and discussed in the light of the existing theories. Extreme care has been exercised in the sample preparation to ensure that the site disorder (invariably present in any alloy system) does not interfere with the compositional disorder brought about by the reduction in the concentration of the magnetic (Ni) atoms. Thus, the observed variation in the magnetic properties with Ni concentration (p) is solely controlled by the compositional disorder. Like site disorder, compositional disorder smears out the sharp features in the density of states (DOS) curve near the Fermi level, E_F, and reduces the DOS at E_F, N(E_F), and thereby causes a fall (an enhancement) in the values (value) of the spontaneous magnetization at 0 K, M₀, the spin-wave stiffness at 0 K, D₀, and the Curie temperature, T_C (zero-field differential susceptibility at 0 K, χ₀). However, compositional disorder, unlike site disorder, gives rise to smooth variations in N(E_F), the inverse Stoner enhancement factor , M₀, D₀, T_C, D₀/T_C and χ₀ with p. These variations in the case of M₀(p), D₀(p) and T_C(p) are very well described by the power laws , and with p>p_c (p_c =  the percolation threshold for the appearance of long-range ferromagnetic order) predicted by the percolation theories for these quantities on a regular three-dimensional (d = 3) percolating network. The alloys in question exhibit a crossover in the spin dynamics from the hydrodynamic (magnon) to critical (fracton) regime at a well-defined temperature T_co^*(p). An elaborate analysis of the magnetization data in terms of the percolation models permits a reasonably accurate determination of the magnon-to-fracton crossover line in the magnetic phase diagram, the percolation-to-thermal crossover exponent, fractal dimension, fracton dimensionality, the percolation critical exponents for spontaneous magnetization, spin-wave stiffness, correlation length and conductivity. The results of this analysis also vindicate the Alexander–Orbach conjecture and the Golden inequality for d = 3 percolating ferromagnetic networks.

Fluorine (F) and boron (B) co-alloyed diamond-like carbon (FB-DLC) films were prepared on polymethyl methacrylate (PMMA), polycarbonate, glass, silicon and Mo sheets by the plasma immersion ion processing (PIIP) technique. A pulse glow discharge plasma was used for the PIIP deposition and was produced at a pressure of 1.33 Pa from acetylene (C₂H₂), diborane (B₂H₆), and hexafluoroethane (C₂F₆) gas. The composition of FB-DLC films was measured by using the ion beam analysis techniques, and the bonding structure was characterized by IR and Raman spectroscopies. The co-alloying of F and B into DLC films resulted in the formation of F–C and B–C hybridized bonding structures. The levels of the F and B concentrations affected the composition, chemical bonding and properties as was evident from the changes observed in hydrogen concentration, optical gap energy, hardness, friction coefficient, and contact angle of water on films. Compared to B-alloyed or F-alloyed DLC films, the F and B co-alloyed DLC films exhibited a reduced hydrogen concentration, high hardness and optical gap energy, and improved hydrophobic and tribological properties.

Theoretical calculations have suggested that the Tl₂Mn₂O₇ pyrochlore, exhibiting colossal magnetoresistance (CMR) properties, is a half-metal. However, no direct evidence for the half-metallicity had been described to date. In this paper we report on the results of an in-depth study of the transport and magnetotransport properties of this material, revealing that only the minority band conduction electrons contribute to the charge transport.

This paper describes a computational study of the mixed metal fluorides LiCaAlF₆ and LiSrAlF₆, doped with divalent (Pb²⁺, Co²⁺ and Ni²⁺), trivalent (Cr³⁺, Fe³⁺ and Y³⁺) and tetravalent (Si⁴⁺) ions. For each of the frameworks, all three cation sites were considered, as well as a range of charge compensation mechanisms. For the divalent dopants, substitution at the divalent host site is preferred, whilst for the trivalent dopants, Co³⁺ and Fe³⁺ prefer the Al³⁺ site, and Y³⁺ shows behaviour similar to the rare earths. Finally, it is found that Al³⁺ is the preferred site for substitution by Si⁴⁺ in both host frameworks.

Most solid-state electronic structure calculations are based on quantum electrons and classical nuclei. These calculations either omit quantum zero-point motion and tunnelling, or estimate it in an extra step. Such quantum effects are especially significant for light nuclei, such as the proton or its analogue, μ⁺. We propose a simple approach to including such quantum behaviour, in a form readily integrated with standard electronic structure calculations. This approach is demonstrated for a number of vacancy-containing defect complexes in diamond. Our results suggest that for the NHV⁻ complex, quantum motion of the proton between three equivalent potential energy minima is sufficiently rapid to time-average measurements at X-band frequencies.

Electron spin resonance (ESR) studies have been performed on newly synthesized Ag^II complexes of octaethylporphyrin (oep) cocrystallized with fullerenes (C₆₀ and C₇₀) using single crystals and polycrystals between 4 and 300 K. We have observed the fine structure in the ESR spectra of Ag^II(oep) C₆₀; the fine structure is ascribed to the triplet spin states due to magnetic dipolar interactions between S = 1/2 spins of Ag^II ions in adjacent oep molecules. The analysis of the angular dependence of the g value and fine-structure splitting width for Ag^II(oep) C₆₀ single crystals determines the angle between the Ag–Ag direction and the normal of the Ag–oep plane as 37°. The results of Ag^II(oep) C₇₀ are similar to those of Ag^II(oep) C₆₀. The spin susceptibility of all complexes almost obeys the Curie law, indicating the exchange interactions between the spins of Ag ions are negligible in the temperature region measured.

The pressure-induced structural changes of LaAlO₃ perovskite, a rhombohedral perovskite with symmetry, have been investigated up to 8.6 GPa in a diamond-anvil cell at room temperature using single-crystal x-ray diffraction. A fit of a third-order Birch–Murnaghan equation of state to the P–V data yields values of K_{T 0} = 177(4) GPa and . The evolution of the structure with pressure shows that compression of the LaO₁₂ site is strongly anisotropic, with the three longest La–O bonds being more compressible than the other nine shorter La–O bond lengths. Consequently the distortion of the LaO₁₂ site decreases with increasing pressure. The rotation angle around the threefold axis of the AlO₆ octahedra is totally determined by the relative compressibilities of the La and Al sites, and decreases significantly with pressure. This variation leads to the rhombohedral to cubic phase transition. A new model, introduced to predict the high-pressure behaviour of the GdFeO₃ (Pbnm)-type perovskites, is extended to rhombohedral perovskites in this paper. The model correctly predicts that the AlO₆ site is more compressible than the LaO₁₂ site in LaAlO₃, and that the rhombohedral to cubic phase transition is controlled by the relative compressibilities of the two cation sites.

Arrays of segmented (Ni/Fe)_m (m = 1,2,3,4,5) composite nanowires about 3 µm in length and with aspect ratios of about 60 were electrodeposited on anodic porous alumina templates using a dual bath. The structure, morphology and magnetic properties of the samples were characterized by means of x-ray diffraction, transmission electron microscopy and vibrating sample magnetometry, respectively. It is found that Fe(110) and Ni(111) orientations along nanowire axis are preferred. The large aspect ratio of the composite nanowires reveals a strong shape magnetic anisotropy. As the number of the Ni/Fe composite segments m increases, the coercivity of the nanowire arrays, with the magnetic field applied parallel to the wire, gradually increases. The coercivity variation of the segmented composite nanowires is closely related to the effective exchange coupling between the Ni and Fe segments.

Marcus et al (2002 J. Phys.: Condens. Matter14 L525) claim that thermodynamic properties of materials under pressure must be computed using the Gibbs free energy G, rather than the internal energy E. Marcus et al state that 'The minima of G, but not of E, give the equilibrium structure; the second derivatives of G, but not of E, with respect to strains at the equilibrium structure give the equilibrium elastic constants'. Both statements are incorrect.

All criticisms by Steinle-Neumann and Cohen of the correctness of our calculations of equilibrium structure and elastic constants under pressure from the Gibbs free energy are answered and the criticisms are rejected. The difference between the free energy and the internal energy as functions of structure is described to clarify the use of the free energy. The meaning of elastic constants in a system under pressure is discussed in order to derive the basic quadratic expansion of the free energy in the strains. The coefficients in the expansion are the elastic constants under pressure and are in agreement with well-known work. We give reasons why calculations based on the Gibbs free energy are simpler and more accurate than the usual calculations based on minima of the energy at constant volume.

In a recent paper (Errandonea et al 2003 J. Phys.: Condens. Matter 15 1277) high-pressure, high-temperature synchrotron x-ray diffraction data of Mg were published. The authors referred to and commented on previous high-pressure studies of Mg. It is shown that some of their statements have to be corrected and more detailed explanations are necessary in order to avoid misinterpretations.

This reply aims to clarify some of the arguments presented in a previous publication (Errandonea et al 2003 J. Phys.: Condens. Matter 15 1277), which have been criticized in the preceding comment by Olijnyk. The article in question reported the existence of a new high-pressure and high-temperature dhcp phase in magnesium and presented strong evidence that invites one to re-study the up-to-now-established room temperature structural sequence of magnesium.

In this comment we discuss, in the light of previous experimental and theoretical results, the melting curve of Mo, Ta, and W. Its aim is to show that the melting estimates reported in Verma et al (2004 J. Phys.: Condens. Matter 16 4799) are not reliable and largely overestimate the melting curves of these metals.

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In a recent paper, Pendry and Ramakrishna (2003 J. Phys: Condens. Matter15 6345) have introduced the concept of optically complementary media. Here it is shown that the focusing ability of such media follows directly from the symmetry of Maxwell's equations.