Showing papers in "Journal of Physics C: Solid State Physics in 1969"
TL;DR: In this article, the crystal potential of the Fermi liquid is discussed and the potential from the ion cores as well as from the valence electrons, and schemes that incorporate essential exchange and correlation effects for the electrons are discussed.
Abstract: Publisher Summary: This chapter discusses two major developments that have taken place over the past decade. First is the enormous wealth of energy band calculations that have had tremendous success in explaining the properties of specific solids, but in which the connection with first principles is not always apparent. Second is the spectacular progress of many-body theory applied to the solid state that has given a number of new results, although often of a rather general and formal nature, such as to provide the justification and a formal basis for a one-electron theory. The electron gas problem is treated in some detail here. The problem of the crystal potential is given due attention. It discusses the potential from the ion cores as well as from the valence electrons, and suggests schemes that incorporate essential exchange and correlation effects for the valence electrons. An energy band calculation that properly includes the effects of exchange and correlation describes the elementary excitations called quasi particles. Quasi-particle properties are usually discussed using the remarkable Landau theory of the Fermi liquid. This chapter gives a brief presentation of the theory and reviews the present status of calculations of the Fermi liquid parameters and how they are determined from experiments. (Less)
1,042 citations
TL;DR: In this article, it is suggested that the high resistance to dislocation motion of D.S. crystals stems from a high Peierls potential, and the effect of this potential on dislocation dynamics is discussed.
Abstract: Publisher Summary This chapter discusses the progress in the field of plasticity of the diamond cubic structure (D.S.) from the standpoint of a micromechanical (dislocation dynamical) theory of macroscopic plastic properties. It is suggested that hat the high resistance to dislocation motion of D.S. crystals stems from a high Peierls potential. The problem is to understand the creation and movement of kinks as the elementary vehicles of dislocation motion. How do kinks interact with each other and with other lattice defects, including phonons? How does a distribution of kinks arise which shows up in the shape of dislocation lines frozen-in after deformation and observed in electron transmission? Semiconductor doping provides a unique possibility for manipulating the core structure of the dislocation in the D.S. and thus the Peierls potential. Its effect shows up microscopically in the dislocation dynamics as well as macroscopically in the deformation curves of D.S. crystals. The study of the charge on a dislocation in a doped semiconductor by measurement of its electrical properties discussed that may serve as a link in understanding the doping effects in dislocation dynamics.
519 citations
TL;DR: In this paper, a special resolution function was used to produce radial distribution functions free of truncation error ripples for vitreous germania, and the results were analyzed to produce the concept of ordered groups of molecules in the glass from the radiation-damaged experiments.
Abstract: Neutron diffraction patterns for vitreous germania, synthetic vitreous silica and radiation-damaged synthetic silica have been obtained to 18 A-1. With the use of a special resolution function the results have been analysed to produce `radial distribution functions' free of truncation error ripples. The function for vitreous germania shows considerable improvement on previous x-ray measurements. Evidence for the concept of ordered groups of molecules in the glass is obtained from the radiation-damaged experiments.
495 citations
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TL;DR: The theory of diffusion has followed two main approaches: (1) the more general thermodynamic approach in which the diffusing material is treated as a continuous medium and the atomic nature of the jump process is ignored, (2) the kinetic approach where a physical description is considered in terms of atomic defect movements as discussed by the authors.
Abstract: Publisher Summary This chapter reviews the advances in the understanding of diffusion in metals, with appreciable emphasis on the experimental as well as the theoretical accomplishments. The theory of diffusion has followed two main approaches: (1) the more general thermodynamic approach in which the diffusing material is treated as a continuous medium and the atomic nature of the jump process is ignored, (2) The kinetic approach where a physical description is considered in terms of atomic defect movements. The kinetic approach is adopted in this chapter although thermodynamic equations are discussed, where necessary, to show the relationship between the two approaches. The theoretical and experimental results for self-diffusion in pure crystals, impurity diffusion in pure crystals, effects of solute additions on self-diffusion, diffusion in concentrated alloys, diffusion in an electrical gradient, diffusion in a chemical concentration gradient, and diffusion in a thermal gradient are presented in the chapter.
313 citations
TL;DR: In this paper, an exactly solvable model of a disordered Hamiltonian, valid in three dimensions, is presented, and the ensemble-averaged Green function, and hence the density of eigenstates, for the model are found exactly.
Abstract: An exactly solvable model of a disordered Hamiltonian, valid in three dimensions, is presented. The ensemble-averaged Green function, and hence the density of eigenstates, for the model are found exactly. It is shown that the states in the tail of the distribution are not localized as has been suggested by several authors.
243 citations
TL;DR: In this paper, the susceptibility of type II superconductors in low-frequency alternating current fields has been measured using a phase sensitive detector and the response is linear at low amplitude and is consistent with a model based on the reversible oscillation of vortices in harmonic wells.
Abstract: The susceptibility of type II superconductors in low-frequency alternating current fields has been measured using a phase sensitive detector. Penetrations of magnetic field of between 300 A and 500 μm can be measured and if it is assumed that a critical state exists the field profile across the specimen can be plotted on this scale. The response is linear at low amplitude and is consistent with a model based on the reversible oscillation of vortices in harmonic wells. It is not consistent with the signal predicted from `flux creep'. The effective potential wells are found to be harmonic up to their edges and only about 25 A in radius. The resolution is sufficient to show that the surface current is not a critical state, but can be described by a single row of vortices pinned by the boundary of the specimen.
237 citations
TL;DR: A theory of collective motion in liquids is described in this paper, which is based upon a new approximation which may be regarded as either a generalization of the random phase approximation or, alternatively, as a generalisation of the phonon theory of solids.
Abstract: A theory of collective motion in liquids is described. This theory is based upon a new approximation which may be regarded as either a generalization of the random phase approximation or, alternatively, as a generalization of the phonon theory of solids. The theory is applied to predict the form of the inelastic coherent neutron scattering from liquids making use of a particular model. Other applications, to the theory of amorphous solids, hot crystals, electron plasmas, etc., are indicated.
178 citations
TL;DR: In this paper, the experimental data for hyperfine fields on a wide range of impurities in ferromagnetic metals are analyzed using a model based on that of Daniel and Friedel, but having s-d hybridization as a dominant mechanism.
Abstract: The experimental data for hyperfine fields on a wide range of impurities in ferromagnetic metals are analysed using a model based on that of Daniel and Friedel, but having s-d hybridization as a dominant mechanism. The host conduction-electron polarization is found to be negative, and the model leads to interpretations of a number of hyperfine field systematics.
171 citations
TL;DR: In this paper, a simple algebraic formulae give the principal energy gap and the position of the minimum in the conduction band along ΓΔX, which agree with the large computer calculations to within about 25%.
Abstract: The band structure of a diamond-type semiconductor near the energy gap can be described simply in terms of the Jones zone. The energy gap is nearly constant over the Jones-zone faces except close to the edges and corners. This accounts for the success of the spherically symmetric Penn model of the dielectric constant . It also explains the qualitative shape of the optical absorption spectrum, in particular the occurrence of the first peak. Specifically covalent effects arise from the fact that the ν(111) Fourier component of the pseudopotential is relatively large and has to be treated beyond lowest order of perturbation theory. Simple algebraic formulae give the principal energy gap and the position of the minimum in the conduction band along ΓΔX, which agree with the large computer calculations to within about 25%. This picture accounts in a simple approximate way for the variation with pressure of the dielectric constant and of the position of the main peak in the optical absorption spectrum. Finally a microscopic calculation of the extra charge Qb located in the covalent bond gives agreement with Phillips' conjecture that Qb = 2-1.
152 citations
TL;DR: In this article, the optical absorption spectra of copper and gold have been measured polarimetrically as a function of temperature, while in ultra-high vacuum, and the main absorption peaks of both metals were found to vary with temperature and by comparison with calculations for the band structure of copper for various lattice parameters, it was possible to identify peak positions with the following transitions: for copper, X5 -> X4prime at 397 eV, L2prime -> L1u at 478 eV and L11 -> EF(L2prime) at 532 e
Abstract: The optical absorption spectra of copper and of gold have been measured polarimetrically as a function of temperature, while in ultra-high vacuum. The copper spectrum was obtained from 17-59 eV over the temperature range 77-920 °K and that of gold from 05-59 eV over the temperature range 295-770 °K. The main absorption peaks of both metals were found to vary with temperature and by comparison with calculations for the band structure of copper for various lattice parameters it was possible to identify peak positions with the following transitions: for copper, X5 -> X4prime at 397 eV, L2prime -> L1u at 478 eV and L11 -> EF(L2prime) at 532 eV, for gold L2prime -> L1u at 408 eV and X5 -> X4prime at 455 eV.
117 citations
TL;DR: In this paper, a general theory of the two-magnon states using Green function methods is developed and the results applied to the spin-only antiferromagnet RbMnF3 and to CoF2 where the orbital contribution to the magnetic moment is important.
Abstract: Recent optical experiments have shown that the two-magnon spectra of antiferromagnets cannot be properly understood using simple non-interacting spin-wave theory. In these experiments two magnons are created close together in real space where they interact strongly to produce large observable effects. They therefore provide an excellent opportunity to study magnon-magnon interactions. A general theory of the two-magnon states using Green function methods is developed and the results applied to the spin-only antiferromagnet RbMnF3 and to CoF2 where the orbital contribution to the magnetic moment is important. The predicted optical properties are in good agreement with experiment.
TL;DR: In this paper, the authors derived the preferred values of the C-C bond length for stages 1 to 6, derived from the value of the a-axis parameter extrapolated to 90° are: Stage 1 143204, Stage 2 142592, Stage 3 14240, Stage 4 142305, Stage 5 142267, and Stage 6 14221.
Abstract: Studies of the x-ray diffraction pattern from different potassium graphites have shown that intercalation of graphite by potassium is accompanied by an expansion of the carbon layers. This expansion is uniform within a single layer and is constant for all n carbon layers separating successive intercalate layers in the stage n compound of composition C12nK (n > 1). Preferred values of the C-C bond length for stages 1 to 6, derived from the value of the a-axis parameter extrapolated to θ = 90° are: Stage 1 143204 (3) A 2 142592 (3) 3 14240 (1) Stage 4 142305 (7) A 5 142267 (6) 6 14221 (1). Lower accuracy in stages 3 and 6 is due to slight variation between samples, attributed to deviations from the ideal stoichiometry. Before intercalation, the C-C bond length of the pyrolytic graphite was 142114 (3) A. The bond-length expansion is consistent with electron transfer from potassium to the antibonding orbitals in the upper π band of the graphitic region between successive intercalate layers. The discontinuous change of bond length with stage can be approximately represented by the relation: C-C (stagen) = (14203+00113/n)A.
TL;DR: In this article, the authors review the indirect exchange interactions in a metal, focusing on the coupling between two nuclear magnetic moments, and secondary emphasis on coupling between the electronic magnetic moments of substitutional paramagnetic ions in a dilute alloy.
Abstract: Publisher Summary This chapter reviews the indirect exchange interactions in a metal. The indirect interaction in a metal proceeds as follows: The magnetic moment of one nucleus of spin I 1 scatters a conduction electron of spin s by means of the hyperfine interaction between electronic and nuclear magnetic moments, and then the magnetic moment of the second nucleus of spin I 2 sees the scattered electron. The two nuclear moments see each other in this way. When the contact I.s part of the hyperfine interaction is dominant, the indirect exchange is isotropic, of the form I 1 .I 2 . The primary emphasis is on the coupling between two nuclear magnetic moments, and secondary emphasis is on the coupling between the electronic magnetic moments of substitutional paramagnetic ions in a dilute alloy. The primary area is the simpler to handle theoretically; the secondary area is of wider scientific and technological importance because of the application to magnetic order in the rare-earth metals.
TL;DR: In this paper, the authors considered the problem of describing the electron states in an assembly of atoms with overlapping bound-state wave functions, and proposed a self-consistent t-matrix formula based on the Anderson theory.
Abstract: The question is: how should we describe the electron states in an assembly of `atoms' with overlapping bound-state wave functions? In a regular lattice, these states are non-localized Bloch functions, forming a band of width B, say. Attention is focused on the effects of `cellular disorder', where a statistical variation wl is imposed on the energy of the bound state of the lth atom. A very simple version of the argument of Anderson (1958) demonstrates his conclusion that the states should all become localized if wl is distributed uniformly over a range of width somewhat greater than B. The same argument applied to the `equiconcentration binary alloy', where wl takes the values ±½W at random, shows that the band of propagating states is not destroyed, but splits into two narrower bands when W>>B. In an attempt to confirm these results, successive approximations for the average Green function in such a system are formulated, starting from the propagator of the Bloch states of the `ordered' system and treating wl as a perturbation. The problem of allowing for the statistical correlations induced by repeated scatterings from the same centre is demonstrated and a simple type of self-consistent t-matrix formula - nearly the same as various other published formulae based upon the same principles - is developed. It turns out, however, that none of these `medium propagator' methods leads to splitting of the band in the equiconcentration alloy. The technique of Matsubara et al. is then sketched out, and shown to be entirely different in principle. As in the Anderson theory, the Green function is expanded in powers of the overlap integral, which `perturbs' the bound states of the isolated atoms. By Fourier transformation, cumulant averaging, and self-consistent approximation, Matsubara et al. obtained formulae which are rather complicated but which appear to be consistent with the Anderson criteria for localization. This is, therefore, much the best approach to the problem. The consequences of `structural' disorder are also discussed, somewhat inconclusively.
TL;DR: In this paper, the theory of states at surfaces and interfaces is formulated by applying the equivalent potential method previously used in the analysis of pseudopotentials, where the surface boundary conditions are replaced by an equivalent ''perturbation'' localized at the surface, which exactly conserves scattering amplitudes and energy eigenvalues.
Abstract: The theory of states at surfaces and interfaces is formulated applying the equivalent potential method previously used in the analysis of pseudopotentials. The surface boundary conditions are replaced by an equivalent `perturbation' localized at the surface, which exactly conserves scattering amplitudes and energy eigenvalues. For an abrupt discontinuity at an interface between two media, A and B, a central formula is obtained which factorizes the surface Green function. The factors involved depend only on the surface values of GA and GB, these being the Green functions of the corresponding medium continued into the entire space. This yields a completely new secular equation for the energies of the surface states, which avoids the need to do a complex band structure calculation. The method can also be used to study surface scattering (e.g. LEED theory) as well as surface impurities.
TL;DR: In this paper, the free energy expression of Wohlfarth for a very weak itinerant ferromagnet is amended by the addition of volume-dependent terms given by Belov, and the forced magnetostriction and pressure dependence of the Curie temperature are calculated.
Abstract: The free energy expression of Wohlfarth for a very weak itinerant ferromagnet is amended by the addition of volume-dependent terms given by Belov. Hence the forced magnetostriction and pressure dependence of the Curie temperature are calculated. The effects depend on the volume dependence not only of the effective interaction energy but also of the fine details of the band structure. Magnetostriction measurements on ZrZn2 by Ogawa and Waki are used to estimate that here partial differentialTc/partial differentialP = -2·4 degK kbar-1. A variety of results relating to the effect is deduced from elementary thermodynamics. For a very weak itinerant ferromagnet corrections to the result deduced from the Belov equation are obtained. Reference is made to recent measurements by Fawcett et al. on dilute platinum and palladium alloys.
TL;DR: In this article, the authors considered the conduction in ferromagnetic metals with two currents in parallel for supward arrow and sdownward arrow electrons and introduced the effect of spin-flip collisions.
Abstract: We consider for the conduction in ferromagnetic metals a model with two currents in parallel for supward arrow and sdownward arrow electrons and introduce the effect of spin-flip collisions. We calculate the contribution of spin wave-electron collisions to the mixing of the two currents and compare with the experimental results.
TL;DR: In this article, the exchange and correlation corrections to the model potential form factor wq(k) and the normalized energy-wavenumber characteristic FN(q) were evaluated for eight simple metals.
Abstract: Expressions for the exchange and correlation corrections to the model potential form factor wq(k) and the normalized energy-wavenumber characteristic FN(q), which were derived in a recent paper by Shaw, are evaluated for eight simple metals. An expression for the second derivative of the Kohn-Sham density functional for the exchange and correlation energy is proposed and then is used in these calculations. The energy-wavenumber characteristic computed from the optimum model potential, corrected for exchange and correlation, is used to calculate the phonon spectrum of magnesium. The predicted spectrum is found to agree very well with the experimental data, and the exchange and correlation corrections are shown to be important in obtaining this agreement. The corrections to FN(q) and wq(k) which are tabulated for eight metals can be used to determine the importance of exchange and correlation in the prediction of other metallic properties.
TL;DR: In this article, the thermal conductivity of sintered semiconductor alloys is calculated using the Klemens-Callaway model assuming that the boundary scattering can be adequately described by a mean free path.
Abstract: The thermal conductivity of sintered semiconductor alloys is calculated using the Klemens-Callaway model assuming that the boundary scattering can be adequately described by a mean free path. It is shown that the relative increase in thermal resistance increases with the amount of alloy disorder scattering and should be substantial in sintered germanium silicon alloys with particle sizes of the order of one micron.
TL;DR: In this article, the authors applied the optimized model potential proposed by Shaw to the problem of determining band-structure energies for simple metals and derived expressions for the structure-dependent contributions to the total energy in Hartree approximation.
Abstract: The optimized model potential proposed by Shaw is applied to the problem of determining band-structure energies for simple metals. Expressions for the structure-dependent contributions to the total energy are derived in Hartree approximation. The derivation is similar to that given by Harrison for pseudopotentials, but has several features which are unique to model potentials. It is shown that the separation of structure-dependent contributions into electrostatic and band-structure energies is not unique and that the choice of effective valence is therefore arbitrary. An expression for the energy-wave-number characteristic is given in terms of the optimized model potential, and is evaluated as a function of scattering momentum for eight simple metals. A comparison is made between results obtained from the full nonlocal theory and those from various local approximations. The results for the energy-wave-number characteristic are used to calculate effective ion-ion interactions and to predict stable crystal structures.
TL;DR: In this paper, measurements of dielectric loss, of optical absorption and of emission spectra have been made on NaCl: Pb2+ and KCl: pb2+) crystals.
Abstract: As part of a study of the aggregation of impurity ions in alkali halides, measurements of dielectric loss, of optical absorption and of emission spectra have been made on NaCl: Pb2+ and KCl: Pb2+ crystals. Changes in the optical absorption and the emission spectra with aggregation of the Pb2+-vacancy pairs are more pronounced in NaCl than in KCl. The main conclusions from the NaCl: Pb2+ measurements are: changes in the absorption and emission spectra result from the same aggregation process studied previously in many alkali halide crystals by dielectric measurements; the emission spectra, but not the absorption, change when the divalent ion-vacancy pairs (dipoles) form the initial aggregates (trimers); later in the aggregation process both absorption and emission change; the optical measurements show that the aggregation takes place in several definite stages and the results are not inconsistent with the model proposed earlier, viz. the initial aggregates are trimers and these grow into pentamers, and then heptamers etc. by the addition of dipoles, two at a time. The dielectric absorption measurements give activation energies for the diffusion of Pb2+-vacancy pairs through NaCl and KCl lattices of 080 ev and 085 ev respectively.
TL;DR: In this paper, two functions of state ξ and η are derived, such that any equation of state for the critical region consistent with the scaling hypothesis can be expressed in the form η = (ξ).
Abstract: Two functions of state ξ and η are derived, such that any equation of state for the critical region consistent with the scaling hypothesis can be expressed in the form η = (ξ). The representation has the useful property that the function has no unphysical singularities (such as the branch points associated with the critical isotherm or elsewhere in the usual representations of scaling-law equations of state).
TL;DR: In this paper, an external magnetic field was applied to a single crystal of γ FeOOH and the magnetic moments were shown to be collinear in the antiferromagnetic state, with the alignment along the c axis.
Abstract: Measurements of the Mossbauer spectra of γ FeOOH show that it is an antiferromagnet with a Neel temperature of 73 °K. The hyperfine field at the 57Fe nuclei is 460±5 kG. By applying an external magnetic field to a single crystal the Fe3+ magnetic moments are shown to be collinear in the antiferromagnetic state, with the alignment along the c axis. From measurements in the paramagnetic state using polarized γ radiation the electric field gradient is shown to be negative in sign, and its major axis lies in the ac plane making an angle of about 55° with the c axis.
TL;DR: In this article, the theory of a magnon sideband on an exciton absorption line is compared with the experimental measurements on Rb2MnF4, and a prediction is made for the two-magnon Raman lineshape, and the energies of localized modes associated with impurities calculated.
Abstract: The magnetic structure of K2NiF4, K2MnF4 and Rb2MnF4 can be approximately regarded as a two-dimensional square lattice, which enables the magnetic Green functions to be expressed in terms of elliptic integrals. Using these, the theory of a magnon sideband on an exciton absorption line is compared with the experimental measurements on Rb2MnF4, giving reasonable agreement. A prediction is made for the two-magnon Raman lineshape, and the energies of localized modes associated with impurities calculated.
TL;DR: The configuration-dependent part of the energy of a binary alloy may be expressed in terms of a single alloying potential, the difference between the two atomic pseudopotentials as discussed by the authors.
Abstract: The configuration-dependent part of the energy of a binary alloy may be expressed in terms of a single alloying potential, the difference between the two atomic pseudopotentials. Ordering can then be explained either in reciprocal space, or in real space using a single concentration-independent interionic potential. In real space the interaction between like atoms has the opposite sign to the interaction between unlike atoms. The total energy of an alloy may also be expressed in terms of the alloying potential alone, if the energy of the two components with the alloy crystal structure is known.
TL;DR: In this article, the L and M X-ray emission bands of metallic copper are calculated in the one-electron approximation using augmented plane wave Bloch functions analysed into s, p and d symmetry components.
Abstract: The L and M X-ray emission bands of metallic copper are calculated in the one-electron approximation using augmented plane wave Bloch functions analysed into s, p and d symmetry components. The effect on the calculated intensity distributions of lifetime broadening due to Auger processes is estimated in a simple manner, and appropriately broadened curves are compared with the available experimental data.
TL;DR: In this paper, an improved energy-independent model Hamiltonian is presented, which is both more rapidly convergent in reciprocal lattice space and much less sensitive to the choice of splitting parameter than that proposed recently by Hubbard and Dalton.
Abstract: The hybrid nearly-free-electron tight-binding first-principle schemes of Hubbard and Jacobs are investigated further, using the Korringa, Kohn and Rostoker equations as starting point. An improved energy-independent model Hamiltonian is presented, which is both more rapidly convergent in reciprocal lattice space and much less sensitive to the choice of splitting parameter than that proposed recently by Hubbard and Dalton. The validity of the approximations made is then tested by calculating the band structures of face-centred cubic copper and iron from first principles. The energy levels of Burdick and Wood are found to be reproduced with a root-mean-square accuracy of better than 0?01 ryd in both cases, with the use of only a 9 ? 9 model Hamiltonian matrix. When a hybrid nearly-free-electron tight-binding model Hamiltonian is used as an empirical interpolation scheme, the expressions derived here show explicitly how the parameters describing both the hybridization and the tight-binding overlap integrals may be expressed in terms of only two constants, namely the energy 0 and width ? of the resonance associated with the d bands.
TL;DR: In this article, the Boudreaux-Heine method of calculating low-energy electron diffraction (LEED) intensities into a matrix form suitable for extension to complicated surface structures is presented.
Abstract: The second paper in this series casts the Boudreaux-Heine method of calculating low-energy electron diffraction (LEED) intensities into a matrix form suitable for extension to complicated surface structures. Calculations are made for the 00 and 01, macron beams reflected from a nickel 111 surface, for norrmal incidence, using the potential described in paper I. Predicted peak positions agree with experiment within ±2 ev and relative intensities agree qualitatively. We interpret our results in terms of band structure. A second calculation for the same face of a nickel crystal with the surface layer displaced by 5% of the bulk spacing between layers is presented, the results of which are interpreted in terms of the large ratio between forward and backward scattering cross section of atoms.
TL;DR: In this article, a method for the approximate calculation of transition-metal band structures originally suggested by Heine can be made to give good accuracy (to about 0?01 ryd) when suitable modifications and refinements are introduced.
Abstract: It has been shown that a method for the approximate calculation of transition-metal band structures originally suggested by Heine can be made to give good accuracy (to about 0?01 ryd) when suitable modifications and refinements are introduced. This method has the advantage as compared with other recently suggested schemes of not involving any adjustable ? parameter and of giving good accuracy using secular equations of minimal size.
TL;DR: In this article, the magnon dispersion relation for MnF2 at 4·2 °K has been measured by means of the triple-axis neutron scattering technique along the symmetry lines in the (010) plane of the Brillouin zone.
Abstract: The magnon dispersion relation for MnF2 at 4·2 °K has been measured by means of the triple-axis neutron scattering technique along the symmetry lines in the (010) plane of the Brillouin zone. Using an exact dipole model, the three nearest-neighbour exchange constants were found to be J1 = 0·028 ± 0·001 mev, J2 = -0·152 ± 0·001 mev and J3 = -0·004 ± 0·001 mev. The second moment was also calculated with this model. The density of magnon states was evaluated by applying a six-parameter simulation of the dispersion surface. The critical points in the density of states agree well with those obtained by optical double-magnon experiments, whereas the detailed shape of the density of states differs significantly, indicating that the effect of magnon-magnon interactions rather than that of distant-neighbour exchange is of primary importance in the optical measurements.