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Showing papers in "Physica B-condensed Matter in 1984"


Journal ArticleDOI
Gerd Binnig1, Heinrich Rohrer1
TL;DR: An overview of the status of Scanning Tunneling Microscopy (STM) is given in this article, where examples are given for reconstructions on metal and semiconductor surfaces and adsorbate structures.
Abstract: An overview of the status of Scanning Tunneling Microscopy (STM) is given. So far, the method has been applied mainly to surface structures. Examples are given for reconstructions on metal and semiconductor surfaces and adsorbate structures. It will become evident that the technique is likewise applicable to chemical investigations of surfaces on an atomic scale.

171 citations


Journal ArticleDOI
TL;DR: In this paper, self-consistent spin-polarized energy-band calculations are used to explain the trends in the ferromagnetic moments of transition-metal alloys.
Abstract: Self-consistent spin-polarized energy-band calculations are used to explain the trends in the ferromagnetic moments oftransition-metal alloys. It is demonstrated that a large amount of magnetization data become interpretable by using the generalized Slater-Pauling curve recently introduced by Williams et al. The discussion includes Heusler alloys of both L21 and Clb structure for which exchange constants and hence the Curie temperatures can be estimated theoretically. CoMnSb is treated in detail and is shown to belong to the class of half-metallic ferromagnets first discovered by de Groot et al. Also included will be Fe3Cr and Au4V which represent interesting examples of itinerant ferromagnetism.

145 citations


Journal ArticleDOI
TL;DR: In this article, the Vogel-Fulcher law is used to characterize the frequency dependence of the temperature of the a.c. susceptibility cusp, T f, which results in nice scaling diagrams for RKKY spin-glasses as well as for short-range interaction spinglasses.
Abstract: The present controversy about the existence or not of a spin-glass transition is partly due to the large variety of magnetic behaviors observed experimentally. The use of a Vogel-Fulcher law to characterize the frequency dependence of the temperature of the a.c. susceptibility cusp, T f , results in nice scaling diagrams for RKKY spin-glasses as well as for short-range interaction spin-glasses. The physical parameters associated allow to predict in which conditions the characteristics of a transition at finite temperature can be determined for some systems and why the interpretation of experimental data remains ambiguous for other systems. Recent measurements of critical exponents and critical lines are discussed.

82 citations


Journal ArticleDOI
TL;DR: In this paper, the diffusion constant of the particle tunneling among many sites is proportional to T 2K−1, where T2K comes from the effective tunneling matrix squared, while T−1 comes from an effective broadening of the individual muon level.
Abstract: A particle moving in a metal and interacting with the metallic electrons is discussed first from a general point of view. The electrons cannot follow the particle adiabatically because of low excitation energies across the fermi surface. One of the non-adiabatic effects is to renormalize the tunneling matrix of the particle by a factor (T/D)K, where D is the width of the electron band, K is a coupling between the particle and the electrons. The diffusion constant of the particle tunneling among many sites is proportional to T2K−1, where T2K comes from the effective tunneling matrix squared, while T−1 comes from an effective broadening of the level of the particle. This temperature dependence explains the observations for the positive muon in copper when K 1 2 . We also consider interaction of the muon with lattice distortion. With both interactions, we obtain a very good agreement with an observation in the whole temperature range, except the lowest temperature where the diffusion constant tends to a constant. We introduce phenomenologically a broadening of the individual muon level. A width of 0.34K explains the observed leveling off.

74 citations


Journal ArticleDOI
TL;DR: In this paper, the authors discuss the phenomenon of heavy-fermion superconductivity by investigating the system CeCu 2 Si 2 in its normal and superconducting states.
Abstract: We discuss the phenomenon of heavy-fermion superconductivity by investigating the exemplary system CeCu 2 Si 2 in its normal and superconducting states. Like the non-superconducting compound CeAl 3 , CeCu 2 Si 2 behaves as a Kondo lattice. We find no evidence for triplet superconductivity in CeCu 2 Si 2 .

63 citations


Journal ArticleDOI
Bertram Batlogg1
TL;DR: In this paper, an extensive single-crystal study of BaPb1−xBixO3 over the whole composition range provides new insight in understanding the high superconducting transition temperature in thin oxide.
Abstract: An extensive single-crystal study of BaPb1−xBixO3 over the whole composition range provides new insight in understanding the high superconducting transition temperature in thin oxide. Superconductivity with narrow transitions is observed only at x=0.25, where the carrier concentration is 2.4 1021 cm−3. The Sommerfeld constant γ has been evaluated in three independent ways and is found to be small: 1.5 mJ/mole K2. The peculiarity of BaPb0.75Bi0.25O3 is that the electron-phonon coupling extends to below 2 meV and its strength exceeds the one in Pb. The high Tc therefore results from a large λ, which is rooted both in the nature of the conduction band derived from O2p-(Pb,Bi)6s states, and the instability of the Perovskite-like structure.

62 citations


Journal ArticleDOI
TL;DR: A theory of coherence relaxation due to electron-electron collisions with small energy transfers in thin wires, films and inversion layers is presented in this article, where a qualitative description of weak localization and anomalous magnetoresistance in normal metals is given.
Abstract: A qualitative description of weak localization and anomalous magnetoresistance in normal metals is given. Such coherent effects as resistance oscillations of a hollow cylinder with magnetic flux and oscillations of current, flowing through a thick SNS-junction, to which a constant voltage is applied, are considered. A theory of coherence relaxation due to electron-electron collisions with small energy transfers in thin wires, films and inversion layers is presented.

60 citations


Journal ArticleDOI
TL;DR: In this article, the authors show that more and more information can be obtained with decreasing temperature even at temperatures below 0.1 K. The authors also show that the structures typical for the quantized Hall effect are observable, if the thermal energy kT is smaller than the energy gaps in the spectrum of a two-dimensional electron gas in a strong magnetic field.
Abstract: The structures typical for the quantized Hall effect (plateaus in magneto-transport measurements) are only observable, if the thermal energy kT is smaller than the energy gaps in the spectrum of a two-dimensional electron gas in a strong magnetic field. This paper discuesses phenomena related to the quantized Hall effect which are influenced by the temperature, and the data demonstrate that more and more information is obtained with decreasing temperature even at temperatures below 0.1 K.

48 citations


Journal ArticleDOI
M.F.H. Schuurmans1, J. van Dijk1
TL;DR: In this paper, a modified exponential energy gap law for nonradiative decay has been derived for 4f-4f transitions where only a few phonons participate in the transition.
Abstract: A modified exponential energy gap law for nonradiative decay has been derived for 4f-4f transitions where only a few phonons participate in the transition. Its preexponential factor varies by only a factor of 10 for different host materials and is purely electronic in nature. The modified law is the usual law (giving a factor of 10 5 variation) modified by using an energy gap which is effectively two (maximum) phonon energies smaller than the energy difference between the initial and the final electronic state. A general relation between the radiative and nonradiative decay rates has been constructed. For 4f-4f transitions this relation enables one to predict the nonradiative decay rate from a knowledge of the radiative decay rate to within one order of magnitude accuracy. The paper also contains a review of the theory of nonradiative and radiative decay in the presence of weak electron-phonon coupling and the Judd-Ofelt theory for forced electric dipole 4f-4f transitions.

46 citations


Journal ArticleDOI
Amand Lucas1
TL;DR: In this paper, the authors give an overview of important technological issues relating to the precipitation of helium gas bubbles in materials subjected to radiation damage in nuclear reactors, including the phenomena of swelling, blistering, flaking, radiation creep and He embrittlement.
Abstract: The paper will first give an overview of important technological issues relating to the precipitation of helium gas bubbles in materials subjected to radiation damage in nuclear reactors. These are the phenomena of swelling, blistering, flaking, radiation creep and He embrittlement. A number of currently debated fundamental issues in the physics of He in metals will be presented, in particular processes of He bubble nucleation and growth, blister formation and ordering of bubbles in superlattices.

41 citations


Journal ArticleDOI
TL;DR: In this article, a theoretical analysis of the behavior of a single-mode laser under weak optical feedback conditions, and for feedback delay times much larger than the roundtrip time in the laser, is presented.
Abstract: We present a theoretical analysis of the behaviour of a single-mode laser under weak optical feedback conditions, and for feedback delay times much larger than the roundtrip time in the laser. One single dimensionless system parameter C > 0 is defined which expresses the effectiveness for the feedback mechanism to change the behaviour of the laser. At C = 1 a transition takes place from monostable ( C C > 1) laser operation. In the latter case the system may exhibit hysterisis effects and fluctuation-induced mode-hopping. Various numerical results are presented.

Journal ArticleDOI
John D. Reppy1
TL;DR: In this article, a superfluid 4 He films adsorbed on Vycor glass, which is a highly interconnected 3D substrate, provide an opportunity for the study of mobile 4 He atoms in the low density limit.
Abstract: Superfluid 4 He films adsorbed on Vycor glass, which is a highly interconnected 3D substrate, provide an opportunity for the study of mobile 4 He atoms in the low density limit. This system shares many of the features of a low density 3D gas and can provide an experimental realization of a dilute weakly interacting Bose fluid.

Journal ArticleDOI
Alexis Baratoff1
TL;DR: In this paper, the direct transmission and transfer Hamiltonian approaches, as well as various approximations developed for scanning tunneling microscopy are reviewed and compared for a free-electron model.
Abstract: The direct-transmission and transfer Hamiltonian approaches, as well as various approximations developed for scanning tunneling microscopy are reviewed and compared for a free-electron model. The second approach provides a deeper insight into the imaging process and should enable one to include effects due to tight-binding bands, surface states and adsorbate-induced modifications. Possible new directions of research and remaining challenges are identified.


Journal ArticleDOI
Daniel S. Fisher1
TL;DR: The dynamic properties of sliding charge density waves are discussed in terms of a classical description of impurity pinning, with emphasis on the behavior near threshold considered as a dynamic critical phenomenon.
Abstract: The dynamic properties of sliding charge density waves are discussed in terms of a classical description of impurity pinning, with emphasis on the behavior near threshold considered as a dynamic critical phenomenon. Scaling behavior is found near threshold. One manifestation of this is ac noise with intensity inversely proportional to the square root of the volume and a diverging amplitude near threshold caused by a diverging correlation length. Below threshold an |ω| cusp is found in the a.c. polarizability along with hysteretic behavior. A discussion of the current experimental situation in light of the present work is presented. Many of the ideas should be applicable to other systems, especially flux flow in weak pinning type II superconductors.

Journal ArticleDOI
TL;DR: In this paper, the lowest lying eigenmodes of a classical fluid have been approximately determined for a wide range of densities and wavenumbers, and the most important eigenmeodes are direct extensions of the three hydrodynamic heat and sound modes to much larger wavenumber.
Abstract: The lowest lying eigenmodes of a classical fluid have been approximately determined for a wide range of densities and wavenumbers. The most important eigenmodes are direct extensions of the three hydrodynamic heat and sound modes to much larger wavenumbers. A new and consistent interpretation of neutron spectra and related molecular dynamics simulations in terms of these modes is made. Also experimental predictions are discussed, some of which seem particularly suitable for investigating with spillation sources.

Journal ArticleDOI
TL;DR: In this article, a brief review of the new field is presented, with a special emphasis on the results essential for the quantum physisc in general, and some even more interesting phenomena have been predicted just recently.
Abstract: In several experiments carried out since 1980, a typical quantum behavior of small-size Josephson junctions as macroscopic objects has been registered. Those experiments have stimulated a rapid development of the related theory, particularly of the effect of damping (viscosity) upon these quantum effects including fluctuations, tunneling and interference. As a result of this development, some even more interesting phenomena have been predicted just recently. In this paper, a brief review of this new field is presented, with a special emphasis on the results essential for the quantum physisc in general.

Journal ArticleDOI
TL;DR: In this paper, the authors presented the full phonon dispersion curves, the Eliashberg functions α 2 F(ω) and the e-ph parameter λ, and employed the tight binding method and are based on first principles energy bands.
Abstract: Electron-phonon calculations for Nb 3 Sn and Nb 3 Ge are presented, including the full phonon dispersion curves, the Eliashberg functions α 2 F(ω) and the e-ph parameter λ. The computations employ the tight binding method and are based on first principles energy bands. Our main results are: 1. 1. Although the energy bands near the Fermi energy E F are three-dimensional, the electron-phonon interaction is dominated by linear (intra-chain) features. Only those phonon modes couple strongly to the electronic state near E F where neighbor Nb atoms of one chain move opposite to each other, either along or perpendicular to the chains. The strong coupling of these modes is a direct consequence of the specific orbital character of the flat energy bands near E F . The modes have strongly depressed frequencies compared to those of the low T c reference materials Nb 3 Sb and Nb 3.2 Ge 0.8 . Furthermore, they exhibit anomalous dispersion, especially along the Λ(ξ,ξ,ξ) direction. The latter results have been confirmed by very recent neutron scattering work of Pintschovius, Takei and Toyota. 2. 2. The cubic-to-tetragonal phase transition is mainly driven by the interaction of the Γ 12 phonon with the electronic Γ 12 state (and the states nearby). It will occur only when the Γ 12 state lies sufficiently close to E F . This appears to be the case only for Nb 3 Sn and V 3 Si, but not for Nb 3 Ge, Nb 3 Ga and Nb 3 Al. 3. 3. The α 2 F(ω) curves and the λ values agree well with tunneling and specific heat data. The increase of λ and thus of T c between the iso-electronic Nb 3 Sn ( λ =1.5) and Nb 3 Ge ( λ =1.9) is attributed to a steric effect: The relatively bigger space available for the Ge atoms leads to much weaker Nb-Ge force constants.

Journal ArticleDOI
TL;DR: A fine structure analysis for the system 5s2pn′s (n′ = 6 to 11) + 5s25pn″d (n″ = 5 to 12)+ 5s5p3 is performed on the basis of available experimental data as mentioned in this paper.
Abstract: A fine structure analysis for the system 5s2pn′s (n′ = 6 to 11) + 5s25pn″d (n″ = 5 to 12)+ 5s5p3 is performed on the basis of available experimental data. The Slater integrals and spin-orbit parameters are determined. For the Slater integrals associated with the high configurations we find a relation of the type R k (a, b)/ R k (c, d) = [n ∗ (c)n ∗ (d)/(n ∗ (a)n ∗ (b))] 3 2 , where a, b, c, d denote a two-electron configuration nln'l' and the n∗(nln'l') are effective quantum numbers of the configurations ns2nln'l' rather than those of the electronic levels. The configuration 5s5p3 is shown to influence strongly the odd level system of Sn I. On the basis of the theoretical results new spectroscopic assignments of the atomic levels involved are given in some cases.

Journal ArticleDOI
TL;DR: The physical description of metal properties poses therefore a many-body problem par excellence as mentioned in this paper, and the history of the physics of metals in particular but certainly also that of condensed matter in general is characterized by many attempts to circumvent the rigorous solution of this problem.
Abstract: Many properties of metals are, stated in very simple terms, determined by the conduction electrons and their interaction with the ionic lattice forming the solid. The physical description of these properties poses therefore a many-body problem par excellence. The history of the physics of metals in particular but certainly also that of condensed matter in general, is characterized by many attempts to circumvent the rigorous solution of this problem. In view of the complexity of this problem, it seems surprising that models assuming free or nearly-free electrons are often quite successful in describing the salient features of thermal or transport properties of metals. It is clear, however, that as soon as quantitative answers are asked for, these models are by far inadequate and further sophistication in the form of considering interactions among the electrons themselves and with the crystal lattice must be envisaged.

Journal ArticleDOI
TL;DR: In this article, the statistical significance of the residual entropies of glasses determined thermoduynamically from specific heats is investigated, and it is shown that the error of the experimentally determined residual entropy, as compared with the residual statistical entropy, is very small.
Abstract: The paper is mainly concerned with the problem of the statistical significance of the residual entropies of glassesdetermined thermoduynamically from specific heats. Using he cocnept of a lictive glass temperature, the error of the experimentally determined residual entropy, as compared with the residual statistical entropy, is estimated to be very small. This result is also illustrated by a simple relaxation model. Iaddition, previous experimental and theoretical work on the residual entropy of glasss and spin glasses, including results of computer simulations of hard- and soft-core fluids and of a spin glass model, is briefly reviewed.

Journal ArticleDOI
TL;DR: In this paper, a modified adiabatic scheme valid in the ground state to overcome the difficulty of orthogonality catastrophe was proposed, where the particle can be viewed as moving in an unmodified potential with the unmodified mass, and the condition for this to occur is k 2 F b 2 ≦ (m / M ) ln(M / m ), where b is the effective range of the particle wave function and m / M the mass ratio.
Abstract: We discuss a heaby particle moving in an arbitrary potential in a metal. Special attention is paid to whether the interaction with metallic electrons causes a mass shift and/or induces an effective potential. The adiabatic approximation, in which the wave function of the metallic electrons follows the instantaneous position of the particle, involves a difficulty due to the orthogonality catastrophe. We propose a modified adiabatic scheme valid in the ground state to overcome the difficulty, where the particle can be viewed as moving in the unmodified potential with the unmodified mass. When the potential is such that the particle is very localized, this scheme breaks down. The condition for this to occur is k 2 F b 2 ≦ ( m / M ) ln( M / m ), where b is the effective range of the particle wave function and m / M the mass ratio. The possibility of self-trapping of the particle is examined.

Journal ArticleDOI
TL;DR: The crystal structure of [(CH 3 ) 3 NH]NiCl 3 ·2H 2 O is found to be orthorhombic, space group Pnma, with a = 16.677(5) A, b = 7.169(2) A and c = 8.103(2).
Abstract: The crystal structure of [(CH 3 ) 3 NH]NiCl 3 ·2H 2 O is found to be orthorhombic, space group Pnma, with a = 16.677(5) A , b = 7.169(2) A and c = 8.103(2) A . The compound is isomorphous with the corresponding Mn 2+ and Co 2+ components. The observer ferromagnetic interaction is consistent with that found in other chlorobibridged octahedral nickel (II) systems. [(CH 3 ) 3 NH]NiCl 3 ·2H 2 O shows a transition ( T c = 3.67 K) to a canted antiferromagnetic phase. Below the tricritical temperature T t = 3.48 K a field-induced metamagnetic transition to the saturated paramagnetic phase occurs for H ‖ c axis ( H c = 310 Oe at 1.20 K). From the location of the tricritical temperature and the value of H c the interchain interactions were estimated as z f J f / k = 1.3 × 10 −1 and z af J af / k = −2.4 × 10 −2 K. The high-temperature zero-field susceptibility yields rather large values for the ferromagnetic interchain exchange ( J / K = 14 K) as well as for the single-ion anisotropy ( D / k = −9 K). However, a description of the low-temperature susceptibilities leads to D / k = −3.7 K and a non-zero value for the orthorhombic component of the single-ion anisotropy E , E / k = 2 K. Preliminary ESR results, corroborating these low temperature data, are reported as well.

Journal ArticleDOI
TL;DR: In this paper, a model for the description of precursor order clusters at ferroelectric phase transitions is proposed, and it is shown that the preconditioned clusters of this type bring about the intrinsic central peak at the low-temperature first-order ferro electric phase transition in proustite (Ag 3 AsS 3 ).
Abstract: A model for the description of precursor order clusters at ferroelectric phase transitions is proposed. In this model the cluster walls separating the paraelectric and ferroelectric regions are obtained as kink solutions of the nonlinear dynamic equations including a damping term. The cases of first- and second-order phase transitions and of the tricritical point are considered. It is shown that the precursor order clusters of this type bring about the intrinsic central peak at the low-temperature first-order ferroelectric phase transition in proustite (Ag 3 AsS 3 ). The analysis of the 75 As nuclear quadrupole resonance and spin-lattice relaxation data for proustite indicates that the central peak for the hydrostatic pressures p ⩽ 3.2 kbar is apparently caused by pretransitional heterophase fluctuations which are described by the above-mentioned model. Beyond the pressure-induced tricritical point at p > 3.2 kbar the central peak is associated with the precursor order clusters of another type also described by this model. The features of spin-lattice relaxation near first-order phase transitions, in particular, in proustite are considered.

Journal ArticleDOI
TL;DR: In this article, the indirect ion-ion interaction arising from electronic screening is treated by an optimized random phase approximation (ORPA), imposing physical requirements as in the original ORPA scheme developed by Weeks, Chandler and Andersen for liquids with strongly repulsive core potentials.
Abstract: This paper presents calculations of the liquid structure factor of the alkali metals near freezing, starting from the classical plasma of bare ions as reference liquid. The indirect ion-ion interaction arising from electronic screening is treated by an optimized random phase approximation (ORPA), imposing physical requirements as in the original ORPA scheme developed by Weeks, Chandler and Andersen for liquids with strongly repulsive core potentials. A comparison of the results with computer simulation data for a model of liquid rubidium shows that the present approach overcomes the well-known difficulties met in applying to these metals the standard ORPA based on a reference liquid of neutral hard spheres. The optimization scheme is also shown to be equivalent to a reduction of the range of the indirect interaction in momentum space, as proposed empirically in an earlier work. Comparison with experiment for the other alkalis shows that a good overall representation of the data can be obtained for sodium, potassium and cesium, but not for lithium, when one uses a very simple form of the electron-ion potential adjusted to the liquid compressibility. The small-angle scattering region is finally examined more carefully in the light of recent data of Waseda, with a view to possible refinements of the pseudopotential model.

Journal ArticleDOI
TL;DR: The biomagnetic approach has proved to be particularly successful in localizing cerebral sources, like those related to primary and higher level brain functions, and in three-dimensional localization of epileptic foci.
Abstract: The unrivaled ability of SQUID magnetometers to measure weak magnetic fields associated with physiological and pathological activity in the human body has started a new field of research which is gaining significant interest both in laboratory and in clinical use. The present state of art of instrumentation is satisfactory even for the most demanding applications. Nevertheless fast improvements are being made to ensure higher feasibility in practical operation. The biomagnetic approach has proved to be particularly successful in localizing cerebral sources, like those related to primary and higher level brain functions. Impressive results have been achieved also in the study of spontaneous brain activity and in three-dimensional localization of epileptic foci.

Journal ArticleDOI
TL;DR: The average M-shell fluorescence yields ω M in Au, Pb, Th and U have been measured using the photoionization of the M shell by 5.9 keV X-rays from a 55Fe radioactive source and analyzing the M X-ray by a Si(Li) low-energy photon spectrometer.
Abstract: The average M-shell fluorescence yields ω M in Au, Pb, Th and U have been measured using the photoionization of the M shell by 5.9 keV X-rays from a 55Fe radioactive source and analyzing the M X-rays by a Si(Li) low-energy photon spectrometer. A comparison of the results is made with the existing experimental data and the values estimated from the subshell fluorescence yields calculated by McGuire, wherever possible. The measurement for Th is reported for the first time.

Journal ArticleDOI
TL;DR: In this article, the electron density determination from continuum emission was compared experimentally with the method of Stark broadening measurement of spectral lines, using a stationary argon cesium discharge.
Abstract: The method of electron density determination from continuum emission is often used in the nonstationary plasma of an MHD-generator because of its simplicity. An assumption in the analysis is that recombinative radiation forms the main contribution to the continuum. Next to this the method carries with it some other uncertainties. In this work the method is compared experimentally with the method of Stark broadening measurement of spectral lines, using a stationary argon cesium discharge. Both techniques involve corrections for plasma inhomogeneities. Agreement within 20% is found. The contribution of Cs 2 molecules to the continuum emission, which is significant in saturated vapor at moderate temperatures (500–1000 K), is estimated to be of minor importance in the generator plasma.

Journal ArticleDOI
TL;DR: In this article, the absorption spectrum of atomic antimony was photographed in the 1000-2300 A region on a 3-metre normal incidence spectrograph using flash pyrolysis technique.
Abstract: The absorption spectrum of atomic antimony was photographed in the 1000–2300 A region on a 3-metre normal incidence spectrograph using flash pyrolysis technique. The new measurements have lead to revision and extension of the earlier analysis. Three series limiting on 5p23P0, six series limiting on 5p23P1 and four series limiting on 5p33P2 of Sb II have been identified. A new value of the ionization potential of Sb I has been found to be Sb II 5 p 2 3 P 0 = 69 432±20 cm -1 (8.61 eV ) .

Journal ArticleDOI
TL;DR: In this article, a rigorous least-squares fitting procedure for the evaluation of the principal values of g and A tensors, as well as the direction cosines of their principal axes, is given.
Abstract: The details of a rigorous least-squares fitting procedure for the evaluation of the principal values of g and A tensors, as well as the direction cosines of their principal axes, are given. Expressions are provided for a quick evaluation of the required energy level differences. In this method all EPR (ENDOR) line positions (frequencies) obtained for several orientation of the external magnetic field in three mutually perpendicular planes are simultaneously fitted to evaluate all the components of the g and A tensors, and to minimize parameter errors. The procedure is illustrated by application to the EPR data analysis of one of the eight inequivalent (BO 4 ) 4- tetrahedral complexes ( S = 1 2 , I = 3 2 ) obtained w hen 11 B 3+ replaces Si 4+ in (SiO 4 ) 4- complex in danburite single crystal (CaB 2 Si 2 O 8 ).