Anisotropic thermal expansion of yttrium metal and yttrium-based rare earth alloys at low temperature

We report on thermal expansion measurements at low temperatures of pure Y and RE (RE: Er, Dy, Tb and Gd) single crystals. We estimate the electronic and lattice contributions for the thermal expansion of pure yttrium. For the dilute RE alloys, the thermal expansion exhibits crystal field effects. These are explained with a free energy including crystal field, elastic and magnetoelastic terms.     

Crystal-lattice coupling to the vortex-melting transition in YBa(2)Cu(3)O(7-delta)

Distinct discontinuities in the thermal expansion of the crystal lattice are observed at the melting transition of the vortex lattice in a naturally untwinned reversible YBa(2)Cu3O(7-delta) single crystal using high-resolution dilatometry. This coupling between the vortex transition and the crystal lattice demonstrates that the crystal lattice is more than a mere host for the vortices, and it is attributed to a strong pressure dependence of the superconducting transition temperature and thus to the condensation energy at the vortex-melting temperature.     

Low temperature pressure dependence of the muon hyperfine fields in iron,cobalt and nickel

The pressure dependence of the μ⁺ local magnetic fields in polycrystalline Fe and Ni and a Co single crystal has been measured at 77 K, up to 0.7 GPa, using a He gas high pressure setup. The pressure derivatives dlnB_μ/dP in units of mT/GPa are +4.4±1.0 (Fe), -0.7±1.1 (Co) and +0.63±0.10 (Ni). From these values the hyperfine field volume derivatives are deduced. Using these values together with previously determined room temperature derivatives the thermal expansion part of the temperature dependence of the hyperfine field can be calculated. The remaining explicit temperature dependence below 300 K, which deviates markedly from the temperature dependence of the bulk magnetization, is discussed.     

由热学性质获取氩晶体原子间各阶力常数

本文基于晶格动力学和量子力学微扰理论推导了氩晶体的热膨胀系数和比热与原子间相互作用的各阶力常数之间的关系公式,在此基础上根据热膨胀系数和比热的数据计算了氩晶体内的原子间相互作用的各阶力常数,并根据这些力常数绘制了原子间相互作用势能曲线,经比对发现该势能曲线与Morse势能曲线能较好吻合,这表明,本文提出的从热膨胀系数和比热获取各阶力常数的方法是正确的。     

由热学性质获取氩晶体原子间各阶力常数

本文基于晶格动力学和量子力学微扰理论推导了氩晶体的热膨胀系数和比热与原子间相互作用的各阶力常数之间的关系公式,在此基础上根据热膨胀系数和比热的数据计算了氩晶体内的原子间相互作用的各阶力常数,并根据这些力常数绘制了原子间相互作用势能曲线,经比对发现该势能曲线与Morse势能曲线能较好吻合,这表明,本文提出的从热膨胀系数和比热获取各阶力常数的方法是正确的。     

A study of interfaces in the microcrystalline alloy Fe3Si by Mössbauer spectroscopy

The microstructure and hyperfine parameters of Fe₃Si powder particles milled in a ball mill are investigated. A model of islands of original structure separated by veins of damaged structure (interfaces) is applied. The contents of both phases derived from Mössbauer spectra are changed by heal treatment. Variations of hyperfine parameters with phase composition are explained as the effect of fluctuations of the magnetization. The isomer shift shows a compression of iron atoms in the interfaces and lattice expansion in the islands of original structure. The enhancement of the hyperfine field in interfaces is explained by the appearance of large “surface-like” magnetic moments.     

Local magnetic moments and hyperfine magnetic fields in Fe-M (M = Si, Sn) alloys at small metalloid concentrations

The main tendencies in the formation of local magnetic moments and hyperfine magnetic fields at Fe nuclei in Fe-Sn and Fe-Si alloys at low metalloid concentrations are analyzed on the basis of “first-principles” calculations. The results of calculations are compared with experimental data. The main differences between these alloys were proved to be due to the differences in their lattice parameters. It is shown that a significant contribution to the formation of the hyperfine field comes from the orbital magnetic moment and the Ruderman-Kittel-Kasuya-Yosida polarization, which depend on the impurity concentration and the distance to an impurity atom in the crystal lattice.     

Dependence of ligand fields in paramagnetic crystals on thermal changes in their structures

Paramagnetic behaviours of the salts of the iron group depend upon the asymmetric ligand fields acting upon the central paramagnetic ion, as also upon the structure and packing of the crystal lattice. A general picture of the energy levels of the paramagnetic ions is, available from the ligand field theory, based upon the coordinated data on X-ray structure, magnetic susceptibility and anisotropy, e.p.r and optical absorption spectra. When all these facts have been taken into account it is observed that there is an almost universal discrepancy between the observed thermal magnetic behaviours, particularly the anisotropy and those theoretically predicted on the assumption that the ligand fields are independent of temperature. The discrepancy cannot usually be covered by the change in the fields due to normal thermal expansion of the lattice. It is pointed out that these may be occasionally due to electric dipole ordering in the crystals at certain temperatures but more generally due to continuous types of transition in the crystal lattice with temperature, which change the lattice packing in an anomalous manner and thus cause a thermal variation in the asymmetric ligand fields.     

Magnetic Resonance and Optical Spectroscopy of Yb<Superscript>3+</Superscript> in CsCaF<Subscript>3</Subscript> Single Crystal: an Analysis of Distortions of the Crystal Lattice near Yb<Superscript>3+</Superscript>

A trigonal Yb³⁺ paramagnetic center in the CsCaF₃ single crystal was studied by magnetic resonance and optical spectroscopy methods. The structural model of the complex and the empirical energy level scheme were established. The transferred hyperfine interaction parameters and the crystal field ones were determined. The crystal field parameters were used to analyze the lattice distortions in the vicinity of Yb³⁺ using the superposition model.     

Effect of magnetoelastic interaction on the thermodynamics of ferromagnets: Simulation by the method of spin-lattice dynamics

Thermodynamic properties of systems with coupled magnetic and lattice degrees of freedom are analyzed by the numerical spin-lattice dynamics (SLD) method. A scheme of numerical integration is developed for SLD equations in a thermostat, that follows the earlier formulated approaches and is modified to describe systems with realistic interatomic interactions. The method proposed allows one to calculate the spectral density of oscillations, heat capacity, magnetization, and thermal expansion coefficient within a single scheme. It is established that, due to short-range magnetic order, the interplay between magnetic and lattice degrees of freedom contributes to the thermodynamic properties of the system even in the paramagnetic state. It is shown that there exist two mechanisms how the spin-lattice interaction influences the thermodynamic properties: static and dynamic mechanisms; the first is determined by its contribution to the thermal expansion of the lattice, and the second, by the dynamic interaction between magnetic moments and crystal lattice vibrations.     

掺铜PTO晶体顺磁共振谱及局域结构的理论研究

基于晶体场理论,本文采用重叠模型和3d⁹电子组态在畸变四角晶场中的g因子和超精细结构常数A的三阶微扰计算公式以及钛酸铅PbTiO₃ (PTO): Cu²⁺晶体的局域结构与EPR谱之间的定量关系,合理解释了PTO: Cu²⁺晶体的EPR谱及局域晶体结构,所得结果与实验观测相符合.      

Low temperature thermal expansion of praseodymium between 0.5 and 25 K

The linear thermal expansion coefficients parallel and perpendicular to the hexagonal axis of single crystal Praseodymium have been measured between 0.5 and 25 K and in external magnetic fields up to 12 kOe. α₆ ? α_⊥ is found to be of the order of 10^?4 at 20 K, decreasing with decreasing temperatures. Below 1 K we found evidence of a nuclear hyperfine contribution to the thermal expansion. A separation of the electronic term allows a determination of the electronic Grüneisenparameter.     

Electrical and thermal transport properties of dilute Pr in Pd

We have measured susceptibility, electrical resistivity thermopower, thermal conductivity, specific heat, thermal lattice expansion and Hall effect of dilute alloys of Pr (x = 0.014, 0.03) and of Lu (x = 0.014) in Pd. We find a rather strong valence instability at room temperature from L_III X-ray absorption (v = 3.1), which manifests itself by a concentration-independent characteristic temperature, by a resistivity minimum and by a strong anomally of the thermopower. The susceptibility also indicates strong magnetic polarisation of the surrounding Pd-atoms through the excited crystal field levels but not through the ground state of the impurity. The neutron scattering shows several sharp crystal field excitations between 0 and 1 meV and a very broad quasi-elastic scattering at higher temperatures with the 4f-form factor. We take this also as evidence for a weak coupling of valence instabilities to the low lying crystal field levels of the impurity and a strong coupling to the higher ones.     

Nuclear hyperfine effects in Dy(OH)3

A crystal field analysis of the experimental data on magnetic, optical and thermal properties of Dy(OH)₃ single crystals have been published The nuclear hyperfine properties of Dy³⁺ in Dy(OH)₃ were studied using a crystal field thus obtained. The hyperfine spectra were computed from 4–20 K with a minimum number of approximations. Under a weak crystal field, the lowest electronic level is a Kramers' doublet For this highly anisotropic crystal, the magnetic hyperfine and the quadrupole interactions are both prominent The quadrupole interaction energy is temperature dependent The value of the magnetic Sternheimer factor R_hf/R is determined to be 0 14 The observed specific heat $\text{C}{}_{\mathrm{hf}}\text{R}$ arising from hyperfine interactions have been explained satisfactorily A maxima is expected at 21 mK.     

Evaluation of asymmetric Mössbauer spectra of a Fe-41.3 at.% Ni invar alloy

Following a model of Billard and Chamberod the asymmetric Mössbauer spectra of a Fe-41.3 at.% Ni invar alloy have been quantitatively interpreted. In the temperature range from about 77 K up to the Curie temperature for each spectrum four parameter values have been obtained. These are the mean hyperfine field H₀, the magnetic field difference h₁ caused by the isotropic contribution of one first Fe-neighbour atom, the corresponding anisotropic difference h₂ and the strength of the anisotropic quadrupole interaction w. A physical interpretation of these parameters and their temperature dependence has been worked out. The last parameter shows an especially unexpected dependence which is strongly connected with the thermal expansion of the lattice. A mechanism seems to exist by which small changes of the lattice constant cause an enhanced variation of w.     

Mössbauer relaxation spectra of an Ising pseudo-doublet: Influence of the off-diagonal hyperfine coupling

The influence of direct relaxation between the states of an Ising pseudo-doublet on the paramagnetic Mössbauer spectra is examined. An analytic expression for the line shape is obtained, and this is used to show the importance of accounting for the off-diagonal hyperfine coupling, even when the crystal field splitting of the electronic states is very much greater than the hyperfine interaction. The fast relaxation limit is found to be independent of the crystal field splitting, and shows the full magnetic hyperfine structure associated with an unsplit Ising doublet. The influence of a small applied magnetic field is examined and the conditions under which the off-diagonal hyperfine coupling may be ignored are delineated.     

The magnetic phases of Mn0.90Fe0.10P studied by Mössbauer spectroscopy

Iron/manganese substitution in MnP has been studied by ⁵⁷Mössbauer spectroscopy. The Curie temperature is 250 K, but not all iron nuclei experience a magnetic hyperfine field even at 170 K. The helical structure is developed below 170 K and show modulations of the hyperfine field. The discrepancies from pure magnetic states (ferromagnetic and circular helix) are explained on the basis of the near surroundings of the iron atoms. The differences in the values of the electric monopole and quadrupole interactions at the iron nuclei for FeP and Mn_0.90F_0.10P are interpreted as an effect of lattice expansion.     

Solid solutions of nickel and cobalt disilicides

Lattice parameters, density, thermal expansion coefficients and electrical conductivity of alloys of higher silicide of nickel with cobalt disilicide were measured. The influence of the completeness of the crystal lattice of the continuous series of solid solutions formed by these compounds was analyzed. The anomalous variation in the lattice parameter observed when nickel is replaced by cobalt was attributed to a reduction in the electron concentration in antibonding states.     

Molecular-dynamics calculation of the thermal conductivity coefficient of the germanium single crystal

The thermal conductivity coefficient of the germanium crystal lattice has been calculated by molecular dynamics simulation. Calculations have been performed for both the perfect crystal lattice and the crystal lattice with defects such as monovacancies. For the perfect germanium single crystal, the dependence of the thermal conductivity coefficient on the lattice temperature has been obtained in the temperature range of 150–1000 K. The thermal conductivity coefficient of the germanium lattice has been calculated as a function of the monovacancy concentration.     

Structure of electromagnetic fields near the surface of an ionic crystal

A NaCl ionic crystal whose (100) face is in contact with vacuum is used as an example to consider static and dynamic contributions to an electromagnetic field in close proximity to its surface. The expression for the potential of the electric field produced by a system of point charges in vacuum (derived by Lennard-Jones and Dent) is taken as the basis. The dynamic correction to the static field has been found. It appears as a result of thermal fluctuations of ions near equilibrium positions in the ionic lattice. Various contributions of the electrostatic field of the ionic lattice, the field of fluctuating ions of this lattice near their equilibrium positions, and of the dipole-type fluctuation field produced by spontaneous deformations of the crystal??s elementary cells to the energy density of the electromagnetic field near the surface of the ionic crystal have been calculated and compared. The periodic structuring of the electromagnetic field??s energy density caused by the presence of static and dynamic ionic lattices of the crystal at small distances from its surface is illustrated graphically. Fields generated by a film with a finite thickness containing an arbitrary number of ion monolayers have also been considered.