An experimental study of the dynamic properties of nanoparticle colloids with identical magnetization but different particle size

Measurements of the frequency dependent complex magnetic susceptibility, χ(ω)=χ′(ω)−iχ″(ω), have been used to determine the dynamic properties of three specially prepared 400 G (0.04 T) magnetic fluids. The samples, denoted by sample 1, sample 2 and sample 3, consisted of magnetite particles of mean diameter 6.4 nm, 7.5 nm and 9 nm respectively and were identical in terms of carrier liquid, surfactant and particle material.     

On the high-frequency measurement of the dynamic properties of nano-particle colloids

Measurement of the magnetic complex susceptibility, χ(ω)=χ′(ω)−iχ″(ω) by means of the transmission line technique, is a well established method for the determination of the dynamic properties of nano-particle colloids, such as magnetic fluids. From polarising studies one can obtain accurate data on the anisotropy constant, K, anisotropy field, H_A, gyromagnetic constant γ, and the damping parameter, α. From data on χ(ω), one can determine the loss tangent, tan δ, of the samples and also a value of the precessional decay time, τ₀. From polarized studies, one can investigate the presence of any hysteresis. The technique is also suitable for the investigation of the magnetic properties of composite samples. In this paper a review of the above mentioned topics are presented with examples of results obtained for a number of magnetic fluids.     

The resonance decay function method in the determination of the pre-factor of the Néel relaxation time of single-domain nanoparticles

In its simple form, the relaxation time of the Néel relaxation process of the magnetic moment of single-domain particles is given by τ_N=τ_0Nexp(σ), σ being the ratio of anisotropy energy to thermal energy. The pre-factor, τ_0N, is normally given a value of 10⁻⁹ s, but values ranging from 10⁻⁸ to 10⁻¹² s have been reported in literature. Here, by means of the field and frequency dependence of the complex magnetic susceptibility, χ(ω,H)=χ′(ω,H)−iχ″(ω,H), of a magnetic fluid sample, in the MHz-GHz range, in conjunction with the determination of the sample decay function, b(t), the pre-factor τ_0N is determined. b(t) is readily obtained through the inverse Fourier transformation relationship, which exists between b(t) and χ″(ω).     

An improved technique for the measurement of the complex susceptibility of magnetic colloids in the microwave region

Measurements by means of the short-circuit (S/C) and open circuit (O/C) transmission line techniques are well established methods for investigating the magnetic and dielectric properties of magnetic colloids, respectively. In particular, the S/C technique has been used in the investigation of the resonant properties of ferrofluids; resonance being indicated by the transition of the real component of the magnetic complex susceptibility, χ(ω)=χ′(ω)−iχ″(ω), from a positive to a negative value at a frequency, f_res. However, under certain circumstances, the accuracy of the S/C technique is affected by the dielectric properties of the sample, hence incurring errors in the measurement of χ(ω) and indeed of f_res. Here we present a model which, by combining short-circuit and open circuit measurements, is developed in a manner in which the permeability, μ, and the permittivity, ε, contribute simultaneously to the calculation of χ(ω), thereby providing superior experimental results in comparison to those obtained by the S/C technique alone. For the two ferrofluid samples measured it is demonstrated that the dielectric properties affect the high frequency content of the susceptibility spectrum.     

Scaling laws and approximate expressions for the dynamic magnetic susceptibility of Brownian nanoparticles

We present simplified expressions for the out-of-phase component of the dynamic susceptibility χ″ of lognormal-sized magnetic nanoparticles under Brownian rotation. These expressions are based on transforming the general integral functions used for χ″ in the convolution of gaussian functions. χ″ can thus be expressed as a sum of gaussians with parameters directly related to those of the size distribution and to the saturation magnetization. The gaussian fit of χ″(ω) (where ω is the ac field frequency) is a simpler way to determine these structural and magnetic parameters as it avoids fitting χ″(ω) to an integral function. The expressions derived for χ″ suggest that χ″T data collapses in a ωη(T)/T scale (where T is the temperature and η the fluids viscosity), which is confirmed by numerical calculations. We also discuss the limits of validity of these approximations in real systems where both Néel and Brownian relaxation mechanisms coexist and we present further approximations for the relation of ω_χ with the average volume (being ω_χ the frequency at which χ″ is maximum). The ωη(T)/T scale can be used to qualitatively evaluate the dominance of the Brownian relaxation mechanism.     

Influence of mobile space charges on electrical properties of ferroelectric Bi3.5La0.5Ti3O12 thin films

Lanthanum-substituted bismuth titanate, Bi_3.5La_0.5Ti₃O₁₂ (i.e., x=0.5 in Bi_4−xLa_xTi₃O₁₂), thin films have been grown on Pt/Ti/SiO₂/Si substrates using pulsed laser deposition. The frequency dependence of the real part ε′(ω) and the imaginary part ε″(ω) of the dielectric constant has been studied. The ε′(ω) does not show any sudden change within the frequency range of 10²-10⁶ Hz. In contrast, the ε″(ω) shows a large dispersion as frequency decreases. The observed relaxation behavior in ε″(ω) can be explained in terms of a migration of oxygen vacancies in (Bi₂O₂)²⁺ layers, not in Bi₂Ti₃O₁₀ perovskite layers.     

Low field AC susceptibility study of intergranular critical current density in Mg-substituted CuBa2Ca3Cu4O12−y high temperature superconductors

Measurements of the a.c.susceptibility (χ=χ′+iχ″) have been made on the Mg substituted high T_C superconducting system, CuBa₂(Mg_xCa_1−x)₃Cu₄O_12−y (Cu-1234) with x=0, 0.10 & 0.20, at different values of the a.c.field amplitude. Estimates of the intergranular critical current density(J_C) made from the field dependent χ″-T curves show an improvement in the Mg-substituted Cu-1234 system. Results have been analysed in the light of the crystal structure and the superconducting anisotropy factor (γ=ξ_ab/ξ_c) of the Cu-1234 system. Lower superconducting anisotropy emanating from Mg substitution has been found to be significant, resulting in better superconducting properties.     

Quasi-Debye response of ion-hopping conduction at lowest frequencies

On the basis of the relaxation mode theory, quasi-Debye response in the dynamic conductivity by hopping ions is theoretically investigated in three-dimensional random lattices with a uniform distribution of activation energies. It is shown at lowest frequencies that the dynamic conductivity is approximately given by σ(ω)∼σ(0)+A″ω^s″, s″=2−n, where n is a non-integer exponent originated from the mode diffusion length and density of states. The numerical analyses give rise to some values of s″<2, for example s″∼1.5, which behaves as s″→2 with increasing temperature.     

Relaxation and conductivity behaviour in the compounds: FeRGe2O7 (R=Pr,Tb)

AC measurements were performed on the thortveitite-like layered compounds, FeRGe₂O (R=Pr,Tb) in order to study their dielectric features, e.g. as a function of temperature. The main electrical response lies on impedance plots composed of two successive arcs with depressed centers. Bulk conductivity behavior is mostly Arrhenius for the measured temperatures. The associated bulk activation energies are close to 1 eV. Raw data were used to follow the temperature dependence of the dynamic parameters, ε′(ω) and σ′(ω). From logarithmic σ′(ω) vs. ω curves the dc component was obtained. ε′(ω) vs. log ω curves exhibit a dispersive behavior at low frequencies, reflecting blocking effects. E_dc and E_ac activation energies were also calculated, the last one obtained from σ′(ω) vs. 1000/T plots. Conductivity results suggest the occurrence of an extrinsic conducting mechanism. A structural instability was detected via the temperature dependence of permittivity, which has been ascribed to the presence of Ga-O-Ga bonds having associated angles different of 180°. Analyses of the results show that the interchange of Tb and Pr in the general formula FeRGe₂O₇ (R=Pr, Tb) involves only small differences in their global ac and dc behavior.     

Critical RF losses in fine particles of La1−xAgyMnO3+δ: Prospects for temperature-controlled hyperthermia

Temperature and frequency dependencies of the real (χ′) and imaginary (χ″) parts of the dynamic magnetic susceptibility were studied experimentally in fine particles of La-Ag manganites prepared by various methods. The samples under study have the Curie points in the range T_C=42-48 °C, which is a medical hyperthermia range of interest. When approaching T_C from below, a critical peak of χ″ was revealed, followed by a steep drop while passing to the paramagnetic phase. The experiments on the magnetic radio-frequency (RF) heating of the manganite aqueous suspensions demonstrated good autostabilization of the temperature near T_C. Peculiar instability is found in the heating kinetics, caused by the observed critical behavior of the RF losses. The prospects of the La-Ag manganites as candidates for application in the temperature-controlled hyperthermia are discussed.     

Dielectric spectroscopy on Bi3Zn2Sb3O14 ceramic: an approach based on the complex impedance

The dielectric properties and loss of Bi_1.5ZnSb_1.5O₇ a poor-semiconducting ceramic were investigated by impedance spectroscopy, in the frequency range from 5 Hz to 13 MHz. Electric measurements were performed from 100 to 700 °C. Pyrochlore type phase was synthesized by the polymeric precursor method. Dense ceramic with 97% of the theoretical density was prepared by sintering via constant heating rate. The dielectric permittivity dependence as a function of frequency and temperature showed a strong dispersion at frequency lower than 10 kHz. The losses exhibit slight dependence with the frequency at low temperatures presenting a strong increase at temperatures higher than 400 °C. A decrease of the loss magnitude occurs with increasing frequency. Relaxation times were extracted using the dielectric functions Z″(ω) and M″(ω). The plots of the relaxation times τ_Z′ and τ_M″ as a function of temperature follow the Arrhenius law, where a single slope is observed with activation energy values equal to 1.38 and 1.37 eV, respectively.     

Study of (Bi2O3)(BaxMo1−xO3) polycrystalline ceramic as relaxor ferroelectric

Solid solutions of bismuth layered (Bi₂O₃)(Ba_xMo_1−xO₃) (0.2≤x≤0.8, x is in step of 0.2) ceramics were prepared by conventional solid-state reaction of the constitutive oxides at optimized temperatures with a view to study its electrical properties. Powder X-ray diffraction has been employed for physical characterization and an average grain size of ∼16 to 22 nm was obtained. XRD study reveals the single phase structure of the samples. Dielectric properties such as dielectric constant (ε′), dielectric loss (tanδ) and ac electrical conductivity (σ_ac) of the prepared ceramics sintered at various temperatures in the frequency range 10¹–10⁷ Hz have been studied. A strong dispersion observed in the dielectric properties shows the relaxor type behavior of the ceramic. The presence of maxima in the dielectric permittivity spectra indicates the ferroelectric behavior of the samples. Impedance plots (Cole–Cole plots) at different frequencies and temperatures were used to analyze the electric behavior. The value of grain resistance increases with the increase in Ba ion concentration. The conductivity mechanism shows a frequency dependence, which can be ascribed to the space charge mainly due to the oxygen vacancies. The relaxation observed for the M″ (ω) or Z″ (ω) curves is correlated to both localized and long range conduction. A single ‘master curve’ for the normalized plots of all the modulus isotherms observed for a given composition indicates that the conductivity relaxation is temperature independent.     

Structural and ac electrical properties of a newly synthesized single phase rare earth double perovskite oxide: Ba2CeNbO6

A single phase rare earth double perovskite oxide Ba₂CeNbO₆ (BCN) is synthesized by solid-state reaction technique for the first time. The X-ray diffraction pattern of the sample at room temperature shows monoclinic structure, with the lattice parameters, a=5.9763 Å, b=5.975 Å and c=8.48 Å and β=90.04°. Impedance spectroscopy is used to study the ac electrical behavior of this material as a function of frequency (10²-10⁶ Hz) at various temperatures (30-450 °C). A relaxation is observed in the entire temperature range. Conduction mechanism is investigated by fitting the complex impedance data to Cole-Cole equation. Complex impedance plane plots show only one semicircular arc, indicating only the grain contribution of dielectric relaxation. The scaling behavior of imaginary part of electric modulus (M″) and imaginary part of electrical impedance (Z″) suggests that the relaxation describes the same mechanism at various temperatures. The frequency dependence of conductivity is interpreted in terms of the jump relaxation model and is fitted to Jonscher's power law. The values of dc conductivities extracted from the Jonscher power law varies from 2.79×10⁻⁷ to 3.5×10⁻⁵ Sm⁻¹ with the increase in temperature from 100 to 450 °C. The activation energies (0.37 eV) extracted from M″(ω) and Z″(ω) peaks are found to follow the Arrhenius law.     

XPS and thermomagnetic characterization of the CeNi4Cr compound

The magnetic, thermodynamic and electronic structure properties are discussed for the CeNi₄Cr compound. The X-ray photoemission spectra (XPS) provide an evidence of a mixed valence behavior with the occupancy of the f states n_f=0.89 and their hybridization with the conduction electrons Δ=30 meV. These values reproduce well the magnetic susceptibility χ(T=0), which is enhanced compared to similar CeNi₄M (M=Al, B, Cu) compounds. In combination with a slightly increased electronic specific heat coefficient (up to 100 mJ mol⁻¹ K⁻²), this compound can be classified as being on the border of the heavy fermion and mixed valence behavior. Using a small magnetic field in the χ(T) measurements reveals a presence of magnetically ordered impurity phase, which is easily damped by higher fields and it is shown that the contribution of this phase is minor. The question of the dependence of the electronic specific heat coefficient on the magnetic field is also addressed and the observations agree well with theoretical predictions based on the Anderson model.     

Magnetic study of Mg0.95Mn0.05Fe2O4 ferrite nanoparticles

The magnetic properties of Mg_0.95Mn_0.05Fe₂O₄ ferrite samples with an average particle size of ∼6.0±0.6 nm have been studied using X-ray diffraction, Mössbauer spectroscopy, dc magnetization and frequency dependent real χ^′(T) and imaginary χ^″(T) parts of ac susceptibility measurements. A magnetic transition to an ordered state is observed at about 195 K from Mössbauer measurements. The zero-field-cooled (ZFC) and field-cooled (FC) magnetization have been recorded at low field and show the typical behavior of a small particle system. The ZFC curve displays a broad maximum at , a temperature which depends upon the distribution of particle volumes in the sample. The FC curve was nearly flat below , as compared with monotonically increasing characteristics of non-interacting superparamagnetic systems indicating the existence of strong interactions among the nanoparticles. A frequency-dependent peak observed in χ^′(T) is well described by Vogel-Fulcher law, yielding a relaxation time and an interaction parameter . Such values show the strong interactions and rule out the possibility of spin-glass (SG) features among the nanoparticle system. On the other hand fitting with the Néel-Brown model and the power law yields an unphysical large value of τ₀ (∼6×10⁻⁶⁹ and 1.2×10⁻²² s respectively).     

Investigation of the non-linear loss properties of magnetic fluids subject to large alternating fields

The non-linear relaxational properties of a water-based magnetic fluid are investigated by means of measuring the frequency dependent complex susceptibility, χ(ω) in the presence of an external potential. The results obtained are discussed in terms of the magnetic analogue of the Coffey and Paranjape model as modified by Déjardin. The loss processes in the magnetic fluid in the non-linear region are investigated in the context of the loss tangent, tan(δ), and the power dissipation per unit volume. These measurements are of importance because of the continuing interest in the clinical applications of magnetic fluids, where large alternating magnetic fields can be applied to magnetic fluids to induce loss processes and heating effects, often driving the magnetic fluid into the non-linear region of magnetisation. We evaluate the increment of the susceptibility, Δχ, due to the non-linear response, through measurement of χ(ω), and extend this formulism to the non-linear increment of the loss tangent, Δ tan(δ) and the increment of the heating rate, ΔU_heat.     

Optical constants and dielectric function of DNA's nucleotides in UV range

We calculated frequency-dependent real n(ω) and imaginary k(ω) parts of the complex refractive index for adenine A, guanine G, cytosine C and thymine T in ultraviolet range using Kramers-Kroning analysis of their absorption spectra. The frequency-dependent real ε′(ω) and imaginary ε″(ω) parts of the dielectric function for the corresponding nucleotides were restored. We calculated also the dependence of the dielectric function on the imaginary frequency ε(iω) for the corresponding nucleotides.     

Ferroelectric relaxor behavior in hafnium doped barium-titanate ceramic

Temperature and frequency dependence of the real (ε′) and imaginary (ε″) parts of the dielectric permitivity of cubic Ba(Ti_0.7Hf_0.3)O₃ ceramic has been studied in the temperature range of 100 K to 350 K at the frequencies 0.1 kHz, 1 kHz, 10 kHz, 100 kHz for the first time. Diffuse phase transition and frequency dispersion is observed in the permittivity-vs-temperature plots. This has been attributed to the occurrence of relaxor ferroelectric behavior. The observed relaxor behavior has been quantitatively characterized based on phenomenological parameters. A comparison with the Zr doped BaTiO₃ has also been presented. For Hf doped samples transmission electron microscopy (TEM) characterization do show the presence of highly disordered microstructure at length scales of few tens of nano-meters.     

High-resolution infrared spectra of bicyclo[1.1.1]pentane

Infrared spectra of bicyclo[1.1.1]pentane (C₅H₈) have been recorded at a resolution (0.0015 cm⁻¹) sufficient to resolve for the first time individual rovibrational lines. This initial report presents the ground state constants for this molecule determined from the detailed analysis of three of the ten infrared-allowed bands, ν₁₄(e′) at 540 cm⁻¹, ν₁₇ (a₂″) at 1220 cm⁻¹, ν₁₈(a₂″) at 832 cm⁻¹, and a partial analysis of the ν₁₁(e′) band at 1237 cm⁻¹. The upper states of transitions involving the lowest frequency mode, ν₁₄(e′), show no evidence of rovibrational perturbations but those for the ν₁₇ and ν₁₈ (a₂″) modes give clear indication of Coriolis coupling to nearby e′ levels. Accordingly, ground state constants were determined by use of the combination-difference method for all three bands. The assigned frequencies provided over 3300 consistent ground state difference values, yielding the following constants for the ground state (in units of cm⁻¹): B₀ = 0.2399412(2), D_J = 6.024(6) × 10⁻⁸, D_JK = −1.930(21) × 10⁻⁸. For the unperturbed ν₁₄(e′) fundamental, more than 3500 transitions were analyzed and the band origin was found to be at 540.34225(2) cm⁻¹. The numbers in parentheses are the uncertainties (two standard deviations) in the values of the constants. The results are compared with those obtained previously for [1.1.1]propellane and with those computed at the ab initio anharmonic level using the B3LYP density functional method with a cc-pVTZ basis set.     

The magnetic susceptibility of hydrogen-doped partially crystalline (Zr76Ni24)1−xHx metallic glasses

The magnetizations of Zr₇₆Ni₂₄ metallic glass and hydrogen-doped partially crystalline (Zr₇₆Ni₂₄)_1−xH_x metallic glasses have been measured in the temperature range 10-300 K and magnetic fields up to 2 T for various dopant concentrations (x=0, 0.024, 0.043, 0.054). It is found that the samples are paramagnetic and magnetic susceptibility at room temperature, χ(300 K), shows a nonmonotonic behaviour upon hydrogenation. The values of χ(300 K) of the hydrogen-doped partially crystalline (Zr₇₆Ni₂₄)_1−xH_x metallic glasses are reduced with increase in hydrogen content up to x=0.043, whereas for x=0.054, an enhancement of χ(300 K) has been revealed. The magnetic susceptibility is weakly temperature dependent down to 110 K, below which an increase is observed. A shallow minimum exists between 90 and 120 K. The form and magnitude of the observed temperature dependence of the magnetic susceptibility are well accounted for by the sum of the quantum corrections to the magnetic susceptibility. Hydrogen reduces the electronic diffusion constant and influences strongly the quantum interference at defects, slowing down the spin diffusion and enhancing the magnetic susceptibility in the temperature range from 110 down to 10 K.