An algorithm for solving Roberts-von Hippel equation: separation ofclose solutions

The proximity of the solutions of the transcendental equation and tanh z/z=c on the complex plane arising in the determination of the complex dielectric permittivity with the short-circuited-line method is studied. A numerical procedure is described which is capable of obtaining the required number of solutions, even those lying very close to each other, from one single initial point. The method is applied to measurements of various organic liquids     

Effect of stress on the law of approach to saturation magnetizationin carbon steels

In high fields where the magnetization is approaching saturation, the resolved magnetic polarization I can be expressed by a power series of the inverse of external field H as: I=I_s-b/H ²-c/H³ . . ., or alternatively in terms of the reversible permeability μ_rev=1+(2b/H³+3c/H⁴+ . . .)/μ₀ where I_s is the spontaneous magnetic polarization and b, c, are constants. These equations express the law of approach to saturation magnetization. The coefficient b for a cubic crystal has been deduced as b=0.0762/I_s[K+1.5(λ₁₀₀-λ ₁₁₁)σ]², where σ is the applied stress and others are magnetic constants. The values of reversible permeability μ_rev under biasing field H were measured for carbon steels with applied stresses. The results showed that the square root of 2b changed linearly with the applied stress, The values of magnetic constant K andλ₁₀₀ -λ₁₁₁ were calculated, They agreed with the standard values, but were affected by chemical composition and heat treatment of materials, especially in λ₁₀₀-λ₁₁₁     

Sintered Sm2(Co, Fe,Cu,Zr)17 magnets withlight rare earth substitutions

The effects of partial substitution of light rare earths for Sm in (Sm_1-xR_x)₂ (Co,Fe,Cu,Zr)₁₇ have been investigated where R=Ce, Pr, Nd, Pr_0.5Nd _0.5, Ce_0.2Pr_0.4Nd_0.4 and x=0-0.5. Experiments show that both remanence and maximum energy product are improved for x=0.1-0.2, depending upon compositions and heat treatments. For a composition Sm_0.8R_0.2(Co_0.633Fe_0.286 Cu_0.061Zr_0.020)_7.59 with R =Ce_0.2Pr_0.4Nd_0.4, the authors obtained B_r=11.57 kG, _MH_c =15.5 kOe, _BH_c=10.33 kOe, H_k=10.03 kOe, and (BH)_max=30 MGOe     

Properties of the W-type hexaferritePbZn2Fe16O27

W-type Pb-hexaferrites were prepared by standard ceramic methods. The lattice constants found by refinement were a=0.59140±0.00006 nm and c=3.29209±0.00041 nm. The X-ray density of a typical composition PbZn_1.9Fe_15.3O_25.8 was ρ=5.32 g/cm³ and the Vickers microhardness value h _v=6 kN/mm². A plot of the saturation magnetization versus temperature is given. The extrapolated value of the saturation magnetization (H→∞, T→0) was σ_s=108 emu×g^-1, and the Curie temperature was T_c=600±20 K     

Quantized Hall resistance measurements

The quantized Hall resistances, R_H(4), of Si MOSFETs were measured at ≈0.5 K in a magnetic field of 15 T. The value of R_H(4) was determined in terms of the Commonwealth Scientific and Industrial Research Organization (CSIRO) realization of the SI ohm. A weighted mean of three determinations gave a value for the quantity R_H(4) of (6453.203,36(52)) Ω_SI-NML which can also be expressed as 6453.2(1.000,000,52(8)) Ω_SI-NML. This R_H (4) value gives a value for h/e² which is about 0.3 p.p.m. larger than the value for h/e² derived from the anomalous moment of the electron, using the quantum electrodynamics (QED) theory     

Determination of the time-dependence of ΩNBS usingthe quantized Hall resistance

The quantum Hall effect is being used to monitor the US legal representation of the ohm, or as-maintained ohm, Ω_NBS. Measurements have been made on a regular basis since August 1983. Individual transfers between the quantized Hall resistance R _H and the five 1-Ω resistors which comprise Ω_NBS can be made with a total of one standard deviation (1σ) uncertainty of ±0.014 p.p.m. This uncertainty is the root-sum-square of 32 individual components. The time-dependent expression for R_H in terms of Ω_NBS is: R_H=25812.8[1+(1.842±0.012)×10^-6 =(0.0529±0.0040)(t-0.7785)×10^-6 /year] Ω_NBS, where t is measured in years from January 1, 1987. The value of Ω_NBS is, therefore, decreasing at the rate of (0.0529±0.0040) p.p.m./year     

Widely extended new method for measuring the impedance (CxRx) at high frequencies withapplications

A method is described for the accurate measurement of the equivalent parallel capacitance C_x and resistance R_x of very high loss materials at high frequencies. The important characteristic of the method is its capability of measuring the value of C_x extending from 10^-2 to 10⁶ pF and R_x from 10 to 100×10⁶ Ω. The authors measure the humidity of tea leaves and rockwool by measuring the capacitance C_x of specimens irrespective of the value of R_x     

Acoustic and microwave resonances applied to measuring the gasconstant and the thermodynamic temperature

Certain experimental and theoretical developments in acoustic and microwave techniques are reviewed, along with the progress in combining them to accurately measure u/c, the ratio of the speed of sound in a gas to the speed of light. Measurements of u/c in dilute monatomic gases can be used to determine the temperature of fixed points with unprecedented accuracy and to interpolate between them. This work also refers to the application of acoustic techniques to the redetermination of the universal gas constant     

Multirate polynomials prediction with unevenly spaced samples

A method for polynomial prediction with unevenly spaced samples is proposed for dynamic upsampling purposes, frequently needed in digital signal-processing applications. The procedure is based on Newton's divided-difference interpolation formula, which allows prediction along a polynomial of degree n if the samples are arbitrarily spaced. For this purpose, it is necessary to store n+1 latest values pairs (x_i, u_i) where x _i is the time instant when the sample y_i is available. Based on the (x_i, y_i ) pairs, the algorithm predicts y-samples for arbitrary values of x. Noise reduction techniques based on bandwidth limiting are discussed. As an application, a velocity measurement system is considered, based on pulse-width measuring, where the primary interest is in improving the accuracy at very low speeds     

Analytical electron microscopy of Sm(Co,Fe,Cu, Zr)9

Electron microscopic studies of as-cast Sm(Co,Fe,Cu,Zr)₉ magnets revealed a hexagonal phase of the type Sm₂(Co,Fe,Cu,Zr)₁₇ with crystal lattice parameters of a=0.84 nm and c=3.2 nm. After a solid solution treatment, only rhombohedral (3R) and hexagonal (2H) grains were found. After an additional annealing treatment at 800°C, grains with a microcellular precipitation structure similar to the one found in Sm(Co,Fe,Cu,Zr)_7.5 magnets occurred. In addition, in the as-cast and after-aged samples, other, partly unidentified Cu- or (Co,Fe)-enriched phases were detected     

Magnetic properties of GdBa2Cu3O7crystals in high magnetic field

The magnetic properties of single crystals of GdBa₂Cu ₃O₇ were investigated in a magnetic field of up to 20 T applied parallel to the c axis in the 1.7-300 K temperature range. In the superconducting state, the field and temperature dependences of the critical current densities were deduced from the hysteresis of the half-cycle using Bean's critical state model. The Gd³⁺ paramagnetic moment was then studied. Above about 20 K, the M(H) isotherms were found to be given, at different temperatures, by the Brillouin function of the free Gd³⁺ ion. Below 20 K, the average magnetization does not obey the Brillouin law. The normal-state susceptibility was described by the free-ion Curie-Weiss law     

Determination of overwrite specification in thin-film head/disksystems

A self-consistent write analysis using the Preisach model is presented and used to calculate overwrite in thin-film head/disk systems. Two overwrite characterization procedures are discussed, and for each of the procedures the calculated values are compared with measurements. Through a correlation of overwrite, nonlinear peak shifts, and readback output voltage the authors determine the overwrite requirement. They show that whereas -30 dB of overwrite will ensure a satisfactory overall performance of the recording system, a much lower overwrite, say -20 dB, can work in certain situations. An analytical implementation of the self-consistent model is presented and verified with measurements. The analytical approach can be used to determine the overwrite at any applied field for any head/disk combination. The authors introduce a normalized effective field h_n, which depends on M_rδ, H_c, and other head/disk parameters. It is shown that a value of h _n greater than 0.8 is needed for overwrite values of better than 25 dB. The importance of various head/disk parameters in optimizing the overwrite is also discussed     

Effect of the n value and the field inhomogeneity on thequench current of superconducting cables [magnet winding]

A model developed to obtain a relation connecting the critical current and the quench current of superconducting (S/C) cables is described. The model is based on the hypothesis that the heat produced inside the cable is only due to the ohmic dissipation, and it is only removed by thermal exchange with the liquid helium bath. The ohmic dissipation is calculated by supposing that the electrical resistance of the S/C cable at the transition to normal state is: Rαlⁿ where l is the current and n (n value) is an integer number. To calculate the function R(I), the field inhomogeneity at the conductor due to the self-field is taken into account, introducing the effective critical field     

Calculation of exact head and image fields of recording heads byconformal mapping

An exact conformal mapping calculation is carried out, which maps the entire upper edge of an idealized ring head and a symmetric thin-film head in the complex z plane to the real axis of the complex t plane, and uses the slotted-plane approximation to obtain the inverse mapping function t(z). The latter is used to calculate not only the head fields of a given geometry, but also the kernal function to evaluate the total demagnetization field of the interaction head-media system including the media self-demagnetization and the image field induced on the head poles. The total demagnetization field contours for a single-bit arctangent transition and a dibit biquadratic transition corresponding to various head configurations have been obtained and their physical meaning elaborated on     

Magnetic properties of Sm2Fe17Nxpowder and bonded magnet

Sm₂Fe₁₇N_x powders were prepared through metallurgical processes such as melting, casting, pulverizing, and gas nitrogenation. Epoxy resin and zinc-bonded magnets were prepared from the powder by a compression molding process. The magnetic properties of magnetically aligned Sm₂Fe₁₇N_x powder were (BH)_max=170 kJ/m³ (21.4 MG-Oe), Br=1.20 T, and H_cJ=547 kA/m (6.87 kOe). Those of an epoxy-bonded magnet were (BH)_max =103 kJ/m³ (13.0 MG-Oe) and Br=0.835 T. H _cJ values in excess of 2 MA/m (25 kOe) were observed in the case of a zinc-bonded magnet     

Recent developments in the PTB RF standard attenuation measuringequipment

Developments in standard equipment for precise attenuation measurements are described. The frequency range of the RF standard attenuation measuring equipment at the Physikalisch-Technische Bundesanstalt (PTB), Germany, has been extended up to 40 GHz in the waveguide bands R 220 and R 320. The total uncertainty of the system is estimated to be equal to or smaller than 0.002 dB for a 30-dB attenuation step     

Hot-pressed Mn-Zn-Ni and Mn-Zn-Co ferrites for magnetic recordingheads

Ni²⁺ and Co²⁺ substituted Mn-Zn ferrites have been developed as high-density magnetic recording materials by hot pressing using optimum sintering parameters. Ferrite series of the composition Mn_0.6Zn_0.4-xNi_xFe₂ O₄ and Mn_0.6Zn_0.4-yCo_yFe₂O₄ were prepared by the hot-pressing technique wherein x and y varied from 0.0 to 0.4 in steps of 0.05. It yielded ferrites with improved magnetic properties having higher hardness (⩾650 Vickers units), low porosity (<0.1%), and small grain size (≈10 μm). The initial permeability increased, whereas the coercive field decreased for an Ni²⁺ concentration x or a Co ²⁺ concentration y equal to 0.05. Maximum values of saturation magnetization equal to 4850 and 5250 G were obtained for x and y equal to 0.225 and 0.275, respectively. The Curie temperature increased appreciably, whereas the DC resistivity decreased for a larger substitution of Ni²⁺ and Co²⁺ ions     

STM control of noninteger residual charge Q0 onthe central electrode of a double-tunnel junction

In a voltage-biased mesoscopic double-tunnel junction, the Coulomb threshold V_C is an e-periodic function of Q ₀, the charge on the inner electrode. In the STM work described here, a large Au tip images 100-Å Ag particles deposited on a cleaved BSCCO crystal substrate. Stable double junctions between the tip, the imaged particle, and the substrate are identified by Coulomb staircase I(V)'s. The control of Q ₀ is demonstrated by the variation of tip-particle spacing. The parameterization of such results permits a discussion of Q ₀ variation mechanisms     

A measurement of the NBS electrical watt in SI units

The National Bureau of Standards (NBS) electric watt in SI units to be: W_NBS/W=K_W =1-(16.69±1.33) p.p.m. The uncertainty of 1.33 p.p.m. has the significance of a standard deviation and includes the best estimate of random and known or suspected systematic uncertainties. The mean time of the measurement is May 15, 1988. Combined with the measurement of the NBS ohm in SI units: Ω_NBS/Ω=K_Ω =1-(1.593±0.022) p.p.m., this leads to a Josephson frequency/voltage quotient of E_J=E₀[1+(7.94±0.67) p.p.m.] where E₀=483, 594 GHz/V