Relative Length Change Research Articles

Thermal expansion of copper, silver, and gold below 30 K

A variable transformer technique has been used to determine the linear thermal expansion coefficients of the noble metals from 4 to 30 K. The precision of the data initially was ±0.04 A, and this was later increased to ±0.015 A, resulting in a sensitivity of approximately 2×10−11 for relative length changes of a 10-cm-long sample. The results agree at all temperatures (to better than 5%) with those of White and Collins who used a differential capacitor technique. The differences are 2% or less above 20 K for Cu, above 8 K for Ag, and at all temperatures for Au. The differences between the two sets of data for the three metals are not systematic (αWC greater for Cu, less for Ag) and may be due to differences in sample purity since much larger low-temperature anomalies were found within each set for certain samples of Cu and Ag. The resulting electronic Gruneisen parameters γe and theT=0 lattice Gruneisen parameters γ0 are as follows: $$\begin{gathered} copper \gamma _{\text{e}} = 0.91 \pm 0.05 \gamma _{\text{0}} = 1.67 \pm 0.02 \hfill \\ silver \gamma _{\text{e}} = 1.18 \pm 0.15 \gamma _{\text{0}} = 2.29 \pm 0.03 \hfill \\ gold \gamma _{\text{e}} = 1.6 \pm 0.5 \gamma _{\text{0}} = 2.96 \pm 0.04 \hfill \\ \end{gathered} $$ The values of γ0 are in reasonable (5% at worst) agreement with elastic constant values.

Anisotropic length changes at the superconducting transition of zinc

The length changes of zinc single crystals have been measured at the field induced transition from the superconducting to the normal state between 0.3 K and 0.8 K. A strong anisotropy in the deformations parallel and perpendicular to the hexagonal axis was observed. At T = 0 K the relative length changes are ( l s− l n)/ l s = 0.4×10 -8 perpendicular to the hexagonal axis. From the experimental data we have calculated the pressure dependences of the critical field H c and the critical temperature T c.

Sensitive Dilatometer for Low Temperatures and the Thermal Expansion of Copper below 10 K

We describe a dilatometer which is an improved version of the one previously used in this laboratory. It consists of a doubly twisted strip of beryllium copper with a mirror attached to its central region. This system is immersed in liquid helium II. Dilations of the sample are sensed by this system via a thin diaphragm, causing rotations of the mirror, which is detected by an external optical lever. The system has a sensitivity to relative length changes Δl/l of 10−11. Copper has been used as the test material to evaluate the performance of the instrument. It has been possible to make direct measurements of α, the coefficient of linear thermal expansion, down to 2 K for ΔT=0.2 deg. These results yield α=1.3×10−10 T+2.7×10−11 T3 deg−1. The ratio of these terms is much more accurately known than the absolute values because of uncertainty in the absolute calibration. The linear term leads to an electronic Grüneisen γ of 0.57. This value is compared with recent theoretical and experimental values.

Thermal expansion of solid methane

Relative length changes in solid methane at its approximate vapor pressure have been measured between 4 and 26 K. The linear-expansion coefficient calculated from these data is found to have a maximum at 19.8 K, 0.6 K lower than the peak found in specific-heat measurements. A negative expansion coefficient has been observed below 8 K. The possibility of nuclear spin-species conversion is discussed in terms of the long equilibration times and the observed length changes below 8 K.

Thermal Expansion in Dysprosium Aluminum Garnet

We have observed the Néel-point anomaly in the linear thermal expansion coefficient α of dysprosium aluminum garnet using the three-terminal capacitance technique. The shape of the λ peak at 2.53°K is similar to the specific-heat peak reported by Keen, Landau, and Wolf, although our measurements have less resolution since the relative length change from 1°–4°K is only approximately 2×10−7. For |1-T/TN|<0.1 the data are consistent with a logarithmic singularity when T<TN and with a power law behavior for T>TN. The predominant magnetic interaction is the dipolar coupling of the Dy3+ ions. We use a thermodynamic relation between the expansion coefficient and the specific heat at the λ transition to estimate - ∂ logTN/∂logV=1.0±0.5 in agreement with theoretical expectations for dipolar coupling.

Magnetic Studies at the Research Institute for Iron, Steel and Other Metals

A brief survey of several investigations is presented. (1) Spin-flopping magnetization measurements up to 80 kOe in α Fe2O3 in the low-temperature state are reported. The temperature dependence of the uniaxial anisotropy constant is obtained therefrom. Its magnitude is of the order of 104 erg/cc and increases with decreasing temperature. Measurements with the field perpendicular to the trigonal axis reveal that at a temperature in the transition region (240°K), the magnetic state moves first toward the high-temperature behavior with weak ferromagnetism, but above 60 kOe it returns to the antiferromagnetic low-temperature state. (2) Thermomagnetic measurements on CaFeO2.5 and CaFe4O7 indicate that a weak ferromagnetism appears at 400°C. From the crystal structure, a Dzyaloshinsky-Moriya canting is suggested to account for the weak moment. (3) High-field measurements of MnAu2 extend to low temperatures the previous data on its transition field (screw-type antiferromagnetism to ferromagnetism). The screw angle appears to be changing slowly even below 80°K. Longitudinal and transverse magnetostriction measurements in MnAu2 are reported through the transition and up to 80 kOe. Relative length changes of about 10−4 are observed and significant volume contractions during the screw-flopping and rotation stages are inferred. (4) Saturation moment and Curie point measurements of Pd-Fe alloys (near 30 at. % Pd) are reported and compared with similar Invar-type behavior in Ni-Fe alloys.

DIFFERENTIAL CONTRACTION OF LARGE AND SMALL CHROMOSOMES IN CULTURED LEUCOCYTS OF MAN.

The summed lengths of chromosomes Nos. 1 and 2 (x) were compared with the summed lengths of the small acrocentric chromosomes, Nos. 21, 22 and in males the Y chromosome (z), in 10 cells from each of 10 males and 5 females. Both chromosome groups varied in length together, but the changes were proportionally less in the small acrocentric chromosomes than in the large chromosomes. This was the case in both sexes. The relative changes in chromosome length were expressed by the regression coefficients z = 0.1461<i> x</i> + 5.55 in males and z = 0.1077<i>x</i> + 4.32 in females. It was considered that this differential contraction might be peculiar to the stage of chromosome contraction examined and that compensatory contraction occurred at other stages, or, on the other hand, that the greater degree of contraction of the large chromosomes involved an additional order of chromosome coiling.

Measurement of the Equilibrium Net Vacancy Concentration in Sodium

Simultaneous measurements of length and lattice thermal expansions have been made on two single-crystal rods of sodium, over a temperature range of -26\ifmmode^\circ\else\textdegree\fi{}C to near the melting point of 97.8\ifmmode^\circ\else\textdegree\fi{}C. The relative length changes were measured by means of two filar micrometer microscopes, and the lattice parameter changes were measured by a back-reflection, translated-sample method. The length and lattice expansions begin to diverge at approximately 10\ifmmode^\circ\else\textdegree\fi{}C, with least-squares-fitted curves leading to a net atomic fraction of vacancies at the melting point of (0.94\ifmmode\pm\else\textpm\fi{}0.11)\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}3}$ and (0.66\ifmmode\pm\else\textpm\fi{}0.15)\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}3}$ for the two samples. These values are lower than some that exist in the literature but agree with one set of electrical resistivity measurements and with one set of specific-heat measurements. In the latter case, anharmonic contributions had been subtracted from the specific-heat data before arriving at a defect concentration. Proceeding on the assumption that only vacancy formation is present, energies of 0.157\ifmmode\pm\else\textpm\fi{}0.014eV and 0.117\ifmmode\pm\else\textpm\fi{}0.023 eV have been obtained by fitting straight lines to semilog plots of the concentration versus reciprocal temperature. These values are lower than any existing in the literature with the possible exception of that of one set of electrical resistivity measurements. Entropies of formation have also been calculated by extrapolating the plots to infinite temperature. These appear to be negative well within the errors. It is quite possible that interstitial formation is present, thus lowering the semilog plots at the high-temperature end and giving erroneously low and negative entropies. Thus these values may be less meaningful than the values for melting-point concentrations. A value is given for the lattice parameter of sodium at 25\ifmmode^\circ\else\textdegree\fi{}C, and the fitted thermal expansion coefficients are presented.

An automatic recording differential dilatometer

The apparatus is suitable for the study of the kinetics of phase transformations and precipitation processes in the solid state. Relative length changes between a specimen and a control are measured by means of a variable inductance transducer. The differential system works to better than 1%, over temperature ranges of up to 1000° C.

Volume-pressure and length-tension measurements in human tracheal and bronchial segments.

Volume-pressure relations of isolated human tracheal and bronchial segments obtained post mortem from 21 patients, representing a wide age range (newborn premature infants to elderly adults), were studied. With intraluminal pressures above atmospheric, there was a progressive decrease in tracheal and bronchial compliance with increasing age. At +10 cm H2O intraluminal pressure, tracheal segments increased from 46 to 101% in volume, the greatest change being in the younger subjects. At +20 cm H2O pressure, tracheal segments increased from 52 to 129% in volume. The bronchi increased from 30% to 60% with +10 cm H2O pressure. When various weights were applied to the segments, there was a greater relative change in length of segments from younger subjects. Submitted on July 5, 1960

Magnetostriction of Yttrium Iron Garnet

An adnesive strain gage was used to measure the magnetostriction of polycrystalline yttrium iron garnet. The relative change in length was plotted against the applied magnetic field. From this curve the saturation magnetostriction constant Λs = --(3.7 plus or minus 0.5) x 10-7 was obtained. This small value appeared to be explained by dipolar interaction.

Measurement of the Equilibrium Concentration of Lattice Vacancies in Silver near the Melting Point

Relative changes in macroscopic length, $\frac{\ensuremath{\Delta}L}{L}$, and x-ray lattice parameter, $\frac{\ensuremath{\Delta}a}{a}$, of a 99.999% silver bar have been measured from 14 to 956\ifmmode^\circ\else\textdegree\fi{}C, using a rigid parallel pair of filar micrometer microscopes and a rotating single-crystal x-ray method. The expansions agree within experimental precision (about 1:${10}^{5}$) at the lower temperatures. At the higher temperatures ($\frac{\ensuremath{\Delta}L}{L}\ensuremath{-}\frac{\ensuremath{\Delta}a}{a}$) progressively increases, showing that atomic sites are added, corresponding to the thermal generation of vacancy-type defects. The concentration of added sites, $\frac{\ensuremath{\Delta}N}{N}=3(\frac{\ensuremath{\Delta}L}{L}\ensuremath{-}\frac{\ensuremath{\Delta}a}{a})$, at the melting point (obtained by a 4\ifmmode^\circ\else\textdegree\fi{} extrapolation) is (1.7\ifmmode\pm\else\textpm\fi{}0.5) \ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}4}$. This value is only $\frac{1}{5.5}$ of the corresponding value previously found for aluminum by the same technique. For reasonable values of the binding energies of vacancy aggregates, it is concluded that more than 90% of these extra sites are present as single vacancies. For an entropy of formation of $(1.5\ifmmode\pm\else\textpm\fi{}0.5)k$ an energy of formation for monovacancies of 1.09\ifmmode\pm\else\textpm\fi{}0.10 ev is obtained. This formation energy is slightly larger than half the activation energy for self-diffusion, as similar measurements have shown for aluminum, and as quenching experiments have indicated for gold.

Wax Secretion in the Cockroach

ABSTRACT The production of massive quantities of waxy materials by bees and similar insects has been known for a very long time, but it was not until 1938 that Bergmann showed the existence of smaller quantities of wax in the cuticle of Bombyx. Ramsay (1935) was the first to demonstrate that a greasy material on the surface of the cuticle was responsible for waterproofing the cockroach, and subsequently the work of Wigglesworth (1945) and Beament (1945) produced evidence for believing that the existence of a thin layer of wax in the epicuticle was widespread throughout the insects, and was the chief mechanism for restricting water-loss. It is now known that wax layers are also present in ticks (Lees, 1947) and in many arthropod eggshells (Beament, 1946, 1951, etc.), while Chibnall, Piper, Pollard, Williams & Sahai (1934) have carried out a detailed analysis of beeswax and of the wax of the white pine chermes. These waxes consist of long chain alcohols, paraffins and acids ; the aliphatic chains always appear to be saturated. The similarity of the physicochemical behaviour of cuticular waxes with beeswax, as outlined by Beament (1945), seems to leave little doubt that the minute but essential amounts of wax in typical insect cuticle are composed of the same type of chemical components as those found in beeswax. The range of melting-points of these materials shows that relative changes in the chain length of the component would be sufficient to account for the differences between the specific properties of waxes derived from different species.