ISSN:0021-8979    

DOI:10.1063/1.1658594

出版商:AIP    

年代:1970

数据来源: AIP

摘要:

The thermodynamics of thermal expansion and of the related Gru¨neisen function &ggr;(T, V) is discussed first for cubic and isotropic solids. Vibrational effects are treated in the quasiharmonic approximation. For central force models two effects are distinguished‐that of the anharmonicity of the pair potential, normally contributing positively to the expansion, and that of the bond ``tensions,'' contributing negatively. The extension of the theory to noncubic solids is summarized, the strongly anisotropic example of zinc being used to illustrate the roles played by anisotropy in the elasticity and in the Gru¨neisen tensor. Recent work on central force lattice models, both ionic and nonionic, is reviewed. For ``internal expansion,'' in which the disposition of atoms within a unit cell varies with temperature, it is convenient to treat both internal and external strains on the same footing.

ISSN:0021-8979    

DOI:10.1063/1.1658595

出版商:AIP    

年代:1970

数据来源: AIP

摘要:

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 &Dgr;l/lof 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 &agr;, the coefficient of linear thermal expansion, down to 2 K for &Dgr;T=0.2 deg. These results yield &agr;=1.3×10−10T+2.7×10−11T3deg−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 Gru¨neisen &ggr; of 0.57. This value is compared with recent theoretical and experimental values.

ISSN:0021-8979    

DOI:10.1063/1.1658596

出版商:AIP    

年代:1970

数据来源: AIP

摘要:

At low temperatures the excitation of conduction electrons in metals gives rise to an electronic contributionC=&Ggr;˜Tto the heat capacity, and also a contribution &bgr;∝Tto the thermal expansion coefficient, whereTis the absolute temperature. The electronic Gru¨neisen parameter is&ggr;=V&bgr;B/C=(d ln&Ggr;˜/d lnV), whereVandBare the crystal volume and bulk modulus, respectively, atT=0. We have used a local pseudopotential model to calculate all the contributions to &Ggr;˜ and its volume derivative, including the electron‐phonon interactions in first‐order perturbation. The calculated &ggr; is 1.18 for Na, 1.01 for K, and 1.63 for Al, while the measured &ggr; is 1.8 for Al. The free electron model predicts &ggr;=⅔. From our calculations it appears that the Umklapp interactions of electrons with transverse phonons give important contributions to &Ggr;˜.

ISSN:0021-8979    

DOI:10.1063/1.1658597

出版商:AIP    

年代:1970

数据来源: AIP

摘要:

Strain‐gauge thermal expansion and anisotropy of susceptibility measurements indicate the existence of three phase transitions below 50°K in alpha uranium. Two of the transitions are of first order and one is of second order.

ISSN:0021-8979    

DOI:10.1063/1.1658598

出版商:AIP    

年代:1970

数据来源: AIP

摘要:

Gerlich has shown that Sheard's model for calculating mode &ggr;'s from hydrostatic pressure derivatives of the elastic moduli of hcp Mg and Cd yields Gruneisen &ggr;'s at both high and low temperatures that are in good agreement with the &ggr;'s derived from thermal‐expansion measurements. For hcp Ti and Zr, however, large differences arise, primarily from very small values fordC44/dP. It is proposed that these small values are caused by the changes inc/aratio with hydrostatic pressure because of a large dependence ofC44on thec/aratio. The disagreement with thermal‐expansion data can be removed by taking into account the difference ind(c/a)/dVbetween hydrostatic‐pressure and thermal‐expansion conditions. The effect of &Dgr;(c/a) is not found in tetragonal TiO2, rutile, where&ggr;¯His in excellent agreement with the thermal expansion &ggr;∞.

ISSN:0021-8979    

DOI:10.1063/1.1658599

出版商:AIP    

年代:1970

数据来源: AIP

摘要:

The temperature dependence of the lattice parameters of ZnO was measured by x‐ray powder‐diffraction methods. Retrograde behavior was found to occur perpendicular to thecaxis at 93°K. Lattice parameters at 4.2°K werea0=3.24826±0.00015Å,c0=5.2033±0.0018 Å. These results are compared with those for some other II‐VI compounds.

ISSN:0021-8979    

DOI:10.1063/1.1658600

出版商:AIP    

年代:1970

数据来源: AIP

摘要:

A quartz tube dilatometer was used to measure the lineal thermal expansion and creep of single lengths of polyethylene terephthalate (PETP) film, polypyromelitimide (PPMI) film, and PETP multifiber yarn, while stressed under constant tension. Tensions below and above the conventionally defined yield strength were used and the sample temperature ranged from 20 to 295 K. Relative creep strain measurements, taken at the constant temperatures 77, 195, and 295 K were found to obey the equation&egr;=exp[−2.3 exp(A′y)]whereyis a function of stress, time, and temperature andA′ is a constant depending on the material. This equation was used to correct the thermoelastic expansion measurements for creep at the higher stresses. PETP multifiber yarn subjected to a slight tension was found to elongate during cooldown from 293 to 20 K. Higher stresses caused less elongation; i.e., the coefficient of expansion increased with stress. This result is believed to be due to changes in crystallinity at the higher stresses. A similar stress effect was found with PETP film but not with PPMI film. The thermoelastic expansion of the film samples was also found to be sensitive to the thickness.

ISSN:0021-8979    

DOI:10.1063/1.1658601

出版商:AIP    

年代:1970

数据来源: AIP

摘要:

The volume expansion of sodium with a potassium impurity content of 100, 200, or 500 ppm (mole) was measured by a capillary method. The temperature region covered extended from 60° up to 100°C. (Melting point of pure sodium 97.83°C.) In the temperature region 60° to about 90°C the results, when combined with x‐ray measurements of the lattice constant, agree well with published values and theoretical estimates. The formation energy of a single vacancy was found to be 0.40±0.05 eV, and 0.45±0.05 eV; the formation entropy, in units of Boltzmann's constant, to be 7.2±1.5, and 7.05±1.5 for the 100‐ and 200‐ppm specimens, respectively. Extrapolation of the single‐vacancy concentration up to the melting point yields 10.5±1.5×10−4and 9.3±1.5×10−4, respectively, again for the two impurity contents, 100 and 200 ppm. The data taken between 90° and 97°C show an excess volume expansion over the extrapolated single‐vacancy values. Several possible mechanisms responsible for this behavior are discussed. The starting point of melting (Tc) was found by a careful analysis of the volume‐expansion curves versus temperature and time. A power law holds for the volume expansion in the region 10−6<(Tc−T)/Tc<10−4. The exponential number is 0.66≈2/3, independent of the potassium content of the sodium sample.

ISSN:0021-8979    

DOI:10.1063/1.1658602

出版商:AIP    

年代:1970

数据来源: AIP

摘要:

The optimum conditions for a high‐temperature x‐ray diffractometer are considered. A furnace with a minimum of compromise with these optimum conditions is described in some detail. Comparisons of previously described furnaces are made. The thermal gradients in the furnace were measured by thermocouple probe at several temperatures, and a novel shielding technique (making use of the x‐ray diffraction beam) was used to establish that the thermal gradients in the furnace were indeed very low. A series of polymorphic transitions which have been studied are presented as a means of obtaining a good calibration for high‐temperature x‐ray studies.

ISSN:0021-8979    

DOI:10.1063/1.1658603

出版商:AIP    

年代:1970

数据来源: AIP