The unit cell dimensions have been measured at temperatures between 93 and 333 K for linear polyethylene samples with long periods of 385, 220, and 99 A. The angular positions of 6 x‐ray diffraction lines were obtained at 5–10 K intervals with a powder diffractometer and the positions corrected for beam penetration so as to agree with powder camera results obtained with more lines at 296 and 155 K. At lower temperatures, the cell dimensions are nearly independent of long period, but at higher temperatures, the basal area of the cell appears to vary linearly with the reciprocal of the long period. The value of the slope increases with temperature and at 293 K is nearly the same for sets of data obtained with a number of different molecular weight distributions, crystallization and annealing conditions as well as for n‐paraffins. The specific volume data for all three polymer samples can be represented between 133 and 333 K with a standard deviation of 2.6×10−4 cm3 g−1 by the equation V=0.8341(1055.5−T)/(93...

Thermal Expansion of Polyethylene Unit Cell: Effect of Lamella Thickness

The coefficient of linear thermal expansion (α) for NaCl has been determined from 50°C to near the melting point (800°C) with an automatic recording dilatometer. The results confirmed the authors' suspicions that the values of α reported by Eucken and Dannohl are systematically high above 450°C. The experimental data are not satisfactorily represented by polynomial curves from the first through the eighth order as there is a decided increase in the thermal expansion above 600°C. Consequently, two second‐order polynomials are employed to adequately fit the data. The difference (Δα) at constant temperature between the high‐temperature polynomial and the extrapolation of the low‐temperature polynomial behaves logarithmically with respect to 1/T at high temperatures. The slope of this curve corresponds to a formation energy of 1.916 eV, which compares favorably with the energy required to form a pair of isolated positive and negative ion vacancies within the crystal (a Schottky defect).

Behavior of the Thermal Expansion of NaCl at Elevated Temperatures

The various instability-based theories of melting are reviewed with special emphasis on a particular type of instability which is both thermodynamic and elastic in nature. This “thermoelastic” instability originates from a decrease in resistance to shear stress, an idea developed by Born, and is characterized by divergent coefficients of thermal expansion (α) and isothermal compressibility at the melting temperature (T m), an ideal first proposed by Herzfeld and Goeppert-Mayer (1934). Evidence is presented from the results of parameter-free equation-of- state calculations for alkali halides and from published thermal expansion results for a variety of materials, which suggests that melting in many materials may be caused by a thermoelastic instability. A study of the potential energy surface for NaF suggests a type of disorder for the liquid phase which is consistent with recent results of molecular dynamics calculations. If α diverges at Tm then the slope of the melting curve can be deduced from...

H. Fischmeister

Papers

The thermal expansion of sodium chloride and some other alkali halides at high temperatures