Temperature variation of the lattice constant and the coefficient of thermal expansion of sodium chlorate

Abstract

Using a back-reflection, flat-film camera and an extrapolation technique, precision determination of the lattice constant of sodium chlorate has been made at different temperatures between the range 30-232 °C. From these, by a graphical treatment, the coefficients of thermal expansion at various temperatures have been evaluated. An equation is also given for evaluating the coefficient of expansion at any temperature.These coefficients of expansion show a temperature rate of variation higher than the one reported by Sharma (1950a) from macroscopic measurements. An explanation for this difference is attempted in terms of imperfections in a single crystal. IntroductionSodium chlorate has been the subject of numerous studies because of its simple structure and many of its interesting properties. Zachariasen (1929) gave the length of the unit cell as 6.570 _+ 0.006 kX. (6.583 /~). Htiber (1940) studied the mixed crystals of sodium chlorate and sodium bromate and gave the lattice constant of sodium chlorate as 6.568*_+ 0.001 •. Solhelm, Konrad & Vegard (1947) report a value of 6.5722* (converted from kX. to /~ units). In view of the discrepancies in these values an accurate redetermination of the lattice constant was thought to be worthwhile.Data on the thermal expansion of this salt have been reported by Mason (1946) and Sharma (1950a

Thermal expansion of ammonium bromide, rubidium bromide and rubidium chloride

“…Flat-film back-reflection photographs were obtained using a Sach-type camera and Cu Ks radiation. The experimental set-up and procedure for evaluating the lattice constants was the same as used by Deshpande & Mudholker (1960). As the flat-film camera recorded only two or three reflections, the accuracy of the procedure was checked by determining the lattice constants at room temperature by using a cylindrical Debye-Scherrer camera and comparing these with the values given by the flat-film method.…”

“…for 16 hrs. The experimental set-up used to obtain X-ray diffraction pictures was the same as described by Deshpande & Mudholker (1960). Three or four ala~ doublets, all with sin e 0 > 0.90, were used to evaluate the lattice parameters.…”

“…Recently, Visvamitra (1959) has reported the absence of any significant difference between the values obtained by the two methods. On the other hand, Deshpande (1960) has shown, from the existing data on a number of cubic and non-cubic crystals, that the gradients of the a-T curves are, in general, higher in the X-ray determinations than in the macroscopic determinations, and that they appear to agree with each other as a limit. It was, therefore, felt that the collection of more data would be useful in extending the range of this comparison.…”

Thermal expansion of sodium fluoride and sodium bromide

“…Recently the author (Deshpande, 1955) has studied both these halides at elevated temperatures by the X-ray method, and the results are reported below. The experimental set-up and the computational procedure have been described elsewhere (Deshpande & Mudholker, 1960;Deshpande & Sirdeshmukh, 1961). The only special feature of the present work is the P20 s in a vacuum dessicator and the use of an air-tight cellophane cover on the specimen, it was possible to obtain quite satisfactory results.…”

The `two-beam' pattern in electron diffraction

“…Conventional methods, involving the use of (i) X-ray back-reflexion powder photography, (ii) least-squares treatment of the film data and (iii) statistical analysis of the results, were employed to obtain precision values of the lattice constants at different temperatures along with estimates of the limits of errors (Deshpande & Mudholker, 1960;Deshpande & Khan, 1963;Jette & Foote, 1935).…”