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The γ-ray densitometer has been designed and fabricated in our laboratory and carried out studies on temperature dependent γ-ray attenuation and thermo physical properties of NaCl, NaBr and NaF. The linear attenuation coefficients (μl) for the pellets of NaCl, NaBr and NaF as a function of temperature have been determined. The coefficients of temperature dependence of density have been reported. The variation of density and thermal expansion of NaCl, NaBr and NaF in the temperature range of 300 K - 1000 K have been studied and compared with results available in the literature. The temperature dependence of density and thermal expansion has been represented by linear equations. Volume thermal expansion coefficients have been reported.

Density and Thermal expansion are fundamental thermo physical properties of solids. The study of temperature dependence of these properties is very important in understanding the temperature variation of other properties like elastic constants, refractive indices, dielectric constants, thermal conductivity, diffusion coefficients and other heat transfer dimensionless numbers. Thermal expansion of solids is of technical importance as it determines the thermal stability and thermal shock resistance of the material. In general the thermal expansion characteristics decide the choice of material for the construction of metrological instruments and in the choice of container material in nuclear fuel technology. Number of methods have evolved for the determination of density and thermal expansion of solids at high temperature like Archimedean method, pycnometry, dilatometry, electromagnetic levitation, Method of maximal pressure in gas bubble, method of sessile drop, hydrostatic weighing, high temperature electrostatic levitation and gamma ray densitometry. Thermal expansion studies on alkali halides have been reported by several workers using X-ray diffraction [1-3], dilatometry [4,5], Fabrey-Perot interference method [

As NaCl, NaBr and NaF are isotropic solids; we extended, for the first time, the γ-ray attenuation technique, to carry out the studies on temperature variation of γ-ray attenuation and thermo physical properties of NaCl, NaBr and NaF. In this communication, we report the temperature dependence of linear attenuation coefficient of γ-radiation, density and thermal expansion of NaCl, NaBr and NaF in the temperature range 300 K - 1000 K. In order to carry out this work, we have designed and fabricated a γ-ray densitometer and a programmable temperature controlled furnace (PTC) which can reach up to a temperature of 1300 K in our laboratory. The data obtained in the present work for coefficient of linear thermal expansion of NaCl, NaBr and NaF as a function of temperature have been compared with experimental and theoretical data available in literature.

The technique of γ-ray attenuation method is based on the fundamental equation

where I_{0}, the intensity of γ-ray before passing through the sample, I, the intensity of γ-ray after passing through the sample, µ, the mass attenuation coefficient of the sample, ρ, the density of the sample and l, the thickness of the sample. It is clear from Equation (1) that any change in the temperature of the solid is accompanied by change in it’s density causing a change in the measured intensity. The density and thermal expansion of the materials studied in the present work have been determined following the method suggested by Drotning [_{ρ}) and coefficient of linear thermal expansion (α_{1}) is given by

where α_{ρ} and α_{l} are mean values over a temperature interval. such that

and _{}

where, etc.

Rewriting Equation (2) as

where z is defined by

Substituting for α_{ρ} from Equation (2) gives

which can be rewritten as

where

The intensities of γ-radiation with sample I and without sample I_{0} are recorded at every temperature. At room temperature T_{1}, thickness of the sample l_{1} is measured and using Equation (1) µ is determined. Further measurements of I and I_{0} at different temperatures enable the determination of z by Equation (4) and hence x can be found from the solution of Equation (6). From the value of x, mean linear thermal expansion (α_{l}) can be determined as a function of temperature.

The experimental setup used for determination of density of materials utilizing γ-ray attenuation technique is called a γ-ray densitometer. A programmable temperature controlled furnace with sample inside the air tight quartz tube is introduced in the γ-radiation path allowing the beam to pass through the sample and to the detector without any interruption. The temperature of the sample is varied to study the attenuation at various temperatures. The block diagram of γ-ray densitometer is shown in

Consists of source housing, programmable temperature control (PTC) furnace with sample holder inside the air tight quartz tube, lead and stainless steel collimators, detector housing. The γ-radiation detector used in our study is a sodium iodide-thallium activated detector. The 3 inch diameter and 3 inch thick crystal is integrally coupled to a 3 inch diameter photo multiplier tube (PMT). The PMT has a 14 pin base and can be mounted on two types of PMT preamplifier units. The one used in our study is a coaxial in-line pre-amplifier. The detector has a resolution of 8.5% for ^{137}Cs.

Consists of amplifier which is fed to multi-channel analyzer where γ-ray spectrum is analyzed.

Consists of PC with Nets win Software and printer to calculate and to store the data. PTC furnace is an electric muffle furnace consisting temperature sensors along with programmable logic controllers (PLC) used for monitoring and recording the temperature. Type K thermocouple is used in the furnace for wide operating temperatures. The operation of furnace is monitored with the help of electronic panel. The cross sectional view of γ-ray densitometer is shown in

The samples studied in the present work were in the form of pellets. The pellets were prepared with fine powder of NaCl, NaBr and NaF with a diameter of 20 mm with varying thicknesses with a die set by applying hydraulic press pressure. NaCl, NaBr and NaF pellets were sintered at a temperature of 800 K for densification. The pellet was then firmly mounted on the round sample holder made of flat stainless steel strip inserted into an air tight quartz tube. The precise sample temperature was measured using a thermocouple sensor. The thermocouple sensor tip was mounted on the sample holder ensuring a perfect physical contact with the sample for recording

precise sample temperature. The sample holder along with the sample and thermocouple was slid through a cork into an air tight quartz tube and was fixed firmly. A diffusion pump was then connected to the sample holder tube for evacuation. For inert atmosphere, argon gas was introduced into the quartz tube through the sample holder tube. Then the quartz tube assembly along with the sample was slid into the programmable temperature controlled (PTC) furnace and fixed at appropriate position ensuring a perfect alignment of sample with collimation on either sides. The PTC furnace was programmed in such a way that the furnace temperature is increased by 25 K in every step starting from room temperature, and stabilizes there for a certain length of time. At each temperature the γ-ray counts of ^{137}Cs with sample (I) and without sample (I_{o}) were detected and recorded using a multichannel analyzer. Measurement of γ-ray attenuation counts at every step of temperature was repeated a minimum of nine times. The γ-ray counts were recorded while heating and cooling the sample. This procedure was repeated until the desired temperature range was covered in each case.

The results obtained for the temperature dependence of the linear attenuation coefficient (μ_{l}), density (ρ) and the coefficient of linear thermal expansion (α) of NaCl, NaBr and NaF are summarized in

Since the measurements have been made in the limited temperature range the coefficient of volumetric thermal expansion (CVTE) was calculated using the equation

where is the first derivative of density with respect to the absolute temperature which is determined from Equation (8). The variation of linear attenuation coefficient and variation of density with temperature of NaCl, NaBr and NaF have been shown in Figures 3 and 4 respectively. The mass attenuation coefficients (µ) of of NaCl, NaBr and NaF are found to be 7.428 × 10^{−3} m^{2}∙kg^{−1}, 7.164 × 10^{−3} m^{2}∙kg^{−1} and 7.289 × 10^{−3} m^{2}∙kg^{−1} respectively these results agree well with the calculated values 7.434 × 10^{−3} m^{2}∙kg^{−1}, 7.187 × 10^{−3} m^{2}∙kg^{−1} and 7.367 × 10^{−3} m^{2}∙kg^{−1} respectively from National Institute of Standards and Technology (NIST-X-COM).

The density of NaCl decreases from a value of 2165 kg∙m^{−3} at 300 K to a value of 1904 kg∙m^{−3} at 1000 K a

decrease of about 12.06%. The temperature dependence of density is a negative^{ }linear function of temperature. For NaCl the temperature dependence of density is represented by linear equation

The coefficient of temperature dependence of density is −0.3130 kg∙m^{−3}∙K^{−1} and the coefficient of volume thermal expansion is 1.446 × 10^{−4} K^{−1} in the temperature range 300 K - 1000 K. The thermal expansion increases linearly with temperature and the results on thermal expansion in the temperature range from 300 K to 1000 K have been analyzed by least squares method and is represented by the linear equation

The density of NaBr decreases from a value of 3210 kg∙m^{−3} at 300 K to a value of 2809 kg∙m^{−3} at 900 K a decrease of about 12.49%. The temperature dependence of density is a negative^{ }linear function of temperature. For NaBr the temperature dependence of density is represented by linear equation

The coefficient of temperature dependence of density is −0.5715 kg∙m^{−3}∙K^{−1} and the coefficient of volume thermal expansion is 1.78 × 10^{−4} K^{−1}. The thermal expansion increases linearly with temperature and the results on thermal expansion in the temperature range from 300 K to 900 K have been analyzed by least squares method and is represented by the linear equation

The density of NaF decreases from a value of 2558 kg∙m^{−3} at 300 K to a value of 2313 kg∙m^{−3} at 1000 K a decrease of about 9.58%. The temperature dependence of density is a negative^{ }linear function of temperature. For NaF the temperature dependence of density is represented by linear equation

The coefficient of temperature dependence of density is −0.2962 kg∙m^{−3}∙K^{−1} and the coefficient of volume thermal expansion is 1.16 × 10^{−4} K^{−1} in the temperature range 300 K - 1000 K. The thermal expansion increases linearly with temperature and the results on thermal expansion in the temperature range from 300 K to 1000 K have been analyzed by least squares method and is represented by the linear equation

The results obtained for the coefficient of thermal expansion in the present work agree well with the values reported from X-ray studies, dilatometry and theoretical models [17-22] as seen from Figures 5-7 of NaCl, NaBr and NaF respectively. However, the results on variation of density and linear attenuation coefficient of NaCl, NaBr and NaF with temperature are not available from other methods for comparison.

The pellets were prepared with fine powder of NaCl,

NaBr and NaF with a diameter of 20 mm with varying thicknesses with a die set by applying hydraulic press pressure. The γ-ray attenuation measurements have been made using a γ-ray densitometer designed and fabricated in our laboratory. The results on the variation of linear attenuation coefficient, density and linear thermal expansion with temperature of these pellets have been reported and these variations have been represented by linear equations. The results on these pellets by using γ-ray attenuation technique are being reported for the first time.

The authors thank University Grants Commission (UGC), New Delhi for the financial assistance through Special Assistance Programme (SAP) No. F. 530/8/DRS/2009 (SAP-1).