Gamma-Ray Densitometry

Temperature and Energy Dependent Gamma-Ray Attenuation

Doctoral Thesis / Dissertation 2014 204 Pages

Physics - Thermodynamics


1.1. General
1.2. Experimental methods to determine density
1.3. Experimental methods to determine thermal expansion
1.4. A review of earlier work on determination of thermophysical properties of materials
1.5. Interaction of radiation with matter
1.6. Introduction to gamma ray attenuation technique
1.6.1. Gamma ray densitometer
1.7. Gamma ray detection and recording
1.8. Scope of present work

2.1. General
2.2. Block diagram
2.3. Principle
2.4. General requirements for the setup
2.4.1. Gamma source
2.4.2. Fabrication
2.4.3. Dimensions of lead and stainless steel items
2.4.4. Accessories fabricated
2.5. Electronic equipment and accessories
2.6. Programmable temperature controlled furnace
2.6.1. General
2.6.2. Programmable controller
2.6.3. Operator interface
2.6.4. Construction of PTC furnace
2.6.5. PTC furnace operation
2.7. Sample preparation and mounting
2.8. Construction of gamma ray densitometer setup
2.9. Installation of gamma ray densitometer setup
2.9.1. Installation
2.9.2. Alignment for good geometry
2.9.3. Standardization of gamma ray densitometer setup

3.1. General
3.1.1. Mass attenuation coefficient
3.1.2. Linear attenuation coefficient
3.1.3. Effective and equivalent atomic number
3.1.4. Electron density
3.1.5. Mean free path
3.1.6. Cross-section
3.2. A review of earlier work
3.3. Objectives
3.4. Theory
3.5. Experimental
3.6. Results and discussion

4.1. General
4.2. A review of earlier work
4.3. Sample preparation
4.4. Experimental details
4.5. Results and discussion
4.5.1. LiCl
4.5.2. LiBr
4.5.3. LiF
4.5.4. NaCl
4.5.5. NaBr
4.5.6. NaF
4.5.7. NaI

5.1. General
5.2. Sample preparation
5.3. Experimental details
5.4. Results and discussion
5.4.1. KCl
5.4.2. KBr
5.4.3. KF
5.4.4. KI
5.4.5. CsCl
5.4.6. CsBr
5.4.7. CsI
5.4.8 RbCl
5.4.9. RbBr
5.4.10. RbI





Alkali halides have attracted the attention of many researchers due to their variety of applications in various fields. As far as thermophysical properties are concerned, the property of thermal expansion of alkali halides has been investigated by many researchers using dilatometry, X-ray diffraction techniques and theoretical methods. Another thermo physical property is density. Density and thermal expansion at high temperatures are important thermophysical properties which contribute to important scientific data for technological applications, since these properties are related to other thermophysical properties such as viscosity, surface tension, thermal conductivity and a variety of heat transfer dimensionless numbers. Though there are considerable reports on the determination of thermal expansion of alkali halides, but the studies on variation of density and linear attenuation coefficient with temperature are lacking. In addition to the thermophysical properties, the knowledge of photon interaction parameters of different materials is very useful in various fields like nuclear diagnostics, radiation protection, nuclear medicine and radiation dosimetry.

We have designed and fabricated a Y-ray densitometer (GRD) which includes a specially designed programmable temperature controlled (PTC) furnace to carry out studies on thermophysical properties of variety of materials. Gamma ray attenuation technique has several advantages over other methods to investigate temperature variation of density and thermal expansion at high temperatures as the Y-beam offers a probe which is neither in thermal contact nor in physical contact with the material. In the present work, I have undertaken a systematic study on the determination of multi energetic photon interaction parameters, density and thermal expansion as a function of temperature of 17 alkali halides using Y-ray attenuation technique. The data obtained for these thermophysical properties have been fit to a second degree polynomial in temperature. This technique has been applied to alkali halides for the first time to measure thermophysical properties and linear attenuation coefficient as a function of temperature.

I am glad to say it has been a pleasure and an honor doing the present work at Central Instrumentation Centre, Kakatiya University, India.

I am highly indebted to my beloved teacher Prof. N. Gopi Krishna, (Department of Physics, Kakatiya University, India). I deem it a privilege to have worked in association with him. I express my deep sense of gratitude and thank Dr. K. Gopal Kishan Rao, (Central Instrumentation Centre, Kakatiya University, India) and Dr. K. Narender in the process of accomplishing the proposed task.

I would be extremely happy to thank my parents Sri A. Purna Chander Rao & Smt. Rukmini, Sri A.R.K Sharma & Smt. Sriranga Vijaya and my wife Dr. P. Kalyani who were silently by my side always and in all my endeavors.

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

Dr. MADHUSUDHAN RAO A.S Professor of Physics



1.1 General

Density and thermal expansion are fundamental thermophysical 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.

Density of a material is its mass per unit volume. In finding out the density of a material determination of the mass is straight forward. Its physical state, whether it is a single piece or fine powder the difficulty is in determination of its volume. Hence, a number of methods have evolved for the determination of density. Thermal expansion of solids is due to the dimensional changes in a solid induced by an increase in temperature. When a solid material is heated, the atoms vibrate with increased amplitudes. The un-harmonic increase in the amplitudes results in the displacement of the effective mean positions of the atoms. This results in an increase in the separation between the atoms, causing the material to expand, hence dimensions of the material increase. If the material does not go through a phase change, the expansion can be easily related to the temperature change. The linear coefficient of thermal expansion (a) describes the relative change in length of a material per degree increase in temperature as shown in the following equation,

Abbildung in dieser Leseprobe nicht enthalten

where A Z is change in length, l is initial length and A T increase in temperature. It must also be understood that thermal expansion can cause significant thermal stress in a component if the design does not allow for expansion and contraction of components. 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 meteorological instruments and in the choice of container material in nuclear fuel technology. As seen from Eqn. (1) the coefficient of thermal expansion («) is temperature dependent and can be measured for samples of a few millimeter thicknesses. Consequently, a number of methods have evolved for the determination of thermal expansion. For the sake of comparison, some of the methods to determine density and thermal expansion are discussed in the following sections.

1.2 Experimental methods to determine density

A number of methods have emerged for the determination of density such as the Archimedean method, method of maximal pressure in gas bubble, sessile drop, pycnometric, dilatometric, electromagnetic levitation and y-ray attenuation methods.

a. Pycnometry

A pycnometer is a glass or metal container with a precisely determined volume. The mass of an irregular solid is determined by weighing. When the solid is placed in a pycnometer filled with a liquid of known density, the volume of the liquid which will overflow is equal to the volume of the solid. The mass of the liquid which overflows is determined as the difference between the sum of the mass of the pycnometer filled with liquid plus the mass of the solid and the mass of the pycnometer filled with liquid after the solid has been placed inside. The volume occupied by this mass is determined from the known density of the liquid. It is necessary that the solid be insoluble in the liquid used. The density of the solid is determined from these measurements of mass and volume.

b. Hydrostatic weighing

Hydrostatic Weighing, a method of measuring the density of liquids and solids based on Archimedes' law. This method of determining the density involves sample being weighed in air and then weighed in a liquid of known density. The volume of the sample is equal to the loss of weight in the liquid divided by the density of the liquid. The density of a solid is determined by weighing it twice, first in air and then in a liquid whose density is known (usually distilled water). During the first weighing the weight of the object is determined. The difference between the results of the two measurements helps in determination of the volume of the object.

In measuring the density of a liquid, an object usually a glass float whose weight and volume are already known is weighed in the liquid. Depending on the degree of accuracy required hydrostatic weighing is done on technical, analytical or standard balances. For weighing massive objects, less accurate balances are widely used which facilitate quicker measurement. Conversely, if the volume of a solid object is accurately known the density of the liquid can be determined by the loss of weight of the immersed object. This is the basis for the hydrometer method.

c. Dilatometry

Capacitance dilatometers possess a parallel plate capacitor with one stationary plate and one movable plate. When the sample length changes, it pushes the movable plate and the gap between the plates change. The capacitance is inversely proportional to the gap.

Connecting rod (push rod) dilatometer: The sample which has to be studied is placed in the furnace. A connecting rod transfers the thermal expansion to a strain gauge which measures the shift. Since the measuring system is exposed to the same temperature as the sample one obtains a relative value, which must be converted later. Matched low-expansion materials and differential constructions can be used to minimize the influence of connecting rod expansion.

Piston dilatometry: Piston dilatometer has been used successfully in the determination of density of molten-metals provided that no leakage occurs. A given mass of metal is held between pistons in a cylinder. As the metal melts to fill the gap it pushes the pistons outwards and the change in entrained volume is determined.

High resolution - laser dilatometer: Highest resolution and absolute accuracy is possible with a Michelson interferometer type laser dilatometer. Resolution goes up to picometers. Above all, the principle of interference measurement gives the possibility for much higher accuracy and it is an absolute measurement technique with no need of calibration.

d. Electromagnetic levitation

This method can be used to measure the density of spherical or irregular samples. It employs two permanent magnets positioned with like poles facing one another with the axis between the poles aligned with gravitational field. A container filled with a paramagnetic medium (such as MnCl2 dissolved in water) is placed between the magnets. Knowing the position assists in the calculation of density of the sample.

The density of the diamagnetic solid is measured by suspending it in the aqueous paramagnetic solution between the two magnets. The balance of gravitational and magnetic forces determines the equilibrium position of every particle or droplet between the magnets and these positions are used to calculate the densities of these particles. Calibration plots are used for comparison of densities of unknown with densities of known particles or droplets and also by using an analytical expression derived from the theory of magnetic levitation. This method is compatible with most types of solids and water insoluble organic liquids with densities in the range of 0.8 - 3.0 g/cm3. This method does not require the measurement of mass or volume of the sample.

1.3 Experimental methods to determine thermal expansion

A number of methods have evolved for the determination of thermal expansion as described in the following sections.

a. Optical methods

Optical methods include interference phenomena and diffraction phenomena to determine thermal expansion of crystalline substances.

(i) Interference methods

The property of interference is used in an interferometer for the measurement of thermal expansion. Here the sample is in the form of a block with one face polished. A glass plate is arranged above this polished face. A beam of monochromatic light is allowed to travel through the arrangement. It has been noticed that reflections occur from the lower surface of the specimen. When these two faces are arranged at a small angle (like a wedge film), the two reflected beams establish interference pattern of straight line fringes. Due to heating, the specimen's surface undergoes expansion and the polished face undergoes displacement which results in the displacement of interference pattern. By measuring the fringe shift the thermal expansion can be calculated. Fizeau was the first to set up interferometer for the measurement of thermal expansion. Frazer and Hollis-Hallet 1, Meincke and Graham 2 and Kirby 3 modified the Fizeau interferometer. The main advances in interferometers are

1. Quartz or glass optical flats are used
2. Partially metalized plates are used
3. Small pieces of sample or cylindrical samples are used
4. Laser is used to obtain sharp fringes
5. Camera or other recording system is used

The measurement of thermal expansion of super-ionic conductors can be done by using a laser.

(ii). Diffraction methods

High temperature X-ray difractometer works on the principle of diffraction. The thermal expansion of crystals is determined with the help of Bragg's law of diffraction i.e

Abbildung in dieser Leseprobe nicht enthalten

where d is the interplaner spacing, A is the wavelength of the X-ray beam used, 0 is the Bragg's reflection angle. The changes in the temperature of the crystal, causes a change in interplanar spacing (d), which is observed as change in the Bragg angle (0). Thus from the changes in the Bragg angle, the lattice constants are determined accurately by using all the available lines. The thermal expansion can be calculated from the temperature variation of lattice constants. The expansion coefficient (a) is calculated from the Eqn. (3) given below. In terms of lattice constant (a)and the change in lattice constant (A a) corresponding to temperature change(A T), a is written as

Abbildung in dieser Leseprobe nicht enthalten

where A a/a is the relative change in lattice constant corresponding to the change in temperature (A T).

b. Dilatometer method

Push-rod dilatometer and Fused quartz dilatometer are simple in design, inexpensive and made from indigenously available components. The main parts of the push-rod dilatometer 4 are the push-rod assembly, the dial-gauge micrometer and the heating arrangement. Fused quartz dilatometers are simple and inexpensive. In this type of dilatometers the sample is enclosed in a fused quartz tube. The end of the sample is in contact with a sensitive dial-gauge. The holder (quartz tube and sample) is placed in heater and the length changes are directly read on the dial gauge.

c. Capacitance method

This method can be used in thermal expansion measurement of a number of solids even at very low temperatures. The overall sensitivity of this method is very high. This method uses a heterodyne oscillator and two capacitors. The equation used to determine the thermal expansion of solid is,

Abbildung in dieser Leseprobe nicht enthalten

where l is initial separation between the plates of the capacitor , A l is the change in plate separation. The plate separation of one of the capacitors is controlled by the thickness of sample and other is a variable capacitance. The sample expands on heating resulting in change of capacitance of the first capacitor, thus altering the frequency. The change in frequency (A f)is measured. The second capacitance is adjusted slightly by (A c) to restore original frequency (f) .

d. Holographic method

This is a non-contact method and is applicable to determine thermal expansion in objects of any shape. He-Ne or a ruby laser source is used in this method. A reference beam and another beam (both from same source) reflected from the object are superposed to give a hologram. Further, the superposition of two holograms with the imposed temperature change occurring between the two exposures results in a fringe pattern. The fringes develop curvature when there is expansion. From these fringe characteristics a is calculated.

e. Ultrasonic method

In this method an ultrasonic high frequency (UHF) acoustic transmission probe and an UHF spectrometer are used. When ultrasonic waves are propagated through a sample the wave amplitude is attenuated, the sample gets expanded. Due to thermal expansion the crystal expands and resonance occurs resulting in standing waves.

Thermal expansion coefficient is given by

Abbildung in dieser Leseprobe nicht enthalten

where V T is the velocity of UHF wave, / the UHF frequency, L 0 the length of sample at room temperature and A T is the change in temperature.

f. Gamma ray attenuation method

Gamma ray attenuation technique is a popular non contact - non invasive method that can be used for measuring thermal expansion and density of materials in solid state as well as in molten state and also through melting temperature. This method has been employed in the present work and has been discussed in detail in section 1.6.

1.4 A review of earlier work on the determination of thermophysical properties of materials

Density and thermal expansion as a function of temperature can be studied by various methods. These studies have been carried out by researchers on different materials. In particular, thermal expansion of alkali halides has been studied using X-ray diffraction and dilatometric techniques. This review pertains to the study of thermophysical properties of different materials by using various techniques.

Archimedean method was used to study the temperature dependence of density and thermal expansion of zinc and cadmium 5 and in Tin (Sn) 6. By an improved Archimedean method, Lianwen Wang et al. 7 studied thermophysical properties in some low melting point metals in liquid phase such as Antimony(Sb), Bismuth(Bi), Lead(Pb) and Tin(Sn). Kirshenbaum et al. 8 estimated the dependence of density of liquid NaCl and KCl on temperature by using Archimedean principle. Been et al. 9 reported the values of density and thermal expansion as a function of temperature for lead-bismuth alloys determined from the method of maximal pressure in gas bubble. Using this method, lead-lithium alloy system has also been studied [10-11]. Thermophysical properties of cobalt, copper and nickel determined from the method of maximal pressure in gas bubble have been reported by Tesfaye et al. 12. Electromagnetic levitation method was used to determine density and thermal expansion at different temperatures by Brillo et al. 13 in silver-gold and silver-copper alloys. Using the same method Li et al. 14 studied Ti-Al-V alloy. Chung et al. 15 used high temperature electrostatic levitation method to determine density as a function of temperature in Ni. Paradis et al. 16 reported the results on thermophysical properties of solid and liquid molybdenum using the same method. Pycnometric method has been used to study density and thermal expansion at different temperatures by Alchagirov et al. [17-18] in lead-bismuth and lead-lithium alloys and Kusuhiro mukai et al. 19 in Ni-Cr alloy. Baxter and Hawkins 20 determined the volume coefficient of KI between 0 0C to 25 0C employing a pycnometer. Dilatometric method has been used to study thermophysical properties of Sn by Wang and Mei 21, Pb-Li alloys by Jauch et al. 22. Using the same method Pstrus et al. 23 reported results of Bi-Au-Zn alloy. Rapp and Merchant 24 investigated thermal expansion of 15 alkali halides from 70 K to 570 K using a high precision differential dilatometer in conjunction with an electronic micrometer. Meincke and Graham 25 made measurements on the coefficient of linear thermal expansion of single crystals of NaCl, NaI, KCl and KBr, by monitoring the changes in length of Fabry-Perot etalon dilatometer. The method of sessile drop has been used by Tesfaye and Taskinen 26 to measure density of Iron as a function of temperature. Kazakova et al. 27 measured densities of Pb-Bi alloys and Schultz et al. 28 studied Pb-Li alloys using the same method. Srivatsava and Merchant 29 reported results on thermal expansion of 12 alkali halides using X-ray diffractometry. Interferometer measurements of low temperature thermal expansion and related thermodynamic properties of CsCl and CsBr between 20 K and 273 K were reported by Bailey and Yates 30. Pathak et al. 31 determined the coefficients of thermal expansions of powder specimens of NaF, KBr and RbBr at different temperatures using X- ray diffraction method. The thermal expansion of KI and RbI at high temperatures has been investigated by both X-ray and macroscopic methods by several workers [32-36]. On examining the results it is found that although the values of thermal expansion agree at lower temperatures, there are deviations at high temperatures. Pathak and Pandya 37 reported the temperature dependence of the thermal expansion of KI and RbI at high temperatures using X-ray diffraction method. Deshpande 38 studied thermal expansion of NaF and NaBr at elevated temperatures by the X-ray method and reported the results along with calculated values and found that the differences are about 1% between experimental and calculated values. Yagi 39 reported results on thermal expansivity of NaF, KF and CsCl at 90 kbar and 800 0C using X-ray diffraction techniques. Yates and Panter 40 reported results on linear thermal expansion of LiF, NaCl, KCl, KBr and KI single crystals in the temperature range 20 K to 270 K by Fizeau interferometric method. The gamma ray attenuation technique was used by several workers to study thermophysical properties such as density and thermal expansion as a function of temperature for several materials. Gamma ray attenuation technique was used by Drotning 41 and Nasch and Steinemann 42 to study density as a function of temperature in aluminum. Drotning is the first researcher to apply Y-ray attenuation technique to materials with low density. Drotning 43 measured the thermal expansion of the group II b liquid metals like zinc, cadmium and mercury. Drotning 44 also made measurements of thermophysical properties in the group VIII transition metals such as iron, cobalt and nickel. Results on density and thermal expansion of highly pure dysprosium in the solid and liquid states have been reported by Stankus and Tyagel'skii 45. Stankus et al. 46 reported results on temperature dependence of density in bismuth. Stankus et al. 47 studied the density and the volume thermal expansion coefficient of lithium in condensed state. Kalinin et al. 48 investigated thermo physical properties of Pb-Li system. Stankus et al. 49 reported the results on density and thermal expansion of eutectic alloys of lead with bismuth and lithium in condensed state. Stankus and Khairulin 50 investigated thermophysical properties of Sn-Pb system. They studied the system in solid and liquid phases using Y-ray attenuation technique in the temperature range from 293-1040 K. Their conclusion is that the results of measurements of the properties of the alloy in the liquid state depend significantly on the homogeneity of the samples. Khairulin et al. 51 carried out a detailed study on the density and coefficients of thermal expansion of liquid magnesium-lead alloys in a wide range of temperatures and concentrations. Recently, Khairulin et al. 52 measured the density and coefficient of thermal expansion of liquid Ag-Sn alloys in the temperature range 300 K to 900 K employing Y-ray attenuation method. They also reported density in the solid state and the density changes during solid-liquid transition. In addition to the work on alkali halides, the work on metals and alloys using Y-ray attenuation method has also been included in the review. The work on metals and alloys has been included only to show how Y-ray attenuation technique has been used extensively to study thermophysical properties. The review reveals that the Y-ray attenuation technique has not been used to study the thermophysical properties of alkali halides at different temperatures.

1.5 Interaction of radiation with matter

Radiation is energy that travels through space or matter in the form of a particle or wave. The interaction of radiation with matter is very important for any experimental physicist, nuclear or particle physicist. For experimental design to study Y-ray interaction with matter, knowledge of these interactions, detection and measurement of the radiation is required. The effect of radiation on matter depends on the type of radiation and how much energy the radiation has. Radiation can be broadly divided into two categories. Radiation consists of particles that have mass and energy and may or may not have an electric charge such as alpha particles, protons, beta particles and neutrons. Electromagnetic radiation consists of photons that have energy but no mass or charge such as X-rays, Y-rays etc. Radiation can also be classified as ionizing radiation (alpha and beta particle) and non-ionizing radiation (photons). Ionizing radiation can be further divided into direct and indirect ionizing radiation.

Charged particles such as electrons, protons and a particle are known as directly ionizing radiations as they penetrate matter whereas the uncharged particles such as neutrons are indirectly ionizing radiations since they liberate ionizing particles from matter when they interact with it.

a. Interaction of ionizing radiation with matter

When ionizing radiation strikes matter interaction between the radiation the electrons and nuclei of the material takes place. The type of interaction and the effect thereof are not only dependent on the type of radiation but also on the energy content of the particle. Such an interaction can be imagined as a collision with electrons situated around the nuclei of the material as a result of which the radiant energy is either entirely or partially or not transferred to the electrons. Depending on the amount of energy an electron is excited to a higher energy state or released from the atom i.e. ionization. Thus the term ionizing radiation is named after.

The passage of a -particle through matter results in exclusively inelastic collisions. This leads to ionizations and excitations. The excited electrons emit X-rays in decaying to the ground state. The number of primary and secondary ionizations and excitations along the path of a - particle is therefore very large. However, the distance a- particle travels in matter before it become thermic is very short.

When y S- particle strikes matter it will go through number of interactions. In each of its interaction loses a little bit of its energy and slightly change the direction. This process repeats until most of its energy is lost before it become thermic. The distance across which a S -particle penetrates matter before it become thermic is finite and is called the range. The processes of interaction can be elastic collisions, inelastic collisions, Bremsstrahlung and Cerenkov radiation. In addition there is a fifth process important for S +-particles (positron) namely annihilation. In this process the proton unites with an electron at which the total mass of the positron-electron couple is converted into characteristic photon.

Since neutrons are uncharged particles they are not slowed down in their movements by charge effects of electrons and nuclei of material. A neutron can thus approach the nucleus of the atom unhindered. The interactions that can take place are elastic collisions and inelastic collisions (nucleus capture). In case the neutron does not enter into interaction it decays to a proton, fr -particle (Ep = 780 keV) and an antineutrino according to: n p + + (T% = 10.6 min.). The higher the energy content of a neutron the faster it moves. The interaction mechanism between neutrons and matter is strongly dependent on the velocity of the neutron.

b. Interaction of non ionizing radiation with matter

When an X-ray or Y-beam passes through a medium energy is transferred to the medium during the interaction with the matter. There is a principal difference between X-rays and Y-rays. Though these two forms of radiation are high energy electromagnetic rays and are therefore virtually the same the difference between them is not what they consist of, but where they come from. If the radiation emerges from a nucleus it is called a gamma-ray and if it emerges from outside the nucleus i.e. from the electron cloud it is called an X-ray.

(i) Interaction of gamma radiation with matter

Photons are electromagnetic radiation with zero mass, zero charge and a velocity that is always equal to the speed of light. Because they are electrically neutral they do not steadily lose energy via columbic interactions as the charged particles. Photons travel considerable distance before undergoing partial or total transfer of the photon energy to electron. These electrons will ultimately deposit their energy in the medium. Photons are far more penetrating than charged particles of similar energy. The interaction of photons with matter involves several distinct processes. The relative importance and efficiency of each process is strongly dependent on the energy of the photons, the density and atomic number of the absorbing medium. The gamma ray interaction with matter broadly classified as scattering, attenuation and absorption. In scattering the gamma beam is forced to deviate from a straight trajectory by one or more localized non-uniformities in the medium through which it passes. Scattering can be either elastic or inelastic. In elastic scattering the gamma ray energy is unchanged except for a negligible amount which is lost due to the recoil of the scattering nucleus acquired by it for momentum conservation. The direction of propagation of the photon is changed by the potential of the target. In this scattering frequency of scattered and incident photon remains the same. The elastic scattering is of different types such as Thomson scattering, Rayleigh scattering, nuclear resonance scattering and Delbruck scattering. In inelastic scattering the gamma ray loses energy and therefore scattered photon frequency is less than the frequency of incident photon. The scattering atom is excited by an amount equal to the energy lost by the gamma ray. Compton scattering comes under this category. If incident photons lose the energy significantly by the interaction with matter then the process is known as absorption. In some contexts absorption is considered as an extreme form of inelastic scattering. Generally speaking, in classical physics absorption and scattering tend to be treated as different phenomenon while in quantum physics absorption is treated as a form of scattering. To be precise absorption cannot occur without some degree of scattering and scattering is rarely completely elastic in a microscopic scale. Attenuation is the reduction in intensity of the primary Y-ray beam as it passes through matter by either absorption or scattering.

Rayleigh scattering

A photon can also scatter from an atom as a whole neither exciting nor ionizing the atom. When that happens, the atom will recoil taking some of the energy and leaving the scattered photon with slightly smaller energy. This process is called Rayleigh scattering and is the main scattering process for very low photon energies but it is still much less probable than the photoelectric effect. Rayleigh scattering is predominant at low photon energies, small scattering angle and high Z absorbers. Thomson scattering

This process includes coherent scattering of gamma rays by free electrons and nucleus as a whole. The oscillating electromagnetic field of the incident photon sets the electron or nucleus into oscillations in the direction of its electric vector. The frequency of these oscillations is the same as those of the incident wave. The interaction results in the emission of electromagnetic waves of the same frequency (energy) as the incident photon. More exactly, energy is absorbed from the incident wave by the electron and re-emitted as electromagnetic radiation.

Nuclear photodisintegration

In this class of processes gamma rays are absorbed by the nuclei and nucleons are ejected from the nuclei. Such processes occur only at high gamma ray energies. Nuclear resonance scattering

The nuclear resonance scattering is one of the elastic scatterings in which the incident gamma photons excite the nucleus to one of its excited levels. It is subsequently de-excited by re-emission of the excitation energy in the form of a gamma quantum. Thus, the emitted gamma energy will be nearly equal to that of the incident photon except for a negligible loss due to the recoil of the nucleus.

Delbruck scattering

In this process photons are scattered by the coulomb potential of the nucleus. The actual mechanism of the process involves the absorption of the incident photon by an electron in the negative energy state followed by the creation of an electron-positron pair and subsequent annihilation of the pair to give a scattered photon of exactly the same energy as the incident photon. This process is called Delbruck scattering and also known as the elastic nuclear potential scattering. This leads to virtual electron pair formation in the nuclear coulomb field.

Compton scattering

The Compton scattering is an inelastic collision between the incident photon and the weak bonded electron (nearly free) in the outer shell of the absorber atoms. The incident photon dissipates a part of its energy and deflects with a scattering angle (0). The electron, recoil electron, is removed from the atom with a kinetic energy depending on the amount of energy transferred from the photon.

The energy transfer varies from zero when 0= 0 to a maximum value when 0=%. Compton coefficient decreases with increasing energy and increase linearly with the atomic number Z of the absorber material. The energies of the recoil electron and the scattered photon are given by:

Abbildung in dieser Leseprobe nicht enthalten

where E 0 is incident photon energy, Er is scattered photon energy, E e is recoil electron energy and m 0 is electron mass.

The Compton scattering probability is almost independent of atomic number Z and decreases as the photon energy increases and directly proportional to the number of electrons per gram which only varies by 20% from the lightest to the heaviest elements (except for hydrogen).

Photoelectric absorption

This mechanism of interaction is very important for gamma and X-ray measurements. The photon with energy slightly higher than the binding energy of atomic electrons interacts with the absorber atoms and disappears i.e. photon absorption occurs. Depending on the photon energy the most bonded orbital electron in K or L shell will absorb the photon energy to be removed completely from the atom with a kinetic energy given by;

Abbildung in dieser Leseprobe nicht enthalten

where E e is photo-electron kinetic energy, hvis photon energy and E b is electron binding energy.

The photo-electrons are energetic electrons and interact with the matter exactly like beta particle. These electrons leave the atom and create an electron vacancy in their inner orbits where either a free electron or an electron from a higher orbit of the atom fills this vacancy and generate X-ray. The generated X-rays interact with the absorber and can produce another photo-electron with less binding energy electron (known as auger electron) than the original photo-electron.

Thus for gamma-ray energies of more than a few hundred keV the photoelectron carries off the majority of the original photon energy. The photoelectric process is the predominant mode of photon interaction at relatively low photon energies (below 0.1 MeV) and high atomic number Z.

Pair production

If a photon enters matter with energy above 1.022 MeV it may interact by a process called pair production. The photon passing near the nucleus of an atom is subjected to strong field effects from the nucleus and may disappear as a photon and reappear as a positive and negative electron pair. The two electrons produced e- and e+ are not the scattered orbital electrons but are created.

The kinetic energy of the electrons produced will be the difference between the energy of the incoming photon and the energy equivalent of two electron masses (2 x 0.511 or 1.022 MeV).

Abbildung in dieser Leseprobe nicht enthalten

Pair production probability increases with increasing photon energy and increases with atomic number approximately as Z

Abbildung in dieser Leseprobe nicht enthalten

Fig. 1.1 shows the relation between atomic number of matter and the interacting energy

Abbildung in dieser Leseprobe nicht enthalten

Fig. 1.1 Atomic number of matter versus interacting energy (From Radiation

Detection and Measurement, 3rd Ed, by G.F. Knoll, John Wiley & Sons, Inc, 1989).


Attenuation is the reduction in intensity of the primary Y-ray beam as it passes through matter by either absorption or scattering. When gamma rays pass through matter their intensity is attenuated according to the exponential law called Beer Lamberts law i.e. Eqn. (11). In the present work gamma ray attenuation method is used to study the temperature dependence of linear attenuation coefficient, density, thermal expansion and the photon interaction parameters of alkali halides.

The exponential decrease of the gamma ray intensity arises from the fundamental nature of the interactions of the gamma rays with matter. When a gamma ray photon undergoes an interaction it is either absorbed completely or scattered away from the incident direction as discussed above. The probability for the interaction essentially depends on the number of interaction centers in the path of the gamma rays as well as on the probability for the interaction. When a beam of gamma rays passes through an absorber the gamma photons interact with the atoms individually and are either absorbed or scattered away from the beam. The intensity of the transmitted beam is consequently attenuated. The total cross-section for attenuation of the incident beam of gamma rays is the sum of the cross- sections per atom for all the three processes of photoelectric, Compton and pair production. Therefore the total cross section is given by

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The equation which describes the beam intensity for monoenergetic narrow beam of gamma radiation is,

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here, I 0 and I are gamma intensities before and after passing through the sample material, p is the material density, l is the material length along beam direction and is mass attenuation coefficient of material.

The data analysis methods for the determination of density and thermal expansion have been discussed in detail in section 4.5 of chapter 4.

1.6 Introduction to gamma ray attenuation technique

The gamma ray attenuation technique is a non invasive method utilizing the gamma beam only as a probe which is neither in physical nor in thermal contact with the sample. The gamma ray attenuation technique used for determination of thermal expansion and density offers several advantages over other methods and it is particularly advantageous at high temperatures as thermal losses are minimized. This technique also ensures the elimination of incompatibility of sample and probe materials. In measurement of density and thermal expansion by this method only the solid or molten material of the samples are involved, eliminating the free liquid surface which has no role to play. Thus a number of problems encountered during the measurement due to viscosity effects, sample vaporization, surface tension effects, formation of oxide films on the surface etc. by other methods and their corresponding corrections in calculations can be safely avoided.

1.6.1 Gamma ray densitometer

The experimental setup used for determination of density of materials utilizing gamma ray attenuation technique is called a gamma ray densitometer. A programmable temperature controlled furnace is introduced in the gamma path allowing the beam to pass through, to the detector without any interruption. It is possible to vary the temperature by programming the programmable temperature controlled (PTC) furnace appropriately making the setup suitable for the studies of temperature dependent gamma ray attenuation in materials both in solid and molten states at various temperatures to determine density and thermal expansion. The details of gamma ray densitometer setup are furnished in chapter 2.

1.7 Gamma ray detection and recording

As illustrated in Fig. 1.2 the collimated gamma radiation from the source strikes the crystal in the detector which is of phosphorus material typically thallium activated sodium iodide. Atomic excitation occurs. The excited electrons lose energy and come to ground state by releasing a photon. The photon after multiple scattering in the crystal will finally fall on a photo cathode which releases photo electron. The photo electron will be multiplied many folds in the photo multiplier tube and finally an electric pulse will be generated. The electric pulse is fed to the linear amplifier and is raised to the required amplitude and is fed to the measuring system such as a multi channel analyzer (MCA) or a single channel analyzer (SCA). The signal received by the MCA will be processed according to different amplitudes and sorting is done. The number of pulses with similar amplitudes is sorted in groups and these analog pulses are converted to digital data and counted by the scalar in the interfaced PC as the number of counts which is the basis of this technique.

1.8 Scope of present work

The very important physical parameter, mass attenuation coefficient for a material can be determined using attenuation technique of mono energetic collimated gamma beam. It is a measurement showing how strongly substance absorbs or scatters radiation at a given wavelength per unit mass. Mass attenuation coefficient is a fundamental parameter to calculate many other photon interaction parameters. The knowledge of physical parameters such as mass attenuation coefficient, atomic and electronic cross-sections, effective atomic number, electron density and photon mean free path plays an important role in understanding the physical properties of composite materials. Their role is invaluable in many applied fields such as nuclear diagnostics, radiation protection, nuclear medicine and radiation dosimetry

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Fig. 1.2 Block diagram of gamma detection apparatus (Fig. 2. Thermal Expansion and Density Measurements of Molten and Solid Materials at High Temperatures by Gamma Attenuation Technique - William D. Drotning - Sandia Laboratories) https://inis.iaea.org/collection/NCLCollectionStore/_Public/10/490/10490576.pdf)

Principle of gamma ray attenuation technique is that the measured mass attenuation coefficient of the material is used to obtain its density. Density is one of the most fundamental properties of a material. It is intrinsically related to other thermo­physical properties. The density and thermal expansion coefficient decide the material behavior in the liquid or solid state. The mass attenuation coefficient is independent of temperature and physical state of the material which gives a scope to carry out the study of temperature dependent gamma ray attenuation by heating the material to determine the values of density, linear attenuation coefficient and thermal expansion of material as a function of temperature.

Alkali halides are inorganic ionic compounds with the chemical formula MX where M is an alkali metal and X is a halogen. The alkali halides have high melting points and have either NaCl or CsCl structure. The study on alkali halides are of particular interest for a number of reasons. These compounds are commercially significant sources of metals and halides. The compounds have wide range of applications in various fields.

From the literature survey, it has been noticed that gamma ray attenuation studies and study of variation of density with temperature on alkali halides are lacking. In our laboratory, thermophysical properties of a variety of materials have been studied using Y-ray attenuation technique. In the present investigation it has been chosen to carry out studies on gamma ray attenuation in 17 alkali halides using gamma ray densitometer. The alkali halide samples were taken in the form of pellets. The details of alkali halides studied in the present work are given in Table 1.1. This is the first attempt of Y-ray attenuation technique on alkali halides to study thermophysical properties of these materials at different temperatures.

To carry out the proposed work, we have designed and fabricated a gamma-ray densitometer and programmable temperature controlled furnace which can reach up to 1300 K. The detailed discussion on design and fabrication of gamma ray densitometer setup is given in chapter 2. The studies on all samples are confined to the solid phase only.

The studies on the determination of photon interaction parameters such as mass attenuation coefficient, atomic and electronic cross-sections, effective atomic number , electron density of 17 alkali halides for photons of Y-energies [(0.0595 MeV), (0.662 MeV), (1.173 MeV & 1.332 MeV)] emitted by 10 mCi 241Am, 30 mci 137Cs and 11.73 p.Ci 60Co radioactive point sources respectively have been carried out. The present study on thermophysical properties of pure alkali halides encourages studying these properties in alkali halide mixed crystal system which find many applications in variousfields.

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attenuation densitometry dependent energy gamma-ray temperature



Title: Gamma-Ray Densitometry