Shodhganga - Particle Induced X-ray Cross Section...

Chapter 3

Experimental Arrangements

In this chapter, brief descriptions on the data acquisition and analysis techniques

used during the x-ray spectroscopy and charged particle backscattering spec-

trometry experiments, are discussed. In the present work, the experiments have

been carried out with the 15 UD pelletron at Inter University Accelerator Centre

(IUAC), New Delhi, the Variable Energy Cyclotron (VEC) at Panjab University,

Chandigarh and the 3 UD Pelletron at Institute of Physics (IOP), Bhubaneswar.

The experimental arrangements used at IUAC and IOP are discussed in this chap-

ter while that of VEC are discussed in chapter 4.

3.1 Detectors used in Ion Beam Analysis

In any ion beam analysis laboratory there are basically two type of detectors

used. One is for the detection of x-/γ-ray generated by the interaction of ion

beam with target and the other is for detection of charged particles coming from

the target. There are various types of detectors available for these purpose having

both advantages and disadvantages with respect to each other. So, the choice

depends upon the availability and requirements of the measurement. In this work,

27

3.1. Detectors used in Ion Beam Analysis

lithium drifted silicon ( Si(Li)) and high purity germanium (HPGe) detectors were

used for the detection of target x-rays and silicon surface barrier (SSB) detector

was used for the detection of scattered charged particles.

3.1.1 Si(Li) Detector

It is a reverse biased PN junction diode. The depletion depth of highest available

purity of silicon is limited to 1 - 2 mm. By the process of lithium drifting, a region

of compensated silicon is created in which the acceptor and donor impurities are

exactly balanced. Using this process a detector of thickness up to 5 -10 mm can be

created. A thin layer of gold (usually around 200 A thick) is evaporated onto the

surface of the p-type region (which faces the x-rays), to act as an electrode. The

lithium-drifted region (called the depletion region) is in the middle. A thin metal

layer (usually around 2000 A of Au) is evaporated onto the surface of the n-type

region to act as another electrode. The Si(Li) detector proves to be a highly-

sensitive tool for detecting x-rays produced with nuclear accelerator, radioactive

sources, or x-ray tubes. The x-ray photons are detected via the photoelectric effect

which, the photons most often undergo inside the silicon crystal. The energy range

of detection is from less than 1 keV to 60 keV. While the lowest detection energy

is dependent upon the thickness of the front dead layer and the end-cap window,

the higher energy side limit is dependent upon the thickness of the active region.

Due to limitation in the maximum available thickness, the Si(Li) detectors become

less efficient in detecting photons of energy > 20 keV. The energy resolution of

the detector is generally 160 - 200 eV for 5.9 keV x-rays emitted by 55Fe.

3.1.2 HPGe Detector

The germanium detector, similar to other semiconductor detectors, is a large

reverse-biased p-n junction diode. Modern germanium detectors are made from

28

3.1. Detectors used in Ion Beam Analysis

high purity germanium (HPGe) containing less than 1010 impurity atoms per cubic

centimetre, making it possible to reach a depletion thickness of several centimetres.

The long radiation length of silicon (94 mm) and the fact that it is difficult to

produce a depletion layer of much more than a few mm, makes silicon unsuitable

for detection of photons of energy > 20 keV. Germanium has a radiation length of

23 mm, making it much more suitable for this purpose. Therefore, the planner (5

-10 mm thick) HPGe detectors are now routinely being used in x-ray spectrometry.

HPGe detector offers better energy resolution in comparison to (Si(Li)) detector

due to a smaller Fano factor. The typical energy resolution of a HPGe detector

ranges from 140 -160 eV for x-rays of 5.9 keV.

3.1.3 Charged Particle Detector

The silicon surface barrier (SSB) detectors are the reversed bias diodes made with

high quality silicon. To make an electrical contact, very thin layer of gold (40

µg/cm2) is evaporated on an etched n-type silicon wafer. The gold evaporation

forms the front rectifying contact of the diode and the rear ohmic contact is com-

posed of 40 µg/cm2 of evaporated Aluminium. The outer housing and the front

surface are normally grounded and the electrical contact from the back surface of

the semi-conductor wafer attaches the centre electrode of the co-axial connector

of the rear of the detectors. Normal surface barriers are usually n-type crystal so

a positive polarity voltage is applied on the Aluminium contact to reverse bias the

junction. The thickness of the depletion region in junction detector increases as

the reverse bias voltage is increased. The limit of thickness is set by the breakdown

voltage of the junction. According to the applied bias voltage the detector can

be depleted partially or totally. In totally depleted detectors, the wafer thickness

must be kept uniform to avoid energy loss variation across the surface of the detec-

tor. However, in the partially depleted detector the active volume of the detector

29

3.2. Signal Processing

is determined by the limited depletion depth, thus, the thickness uniformity is not

so critical. The totally depleted detectors have low noise and better resolution

compared with the other configurations. For 5.48 MeV α-particles emitted by

241Am, the typical energy resolution of SSB detectors is about 16 keV.

3.2 Signal Processing

Generally, x rays from PIXE are measured with a detection system based on a

Si(Li) or HPGe detector. In backscattering spectroscopy, the scattered particles

are measured with a solid-state surface barrier (SSB) detector system. The output

of each of these detectors is of the order of milivolts with a exponential tail.

Hence the signal from the detectors has to be suitably processed before recording

the data. To achieve this, standard NIM-model electronic equipment including

preamplifier, linear amplifier and analogue to digital converter (ADC) are used.

Practically the electronic systems are designed to maintain linear relationship

between the energy of the radiation and the charge signal created in the detector.

3.2.1 Preamplifier

The basic function of a preamplifier is to amplify weak signal from a detector and

to drive it through the cable that connects the preamplifier with the rest of the

equipment. At the same time, it should add least amount of noise possible. Since

the input signal at the preamplifier is generally weak, preamplifiers are normally

mounted as close as possible to the detector so as to minimise cable length. In

this way, pickup of stray electromagnetic fields is reduced and cable capacitance,

which decreases the signal-to-noise ratio, is minimised. Another function of the

preamplifier is to present the correct impedances to the detector and the electron-

ics. There are three type of preamplifiers namely; i) voltage sensitive, ii) current

30

3.2. Signal Processing

sensitive and iii) charge sensitive. The charge sensitive preamplifier provides edge

over the other two configurations because it is independent of the capacitance of

the detector and supports high input impedance. In charge sensitive preamplifiers

basic idea is to integrate the charge carried by the incoming pulse on the feedback

capacitor, so that all dependence on the detector capacitance has been removed.

3.2.2 Amplifier

The amplifier serves two main purposes; (i) Amplifies the signal from the pream-

plifier and (ii) Shapes it to a convenient form for further processing. In both cases,

the amplifier must always preserve the information of interest. If pulse height in-

formation is desired, a strict proportionality between input and output amplitudes

must be preserved (linear amplifier). In many of the latter, an adjustable gain

over a wide range is provided so as to allow a scale adjustment in a spectrum

analyser. For spectroscopy amplifiers one of the most important factors is the

pulse shaping characteristic. In general, the pulse coming from the preamplifier is

characterised as an exponential with a long tail lasting anywhere from 10 - 100 µs.

The amplitude of this pulse is proportional to energy. If a second signal arrives

within the period, τ , it will ride on the tail of the first and its amplitude will be

increased. Hence, the energy information contained in this second pulse is thus

distorted and is known as pile-up. To avoid this effect, either the counting rate is

restricted to less than 1τ counts/s or the tail is shortened by reshaping. A second

reason for pulse-shaping is the optimisation of the signal to noise ratio. For a given

noise spectrum, there usually exists an optimum pulse shape in which the signal

is least disturbed by noise. Tail pulses in the presence of typical noise spectra

are not ideal, in fact and it would be more advantageous to have a Gaussian or

triangular form. Thus, even at low counting rates where pile-up is not a problem,

pulse-shaping remains important.

31

3.3. The energy spectrum

3.2.3 Analog to Digital Converter (ADC)

The analog-to-digital converter measures the maximum amplitude of an analog

pulse and converts that value to a digital number. The digital output is a propor-

tional representation of the analog amplitude at the ADC input. For sequential

arriving pulses, the digital outputs from the ADC are fed to a dedicated memory,

or to a computer, and sorted into a histogram that represents the spectrum of

input pulses heights. If the input pulses come from an energy spectroscopy ampli-

fier, the histogram corresponds to the energy spectrum observed by the associated

detector.

3.3 The energy spectrum

3.3.1 The x-ray spectrum

An x-ray spectrum produced by the bombardment of heavy charged particles usu-

ally consists of two major components; (i) peaks due to characteristic x-rays and

(ii) background continuum. In addition to these, escape peaks, exponential tails

and low energy steps corresponding to each characteristic x-ray may be present

which are called as spectrum artefacts arising due to the various physical processes

occurring in the detector element and, to some extent, the imperfections present

in the detector.

Production of x-rays

The characteristic x-rays of elements in the specimen result from the deexcita-

tion of vacancies produced by ionization through the Coulomb interaction of the

charged beam particles with inner shell electrons. Three major processes are re-

sponsible for the productions continuous background.

32


The first, and most prominent in the low energy regime (< 6 keV) is believed

to be largely due to the secondary electron bremsstrahlung (SEB) caused by the

secondary electrons ejected from the target atoms during the collision process.

This has a maximum energy Ee(max) given by,

Ee(max) = 4

(me

Mp

)EP . (3.1)

Where, Mp and Ep are the mass and energy of the projectile and me is the

electron mass. The primary process in both the production of characteristic x-rays

and SEB is the ionisation. Therefore the ratio of the height of the x-ray peaks

to the background is more or less the same for all heavy projectile species having

the same velocity. In brief, as SEB is usually the dominant form of background,

all projectiles heavier than (and including) protons will have the same signal to

noise ratio. In other words using heavier projectiles do not improve the peak

to background ratio. In principle, the background could be reduced by making

the sample matrix as thin as possible but experimentally a practical limit is soon

reached.

The second process is the projectile bremsstrahlung (PB) produced due to

slowing down of the projectile in the target through the Coulomb interaction with

the electrons and the nuclei. The differential cross section for this process is given

by [1],

dσ

dEpx

= CAp Z

2p Z

2T

EpEpx

(Zp

Ap

− ZT

AT

)2

(3.2)

Where Epx is the energy of the background radiation, Zp, Ap, Ep are the atomic

number, atomic mass and energy of the incident particle and ZT & AT are the

atomic number & atomic mass of the target. C is a slowly varying factor depen-

dent on Zp, ZT and Ep having a value of about 2-3 eV barns. This background

appears to be a major cause of background at the higher x-ray energies. From

33


Equation (3.2) it can be seen that the cross-section and hence the yield would

decrease with increasing energy. Moreover, if Z/A is the same for the projectile

and the matrix, this form of bremsstrahlung disappears. For most matrices en-

countered ZT/AT has the value of approximately 0.5. Consequently there should

be little or no incident projectile bremsstrahlung from alpha particles and heav-

ier ions (where Zp/Ap is also approximately 0.5). Thus PIXE experiments using

heavy ions produce cleaner spectra. But the limiting factor is the availability of

a reliable database of innershell ionisation cross sections for heavy ions; as there

is a vast discrepancy between the experimental measurements and the predictions

of different theoretical models.

When a projectile is involved in a nuclear reaction, of a type such as (p, γ),

(p, p′γ) or (α, γ), with the target, γ radiation may be emitted which will produce

a high energy tail in the spectrum due to Compton scattering in the detector.

Moreover if the rays are of low energy, they may be directly detected in the

detector and give rise to discrete peaks which may be mistaken for characteristic

x-ray peaks. The γ radiation production depends on the projectile energy and to

a high degree on the elemental composition of the target matrix. The structural

composition and the physical design of the target chamber and its contents also,

to some extent, affect this background by providing sources for γ ray scattering.

This background is dominant at photon energies where the K shell x-rays from

elements having Z>30 occurred and at proton energies between 3-5 MeV.

The spectrum artefacts

Several effects are involved to produce artefacts discussed earlier, some internal

to the detector and some external. The detector peripheral and front plays an

important role for low energy tailing of the ideally Gaussian x-ray peak as a source

of internal artefacts. The incomplete charge collection due to the increased defect

34


concentration near the front surface of the detector and the surface dead layer

gives rise to the exponential tail feature. The partial escape of photoelectrons

and Auger electrons from the sensitive region of the crystal contribute to the

low energy shelf features in the spectrum. The intensity of this tail relative to

the overall peak area decreases very rapidly with increasing photon energy. The

escape peak arises due to the photoelectric effect in the detector and escape of the

x-ray photon emitted as a result of the photoelectric effect from the sensitive part

of the detector. The contribution of escape peak is maximum for x-ray energies

just above the K-edge energy of the detector element (i.e. 1.839 keV for Si and

11.103 keV for Ge).

3.3.2 The backscattered particle spectrum

The energy of the scattered projectiles from a target follows the scattering kine-

matics and is expressed as the kinematic factor (K) given by [2];

K =EScattered

EIncident

=

[1−

(M1 sinφ

M2

)2]1/2

+M1 cosφ

M2

1 +M1

M2

2

. (3.3)

Where M1 and M2 are the mass of the projectile and target respectively and φ is

the scattering angle in the laboratory frame.

So, from the energy of the scattered particle it is possible to determine the

mass of the target. In case of very thin targets the energy of the scattered particle

shows as a Gaussian peak in the spectrum. As the thickness of the target increases,

the peak is broadened to the lower energy side and looks as a broad step. If the

target is thick enough to entirely stop the incident beam the step broadens up to

zero energy due to the scattered particles coming from every possible depth of the

35

3.4. Analysis of the experimental data

target and having every possible energy.

3.4 Analysis of the experimental data

3.4.1 X-ray production cross section

Depending upon the energy resolution of the detection system, the various com-

ponents of the K and L x-ray lines of the target element form different Gaussian

shaped peaks in the energy spectrum. The intensity of each resolvable component

of the x-ray line is determined by using a curve fitting routine. If the target is thin

enough (a few µg/cm2) so that the energy loss of the incident charged particle

while traversing through the target is negligible then, the x-ray yield is given by,

Y xi =

σxi nt np εi Ωx

4π. (3.4)

Where, Y xi is the intensity of the ith x-ray line, σx

i is the x-ray production cross

section for the ith line, nt is the target thickness in the form of atoms/cm2, np is

the total number of projectiles, εi is the x-ray detector efficiency for the ith line

including the correction factor due to the absorption of x-rays in the chamber

window and Ωx is the solid angle subtended by the detector.

The target thickness nt can be calculated as,

nt =NA t

A cos θ, (3.5)

where NA is the Avogadro’s number, t is the target thickness in g/cm2 A is the

atomic mass of the target and θ is the angle between the beam and the target

normal. The number of incident projectiles is determined by measuring the total

36


charge collected at the Faraday cup using a current integrator. Therefore,

np =Q

qe, (3.6)

where Q is the total charge collected, e is the electronic charge given by 1.602 ×10−19 Coulombs and q is the charge state of the projectile. On the other hand,

the number of incident projectiles is also determined by measuring the number of

projectiles scattered at an angle from the target, which is expressed as,

Yp = σR(φ)nt npΩp . (3.7)

Where, Yp is the number of scattered projectiles detected, Ωp is the solid angle

subtended by the charged particle detector and σR(φ) is the differential Rutherford

scattering cross section at an angle φ, is given by [2,3],

σR(φ) =

(Z1Z2e

2

4E

)24

sin4 φ

√

1−(M1

M2

sinφ

)2

+ cosφ

2

√1−

(M1

M2

sinφ

)2(3.8)

Where Z1, Z2 are the atomic numbers of the projectile and target respectively,

M1, M2 are the atomic masses of the projectile and target respectively and φ is the

angle of scattering. Now using Equation (3.7) the x-ray yield given in Equation

(3.4) can be rewritten as,

Y xi =

σxi nt Yp εi Ωx

4πσR(φ)Ωp

. (3.9)

The experimental x-ray production cross section for different K and L x-ray lines

can be determined using Equation (3.9). The K-shell x-ray production cross

37


sections can be expressed in terms of ionization cross section as,

σxkj = σi

k ωk Fkj (j = α, β) , (3.10)

where σxkj is production cross section, σi

k is ionization cross section that can be

obtained from different theories, ωk is the K-shell fluorescence yield, and Fkj is the

fractional emission rate for the Kj group of x-rays. Similarly, the x-ray production

cross sections for the most commonly resolved Lα, Lβ and Lγ series peaks are

then related to the three ionization sub shell cross sections σIi (i=1,2,3) in the

following way:

σxl =

[σI1(f12f23 + f13) + σI

2f23 + σI3

]ω3Sl,3 , (3.11)

σxα =

[σI1(f12f23 + f13) + σI

2f23 + σI3

]ω3Sα,3 , (3.12)

σxη =

[σI1f12 + σI

2

]ω2Sη,2 , (3.13)

σxβ = σI

1 [ω1Sβ,1 + f12ω2Sβ,2 + (f12f23 + f13)ω3Sβ,3] (3.14)

+σI2 [ω2Sβ,2 + f23ω3Sβ,3] + σI

3ω3Sβ,3 ,

σxγ = σI

1 [ω1Sγ,1 + f12ω2Sγ, 2] + σI2ω2Sγ,2 , (3.15)

σxγ1 = σI

1f12ω2Sγ1,2 + σI2ω2Sγ1,2 , (3.16)

σxγ5 = σI

1f12ω2Sγ5,2 + σI2ω2Sγ5,2 , (3.17)

σxγ2+3 = σI

1ω1Sγ2+3,1 , (3.18)

σxγ4+4′ = σI

1ω1Sγ4+4′,1 , (3.19)

38


σTOT = ωLσITOT = [ω1 + f12ω2 + (f13 + f12f23)ω3] σ

I1 (3.20)

+ [ω2 + f23ω3] σI2 + ω3σ

I3 .

Where, Sp,i is the fraction of the radiative transition to the ith (i = 1,2,3) sub

shell associated with the Lp peak, ωi is the sub-shell fluorescence yields and fij

(i=1,2; j=2,3) is the Coster-Kronig (CK) transition probabilities.

3.4.2 Analysis of PIXE data

Among the various available software packages for the qualitative and quantitative

analysis of PIXE spectra, the GUPIX code [4-6] developed by the PIXE group

at university of Guelph, Canada has been chosen for our purpose. GUPIX code

determines the intensities of characteristic x-ray peaks in a PIXE spectrum by

fitting a model spectrum to the measured spectrum using the nonlinear least

squares fitting technique. The model spectrum is constructed using a data base

of K, L and M x-ray energies, fluorescence and Coster-Kronig probabilities and

relative line intensities. The line intensities are modified to reflect the effects of

detector efficiency, absorber effects and matrix effects. The matrix effects in turn

are computed using a data base of proton ionization cross sections and stopping

powers, and x-ray mass attenuation coefficients. The continuous background,

however, is not modelled, and the model spectrum contains only characteristic x-

ray contributions. For the ionization cross section, the software uses the calculated

values based on ECPSSR [7] theory. Also there is a option to use the reference cross

sections which are chosen from various experimental data [6]. The characteristic

x-ray peaks are described by using a modified Gaussian line shape function, an

exponential and two error functions to represent the ideal peak and the low energy

tails arising due to various processes described in previous section.

The continuous background is dealt with by applying a simple digital filter

39


operator to both the measured and the model spectra prior to least-squares fitting.

This operator, like a frequency band-pass filter, is designed to attenuate the low-

frequency spectral components (continuum) while passing the higher frequencies

(peak structure) [8]. As the background continuum in the PIXE spectrum varies

sufficiently slowly, it can be assumed to be linear in any local region. Therefore,

the above filtering procedure proves to be effective in omitting the background

component from the spectrum.

The intensities of the characteristic x-ray peaks is then determined by fitting

the model spectrum to the measured spectrum using non linear least squares fitting

technique [4]. The fit proceeds by minimising the value of Chi-squared (χ2) with

respect to each of the variables used in the fitting procedure. While the measured

spectrum needs to be filtered only once, the model spectrum has to be filtered

prior to each loop of the fit. From the fit results, the peak intensities and their

associated errors are calculated. These are converted to elemental concentrations

(either bulk concentrations (in ppm) or areal densities (in ng/cm2) depending on

whether the specimen is thick or thin) and corresponding error estimates by a

procedure that is essentially a fundamental parameter approach normalised by a

user-determined instrumental constant. In addition to concentrations and their

uncertainties, the program output also presents limits of detection (LOD) for each

element in the specific case. This is preferable to a more generalized definition of

LODs, because for a particular element the LOD can be influenced strongly by

the concentrations of its neighbours in the spectrum.

Evaluation of spectra recorded from different kinds of specimen can now be

performed. These targets can be thin, intermediate, thick and multilayered. This

code also permits the inclusion of ”invisible” elements and complexes that may be

independent or stoichiometrically related to the elements whose x-rays are visible

in the spectrum [5]. Also in case of thick targets, the analysis can be carried

40


out in the both the cases where the major elements concentration of the matrices

are known and where the matrix composition is unknown. GUPIX can evaluate

a spectrum with up to 60 elements included in the fit. It can use the K x-rays

from elements 11 ≤ Z ≤ 60, L x-rays of 28 ≤ Z ≤ 92 and M x-rays of 72 ≤ Z

≤ 92 to generate the model spectra. Additionally, up to 10 temporary elements

can be used to describe the lines that are not in the library. Finally the package

allows the user to interpolate the data base and to generate detector efficiencies,

absorber transmission and other experimental parameters.

3.4.3 Analysis of proton backscattering data

Several computer programs for the simulation and analysis of spectra obtained in

MeV ion beam analysis are available [9] which can analyse the data for Rutherford

backscattering spectroscopy (RBS), nuclear reaction analysis (NRA) and elastic

recoil detection analysis (ERDA). SIMNRA [10] and RUMP [11] are two widely

used packages for the analysis of backscattering data. In this work the SIMNRA

software has been used for the analysis of the proton backscattering experiments

carried out at the VEC, Chandigarh.

The SIMNRA software uses the experimental details provided by the user to

simulate a spectrum of scattered particles from the target. The target is sub-

divided into shallow sublayers. Each simulated spectrum is made up of the su-

perimposed contributions from each isotope of each sublayer of the target. The

thickness of each sublayer is chosen in such a way that the energy loss in each

sublayer is about the stepwidth of the incoming particles. When the incident par-

ticles penetrate a sublayer, they lose energy due to electronic and nuclear energy

loss and the beam energy is spread due to straggling. After accounting for these

two processes, SIMNRA calculates the energy of backscattered particles from the

front and the backside of the sublayer, and the energy of these particles which

41

3.5. The experimental setup at IUAC

reach the detector after passing to the target surface and traversing a foil in front

of the detector. The contribution of each isotope in each sublayer is be referred

to as a brick. The brick area is determined from the mean reaction cross section

in the sublayer, while its shape (i.e. the heights of the front and back edges) is

determined from the cross sections at the entrance and exit of the sublayer and

the change of the stopping power.

3.5 The experimental setup at IUAC

3.5.1 The accelerator

The 15 UD pelletron accelerator at Inter University Accelerator Centre (IUAC),

New Delhi is a large tandem Van de Graaff type electrostatic accelerator capable

of accelerating almost any ion from Hydrogen to Uranium to energies from a few

tens of MeV to hundreds of MeV. Basically, negative ions are produced and pre-

accelerated to about 300 keV, mass analysed, and are injected into the electrostatic

field inside the accelerator. At the centre of accelerator, there is a terminal which

is maintained at a high potential (up to 15 million volts). The schematic diagram

of this pelletron is shown in Figure 3.1.

Essentially the negative ions are produced in an ion source housed in a high

voltage deck biased to a negative potential are injected into the accelerator. The

ions are accelerated to the terminal and then partly stripped of the electrons to

become positive ions with multiple charge q. These ions are further accelerated

while travelling to the bottom of the accelerating tube kept at the ground poten-

tial. As a result the ions emerging out of the accelerator gain energy (E) given

by,

E = [Einj + (1 + q)V ] MeV. (3.21)

42


Figure 3.1: Schematic diagram of the 15UD Pelletron accelerator at IUAC, NewDelhi.

Where, V is the terminal potential in MV (million volts) and q is the charge state

of the ion after stripping and Einj is the energy of the injected ions in MeV. The

ions are bent by an analysing magnet through 90 depending on the mass, energy

and charge state of the ion. The magnetic field of this magnet can be set to select

the particular ion of required energy and charge state.

43


Figure 3.2: The experimental set up installed at the GPSC beam line.

3.5.2 Experimental set up

The experimental set up installed at the beam exit port of general purpose scatter-

ing chamber (GPSC) is shown in Figure 3.2. The scattering chamber consists of a

multiple target holder with rotatable mount to manipulate the beam-target angle.

The target ladder can accommodate 7 thin foil targets of 10 mm diameter (total

size 20 mm × 20 mm including the mounting frame). There are two ports at 90

and 270 which facilitate the positioning to x-ray detectors. At the 90 port one

HPGe x-ray detector was used to detect both the K and L x-rays. The detector

is of Canberra Inc. USA manufactured with 5 mm crystal thickness and 30 mm2

active area, 0.3 µm dead layer, 25 µm beryllium window with energy resolution of

150 eV at 5.9 keV. At the other port a Si(Li) detector supplied by Ortec Inc. USA

was placed to detect the L x-rays. The Si(Li) detector had a crystal of thickness 5

mm with 10 mm active diameter, beryllium window of thickness 25 m, gold layer

44


GPSC

InsertableFaraday Cup

Si(Li)Detector

HPGeDetector

SSBDetectors

Target

View Port

45O

15.5O

ElectronSuppressor

°

Figure 3.3: Schematic drawing of the experimental set up installed at the GPSCbeam line.

thickness 200 A and a dead layer of 0.1 µm with energy resolution of 180 eV at

5.9 keV. Two SSB detectors mounted at 15.5 with respect to beam, monitor the

scattered projectiles. These detectors are of 100 mm2 active area with a depletion

thickness of 300 µm. An insertable Faraday cup was used as a beam dump and

connected to the current integrator to monitor the total incident flux. The block

diagram of the experimental setup at IUAC is shown in Figure 3.3.

3.5.3 Data acquisition setup

The data acquisition system at IUAC is based on the LINUX based Pentium

machines for computation and graphics for I/O operations. The analog signals

are digitised the AD811 Analog to Digital Converter (ADC). This ADC accepts

positive unipolar or bipolar signals from the nuclear shaping amplifiers in the range

0 to 10.0 volt. It contains eight channels measuring analog to digital converter

packaged in a single width CAMAC (Computer Automated Measurement and

45

3.6. The experimental facility at IOP

Figure 3.4: Schematics of the ion beam laboratory at IOP, Bhubaneswar.

Control) module. The data acquisition and control of the CAMAC system is

carried out by the FREEDOM [12] software developed in house by IUAC.

3.6 The experimental facility at IOP

3.6.1 The accelerator

The 3 UD pelletron accelerator at IOP operates under the same principle as that of

the 15 UD pelleron at IUAC described in the previous section. The only difference

being the maximum terminal potential which is 3 MV in this case as opposed to 15

MV at IUAC. The energy of protons provide by this accelerator is most suitable

for the PIXE analysis. The schematic diagram of the entire accelerator facility is

shown in Figure 3.4.

46

3.6. The experimental facility at IOP

3.6.2 The experimental set up

The external beam PIXE set up at the IOP is at the 0 beam line of the pelletron.

The proton beam obtained from the 3 MV tandem-type pelletron accelerator

was collimated by a graphite collimator to a beam size of 3 mm diameter inside

the scattering chamber with an inner diameter of 80 cm. The beam is then ex-

tracted into air through the 0 port of the scattering chamber. An 8 µm thick

Kapton R© foil at the exit point of a vacuum scattering chamber serves as the

beam exit foil. The beam is first focused and centred at the target location inside

the scattering chamber and then let through the thin Kapton R© foil placed at

the exit port. The chamber is pumped by a high throughput diffstack pump to

maintain a vacuum in the range of 10−7 mbar in the chamber and the beam line.

The Kapton R© foil is used as exit window due to its several special characteris-

tics like low beam-induced background emission, minimal energy loss and greater

resistance to radiation damage.

According to the demand of the experiment the beam can be extracted up to

60 mm from the exit foil without any considerable broadening in the beam spot

size. A schematic view of the external PIXE set-up is shown in Figure 3.5. Beam-

charge measurement is carried out using a rotating vane chopper of adjustable

length. The chopper disc of diameter 15 mm is placed between the exit window

and the sample at a distance of 3 mm from the exit window. The chopper vane

was electrically isolated from the electrical motor as well the beam line using

insulation, and is connected to the current integrator for recording the charge.

For our measurements to be described in chapter 6, the initial proton beam

energy was 3.5 MeV and the target was placed at a distance of 45 mm from the

exit foil. Therefore, the energy of the protons irradiating the targets was 2.9 MeV.

A ORTEC Inc. supplied Si(Li) detector was positioned at an angle of 50 to the

target normal at a distance of 30 mm. The detector element had an active area

47

3.7. X-ray detector efficiency

Figure 3.5: Schematic diagram of the external beam PIXE set up at IOP.

of 30 mm2 and housed behind an 8 µm thick beryllium entrance window. The

energy resolution of the detector was 165 eV at 5.9 keV.

3.6.3 Data acquisition setup

The signal from the detector was amplified with an ORTEC 571 spectroscopy

amplifier and the signal was fed to a PC based Canberra S-100 multichannel

analyser to record the x-ray spectra. The charge collected by the chopper vane

was integrated by a Danfysik current integrator.

3.7 X-ray detector efficiency

Reliability of the data on measurement of the cross section for the atomic inner

shell ionization depends up on the accuracy of the detection efficiency of the x-ray

detector. Therefore, the detection efficiency of both the Si(Li) and HPGe x-ray

detectors at IUAC was determined experimentally. For experimental efficiency

48


measurement, x-rays and -rays emitted by circular radioactive sources of 55Fe,

57Co, 152Eu and 241Am with a 2 mm active diameter were detected by the de-

tector. The activities of 55Fe, 57Co and 241Am were 8.8758 µCi, 4.3423 µCi and

0.29957 µCi respectively at the time of the measurement after applying necessary

decay corrections. The activity of the 152Eu radioisotope was not known. All the

radioisotopes were supplied by the Board of Radiation and Isotope Technology

(BRIT), India. The radioactive sources were placed on the target ladder inside

the vacuum chamber in which the experiment was to be carried out. The chamber

had a 20 µm thick Mylar exit window for the x-rays. The source and detector

were placed in a parallel plane with the source centre lying along the detector

axis. Distance between source and the HPGe detector crystal was 43 mm out of

which 13 mm was air gap. Teflon collimators with 5.6 mm diameter aperture and

total length of 15 mm were used in front of the detector to collimate the photons

emitted by the source. A schematic diagram of the arrangements is shown in

Figure 3.6. The arrangement for the measurement of Si(Li) detector efficiency is

similar in geometry. This detector was also placed axially in front of the source

at a distance of 21 mm. A 12 mm long circular collimator with 10 mm aperture

was used in between the detector and the source. The photo peak areas of x-rays

and gamma rays in the spectra recorded from the detectors were extracted using

computer program FREEDOM [12]. The efficiency curve is estimated by using

the relation;

ε =Number of particles detected(Nd)

Number of particles emitted(Ne). (3.22)

Where, number of particles detected is the area under the photo peak of a par-

ticular x-ray or γ-ray line and the number of emitted particles is calculated using

the following relation;

Ne = I N0 e−λt , (3.23)

49


43 mm

SourceRadioactive

Teflon housing

Germaniumcrystal

Stainless steelhousing

Vacuum Air

Vacuum

Stainless steelchamber parts

Berylliumwindowwindow

Mylar

Tefloncollimator

Figure 3.6: Schematic view of the detector efficiency measurement setup.

with I being the absolute intensity of the line of interest; N0 , the initial activity

of the radioactive source; λ, the decay constant and t, the elapsed time. From this

relation it is evident that accuracy of the efficiency curve depends mostly upon

the peak area and the intensity of the line of interest. Final uncertainty in the

measured efficiency was evaluated from the uncertainties in intensity of the x-ray

or γ-ray lines, initial activity (≤ 1%), elapsed time (≤ 0.6%) and the peak area (≤3%). The major source of error was due to the uncertainties of the line intensities

which vary for strong and weak lines. Finally, for most of the efficiency points,

the total error in our case was estimated to be less than 6%.

Theoretical detector intrinsic efficiency was evaluated using detector param-

eters like thickness and density of detector crystal, contact layer and detector

entrance window applying the model based on photon atom interaction [13]. The

50


semi empirical model used for efficiency (ε) evaluation is given by the equation;

ε =Ω

4π

[exp

(−

n∑i=1

µidi

)]fE [1− exp (−µCD)] . (3.24)

Where, Ω4π is the fractional solid angle subtended by the detector crystal at the

source and i denotes the medium between the source and the beryllium window,

the window itself, a possible ice layer, the gold electrode, the frontal crystal dead

layer etc. The di are the thickness of these absorbers and µi are their linear ab-

sorption coefficients taken from XCOM [14] database. The term fE represents the

escape peak correction factor. The µC is the photoelectric absorption coefficient of

the detector crystal of thickness D. The fractional solid angle, Ω4π , was calculated

using the formula derived by Nelson Blachman and published by Burtt [15] which

is valid for a wide range of source detector geometries except for large sources

close to the detector [16,17]. If h represents the distance between source of radius

r and the detector of radius R placed in a axial geometry, then the fractional solid

angle subtended by the detector at the source is given by;

Ω

4π=

1

2

[1− 1

(1 + α)1/2− 3

8

αβ

(1 + α)5/2

](3.25)

+β2

2

[5

16

α

(1 + α)7/2− 35

16

α2

(1 + α)9/2

]

−β3

2

[35

128

α

(1 + α)9/2− 315

256

α2

(1 + α)11/2+

1155

1024

α3

(1 + α)13/2

],

with α =

(R

h

)2

, β =( rh

)2

.

The experimental efficiency along with the model based efficiency for the Si(Li)

detector is shown in Figure 3.7. As it is evident from the figure, a reasonable

good agreement between the experimental and the model efficiency is achieved.

The maximum difference between the measured efficiencies and the corresponding

51


0 10 20 30 40 50 60-40

-30

-20

-10

0

10

20

30

40

Diffe

rence (

%)

Energy (keV)

(b)

0 10 20 30 40 50 60

4.0x10-3

8.0x10-3

1.2x10-2

1.6x10-2

E

ffic

iency

Energy (keV)

Experimental

Model

(a)

Figure 3.7: (a) Experimental efficiency points and model based efficiency curvefor the Si(Li) detector, (b) % difference between the two efficiency points.

52


model based value is ∼ 6% i.e. within the experimental error. From this compar-

ison it is concluded that the methods for the experimental as well as the model

based calculations are reliable. An inappropriate selection of intensity values for

the radioisotopes can give large errors as it is found when the intensity values

for different Np L x-ray lines coming from 241Am are taken from the table of

radioactive isotopes (TORI) [18]. Therefore the use of already experimentally

verified intensities as reported by Johnston [19] and the IAEA values [20] are

recommended.

10 10010

-4

10-3

Eff

iency

Energy (keV)

Experimental

Model

Ge K edge

Figure 3.8: Experimental efficiency points along with model based efficiency curvefor a dead layer of 0.3 µm.

Based on above experimental method and model based calculation we com-

pared the efficiency for the low energy HPGe detector as shown in Figure 3.8. The

detector parameters taken are those provided by the manufacturer which includes

a dead layer of 0.3 µm thick. It is evident that there is a large deviation which,

for a few energies deviates by a factor of 3. Initially it was thought to be the error

53


in calculating the escape peak correction factor in low energy HPGe detectors.

However, existing literature shows that the maximum contribution of escape peak

in Ge detectors can be only up to 20% [21]. Except for the frontal crystal dead

layer, the values of other absorber layers mentioned in Equation (3.24) are quite

small for x-rays with energy > 3 keV. Moreover, the thickness of Mylar window

and the air gap are measured quite precisely and the manufacturer declared value

of Be window thickness are reliable. Hence these observed deviations can not be

attributed to any uncertainties associated with these absorbers.

Recently Salgado et al. [22] have compared the experimental efficiency of

HPGe detector with the Monte Carlo model based calculations in the 20-150 keV

region. Their detector consisted of a planar crystal with p+ ion implanted front

contact. To the best of our knowledge this is the only detector of its type whose

efficiency has been reported. In order to achieve a good agreement (within 5%)

between the model efficiency points and the experimental ones they had to take a

dead layer thickness of 4 µm instead of quoted value of just 0.5 µm. Recent studies

by Shariff et.al. [23] and Campbell et al. [24] have not reported any comparison

of the experimental and the modelled efficiency points and have mainly focused

on the line shapes.

In order to understand the efficiency for the HPGe detectors, considering the

above fact that all the physical quantities except the dead layer thickness are

quite reliable, we tried to vary the crystal dead layer thickness to achieve a better

fit between the experimental and the model calculations. For this purpose, in

the model calculations, the dead layer thickness was varied from 0.3 to 20 µm.

The percentage difference between the calculated values and experimental data

were extracted for every dead layer thickness. The average percentage difference,

determined using the absolute values of these differences for all the energy points,

is found to be decreasing with increasing dead layer thickness up to 15 µm after

54

3.8. Fabrication of targets

which, it started increasing till 20 µm. A comparison of experimental efficiency

points to that of model calculations are given in Table 3.1 for five different dead

layer thicknesses. It can be observed that, for a dead layer of 15 µm thick, the

model calculations become closest to the experimental values for majority of the

energy points of our interest. As shown in Figure 3.9, the experimental efficiency

values match well with the calculated efficiency at almost all energies except at

3.3 keV which, may be because of a possible overestimation of the area under 3.3

keV line due its overlap with the Ge K escape peak of 13.9 keV line.

From the comparison of the modelled efficiency based on modified dead layer

thickness and the experimental points, it is evident that the reported dead layer

from the manufactures for the low energy HPGe detector can not be relied upon for

the model calculations. Therefore it becomes necessary to determine the efficiency

of the detector experimentally prior to any x-ray spectroscopy experiments. This

work has been published by our group [25].

3.8 Fabrication of targets

To successfully carry out experiments on the inner shell ionization process, the

targets should be thin, uniform and free from other metal contaminants. There

are different techniques available for preparation of thin metal foils out of which

the physical vapour deposition (PVD) process is most commonly employed for

its efficiency, fastness and reliability. PVD process coupled with electron beam

evaporation can easily produce thin targets of metals having high melting points.

In general, thin carbon foils are used as the backing material to deposit thin

metal films by electron beam deposition due to their good mechanical strength

and stability at high temperature environment which arises during deposition

process. In case of inner shell ionization studies, targets with carbon backing are

55


Table 3.1: Experimental and calculated HPGe detector efficiency for the x-rayenergies from different sources used. The calculated efficiency for five dead layersviz. 0.3, 4, 10 ,15 and 20 µm are given.

Source Energy Efficiency (× 10−4)

(keV) Expt. 0.3 µm 4 µm 10 µm 15 µm 20 µm

241Am 3.3 1.46 (16) 2.21 0.517 0.049 0.0069 0.00098

55Fe 5.9 3.34 (13) 7.8 5.74 3.49 2.31 1.52

152Eu 6.34 3.52 (26) 8.24 6.41 4.27 3.04 2.17

57Co 6.4 3.60 (17) 8.3 6.5 4.37 3.14 2.26

55Fe 6.49 3.60 (12) 8.37 6.61 4.52 3.29 2.39

57Co 7.06 3.89 (18) 8.77 7.28 5.38 4.18 3.25

241Am 11.87 2.36 (19) 7.94 5.76 3.42 2.21 1.43

241Am 13.9 3.04 (19) 8.49 6.82 4.78 3.56 2.65

57Co 14.41 3.16 (15) 8.61 7.05 5.1 3.9 2.98

241Am 17.75 3.77 (24) 9.17 8.22 6.88 5.93 5.11

241Am 21.1 5.12 (37) 9.45 8.8 7.85 7.14 6.49

241Am 26.34 7.33 (42) 9.75 9.42 8.9 8.49 8.1

241Am 33.2 9.36 (73) 9.95 9.79 9.54 9.33 9.13

152Eu 39.52 8.44 (54) 10.04 9.96 9.82 9.71 9.6

152Eu 40.12 8.38 (54) 10.05 9.97 9.84 9.74 9.63

152Eu 42.31 10.59 (70) 10.07 10.01 9.91 9.82 9.73

152Eu 42.99 10.49 (69) 10.08 10.02 9.93 9.85 9.77

152Eu 45.4 9.26 (58) 10.1 10.06 9.99 9.93 9.87

152Eu 46.6 7.94 (50) 10.11 10.07 10.01 9.96 9.91

152Eu 48.65 12.04 (81) 10.13 10.11 10.07 10.1 10

241Am 59.54 10.14 (59) 10.14 10.14 10.14 10.14 10.14

56


10 100

-80

-40

0

40

80

Diffe

rence (

%)

Energy (keV)

(b)

10 100

10-6

10-5

10-4

10-3

E

ffic

iency

Energy (keV)

Experimental

15 µm

Ge K edge(a)

Figure 3.9: (a) Comparison of experimental efficiency points with model basedefficiency curve for dead layer thickness of 15 µm, (b) % difference between thetwo efficiency points.

57


also considered to be suitable as they have negligible contribution to the x-ray

background and are relatively free from other metal contaminants.

The fabrication of targets were carried out at Inter University Accelerator

Centre (IUAC) using a high vacuum (HV) evaporator and a ultra high vacuum

(UHV) evaporator. The HV evaporator is equipped with a rotary vane pump

and a diffusion pump with liquid nitrogen trap providing a vacuum of 2×10−7

Torr. The UHV evaporator is equipped with a scroll pump, turbo-molecular pump

and a cryopump. This chamber provides a vacuum of 2×10−8 Torr. Both the

evaporators have provisions for resistive heating and electron beam evaporation

and are equipped with a quartz crystal thickness monitor for monitoring deposition

rate and thickness.

Carbon foils of thickness 10 - 20 µg/cm2 were prepared in the HV evapora-

tor. The deposition was carried out using electron beam heating of a high purity

graphite rod. Glass slides, coated with Teepolr detergent, were placed at a dis-

tance of 20 cm from the evaporation source act as substrates. Using deionised

water, the carbon foils were peeled off from these glass slides and then mounted

on 10 mm diameter target holders. These mounted foils were then used as sub-

strates for the deposition of different elements. Using this technique, thin targets

of Ti, Ni, Ba and Au were fabricated. But this technique was not successful during

the fabrication of enriched isotopic targets of Sm, Gd, Pb and targets of Ta, W

and Os. In the first case, it was the shorter distance between source and substrate,

which was necessary keeping in view of the small amounts (∼ 100 mg each) of

available expensive enriched materials, being the reason behind the destruction

of the carbon foil during the deposition process. Whereas, the high temperature

of the source during the evaporation of these high melting point metals was re-

sponsible for the failure of the process, in the later case. Then the metals were

deposited on the glass slide with BaCl2 and carbon coating. But most of the

58


time the carbon film got damaged and the target did not float. One deposition of

natural Gd was successful but after floating the target the thin metal foil peeled

off from the carbon backing.

Earlier, 6 µm thick aluminised polypropylene, used as a backing material for

x-ray spectroscopy experiments [26, 27] was found to be free from other unwanted

metal impurities and having little contribution to the background. Therefore, it

was decided to fabricate these targets on aluminised polypropylene backing.

Placing the polypropylene substrate at a proper distance for successful depo-

sition was found to be challenging. Because, at a closer source substrate distance,

the heat radiated by the source becomes too high for the polypropylene foil which

melts during the evaporation process. For example, power radiated by the source

at a temperature around the melting point of Gd (1598 K) is about 13 watts. If the

source - substrate distance is kept at 12 cm, then the temperature of the polypropy-

lene substrate will arise by 8 C/sec which is sufficient to destroy it within few

seconds. In order to dissipate this heat generated at the substrate, a substrate

cooling system was necessary which would help in keeping the polypropylene foil

at a temperature sufficiently below its melting point throughout the deposition.

The developed substrate cooling system consisted of a hollow stainless steel

disc of 20 cm diameter and 1.7 cm thickness with inlet and outlet ports on its

side wall for the circulation of the coolant. A solid steel rod was welded on the

side wall just opposite to these ports which helped in mounting the disc inside the

deposition chamber. The substrates could directly be stuck to the lower surface of

the disc facing the source. The inlet and outlet ports were coupled to the vacuum

feedthrough on the chamber wall using flexible stainless steel hoses. Metal gaskets

were used for all these couplings which provided a vacuum of 3×10−8 Torr in

the chamber. The vacuum integrity of the system was tested using both liquid

nitrogen and chilled water as coolants. With water, the system was perfectly

59


fine whereas, low temperature leaks on the stainless steel hoses were observed

while using liquid nitrogen. Cooling water at a temperature of < 20 C was

flowed continuously through the cooling disc with a pressure of 20 psi. Theoretical

calculations were carried out to verify the effectiveness of chilling water during the

deposition process. Figure 3.9 shows the vapour pressure of some of the elements

at different temperature and the heat received at the substrate at those source

temperatures. Also the heat energy transmitted by the chilling water at different

substrate temperatures is shown. From the figure, it is clear that, all the required

targets can be deposited using this technique and the substrate temperature does

not exceed 55 C during the process.

Aluminised polypropylene foils of 20 mm × 15 mm size were mounted on

stainless steel target frames with the help of silver paste in such a way that the

aluminium coated side was in contact with the frame. These frames were then

directly stuck to the surface of the cooling disc with the foil in direct contact.

Further more, glass slides were used to press the frames by their sides to ensure

firm contact with the disk surface. The UHV deposition unit was used for the

deposition. The cooling disc with the foils was placed above the crucible at a

distance of 12 cm. The substrate temperature was continuously monitored and

the rate of deposition was kept below 0.2 A/s at the substrate. The temperature

at the substrate was never allowed to exceed beyond 40 C during any of the

depositions. For targets of higher thickness (100 - 200 µg/cm2), the required

thickness was deposited in five equal steps with 10 - 15 min time in between to

allow the substrate to cool down. In this process, thin targets of 157Gd, 160Gd,

148Sm, 149Sm, 207Pb, Pt, Ta, Os and W were fabricated.

Thicknesses of the targets fabricated on carbon foil backing were determined

by alpha particle transmission method [28]. In this method the energy loss by the

5.48 MeV alpha particles emitted by a 241Am alpha radioactive source were used.

60


1000 1500 2000 2500 3000 3500 4000 450010-4

10-3

10-2

10-1b

received by substrate transmitted at 220 C transmitted at 350 C transmitted at 550 C

Hea

t Ene

rgy

(J)

Source Temperature (K)

10-11

10-10

10-9

10-8

10-7

10-6

10-5

10-4

10-3

10-2

V

apou

r Pre

ssur

e (T

orr)

Gd Au Pt Os Ta W

a

Figure 3.10: (a) Vapour pressure of different metals at different temperatures. (b)The amount of heat received by the substrate at those source temperatures. Thehorizontal lines represent the heat transmitted to the chilling water at differentsubstrate temperatures. The two vertical lines are drawn to show the vapour pres-sure of different metals corresponding to the source temperature, if the substratetemperature is be maintained at 22 C and 55 C.

61


The 241Am source was kept at a distance of 40 mm from a 300 µm thick SSB

detector with a 5 mm collimator in a vacuum chamber. The target foil was placed

between the source and the detector along with their axis. The vacuum chamber

was evacuated with the help of a rotary pump down to a pressure of 1×10−3 Torr.

Energy spectra of the α-particles were recorded both with (E′) and without (E)

the target foil in-between. The energy loss of the α-particle during transmission

through the foil is

∆E = E − E ′ (3.26)

The stopping power for α-particle is given by

S =−dE

dx(3.27)

Where dE is the energy loss and dx is the thickness of the material expressed as

the areal density. So

dx =−dE

S(3.28)

First, the thicknesses of the carbon foils and aluminised polypropylene were

determined before depositing the target materials on them. After deposition, the

targets were placed between the source and detector with the carbon backing

side facing the source. So, the previously determined transmitted energy of the

α-particle through the backing becomes the incident energy for the target layer.

The stopping power (S) values were calculated using SRIM 2003 [29]. In case of

aluminised polypropylene backing, the energy loss suffered by the 5.48 MeV α-

paricles while passing through is very high (∼ 554 keV) and the uncertainty in the

determination of peak centroid was high due to considerable increase in the peak

width of transmitted alphas. The targets deposited on this backing were of 5 -100

µg/cm2 thick which translated into a shift of a few (1 - 20) channels in a 4K channel

spectrum. Hence, precise determination of the thicknesses of targets prepared on

62


aluminised polypropylene backing was not possible by this method. Thicknesses

of these targets were determined by using PIXE and Rutherford Backscattering

(RBS) techniques. The maximum difference between measured thicknesses and

estimated thickness (reading of the crystal thickness monitor during evaporation)

was found to be 20% which was within the tolerance of our experimental require-

ment.

63


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