Chapter 4

Measurements of M X-ray Production Cross-Sections

75 Chapter 4

4.1 INTRODUCTION

In X-ray fluorescence (XRF) studies, the probabilities of photon induced X-ray

emission i.e. X-ray fluorescence cross-section (σ*) is an important most sought

parameter. It is a composite parameter as product of photoionization cross-section (),

fluorescence yield () and fractional radiative decay rates (F). Applications of low

energy fluorescent X-rays in various fields such as material science, forensic science,

dosimetric computation, elemental analysis and nuclear, atomic and molecular physics

etc. have raised the importance of data on L and M shell X-ray fluorescence cross

sections. The experimental data for K shell as compared to that of L and M shells is

almost well established while it is scanty for M and higher shells but moderate for L X-

ray fluorescence cross-sections (Campbell, 2010) as discussed in chapter 1. The

scantiness of data on M X-ray production cross-section is because of its structural

complexities as it consists of five sub-shells and complexities involved in the M shell X-

ray spectra. There is a number of intra shell Coster-Kronig/Super Coster-Kronig

transitions leading to modification of initial M sub-shell vacancy distribution from

excitations. The interaction of photons of energies <10 keV and elements with Z70

involve only M and higher shell electrons and it has raised the significance of M X-ray

productions in low energy range. Moreover, to check the fine details of the atomic

structure, data on individual M X-ray line/group of lines XRF cross-sections would play a

vital role.

The data on total M shell X-ray cross-sections has been evaluated by Ertugrul et

al. (2004) for the elements 70Z92 in the energy range 1-1500 keV using radiative

transition rates and photoionization cross-sections from relativistic Hartree-Slater model

Chapter 4 76

of Scofield (1973, 1974c), non-radiative transition rates from DHS model (Chen et al.,

1979) and average M shell fluorescence yields from Hubbell et al. (1994). Chauhan et al.

(2009) evaluated two sets of data on M X-ray line/group of lines fluorescence cross-

sections for Mg (g = , , , , , , m1 and m2) groups of X-rays for all the elements with

67Z92 at incident photon energies ranging EM1<Einc150 keV. In both the sets, they

used DHS model based CK yields (Chauhan and Puri, 2008) and photoionization cross-

section of Scofield (1973). The difference in two sets is the data used for X-ray emission

rates and M sub-shell fluorescence yields. One set of M XRF data (DF model) uses DF

model based fractional emission rates (Puri, 2007 and Chen and Crasemann, 1984) and M

sub-shell fluorescence yields (Chauhan and Puri, 2008) and the other set (DHS model)

uses DHS model based fractional emission rates of Puri (2007) and Bhalla (1970)

fluorescence yields (Chauhan and Puri, 2008). In the context of experimental

measurements, the dependence of X-ray emission probability on incident photon energy

requires the precise value of incident photon energies and hence the corresponding

photon sources. The widely used photon sources are radioactive sources in single/double

reflection set-up, X-ray tubes in double reflection set-up and synchrotron sources. The

use of radioactive sources in single reflection (Shatendra et al., 1985; Garg et al., 1991;

Puri et al., 1993b; Ertugral et al., 1996; Durak and Ozdemir, 2001; Apaydin, 2005;

Ozdemir, 2007; Apaydin et al., 2008a; Kucukonder et al., 2008 and Han et al., 2009b)

and double reflection set-up (Mann et al., 1990a and Allawadhi et al., 1994) imposes

limitations on energies and intensities of incident photons. The synchrotron photon

sources take care of these limitations but it is a multi user facility and involves huge

expenses, infrastructure and manpower and only limited numbers of these facilities are

77 Chapter 4

available in the world (http://www.lightsources.org/cms/?pid=1000098). Therefore, X-

ray tube photon sources with photon intensities better than those of radioactive sources

become the appropriate choice. The available M XRF measurements with X-ray tube

photon sources are also at some specific discrete photon energies derived from primary

excitations of suitable targets in double reflection set-ups (Rao et al., 1995, 1996). Again

this results in limitations on energies of exciting photons. To have single energy photons

from X-ray tube in single reflection set-up is cumbersome where continuous

Bremsstrahlung excites the target elements and it is complicated to determine the single

energy of exciting Bremsstrahlung.

Moreover, due to the complex M X-ray spectra arising from sub-shell structure of

M shell, it is more difficult to measure individual line/group production cross-section for

the shell. Only measurements of Sharma et al. (2006b) on individual M sub-shell X-ray

fluorescence cross-sections are available. They measured M X-ray fluorescence cross-

section for Mξ, Mαβ, Mγ and Mm groups in the elemental range 71Z92 at 5.96 keV.

Still, more data is required on M sub-shell X-ray fluorescence cross-sections at variable

energies to have a better insight into atomic structure and to check theory against

experiment.

In the present study, the X-ray tube has been used as photon source of desired

energy simply by adjusting its anode voltage and individual M X-ray line/group of lines

Mξ, Mαβ, M and Mm XRF cross-sections have been measured at five different energies

for each of the Pt, Au, Pb, Th and U elements. The selective creation of only M shell

vacancies at five different energies in experimental targets has been done with photons

from the tube. Since, Bremsstrahlung X-rays from the tube are continuous in energy;

Chapter 4 78

therefore, weighted average energy Eavg of incident tube photons lying between M5 edge

energy of experimental target and the tube anode voltage was determined following a

separate experiment and calculation procedure to evaluate a single energy value at which

the cross-sections *Mg for groups of M X-rays were to be measured. The details of the

measurements, adopted procedure, results and discussions are being given here.

4.2 MEASUREMENTS PROCEDURE

Experimental measurements were done with the elements Pt, Au, Pb, Th and U.

Spec-pure metallic targets of elements each of dia. 4cm have been used. The

experimental arrangement consisted of X-ray tube as a photon source along with a Peltier

cooled Si-PIN detector in 90° single reflection set-up (Chapter 2, Fig. 2.12). The detector

resolution was ~220 eV at 5.959 keV. Selective excitation of M shell of each target was

done by adjusting the five tube anode voltages between the L3 and M1 edge energies of

the target. For total range of excitation energy of all the targets, comprising five energies

for each, tube power was varied in the range 6-14 kV/0.2-0.9 mA. The filament current of

the X-ray tube was adjusted so as to control the dead time loses of the detector <1%. In

order to reduce the statistical error in the measurements and to assure the reproducibility

of results, three sets of spectra for each element at each energy were recorded. The tube

radiation scattered from the target were accounted by recording the spectra with

equivalent Al targets (Mann et al., 1990b) of experimental targets and subtracted from

the corresponding target spectrum.

Since, M shell consists of five sub-shells and the X-rays from the target consist of

a number of transition lines, but due to limited resolution of present set-up, the X-ray

lines fall within different groups of M X-rays. The grouping of M X-rays has been done

79 Chapter 4

by selecting the energies of M X-ray lines falling in the regions of intense M line

detector resolution. The emerged four main groups (Mg) are Mξ, Mαβ, M and Mm. The

grouped transitions of different groups are Mξ (M4-N2, 3; M5-N3 ), Mαβ (M5-N6, 7, O3;

M4-N7), M (M2-N1; M3-N4, 5) and Mm (M3-O1, 4, 5; M3-N6, 7; M2-N4; M1-N2, 3) and are

shown below in Fig. 4.1.

Fig. 4.1 Grouping of M X-ray lines based upon line intensities and resolution of Si-PIN detector.

Chapter 4 80

The weighted X-ray energy of different groups of M X-rays EMg were calculated

using radiative transition probabilities of Chen and Crasemann (1984) and level energies

from tables of Storm and Israel (1970) and were marked in the net subtracted spectra

after their precise energy calibrations and have been listed below in table 4.1.

Table 4.1 Weighted X-ray energies of different groups of M X-rays for 78Z92.

M X-ray

group

EMg (keV)

Pt Au Pb Th U

M 1.60 1.66 1.84 2.35 2.49

Mβ 2.09 2.16 2.39 3.07 3.26

M 2.33 2.40 2.65 3.38 3.58

Mm 2.71 2.80 3.12 4.07 4.34

The experiment was run for sufficient time to obtain the statistics of counts <1%

under various peaks of the background subtracted net spectrum. A typical set of spectra

for Au at anode voltage/filament current 9 kV/0.2 mA is shown in Fig. 4.2.

Because of M shell excitation with continuous Bremsstrahlung photons lying in

the region from M5 level edge energy to energy corresponding to the tube anode voltage,

a separate experiment and calculation procedure has been followed to find a single

average energy for continuous Bremsstrahlung used in M shell excitation.

4.2.1 Procedure for Evaluation of Weighted Average Energy and Intensity of

Continuous Bremsstrahlung

High flux output from X-ray tube could not be recorded directly with Si-PIN

detector because of its dead time problem. Therefore, for each excitation the spectrum of

tube photons scattered from a low Z target aluminum (Al) was recorded in the same set-

up at the same anode voltage/filament current of the tube as in case of experimental

81 Chapter 4

(a)

(b)

Fig. 4.2 M shell X-ray spectra recorded with Si-PIN detector in single reflection set-up for a) Au and its equivalent Al and b) background subtracted net spectrum, when irradiated with photons from X-ray tube operated at 9 kV/0.2 mA.

1.0 1.5 2.0 2.5 3.0 3.50

3000

6000

9000Au M X-ray region (1.66-2.80 keV)

Au Al

Cou

nts/

7200

sec

Energy (keV)

1.0 1.5 2.0 2.5 3.0 3.50

3000

6000

9000

Background subtracted Au

Mm (2.80 keV)M (2.40 keV)

M (2.16 keV)

(1.66 keV) M

Coun

ts/72

00se

c

Energy (keV)

Chapter 4 82

target. The recorded scattered Bremsstrahlung was then fitted with a polynomial fit in

ORIGIN 6.0 to have a best smooth Bremsstrahlung spectrum free from spurious peaks

and close to actual count values. To evaluate weighted average energy of incident flux,

the fitted region between the M5 edge energy of experimental target and energy

corresponding to applied voltage was divided into n number of strips. Each strip was of

width 200 eV (~detector resolution) as shown in Fig. 4.3 at tube power 9 kV/0.2 mA for

Au excitation.

Fig. 4.3 Polynomial fitting of X-ray tube Bremsstrahlung scattered from Al scatter at tube power 9 kV/0.2 mA.

1 2 3 4 5 6 7 8 9 10

1

10

100

1000

Au M5 edge=2.206 keV

200eV

Energy (keV)

Coun

ts/36

00 se

c

Scattered Bremsstrahlung Polynomial fit

83 Chapter 4

To determine the intensity of incident flux falling on target area seen by the

detector for each strip from the collected number of scattered counts in nth strip,

efficiency of the detector at that strip mean energy (En) and Al self absorption correction

for the incident and scattered energies of the strip, the procedure was adopted as given

here.

The counts nN per unit time under nth strip is,

nAlnincncohAlEnAl

Al

vnn EEEeit

MAIN 90, (4.1)

where,

In is the incident flux for nth strip falling upon the target area seen by the detector

(to be evaluated),

Av is Avogadro’s number,

MAl is molecular weight of Al target,

tAl is the Al target thickness in g/cm2,

AlEn ei, of nth strip is self absorption correction factor for Al at incident i and

scattered e photon energies,

’s(En) are the coherent and incoherent scattering cross-sections of Al in b/atom,

(En) is extrinsic detector efficiency at energy En.

For all strips, the factor AlAl

v tM

A * number of atoms per unit area of target were

same, therefore, for each strip; (a) incoherent Klien-Nishina and coherent Rayleigh

scattering cross-sections of Al (Hubbell et al., 1975) at 90°, (b) effective thickness βt of

Al target and (c) absolute detector efficiency ε(En ) were needed to be evaluated.

Chapter 4 84

(a) Coherent and incoherent scattering cross-sections at the strip mean energy were

calculated by using formulation given by Hubbell et al. (1975).

Coherent Rayleigh scattering cross-section per atom,

cos,cos1

83 2

1

1

2 dZxFTcoh

(4.2)

where, 3

8 2e

Tr (Classical Thomson scattering cross-section from an electron),

re2 = 0.0794b is classical electron radius,

is the scattering angle,

F(x,Z) is atomic form factor with Z as the atomic number of the target,

)(2

sin

Ax

(A) is the wavelength of scattered radiation in Angstrom units.

For the used set-up, scattering from Al at 90°, Coherent scattering cross-section

becomes,

290 ,83 ZxFTAlcoh (4.3)

and the incoherent scattering cross-section per atom at 90°is

ZxSk

kkreAlinc ,

111

2

22

2

90

(4.4)

where, S(x,Z) is incoherent scattering function and

k= E(eV)/511003.4

Total scattering cross-section for Al at 90 is,

909090 AlincAlcohAltotal (4.5)

85 Chapter 4

(b) Al self-absorption correction factor,

Al

ei

Alei

AlEn

tei

tei

ei

coscos

coscosexp1

, (4.6)

i and e are the angles between incident radiation & target normal and target

normal & detector and were equal to 45,

At energies <10 keV, the incoherent scattered energy is <200 eV (strip width)

away from incident energy, therefore, in a strip both incident and scattered

energies were taken as mean energy En of strip i.e. En(i)=En(e)=En.

(c) The number of scattered photons in a strip detected by the detector depends upon

the absolute efficiency ε of the detector. In turn, the efficiency depends upon the

transmission of X-rays through the air column between target and detector,

detector window and the absorption of X-rays in the detector material.

Thus, ε(En), efficiency of detector is to be calculated at the strip mean energy

using formulation,

SinSiBenBeairnairn tEtEtEE exp1expexp (4.7)

where,

μair, μBe and μSi are the absorption coefficients of air, Be and Si at En energy and

tair is air column between target and detector window,

tBe and tSi are thickness of Be window and detector material.

From relation (4.1), intensity In of each strip falling on the target area is evaluated as,

nAlAlEnAlntotal

AlEn EteiE

MNI n

,90

(4.8)

Chapter 4 86

The weighted average energy of the Bremsstrahlung is,

nn

nnn

avg I

IEE (4.9)

Total intensity falling on the target,

n

nII (4.10)

The coherent Rayleigh and incoherent Klien-Nishina scattering cross-section were

calculated for Al at the mean strip energies from F(x,Z) and S(x,Z) tabulations of Hubbell

et al. (1975) and absorption coefficients at different energies were determined from

XCOM program (Berger et al., 1987). Hence the weighted average energy and intensity

values have been used as characters of incident exciting flux from X-ray tube.

4.2.2 Calculations of Mg X-Ray Fluorescence Cross-sections

Counts under the Mg group of X-rays are given as already explained in chapter 2 by eqn.

(2.5),

MgtMAeaiaSN MgMg

M

vairairoMg

*21

44

(4.11)

The involved terms have their usual meanings and correspond to M

target and Mg group of X-rays. The corresponding fluorescence cross-section,

GSMgtAMN

oMgv

MMgMg

* (4.12)

where eaiaG airair 4421

(4.13)

GSo factor is the incident photons falling upon the target area seen by the detector.

87 Chapter 4

The factor GSo for an experimental target in the set-up at excitation energy was

determined by irradiating a selected low Z target to excite its K shell in the same set-up

with the same flux. The selection of low Z target for each experimental target was made

such that M5 edge energy of experimental target was equal to K edge energy of low Z

target nearly within the detector resolution. Table 4.2 shows the combination of low Z

target and experimental targets.

Table 4.2 List of edge energies in combinations; M5 edge of experimental targets (U, Th, Pb, Au and Pt) and K edge of targets in combination (K, S and P).

(experimental target,

low Z element)

(M5 edge, K edge)

(Energies in keV)

(U, K) (3.552, 3.607)

(Th, K) (3.332, 3.607)

(Pb, S) (2.484, 2.472)

(Au, P) (2.206, 2.144)

(Pt, P) (2.122, 2.144)

Wherever the difference in the K and M5 edge energies were greater than 200 eV,

the width of the strip at lowest energy was increased exactly equal to the difference

energy (e.g. in case of (Th, K), it was made 275 eV).

In this way, the weighted average energy and intensity remain the same for each

combination and are being given in table 4.3.

Chapter 4 88

Table 4.3 Weighted average energies and total intensity at different voltages for different combinations of targets.

Voltage (kV)

Eavg (keV)/I (Pt, P) (Au, P) (Pb, S) (Th, K) (U, K)

6 3.05/20565 3.05/205645 3.366/14808 4.145/6117

6.5 4.47/6769

8 3.4/65100 3.4/65100 4.05/41100 5.19/21200 5.19/21200 9 3.57/80600 3.57/80600

10 3.59/105000 3.59/105000 4.19/72100 5.27/40600 5.27/40600 11 4.03/111000 4.03/111000

12 4.98/116000 6.29/71900 6.29/71900

13 5.63/115000

14 7.38/109000 7.38/109000

For K excitations of low Z targets,

*0

KK

KK

KtMNGS

(4.14)

the terms on R.H.S. are for K X-ray targets.

The expression for production cross-section in b/atom for a group of M X-rays, Mg (g=

ξ, αβ, γ & m) becomes;

MgtMN

KtMN

MgKK

KMMgMg

K

(4.15)

For each *Mg calculation, ’s and ε’s were evaluated as mentioned in relations

(4.6) & (4.7) for desired incident and emitted energies. K X-ray production cross-section

*K has been known at the net incident energy from computer software KCSPIF

developed earlier in our laboratory (Bansal and Mittal, 2009).

89 Chapter 4

Peak area extraction for gth (g=, , ) group of M X-rays has been done by

marking the centroid of groups on a calibrated energy scale. In case of hump, the gross

area of half peak on the side of centroid that is comparatively free from adjacent peak

interference was selected by highlighting the channels under half peak. Doubling this

area gives us the total gross area for the gth group. For background subtraction, lowest

background counts on that side was multiplied by the total number of channels covered

by the group and subtracted from the gross area. For Mm group where peak hump was

diminishing, counts have been collected by Gaussian fitting software in ORIGIN 6.0.

Different M X-ray peaks extracted for Au at 9 kV/0.2 mA tube power along with actual

background subtracted spectrum have been shown below (Fig. 4.4).

After determining the peak area under various peaks, target self absorption

corrections factors and detector efficiency at element energies and production cross-

section for low Z element used in combination (listed in table. 4.4), M sub-shell X-ray

fluorescence cross-section have been evaluated and listed in last column of table 4.4

alongwith experimental errors.

Chapter 4 90

Fig. 4.4 Various M X-ray groups (M, M, M, Mm) resolved for Au at 9 kV/0.2 mA.

60 80 100 120 140 160 180 200 220 2400

4000

8000

12000

16000

116 118 120 122 124 1260

20406080

100120140160

M

Cou

nts/

7200

sec

Channel number

Background subtracted Actual Spectra

M peak

Mm

M

M

M

Coun

ts/14

400s

ec

Channel number

Background subtracted Actual Spectra

M peak M peak M peak Mm peak

91 Chapter 4

Table 4.4 List of counts (NMg) under various peaks, detector efficiency (Mg) at element energies and target self absorption correction factors Mg for both experimental and low Z element along with K XRF cross-section of low Z element and hence evaluated M XRF cross-sections.

Element Excitation

Energy in

keV

Experimental Element Low Z element Measured

Mg in

b/atom

Group Mg

(energy in keV)

Counts in

7500 sec

(NMg)

ε (Mg) (t)Mg Group Kg

(energy in keV)

Counts in

(NK) (K) t(Mg)

K in

b/atom

U/K 4.466 M (2.49) 21750 0.14029 0.00030 K (3.31) 929.7 0.40439 0.00152 5278.0 556 (44)

M (3.26) 2067750 0.38585 0.00039 15276 (1069)

M (3.56) 107250 0.48044 0.00029 K (3.59) 144 0.48924 0.00164 504.1 686 (55)

Mm (4.16) --- 0.62899 0.00029 ---

5.19 M 10500 0.14029 0.00035 K (3.31) 492.4 0.40439 0.00195 3558.7 385 (31)

M 932250 0.38585 0.00047 9239 (647)

M 51000 0.48044 0.00033 K (3.59) 80.9 0.48924 0.00214 346.8 452 (36)

Mm --- 0.62899 0.00034 ---

5.27 M 18000 0.14029 0.00036 K (3.31) 814.4 0.40439 0.00199 3418.0 385 (31)

M 1590000 0.38585 0.00048 9168 (642)

M 99750 0.48044 0.00034 K (3.59) 131.9 0.48924 0.00219 333.6 528 (42)

Mm --- 0.62899 0.00035 ---

6.29 M 27750 0.14029 0.00041 K (3.31) 1073.5 0.40439 0.00253 2140.0 308 (25)

M 2196750 0.38585 0.00059 6243 (437)

M 148500 0.48044 0.00039 K (3.59) 178.8 0.48924 0.00287 210.3 415 (33)

Mm --- 0.62899 0.0004 ---

7.38 M 36000 0.14029 0.00046 K (3.31) 1428.1 0.40439 0.00299 1395.3 208 (17)

M 2810250 0.38585 0.00069 3936 (276)

M 209250 0.48044 0.00043 K (3.59) 273.3 0.48924 0.00348 136.1 271 (22)

Mm --- 0.62899 0.00046 ---

Chapter 4 92

Element Excitation

Energy in

keV

Experimental Element Low Z element Measured

Mg in

b/atom

Group Mg

(energy in keV)

Counts in

7500 sec

(NMg)

ε (Mg) (t)Mg Group Kg

(energy in keV)

Counts in

(NK) (K) t(Mg)

K in

b/atom

Th/K 4.145 M (2.35) 12000 0.09834 0.00028 K (3.31) 691.7 0.40439 0.00133 6388.10 691 (55)

M (3.07) 1699500 0.34946 0.00035 21273 (1489)

M (3.36) 48000 0.42176 0.00026 668 (53)

Mm (4.08) --- 0.61301 0.00026 K (3.59) 100.7 0.48924 0.00141 605.52 ---

5.19 M 7500 0.09834 0.00034 K 492.4 0.40439 0.00195 3558.70 373 (30)

M 1032000 0.34946 0.00046 11210 (785)

M 37500 0.42176 0.00032 484 (39)

Mm --- 0.61301 0.00032 K 80.9 0.48924 0.00214 346.80 ---

5.27 M 11925 0.09834 0.00035 K 814.4 0.40439 0.00199 3418.00 365 (29)

M 1756500 0.34946 0.00047 11102 (777)

M 66750 0.42176 0.00033 505 (40)

Mm --- 0.61301 0.00032 K 131.9 0.48924 0.00219 333.60 ---

6.29 M 17250 0.09834 0.00040 K 1073.5 0.40439 0.00253 2140.00 276 (22)

M 2475750 0.34946 0.00059 7635 (534)

M 96750 0.42176 0.00037 386 (31)

Mm --- 0.61301 0.00037 K 178.8 0.48924 0.00286 210.30 ---

7.38 M 20250 0.09834 0.00045 K 1428.1 0.40439 0.00299 1395.30 171 (14)

M 3060750 0.34946 0.00068 4700 (329)

M 125250 0.42176 0.00041 263 (21)

Mm --- 0.61301 0.00041 K 273.3 0.48924 0.00347 136.08 ---

93 Chapter 4

Element Excitation

Energy in

keV

Experimental Element Low Z element Measured

Mg in

b/atom

Group Mg

(energy in keV)

Counts in

15000 sec

(NMg)

ε (Mg) (t)Mg Group Kg

(energy in keV)

Counts in

(NK) (K) t(Mg)

K in

b/atom

Pb/S 3.37 M (1.84) 3300 0.00888 0.00022 K (2.31) 219.3 0.08667 0.00056 3663.0 590 (53)

M (2.39) 1320000 0.11182 0.00028 14997 (1050)

M (2.65) 30000 0.19670 0.00017 K (2.47) 23.1 0.13427 0.00058 170.6 215 (17)

Mm (3.09) 31500 0.35694 0.00019 117 (9)

4.05 M 1200 0.00888 0.00026 K 85.2 0.08667 0.00081 2251.2 419 (38)

M 469500 0.11182 0.00034 10405 (7280

M 27000 0.19670 0.00019 K 19.1 0.13427 0.00085 107.3 194 (16)

Mm 54000 0.35694 0.00021 196 (16)

4.19 M 1650 0.00888 0.00027 K 133.4 0.08667 0.00086 2058.3 343 (31)

M 771000 0.11182 0.00036 9606 (672)

M 31500 0.19670 0.00020 K 35.3 0.13427 0.00090 98.2 112 (9)

Mm 93000 0.35694 0.00022 173 (14)

4.98 M 1575 0.00888 0.00031 K 180.5 0.08667 0.00115 1302.1 177 (16)

M 1023000 0.11182 0.00044 6440 (451)

M 43500 0.19670 0.00023 K 52.9 0.13427 0.00124 61.7 80 (6)

Mm 105000 0.35694 0.00025 99 (8)

5.63 M 2250 0.00888 0.00034 K 203.5 0.08667 0.00138 935.7 176 (16)

M 1173000 0.11182 0.00050 4951 (347)

M 66000 0.19670 0.00024 K 64.7 0.13427 0.00151 43.8 82 (7)

Mm 139500 0.35694 0.00027 86 (7)

Chapter 4 94

Element Excitation

Energy (keV)

Experimental Element Low Z element Measured

Mg in

b/atom

Group(energy in

keV)

Counts in

15000 sec

(NMg)

Ε t Group(energy in

keV)

Counts/sec t 휎∗

Au/P 3.05 M (1.67) 600 0.00179 0.00019 K (2.02) 60.42 0.02744 0.00052 3195.3 515 (62)

M (2.16) 477600 0.05267 0.00024 11942 (836)

M (2.40) 10650 0.11439 0.00017 180 ()14

Mm (2.80) 12000 0.25143 0.00016 95 ()8

3.40 M 150 0.00179 0.00021 K 16.54 0.02744 0.00064 2402.5 509 (61)

M 131100 0.05267 0.00028 9794 (686)

M 7800 0.11439 0.00018 412 (33)

Mm 8850 0.25143 0.00018 218 ()17

3.57 M 180 0.00179 0.00022 K 20.86 0.02744 0.00070 2114.2 370 (44)

M 180000 0.05267 0.00028 9839 (689)

M 10800 0.11439 0.00019 423 (34)

Mm 10500 0.25143 0.00018 191 (15)

3.59 M 270 0.00179 0.00022 K 25.72 0.02744 0.00071 2083.5 428 (51)

M 202350 0.05267 0.00029 8861 (620)

M 12000 0.11439 0.00019 379 (30)

Mm 15900 0.25143 0.00018 232 (19)

4.03 M 300 0.00179 0.00179 K 29.56 0.02744 0.00088 1538.9 354 (42)

M 32400 0.05267 0.05267 7650 (536)

M 36000 0.11439 0.11439 377 (30)

Mm 42000 0.25143 0.25143 178 (14)

95 Chapter 4

Element Excitation

Energy

(keV)

Experimental Element Low Z element Measured

Mg in

b/atom

Group Mg

(energy in keV)

Counts in

15000 sec

(NMg)

ε (Mg) (t)Mg Group Kg

(energy in keV)

Counts in

(NK) (K) t(Mg)

K in

b/atom

Pt/P 3.05 M (1.60) 285 0.00091 0.00019 K (2.02)

60.41 0.02744 0.00052 3195.3 514 (62)

M (2.09) 336900 0.03846 0.00024 11777 (824)

M (2.33) 13350 0.09293 0.00016 286 (23)

Mm (2.71) 10200 0.21749 0.00016 95 (8)

3.4 M 81 0.00091 0.00021 K 16.54 0.02744 0.00064 2402.5 458 (55)

M 114450 0.03846 0.00027 11844 (829)

M 5550 0.09293 0.00018 368 (29)

Mm 7200 0.21749 0.00017 210 (17)

3.57 M 150 0.00091 0.00022 K 20.86 0.02744 0.00070 2114.2 387 (46)

M 147150 0.03846 0.00029 10875 (761)

M 7350 0.09293 0.00018 360 (29)

Mm 9300 0.21749 0.00018 199 (16)

3.59 M 150 0.00091 0.00023 K 25.72 0.02744 0.00071 2083.5 494 (59)

M 162600 0.03846 0.00029 9627 (674)

M 8700 0.09293 0.00019 339 (27)

Mm 9750 0.21749 0.00018 167 (13)

4.03 M 156 0.00091 0.00025 K 29.56 0.02744 0.00088 1538.9 345 (41)

M 186150 0.03846 0.00034 7480 (524)

M 9300 0.09293 0.00020 262 (21)

Mm 11700 0.21749 0.00019 145 (12)

Chapter 4 96

4.3 RESULTS AND DISCUSSION

The measured experimental M X-ray group cross-sections listed in last column of

table 4.4 are alongwith experimental errors. The error in the values is the squared sum of

uncertainties in different individual parameters used to measure X-ray production cross-

section as target self absorption correction factor (~7%), detector efficiency (5-7%), peak

area extraction (0.1 to 12% for M, < 0.5% for M, <1% M and Mm) etc.

The authenticity and reliability of present method of measurements and

calculations has been judged in terms L X-ray fluorescence cross-section measurements

as data on L cross-sections is moderate as compared to that for M X-rays. L X-ray

measurements on Ag at 6.5 kV anode voltage (Eavg = 4.466 keV) were performed with

potassium as K X-ray target for incident flux normalization as the edge energies 3.351

and 3.607 keV for L3 of Ag and K of potassium are just 256 eV apart. The measured

cross-sections with 7% uncertainties for L, L, L and L group of Ag along with semi-

empirical/theoretical values generated from software LCSGEN (Mittal et al., 2001) are

listed in table 4.5.

Table 4.5 List of measured L, L, L and L fluorescence cross-sections along with semi-empirical/theoretical values generated from software LCSGEN (Mittal et al., 2001) for Ag at 4.466 keV photon energy.

(L X-ray group,

Lg)

*Lg (b/atom)

Experimental semi-empirical/theoretical L 188(13) 169/193

L 5242(367) 4647/5328

L 1952(137) 2793/2910

L 275(19) 259/260

97 Chapter 4

The good agreement of measured values within uncertainties with semi-

empirical/theoretical values (except for L) supports the present method of measurement

and result evaluation procedure.

At this stage no experimental or theoretical values of the cross-sections at such

low energies are available for comparison and to check the present results. Therefore,

theoretical cross-section values at experimental incident energies were evaluated from the

available tabulated data on fine parameters.

Theoretical M X-ray fluorescence cross-sections

Theoretical values of cross-sections have been calculated by using two sets of

fluorescence yields Mi and fractional radiative decay rates MigF based on DHS and DF

models using the formulations (eqn. 1.7) already given in chapter 1;

In the first set, DF model based fluorescence yield (Chauhan and Puri, 2008) and

fractional decay rates of Chen and Crasemann (1984) were used. In the second set, DHS

model based fluorescence yields (Chauhan and Puri, 2008) and fractional radiative decay

rates of Bhalla (1970) were used. In both the sets Coster-Kronig transition yields Mijf of

Chauhan and Puri (2008) and photoionization cross-sections Mi of Scofield (1973) were

used. The experimental and calculated theoretical M X-ray cross-section values are being

given in table 4.6.

Chapter 4 98

Table 4.6 List of measured and theoretical M X-ray production cross-sections.

Element Voltage

(kV)

Cross-section (b/atom) *M *

M * M *

Mm

Exp. Theory

DF/DHS

Exp. Theory

DF/DHS

Exp. Theory

DF/DHS

Exp. Theory

DF/DHS

Pt 6 514 (62) 577 /525 11777 (824) 12549/11689 286 (23) 393/365 95 (8) 158/119

8 458 (55) 464/421 11844 (829) 10092/9401 368 (29) 379/352 210 (17) 197/154

9 387 (46) 411/374 10875 (761) 8953/8340 360 (29) 350/325 199 (16) 184/144

10 494 (59) 406/369 9627 (674) 8831/8227 339 (27) 346/322 167 (13) 183/143

11 345 (41) 306/278 7480 (524) 6666/6210 261 (21) 286/265 145 (12) 155/122

Au 6 515 (62) 579/521 11942 (836) 12871/12107 180 (14) 386/364 95 (8) 63/31

8 509 (61) 480/432 9794 (686) 10583/9952 412 (33) 355/333 218 (17) 152/113

9 370 (44) 446/401 9839 (689) 9838/9252 423 (34) 377/355 191 (15) 203/160

10 428 (51) 440/396 8861 (620) 9705/9126 379 (30) 374/351 232 (19) 201/156

11 354 (42) 332/299 7650 (536) 7325/6888 377 (30) 308/289 178 (14) 171/133

Pb 6 590 (53) 567/520 14997(1050) 13250/12708 215 (17) 413/345 117 (9) 81/71

8 419 (38) 406/373 10405 (728) 9436/9051 194 (16) 388/326 196 (16) 223/198

10 343 (31) 373/343 9606 (672) 8660/8306 112 (9) 366/307 173 (14) 212/188

12 177 (16) 242/223 6440 (451) 5633/5402 80 (6) 272/228 99 (8) 163/144

99 Chapter 4

13 176 (16) 185/170 4950 (347) 4331/4154 82 (7) 217/182 88 (7) 134/93

Th 6 691 (55) 610/596 21273(1489) 15641/15468 668 (53) 593/551 --- 162/162

8 373 (30) 387/378 11210 (785) 9844/9747 484 (39) 520/480 --- 320/292

10 365 (29) 314/364 11103 (777) 9471/9377 505 (40) 506/467 --- 314/285

12 275 (22) 238/232 7635 (534) 6043/5984 386 (31) 368/340 --- 240/218

14 171 (14) 158/154 4700 (329) 4009/3970 263 (21) 274/253 --- 184/167

U 6.5 556 (44) 567/571 15276(1069) 15025/15125 686 (55) 588/559 --- 161/179

8 385 (31) 381/384 9239 (647) 10126/10190 452 (36) 463/440 --- 127/141

10 385 (31) 400/404 9168 (642) 10493/10580 528 (42) 490/466 --- 238/250

12 308 (25) 266/269 6243 (437) 6994/7050 415 (33) 408/388 --- 248/257

14 208 (17) 177/178 3936 (276) 4641/4678 271 (22) 304/290 --- 192/198

Chapter 4 100

The comparison of measured values of M x-ray production cross-section for the

groups Mξ, Mαβ, Mγ and Mm for experimental targets Pt, Au, Pb, Th and U with the

calculated theoretical values based on DF and DHS models shows the experimental

values of the cross-sections, generally, agree with the theoretical values within

experimental uncertainties (~ 10%) but certain exceptions are there. In Pt, for M group

at 10 kV the agreement is within 20%, the values are within 15% of DHS values for M

group and the measured values at 6 kV agree with DHS approach within 20% uncertainty

for M and Mm groups. In Au, for M group, results approach theory with uncertainties

>20% at 6 and 11 KV anode voltage, Mm group agrees more with DF approach than

DHS but agreement increase with energy. In case of Pb, for M group, experimental

results are 50% of the theoretical results. This may be due the error in peak area

extraction as M group falls in the region of Ar K x-rays. For Th, M group value

agrees within 20%. For Th and U, measurements could not be possible for Mm group as

it falls in the region of Bramsstrahlung where some spurious peaks are there from the

experimental set-up. So, the accurate peak area extraction could not be procured.

From all the above comparisons, it is justified that the present method of analysis

for XRF cross-section measurements is compatible with the existing methods in literature

as mentioned in the introduction section. The quantification of continuous Bremssrahlung

in terms of weighted average energy and intensity that produced M X-ray fluorescence

cross-sections fairly supported by theoretical values can be used confidently in future for

further studies. So far in literature, such approach to quantify continuous Bremsstrahlung

in terms of weighted average energy and intensity has not been followed for similar work

but present measurements lead to the confidence to make use of such an approach.