Annexure to the published paper “Trapping rate of positrons, DBAR line shape parameters and calculation of free volume hole size in polymeric materials using PALS data” by Blaise Lobo et al., International Journal of ChemTech Research[CODEN (USA): IJCRGG ISSN: 0974-4290] Vol 6, No. 3, pp 1847-1849, May-June 2014.
Extraction of Line-Shape Parameters from DBAR Spectrum using a Fortran-77 program.
Preeti B Hammannavar1, Manjunath Y H1, Chetan H1, Priyanka I1, Basavarajeshwari M B1, Bhajantri R F2, Ravindrachary V3 and Blaise Lobo1*
1Department of Physics, Karnatak Science College, Karnatak University, Dharwad 580001, India.
2Department of Physics, Karnatak University, Pavatenagar, Dharwad 580001, Karnataka, India.
3Department of Physics, Mangalore University, Mangalagangothri , Mangalore 574199, India.
*E-Mail :
Abstract.
A source code in Fortran-77 in order to extract the line-shape parameters from the Doppler Broadening of Annihilation Radiation (DBAR) spectrum is presented. This is preceded by a discussion on the significance of line-shape parameters, especially the S-parameter and W- parameter, and the experimental difficulties involved in extracting the latter.
Keywords: Positronium, Polymeric Materials, Positron Annihilation Spectroscopy, DBAR, Line shape parameters.
PACS: 36.10.Dr, 78.70.Bj, 71.60.+z, 83.80.Xz, 71.10.-w
INTRODUCTION:
Positron annihilation spectroscopy (PAS) is an established nuclear technique for the study of microstructure of condensed matter[1], using positron as a nano-probe. PAS comprises of three conventional techniques, namely Positron Annihilation Lifetime Spectroscopy (PALS), Angular Correlation of Annihilation Radiation (ACAR) and Doppler Broadening of Annihilation Radiation (DBAR). The development of slow positron beams has led to surface studies and a study of microstructure of materials at desired depths within the material under study.
The positrons from either a slow positron beam or a radio-isotope (like sodium-22, for example), when incident on the material undergoes a process of thermalization and diffusion in the material, and ultimately annihilates with one of the electrons in the material, resulting in the emission of usually two gamma ray photons (511 keV) from the annihilation site in opposite direction. These annihilation photons contain information about the electron density and momentum distribution at the site of positron-electron annihilation in the material[2]. The gamma rays easily penetrate out of the sample and can be studied using well established energy spectroscopy and timing spectroscopy techniques of experimental nuclear physics[3]. Hence, PAS is a non-destructive set of techniques for probing the micro-structure of materials. DBAR is one of the popular conventional techniques of PAS, since it requires only an hour to acquire the DBAR spectrum for a particular sample, whereas acquisition of an ACAR spectrum takes several days. However, the resolution of ACAR spectrum is at least five times better than that of DBAR spectrum, for extracting momentum distribution of electrons at the site of positron annihilation.
EXPERIMENTAL:
A source-sample sandwich was prepared with a 10 μCisodium 22 (Na22) source deposited on a thin kapton foil, sandwiched on both sides by polymeric samples (polyvinylalcohol: PVA) in the form of a thick film (1mm). The source sample sandwich was placed at a distance of 10 cm from the beryllium window of the HPGe detector (92 cc). The energy spectrum was recorded using a high resolution HPGe (High Purity Germanium Detector). The detectorhas an energy resolution of 1.6 keV, measured at 662 keV.Hence, it is expected from the linearity of the energy resolution (calibration curve) that the full width at half maximum (FWHM) of a normally broadened photo-peak at 511 keV is 1.3 keV; however, we get a FWHM of 2.6 keV for the 511 keV annihilation peak, due to additional broadening caused by Doppler effect. The spectrum was acquired to get a peak count of the order of 105 at 511 keV. The energy spectrum was analyzed using a DB program (in Fortran 77 code) developed by us, in order to extract the line-shape parameters. The details of the source code are discussed in this paper.
RESULTS AND DISCUSSION:
The technique Doppler Broadening of Annihilation Radiation (DBAR), also known as Doppler Broadening Spectroscopy (DBS) is used to extract information about the momentum distribution of electrons at the site of positron-electron annihilation in the material. The finite momentum of the annihilating electron – positron pair results in the annihilation photons getting Doppler shifted from 511 keV by an amount ΔE = (c × PL /2), where c is the velocity of light in vacuum and PL is the longitudinal component of momentum the annihilating electron-positron pair[4]. A large number of such annihilation events (say 106 to 107, depending on activity of the positron source and the acquisition time) are measured using a high resolution HPGe detector, to form the DBAR energy spectrum. The energy profile, which peaks at 511 keV, has a Full Width at Half Maximum (FWHM) more than double that expected from normal broadening at that energy. The overall broadening around 511 keV is due to accumulation of individual Doppler Shifts along the direction of annihilation. Since Doppler changes in energy are small, typically having a maximum value of ΔE of the order of 20 keV, we need to use a high resolution detector for DBAR energy spectroscopy. The energy spectrum is used to extract two line-shape parameters; namely, S- parameter and W- parameter. The S- parameter is the ratio of the area under a carefully selected region around the 511 keV peak to the total area under the spectrum (energy profile) in the region of interest (ROI). The S- parameter corresponds to positrons annihilating with low momentum electrons, for example, valence electrons, and is sensitive to open volume defects like vacancies and free volume holes in materials[5]. An increase in S –parameter implies the presence of vacancy type defects in the material.
Figure (1): Anillustrative DBAR spectrum, corresponding to the Doppler Broadened 511 keV annihilation gamma in a polymer sample. The S- parameter is the area under the curve in the central (peak) region divided by the total area in the region of interest (ROI). The W- parameter is the area under the wing regions (shaded on either side) divided by the total area of the region of interest. For the program presented in this paper, a total of 1000 channels are considered (ROI), with peak around 500.
The W- parameter is calculated as the area in wing regions on either side of the 511 keVpeak, significantly far from the peak region, divided by the total area in the region of interest. The W- parameter extracted from DBAR spectrum contains information about core electron structure in the material, although it still contains some information about the valence electrons. However, using a single HPGe detector, there is a major difficulty in calculating the S- parameter due to high background (from Compton scattering of birth and annihilation gamma as well as charge collection pile- up) and also a low count rate at high ΔE.
Although the W- parameter contains information about positrons annihilating with core electrons in the material medium, this information is masked by the high background. So, core electron information cannot be satisfactorily extracted using a single HPGe detector. Hence, element specific information is lost. In order to overcome this problem, Coincidence Doppler Broadening Spectroscopy (CDBS) can be used.In CDBS, the positron – electron annihilation spectra are recorded using two HPGe detectors in coincidence mode. This significantly improves the peak to background ratio, especially in the wing regions surrounding the 511 keV annihilation gamma energy profile. Therefore, the contribution from core electrons and also, element- specific information can be extracted using CDBS. In other words, the experimental arrangement of CDBS results in very low background levels. This permits core electrons to be observed accurately, and helps to determine the chemical environment at the annihilation site of the positron. CDBS is desirable over ACAR due to the simplicity of its operation and also an additional benefit of probing the chemical environment at the positron- electron annihilation site.
The Source Code for extracting Line-shape parameters from the DBAR / CDBS spectrum follows:
C Program in Fortran-77 for DB Spectrum Analysis
C Program to extract Line Shape parameters
C First cut out a portion containing 1000 channels….
C from the energy spectrum, with 511 keV peak at Channel 500
C The output file is dbo.out and should be renamed as required
dimension id(1000), idd(1000)
integera,count,peak
write (*,*)' Program for DB spectrum analysis'
max = 0
write (*,*)'Enter the input file name'
do 10 count=1,1000
read (1,*)id(count)
a=id(count)
if (a.gt.max) then
max = a
peak = count
endif
if ((count.ge.850).and.(count.le.999))then
b1= b1+id(count)
endif
if ((count.ge.1).and.(count.le.150))then
b2= b2+id(count)
endif
10 continue
bkg1 = b1/150
bkg2=b2/150
do 20 ic=1,500
idd(ic)=id(ic)-bkg2+40
20 continue
do 25 ic=501,1000
idd(ic)=id(ic)-bkg1+35
25 continue
total = 0
open (unit=2,file='dbo.out',status='new')
do 30 iv=1,1000
write (2,*)idd(iv)
30 continue
write (*,*)'Enter the region of interest wrt peak'
read (*,*)ix
ix1=peak-ix
ix2=peak+ix
do 35 id1= ix1,ix2
total = total+idd(id1)
35 continue
write (2,*) 'Peak is at',peak
write (2,*)' Peak Count is', max
write (2,*)' Total is', total
write (*,*)'Enter the S parameter region of interest '
read (*,*)is
is1=peak-is
is2=peak+is
do 40 ic=is1,is2
psum=psum+idd(ic)
40 continue
S= psum/total
write (2,*)' S-parameter is',S
write (*,*)'Enter the W parameter region of interest'
write(*,*)' Enter lower value first & then higher value'
read (*,*)iw, iwa
iw1=peak-iwa
iw2=peak-iw
ws1=0
do 45 ic=iw1,iw2
ws1=ws1+idd(ic)
45 continue
iw3=peak+iw
iw4=peak+iwa
ws2=0
do 55 ic=iw3,iw4
ws2=ws2+idd(ic)
55 continue
W= (ws1+ws2)/total
write (2,*)' W-parameter is',W
y=ws1+ws2
write (2,*)' Y-parameter is',y
sbw = s/w
write (2,*)'SBW-parameter is',sbw
r=(S-W)/(S+W)
write (2,*)' R-parameter is',r
stop
end
CONCLUSION:
A source code in Fortran-77 has been written in order to calculate the Line-shape parameters like S- parameter, W-parameter etc., which are vital for the understanding of momentum distribution of electrons in the sample studied using Doppler Broadening of annihilation radiation. This source code has been compiled to form an executable file using a Fortran 77 compiler, and the executable file has been successfully used for the extraction of line-shape parameters from the DBAR spectrum. The DBAR program extracts the background information from the input file. The S and W parameters obtained from the program can be used in research work provided care is taken to select a proper number of channels about the peak (peak region and wing regions).
[1]Dupasquier A E, Hautojärvi P in “Positrons in Solids” Berlin: Springer-Verlag, 1979.
[2]R W Siegel “Positron Annihilation Spectroscopy”, Annual Review of Materials Science10 (1), 393-425, 1980.
[3]W Brandt and A Dupasquier “Positron Solid State Physics” North Holland, Amsterdam, 1983.,
[4]Blaise Lobo “Iodine Doping and heat treatment studies on some polymers using positron annihilation spectroscopy and thermal analysis” Ph.D Thesis, Mangalore University Mangalgangothri, Karnataka, India, 1999.
[5]Lobo Blaise, Ranganath M R, Ravichandran T S G, Ravindrachary V, VenugopalRao G and Gopal S “Iodine doped polyvinylalcohol using positron annihilation spectroscopy” Phys. Rev. B 1999, 59, 13693-13698.