- Email: [email protected]
An accurate calculations of the 511 keV line background in positron annihilation doppler broadening studies
Nuclear Instruments and Methods 187 (1981) 581-585 North-Holland Publishing Company
581
AN ACCURATE CALCULATION OF THE 511 keV LINE BACKGROUND IN POSITRON ANNIHILATION DOPPLER BROADENING STUDIES I. CHAGLAR, P. RICE-EVANS, F.A.R. EL KHANGI and A.A. BERRY Department of Physics, Bedford College, University of London, Regent's Park, London, NW1 4NS, England Received 5 March 1981
A simple method for an accurate subtraction of the underlying non-linear background from positron annihilation spectra is described. The method employs a step-function, complemented by a modified version of the error function, without assuming any functional form of the 511 keV peak. Evidence of the accuracy of the method is presented.
1. Introduction Positron annihilation studies have over the last two decades been the subject of a continuously growing interest. The value of the positron annihilation technique has been demonstrated by many investigators in studies of the properties of lattice defects and the internal structure of materials [1,2]. In the absence of defects in a metal positrons annihilate mainly with low-momentum conduction electrons and With higher momentum core electrons in proportions characteristic of the~metal. In metals containing defects positrons are likely to be trapped in potential wells created by the lattice irregularities and the resulting annihilation characteristics will be correspondingly different. The Doppler broadening technique is one of the three established methods used in the studies of annihilation in m a t t e r - t h e others being measurements on the photon angular correlations and on the positron lifetimes. The latter assesses electron densities at the annihilation sites; and in the first two, thermalised positrons are assumed to probe the momentum distributions of the annihilating electrons. Although the Doppler broadening approach does not possess the fine resolving power offered by the angular correlation technique, its improved statistics due to fast data accumulation and its versatility compensate for this and make it most suitable for many defect studies. The distribution of the momentum component of the annihilating positron-electron pair along the line of the photon emission is due mainly to the motion of the electron and to a lesser extent to that of the 0029-554X/81/0000-0000/$02.50 © North-Holland
positron. This momentum profile is transformed into the intrinsic energy distribution of the 511 keV quanta and is depicted in the observed spectrum after having been broadened by the spectroscopy system. In Doppler broadened gamma-ray peak shape analysis, the changes in the shape of the annihilation line are relatively small and highly sensitive line shape parameters are therefore required for their study. In such analysis it is expected that the background underlying the 511 keV peak has been removed. Despite the importance of this, very little mention has been made in the literature of details of background subtraction methods. In this article we present results of a simple and model-independent positron annihilation background subtraction technique suitable for line shape analysis.
2. Expedmental procedure The Doppler broadened gamma-ray spectra for these studies were recorded using a high resolution intrinsic germanium planar detector, incorporated with an optical feedback pre-amplifier. The pre-amplitier pulses were amplified by a spectroscopy amplifier and unipolar output pulses from the amplifier were then fed directly to 8192 channel analog-to-digital converter with a conversion time of 4.5/as plus pulse rise time. Each pulse was digitised linearly according to its amplitude and subsequently stored in an 8k analyser memory. During the experiment the whole system was kept in a temperature controlled room (-+0.1°C stability)
582
L Chaglar et al. / Calculation of the 511 ke V line background
and operated remotely from outside. The energy dispersion of the analyser and the overall resolution of the system were respectively 94 eV/channel and 1.15 keV for the 514 keV 8SSr line. The specimen material was single crystal cadmium of 6N purity. Carrier-free 22Na -C1 positron sources were evaporated onto the central regions of two 10 mm diameter specimen discs which were then assembled in a sandwich configuration. Although 22Na, because of its easy availability and long half-life, is one of the most commonly used positron emitters, it presents in Doppler studies the handicap of a high background from the 1.28 MeV gamma-ray. Measurements were conducted between 4.2 K and 420 K in a cryostat, and between 293 K and the specimen melting temperature in a furnace. For both experimental arrangements the vacuum condition was about 10 -6 Torr. Over the temperature range 4 . 2 -
28.00
o
I00 K the cryostat was cooled with liquid helium, and from 77 K to 420 K with liquid nitrogen [3]. Each point, shown in fig. 2, corresponds to a line conraining 900 000 counts.
3. Significance of background underlying the 511 keV peak Gamma-ray peaks obtained with semiconductor detectors are usually asymmetric and have generally a non-linear underlying background. These are caused partly by incomplete charge collection and p h o t o electron escape from the active volume of the detector and partly by scattering of gamma-rays. It can be seen from fig. 1 that the underlying background, extending from both the low and the high energy sides of the peak, can be split into three sec-
¢N
e
0
x
X
o
24.00
16 14
°° o o
1210-
20.00, 8 e
6
o
4
16,00 o
80
40
o
12.00
120
160
o
o CE)
e
e
o
o o
8.00
ee
o
et)
4.00 e --~% °
d~o
o .
.
.
.
o
e~°
o o
ee o oe
o e
o
o e 8
: e~
~'~-
0.00
~ _ ~
C I
0.00
~ o~ooo
l 40.00
l
1
80.00
I 120.00
CHANNEL
I
D I
1
160.00
NUMBER
Fig. 1. Annihilation line shape with the non-linear part of the underlying background, The background subtracted line is shown in the inset. The solid line in either case represents the step-function background.
L Chaglar et aL / Calculation o f th e 511 ke V line background
tions: the low and the high energy parts AB and CD show a similar, linear character and the smoothly varying nonqinear central region joins these two wings. The high energy wing, CD, is generated by the 1.28 MeV gamma-rays in 22Na and the natural background, and is present at a reasonably constant level throughout the defined region AD. Other contributions present in the region AC result from the 511 keV photons. The asymmetry of a gamma-ray peak, the nonlinearity of its underlying background, and the ratio of the overall intensity of the background to that of the actual peak are dependent on the gamma-ray spectroscopy system. The instrumental contribution to the observed broadening of the intrinsic energy distribution of the annihilation quanta also includes these characteristics of the system. Ideally, in a detailed line shape analysis, these should be taken into account separately. In the studies of positron annihilation spectra one of the common methods used to characterise changes in Doppler broadened line shapes is the analysis of the line-shape parameter, F. Here F is defined as the ratio of the number of counts in a chosen central region of the line divided by the peak integral counts. Further, if various modes of annihilation occur with frequency f/, each having line-shape parameter Fi, then the observed F is a linear combination, viz.
i
• 44
+.
j r~_
•
]
00
•
C
i
i
(1)
This parameter is highly sensitive even to very small changes in the shape of the line. In principle, the line-shape parameter F calculated on an experimental annihilation line which is folded with the response function of the system is expected to provide the same information as that calculated on the same line after the instrumental resolution has been deconvohited [4]. On the other hand, deconvolution techniques tend to be too involved and complicated an approach to afford simple parameters that can reliably correlate with the phenomena at hand. Thus information on the electronic structural properties of defects (e.g. equilibrium vacancies) and their formation entropies and enthalpies can be obtained by the simple line-shape analysis. It is obvious from a visual examination of the line shown in fig. 1 that: (a) the background underlying the peak degrades the sensitivity of F; (b) since the non-linear part under the peak is generated by the peak itself it is expected to vary as the peak shape
• 4'
°o
_~°°
~_
~.-~ o
~vwv~• 42
o
o 0°% ° i
B
I~
0°0°°
i
cO °
Oo
. .,.....,~
+~+~"°cO~
0°
,i, °
0
A
• 38'
0 0
i
3000 O0°
t
oo
:
~ fiFi/ ~ f i .
•
ooeoo
~,
O•
•
414
(~
,,e."
+e°° 0
i
F=
583
: 0
oOO° °
~ooc°~'~ 200
Temperature
400
600
K
Fig. 2. The variation of line-shape parameter F with temperature shown for (A) no background subtraction, (B) constant
background subtraction, and (C) step-function background subtraction. changes. Also in many studies it is often necessary to switch the sample under investigation from a cryostat to a furnace in which case the different nature of the background creates undesirable normalisation difficulties. These are illustrated in fig. 2. In this study we have chosen a particular set of data on a single crystal of cadmium because the temperature variations exhibited by the F-parameter in both the liquid helium-liquid nitrogen and the cryostat-furnace (between 290 K and 320 K) cross-over regions were small. This is particularly convenient as it facilitates closer examination of the points in the cross-over regions.
584
L Chaglar et aL / Calculation of the 511 keV line background
4. Methods of subtraction of the background Various attempts [5-10] have been made to define backgrounds underlying monoenergetic gamma-ray lines. In these approaches, the background is usually represented by a third degree polynomial. Such a function allows for easy representation of the smoothly changing, non-linear region when the rest of the peak is fitted by a deformed Gaussian with a tail distortion on the low energy side. However, in this representation, the freely varying polynominal can throw excessive weight onto the tail distortion parameters and, under these conditions, an accurate representation of the background cannot be expected. Jackman et al. [4] describe the background of annihilation lines by the least-squares fitting of linear functions to the low and high energy tails. The fitted line on the low energy side, with a small positive slope, and that on the high energy side, having a slightly negative slope, were extrapolated to 503 keV and 518 keV respectively where they were joined by a straight line. While this approach can be expected to be appropriate to a study in which the line shape exhibits small changes it cannot be relied upon to satisfy the more rigorous requirements associated with the changes in peak shape encountered during a trapping study. Since the peak is responsible for the step-like non-linear part of the background (BC, fig. 1) changes in the shape of the peak are expected to affect this part of the background most. Any function employed to represent the background underlying the peak should, therefore, incorporate explicitly parameters characterising the peak. The step-function representation (based on the complementary error function) employed by Jorch and Campbell [ 10] in their monoenergetic gamma-ray line fittings incorporates the width and centroid parameters of the main Gaussian. As a result of the constraints implicit in their function, the method of Jorch and Campbell seemed to provide a more stable shape for the background with a minimum number of free parameters. In its application to well defined annihilation gamma-ray peaks we found that the height (H) was the dominant parameter in their stepfunction representation, S(i)
H [1
orf( )l i - io
where i0 is the peak centroid and o is the Gaussian width. For an annihilation line, however, the only
parameter available without having recourse to a fitting of the main part of the peak, which in any case is not Gaussian in character, is the full width at halfmaximum (fwhm). The optimum value to replace ~/2o in eq. (2) was found experimentally to be 0.9 fwhm. However, it is thought that this factor is system-dependent and the appropriate value would have to be determined by an iterative process. In this model the first step was to subtract from the entire spectrum a constant background equal to an average of the contents of the channels at the high energy end of the peak. In a similar fashion, an average background for the low energy end of the spectrum was calculated over the region where it is almost flat. H was given by the difference between the two background levels. The peak centroid and the amplitude were then determined by fitting a fourth degree polynomial to the upper part of the peak. Finally, the fwhm was calculated and the values of H, peak centroid, and fwhm were used in eq. (2). The inset of fig. 1 shows the annihilation line after the subtraction of the step-function background.
5. Results and discussions The background subtraction procedure has been applied in two steps to positron annihilation spectra. The first step was to subtract a constant background from all the channels. This was followed by the subtraction of the smoothly varying step-function profile. Fig. 2 shows, on the same scale, the variation of the line-shape parameter F as a function of the temperature for the observed data (A); after the application of the first step (B); and the second step (C). As can be seen from fig. 2B that although the subtraction of the constant background brought together the F-parameter points corresponding to the liquid helium-liquid nitrogen crossover region, it was by no means sufficient for the "normalisation" of the cryostat-furnace cross-over. This insufficiently is in line with expectation because of the significant differences in gamma-ray scattering environments resulting from the switching of the sample from cryostat to furnace. Fig. 2C provides evidence of the success of the non-linear background subtraction procedure in respect of "normalisation", in that the mean variation between F values in both cross-over regions was within the respective mean standard deviation limits. Moreover, it demonstrates an increased sensitivity of
L Chaglar et al. / Calculation o f the 511 keV line background
F. The overall change in F from 4.2 K to 590 K, calculated on the step-function background subtracted data, is 13% higher than the one calculated on the constant background subtracted data. This figure goes up to over 25% when (A) and (C), in fig. 2, are compared. The particular definition of F used in fig. 2 was the o p t i m u m according to the sensitivity criteria of Campbell [11]. However, this background subtraction technique was employed for a wide range of F definitions and was found to yield equally satisfactory results. To conclude, an accurate subtraction of the background beneath the 511 keV line increases the sensitivity o f the parameter F. This opens up the prospect of revealing new features in experiments (as perhaps indicated in cadmium in the region 5 0 - 1 3 0 K and near the melting point). The technique therefore offers the further promise o f more detailed study of the distinct features of different line-shape parameters discussed b y Hood and Schulz [12]. It is a pleasure to thank Prof. E.R. Dobbs and Dr. M.J. Lea for their interest. One o f us (F.A.R. E1
585
Khangi) would like to thank the Sudanese Atomic Energy Commission for the award of the scholarship. We are grateful to the Science Research Council for financial aid.
References [1] A. Seeger, Crystal Lattice Defects 4 (1973) 221. [2] R.N. West, Positrons in solids, ed. P. Hautoj//rvi (Springer Verlag, Heidelberg, (1979). [3] P. Rice-Evans, I. Chaglar and F. E1 Khangi Phys. Rev. Lett. 40 (1978) 716. [4] T.E. Jackman, P.C. Lichtenberger and C.W. Schulte, App. Phys. 5 (1974) 259. [5] D.C. Robinson, Nucl. Instr. and Meth. 78 (1970) 120. [6] J. Kern, Nucl. Instr. and Meth. 79 (1970) 233. [7] L.A. McNelles and J.L. Campbell, Nucl. Instr. and Meth. 127 (1975) 73. [8] K. Shizuma, Nucl. Instr. and Meth. 150 (1978)447. [9] R.L. Graham, J.S. Geiger and M.W. Johns, Can. J. Phys. 50 (1972) 513. [10] H.H. Jorch and J.L. Campbell, Nucl. Instr. and Meth. 143 (1977) 551. [11] J.L. Campbell, Appl. Phys. 13 (1977) 365. [12] G.M. Hood and R.J. Schultz, J. Phys. F: Metal Phys. 10 (1980) 545.
581
AN ACCURATE CALCULATION OF THE 511 keV LINE BACKGROUND IN POSITRON ANNIHILATION DOPPLER BROADENING STUDIES I. CHAGLAR, P. RICE-EVANS, F.A.R. EL KHANGI and A.A. BERRY Department of Physics, Bedford College, University of London, Regent's Park, London, NW1 4NS, England Received 5 March 1981
A simple method for an accurate subtraction of the underlying non-linear background from positron annihilation spectra is described. The method employs a step-function, complemented by a modified version of the error function, without assuming any functional form of the 511 keV peak. Evidence of the accuracy of the method is presented.
1. Introduction Positron annihilation studies have over the last two decades been the subject of a continuously growing interest. The value of the positron annihilation technique has been demonstrated by many investigators in studies of the properties of lattice defects and the internal structure of materials [1,2]. In the absence of defects in a metal positrons annihilate mainly with low-momentum conduction electrons and With higher momentum core electrons in proportions characteristic of the~metal. In metals containing defects positrons are likely to be trapped in potential wells created by the lattice irregularities and the resulting annihilation characteristics will be correspondingly different. The Doppler broadening technique is one of the three established methods used in the studies of annihilation in m a t t e r - t h e others being measurements on the photon angular correlations and on the positron lifetimes. The latter assesses electron densities at the annihilation sites; and in the first two, thermalised positrons are assumed to probe the momentum distributions of the annihilating electrons. Although the Doppler broadening approach does not possess the fine resolving power offered by the angular correlation technique, its improved statistics due to fast data accumulation and its versatility compensate for this and make it most suitable for many defect studies. The distribution of the momentum component of the annihilating positron-electron pair along the line of the photon emission is due mainly to the motion of the electron and to a lesser extent to that of the 0029-554X/81/0000-0000/$02.50 © North-Holland
positron. This momentum profile is transformed into the intrinsic energy distribution of the 511 keV quanta and is depicted in the observed spectrum after having been broadened by the spectroscopy system. In Doppler broadened gamma-ray peak shape analysis, the changes in the shape of the annihilation line are relatively small and highly sensitive line shape parameters are therefore required for their study. In such analysis it is expected that the background underlying the 511 keV peak has been removed. Despite the importance of this, very little mention has been made in the literature of details of background subtraction methods. In this article we present results of a simple and model-independent positron annihilation background subtraction technique suitable for line shape analysis.
2. Expedmental procedure The Doppler broadened gamma-ray spectra for these studies were recorded using a high resolution intrinsic germanium planar detector, incorporated with an optical feedback pre-amplifier. The pre-amplitier pulses were amplified by a spectroscopy amplifier and unipolar output pulses from the amplifier were then fed directly to 8192 channel analog-to-digital converter with a conversion time of 4.5/as plus pulse rise time. Each pulse was digitised linearly according to its amplitude and subsequently stored in an 8k analyser memory. During the experiment the whole system was kept in a temperature controlled room (-+0.1°C stability)
582
L Chaglar et al. / Calculation of the 511 ke V line background
and operated remotely from outside. The energy dispersion of the analyser and the overall resolution of the system were respectively 94 eV/channel and 1.15 keV for the 514 keV 8SSr line. The specimen material was single crystal cadmium of 6N purity. Carrier-free 22Na -C1 positron sources were evaporated onto the central regions of two 10 mm diameter specimen discs which were then assembled in a sandwich configuration. Although 22Na, because of its easy availability and long half-life, is one of the most commonly used positron emitters, it presents in Doppler studies the handicap of a high background from the 1.28 MeV gamma-ray. Measurements were conducted between 4.2 K and 420 K in a cryostat, and between 293 K and the specimen melting temperature in a furnace. For both experimental arrangements the vacuum condition was about 10 -6 Torr. Over the temperature range 4 . 2 -
28.00
o
I00 K the cryostat was cooled with liquid helium, and from 77 K to 420 K with liquid nitrogen [3]. Each point, shown in fig. 2, corresponds to a line conraining 900 000 counts.
3. Significance of background underlying the 511 keV peak Gamma-ray peaks obtained with semiconductor detectors are usually asymmetric and have generally a non-linear underlying background. These are caused partly by incomplete charge collection and p h o t o electron escape from the active volume of the detector and partly by scattering of gamma-rays. It can be seen from fig. 1 that the underlying background, extending from both the low and the high energy sides of the peak, can be split into three sec-
¢N
e
0
x
X
o
24.00
16 14
°° o o
1210-
20.00, 8 e
6
o
4
16,00 o
80
40
o
12.00
120
160
o
o CE)
e
e
o
o o
8.00
ee
o
et)
4.00 e --~% °
d~o
o .
.
.
.
o
e~°
o o
ee o oe
o e
o
o e 8
: e~
~'~-
0.00
~ _ ~
C I
0.00
~ o~ooo
l 40.00
l
1
80.00
I 120.00
CHANNEL
I
D I
1
160.00
NUMBER
Fig. 1. Annihilation line shape with the non-linear part of the underlying background, The background subtracted line is shown in the inset. The solid line in either case represents the step-function background.
L Chaglar et aL / Calculation o f th e 511 ke V line background
tions: the low and the high energy parts AB and CD show a similar, linear character and the smoothly varying nonqinear central region joins these two wings. The high energy wing, CD, is generated by the 1.28 MeV gamma-rays in 22Na and the natural background, and is present at a reasonably constant level throughout the defined region AD. Other contributions present in the region AC result from the 511 keV photons. The asymmetry of a gamma-ray peak, the nonlinearity of its underlying background, and the ratio of the overall intensity of the background to that of the actual peak are dependent on the gamma-ray spectroscopy system. The instrumental contribution to the observed broadening of the intrinsic energy distribution of the annihilation quanta also includes these characteristics of the system. Ideally, in a detailed line shape analysis, these should be taken into account separately. In the studies of positron annihilation spectra one of the common methods used to characterise changes in Doppler broadened line shapes is the analysis of the line-shape parameter, F. Here F is defined as the ratio of the number of counts in a chosen central region of the line divided by the peak integral counts. Further, if various modes of annihilation occur with frequency f/, each having line-shape parameter Fi, then the observed F is a linear combination, viz.
i
• 44
+.
j r~_
•
]
00
•
C
i
i
(1)
This parameter is highly sensitive even to very small changes in the shape of the line. In principle, the line-shape parameter F calculated on an experimental annihilation line which is folded with the response function of the system is expected to provide the same information as that calculated on the same line after the instrumental resolution has been deconvohited [4]. On the other hand, deconvolution techniques tend to be too involved and complicated an approach to afford simple parameters that can reliably correlate with the phenomena at hand. Thus information on the electronic structural properties of defects (e.g. equilibrium vacancies) and their formation entropies and enthalpies can be obtained by the simple line-shape analysis. It is obvious from a visual examination of the line shown in fig. 1 that: (a) the background underlying the peak degrades the sensitivity of F; (b) since the non-linear part under the peak is generated by the peak itself it is expected to vary as the peak shape
• 4'
°o
_~°°
~_
~.-~ o
~vwv~• 42
o
o 0°% ° i
B
I~
0°0°°
i
cO °
Oo
. .,.....,~
+~+~"°cO~
0°
,i, °
0
A
• 38'
0 0
i
3000 O0°
t
oo
:
~ fiFi/ ~ f i .
•
ooeoo
~,
O•
•
414
(~
,,e."
+e°° 0
i
F=
583
: 0
oOO° °
~ooc°~'~ 200
Temperature
400
600
K
Fig. 2. The variation of line-shape parameter F with temperature shown for (A) no background subtraction, (B) constant
background subtraction, and (C) step-function background subtraction. changes. Also in many studies it is often necessary to switch the sample under investigation from a cryostat to a furnace in which case the different nature of the background creates undesirable normalisation difficulties. These are illustrated in fig. 2. In this study we have chosen a particular set of data on a single crystal of cadmium because the temperature variations exhibited by the F-parameter in both the liquid helium-liquid nitrogen and the cryostat-furnace (between 290 K and 320 K) cross-over regions were small. This is particularly convenient as it facilitates closer examination of the points in the cross-over regions.
584
L Chaglar et aL / Calculation of the 511 keV line background
4. Methods of subtraction of the background Various attempts [5-10] have been made to define backgrounds underlying monoenergetic gamma-ray lines. In these approaches, the background is usually represented by a third degree polynomial. Such a function allows for easy representation of the smoothly changing, non-linear region when the rest of the peak is fitted by a deformed Gaussian with a tail distortion on the low energy side. However, in this representation, the freely varying polynominal can throw excessive weight onto the tail distortion parameters and, under these conditions, an accurate representation of the background cannot be expected. Jackman et al. [4] describe the background of annihilation lines by the least-squares fitting of linear functions to the low and high energy tails. The fitted line on the low energy side, with a small positive slope, and that on the high energy side, having a slightly negative slope, were extrapolated to 503 keV and 518 keV respectively where they were joined by a straight line. While this approach can be expected to be appropriate to a study in which the line shape exhibits small changes it cannot be relied upon to satisfy the more rigorous requirements associated with the changes in peak shape encountered during a trapping study. Since the peak is responsible for the step-like non-linear part of the background (BC, fig. 1) changes in the shape of the peak are expected to affect this part of the background most. Any function employed to represent the background underlying the peak should, therefore, incorporate explicitly parameters characterising the peak. The step-function representation (based on the complementary error function) employed by Jorch and Campbell [ 10] in their monoenergetic gamma-ray line fittings incorporates the width and centroid parameters of the main Gaussian. As a result of the constraints implicit in their function, the method of Jorch and Campbell seemed to provide a more stable shape for the background with a minimum number of free parameters. In its application to well defined annihilation gamma-ray peaks we found that the height (H) was the dominant parameter in their stepfunction representation, S(i)
H [1
orf( )l i - io
where i0 is the peak centroid and o is the Gaussian width. For an annihilation line, however, the only
parameter available without having recourse to a fitting of the main part of the peak, which in any case is not Gaussian in character, is the full width at halfmaximum (fwhm). The optimum value to replace ~/2o in eq. (2) was found experimentally to be 0.9 fwhm. However, it is thought that this factor is system-dependent and the appropriate value would have to be determined by an iterative process. In this model the first step was to subtract from the entire spectrum a constant background equal to an average of the contents of the channels at the high energy end of the peak. In a similar fashion, an average background for the low energy end of the spectrum was calculated over the region where it is almost flat. H was given by the difference between the two background levels. The peak centroid and the amplitude were then determined by fitting a fourth degree polynomial to the upper part of the peak. Finally, the fwhm was calculated and the values of H, peak centroid, and fwhm were used in eq. (2). The inset of fig. 1 shows the annihilation line after the subtraction of the step-function background.
5. Results and discussions The background subtraction procedure has been applied in two steps to positron annihilation spectra. The first step was to subtract a constant background from all the channels. This was followed by the subtraction of the smoothly varying step-function profile. Fig. 2 shows, on the same scale, the variation of the line-shape parameter F as a function of the temperature for the observed data (A); after the application of the first step (B); and the second step (C). As can be seen from fig. 2B that although the subtraction of the constant background brought together the F-parameter points corresponding to the liquid helium-liquid nitrogen crossover region, it was by no means sufficient for the "normalisation" of the cryostat-furnace cross-over. This insufficiently is in line with expectation because of the significant differences in gamma-ray scattering environments resulting from the switching of the sample from cryostat to furnace. Fig. 2C provides evidence of the success of the non-linear background subtraction procedure in respect of "normalisation", in that the mean variation between F values in both cross-over regions was within the respective mean standard deviation limits. Moreover, it demonstrates an increased sensitivity of
L Chaglar et al. / Calculation o f the 511 keV line background
F. The overall change in F from 4.2 K to 590 K, calculated on the step-function background subtracted data, is 13% higher than the one calculated on the constant background subtracted data. This figure goes up to over 25% when (A) and (C), in fig. 2, are compared. The particular definition of F used in fig. 2 was the o p t i m u m according to the sensitivity criteria of Campbell [11]. However, this background subtraction technique was employed for a wide range of F definitions and was found to yield equally satisfactory results. To conclude, an accurate subtraction of the background beneath the 511 keV line increases the sensitivity o f the parameter F. This opens up the prospect of revealing new features in experiments (as perhaps indicated in cadmium in the region 5 0 - 1 3 0 K and near the melting point). The technique therefore offers the further promise o f more detailed study of the distinct features of different line-shape parameters discussed b y Hood and Schulz [12]. It is a pleasure to thank Prof. E.R. Dobbs and Dr. M.J. Lea for their interest. One o f us (F.A.R. E1
585
Khangi) would like to thank the Sudanese Atomic Energy Commission for the award of the scholarship. We are grateful to the Science Research Council for financial aid.
References [1] A. Seeger, Crystal Lattice Defects 4 (1973) 221. [2] R.N. West, Positrons in solids, ed. P. Hautoj//rvi (Springer Verlag, Heidelberg, (1979). [3] P. Rice-Evans, I. Chaglar and F. E1 Khangi Phys. Rev. Lett. 40 (1978) 716. [4] T.E. Jackman, P.C. Lichtenberger and C.W. Schulte, App. Phys. 5 (1974) 259. [5] D.C. Robinson, Nucl. Instr. and Meth. 78 (1970) 120. [6] J. Kern, Nucl. Instr. and Meth. 79 (1970) 233. [7] L.A. McNelles and J.L. Campbell, Nucl. Instr. and Meth. 127 (1975) 73. [8] K. Shizuma, Nucl. Instr. and Meth. 150 (1978)447. [9] R.L. Graham, J.S. Geiger and M.W. Johns, Can. J. Phys. 50 (1972) 513. [10] H.H. Jorch and J.L. Campbell, Nucl. Instr. and Meth. 143 (1977) 551. [11] J.L. Campbell, Appl. Phys. 13 (1977) 365. [12] G.M. Hood and R.J. Schultz, J. Phys. F: Metal Phys. 10 (1980) 545.