12 A N N P E A K : A Program for Lineshape Analysis of Doppler Broadening of Positron
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Annihilation Photons 1
JAMES J. KELLY and RICHARD M. LAMBRECHT
Chemistry Department, Brookhaven National Laboratory, Upton, NY 11973
A flexible program for the lineshape analysis of Doppler broadend spectra of positron annihilation photons was developed to calculate the lineshape parameters Q, W, L, FWHM, μ, and σ from a normalized annihilation spectrum. An improved linear selection method was used to limit line shape dependence on the background correction. This pro gram was used to analyze the Doppler broadened annihila tion spectra obtained with a spectrometer using two-point digital stabilization. Nuclear lines of Ba and Bi were used for energy calibration purposes. The program de scribed has convenient options for optimization and output of data. M
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" p o s i t r o n annihilation spectroscopy ( P A S ) is becoming widely used i n applied and fundamental studies i n chemical physics, applied physics, materials science, and energy-related research ( F o r a comprehensive b i b liography of the field, see Réf. 1). The Doppler broadening of positron annihilation photons w i t h high-resolution G e ( L i ) detectors is now gaining acceptance, though its use has been advocated strongly for several years (2). The methods of lineshape analysis are often unique to a given investigator and are generally semi-empirical (2-11). W e have incorporated a variety of the lineshape parameters that have been used previously into an analytical routine called A N N P E A K . O u r experience w i t h this program and the instrumentation used to develop it is described.
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Person to whom inquiries should be addressed. 0-8412-0417-9/79/33-175-271$05.00/l © 1979 American Chemical Society
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Doppler broadened lineshapes can be approximately represented as a distribution comprised of the convolution of the instrumental resolution function and the superposition of an inverted parabola and a Gaussian. The difference between positron(ium) annihilation w i t h low momentum conduction electrons (inverted parabola) and high momentum conduction electrons are extracted by a measurement of the differences between the extremes. Figure 1 illustrates a sample normalized spectrum and depicts the arbitrary channel boundaries used for the determination of the lineshape parameters denoted by the letters Q, W , and L , and the full w i d t h at halfmax ( F W H M ) . The regions of maxi-
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Figure I .
Definition of lineshape parameters for Doppler broadened annihilation photons
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mum change i n the normalized spectra are i n the area ( A ) of the narrowcentral region and i n the areas of the wings associated with the broadest part of the distribution. Q is the ratio of the area ( A ) , the sum N of events, i n the central region of thepeak divided by the integral area ( i ) in the complete normalized spectrum. W is sensitive to changes i n the fraction of annihilation events occurring with high momentum electrons ( C - B ) divided by (I) i n the spectrum. C and Β are chosen to be sym metrical regions of the wings of either side of the central region to the area of the spectrum. The definition of Q is identical to MacKenzie's (2) definition of S. However, the notation S has not been consistently used to denote a value identical to the L parameter ( I I ) . The selection of the channel boundaries for A , B, and C are selected arbitrarily to enhance changes i n Q, W, or L . To a rough approximation, Q is a reflection of annihilation w i t h conduction electrons, whereas W is a reflection of annihilation with core electrons. L can be related to the ratio of conduction-to-core electrons ( L = Q/W) provided the boun daries of A, B, and C are selected properly. The centroid (μ) and the variance, i.e., second moment ( σ ) are calculated by
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μ = I ( S i N i ) and σΜ? = r » ( 3 ( i i i - 1
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where I is the area of the spectrum and N i represents the number of de tected events i n channel i of the annihilation spectrum. The total energy of the annihilating system can be calculated from μ; whereas σ is an indicator of the shape of the spectrum. Campbell (7) has discussed the statistical properties of four lineshape parameters. The purpose of this chapter is to make the data reduction routine available to other workers i n the field and to facilitate increased u n i formity i n the manner i n w h i c h lineshape parameters for the Doppler broadening of positron annihilation photons are reported (Singru, L a i , Tao, and Lambrecht have tabulated Doppler broadening results w h i c h have appeared i n the 1949-1975 literature) ( I I ) . Μ
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Experimental Spectra were collected w i t h a P G T intrinsic Ge detector having a resolution of 1.098 keV for the 511.865 k e V nuclear line of R u . A C a n berra spectroscopy amplifier (2010) and a Northern Scientific ( N S 720A) 4096 channel pulse height analyzer equipped w i t h a two-point digital sta bilizer (NS-454) were operated at a dispersion of approximately 63 eV channel" . O u r approach has been to stabilize on nuclear lines rather than on a puiser, and to avoid gain stabilization on the 511-keV annihilation peak. In our experiments, zero stabilization was performed on the 356.005keV line of B a and gain stabilization was performed on the 569.670-keV 1 0 6
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line of B i . The background from B a and B i i n the region of annihilation photopeak is low and linear. W e are cautious of using R u (497 k e V ) for gain stabilization because of its proximity to the annihilation photopeak, and the distortion it can introduce on lineshape analysis of the 511-keV photopeak. A linear calibration of each recorded spectrum is obtained by use of the 356.005 and 383.851-keV photons of B a and the 569.670-keV photons of B i . These nuclides are useful because of their suitability for twopoint stabilization and for use i n establishing the energy calibration of each spectrum. A N N P E A K can handle an arbitrary number of calibration and stabilization reference peaks. The dispersion of the system has proved stable to three parts i n 10 , when the laboratory temperature was monitored at 22° =fc 1°C. W e observed that for the large total count rate, the apparent lineshape of the annihilation photopeak was sensitive to count rate, but that for low total count rate it was essentially independent of count rate. This is an important consideration. The calibration was independent of the low count rate maintained in the references. The multichannel analyzer (MCA) was interfaced to an NS-708F control unit, and the data was recorded automatically by a W a n g Co. M o d 7/8 magnetic tape drive. The tapes were subsequently reduced on a C D C 7600 computer by A N N P E A K , using the tape reading routines provided. 2 0 7
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Results and Discussion The background substraction problem for solid-state detectors has been a subject of considerable discussion (see for example Refs. 3-10 and 14-18). One must avoid introducing an artificial shape dependence into the lineshape parameters. Generally a least-squares analysis is used to remove a linear background. If the regions from which the background is determined are preset, fixed intervals, then relatively more w i l l be subtracted out of a wide peak than a narrow peak. The use of a linear background usually can be justified if care is taken to select the endpoints for the least-squares analysis such that artifacts of lineshape dependence are minimized. The method used by A N N P E A K is to supply a background optimization option w i t h an arbitrary number of trial widths ( A W I D T H ) which are marked off symmetrically from the maximum count rate channel of the 511-keV photopeak. The calculation of the lineshape parameters is repeated for each A W I D T H . The optimum A W I D T H is then located by examination of the A W I D T H dependence of lineshape parameters. Figure 2 depicts the dependence of the F W H M , Q, W , L, and the centroid on the value of A W I D T H . The same type of lineshape parameter dependence on A W I D T H also was observed using a G e ( L i ) detector with a resolution of 2.5 k e V for the 514-keV line of K r . Therefore, A W I D T H is preferably chosen on the flat portion of a l l the plateaus as illustrated i n Figure 2. The smallest least-squares linear background is then subtracted from the wings of the photopeak without 8 5
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FWHM
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