A novel method of Mössbauer data calibration using a laser interferometer

,NUCLEAR INSTRUMENTS

AND METHODS

145 ( 1 9 7 7 )

359-360

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NORTtI'HOLt, AND PUBLISttlNG

CO.

A NOVEL METHOD OF MOSSBAUER DATA CALIBRATION USING A LASER INTERFEROMETER D. W. C A R S O N Solid Stat(, S(,(.oon. Canada ('('n/re .lor Mineral and EnerKv "l(,chnoloKv. 555 Booth Street. Ottawa. Ontario. K I A OGI Canada Received 7 March 1977 A u n i q u e m e t h o d of M6ssbauer data calibration is described whereby the laser and MiSssbauer data are used to foi'm a new M6ssbauer data matrix. Each channel of the new matrix has a discreet velocity and is separated from adjacent c h a n nels by a c o n s t a n t velocity difference. T h i s corrects for any non-lincarity in the velocity scale and t h u s e n h a n c e s the Lorentzian curve fitting procedure.

1. Introduction From the theory of the Mt~ssbauer phenomenon it is predicted that the absorption peaks are of Lorentzian shape in energy (velocity). Since a multichannel analyser accumulates the spectrum in the time mode (each channel is equally spaced in time) then non-linearity in the motor drive wavelorm will result in a distortion of the peaks. If the data from the analyser can be transformed from the time axis back to the velocity axis, the original Lorentzian peaks will be recovered. The usual method of calibrating a M6ssbauer spectrum using a laser interferometer~) in the constant acceleration scheme is to fit the laser velocity information by a cubic equation reduce the Mi3ssbauer data by the usual method of leastsquares curve-fitting of the peaks by Lorentzian lines using channel numbers (or time) as coordinate, and then to convert the peak positions from channel numbers to velocities (ram/s) using the calculated cubic coefficients. This report describes a new method of data reduction using the laser information and the M~3ssbauer data to create a new M~ssbauer data matrix where each channel has a discrete velocity in m m / s and is separated from adjacent channels by a constant velocity difference. By converting the Mi3ssbauer data from the time to the velocity axis in this manner, not only is a more accurate relationship between channels and m m / s obtained, but the resulting linear relationship between channels and m m / s enhances the Lorentzian fitting procedure, since the M6ssbauer fit program assumes linear combinations of Lorentzian lines. A Fortran program was written to reduce the

SOURCE

MOVEABLE MIRROR DETECTOR

~BEAM SPLITTER

-,//,

"I/1 STATIONARY MIRROR

Fig. 1. M i c h e l s o n ' s interferometer.

data in this manner and produce card output for M6ssbauer analysis. This program can be obtained by contacting the author.

2. Description Fringe patterns occur if coherent light travelling from a source, is split into two paths and these two beams of light arrive at a detector after having travelled different distances. A Michelson interferometer (see fig. 1) measures lengths or changes in lengths with great accuracy using this phenomenon. Every time the mirror moves by one-half wavelength a light fringe is counted since the light path has changed by one full wavelength. In the M~Sssbauer setup the moveable mirror is attached to the M6ssbauer source and the number of fringes are counted over a channel interval. This is done periodically throughout the spectrum in intervals of 2, 4, 8 or 16 channels, such that the M6ssbauer spectrum is interlaced with laser velocity data. Since the direction of motion of the mirror is irrelevant in producing the fringes, a sweep from maximum negative to maximum positive velocities at constant acceleration results in a

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V-shaped velocity spectrum with its vertex at zero. A 50 kHz clock is counted in the first few channels to determine the time of the channel interval. With this information along with the wavelength of the laser light, the velocity at each laser channel can be easily determined. In the constant accleration mode, a correction in the background intensity of the M6ssbauer data must be made due to the continuous motion of the source. This can be accomplished by either fitting a background parabola to the data, or duplicating the data with a symmetric velocity profile and combining the two parts. Since we use the second method,the complete spectrum consists of a W-shaped velocity spectrum and a duplicate set of MSssbauer peaks. We accumulate this data in a 2048-channel Northern Scientific Analyser. To transform the laser data from the time axis to the velocity axis, the velocity (laser) information, converted from fringe-counts to r a m / s , is first searched to determine the velocity range of the spectrum. With this and the criteria of creating a M6ssbauer matrix of five hundred elements, values for the starting velocity and the velocity increment in millimeters per second, and then counts, are determined. The method of transforming the data is divided into two parts, an algorithm for conversion about the two areas of zero velocity and another for the rest of the spectrum. Using the starting velocity value in counts, the laser spectrum is searched until this velocity value is located between two laser data points. Assuming a linear relationship in this region, by interpolation, each M6ssbauer data point in that interval is assigned a velocity value. An inner search is once again conducted to locate the starting velocity value between two M6ssbauer data points. From the ratio of the distance calculated from the velocity values a corresponding M6ssbauer data value is determined. This value is then the first Mbssbauer data value of the new matrix. The velocity value is then incremented or decremented depending upon which quadrant is being searched, the number of counts determined and the procedure repeated until the new data matrix is filled. The following example illustrates this procedure. The values used are representative and do not constitute real data. Assume that the calculated starting velocity value is 96.5 counts. As can be seen from the diagram (fig. 2) the starting velocity value which will be the velocity value (converted

(' A R S O N STARTING VALUE (96,5]

LASER DATA

MOSSBAUER DATA

LASER DATA

,i

9

0

C

0

IO

II

12

X C

0

13

14

,'5 15

0 16

0 17 CHANNEL NUMBER

Fig. 2. Mossbauer data channels.

r-C

Lq- n

NUMBER

VALUE

qVALUES

I VELOCITY

T-76o I0 II 12 13 14 15 16 17

I010 1020 IOlO 1030 1060 1040 I010 92

99 98

9"I 96 95 9493

Fig. 3. Table of data values. 96 - 97

1030 - 1010

96-5- 97

X - I010

X • 1020 9 7 -" ~ / I010

Fig.

-" X

4 1030

4. I n t e r p o l a t i o n scheme.

to m m / s ) of the first position of the new data matrix, is located between laser channel 9 and 17. By interpolation, each of the M6ssbauer data channels in this region is assigned a velocity value. These values are listed in column three of the table of fig. 3. Another search locates the starting value between M6ssbauer channels 12 and 13. Again by interpolation as illustrated in fig 4, the corresponding M6ssbauer value (1020) is determined. In the two zero-velocity regions there are few fringes to be counted and thus to get a relatively accurate velocity spectrum the laser points in this region are fitted by a cubic equation. The resulting coefficients are then used to convert the data to m m / s instead of the actual laser values. Otherwise the procedure is the same as previously described. When the complete spectrum (the symmetric spectra) has been translated,, the first MBssbauer spectrum is added to the second and then averaged to remove the background parabola. This final matrix is then punched on computer cards to be used as input to the M6ssbauer least-squares curve-fit program2). References i) j. G. Cosgrove and R. L. Collins, Nucl. Instr. and Meth. 95 {1971) 269. 2) D. W Carson, Mineral Sciences Laboratories. Internal Report MS 7(}-102.