A microprocessor controlled spectrometer for thermal scan Mössbauer spectroscopy

Nuclear Instruments and Methods 207 (1983) 459-463 North-Holland Publishing Company

A MICROPROCESSOR

CONTROLLED

459

SPECTROMETER

FOR

THERMAL

SCAN

MOSSBAUER

SPECTROSCOPY Gerhard NOLLE,

Heinz ULLRICH,

Jiirgen Bolko MULLER

and Jtirgen HESSE

lnstitut A fiir Physik der TU Braunschweig, Mendelssohnstr. 3, 33 Braunschweig, Germany Received 4 October 1982

To determine the ordering temperature of ferromagnetic alloys by use of the M6ssbauer effect, a "thermal scan" measurement of counting rate at the center of gravity of the spectrum is necessary. We present a low cost microcomputer controlled system, which sets up the temperatures, takes the spectra and evaluates the ordering temperature from a sequence of measurements. As an example the Curie temperatures of disordered fcc FePt-Invar alloys are given.

I. Introduction In 1962, Preston et al. [1] determined the temperature of the magnetic phase transition of a ferromagnetic sample by 57Fe M 6 s s b a u e r effect m e a s u r e m e n t s using a " t h e r m a l scan" method. For various temperatures T, they determined the c o u n t i n g rate Z(vs) at the gravity center of the spectrum. The temperature of the magnetic phase transition then was evaluated from the curve of

Z(v~, T). This m e t h o d to determine the phase transition exhibits a lot of advantages c o m p a r e d with usual methods, e.g. magnetization measurements. Neither an external field, nor extrapolation to zero field is necessary. Therefore, this m e t h o d can be applied on antiferromagnetic materials, too [2]. Furthermore, the d e t e r m i n a t i o n of the magnetic phase transition by use of the MOssbauer effect is of special interest, because the M 6 s s b a u e r effect measurem e n t s take place in a very different time scale c o m p a r e d to the magnetization m e a s u r e m e n t (about 10 7 s for 57Fe). The great time effort which is necessary to obtain the spectra is an i m p o r t a n t disadvantage of the thermal scan method. Therefore we present a low cost microprocessor controlled M 6 s s b a u e r spectrometer, which allows to determine the transition t e m p e r a t u r e of magnetic samples at very high accuracy. We use this spectrometer for 57Fe M 6 s s b a u e r spectroscopy.

2. Evaluation of the transition temperature

ordering the spectrum Z ( v ) splits into six well resolved lines, caused by the internal hyperfine field H ( T ) (Zeem a n effect). The resonance velocities of these lines are given by VR, i = o~iH(T). It is convenient to introduce the reduced temperature r = ( T - T c ) / T c. At sample temperatures near b u t below the transition temperature (~" < 0), the six absorption lines overlap so that only one b r o a d line is observed (fig. 1). A b o v e the Curie temperature (T > 0) the internal field H(~-) disappears a n d the six a b s o r p t i o n lines degenerate to a narrow single line (fig. 2).

I(v,,r)_Z(~)=Z(

0 1 6 7 - 5 0 8 7 / 8 3 / 0 0 0 0 - 0 0 0 0 / $ 0 3 . 0 0 © 1983 N o r t h - H o l l a n d

KfA('r)ci

i 1+

C

(1) where

Z(v)

= counting rate at source velocity v, = constant,

K

tO0

-r(vs,'c)

..

~.~

9C E

O~

v

-8

In the a p p r o x i m a t i o n of thin absorbers the analytic expression for a MOssbauer spectrum is given by eq. (1). F a r below the (Curie) t e m p e r a t u r e Tc of magnetic

v ) =~"~

Z(~)

-5

--4

-3

-2

-1

|

1

2

3

in

mm/5

4

5

Fig. 1. M6ssbauer spectrum of a FeNi alloy very near but below the Curie temperature Tc [,r = ( T - Tc)/Tc; ~-< 0]. The peak depth l(v~, "r) is small.

G. NOlle et al. / Microprocessor controlled spectrometer

460

6oo~I t

~oo~

M

5oo~

400 t

I ¢ ~ , "c)

3oo]

9O E

200 !

8O -6

-5

"-4

-~

-2

-1

g

1

2

v in

mrn/5

3

4

S

Fig. 2. Mfissbauer spectrum of a FeNi alloy very near but above the Curie temperature Tc [,r = ( T - T c ) / T c ; r > 0]. The peak depth l(v~, "r) is large.

%o,1 . . . . . . . . . . .

25

"

30

35

Fig. 4. Results of a thermal scan measurement series: the Curie temperatures of disordered FePt Invar alloys vs. platinum concentration.

o(r)o~H(,r):Ho(fl,r)V

with { / 3 : - 1 /3 = 0

for r < 0, for "r >7 0,

(2) c,

= relative transition probability for the i t h Z e e m a n transition, E c~ = 1, fA = D e b y e - W a l l e r factor of the absorber, a, = calibration factor for the resonance velocity, v~ = center of gravity shift of the spectrum, F = 0.5 × half-width of the Lorentzian, H ( r ) = hyperfine field at the nucleus, ~= reduced temperature = ( T - T ¢ ) / T . Assuming the magnetization o ('r) of the sample being propertional to H(~'), the measured curve of H(~') provides information on o(~') and therefore on the ordering temperature Tc. Measured counting rates l ( v s, "r) versus temperature are plotted in fig. 3. The typical shape of this curve can be explained as follows. Eqs. (2) a n d (3) are valid in the a p p r o x i m a t i o n [~1 << 1 (A, H 0 are constants).

fA (-r) = fA (To.) - A ' r .

(3)

The temperature dependence of the D e b y e - W a l l e r factor fA(~') is assumed to b e linear as given by eq. (3). Taking into account eq. (1), (2) and (3), l(v~, "r) is given by

l(vs,~')=

Kci F2 i-2+[a/U(T)]

[/A(Tc)-A~']~/

2'

(4)

with the assumption [ a i H ( T ) ] / F << 1 one gets:

I(vs, ~)= K[ f~(T<.)- ~ .~]

i(~,, ,) = K [ A ( T c ) - A -

, l [ l - B(/3,12'],

where B = Zfl=c, a2,H2o/F2. B >> A results in:

l(v~, r)=K[ I(v s , r)

•

/~o,,

005

O 0 - . n ~

A 0

o,-

0

O.O3 0O2

-0.07

3~o

~:

~oo

016

4~o . . . .

J~ ,E .

sbo

- B(/3~')zv] ( a ) f o r ~-< 0, ( b ) for r>~ 0. (5)

The ordering temperature -r = 0 can be estimated from the p o i n t of intersection of the two curves (a) a n d (b) [eq. (5)]. In the molecular field a p p r o x i m a t i o n the critical exponent ¥ equals 1/2. In this a p p r o x i m a t i o n the phase transition temperature is given by the intersection point of two nearly straight lines [eqs. (5a) a n d (5b), compare fig. 3].

f

004

ooto.oo L i QO0 ',r~

fa(Tc)[l [fA(rc)_A,.r,

3. Requirements on the measurement T[K]

388 K

Fig. 3. Results of a thermal scan plot of the peak depth l(v~, "r) vs. reduced temperature "r = ( T - Tc ) / T c for a FePt0 z9z alloy. The determined Curie temperature is Tc = (388 _+ 1) K.

T o obtain the two lines one has to take Mi3ssbauer spectra at various temperatures in the region near the Curie temperature. F r o m each spectrum the peak l ( v s, "r) (figs. 1 a n d 2) has to be determined. The accuracy of the Curie temperature determined by the ther-

461

G. N6lle et aL / Microprocessor controlled spectrometer

mal scan method, as described in section 2, depends on a) The n u m b e r of data points on the lines (a) and (b), that means one has to take a great n u m b e r of spectra. b) The uncertainty of l ( v s, ~'). To minimize the error, it is necessary to sample smooth spectra, the statistical fluctuation of the c o u n t i n g rates should be as small as possible. This requires very long accumulation times. If a theory function is fitted to the spectrum, the c o u n t i n g rate l(v~, T) can be determined with better accuracy. c) The accuracy in measuring a n d controlling the sample temperature. In our case the t e m p e r a t u r e of phase transition for various fcc FeNi a n d fcc FePt alloys had to be det e r m i n e d with high accuracy. To estimate the transition t e m p e r a t u r e of FePt alloys we p l a n n e d to take 30 spectra for each alloy. The measuring time for one spectrum was between 4 to 5 h. This time is a c o m b i n a t i o n of the accumulation time, the setting time of the temperature controller as well as the time to fit the spectrum. To minimize this effort and to optimize the errors the spectrometer was extended so that the complete m e a s u r e m e n t is now done automatically, controlled by

a microcomputer. In general an a u t o m a t i o n only will be convenient if there are: a) n u m e r o u s similar measurements, b) samples which require very long accumulation times, e.g. absorbers with small effectivity.

4. The spectrometer The principal a r r a n g e m e n t of the spectrometer is s h o w n in fig. 5. The c o m m o n M 6 s s b a u e r spectrometer is plotted above the b r o k e n line. To control the spectrometer a C o m m o d o r e microcomputer (t~C) was available. The multichannel analyser ( M C A ) was equipped with an IEC625-interface enabling the c o m p u t e r to remote the M C A a n d to read the data. A second IEC-interface has been designed to provide the temperature controller (TC) with remote functions: a D / A - c o n v e r t e r generates the reference voltage Ure f for the T C a n d the /~C can read and write the TC status. The flow chart of the control program for the complete system is shown in fig. 6. First the c o m p u t e r asks for the start temperature T,, the end t e m p e r a t u r e T E a n d the temperature interval dT. Further inputs are the

Input from keyb. Starttemp. Ts Endtemp TE Temp. step dT

SUBROUTINE EVALUAtiON

TC." Temperature Controller MCA Multi Channel Anolyser DVM, Dig#a/- Voltmeter

Temp. error 5r

I I ~ . t fr~MCA.'~4rA I I

IOutputt°oP~kDATA I

, Accum.time At

I

I

r., : r, Compute U~,~IT, ) 6Ur t6r )

:b

I

I output to TC : u~., c) o

I~ I Rf~t

i

:

'oMCA ERASEI I clock

t...o

I

" t I ~.t ~. ~u~l c) o

Nt~, ~ ~

.'ERASEI

~

I Start clock

I

I YE5 I

SUBROUTINE

Ic~,,u~,t~,) MICROCOMPUTER CBM 4032

FLOPPY DISC I CBM 4040

PRINTER

Fig. 5. Sketch of the computer controlled MOssbauer spectrometer for thermal scan measurements. In the upper part the usual M6ssbauer spectrometer is shown. In the lower part the extensions to remote control of the spectrometer are drawn.

k~tp,,, ,o ~c..u~., I

TYE5

[ stop cloi*

l

I

JUMP 5UBROUTII~ EVALUIAT/ON I

EVALUATION

] Compute Tc from linear Regression

I

Fig. 6. Flow chart of the program to control the thermal scan experiment.

Fig. 7. Listing of a fit program for nonlinear our case the theory function is given by: z(~)=P(*)-P(l)/jl-[~~~J1):

theory functions.

P(I)=Z(sa);

The function

to he fitted is embedded

P(z)=z(P)--Z(L’,):

in the subroutine

P(3)=0,:

THEORY.

P(4)=1‘.

In

G. Nrlle et a L / Microprocessor controlled spectrometer maximum temperature deviation 6 r and the accumulation time 6t. The programm starts taking Ts as actual temperature. The corresponding reference (thermocouple) voltage for the TC is computed and stored into the D / A converter. T h e / z C clears the M C A and resets the clock. Then the/~C remains in a waiting loop until the temperature difference between the sample temperature Usam [thermocouple voltage, measured by the digital voltmeter (DVM)] and the reference temperature Ure f is smaller than the given limit 6 U ( r T ) . Then the M C A and the clock are started. During accum/alation time the p C reads the clock and checks the actual sample temperature. If the deviation is greater than 8v, the M C A and the clock are stopped and the program jumps back to the waiting loop. In this way it is guaranteed that the taken spectrum is associated to a well known temperature interval. If the given accumulation time is reached, the next temperature point is calculated. If it is not greater than T E this value is tranferred to the TC. During the setting time of the TC the /~C reads the spectrum from the MCA, stores the data on disk and fits a theoretical function to the spectrum. Thereafter the M C A is started again to accumulate the next spectrum. After the evaluation of the last spectrum, the phase temperature is calculated from the fitted values of l(Vs, ,c). Each measurement is documented on the printer. For a visuall control of the system, the actual state is shown on the monitor of the/~C. As the processes to be controlled change rather slowly, the complete program could be written in BASIC, so that similar problems can be adapted easily.

463

segments. The first segment provides the initial values and assigns the data to the different matrices. The subroutines FIT, M A T I N V , and T H E O R Y are listed in fig. 7. In the routine T H E O R Y the lorentzian and its derivations with respect to the parameters are computed. It was possible to carry out all evaluations with the /tC. The average computation time to fit the 4 parameters of a lorentzian to 256 data points was 10-15 min. Fitting the spectra one gets also information on vs(~"). The advantages of the described/~C controlled spectrometer are: a) effective use of the spectrometer, b) exact known sample temperatures, c) high reliability, d) fast and accurate evaluation of the spectra, e) getting the shift of the center of gravity vs as function of temperature in addition to Tc. Moreover the spectrometer can easily be programmed to carry out any desired series of measurements.

6. Measurements We used the described Mrssbauer spectrometer to determine magnetic phase transition temperatures of FeNi and FePt alloys. As an example we present the evaluation of the Curie temperature of a statistical ordered fcc FePt0.292 Invar alloy (fig. 3). In fig. 4 the different ordering temperatures, determined by the described thermal scan method, are shown. We wish to thank Prof. Ch. Schwink and Prof. H. Br/3mer for continuous support of the Mrssbauer spectroscopy group. The grant by the Deutsche Forschungsgemeinschaft is gratefully acknowledged.

5. Evaluation of l(v~, ~) To get l ( v s, ,r) with a small error, a Lorentzian line was fitted to the spectrum Z ( v ) . There are 4 parameters: the background rate Z ( ~ ) , the peak height Z(oo) Z(vs), the half-width F and the shift of the center of gravity vs. An algorithm to fit a nonlinear function to a spectrum is described by Bevington [3]. Our program, written in C o m m o d o r e BASIC syntax, consists of four -

References [1] R.S. Preston, S.S. Hanna and J. Heberle, Phys. Rev. 128 (1962) 2207. [2] U. Gonser, C.J. Meechan, A.H. Muir and H. Wiedersich, J. Appl. Phys. 34 (1963) 2373. [3] P.R. Bevington, Data reduction and error analysis for the physical sciences (McGraw-Hill, New York, 1969).