Z. Physik 270, 203-208 (1974) 9 by Springer-Verlag 1974

Temperature Dependence of the Knight Shift for Cadmium in Palladium H. Bertschat, H. Haas, F. Pleiter*, E. Recknagel, E. Schlodder and B. Spellmeyer** Hahn-Meitner-Institut fir Kernforschung Berlin GmbH, Bereich Kern- und Strahlenphysik and Freie Universit~it Berlin, Fachbereich Physik, Berlin-West, Germany Received June 11, 1974 Abstract. The Knight shift and its temperature dependence for a Cd impurity in palladium metal were measured by means of DPAD- and DPAC-methods utilizing the well known 5/2 +, 247-keV state in 11~Cd. The shift at 80 K was found to be KS (CdPd, 80 K)= - 0 . 8 (2)%. The observed variation of the KS in the temperature range from 80 K up to 1400 K is 0.5 %. For calibration purposes an accurate remeasurement of the magnetic moment of the 5/2 + state in m C d was necessary and yielded # (mCd, 5/2 +, 247 keV)= - 0.7697 (20) n.m.

1. Introduction

Knight shift (KS) measurements on transition metals and their alloys have been performed in most cases by means of NMR-techniques [1]. From such measurements the KS for Pd in palladium is known to be negative and strongly dependent on temperature [2]. The temperature dependence is the same as that of the susceptibility of palladium metal and the shift reaches its largest value of KS ( P d P d ) = - 4 . 5 % at about 80 K. The KS at Ag infnitely diluted in palladium has been extrapolated from NMR-measurements on a series of Pd-Ag alloys to be KS (AgEd_)= - 1.46 % at 1-4 K [3]. Recently this shift and its temperature dependence [4] were measured applying the method of time differential observation of the perturbed angular distribution of 7-rays following a nuclear reaction (DPAD [5]). At low temperatures a good agreement with the NMRdata was obtained. The temperature dependence of the KS was found to be similar to that observed for palladium. * Present address: Laboratorium voor Algemene Natuurkunde, University of Groningen, Groningen, The Netherlands. '~* Work performed in partial fulfillment of the requirements for a doctorate in science.

The KS for Cd impurities in palladium has been observed during a DPAD measurement of the magnetic moment of an isomeric 11/2- state in ~~ [6]. Because of the large error of the KS values obtained in these measurements due to the small magnetic moment and the half life of the state involved, a more accurate determination of this KS and its temperature dependence was performed by means of the DPAD method utilizing the 5/2 +, 247-keV state in ll~Cd populated via the x~ n) reaction. At room temperature an additional measurement of the KS and a remeasurement of the magnetic moment of the state involved were performed by the well known method of the time differential observation of the perturbed angular correlation (DPAC [7]). The large negative shift and the temperature dependence for the PdPd system are known to be due to the d-electron induced core polarisation which dominates the contact hyperfine interaction of s-like electrons. The impurity charge in the Ag_P_d_and CdPd systems may alter the influence of the involved hyperfine interaction processes. From the comparison of the KS data of the three systems PdPd, AgEd_ and CdPd and of their temperature dependence it is hoped to get more

204

Z. Physik 270 (1974)

insight into the hyperfine interaction processes causing the KS at impurity sites.

ABCD

~'1

ABCD

~(2

BD

BD

2. Experimental Details 2.1. Electronics:

For the DPAD- and the DPAC-experiments nearly the same electronic set up was used to detect the y-rays. For one detector of a two detector DPAD arrangement the slow fast coincidence circuit is shown in Fig. 1. The v-rays were observed by 3.7 cm x 3.7 cm diam. NaI (T1) crystals mounted via light pipes onto 56 DVP multipliers. (A fast signal is obtained from the multiplier anode carrying the timing information, while a slow one is taken from the l l t h dynode carrying the energy information,) After amplification the fast signal is used to trigger a leading-edge discriminator (LEDisc) and deplayed by a 50f~ cable. After pulse shaping the signal is fed into a differential discriminator (DD) as described in Ref. 8, which combines a single channel discriminator and a fast gate. In the Fig. 1 two DD units in the slow-fast coincidence circuit are shown enabling the simultaneous observation of two y-rays transitions. The signals from the two detectors A and B are mixed and provide the stop pulse for the time to amplitude converter (TAC), which is started by a pick up signal influenced by the pulsed beam upstream the target. The output signals of the TAC

pick-upsignal

slow

circuit signal fastsignal

\

~ 2 8

) k

29210211 Routing

Fig. 2. Routing system used in the four detector D P A C arrangement to store 16 different spectra in the multichannel analyzer

are stored in different parts of a multichannel analyser as indicated in Fig. 1. The time resolution achieved in the DPAD experiments depends on the pulse width of the ion beam and amounted to 7 ns (FWHM of the prompt peak). The DPAC-experiments were performed with a four detector apparatus, with a slow-fast coincidence circuit as described above for each detector. The two differential discriminator signals correspond to the 150 keV start and the 247 keV stop 7-ray transition of the Y-7 correlation. The routing system shown in Fig. 2 allows to store the 16 different time spectra resulting from the possible combinations of the start and stop signals in the memory of a 4 K multichannel analyser. The time resolution achieved in the DPAC experiments was better than 2 ns. 2.2. D P A C-Measurements

E _ __

_A5'1

Start Stop By] Fig. 1. Electronic set up for a two detector DPAD-system. The slow fast coincidence circuit of only one detector is shown

The magnetic moment of the 5/2 +, 247-keV state in tllCd was remeasured using the DPAC-method. The source consisted of a dilute solution of mInC13. The radioactivity was obtained by cyclotron irradiation of natural cadmium with 14 MeV protons*. The measurements of the absolute value demands a proper calibration of the magnetic field and of the time scale of the electronics used. The Hall stabilized magnetic field of about 20 kOe was measured by a rotating gaussmeter and found to be constant within 0.05 %. The rotating gaussmeter itself was calibrated by a temperature stabilized standard magnet. In this experiment the uncertainty due to the time calibration was improved by taking only four spectra each of 1024 channel length. In spite of this, the uncertainty * We appreciate the cooperation with the Institut fiir Kern- und Strahlenphysik der Technischen Universitiit Berlin in preparing the 111In radioactivity.

H. Bertschatet al.: TemperatureDependenceof the KnightShiftfor Cadmiumin Palladium in the final result is almost completely determined by the limited accuracy (about 0.3%) of the time calibration. The KS of Cd in palladium and silver was measured by comparing the magnetic spinrotation of m C d in palladium and silver metal with that of HtCd in an aqueous solution of ~l~InC13. The metal sources were prepared by electroplating the l~aIn activity from an acid indium sulfat solution onto the metal foils. The activity was diffused into the metal by heating the samples in an argon atmosphere about 200 ~ below the melting point for several hours. Residual activity was etched from the surface of the foils by chloric acid.

2.3. DPAD-Measurements The temperature dependence of the KS of Cd in palladium was measured using the DPAD-method. The isomeric state in m C d was populated via the l~ reaction using a pulsed e-particle beam (repetition time: 1 gs, pulse width: 7-10 ns). The targets were made by melting 98 % isotopically enriched metallic powder in an argon atmosphere and rolling the ingots to foils of about 100mg/cm 2. To get a proper metal structure the foils were annealed in vacuum 100 ~ below the melting point for several hours. For measurements below 300 K the ~~ foils were mounted on the cold finger of a continuous flow cryostat as described in Ref. 9. The target arrangement for high temperatures is described in Ref. 10. In between the different measurements of the temperature dependence of the KS the magnetic field was calibrated by measuring the Larmor frequency of the 5/2 +, 198-keV state in ~9F with the well known g-factor g=-1.442(3) [11]. The results of these calibration measurements were constant within 0.1%.

205

pressions:

R: (t) =

l(t, B, O)-I(t, B, 0 + ~/2) I(t, B, O)+ I(t, B, 0 + 7~/2)

b2 cos 2(0-c%t) 1 + b4 cos 4 ( 0 - coLt) ' R4(t)-

(4)

I(t, B, O)-I(t, B, 0 + ~/2) 2 I0 exp - t/z

= 1 +b~ cos 4 ( 0 - ~oLt)

(5)

where R 2(t) and R4(t) are mainly determined by the

anisotropy coefficients A22 and A44, respectively. The parameters b2, b4, 0 and coL were determined from least squares fits of the Eqs. (4) and (5) to the experimental ratios R 2 (t) and R4(t ). In a recent experiment Bertschat et al. [-12] have observed a quadrupole interaction in cubic palladium which was attributed to the coupling of the large quadrupole moment of the mCd-state [13] to the static or fluctuating electric field gradients originating from radiation induced point defects. The distribution of the quadrupole interaction constants has been measured in the same temperature range as that applied in the present work. Perturbation functions calculated for the combined interaction of the broadly destributed electric field gradients and the magnetic field were used to fit the modulation spectra obtained in the DPADexperiment. The influence of the combined interaction is a temperature dependent damping of the amplitude and a shift of the modulation frequency by +0.3 % at low (T<100 K) and 0.15% at high temperatures (T > 100 K).

3. Experimental Results

2.4. Analysis of the Data

3.1. DPA C-Measurements

For a pure magnetic perturbation with a magnetic field perpendicular to the detection plane the angular correlation between the emitted 7-rays has been described by Frauenfelder and Steffen [7]:

One spin precession spectrum obtained in the remeasurement of the g-factor of the 5/2 +, 247-keV state in m C d is shown in Fig. 3. The weighted average of the results of four measurements is

W(t, B, 0)=I o exp(-t/z)[1 +b2 cos 2(0-col t)

g (111Cd, 5/2 +, 247 keV) = - 0.3060 (10).

+ b4 cos 4 (0 - coLt)],

(1)

48 A22 + 20 A44 b2 = 64+ l(~Az2+9A44

(2)

35 A44 b4 = 64 + 16 A2e + A44 "

(3)

To analyze the DPAC measurements the appropriate spectra were added and fitted by the following ex-

A correction of 0.05 % for diamagnetic shielding has been applied [-143. Recently, Kriiger et al. [-15] have investigated the concentration dependence of the chemical shift for Cd in various aqueous solutions of Cd-salts. Their results do not affect our value since the chemical shifts found were not larger than 0.01%. Perturbed angular correlation measurements of the lXlCd g-factor published so far are summarized in Fig. 4.

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Z. Physik 270 (1974)

Rlt)o.1 I l l C d ; 5 1 2 " ;

247keY;

[

0

-O.l

0

100

200

300

400

500 Oetcty [ns]

The result of the DPAC-measurement on the KS of Cd in palladium is KS (CdP__dd)= - 0.8 (1) %, which is in good agreement with the DPAD-measurements. For the KS of Cd in silver we found KS (CdAg) = + 0.3 (1)% being considerably smaller than the value of +0.6% extracted from NMR-measurements on Cd-Ag alloys [21]. The KS measured at the Cd-site of these alloys varies from + 0.460 (1) %, for Cd in cadmium [22] up to +0.6 % at the Ag-rich site, larger than the value of the KS for Ag in silver 0.522 (2) % [23]. The KS at the Cd-site in the alloy has its minimum of + 0.3 % for alloys having 7-crystal structure [21-]. The disagreement of our DPAC-measurement with the NMR-measurements may therefore be due to an inhomogenous metal structure or/and chemical source contamination.

Fig. 3. Spin rotation spectrum of the 247 keV v-rays following the decay of rain in a dilute InC13 solution

3.2. DPAD-Measurements

The temperature dependence of the KS was observed from 25 K up to 1410 K. The modulation spectrum taken at 1410 K showed no damping of the modulation amplitude and could be fitted by the expressions (4) and (5). The result is shown in Fig. 5. The modulation spectra observed at temperatures from 25 up to 630 K showed a weak temperature dependent damping of the modulation amplitude. Two of the fits obtained by taking into account the radiation damage induced quadrupole interaction are shown in Fig. 6. The results of the KS measurements corrected for the frequency shifts discussed in Section 2.4 are summarized in Fig. 7. The error bars only represent the statistical uncertainties that follow from the least squares fits. The zero for the KS is uncertain by 0.4 % due to the uncertainty of the used g-factors of the isomeric states in 111Cd and in 19F. The close agreement

R2(t]

108pdict,n)111Cd Ey=247keV Ir~= 5+ T=1410K 2

+0.1 -0.32

t , -0.1

-0.30

R4(t)-I

~0.02 -0.02 Rz(t) +0.1

-0.28

-0.26

(ct)

[b)

(c)

(d)

[e)

(f)

Fig. 4 a - f . Compilation of different g-factor measurements. Time integral measurements are indicated by squares, time differential measurements by filled circles. (a) Ref. 16, (b) Ref. 17, (c) Ref. 18, (d) Ref. 19, (e) Ref. 20, (1) this work. (See also Fig. 11 in Ref. 19)

-0.1

0

100

200

300

Delay [nsl Fig. 5. Spin rotation spectra of the 247 keV 7-rays following the l~ n) reaction observed at 1410 K. The ratio Rz(t ) represents mainly the A22 term, the ratio R4(t) the A44 term. For calibration of the frequency the spin rotation spectrum of 19F was used

H. Bertschat ei aL: Temperature Dependence of the Knight Shift for Cadmium in Palladium

l~

R(t)

In= 5--§

E,y=247keV T = 25 K

207

o \

2

Hex t = 19, 3 kOe

c

0.05

A PdPd

~" ~ . . - -

8

o

0

AgPd

c CdPd

r"/.]

-0.05

0.05

I -I

I

I

~

I ! 5 • x 10 t' l'emulmole]

I

I

I

10

Fig. 8. KS versus susceptibility diagram for the three systems PdPd (taken from Ref. 2), AgPd [43, and CdPd. The KS-data of the simple metals are shown as points a for Pd, b for Ag and c for Cd and taken from the Refs. 2, 22, 23, respectively

-O.OE

0

100

200

300 Delay [ns l

Fig. 6. Spin rotation spectra of the 247 keV y-rays at two different temperatures following the 10sPd (~, n) reaction. The damping of the modulation amplitude is due to a quadrupole interaction caused by radiation damage effects

KS

[%]

111Cd

4. Discussion

From the work of Seitchik et al. [2-] the temperature dependence of the KS of Pd in palladium is known and found to be linearily related to the susceptibility. In the framework of a simple two band model of sand d-like electrons the temperature dependence of the KS was described by

in Pd

KS(T) =asZ~ +c~ez~(T) + fl Zvv

0i -1

I I

where ~sZ~ denotes the contribution arising from the contact hyperfine interaction of the s-electrons, edZd the contribution from the d-electron induced core polarisation and flZv~ the orbital contribution. At 80 K the KS reaches its largest value of

+ DPAD

9

a DPAC

-2

KS (PdPd, 80 K)= -4.5 %.

From the theory of the KS [24] it is expected that 1500 the KS at an impurity site is also proportional to the T Ew] susceptibility of the host lattice. This behaviour was Fig. 7. Temperature dependence of the KS for Cd in palladium observed for the temperature dependence of the KS of measured by the DPAD-method. The value obtained by the DPACAg in palladium [4]. In this experiment the shift at method is also shown. The error bars correspond to one standard 80 K measured to be KS (AgPd, 80 K) = - 1.4(3) % in deviation. Possible systematic errors which are below 0.4 % are not good agreement with the value extrapolated from included NMR-experiments on Ag-Pd alloys [3]. In the experiments reported in this paper, a similar relation between the KS and the susceptibility of the of the DPAC and the DPAD results at room tempera- palladium host was observed. The KS-data of the three systems PdPd, AgPd and CdPd are compared in a KS ture, however, proves the reliability of the DPAD versus susceptibility plot in Fig. 8. The curve for PdPd measurements. For temperatures above 100 K a slight decrease of the negative shift is observed. At 80 K the is taken from Ref. 2 and represents the extrapolation of low temperature NMR-experiments. Within the shift was found to be experimental errors the KS for all three systems is linearily related to the susceptibility of the Pd host. KS (CdPdd,80 K) = --0.8 (2) %. I

I

I

I

I

500

I

I

r

I

I

lO00

I

I

I

I

208

Z. Physik 270 (1974)

Table 1. Knight shift and ea-vaIues for the systems PdPd, AgPd and CdPd System

PdPd AgPd CdPd a Ref. 2.

KS (80 K)

[%]

-4.5 - 1.4 (3) -0.8 (2) u Ref. 4.

c%= A KS (T)/Az(T) -62 a - 18 b - 6.5 c

c This work.

This and the negative sign for the shift indicates that even in the CdPd system the core polarisation contribution of the d-electrons of the Pd-host is the dominant contribution to the KS. With increasing atomic number of the impurity the absolute value of the shift decreases and the temperature dependence of the shift becomes less pronounced. The relevant data for the three systems are listed in Table 1. For temperatures near the melting point the KS is expected to approach that of the pure metal. These shifts for the simple metals are indicated in Fig. 8 by three points a) PdPdd, taking only the contact hyperfine interaction term and the orbital contribution to the KS into account [2-1, b) KS(AgAg)= +0.522(2)% [19] and c) KS(CdC_d_d)= +0.414(2)% [20]. In the palladium and silver cases good agreement with this assumption is obtained, whereas for Cadmium a discrepancy of 0.4% appears, which may be due to experimental uncertainties and to errors in the g-factors used. It should be noted that within the experimental errors the magnetic hyperfine fields of Pd, Ag and Cd in Nickel 1-25] are proportional to the temperature dependent part of the KS of these elements in palladium. One of the main problems in applying the DPADmethod to solid state physics problems is the creation of lattice defects in the target material by the irradiation. Radiation effects should influence the frequency and the amplitude of the measured spin rotation spectra. For the system AgPd no damping of the modulation amplitude was observed and the measured KS at low temperatures was in good agreement with the results of NMR-measurements. In the measurements on the discussed CdPd system the damping of the amplitude clearly indicates a radiation damage induced quadrupole interaction, which influences the frequency. The observed large negative shifts at temperatures below T = 8 0 K , however, cannot be explained by the effect of a quadrupole interaction. They are probably due to very dilute magnetic impurities in the target material. Preliminary measure-

ments on alloys of Pd with 3 d-metals in small concentrations have shown extremely large negative shifts at low temperatures. This work was financially supported by the Bundesminister fiir Forschung und Technologie.

References 1. Drain, L.E.: Met. Rev. 119, 197 (1967) 2. Seitchik, J.A., Gossard, A.C., Jaccarino, V.: Phys. Rev. 136, A l l 1 9 (1964) 3. Narath, A.: J. Appl. Phys. 39, 553 (1968) 4. Bertschat, H., Maier, K.H., Recknagel, E., Spellmeyer, B.: Phys. Lett. A47, 159 (1974) 5. Recknagel, E.: Nuclear Spectroscopy and Reactions, ed. Cerny Chpt. VII C. New York: Academic Press Inc. 1974 6. Bertschat, H., Haas, H., Pleiter, F., Recknagel, E., Schlodder, E., Spellmeyer, B.: Nucl. Phys, 222, 399 (1974) 7. Frauenfelder, H., Steffen, R.M.: Alpha-, Beta- and GammaSpectroscopy, ed. K. Siegbahn, Vol. 2, p. 997. Amsterdam: North Holland 1965 8. Lauch, J., Nachbar, H.U.: Nucl. Inst. Meth. 73, 292 (1969) 9. Bertschat, H., Haas, H., Pleiter, F., Recknagel, E., Schlodder, E., Spellmeyer, B.: Z. Physik 267, 299 (1974) 10. Bertschat, H., Leith~iuser, U., Maier, K.H., Recknagel, E., Spellmeyer, B.: Nucl. Phys. A 215, 486 (1973) 11. Bleck, J., Haag, W.D., Ribbe, W.: Nucl. Inst. Meth. 67, 169 (1969) 12. Bertschat, H., Haas, H., Pleiter, F., Recknagel, E., Schlodder, E., Spellmeyer, B.: Contribution to the International Conference on Hyperfine Interactions. Uppsala 1974 and to be published 13. Bodenstedt, E., Ortabasi, U., Ellis, W.H.: Phys. Rev. B6, 2909 (1972) 14. Kopfermann, H.: Nuclear Moments, p. 450. New York: Academic Press, Inc. 1958 15. Krtiger, H., Lutz, O., Schwenk, A., Stricker, G.: Z. Physik 266, 123 (1974) 16. Aeppli, H., Albers-Sch/Snberg, H., Frauenfelder, H., Scherrer, P.: Helv. Phys. Acta 27, 547 (1954) 17. Albers-Sch6nberg, H., Heer, E., Novey, T.B., Scherrer, P.: Helv. Phys. Acta 27, 547 (1954) 18. Steffen, R.M, Zobel, W.: Phys. Re?. 103, 126 (1956) 19. Matthias, E., Bostr6m, L., Maciel, A., Salomon, M., Lindquist, T.: Nucl. Phys. 40, 656 (1963) 20. Bonacalza, E.C.O., Holm, G.B.: Phys. Lett. 4, 343 (1963) 21. Drain, L.E.: Phil. Mag. 4, 484 (1959) 22. Seymour, E.F., Styles, G.A.: Phys. Lett. 10, 269 (1964) 23. Sogo, B.P., Jeffries, C.D.: Phys. Rev. 93, 174 (1954) 24. Knight, W.D.: Solid State Physics, ed. Seitz, F., Turnbull, D., vol. 2, p. 93. New York: Academic Press, Inc. 1956 25. Koster, T.A., Shirley, D.A.: Hyperfine Interactions, ed. Goldring, G, Kalish, R., vol. 4, p. 1239. New York: Gordon and Breach Sc. Publ. 1971 H. Bertschat H. Haas F. Pleiter E. Recknagel E. Schlodder B. Spellmeyer Hahn-Meitner-Institut fiir Kernforschung GmbH D-1000 Berlin 39 Glienicker Stral3e 100