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The hybridization contribution to the Mössbauer isomer shift in intermetallic compounds containing 151Eu
Physica 128B (1985) 309-312 North-Holland, Amsterdam
THE H Y B R I D I Z A T I O N C O N T R I B U T I O N T O THE M()SSBAUER ISOMER S H I F T IN I N T E R M E T A L L I C C O M P O U N D S C O N T A I N I N G 151Eu J.W.C. D E V R I E S * and R.C. T H I E L Kamerlingh Onnes Laboratorium der Rijksuniversiteit Leiden, Nieuwsteeg 18, 2311 SB Leiden, The Netherlands
K.H.J. B U S C H O W Philips Research Laboratories, 5600 JA Eindhoven, The Netherlands
Received 18 October 1984 The M6ssbauer isomer shift in intermetallic compounds analysed with the cellular model of Miedema and Van der Woude is composed of three contributions. One of these contributions (R') is the hybridization of the s and p electrons of a non-transition metal with the d electrons of the M6ssbauer atom. In Gd-based compounds R' is regarded as a constant. In a previous work, on the other hand, we found in Eu-based compounds a strong correlation between R' and the number of outer p electrons of the non-transition metal. We will show in this study that this correlation is artificial and can be attributed to a volume contraction of the Eu atoms.
1. Introduction In a previous study [1] we have investigated the 151Eu isomer shift (IS) in terms of the model of M i e d e m a and Van der W o u d e [2]. In this model the strain free dilute limit 8m~ A of the IS at the A site in the system AxBI_ x is expressed as the sum of three terms. T h e first term is proportional to the electronegativity difference A~b* = ~b~ - ~b~ and takes account of the charge transfer upon alloying or compounding. T h e second term is proportional to the difference in electron density at the Wigner-Seitz cell boundaries Anws = n~8 _ n~A and is a measure of the intra-atomic s--d electron rearrangement accompanying c o m p o u n d formation. A third term ( R ' ) taking account of hybridization effects has to be added when the c o m p o u n d contains non-transition metal atoms. The expression for the dilute limit of the IS is then A
8ma x =
t
A
P'Adp* + Q A n , , s / n ~ + R ' .
The constants P ' and Q ' can be derived from IS m e a s u r e m e n t s on compounds where the R ' term is not present, i.e. compounds containing transition metals, noble metals, or rare-earth eleA ments. The value of 8m~ can be obtained by extrapolation to the B-rich side in a plot of the IS versus the co6rdination fraction fA. This is the degree in which A atoms are surrounded by B atoms, and fA depends on the concentration x and the molar volume V m of the A and B atoms: s
(2a)
C ~ ~--- X A V2A/3[XA V A~3 "l- X B V ~ 3 ] -1 .
(2b)
F r o m the thus obtained dilute limit values and the appropriate values of ~b* and nws [2, 3], the constants P ' and Q ' can be calculated. Then, in principle, the IS of any c o m p o u n d can be calculated by using the expression ~A
(1)
* Present address: Philips Research Laboratories, 5600 JA Eindhoven, The Netherlands.
s 2
fA = C~[1 + 8(CACn) 1,
A A
= faSm~.
(3)
For t51Eu the constants P ' and Q ' were found to be: P ' = - 2 . 3 1 m m / s V and O ' = + 0 . 7 3 m m / s [1].
0378--4363/85/$03.30 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
J. W.C. de Vries et al. / M6ssbauer isomer shift in intermetallic compounds
310
The hybridization contribution R ' can only be determined by matching the experimental dilute A limit 8~ p to the value of p ' A ¢ * + Q tAnwJnw~. In the case of 151Eu compounds, a strong correlation was found to exist between R ' and the number of outer p electrons of the partner metal [1] (see fig. 2a). Application of this model to the IS of ~SSGd, on the other hand, yielded no such correlation of R'. Analysis of the IS data of the Gd compounds made clear that a correction to the expected linear behaviour (eq. (3)) of the IS was necessary. This correction is associated with the intraatomic redistribution of charge accompanying the volume contraction of the rare-earth atom, which in turn influences the IS [4, 5]. The volume correction can be represented by C=
A p
A
XAf s~v a Vmax/V
A
.
(4)
From the analysis of the IS of ~SSGdand 151Eu, it follows that the constant AS can be identified as the coefficient A, which describes the normal volume effect of the IS. The volume change of the A atoms is at a maximum in the dilute limit and is denoted as A vA.,. Including this volume correction implies anoA ther extrapolation to obtain 8m, w We first correct the IS of the most dilute compound before we extrapolate to fA = 1: A__ 8A -
-
c.
(5)
The values of the dilute limit will hence be different from those found earlier [1, 6, 7], and consequently the values of P ' and Q' will be different. In this report it will be shown that the correlation of R ' with the number of outer p electrons is an artifact, which is no longer present when the IS data are corrected for the volume effect. In fact we will show that the correlation originally found is to be attributed to the volume contraction of the Eu atoms.
2. Analysis In fig. 1 we show schematically how the dilute
6exp max
~,exp max
Fig. 1. Schematic representation of the extrapolations to obtain the dilute limit. (Fq) Data point without volume correction (SgP). (1) Data point with volume correction ((7) according to eqs. (4) and (5) (8 rexp m~x)-
limit 8.,~ E~ is obtained. The experimental IS value (8) of the most dilute compound is shown (Fq) in a plot of the IS versus the coordination fraction fEL By extrapolating from the IS value of Eu metal at f a~ = 0 to f ~ = 1, we find the dilute limit ~cxp. max
•
8~:£ = B/ f E" .
(6)
The values of P', Q', and R ' obtained from this situation will be denoted as P'I, Ql', R ' r Included in fig. 1 is the correction applied to 8 from eq. (5) (1), and the appropriate extrapolation yielding a corrected value of the dilute limit 8' exp. m$x" 8 , nlax-- ( 8 - c)/f
(7)
u
We will denote the values of P', Q', and R ' as obtained from these corrected values as: P~, Q~, R~. From (6) and (7) it follows for the hybridization term: t
Eu
R ' 1 = 8 I f E" - (P~A~b * + O l A n w d n ~ )
,
R ~ = 8 / f E" - C / f E" - (P~Adp*+ Q ~ n ~ / n ~ ) .
(8a) (8b)
We can now express the term R'~, which shows the correlation with the number of outer p electrons, as R '1 = C / f E" + A P ' A ¢ *
E, + R ~ , + A Q 'An,~/nws
(9)
where Ap' = p~ - p~ and A Q ' = Q~ - Q'r We have listed in table I the terms of eq. (9) for the various systems of mEu which we have studied. Included in this table is the averaged
J. W.C. de Vries et al. / M6ssbauer isomer shift in intermetallic compounds
311
Table I Values of the terms from eq. (9) for various Eu systems. Included are the average (x) and the standard deviation tr in %. Also given are (x) and tr of AP'Adp* + A Q ' A n w d n ~ + R~. All quantitues are in mm/s. System
R~
Eu-Mg Eu-AI Eu-Si Eu-Zn Eu--Ga Eu--Ge Eu--Cd Eu-In Eu-Sn Eu-Hg Eu-Pb
-2.8 -1.7 -0.7 -2.7 -2.0 - 1.2 -2.9 -1.7 -0.5 -1.1 - 1.0
(x) or[%]
- 1.66 51
AP'A4a*
A Q 'Anws/n~ Eu
R2,
0.43 1.44 3.11 0.49 1.36 2.90 0.55 1.48 1.76 1.57 1.70
-0.04 -0.07 -0.09 -0.06 -0.06 -0.08 -0.06 -0.06 -0.07 -0.07 -0.06
-0.67 -1.48 -1.98 -1.19 -1.15 - 1.39 -0.90 -0.67 -0.90 -0.90 -0.61
-2.6 -1.6 -1.8 -2.0 -2.6 -2.7 -2.5 -2.5 - 1.3 -1.7 -2.0
1.53 58
-0.07 11
- 1.08 39
-2.12 24
C/f~ ~
(x) (r[%]
-3.26 17
value of all of these terms separately, with the standard deviation or. F r o m this t a b l e it can be inferred, that instead of R~, now C/f E~ shows a systematic behaviour as R ' 1 does. This is graphically shown in fig. 2, where both R ' 1 and C/f~ u are plotted versus n p m, the n u m b e r of outer p electrons. The values of or as listed in table I also indicate that AP'Adp*, AQ'An.Jn.,s,~u
~' -1
~ 2I_,.~l_
np0 np1 np2
~
np0 np1 np2
Fig. 2. Hybridization term (R~) as obtained in ref. [1] versus the n u m b e r of outer p electrons np = of the partner metal for various rows in the periodic table (a). V o l u m e correction C / f ~" versus n p " 0a). D a t a from table I. ( ! 3p" ; • 4p = ; • 5p= ; • 610".) T h e full lines are guides to the eye.
R~, as well as the sum of these three terms, are m o r e or less constant c o m p a r e d with R '1and C/f~ u.
3. Conclusion In conclusion we can say that, as suggested earlier [5], the systematic behaviour of the hybridization term is due to a systematic effect in the volume contraction of the Eu atoms, rather than to the number of outer p electrons of the partner metal. Such a correlation was not found in the case of the Gd compounds. This may be attributed to the smaller volume changes of the Gd atoms upon compound formation than of the Eu atoms. Note that Gd is more electronegative than Eu. Since the difference A~b* is a measure of the charge transfer and hence of the volume contraction, the volume effects in the Eu compounds will be larger than in the G d compounds
18]. Acknowledgements We wish to thank Prof. W.J. Huiskamp for his interest in this work.
312
J.W.C. de Vries et al. / M6ssbauer isomer shift in intermetallic compounds
Part of this investigation was performed as a continuation of the research program of the 'Stichting voor Fundamenteel Onderzoek der Materie' (F.O.M.) with financial support from the 'Nederlandse Organisatie voor Zuiver Wetenschappelijk Onderzoek' (Z.W.O.). References [1] J.W.C. De Vries, R.C. Thiel and K.H.J. Buschow, Physica 121B (1983) 100.
[2] A.R. Miedema and F. van der Woude, Physica 100B (1980) 145. [3] A.K. Niessen, F.R. De Boer, R. Boom, P.F. de Ch:~tel, W.C. Mattens and A.R. Miedema, Calphad 7 (1983) 51. [4] J.W.C. de Vries, R.C. Thiel and K.H.J. Buschow, J. Phys. F: Metal Phys., to be published. [5] J.W.C. de Vries, Thesis, Leiden University (1984). [6] H. de Graaf, R.C. Thiel and K.H.J. Buschow, J. Phys. F: Metal Phys. 12 (1982) 2079. [7] H. de Graaf, Thesis, Leiden University (1982). [8] A.R. Miedema and A.K. Niessen, Physica I14B (1982) 367.
THE H Y B R I D I Z A T I O N C O N T R I B U T I O N T O THE M()SSBAUER ISOMER S H I F T IN I N T E R M E T A L L I C C O M P O U N D S C O N T A I N I N G 151Eu J.W.C. D E V R I E S * and R.C. T H I E L Kamerlingh Onnes Laboratorium der Rijksuniversiteit Leiden, Nieuwsteeg 18, 2311 SB Leiden, The Netherlands
K.H.J. B U S C H O W Philips Research Laboratories, 5600 JA Eindhoven, The Netherlands
Received 18 October 1984 The M6ssbauer isomer shift in intermetallic compounds analysed with the cellular model of Miedema and Van der Woude is composed of three contributions. One of these contributions (R') is the hybridization of the s and p electrons of a non-transition metal with the d electrons of the M6ssbauer atom. In Gd-based compounds R' is regarded as a constant. In a previous work, on the other hand, we found in Eu-based compounds a strong correlation between R' and the number of outer p electrons of the non-transition metal. We will show in this study that this correlation is artificial and can be attributed to a volume contraction of the Eu atoms.
1. Introduction In a previous study [1] we have investigated the 151Eu isomer shift (IS) in terms of the model of M i e d e m a and Van der W o u d e [2]. In this model the strain free dilute limit 8m~ A of the IS at the A site in the system AxBI_ x is expressed as the sum of three terms. T h e first term is proportional to the electronegativity difference A~b* = ~b~ - ~b~ and takes account of the charge transfer upon alloying or compounding. T h e second term is proportional to the difference in electron density at the Wigner-Seitz cell boundaries Anws = n~8 _ n~A and is a measure of the intra-atomic s--d electron rearrangement accompanying c o m p o u n d formation. A third term ( R ' ) taking account of hybridization effects has to be added when the c o m p o u n d contains non-transition metal atoms. The expression for the dilute limit of the IS is then A
8ma x =
t
A
P'Adp* + Q A n , , s / n ~ + R ' .
The constants P ' and Q ' can be derived from IS m e a s u r e m e n t s on compounds where the R ' term is not present, i.e. compounds containing transition metals, noble metals, or rare-earth eleA ments. The value of 8m~ can be obtained by extrapolation to the B-rich side in a plot of the IS versus the co6rdination fraction fA. This is the degree in which A atoms are surrounded by B atoms, and fA depends on the concentration x and the molar volume V m of the A and B atoms: s
(2a)
C ~ ~--- X A V2A/3[XA V A~3 "l- X B V ~ 3 ] -1 .
(2b)
F r o m the thus obtained dilute limit values and the appropriate values of ~b* and nws [2, 3], the constants P ' and Q ' can be calculated. Then, in principle, the IS of any c o m p o u n d can be calculated by using the expression ~A
(1)
* Present address: Philips Research Laboratories, 5600 JA Eindhoven, The Netherlands.
s 2
fA = C~[1 + 8(CACn) 1,
A A
= faSm~.
(3)
For t51Eu the constants P ' and Q ' were found to be: P ' = - 2 . 3 1 m m / s V and O ' = + 0 . 7 3 m m / s [1].
0378--4363/85/$03.30 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
J. W.C. de Vries et al. / M6ssbauer isomer shift in intermetallic compounds
310
The hybridization contribution R ' can only be determined by matching the experimental dilute A limit 8~ p to the value of p ' A ¢ * + Q tAnwJnw~. In the case of 151Eu compounds, a strong correlation was found to exist between R ' and the number of outer p electrons of the partner metal [1] (see fig. 2a). Application of this model to the IS of ~SSGd, on the other hand, yielded no such correlation of R'. Analysis of the IS data of the Gd compounds made clear that a correction to the expected linear behaviour (eq. (3)) of the IS was necessary. This correction is associated with the intraatomic redistribution of charge accompanying the volume contraction of the rare-earth atom, which in turn influences the IS [4, 5]. The volume correction can be represented by C=
A p
A
XAf s~v a Vmax/V
A
.
(4)
From the analysis of the IS of ~SSGdand 151Eu, it follows that the constant AS can be identified as the coefficient A, which describes the normal volume effect of the IS. The volume change of the A atoms is at a maximum in the dilute limit and is denoted as A vA.,. Including this volume correction implies anoA ther extrapolation to obtain 8m, w We first correct the IS of the most dilute compound before we extrapolate to fA = 1: A__ 8A -
-
c.
(5)
The values of the dilute limit will hence be different from those found earlier [1, 6, 7], and consequently the values of P ' and Q' will be different. In this report it will be shown that the correlation of R ' with the number of outer p electrons is an artifact, which is no longer present when the IS data are corrected for the volume effect. In fact we will show that the correlation originally found is to be attributed to the volume contraction of the Eu atoms.
2. Analysis In fig. 1 we show schematically how the dilute
6exp max
~,exp max
Fig. 1. Schematic representation of the extrapolations to obtain the dilute limit. (Fq) Data point without volume correction (SgP). (1) Data point with volume correction ((7) according to eqs. (4) and (5) (8 rexp m~x)-
limit 8.,~ E~ is obtained. The experimental IS value (8) of the most dilute compound is shown (Fq) in a plot of the IS versus the coordination fraction fEL By extrapolating from the IS value of Eu metal at f a~ = 0 to f ~ = 1, we find the dilute limit ~cxp. max
•
8~:£ = B/ f E" .
(6)
The values of P', Q', and R ' obtained from this situation will be denoted as P'I, Ql', R ' r Included in fig. 1 is the correction applied to 8 from eq. (5) (1), and the appropriate extrapolation yielding a corrected value of the dilute limit 8' exp. m$x" 8 , nlax-- ( 8 - c)/f
(7)
u
We will denote the values of P', Q', and R ' as obtained from these corrected values as: P~, Q~, R~. From (6) and (7) it follows for the hybridization term: t
Eu
R ' 1 = 8 I f E" - (P~A~b * + O l A n w d n ~ )
,
R ~ = 8 / f E" - C / f E" - (P~Adp*+ Q ~ n ~ / n ~ ) .
(8a) (8b)
We can now express the term R'~, which shows the correlation with the number of outer p electrons, as R '1 = C / f E" + A P ' A ¢ *
E, + R ~ , + A Q 'An,~/nws
(9)
where Ap' = p~ - p~ and A Q ' = Q~ - Q'r We have listed in table I the terms of eq. (9) for the various systems of mEu which we have studied. Included in this table is the averaged
J. W.C. de Vries et al. / M6ssbauer isomer shift in intermetallic compounds
311
Table I Values of the terms from eq. (9) for various Eu systems. Included are the average (x) and the standard deviation tr in %. Also given are (x) and tr of AP'Adp* + A Q ' A n w d n ~ + R~. All quantitues are in mm/s. System
R~
Eu-Mg Eu-AI Eu-Si Eu-Zn Eu--Ga Eu--Ge Eu--Cd Eu-In Eu-Sn Eu-Hg Eu-Pb
-2.8 -1.7 -0.7 -2.7 -2.0 - 1.2 -2.9 -1.7 -0.5 -1.1 - 1.0
(x) or[%]
- 1.66 51
AP'A4a*
A Q 'Anws/n~ Eu
R2,
0.43 1.44 3.11 0.49 1.36 2.90 0.55 1.48 1.76 1.57 1.70
-0.04 -0.07 -0.09 -0.06 -0.06 -0.08 -0.06 -0.06 -0.07 -0.07 -0.06
-0.67 -1.48 -1.98 -1.19 -1.15 - 1.39 -0.90 -0.67 -0.90 -0.90 -0.61
-2.6 -1.6 -1.8 -2.0 -2.6 -2.7 -2.5 -2.5 - 1.3 -1.7 -2.0
1.53 58
-0.07 11
- 1.08 39
-2.12 24
C/f~ ~
(x) (r[%]
-3.26 17
value of all of these terms separately, with the standard deviation or. F r o m this t a b l e it can be inferred, that instead of R~, now C/f E~ shows a systematic behaviour as R ' 1 does. This is graphically shown in fig. 2, where both R ' 1 and C/f~ u are plotted versus n p m, the n u m b e r of outer p electrons. The values of or as listed in table I also indicate that AP'Adp*, AQ'An.Jn.,s,~u
~' -1
~ 2I_,.~l_
np0 np1 np2
~
np0 np1 np2
Fig. 2. Hybridization term (R~) as obtained in ref. [1] versus the n u m b e r of outer p electrons np = of the partner metal for various rows in the periodic table (a). V o l u m e correction C / f ~" versus n p " 0a). D a t a from table I. ( ! 3p" ; • 4p = ; • 5p= ; • 610".) T h e full lines are guides to the eye.
R~, as well as the sum of these three terms, are m o r e or less constant c o m p a r e d with R '1and C/f~ u.
3. Conclusion In conclusion we can say that, as suggested earlier [5], the systematic behaviour of the hybridization term is due to a systematic effect in the volume contraction of the Eu atoms, rather than to the number of outer p electrons of the partner metal. Such a correlation was not found in the case of the Gd compounds. This may be attributed to the smaller volume changes of the Gd atoms upon compound formation than of the Eu atoms. Note that Gd is more electronegative than Eu. Since the difference A~b* is a measure of the charge transfer and hence of the volume contraction, the volume effects in the Eu compounds will be larger than in the G d compounds
18]. Acknowledgements We wish to thank Prof. W.J. Huiskamp for his interest in this work.
312
J.W.C. de Vries et al. / M6ssbauer isomer shift in intermetallic compounds
Part of this investigation was performed as a continuation of the research program of the 'Stichting voor Fundamenteel Onderzoek der Materie' (F.O.M.) with financial support from the 'Nederlandse Organisatie voor Zuiver Wetenschappelijk Onderzoek' (Z.W.O.). References [1] J.W.C. De Vries, R.C. Thiel and K.H.J. Buschow, Physica 121B (1983) 100.
[2] A.R. Miedema and F. van der Woude, Physica 100B (1980) 145. [3] A.K. Niessen, F.R. De Boer, R. Boom, P.F. de Ch:~tel, W.C. Mattens and A.R. Miedema, Calphad 7 (1983) 51. [4] J.W.C. de Vries, R.C. Thiel and K.H.J. Buschow, J. Phys. F: Metal Phys., to be published. [5] J.W.C. de Vries, Thesis, Leiden University (1984). [6] H. de Graaf, R.C. Thiel and K.H.J. Buschow, J. Phys. F: Metal Phys. 12 (1982) 2079. [7] H. de Graaf, Thesis, Leiden University (1982). [8] A.R. Miedema and A.K. Niessen, Physica I14B (1982) 367.