- Email: [email protected]
Influence of thermal defects on the optical properties of the intermetallic phases NiAl and FeAl
..
J. Phvs. Chem. Solids Vol. 55. No. 5. tn. 421-426. I!994 Copyright 6 1994 Elwvier S&e Ltd Printed in Great Britnin. All rights reserved 0022~3697194 $7.00 + 0.00
Pergamon
INFLUENCE OF THERMAL DEFECTS ON THE OPTICAL PROPERTIES OF THE INTERMETALLIC PHASES NiAl AND FeAl K. SCHLEMPER and L. K. THOMAS Institut fiir Metallforschung, Technische Universitiit Berlin, Sekr. PN 2-3, Hardenbergstr. Berlin 10623, Germany (Received 9 October
1992; accepted in revised form 22 December
36,
1993)
Abstract-Stoichiometric intermetallic alloys of NiAl and FeAl were quenched from temperatures up to 1100°C in order to produce thermal defects. The influence of this treatment to the optical properties was investigated by differential reflectometry (DR). The results could be interpreted by the assignment of the
optical absorptions to the electronic structure. No additional transitions (localized states) were found. A formation enthalpy of 1.04eV for the vacancies was obtained from the optical measurements and an electron transfer of 0.5 electrons/vacancy was concluded from the comparison of optical measurements with thermal defects and so-called structural defects, induced by a change of composition. Keywords:
Optical
properties,
differential
reflectometry,
thermal
defects,
intermetallic
phases,
vacancies.
we are only concerned with thermal defects. This may provide further information since thermal defects correspond to defects caused by a change in composition. It was interesting to investigate if both types of defects had similar electronic properties.
1. INTRODUCTION
FeAl, CoAl and NiAI are part of a family of intermetallic compounds that are built up of group VIII elements (transition metals) and group III elements. They show the B2 crystallographic structure and are of the Hume-Rothery type [l]. These materials exhibit together with a high formation energy, a high defect concentration and a specific defect structure, which is known as triple-defect [2]. This means that the predominant-in most cases the only-defects are combinations of the so-called antistructure atomsone transition metal atom on an Al-site, and vacancies on transition metal sites. The defect concentrations can be influenced by change of composition and heat treatment [3-lo]. The electronic structure of these materials is of major interest [l I-211. Theoretical calculations have been done for ordered compounds. The abovementioned defects at high concentration offer the possibility of investigating the order-disorder transition by an increasing number of crystal defects. On the other hand, optical measurements may give a good insight into the electronic structure near the Fermi level. Recently we discussed and analysed the optical properties of these materials in detail and correlated the results to the electronic band structure given by theoretical calculations in the literature [22]. The influence of the defects on the optical properties and the electronic structure caused by change of composition was investigated. In this present paper
2. EXPERIMENTAL For our measurements the differential reflectometry (DR) is used. This method is very sensitive to small variations of the reflectivity since only the difference in reflectivity of two samples is detected. For the second sample, the reference sample, an annealed sample of stoichiometric composition was used. The signal of DR is defined as:
represent the absolute reflecwhereSample and kference tivities of the sample and the reference, respectively. All measurements were performed with an apparatus described recently [23]. The preparation of the NiAl and FeAl alloys is described elsewhere [22]. For these measurements samples of stoichiometric composition of NiAl and FeAl were quenched from temperatures up to 1100°C in water. The planned quenching of CoAl could not be performed since this material showed a 421
K. SCHLEMPERand
422
very distinct brittleness-the samples broke when quenched. The samples were enclosed in quartz tubes in an argon atmosphere at 300 mbar and held at the desired temperature in a vertically fixed oven. To achieve a high quenching rate, the tube with the sample then dropped and was broken by a magnetically-driven hammer, so that the quenching medium contacted the sample directly. Because of some oxidation during the heat treatment the samples had to be cleaned and polished prior to the measurements. The influence of this polishing procedure was investigated. The standard state of the samples, referred to as the initial state, is characterized as the state directly after the oxidation layer was removed. It is recognized in an optical microscope as a very smooth but not flat topography of the sample’s surface. The removal of the oxide layer can also be observed with DR in the u.v.-region [24]. 3. ANALYSIS
OF DATA
Some information
will be deduced directly from the value for a fundamental discussion of the optical properties is the imaginary part of the dielectric function t2. Maxima in e2 can be interpreted as maxima in the absorption of the material. The dielectric function may be derived from reflectance by Kramers-Kronig analysis [22,25,26]. This was done for the present investigation. For the Kramers-Kronig analysis of AR/R data the absolute value of the dielectric function of the reference sample (stoichiometric sample) is necessary. This was taken from the literature [27], where, among other data, values on the optical properties of NiAl and CoAl are reported. We calculated values for FeAl by variation of the dielectric function of CoAl until the reflectivity obtained agreed with our measured values. This procedure is explained and justified in AR/R spectra. A more important
WI.
This function
provides the physical parameters:
wgi: resonance frequency (of the energy of the absorption), yi: attenuation 1;: intensity of the absorption (per electron). The free electron contribution
pl-wp+
2
W2+W:
(2) 2 wlwP w(w2+w:)
+
is represented by:
up: plasma frequency w, : attenuation. All these parameters have been calculated. Starting with a qualitative fitting by hand, an accurate fitting was calculated by the method of least squares. Depending on the number of absorptions to be fitted simultaneously this took several hours on an HP 9000 computer. N is the number of electrons per unit cell and was set to 3, but it may also be combined with f;. Then f; would give the intensity per unit cell instead of the intensity per electron. The sum is taken over a number of oscillators which is determined by the form of the c,-spectrum to be fitted. The resonance frequencies ogi will be of major interest in the following discussion. They are mainly determined by the energy of relative maxima (absorptions) in c2. The accuracy of the calculated resonance frequencies which represent the absorption energies was estimated to be better than 0.03 eV. It depends on the form and strength of the absorption. For pronounced maxima it was found to be about 0.005 eV. The parametersJ; are given by the strength and the attenuations yi by the widths of these absorptions. Details of both, Kramers-Kronig analysis and the Kramers-Heisenberg model, are presented elsewhere
PI. 4. RESULTS
Even more information will be obtained by a fit of the dielectric function by a proper mathematical expression. For this mathematical expression we used a sum of harmonic oscillators. This is known as the Kramers-Heisenberg model [28] (eqns (2) and (3))
C2=
L. K. THOMAS
AND DISCUSSION
4.1. AR/R spectra of NiAl In Fig. 1 the AR/R spectra for quenched NiAl are given. NiAl shows three maxima at 260, 350 and 680nm and a AR/R up to 15% induced by thermal treatment. The effects are obviously correlated to the quenching temperature. The spectra are very similar to those for NiAl of different compositions as shown in Fig. 2 (taken from [22]). Figure 3 shows the c2 spectra calculated from the measured values by Kramers-Kronig analysis. A pronounced maximum near 300 nm is changed only slightly, while an absorption near 480 nm is diminished for higher quenching temperatures, and another
Optical properties of the intermetallic phases NiAl and FeAl
423
1100~C -900.
c _.-soo*c ,. 700.C
wavelength
Fig. I. AR/R
Cnml
spectra of quenched NiAl (stoichiometric composition).
one near 700 nm increases in strength. This corresponds to the results on NiAl for Ni-rich compositions. In [22] it was found that the absorption near 300 nm is caused by a transition from the second to the seventh band near the symmetry directions A and ,?Zand the Fermi level is not involved, while for the other two absorptions the Fermi level is related as ground state (480 nm) or final state (700 nm). For a higher concentration of antistructure atoms the Fermi level shifts to lower energies and causes the change in the absorption near 480 nm and 700 nm. This corresponds to the results found for thermal defects. In Fig. 4a the intensities of the absorptions calculated by the fit of the Kramers-Heisenberg model are given. In Fig. 4b the attenuation yi for the three absorptions and the free electron contribution are presented. They all increase for higher temperatures and therefore higher defect concentrations. This was expected since an increased defect concentration should result in a higher scattering rate of the electrons and therefore an increased attenuation.
4.2. Formation enthalpy of vacancies For further information the AR/R spectra have to be compared with the spectra of different compositions of these alloys. Both show an apparently similar form (see Figs 1 and 2). It was also shown in [22] that some features in the AR/R spectra could be assigned to the number of vacancies or the antistructure atoms alone. The intensity of the maximum at 680 nm could be correlated very easily to the
(4
lad
lnte”8lty
1001
300 nm 0.4 480
“ill
0.2:t ? 0.0
’
800
700
800
temperature
900
ICI
(b!tten”atlon 110”11.1
‘I
91% NI -93% NI -_-_
53% Nl
I
0’
so0
700
800
800
,000
1100
temperature I%1
Fig. 2. AR/R
spectra of annealed NiAl for N&rich alloys.
Fig. 4. (a) Intensities of the absorption maxima in Fig. 3 resulting from the fit of the Kramers-Heisenberg model; (b) attenuation according to the Kramers-Heisenberg model.
K. SCHLEMPER~~~ L.K.
424
THOMAS
of vacancies is in good agreement with the literature.
60
60
70IWel:
60
100
11
110
[l/K1
Fig. 5. Arrhenius plot of the vacancy concentration in quenched NiAl, calculated from the AR/R spectra.
concentration of antistructure atoms C,, . The maximum depends linearly on the C,,, taken from the literature [3]. Using these results the C,, can be calculated easily by eqn (4) from the spectra in Fig. 1
C,,,[%] = (AR/R,,
- AR/Rrooo,,)[“/]/7.6 -t 0.5. (4)
The value of 7.6 is the proportionality constant found with C,,, values of [22] and 0.5 is the C,, of the stoichiomet~c reference sample [3]. The value of ARJR at the wavelength 1000 nm is taken as a reference value. The constants 7.6 and 0.5 are valid for this particular case. For other materials, a corresponding evaluation would have to be made. Since the spectra found for different heat treatments are similar to those for different compositions it is reasonable to use eqn (4) for the present case. For a sample of stoichiometric composition the equation holds if only antistructure atoms (ASA) of the transition metal and vacancies (V) in the transition metal sublattice are allowed according to the triple-defect model
Henig and Lukas [29] determined a formation enthalpy of 1.07 eV from calorimetric measurements and Parthasarathi and Fraser [30] estimated I .45 f 0.2 eV from TEM-measurements. To our knowledge this is the first time that the formation enthalpy has been measured by an optical method. We assume that this will be possible for other materials too, especially where the Fermi level is involved in the optical absorptions as the ground or final state. 4.3. Electron transfer to the vacancy
The major changes of the re~ectivity for NiAl are caused by the antist~cture atoms. But it was one of the initial reasons for this investigation to look for the influence of vacancies or even localized states at the vacancies. No localized states could be found neither at the vacancies nor at the antistructure atoms. An iniiuence of the vacancies coutd be separated by comparing the spectra of quenched stoichiometric samples to the spectra of nonstoichiometric compositions with the same antistructure atom concentration. The quenched sample will show in addition to the antistructure atoms a number of vacancies given by eqn (5), whereas annealed samples will show no or only an insignificant concentration of vacancies. To compare those two situations-only antistructure atoms in N&rich compounds in [22] and the quenched samples with the same amount of antistructure atoms but additional vacancies-we plotted the shift of the absorption near 480 nm in Fig. 6. For the x-axis the concentration of antistructure atoms is used, so the results of both investigations can be plotted together in one diagram. A systematic difference between the Ni-rich and the quenched samples is to be seen. A greater shift of the quenched samples is obvious. These samples differ
By means of eqns (4) and (5) the concentration of vacancies can be calculated from the optical measurements. The result is shown in an Arrhenius plot in Fig. 5. A good linear dependence is found. From this the formation enthalpy was deduced to be 1.04 rf: 0.07 eV and the vacancy concentration is given by: Cv =(4 + 2)* e(-(l.~io.07)/~~~)
(6)
The two in the denominator of the exponent represents the simultaneous generation of two vacancies necessary for the preservation of order in the B2 lattice. Our value for the formation enthalpy
ASA-Cono. [%I
Fig. 6. Shift of the energy of the absorption near 480nm caused by change of composition [22] and quenching (this work) and difference of both.
425
Optical properties of the intermetallic phases NiAl and FeAl
spectra by different durations of polishing at a quenching temperature of 1000°C.
Fig. 7. Change of AR/R
Fig. 9. AR/R
from the other ones only by the above mentioned vacancies. The shift of the Fermi level for Ni-rich
of the intensity of the spectra is obvious. In Fig. 8 the value of the maximum near 700 nm is given for three different temperatures. It is seen that
compounds to lower energies is caused by the lack of three electrons per antistructure atom. Additional vacancies increase this shift. The amount of this increase corresponds to the curve for the difference between quenched and annealed samples in Fig. 6. The slope of this curve is about l/6 of the curve for the annealed samples, so that about 3/6 = 0.5 electrons are connected to one vacancy. This is in agreement with the theoretical calculation, which predict a transfer of about 1 electron to the vacancy.
Influence of polishing
4.4.
Since the optical properties may be sensitive to polishing this problem was investigated separately. The samples were measured immediately after the quenching and during the removal of the oxide layer as described above. The influence of the oxide layer was discussed in [24]. Then polishing was continued and measurements were taken after distinct intervals. The curve indicated as 0 s in Fig. 7 represents the situation of the sample directly after the oxide layer was removed. For longer polishing periods a decrease maximum
I*1
25,
0
10
I
20
SO
40
so
00
70
80
polishing in eeconde
Fig. 8. Influence of the polishing on the maximum value of AR/R near 700 nm for three quenching temperatures.
spectra of quenched composition).
FeAl (stoichiometric
the intensity depends to a large degree on the polishing. However, it seems to be controllable for the first 10 s of polishing. For polishing periods longer than those presented here an effect of quenching remained obvious for quenching temperatures of 1000°C and above. The decreasing
optical
effect
and
therefore
the
decreasing concentration of thermally-created defects by the polishing can be understood by an increased mobility of the defects (vacancies and antistructure atoms), which is caused by the mechanical energy induced by the polishing. This will lead to an ‘annealing’ similar to the annealing where voids are formed. 4.5.
AR/R
at constant
temperature,
spectra of FeAl
No linear dependence of the AR/R spectra and the quenching temperature was found (Fig. 9). As seen for different compositions [22] the structure of these spectra is less pronounced and therefore a quantitative correlation to the defect structure (which also is less investigated and therefore uncertain) is ambiguous. Qualitatively it can be seen that there is a similarity to the measurements to varying composition, which is less clear especially for the shorter wavelength. The biggest change of the reflectivity was observed for 950°C. The intensity of the only maximum between 450 and 500nm decreased for increased quenching temperatures above 950°C. This is in agreement with the defect concentration measured by Paris and Lesbats [6]. Below 950°C they observed the expected triple-defect mechanism. Above this temperature they found vacancies in both sublattices and therefore a decreasing number of antistructure atoms. No further quantitative analysis was performed.
K. SCHLEMPER and L. K. THOMAS
426 5. CONCLUSION
In addition to our own results concerning the optical properties of the intermetallic compounds
NiAl, CoAl and FeAl we supply in this paper the results from measurements on NiAl and FeAl for quenched, stoichiometric samples. It is shown that the results can be understood by the interpretation of the optical properties and their correlation to the electronic structure. No qualitatively new influence on the optical properties was found. By the optical method the formation enthalpy of
vacancies in NiAl could be measured and was found to be 1.04eV. A transfer of about 0.5 electrons to a vacancy
is deduced
from these new results.
REFERENCES 1. Hume-Rotherv W.. J. Inst. Met. 35, 295 (1926). 2. Wasilewski RI J., J. Phys. Chews. Solids 29, 39’(1968). 19. 701 3. Jacobi H. and Enaell H.-J.. Acra Metalluraica I
(1971).
-
4. Meyer R., Wachtel E. and Gerold V., Z. Metallkde. 67, 97 (1976). 5. Rev&e J. P., Mat. res. Bull. 12, 995 (1977). 6. Paris D. and Lesbats P., J Nuclear Materials 69 & 70, 628 (1978). 7. Dinhut J. F., Riviere J. P. and Moine P., J. Nucl Mar. 69 & 70, 685 (1978). 8. Yang W. J., Lin F. and Dodd R. A., Scripta Metallurgica 12, 237 (1978). 9. Ho K. and Dodd R. A., Scripta Metalhogica 12, 1055 (1978).
10. Hiinecke J., Kim I., Frohberg G. and Wever H., Lattice disorder in /l-electron compounds. Mat. Sci. For. IS-18, 1311 (1987).
I 1. Knab D. and Koenig C., J. Phys.: Condensed Materials, 465 (1990).
12. Miiller C. H., Blau W. and Ziesche P., Phys. Stat. Sol. (b) 116, 561 (1983). 13. Okocbi M. and Yagisawa K., J. Phy. Sot. J. 51, 1166 (1982).
14. Koenig C. and Khan M. A., Phys. Rev. B 27, 6129 (1983). 15. Miiller C. H. and Ziesche P., Phys. Stat. Sol. (b) 114, 523 (1982). 16. Pechter K., Rastl P., Neckel A., Eibler R. and Schwarz K., Monatshefre fur Chemie 112, 317 (1981). 17. Eibler R. and Neckel A., J. Phys. F: Metal Phys. 10, 2179 (1980). 18. Miiller C. H., Worm H., Blau W., Zie&e P. and Krivitskii V. P., Phys. Stat. Sol. (b) 95, 215
(1979). 19. Peterman D. J., Rosei R., Lynch D. W. and Moruzzi V. L., Phys. Rev. B 21, 5505 (1980). 20. Kim Kwang Jo, Harmon B. N. and Lynch D. W., Phys. Reu. B 43, 21. Pornoi K. Lozovoi A. 22. Schlemner
1948 (1990).
I., Faberovich
0. V., Vlasov S. V. and
Yu, Opt. Spekrrosk. 63, 656 (1987).
K., Thesis, TU Berlin, D83 (1991); Schlem-Per K. and Thomas L. K., Phys. Reo. R, submitted. 23. Schlemper K. and Thomas L. K., Meas. Sci. Technol.
2, 1064 (1991). 24. Schlemner K.,
Rosiwal S., Bergmann H.-W. and Thomas L., Z.f. Metallkde 81, 761(1990).
25. Cardona M.. Solid State Phvs. Suppl. 11. (1969). 26. Balzarotti A_ Colavita E., ‘Gentile S. and Rosei R., Appl. Opt. 14, 2412 (1975). 27. Kiewit D. A. and Brittain J. O., J. appl. Phys. 41, 710 (1970). 28. Kuzmany H., Festkiirperspektroskopie, Chap. 7.
Springer-Verlag, Berlin (1989). 29. Henig E.-T. and Lukas H. L., Z. Mefallkde 66, 98 (1975). 30. Parthasarathi (1984).
A. and Fraser H. L., Phil. Mag. A SO, 89
J. Phvs. Chem. Solids Vol. 55. No. 5. tn. 421-426. I!994 Copyright 6 1994 Elwvier S&e Ltd Printed in Great Britnin. All rights reserved 0022~3697194 $7.00 + 0.00
Pergamon
INFLUENCE OF THERMAL DEFECTS ON THE OPTICAL PROPERTIES OF THE INTERMETALLIC PHASES NiAl AND FeAl K. SCHLEMPER and L. K. THOMAS Institut fiir Metallforschung, Technische Universitiit Berlin, Sekr. PN 2-3, Hardenbergstr. Berlin 10623, Germany (Received 9 October
1992; accepted in revised form 22 December
36,
1993)
Abstract-Stoichiometric intermetallic alloys of NiAl and FeAl were quenched from temperatures up to 1100°C in order to produce thermal defects. The influence of this treatment to the optical properties was investigated by differential reflectometry (DR). The results could be interpreted by the assignment of the
optical absorptions to the electronic structure. No additional transitions (localized states) were found. A formation enthalpy of 1.04eV for the vacancies was obtained from the optical measurements and an electron transfer of 0.5 electrons/vacancy was concluded from the comparison of optical measurements with thermal defects and so-called structural defects, induced by a change of composition. Keywords:
Optical
properties,
differential
reflectometry,
thermal
defects,
intermetallic
phases,
vacancies.
we are only concerned with thermal defects. This may provide further information since thermal defects correspond to defects caused by a change in composition. It was interesting to investigate if both types of defects had similar electronic properties.
1. INTRODUCTION
FeAl, CoAl and NiAI are part of a family of intermetallic compounds that are built up of group VIII elements (transition metals) and group III elements. They show the B2 crystallographic structure and are of the Hume-Rothery type [l]. These materials exhibit together with a high formation energy, a high defect concentration and a specific defect structure, which is known as triple-defect [2]. This means that the predominant-in most cases the only-defects are combinations of the so-called antistructure atomsone transition metal atom on an Al-site, and vacancies on transition metal sites. The defect concentrations can be influenced by change of composition and heat treatment [3-lo]. The electronic structure of these materials is of major interest [l I-211. Theoretical calculations have been done for ordered compounds. The abovementioned defects at high concentration offer the possibility of investigating the order-disorder transition by an increasing number of crystal defects. On the other hand, optical measurements may give a good insight into the electronic structure near the Fermi level. Recently we discussed and analysed the optical properties of these materials in detail and correlated the results to the electronic band structure given by theoretical calculations in the literature [22]. The influence of the defects on the optical properties and the electronic structure caused by change of composition was investigated. In this present paper
2. EXPERIMENTAL For our measurements the differential reflectometry (DR) is used. This method is very sensitive to small variations of the reflectivity since only the difference in reflectivity of two samples is detected. For the second sample, the reference sample, an annealed sample of stoichiometric composition was used. The signal of DR is defined as:
represent the absolute reflecwhereSample and kference tivities of the sample and the reference, respectively. All measurements were performed with an apparatus described recently [23]. The preparation of the NiAl and FeAl alloys is described elsewhere [22]. For these measurements samples of stoichiometric composition of NiAl and FeAl were quenched from temperatures up to 1100°C in water. The planned quenching of CoAl could not be performed since this material showed a 421
K. SCHLEMPERand
422
very distinct brittleness-the samples broke when quenched. The samples were enclosed in quartz tubes in an argon atmosphere at 300 mbar and held at the desired temperature in a vertically fixed oven. To achieve a high quenching rate, the tube with the sample then dropped and was broken by a magnetically-driven hammer, so that the quenching medium contacted the sample directly. Because of some oxidation during the heat treatment the samples had to be cleaned and polished prior to the measurements. The influence of this polishing procedure was investigated. The standard state of the samples, referred to as the initial state, is characterized as the state directly after the oxidation layer was removed. It is recognized in an optical microscope as a very smooth but not flat topography of the sample’s surface. The removal of the oxide layer can also be observed with DR in the u.v.-region [24]. 3. ANALYSIS
OF DATA
Some information
will be deduced directly from the value for a fundamental discussion of the optical properties is the imaginary part of the dielectric function t2. Maxima in e2 can be interpreted as maxima in the absorption of the material. The dielectric function may be derived from reflectance by Kramers-Kronig analysis [22,25,26]. This was done for the present investigation. For the Kramers-Kronig analysis of AR/R data the absolute value of the dielectric function of the reference sample (stoichiometric sample) is necessary. This was taken from the literature [27], where, among other data, values on the optical properties of NiAl and CoAl are reported. We calculated values for FeAl by variation of the dielectric function of CoAl until the reflectivity obtained agreed with our measured values. This procedure is explained and justified in AR/R spectra. A more important
WI.
This function
provides the physical parameters:
wgi: resonance frequency (of the energy of the absorption), yi: attenuation 1;: intensity of the absorption (per electron). The free electron contribution
pl-wp+
2
W2+W:
(2) 2 wlwP w(w2+w:)
+
is represented by:
up: plasma frequency w, : attenuation. All these parameters have been calculated. Starting with a qualitative fitting by hand, an accurate fitting was calculated by the method of least squares. Depending on the number of absorptions to be fitted simultaneously this took several hours on an HP 9000 computer. N is the number of electrons per unit cell and was set to 3, but it may also be combined with f;. Then f; would give the intensity per unit cell instead of the intensity per electron. The sum is taken over a number of oscillators which is determined by the form of the c,-spectrum to be fitted. The resonance frequencies ogi will be of major interest in the following discussion. They are mainly determined by the energy of relative maxima (absorptions) in c2. The accuracy of the calculated resonance frequencies which represent the absorption energies was estimated to be better than 0.03 eV. It depends on the form and strength of the absorption. For pronounced maxima it was found to be about 0.005 eV. The parametersJ; are given by the strength and the attenuations yi by the widths of these absorptions. Details of both, Kramers-Kronig analysis and the Kramers-Heisenberg model, are presented elsewhere
PI. 4. RESULTS
Even more information will be obtained by a fit of the dielectric function by a proper mathematical expression. For this mathematical expression we used a sum of harmonic oscillators. This is known as the Kramers-Heisenberg model [28] (eqns (2) and (3))
C2=
L. K. THOMAS
AND DISCUSSION
4.1. AR/R spectra of NiAl In Fig. 1 the AR/R spectra for quenched NiAl are given. NiAl shows three maxima at 260, 350 and 680nm and a AR/R up to 15% induced by thermal treatment. The effects are obviously correlated to the quenching temperature. The spectra are very similar to those for NiAl of different compositions as shown in Fig. 2 (taken from [22]). Figure 3 shows the c2 spectra calculated from the measured values by Kramers-Kronig analysis. A pronounced maximum near 300 nm is changed only slightly, while an absorption near 480 nm is diminished for higher quenching temperatures, and another
Optical properties of the intermetallic phases NiAl and FeAl
423
1100~C -900.
c _.-soo*c ,. 700.C
wavelength
Fig. I. AR/R
Cnml
spectra of quenched NiAl (stoichiometric composition).
one near 700 nm increases in strength. This corresponds to the results on NiAl for Ni-rich compositions. In [22] it was found that the absorption near 300 nm is caused by a transition from the second to the seventh band near the symmetry directions A and ,?Zand the Fermi level is not involved, while for the other two absorptions the Fermi level is related as ground state (480 nm) or final state (700 nm). For a higher concentration of antistructure atoms the Fermi level shifts to lower energies and causes the change in the absorption near 480 nm and 700 nm. This corresponds to the results found for thermal defects. In Fig. 4a the intensities of the absorptions calculated by the fit of the Kramers-Heisenberg model are given. In Fig. 4b the attenuation yi for the three absorptions and the free electron contribution are presented. They all increase for higher temperatures and therefore higher defect concentrations. This was expected since an increased defect concentration should result in a higher scattering rate of the electrons and therefore an increased attenuation.
4.2. Formation enthalpy of vacancies For further information the AR/R spectra have to be compared with the spectra of different compositions of these alloys. Both show an apparently similar form (see Figs 1 and 2). It was also shown in [22] that some features in the AR/R spectra could be assigned to the number of vacancies or the antistructure atoms alone. The intensity of the maximum at 680 nm could be correlated very easily to the
(4
lad
lnte”8lty
1001
300 nm 0.4 480
“ill
0.2:t ? 0.0
’
800
700
800
temperature
900
ICI
(b!tten”atlon 110”11.1
‘I
91% NI -93% NI -_-_
53% Nl
I
0’
so0
700
800
800
,000
1100
temperature I%1
Fig. 2. AR/R
spectra of annealed NiAl for N&rich alloys.
Fig. 4. (a) Intensities of the absorption maxima in Fig. 3 resulting from the fit of the Kramers-Heisenberg model; (b) attenuation according to the Kramers-Heisenberg model.
K. SCHLEMPER~~~ L.K.
424
THOMAS
of vacancies is in good agreement with the literature.
60
60
70IWel:
60
100
11
110
[l/K1
Fig. 5. Arrhenius plot of the vacancy concentration in quenched NiAl, calculated from the AR/R spectra.
concentration of antistructure atoms C,, . The maximum depends linearly on the C,,, taken from the literature [3]. Using these results the C,, can be calculated easily by eqn (4) from the spectra in Fig. 1
C,,,[%] = (AR/R,,
- AR/Rrooo,,)[“/]/7.6 -t 0.5. (4)
The value of 7.6 is the proportionality constant found with C,,, values of [22] and 0.5 is the C,, of the stoichiomet~c reference sample [3]. The value of ARJR at the wavelength 1000 nm is taken as a reference value. The constants 7.6 and 0.5 are valid for this particular case. For other materials, a corresponding evaluation would have to be made. Since the spectra found for different heat treatments are similar to those for different compositions it is reasonable to use eqn (4) for the present case. For a sample of stoichiometric composition the equation holds if only antistructure atoms (ASA) of the transition metal and vacancies (V) in the transition metal sublattice are allowed according to the triple-defect model
Henig and Lukas [29] determined a formation enthalpy of 1.07 eV from calorimetric measurements and Parthasarathi and Fraser [30] estimated I .45 f 0.2 eV from TEM-measurements. To our knowledge this is the first time that the formation enthalpy has been measured by an optical method. We assume that this will be possible for other materials too, especially where the Fermi level is involved in the optical absorptions as the ground or final state. 4.3. Electron transfer to the vacancy
The major changes of the re~ectivity for NiAl are caused by the antist~cture atoms. But it was one of the initial reasons for this investigation to look for the influence of vacancies or even localized states at the vacancies. No localized states could be found neither at the vacancies nor at the antistructure atoms. An iniiuence of the vacancies coutd be separated by comparing the spectra of quenched stoichiometric samples to the spectra of nonstoichiometric compositions with the same antistructure atom concentration. The quenched sample will show in addition to the antistructure atoms a number of vacancies given by eqn (5), whereas annealed samples will show no or only an insignificant concentration of vacancies. To compare those two situations-only antistructure atoms in N&rich compounds in [22] and the quenched samples with the same amount of antistructure atoms but additional vacancies-we plotted the shift of the absorption near 480 nm in Fig. 6. For the x-axis the concentration of antistructure atoms is used, so the results of both investigations can be plotted together in one diagram. A systematic difference between the Ni-rich and the quenched samples is to be seen. A greater shift of the quenched samples is obvious. These samples differ
By means of eqns (4) and (5) the concentration of vacancies can be calculated from the optical measurements. The result is shown in an Arrhenius plot in Fig. 5. A good linear dependence is found. From this the formation enthalpy was deduced to be 1.04 rf: 0.07 eV and the vacancy concentration is given by: Cv =(4 + 2)* e(-(l.~io.07)/~~~)
(6)
The two in the denominator of the exponent represents the simultaneous generation of two vacancies necessary for the preservation of order in the B2 lattice. Our value for the formation enthalpy
ASA-Cono. [%I
Fig. 6. Shift of the energy of the absorption near 480nm caused by change of composition [22] and quenching (this work) and difference of both.
425
Optical properties of the intermetallic phases NiAl and FeAl
spectra by different durations of polishing at a quenching temperature of 1000°C.
Fig. 7. Change of AR/R
Fig. 9. AR/R
from the other ones only by the above mentioned vacancies. The shift of the Fermi level for Ni-rich
of the intensity of the spectra is obvious. In Fig. 8 the value of the maximum near 700 nm is given for three different temperatures. It is seen that
compounds to lower energies is caused by the lack of three electrons per antistructure atom. Additional vacancies increase this shift. The amount of this increase corresponds to the curve for the difference between quenched and annealed samples in Fig. 6. The slope of this curve is about l/6 of the curve for the annealed samples, so that about 3/6 = 0.5 electrons are connected to one vacancy. This is in agreement with the theoretical calculation, which predict a transfer of about 1 electron to the vacancy.
Influence of polishing
4.4.
Since the optical properties may be sensitive to polishing this problem was investigated separately. The samples were measured immediately after the quenching and during the removal of the oxide layer as described above. The influence of the oxide layer was discussed in [24]. Then polishing was continued and measurements were taken after distinct intervals. The curve indicated as 0 s in Fig. 7 represents the situation of the sample directly after the oxide layer was removed. For longer polishing periods a decrease maximum
I*1
25,
0
10
I
20
SO
40
so
00
70
80
polishing in eeconde
Fig. 8. Influence of the polishing on the maximum value of AR/R near 700 nm for three quenching temperatures.
spectra of quenched composition).
FeAl (stoichiometric
the intensity depends to a large degree on the polishing. However, it seems to be controllable for the first 10 s of polishing. For polishing periods longer than those presented here an effect of quenching remained obvious for quenching temperatures of 1000°C and above. The decreasing
optical
effect
and
therefore
the
decreasing concentration of thermally-created defects by the polishing can be understood by an increased mobility of the defects (vacancies and antistructure atoms), which is caused by the mechanical energy induced by the polishing. This will lead to an ‘annealing’ similar to the annealing where voids are formed. 4.5.
AR/R
at constant
temperature,
spectra of FeAl
No linear dependence of the AR/R spectra and the quenching temperature was found (Fig. 9). As seen for different compositions [22] the structure of these spectra is less pronounced and therefore a quantitative correlation to the defect structure (which also is less investigated and therefore uncertain) is ambiguous. Qualitatively it can be seen that there is a similarity to the measurements to varying composition, which is less clear especially for the shorter wavelength. The biggest change of the reflectivity was observed for 950°C. The intensity of the only maximum between 450 and 500nm decreased for increased quenching temperatures above 950°C. This is in agreement with the defect concentration measured by Paris and Lesbats [6]. Below 950°C they observed the expected triple-defect mechanism. Above this temperature they found vacancies in both sublattices and therefore a decreasing number of antistructure atoms. No further quantitative analysis was performed.
K. SCHLEMPER and L. K. THOMAS
426 5. CONCLUSION
In addition to our own results concerning the optical properties of the intermetallic compounds
NiAl, CoAl and FeAl we supply in this paper the results from measurements on NiAl and FeAl for quenched, stoichiometric samples. It is shown that the results can be understood by the interpretation of the optical properties and their correlation to the electronic structure. No qualitatively new influence on the optical properties was found. By the optical method the formation enthalpy of
vacancies in NiAl could be measured and was found to be 1.04eV. A transfer of about 0.5 electrons to a vacancy
is deduced
from these new results.
REFERENCES 1. Hume-Rotherv W.. J. Inst. Met. 35, 295 (1926). 2. Wasilewski RI J., J. Phys. Chews. Solids 29, 39’(1968). 19. 701 3. Jacobi H. and Enaell H.-J.. Acra Metalluraica I
(1971).
-
4. Meyer R., Wachtel E. and Gerold V., Z. Metallkde. 67, 97 (1976). 5. Rev&e J. P., Mat. res. Bull. 12, 995 (1977). 6. Paris D. and Lesbats P., J Nuclear Materials 69 & 70, 628 (1978). 7. Dinhut J. F., Riviere J. P. and Moine P., J. Nucl Mar. 69 & 70, 685 (1978). 8. Yang W. J., Lin F. and Dodd R. A., Scripta Metallurgica 12, 237 (1978). 9. Ho K. and Dodd R. A., Scripta Metalhogica 12, 1055 (1978).
10. Hiinecke J., Kim I., Frohberg G. and Wever H., Lattice disorder in /l-electron compounds. Mat. Sci. For. IS-18, 1311 (1987).
I 1. Knab D. and Koenig C., J. Phys.: Condensed Materials, 465 (1990).
12. Miiller C. H., Blau W. and Ziesche P., Phys. Stat. Sol. (b) 116, 561 (1983). 13. Okocbi M. and Yagisawa K., J. Phy. Sot. J. 51, 1166 (1982).
14. Koenig C. and Khan M. A., Phys. Rev. B 27, 6129 (1983). 15. Miiller C. H. and Ziesche P., Phys. Stat. Sol. (b) 114, 523 (1982). 16. Pechter K., Rastl P., Neckel A., Eibler R. and Schwarz K., Monatshefre fur Chemie 112, 317 (1981). 17. Eibler R. and Neckel A., J. Phys. F: Metal Phys. 10, 2179 (1980). 18. Miiller C. H., Worm H., Blau W., Zie&e P. and Krivitskii V. P., Phys. Stat. Sol. (b) 95, 215
(1979). 19. Peterman D. J., Rosei R., Lynch D. W. and Moruzzi V. L., Phys. Rev. B 21, 5505 (1980). 20. Kim Kwang Jo, Harmon B. N. and Lynch D. W., Phys. Reu. B 43, 21. Pornoi K. Lozovoi A. 22. Schlemner
1948 (1990).
I., Faberovich
0. V., Vlasov S. V. and
Yu, Opt. Spekrrosk. 63, 656 (1987).
K., Thesis, TU Berlin, D83 (1991); Schlem-Per K. and Thomas L. K., Phys. Reo. R, submitted. 23. Schlemper K. and Thomas L. K., Meas. Sci. Technol.
2, 1064 (1991). 24. Schlemner K.,
Rosiwal S., Bergmann H.-W. and Thomas L., Z.f. Metallkde 81, 761(1990).
25. Cardona M.. Solid State Phvs. Suppl. 11. (1969). 26. Balzarotti A_ Colavita E., ‘Gentile S. and Rosei R., Appl. Opt. 14, 2412 (1975). 27. Kiewit D. A. and Brittain J. O., J. appl. Phys. 41, 710 (1970). 28. Kuzmany H., Festkiirperspektroskopie, Chap. 7.
Springer-Verlag, Berlin (1989). 29. Henig E.-T. and Lukas H. L., Z. Mefallkde 66, 98 (1975). 30. Parthasarathi (1984).
A. and Fraser H. L., Phil. Mag. A SO, 89