- Email: [email protected]
A new method of producing uniformly distributed alumina particles in Al-based metal matrix composite
Materials Letters 58 (2004) 679 – 682 www.elsevier.com/locate/matlet
A new method of producing uniformly distributed alumina particles in Al-based metal matrix composite Peng Yu *, Cheng-Ji Deng, Nan-Gang Ma, Dickon H.L. Ng Department of Physics, The Chinese University of Hong Kong, Hong Kong, China Received 11 February 2003; received in revised form 13 June 2003; accepted 23 June 2003
Abstract Alumina particles reinforced aluminum-based metal matrix composite is produced by sintering an Al – 10 wt.%ZnO sample at 1000 jC. During sintering, alumina particles are in situ formed by the displacement reaction between Al and ZnO. Some of the reduced Zn dissolves into the molten Al, while most of them vaporize at high temperature. It is found that the distribution of the alumina particles strongly depends on the rate of cooling of the sintered product. In comparison, the alumina particles are distributed more uniformly in the Al(Zn) solid solution matrix of the oil-quenched sample than that in the furnace-cooled sample. D 2003 Elsevier B.V. All rights reserved. Keywords: Composite materials; Microstructure; Zinc oxide; Alumina
1. Introduction Particles reinforced aluminum-based metal matrix composites (Al-MMCs), which possess high-specific elastic modulus and strength, are being widely used in the aerospace and automobile industries [1]. Traditionally, the AlMMCs are produced by directly adding reinforcements into the Al matrices [2]. Recently, some in situ methods have been developed and are being adopted in the production of Al-MMCs [3]. One commonly adopted in situ method involves the reaction between metal oxide, such as NiO [4], TiO2 [5], MoO3 [6], and Fe2O3 [7], and Al to produce Al2O3 particle or whisker reinforcements. After the reaction, the reduced metal usually further reacts with Al to form intermetallic phases, which also act as reinforcements in the matrix of the composite. Zinc oxide is a possible candidate to produce in situ AlMMCs because Zn will react readily with Al at elevated temperature, but this type of work on Al – ZnO system has not been reported so far. It is because Zn will not form intermetallic phase with Al [8], moreover, the Zn reduced from ZnO will remain in the composite as a free entity. Since Zn is soft, its presence in the Al matrix will lower the
* Corresponding author. 0167-577X/$ - see front matter D 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.matlet.2003.06.001
mechanical strength of the composite. Nevertheless, a small amount of Zn in the composite will enhance the strength of the composite, because Zn will dissolve into Al to form a matrix of Al(Zn) solid solution, which is tougher and having higher hardness value than that of a pure Al matrix. In this letter, we report a method of producing high quality Al2O3 reinforced Al(Zn)-based MMC by using the displacement reaction method while the excessive amount of Zn is eliminated by high temperature sintering.
2. Experiments A powder mixture that contained 90 wt.%Al (99.7% purity) and 10 wt.%ZnO (99.7% purity) is mixed, ground, and cold-pressed under 500 MPa to form green compact discs with diameter of 10 mm. Differential thermal analysis (DTA) is conducted to determine the reaction temperatures of the Al – ZnO system during sintering. During the analysis, the sample is heated in argon atmosphere in the DTA furnace in which the temperature is increased from ambient to 1000 jC at a heating rate of 5 jC/min. In the fabrication of the Al-MMC sample, the green sample is sintered at 1000 jC for half an hour in a tube furnace in an argon atmosphere. The target temperature is 1000 jC, which is not only above the temperature at which the displacement
680
P. Yu et al. / Materials Letters 58 (2004) 679–682
reaction between Al and ZnO occurs, but is also slightly above the boiling temperature of Zn (913 jC) [9]. The sample is then allowed to cool down to room temperature inside the furnace with the power turned off. In the study of the effect of cooling rate, another green sample is sintered at 1000 jC for half an hour and cooled to 800 jC (temperature slightly above the liquidus line of Al – Zn alloy) before the sample—ceramic sample holder assembly is drawn out from the tube furnace and dropped into a pool of vacuum pump oil at room temperature. Since the time for such a rapid-quench is less than 2 s, there is no possible reaction between the sample and the oil. The X-ray powder diffractometry (XRD) with Cu-Ka radiation is used to obtain the diffraction patterns of the samples in order to determine the phases in the sintered products. Small pieces are cut from the green sample, the furnace-cooled sample and the oilquenched samples. They are grounded into powders for XRD. In the study of the microstructures of the sintered products, the samples are polished and examined by using a LEO scanning electron microscope (SEM). The elemental analysis and quantitative compositions of the samples are determined by the energy dispersive X-ray spectroscopy (EDX).
Fig. 2. The XRD patterns of (a) the green sample, (b) the furnace-cooled sample, and (c) the oil-quenched sample.
Al and ZnO. The possible reaction is given by the following equation. Alðl;sÞ þ ZnOðsÞ ¼ ZnðlÞ þ Al2 O3ðsÞ
ð1Þ
3. Results and discussion The DTA curve of the Al – 10 wt.%ZnO sample is shown in Fig. 1. Endothermic and exothermic peaks are found in this curve. The endothermic peak occurs at a temperature about 660 jC, which is the melting point of Al. The exothermic peak is located in the temperature range between 640 and 720 jC, and it is split into two parts by the endothermic dip of Al. Such an exothermic peak obviously corresponds to the chemical reaction between
Fig. 1. The DTA curve of an Al – 20 wt.%ZnO sample. The endothermic peak at 660 jC corresponds to the melting of Al, and the exothermic peak in the temperature range between 640 and 720 jC corresponds to the reaction between Al and ZnO.
where the subscripts s and l stand for the solid and liquid forms of the substances. During sintering, the sample is kept at 1000 jC for half an hour. Most of the Zn from reaction (1) vaporizes, and is removed from the sample. ZnðlÞ ! ZnðgÞ
ð2Þ
The XRD patterns of the green sample and the two sintered samples are shown in Fig. 2. As a matter of fact, peaks in the pattern of the green sample correspond to those of Al and ZnO, while peaks of the two sintered samples are related to those of Al and a-Al2O3. Such a result indicates that all of the ZnO initially added into the green sample has been consumed in the displacement reaction during sintering, and that the reduced Zn has vaporized and escaped from the sintered samples. A study on the peak positions of Al in the XRD patterns reveals that a small amount of Zn still remains in the Al-based matrix. We find that the Al peaks in the patterns of the two sintered samples have shifted slightly to higher angles when they are compared to those Al peaks in the pattern of the green sample. Fig. 3 shows that the (420) peaks of Al of the two sintered samples are in the same position, which is 0.1j higher than that of the green sample. Such a difference suggests that the lattice parameters of the sintered samples are smaller than that of the green sample, and it is caused by the dissolution of Zn into Al forming the Al(Zn) solid solution. It is commonly known that the atomic radius of Zn is smaller than that of Al (rAl = 0.1432 nm, rZn = 0.1332 nm) [10], when some of the
P. Yu et al. / Materials Letters 58 (2004) 679–682
681
Fig. 5. A SEM micrograph of the oil-quenched sample which shows that the Al2O3 particles (bright) are distributed evenly in the Al(Zn) matrix (dark). Fig. 3. Enlarged portion of the XRD patterns which show the Al (420) peak of the green sample (curve a), the furnace-cooled sample (curve b) and the oil-quenched sample (curve c). The positions of the Al peaks of the sintered samples are about the same, and their diffraction angles are about 0.1j larger than that of the green sample.
Al atoms in the lattice are replaced by Zn, the resultant Al(Zn) solid solution will have a smaller lattice parameter. The SEM micrographs of the furnace-cooled sample and the oil-quenched sample are shown in Figs. 4 and 5, respectively. The dark background in both micrographs is the Al matrix. The EDX reveals that the matrix of both sintered samples contains mostly Al, but with some traces of Zn. This further supports our previous claim that a small quantity of Zn remains in the composite and forms solid solution with Al. The white particles in the micrographs are identified by EDX as Al2O3. In Fig. 6, an enlarged image of the oil-quenched sample shows that these Al2O3 particles have a rather narrow size distribution and an average size of about 10 Am. It is also evident that the Al2O3 is closely
Fig. 4. A SEM micrograph of the furnace-cooled sample after sintering at 1000 jC. The Al2O3 particles (bright) are segregated in some local regions in the Al(Zn) matrix (dark).
bonded to the Al(Zn) matrix since no structural defects, such as voids or cracks, are observed in the Al(Zn)/Al2O3 interface. In comparison, it can be seen that the Al2O3 particles are distributed more uniformly in the Al(Zn) matrix of the oil-quenched sample than those in the Al(Zn) of the furnace-cooled sample. In the furnace-cooled sample (Fig. 4), the Al2O3 particles are found segregating in some local regions of the Al(Zn) matrix. The reason for this segregation is because of the redistribution of the Al2O3 particles during the solidification of the Al-rich molten phase. It is known that the interfacial energy of Al2O3/solid-Al is larger than that of the Al2O3/liquid-Al [11]. As such, during the solidification of the furnace-cooled sample, the difference of the two interfacial energies acts a driving force for the growing solid-Al(Zn) to push the Al2O3 particles into the molten Al and secure their position in the liquid Al. This phenomenon called ‘‘particle pushing’’ was firstly reported by Uhlmann et al. [12], and was observed by many others.
Fig. 6. A SEM micrograph of the oil-quenched which shows that the average size of the Al2O3 particles are about 10 Am. Structural defects such as cracks or voids have not been found in the Al/Al2O3 interface.
682
P. Yu et al. / Materials Letters 58 (2004) 679–682
[11,13,14] As a result of this particle pushing, the Al2O3 particles of the composite are redistributed or segregated into those regions that are finally solidified. It was also reported [11] that this particle pushing could only take place under the condition that the growth velocity of the solid phase was lower than that of the velocity of particle pushing. Therefore, when the rate of solidification is high, as in our case of the rapid oil-quenched sample, the suspended Al2O3 particles in the molten Al have not been pushed away, and they tend to be stationary. As a result, there is little or no redistribution of the Al2O3 particles during the growing process of the solid phase, and the Al2O3 particles are distributed evenly in the Al(Zn) matrix as it was in the molten Al-rich phase.
4. Conclusions A new method is developed to fabricate Al2O3 particles reinforced Al(Zn) matrix composite by the reaction sintering of an Al– 10 wt.%ZnO sample. During sintering, Al2O3 particles are in situ formed by the displacement reaction between Al and ZnO, while most of the Zn produced in this reaction vaporizes as the sintering temperature is above the boiling point of Zn. At the same time, a small amount of Zn dissolves into Al to form Al(Zn) solid solution. The distribution of the Al2O3 particles in the Al(Zn) matrix of the sintered product strongly depends on the rate of cooling. The distribution of the Al2O3 particles can be made more uniform by oil-quenching the sample after being sintered at 1000 jC.
Acknowledgements This work is supported by the RGC Earmarked Research Grant-2001, project code: 2150303.
References [1] J.M. Wu, Z.Z. Li, J. Alloys Compd. 299 (2000) 9. [2] M. Taya, R.J. Arsenault, Metal Matrix Composite, Pergamon, Oxford, 1989, p. 210. [3] S.C. Tjong, Z.Y. Ma, Mater. Sci. Eng., A Struct. Mater.: Prop. Microstruct. Process. 29 (2000) 49. [4] D. Padmavardhani, A. Gomez, R. Abbaschian, Intermetallics 6 (1998) 229. [5] H.X. Peng, D.Z. Wang, L. Geng, C.K. Yao, Scr. Mater. 37 (1997) 199. [6] Y-F. Li, C-D. Qin, D.H.L. Ng, J. Mater. Res. 14 (1999) 2997. [7] R. Subramanian, C.G. McKamey, J.H. Schneibel, L.R. Buck, P.A. Menchhofer, Mater. Sci. Eng., A Struct. Mater.: Prop. Microstruct. Process. 254 (1998) 119. [8] American society for metals, Metal Handbook, 1973, p. 265, Metals Park, OH. [9] G.W.C. Kaye, T.H. Laby, Table of Physical and Chemical Constants, Longman, London, 1975, p. 152. [10] D.R. Askeland, The Science and Engineering of Materials, PWS, Boston, 1994, p. 796. [11] A. Mortensen, I. Jin, Int. Met. Rev. 37 (1992) 101. [12] D.R. Uhlmann, B. Chalmers, K.A. Jackson, J. Appl. Phys. 35 (1964) 2986. [13] J. Cisse, G.F. Bolling, J. Cryst. Growth 10 (1971) 67. [14] S.N. Omenyi, A.W. Neumann, J. Appl. Phys. 47 (1976) 3956.
A new method of producing uniformly distributed alumina particles in Al-based metal matrix composite Peng Yu *, Cheng-Ji Deng, Nan-Gang Ma, Dickon H.L. Ng Department of Physics, The Chinese University of Hong Kong, Hong Kong, China Received 11 February 2003; received in revised form 13 June 2003; accepted 23 June 2003
Abstract Alumina particles reinforced aluminum-based metal matrix composite is produced by sintering an Al – 10 wt.%ZnO sample at 1000 jC. During sintering, alumina particles are in situ formed by the displacement reaction between Al and ZnO. Some of the reduced Zn dissolves into the molten Al, while most of them vaporize at high temperature. It is found that the distribution of the alumina particles strongly depends on the rate of cooling of the sintered product. In comparison, the alumina particles are distributed more uniformly in the Al(Zn) solid solution matrix of the oil-quenched sample than that in the furnace-cooled sample. D 2003 Elsevier B.V. All rights reserved. Keywords: Composite materials; Microstructure; Zinc oxide; Alumina
1. Introduction Particles reinforced aluminum-based metal matrix composites (Al-MMCs), which possess high-specific elastic modulus and strength, are being widely used in the aerospace and automobile industries [1]. Traditionally, the AlMMCs are produced by directly adding reinforcements into the Al matrices [2]. Recently, some in situ methods have been developed and are being adopted in the production of Al-MMCs [3]. One commonly adopted in situ method involves the reaction between metal oxide, such as NiO [4], TiO2 [5], MoO3 [6], and Fe2O3 [7], and Al to produce Al2O3 particle or whisker reinforcements. After the reaction, the reduced metal usually further reacts with Al to form intermetallic phases, which also act as reinforcements in the matrix of the composite. Zinc oxide is a possible candidate to produce in situ AlMMCs because Zn will react readily with Al at elevated temperature, but this type of work on Al – ZnO system has not been reported so far. It is because Zn will not form intermetallic phase with Al [8], moreover, the Zn reduced from ZnO will remain in the composite as a free entity. Since Zn is soft, its presence in the Al matrix will lower the
* Corresponding author. 0167-577X/$ - see front matter D 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.matlet.2003.06.001
mechanical strength of the composite. Nevertheless, a small amount of Zn in the composite will enhance the strength of the composite, because Zn will dissolve into Al to form a matrix of Al(Zn) solid solution, which is tougher and having higher hardness value than that of a pure Al matrix. In this letter, we report a method of producing high quality Al2O3 reinforced Al(Zn)-based MMC by using the displacement reaction method while the excessive amount of Zn is eliminated by high temperature sintering.
2. Experiments A powder mixture that contained 90 wt.%Al (99.7% purity) and 10 wt.%ZnO (99.7% purity) is mixed, ground, and cold-pressed under 500 MPa to form green compact discs with diameter of 10 mm. Differential thermal analysis (DTA) is conducted to determine the reaction temperatures of the Al – ZnO system during sintering. During the analysis, the sample is heated in argon atmosphere in the DTA furnace in which the temperature is increased from ambient to 1000 jC at a heating rate of 5 jC/min. In the fabrication of the Al-MMC sample, the green sample is sintered at 1000 jC for half an hour in a tube furnace in an argon atmosphere. The target temperature is 1000 jC, which is not only above the temperature at which the displacement
680
P. Yu et al. / Materials Letters 58 (2004) 679–682
reaction between Al and ZnO occurs, but is also slightly above the boiling temperature of Zn (913 jC) [9]. The sample is then allowed to cool down to room temperature inside the furnace with the power turned off. In the study of the effect of cooling rate, another green sample is sintered at 1000 jC for half an hour and cooled to 800 jC (temperature slightly above the liquidus line of Al – Zn alloy) before the sample—ceramic sample holder assembly is drawn out from the tube furnace and dropped into a pool of vacuum pump oil at room temperature. Since the time for such a rapid-quench is less than 2 s, there is no possible reaction between the sample and the oil. The X-ray powder diffractometry (XRD) with Cu-Ka radiation is used to obtain the diffraction patterns of the samples in order to determine the phases in the sintered products. Small pieces are cut from the green sample, the furnace-cooled sample and the oilquenched samples. They are grounded into powders for XRD. In the study of the microstructures of the sintered products, the samples are polished and examined by using a LEO scanning electron microscope (SEM). The elemental analysis and quantitative compositions of the samples are determined by the energy dispersive X-ray spectroscopy (EDX).
Fig. 2. The XRD patterns of (a) the green sample, (b) the furnace-cooled sample, and (c) the oil-quenched sample.
Al and ZnO. The possible reaction is given by the following equation. Alðl;sÞ þ ZnOðsÞ ¼ ZnðlÞ þ Al2 O3ðsÞ
ð1Þ
3. Results and discussion The DTA curve of the Al – 10 wt.%ZnO sample is shown in Fig. 1. Endothermic and exothermic peaks are found in this curve. The endothermic peak occurs at a temperature about 660 jC, which is the melting point of Al. The exothermic peak is located in the temperature range between 640 and 720 jC, and it is split into two parts by the endothermic dip of Al. Such an exothermic peak obviously corresponds to the chemical reaction between
Fig. 1. The DTA curve of an Al – 20 wt.%ZnO sample. The endothermic peak at 660 jC corresponds to the melting of Al, and the exothermic peak in the temperature range between 640 and 720 jC corresponds to the reaction between Al and ZnO.
where the subscripts s and l stand for the solid and liquid forms of the substances. During sintering, the sample is kept at 1000 jC for half an hour. Most of the Zn from reaction (1) vaporizes, and is removed from the sample. ZnðlÞ ! ZnðgÞ
ð2Þ
The XRD patterns of the green sample and the two sintered samples are shown in Fig. 2. As a matter of fact, peaks in the pattern of the green sample correspond to those of Al and ZnO, while peaks of the two sintered samples are related to those of Al and a-Al2O3. Such a result indicates that all of the ZnO initially added into the green sample has been consumed in the displacement reaction during sintering, and that the reduced Zn has vaporized and escaped from the sintered samples. A study on the peak positions of Al in the XRD patterns reveals that a small amount of Zn still remains in the Al-based matrix. We find that the Al peaks in the patterns of the two sintered samples have shifted slightly to higher angles when they are compared to those Al peaks in the pattern of the green sample. Fig. 3 shows that the (420) peaks of Al of the two sintered samples are in the same position, which is 0.1j higher than that of the green sample. Such a difference suggests that the lattice parameters of the sintered samples are smaller than that of the green sample, and it is caused by the dissolution of Zn into Al forming the Al(Zn) solid solution. It is commonly known that the atomic radius of Zn is smaller than that of Al (rAl = 0.1432 nm, rZn = 0.1332 nm) [10], when some of the
P. Yu et al. / Materials Letters 58 (2004) 679–682
681
Fig. 5. A SEM micrograph of the oil-quenched sample which shows that the Al2O3 particles (bright) are distributed evenly in the Al(Zn) matrix (dark). Fig. 3. Enlarged portion of the XRD patterns which show the Al (420) peak of the green sample (curve a), the furnace-cooled sample (curve b) and the oil-quenched sample (curve c). The positions of the Al peaks of the sintered samples are about the same, and their diffraction angles are about 0.1j larger than that of the green sample.
Al atoms in the lattice are replaced by Zn, the resultant Al(Zn) solid solution will have a smaller lattice parameter. The SEM micrographs of the furnace-cooled sample and the oil-quenched sample are shown in Figs. 4 and 5, respectively. The dark background in both micrographs is the Al matrix. The EDX reveals that the matrix of both sintered samples contains mostly Al, but with some traces of Zn. This further supports our previous claim that a small quantity of Zn remains in the composite and forms solid solution with Al. The white particles in the micrographs are identified by EDX as Al2O3. In Fig. 6, an enlarged image of the oil-quenched sample shows that these Al2O3 particles have a rather narrow size distribution and an average size of about 10 Am. It is also evident that the Al2O3 is closely
Fig. 4. A SEM micrograph of the furnace-cooled sample after sintering at 1000 jC. The Al2O3 particles (bright) are segregated in some local regions in the Al(Zn) matrix (dark).
bonded to the Al(Zn) matrix since no structural defects, such as voids or cracks, are observed in the Al(Zn)/Al2O3 interface. In comparison, it can be seen that the Al2O3 particles are distributed more uniformly in the Al(Zn) matrix of the oil-quenched sample than those in the Al(Zn) of the furnace-cooled sample. In the furnace-cooled sample (Fig. 4), the Al2O3 particles are found segregating in some local regions of the Al(Zn) matrix. The reason for this segregation is because of the redistribution of the Al2O3 particles during the solidification of the Al-rich molten phase. It is known that the interfacial energy of Al2O3/solid-Al is larger than that of the Al2O3/liquid-Al [11]. As such, during the solidification of the furnace-cooled sample, the difference of the two interfacial energies acts a driving force for the growing solid-Al(Zn) to push the Al2O3 particles into the molten Al and secure their position in the liquid Al. This phenomenon called ‘‘particle pushing’’ was firstly reported by Uhlmann et al. [12], and was observed by many others.
Fig. 6. A SEM micrograph of the oil-quenched which shows that the average size of the Al2O3 particles are about 10 Am. Structural defects such as cracks or voids have not been found in the Al/Al2O3 interface.
682
P. Yu et al. / Materials Letters 58 (2004) 679–682
[11,13,14] As a result of this particle pushing, the Al2O3 particles of the composite are redistributed or segregated into those regions that are finally solidified. It was also reported [11] that this particle pushing could only take place under the condition that the growth velocity of the solid phase was lower than that of the velocity of particle pushing. Therefore, when the rate of solidification is high, as in our case of the rapid oil-quenched sample, the suspended Al2O3 particles in the molten Al have not been pushed away, and they tend to be stationary. As a result, there is little or no redistribution of the Al2O3 particles during the growing process of the solid phase, and the Al2O3 particles are distributed evenly in the Al(Zn) matrix as it was in the molten Al-rich phase.
4. Conclusions A new method is developed to fabricate Al2O3 particles reinforced Al(Zn) matrix composite by the reaction sintering of an Al– 10 wt.%ZnO sample. During sintering, Al2O3 particles are in situ formed by the displacement reaction between Al and ZnO, while most of the Zn produced in this reaction vaporizes as the sintering temperature is above the boiling point of Zn. At the same time, a small amount of Zn dissolves into Al to form Al(Zn) solid solution. The distribution of the Al2O3 particles in the Al(Zn) matrix of the sintered product strongly depends on the rate of cooling. The distribution of the Al2O3 particles can be made more uniform by oil-quenching the sample after being sintered at 1000 jC.
Acknowledgements This work is supported by the RGC Earmarked Research Grant-2001, project code: 2150303.
References [1] J.M. Wu, Z.Z. Li, J. Alloys Compd. 299 (2000) 9. [2] M. Taya, R.J. Arsenault, Metal Matrix Composite, Pergamon, Oxford, 1989, p. 210. [3] S.C. Tjong, Z.Y. Ma, Mater. Sci. Eng., A Struct. Mater.: Prop. Microstruct. Process. 29 (2000) 49. [4] D. Padmavardhani, A. Gomez, R. Abbaschian, Intermetallics 6 (1998) 229. [5] H.X. Peng, D.Z. Wang, L. Geng, C.K. Yao, Scr. Mater. 37 (1997) 199. [6] Y-F. Li, C-D. Qin, D.H.L. Ng, J. Mater. Res. 14 (1999) 2997. [7] R. Subramanian, C.G. McKamey, J.H. Schneibel, L.R. Buck, P.A. Menchhofer, Mater. Sci. Eng., A Struct. Mater.: Prop. Microstruct. Process. 254 (1998) 119. [8] American society for metals, Metal Handbook, 1973, p. 265, Metals Park, OH. [9] G.W.C. Kaye, T.H. Laby, Table of Physical and Chemical Constants, Longman, London, 1975, p. 152. [10] D.R. Askeland, The Science and Engineering of Materials, PWS, Boston, 1994, p. 796. [11] A. Mortensen, I. Jin, Int. Met. Rev. 37 (1992) 101. [12] D.R. Uhlmann, B. Chalmers, K.A. Jackson, J. Appl. Phys. 35 (1964) 2986. [13] J. Cisse, G.F. Bolling, J. Cryst. Growth 10 (1971) 67. [14] S.N. Omenyi, A.W. Neumann, J. Appl. Phys. 47 (1976) 3956.