- Email: [email protected]
Reinforcement of Al–Fe–Ni alloys with the in situ formation of composite materials
Journal of Alloys and Compounds 483 (2009) 178–181
Contents lists available at ScienceDirect
Journal of Alloys and Compounds journal homepage: www.elsevier.com/locate/jallcom
Reinforcement of Al–Fe–Ni alloys with the in situ formation of composite materials G. Vourlias ∗ , N. Pistofidis, E. Pavlidou, G. Stergioudis Department of Physics, Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece
a r t i c l e
i n f o
Article history: Received 30 August 2007 Received in revised form 11 July 2008 Accepted 21 July 2008 Available online 11 December 2008 Keywords: Metal matrix composites Nanostructured materials X-ray diffraction Scanning electron microscopy Transmission electron microscopy
a b s t r a c t One of the most effective methods for the improvement of the mechanical properties of metals is their reinforcement with non-metallic materials. In the present work powder of K2 TiF6 and KBF4 was added in an Al–Fe–Ni alloy while the alloy was in liquid form at 1060 ◦ C with a 5 wt.% mixture of powders and with simultaneous stirring for 30 min. The liquid was squeeze-casted at 150 bar. The as-cast specimens were examined with electron microscopy and X-ray diffraction. SEM analysis revealed that the as-formed material is composed by needle-like crystallites along with a dentritic form and an interdendritic phase. The composition of the needle-like crystallites may presumably be expressed by the formula (Fe-Ni)Al3 . The rest of the matrix consists of almost pure Al grown dentritically, while the interdendritic phase contains Fe and Ni dissolved in Al. EDS analysis also proved the existence of spots with high Ti concentration, which probably refer to the Ti–B compounds. Finally TEM verified the presence of nanocrystals in the matrix. © 2008 Elsevier B.V. All rights reserved.
1. Introduction Metal matrix composite materials are ideal for structural applications where high strength-to-weight and stiffness-to-weight ratios are required [1,2]. Aluminum alloys are one of the preferable metallic matrices for this kind of materials. A usual method for their production is based on the dissolution of solid iron or ferrous alloys in liquid aluminum, which leads to the enrichment of aluminum in iron and/or other alloying elements. This process results in a subsequent growth of intermetallic and intermediate layers [3,4]. The simultaneous addition of inorganic salts (such as K2 TiF6 and KBF4 ), which react with each other in the liquid phase, results in the formation of ceramic particles in situ that are dispersed in the matrix and behave as reinforcement as they impede the dislocation movement [5–7]. Dissolution of metals in liquid aluminum mainly depends on thermodynamic conditions and experimental parameters such as temperature, stirring time, the degree of aluminum saturation and the chemical composition of the ferrous alloys in the reaction zone. The above-mentioned factors play also an important role to the formation of the different phases during dissolution and to the reaction of the salts that form the reinforcement material. Furthermore, it was established that the growth of the intermetallic
∗ Corresponding author. Tel.: +30 2310 998066. E-mail address: [email protected] (G. Vourlias). 0925-8388/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.jallcom.2008.07.173
phases is controlled by physicochemical reactions at the interfaces of the liquid and the solid phase and by interdiffusion through the different phases [3,4]. In any case, all these factors (matrix composition, dispersion and size of the reinforcement particles) affect the mechanical behavior of the as-formed material and the above phenomena are enhanced when the matrix is nanostructured (e.g. part of its crystals is nanosized), since in this case the amount of intergranular boundaries is increased. As a result increased mechanical resistance is achieved [8]. In any case the main objective of this study is the investigation of the structure of in situ composite materials in a Al–Fe–Ni matrix. After a brief review of the development of the diffusion structures of a Fe–Ni alloy dissolved in pure aluminum, the material was examined with electron microscopy in order to track nanocrystals in its mass and the results of the above research were connected with the improvement of the mechanical properties of the aluminum matrix. 2. Experimental In the present work a Fe–Ni rod containing 97 wt.% Fe and 3 wt.% Ni was dissolved in liquid Al. The as-formed matrix was heated up to 1060 ◦ C and a 5 wt.% mixture of K2 TiF6 and KBF4 was added with simultaneous stirring for 30 min. The liquid was squeeze-cast at 150 bar. The initial observation of a polished surface of the as-cast specimens took place with a Karl Zeiss M8 low magnification binocular light microscope equipped with a CCD camera for image capture. Afterwards cross-sections have been cut from each sample, mounted in bakelite, polished down to 5 m alumina emulsion and etched with Keller solution (1% HF, 1.5% HCl, 2.5% HNO3 , 95% H2 O). The as-prepared coupons were examined with scanning electron microscopy with a 20kVolt JEOL 840A SEM
G. Vourlias et al. / Journal of Alloys and Compounds 483 (2009) 178–181
179
Fig. 1. SE micrographs of the composite (a) at low magnification, (b) at higher magnification). Point #1 refers to the needle-like crystallites, point #2 to the base phase and point #3 to the gray interdendritic phase.
equipped with an OXFORD ISIS 300 EDS analyzer and the necessary software to perform line scan and chemical mapping of the samples. X-ray diffraction was also used for their structural characterization. For this purpose a Bragg-Brentano Philips D5000 diffractometer was used, where CuK␣ radiation ( = 1.54406 Å) was chosen. Selected specimens were also observed with conventional transmission electron microscopy (CTEM) and high resolution electron microscopy (HREM) with a 100 kV JEOL 100CX TEM and a 200 kV JEOL 2011 HREM respectively, after the suitable sample pretreatment [9]. TEM was used because it is characterized by higher mass resolution with regard to X-rays. Thus, one phase can be identified by electron diffraction even if it exists only in a small portion in the material. For this reason, in the present work TEM analysis was mainly used for the Al–Fe phase examination.
3. Results and discussion Fig. 1a shows a SEM micrograph of a coupon of the material formed at low magnification. What is rather characteristic is the presence of needle-like formations that overrun its surface. The examination of the same area at higher magnification reveals more details (Fig. 1b). Three distinct areas are observed based on their relief, which consist of white needle-like crystallites randomly dispersed in the whole matrix, a gray area developed in an interdentritic form and a dark base phase.
Fig. 2. Chemical mapping of Fig. 1(b).
180
G. Vourlias et al. / Journal of Alloys and Compounds 483 (2009) 178–181
Fig. 3. X-ray pattern of the as cast material.
The concentration profiles of the elements (which were measured with SEM-EDS and are summarized in a graphical form in Fig. 2) in the so-called reaction zone, which in this case was extended from the boundary of the pure aluminum to about 10 m into the white crystallites, are very interesting. The interface between the matrix and the white crystallites was assumed to be the zero point. As a result we were able to calculate the concentration of the elements across these crystallites. In the reaction zone the crystallites contain 76–73 at.% of Al, 22–25 at.% of Fe and 3–2 at.% of Ni. Hence the composition of this zone may presumably be expressed by the formula (Fe–Ni)Al3 . Interplanar distances (dspacing) corresponding to X-ray patterns of Fig. 3, were found to be rather close to those of FeAl3 phase. In spite the fact that it was not easy to arrive at definite conclusions concerning the phases of the layers in the reaction zone, the experimental observations led us to assume that some equilibrium phases such as (Fe–Ni)2 Al5 seem to be at very low concentration. Since this layer is known to develop near the area richer in iron, it was very probable that the (Fe–Ni)Al3 layer, which grown at the early stage of dissolution process temporarily acts as barrier between melting aluminum and pure iron, giving rise to interdiffusion process. In any case the differentiation of (Fe–X)2 Al5 from (Fe–X)Al3 is rather difficult due to the fact that the most characteristic reflections coincide for both
Fig. 4. TEM micrograph of the aluminum matrix that shows stacking faults.
Fig. 5. TEM micrograph of the Al base phase with the corresponding electron diffraction pattern which refers to a Fe–Ni–Al phase.
cases or they are very close. Furthermore shifting due to the presence of the X admixtures or due to the stresses may further confuse the analysis. As regards to the area next to reacting zone experimental concentration profiles revealed that some additional layers developed, probably by a diffusion process. Surprisingly these layers did not correspond to any of binary aluminides or ternary phases identified on the Fe–Ni–Al system. The first of the new layers designated as (Fe–Ni)2 Al3 based on the composition found after a detailed elementary analysis which was accomplished by EDS-SEM. By extending the observation to the inner diffusion zone a layer with the (Fe–Ni)Al seemed to have been formed. The borders of the two layers were not clear, but a sharp change in the concentrations which occurs, helped to identify this layer as (Fe–Ni)Al taking into account previous findings. The rest of the aluminum matrix consists mainly of two distinct areas (Fig. 1). The gray area, which develops in an interdentritic form, is composed by aluminum with iron and nickel and appears in the XRD pattern as (Fe, Ni). It was rather unexpected that the amount of nickel is high enough to this area overcoming the average percentage of nickel in the alloy. This is ascribed to a selective dissolution of nickel in the pure aluminum. The base phase (dark one) consists almost of pure aluminum strongly stressed due to heterogeneous nucleation. Stacking faults in this area due to internal stresses were also observed with TEM (Fig. 4).
Fig. 6. TEM micrograph of the reinforcement particles with the corresponding electron diffraction pattern.
G. Vourlias et al. / Journal of Alloys and Compounds 483 (2009) 178–181
181
EDS analysis revealed only Ti as the detection of low atomic weight elements such as B is not possible due to inherent limitations of the electron microscope used. TEM examination revealed the presence of crystals of different sizes ranging from a few micrometers up to a few nanometers, as we see in Figs. 5–7. In the micrograph of Fig. 5 which refers to the base phase, Fe–Ni–Al crystals with size of about 0.1–3 m appears. However in the same phase smaller crystals appear with spherical shape, whose the electron diffraction pattern refers to Ti compounds (Fig. 6). Consequently they refer to products of the reinforcement reaction. In Fig. 7 it is also possible to distinguish Fe–Ni–Al nanocrystals (Al–Ni, Al–Fe, Al–Ni–Fe). To verify their presence the same area was also examined with HREM (Fig. 8). In this micrograph nanocrystals are observed with d-spacing referring to Fe–Ni–Al. From this examination it is obvious that the material examined contains also nanocrystals, at least in the Al base phase. These crystals were probably formed due to rapid cooling of the system when it was cast. Since squeeze casting was used for its formation, local overcooling at the contact surface with the mould is very likely. This phenomenon could lead to rapid solidification at these areas and thus the size of the as-formed crystals remained small. 4. Conclusions Fig. 7. TEM micrograph of the Al base phase with the corresponding electron diffraction pattern, showing Fe–Ni–Al nanocrystals.
The present microstructural examination of the Al matrix composites revealed that three distinct areas, consisting of white needle-like crystallites randomly dispersed in the whole matrix, a gray area developed in an interdentritic form and a dendritic base phase were formed. Their composition could be presumably expressed by the formulas (Fe–Ni)Al3 , (Fe, Ni) and pure Al, respectively. Reinforcement particles were also detected in the base phase, which means that the initially added salts reacted and formed the reinforcing phase. Furthermore in the base phase Fe–Ni–Al nanocrystals are present. Their formation is very favorable for the system as they enhance its mechanical behavior. References
Fig. 8. HREM micrograph of the Al base phase showing Fe–Ni–Al nanocrystals.
In the mapping of Fig. 2 titanium was also detected. XRD revealed also the presence of Ti–B compounds. Their presence is very important because it verifies the formation of the reinforcement particles. The reaction of the salts added (K2 TiF6 and KBF4 ) leads to the formation of TiB2 , while the rest of the reaction products are evolved from the system as they are very volatile. However
[1] R.M. Jones, Mechanics of Composite Materials, Taylor & Francis, Philadelphia, 1998. [2] F.L. Mathews, R.D. Rawlings, Composite Materials: Engineering and Science, CRC Press, Woodhead, Cambridge, 1999. [3] V.I. Dybkov, J. Mater. Sci. 21 (1986) 3078. [4] V.I. Dybkov, J. Mater. Sci. 25 (1990) 3615. [5] C.F. Feng, L. Froyen, J. Mater. Sci. 35 (2000) 837. [6] A. Jha, C. Dometakis, Mater. Des. 18 (1997) 297. [7] J.V. Wood, P. Davies, J.L.F. Kellie, Mater. Sci. Technol. 19 (1993) 833. [8] J.F. Li, H. Liao, X.Y. Wang, C. Coddet, H. Chen, C.X. Ding, Thin Solid Films 17 (2004) 101. [9] D.B. Williams, C.B. Carter, Transmission Electron Microscopy, Plenum Press, 1996.
Contents lists available at ScienceDirect
Journal of Alloys and Compounds journal homepage: www.elsevier.com/locate/jallcom
Reinforcement of Al–Fe–Ni alloys with the in situ formation of composite materials G. Vourlias ∗ , N. Pistofidis, E. Pavlidou, G. Stergioudis Department of Physics, Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece
a r t i c l e
i n f o
Article history: Received 30 August 2007 Received in revised form 11 July 2008 Accepted 21 July 2008 Available online 11 December 2008 Keywords: Metal matrix composites Nanostructured materials X-ray diffraction Scanning electron microscopy Transmission electron microscopy
a b s t r a c t One of the most effective methods for the improvement of the mechanical properties of metals is their reinforcement with non-metallic materials. In the present work powder of K2 TiF6 and KBF4 was added in an Al–Fe–Ni alloy while the alloy was in liquid form at 1060 ◦ C with a 5 wt.% mixture of powders and with simultaneous stirring for 30 min. The liquid was squeeze-casted at 150 bar. The as-cast specimens were examined with electron microscopy and X-ray diffraction. SEM analysis revealed that the as-formed material is composed by needle-like crystallites along with a dentritic form and an interdendritic phase. The composition of the needle-like crystallites may presumably be expressed by the formula (Fe-Ni)Al3 . The rest of the matrix consists of almost pure Al grown dentritically, while the interdendritic phase contains Fe and Ni dissolved in Al. EDS analysis also proved the existence of spots with high Ti concentration, which probably refer to the Ti–B compounds. Finally TEM verified the presence of nanocrystals in the matrix. © 2008 Elsevier B.V. All rights reserved.
1. Introduction Metal matrix composite materials are ideal for structural applications where high strength-to-weight and stiffness-to-weight ratios are required [1,2]. Aluminum alloys are one of the preferable metallic matrices for this kind of materials. A usual method for their production is based on the dissolution of solid iron or ferrous alloys in liquid aluminum, which leads to the enrichment of aluminum in iron and/or other alloying elements. This process results in a subsequent growth of intermetallic and intermediate layers [3,4]. The simultaneous addition of inorganic salts (such as K2 TiF6 and KBF4 ), which react with each other in the liquid phase, results in the formation of ceramic particles in situ that are dispersed in the matrix and behave as reinforcement as they impede the dislocation movement [5–7]. Dissolution of metals in liquid aluminum mainly depends on thermodynamic conditions and experimental parameters such as temperature, stirring time, the degree of aluminum saturation and the chemical composition of the ferrous alloys in the reaction zone. The above-mentioned factors play also an important role to the formation of the different phases during dissolution and to the reaction of the salts that form the reinforcement material. Furthermore, it was established that the growth of the intermetallic
∗ Corresponding author. Tel.: +30 2310 998066. E-mail address: [email protected] (G. Vourlias). 0925-8388/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.jallcom.2008.07.173
phases is controlled by physicochemical reactions at the interfaces of the liquid and the solid phase and by interdiffusion through the different phases [3,4]. In any case, all these factors (matrix composition, dispersion and size of the reinforcement particles) affect the mechanical behavior of the as-formed material and the above phenomena are enhanced when the matrix is nanostructured (e.g. part of its crystals is nanosized), since in this case the amount of intergranular boundaries is increased. As a result increased mechanical resistance is achieved [8]. In any case the main objective of this study is the investigation of the structure of in situ composite materials in a Al–Fe–Ni matrix. After a brief review of the development of the diffusion structures of a Fe–Ni alloy dissolved in pure aluminum, the material was examined with electron microscopy in order to track nanocrystals in its mass and the results of the above research were connected with the improvement of the mechanical properties of the aluminum matrix. 2. Experimental In the present work a Fe–Ni rod containing 97 wt.% Fe and 3 wt.% Ni was dissolved in liquid Al. The as-formed matrix was heated up to 1060 ◦ C and a 5 wt.% mixture of K2 TiF6 and KBF4 was added with simultaneous stirring for 30 min. The liquid was squeeze-cast at 150 bar. The initial observation of a polished surface of the as-cast specimens took place with a Karl Zeiss M8 low magnification binocular light microscope equipped with a CCD camera for image capture. Afterwards cross-sections have been cut from each sample, mounted in bakelite, polished down to 5 m alumina emulsion and etched with Keller solution (1% HF, 1.5% HCl, 2.5% HNO3 , 95% H2 O). The as-prepared coupons were examined with scanning electron microscopy with a 20kVolt JEOL 840A SEM
G. Vourlias et al. / Journal of Alloys and Compounds 483 (2009) 178–181
179
Fig. 1. SE micrographs of the composite (a) at low magnification, (b) at higher magnification). Point #1 refers to the needle-like crystallites, point #2 to the base phase and point #3 to the gray interdendritic phase.
equipped with an OXFORD ISIS 300 EDS analyzer and the necessary software to perform line scan and chemical mapping of the samples. X-ray diffraction was also used for their structural characterization. For this purpose a Bragg-Brentano Philips D5000 diffractometer was used, where CuK␣ radiation ( = 1.54406 Å) was chosen. Selected specimens were also observed with conventional transmission electron microscopy (CTEM) and high resolution electron microscopy (HREM) with a 100 kV JEOL 100CX TEM and a 200 kV JEOL 2011 HREM respectively, after the suitable sample pretreatment [9]. TEM was used because it is characterized by higher mass resolution with regard to X-rays. Thus, one phase can be identified by electron diffraction even if it exists only in a small portion in the material. For this reason, in the present work TEM analysis was mainly used for the Al–Fe phase examination.
3. Results and discussion Fig. 1a shows a SEM micrograph of a coupon of the material formed at low magnification. What is rather characteristic is the presence of needle-like formations that overrun its surface. The examination of the same area at higher magnification reveals more details (Fig. 1b). Three distinct areas are observed based on their relief, which consist of white needle-like crystallites randomly dispersed in the whole matrix, a gray area developed in an interdentritic form and a dark base phase.
Fig. 2. Chemical mapping of Fig. 1(b).
180
G. Vourlias et al. / Journal of Alloys and Compounds 483 (2009) 178–181
Fig. 3. X-ray pattern of the as cast material.
The concentration profiles of the elements (which were measured with SEM-EDS and are summarized in a graphical form in Fig. 2) in the so-called reaction zone, which in this case was extended from the boundary of the pure aluminum to about 10 m into the white crystallites, are very interesting. The interface between the matrix and the white crystallites was assumed to be the zero point. As a result we were able to calculate the concentration of the elements across these crystallites. In the reaction zone the crystallites contain 76–73 at.% of Al, 22–25 at.% of Fe and 3–2 at.% of Ni. Hence the composition of this zone may presumably be expressed by the formula (Fe–Ni)Al3 . Interplanar distances (dspacing) corresponding to X-ray patterns of Fig. 3, were found to be rather close to those of FeAl3 phase. In spite the fact that it was not easy to arrive at definite conclusions concerning the phases of the layers in the reaction zone, the experimental observations led us to assume that some equilibrium phases such as (Fe–Ni)2 Al5 seem to be at very low concentration. Since this layer is known to develop near the area richer in iron, it was very probable that the (Fe–Ni)Al3 layer, which grown at the early stage of dissolution process temporarily acts as barrier between melting aluminum and pure iron, giving rise to interdiffusion process. In any case the differentiation of (Fe–X)2 Al5 from (Fe–X)Al3 is rather difficult due to the fact that the most characteristic reflections coincide for both
Fig. 4. TEM micrograph of the aluminum matrix that shows stacking faults.
Fig. 5. TEM micrograph of the Al base phase with the corresponding electron diffraction pattern which refers to a Fe–Ni–Al phase.
cases or they are very close. Furthermore shifting due to the presence of the X admixtures or due to the stresses may further confuse the analysis. As regards to the area next to reacting zone experimental concentration profiles revealed that some additional layers developed, probably by a diffusion process. Surprisingly these layers did not correspond to any of binary aluminides or ternary phases identified on the Fe–Ni–Al system. The first of the new layers designated as (Fe–Ni)2 Al3 based on the composition found after a detailed elementary analysis which was accomplished by EDS-SEM. By extending the observation to the inner diffusion zone a layer with the (Fe–Ni)Al seemed to have been formed. The borders of the two layers were not clear, but a sharp change in the concentrations which occurs, helped to identify this layer as (Fe–Ni)Al taking into account previous findings. The rest of the aluminum matrix consists mainly of two distinct areas (Fig. 1). The gray area, which develops in an interdentritic form, is composed by aluminum with iron and nickel and appears in the XRD pattern as (Fe, Ni). It was rather unexpected that the amount of nickel is high enough to this area overcoming the average percentage of nickel in the alloy. This is ascribed to a selective dissolution of nickel in the pure aluminum. The base phase (dark one) consists almost of pure aluminum strongly stressed due to heterogeneous nucleation. Stacking faults in this area due to internal stresses were also observed with TEM (Fig. 4).
Fig. 6. TEM micrograph of the reinforcement particles with the corresponding electron diffraction pattern.
G. Vourlias et al. / Journal of Alloys and Compounds 483 (2009) 178–181
181
EDS analysis revealed only Ti as the detection of low atomic weight elements such as B is not possible due to inherent limitations of the electron microscope used. TEM examination revealed the presence of crystals of different sizes ranging from a few micrometers up to a few nanometers, as we see in Figs. 5–7. In the micrograph of Fig. 5 which refers to the base phase, Fe–Ni–Al crystals with size of about 0.1–3 m appears. However in the same phase smaller crystals appear with spherical shape, whose the electron diffraction pattern refers to Ti compounds (Fig. 6). Consequently they refer to products of the reinforcement reaction. In Fig. 7 it is also possible to distinguish Fe–Ni–Al nanocrystals (Al–Ni, Al–Fe, Al–Ni–Fe). To verify their presence the same area was also examined with HREM (Fig. 8). In this micrograph nanocrystals are observed with d-spacing referring to Fe–Ni–Al. From this examination it is obvious that the material examined contains also nanocrystals, at least in the Al base phase. These crystals were probably formed due to rapid cooling of the system when it was cast. Since squeeze casting was used for its formation, local overcooling at the contact surface with the mould is very likely. This phenomenon could lead to rapid solidification at these areas and thus the size of the as-formed crystals remained small. 4. Conclusions Fig. 7. TEM micrograph of the Al base phase with the corresponding electron diffraction pattern, showing Fe–Ni–Al nanocrystals.
The present microstructural examination of the Al matrix composites revealed that three distinct areas, consisting of white needle-like crystallites randomly dispersed in the whole matrix, a gray area developed in an interdentritic form and a dendritic base phase were formed. Their composition could be presumably expressed by the formulas (Fe–Ni)Al3 , (Fe, Ni) and pure Al, respectively. Reinforcement particles were also detected in the base phase, which means that the initially added salts reacted and formed the reinforcing phase. Furthermore in the base phase Fe–Ni–Al nanocrystals are present. Their formation is very favorable for the system as they enhance its mechanical behavior. References
Fig. 8. HREM micrograph of the Al base phase showing Fe–Ni–Al nanocrystals.
In the mapping of Fig. 2 titanium was also detected. XRD revealed also the presence of Ti–B compounds. Their presence is very important because it verifies the formation of the reinforcement particles. The reaction of the salts added (K2 TiF6 and KBF4 ) leads to the formation of TiB2 , while the rest of the reaction products are evolved from the system as they are very volatile. However
[1] R.M. Jones, Mechanics of Composite Materials, Taylor & Francis, Philadelphia, 1998. [2] F.L. Mathews, R.D. Rawlings, Composite Materials: Engineering and Science, CRC Press, Woodhead, Cambridge, 1999. [3] V.I. Dybkov, J. Mater. Sci. 21 (1986) 3078. [4] V.I. Dybkov, J. Mater. Sci. 25 (1990) 3615. [5] C.F. Feng, L. Froyen, J. Mater. Sci. 35 (2000) 837. [6] A. Jha, C. Dometakis, Mater. Des. 18 (1997) 297. [7] J.V. Wood, P. Davies, J.L.F. Kellie, Mater. Sci. Technol. 19 (1993) 833. [8] J.F. Li, H. Liao, X.Y. Wang, C. Coddet, H. Chen, C.X. Ding, Thin Solid Films 17 (2004) 101. [9] D.B. Williams, C.B. Carter, Transmission Electron Microscopy, Plenum Press, 1996.