- Email: [email protected]
Microstructural study of Ce–Nd alloys
Journal of Alloys and Compounds 427 (2007) 104–109
Microstructural study of Ce–Nd alloys Orly Hachimi a , S. Hayun a , A. Venkert b , M.P. Dariel a,∗ a
Department of Materials Engineering, Ben-Gurion University of the Negev, Beer-Sheva, Israel b Nuclear Research Centre-Negev, P.O. Box 9100, Beer-Sheva, Israel
Received 23 January 2006; received in revised form 22 February 2006; accepted 23 February 2006 Available online 27 April 2006
Abstract The present work is concerned with the grain structure and grain growth in some cerium–neodymium alloys. The grain size in a Ce–10 wt.% Nd alloy is determined by the rate of cooling through the two-phase ␥ + ␦ region. Grain growth in the upper ␥-phase is a diffusion-controlled process with activation energy close to that associated with self-diffusion of cerium. In the course of spontaneous oxidation, epitaxial CeO2 layers grow on the Ce-alloy surface. The presence of such layers has been previously observed on a variety of substrate materials but not on the parent metal cerium. As these layers become thicker, coherency strains give rise to a network of cracks that develop within the oxide layer. The coherence between the cerium–substrate and the oxide layer is maintained even across the initially formed intermediate sub-oxide layers. © 2006 Elsevier B.V. All rights reserved. Keywords: Rare-earth alloys; Microstructure; Oxidation; Grain boundaries
1. Introduction Studies focused on the physical metallurgy of rare-earth metals and intra-rare earth alloy systems are relatively scarce. The paucity of investigations in this field can be attributed to several reasons. Foremost is the limited use of metallic rare-earth metals and alloys in technology, in contrast to their extensive use as more or less minor additions to other metals and in contrast to their usefulness in a plethora of intermetallic compounds displaying interesting and, in some instances, unique physical properties. The limited use of rare-earth based metallic systems is due to their strong tendency to undergo oxidation, their relatively elevated cost on account of difficulties in their preparation at required purity and their poor mechanical properties. On the other hand, the rare-earth metals display interesting features such as the presence of several kinds of allotropic transformations, systematic variations of some of their properties as one goes along the lanthanide series. These features of the rare-earth metals make them propitious candidates for the study of some basic aspects of materials science.
∗
Corresponding author. Tel.: +972 8 6461472; fax: +972 6477148. E-mail address: [email protected] (M.P. Dariel).
0925-8388/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.jallcom.2006.02.050
Recently an interesting feature in some cerium-based alloys has been encountered, namely, the possibility of growing epitaxial oxide layers on cerium and cerium-rich alloys. An example of such oxide layers that reflect the underlying metal structure is shown in Fig. 1. Since it was of interest to further probe this surprising and unexpected observation, it became important to gain control of the grain size of the cerium-based metallic substrate. At room temperature, cerium displays an fcc structure that transforms to bcc at elevated temperature, prior melting. The room temperature grain structure of cerium is determined by the bcc-to-fcc transformation on cooling from the melt. This transformation in pure cerium, in the absence of kinetic barriers, takes place at an invariant temperature. In order to provide some additional degree of freedom for the study, it was advantageous to carry out the investigation on a single-phase binary cerium-rich alloy, in which the bcc-to-fcc transformation takes place over a finite interval of temperatures. The solubility of most non-rare-earth metals in cerium is very restricted, in contrast to intra-rare-earth alloys, which display extensive regions of mutual solubility. One such system is the cerium–neodymium binary, the phase diagram of which is shown in Fig. 2 [1]. Cerium and neodymium are close neighbors in the periodic table (Z = 58 and 60, respectively) with very close atomic radii, at least for the tri-valent form of cerium. As a consequence of the size and chemical similarity, cerium–neodymium alloys display a nearly
O. Hachimi et al. / Journal of Alloys and Compounds 427 (2007) 104–109
105
turned over, remelted several times and finally chill cast in split copper molds to yield 3 cm high, 0.5 cm diameter rods. The Ce–Nd alloys were sliced into 4 mm high discs wrapped in thin Ta foils and sealed within quartz ampoules that had been evacuated to 5 × 10−2 mbar. Heat treatments were carried out in a furnace with the temperature controlled to within 0.5 ◦ C and in which the heating rate and the cooling rate, above 400 ◦ C, could be controlled within a wide range from quenching in water to 0.25 ◦ C/s. The fastest cooling rate through the ␦ → ␥ transformation was achieved by heating the samples, sealed in the quartz capsules to the ␦-phase region at 740 ◦ C and quenching by immersing and crushing the ampoule under water. It is estimated that this procedure allowed attaining a cooling rate of several thousands of degrees per minute. Slower cooling rates were achieved by taking advantage of the temperature control system of the furnace that allowed controlled and accurate cooling.
2.2. Metallographic preparation and image analysis Fig. 1. As cast Ce–10 wt.% Nd alloy. Most grains display a crack network consisting of nearly straight border-to-border cracks in the surface oxide layer. These cracks were formed in the oxide layer built up on ␥-phase fcc cerium substrate grains. In some grains (put in evidence by the black circles) the crack network consists of short, tortuous cracks built in the oxide phase grown on the top of -phase dhcp-Ce grains.
The metallographic preparation of the samples consisted of: (a) mounting the samples in a quick setting resin; (b) pressureless grinding for 20 s on 500 and 1200 grit SiC paper with ethanol cooling; (c) polishing DP-Mol on (Struers) 5–7 m and DP-Nap (Struers) cloth impregnated with 5–7 and 1 m diamond paste, respectively for 2 min each, rinsing with ethanol; (d) gentle swab etching with 2% Nital solution. Image analysis was performed using the ThixometTM picture analysis program to determine the average grain size and its distribution. This program allows collecting and analyzing a large number of contiguous fields of view, thereby improving significantly the statistics of the data collection. Two particular features, characteristic of the etched and oxidized surface of the cerium-alloys hinder a straightforward automatic identification of the grainsize. The first is due to the reactivity of cerium–neodymium alloys and their tendency to undergo oxidation. During the casting and the subsequent annealing treatments, process contaminations and inclusions show up on the surface. Next, the presence of the numerous parallel crack lines, which reflect the strain release in the epitaxial oxide layers render proper grain–boundary identification by the software almost impossible. These drawbacks were overcome by manually drawing the true grain boundaries on transparencies placed upon the original micrographs. An example of the original and the corrected copy are shown in Fig. 3. The digitized corrected copy was fed to the image analysis software whose output yielded histograms based on the measured parameters, namely area, maximum, minimum and average diagonals, aspect ratios of the grains. On examining the data that was obtained, it appeared that choice of the grain surface
Fig. 2. The cerium–neodymium phase diagram according to ref. [2].
ideal solution behavior. The ideal solution behavior finds its expression in the quasi-coincident liquidus and solidus lines in the phase diagram. The two-phase region (␥Ce,Nd) + ␥Ce is drawn only tentatively in the phase diagram but it is reasonable to accept its finite width that provides some latitude in varying the kinetics of the bcc-to-fcc transformation. On the basis of these premises, a study of the grain size in this binary system was initiated as a function of controllable parameters such as cooling rate and grain-growth heat treatments. 2. Experimental 2.1. Sample preparation and heat treatments Cerium and neodymium lumps were purchased from Alfa Aeser and were stated by the supplier to be 99.9% pure with no information regarding the interstitial impurity content. Weighed amounts of the two metals were melted on the hearth of an arc furnace under a 99.5% pure argon atmosphere. The buttons were
Fig. 3. Micrographs of a Ce–10 wt.% Nd, arc-cast alloy. The actual micrograph is shown in the upper figure. Grain boundaries delineated on transparency in the lower figure. Areas in which it was difficult to determine grain boundaries were painted in black.
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area appeared to be the most reliable measure of the grain size. From the surface area of the arbitrary shaped grains as they appeared in the 2-D micrograph, a distribution of the diameters of hypothetical circular grains having the same surface area was derived. The distribution of grain-size deduced from the data and based on the assumption that the hypothetical circular 2-D grains represented the cross section of spherical grains in the bulk of the sample.
2.3. Structural characterization Structural analysis was performed using a Rigaku RINT 2100 diffractometer with a Cu K␣ radiation. The results were analyzed using Atomic Powder Diffraction (APD) and Powder Cell for Windows (PCW) software. The analysis allowed to deconvolute superposed diffraction peaks and to derive the relative fraction of the phases present in the sample and their lattice parameter.
3. Results and discussion 3.1. Grain size A micrograph of an as-cast Ce–10 wt.% Nd alloys is shown in Fig. 3. Attached is also the manually determined grain boundary network that was used in conjunction with the image analysis software for grain size determination. The average grain size and its standard deviation derived from the calculated distribution are shown in Fig. 4 as a function of the cooling rate (on a logarithmic scale) through the ␦ → ␥ phase transition. The figure suggests that the grain size tends to stabilize at constant values, approximately 20 m at high cooling rates, attainable in the experimental set-up, and 80 m at the low cooling rates. It is also noteworthy that the width of the grain size distribution, as is expressed by the standard deviation, is much larger at low cooling rates than at the high ones. Apparently the particular microstructure of the alloy with its inclusions reaches a quasi-equilibrium grain size distribution of 80 m. On the other side, within the range of cooling rates that was available, 15 m was the smallest average grain diameter that was observed. The significant variation of grain size occurs within a change of the cooling rate in the 10–100 ◦ C/min range.
Table 1 Grain-growth treatment parameters Duration of the grain growth treatment (h)
Temperature ◦ C
4, 8 12, 24, 168 1,8,30 12, 24, 168
610 640 660 690
The ␦ → ␥ transformation takes place by nucleation and growth. The high temperature ␦, bcc phase, cannot be retained at room temperature; it is not possible, therefore, to follow by micrographical methods the evolution of the transformation. One can, however, gain some insight in the growth kinetics of the fcc ␥-phase, by carrying out isothermal anneals after a well defined initial structure. This initial structure was that of the arcmelted samples with an average grain size of 23 ± 10 m in a quasi single-phase ␥ structure. The heat-treatment parameters are shown in Table 1. The encapsulated samples after identical treatments in the ␦-phase where removed and quickly inserted into a furnace that had been stabilized at the desired temperature in the ␥-phase. As mentioned previously, there is no significant dependence of the microstructure on the temperature to which the samples were cooled from the ␦-phase. Assuming a diffusion driven normal growth regime of the grain-size, the average ¯ can be derived from the expression: grain size, D, ¯ t2 − D ¯ 02 = 4MσV␣ t D β
(1)
¯ 2 and D ¯ t2 are the average grain size at the beginning and where D 0 after a duration t, of the grain growth treatment, M the mobility of the rare-earth atom in and across the grain boundary, Va its molar volume, σ the pressure difference across a grain boundary and β, a constant dependent on the dispersion of the grain size. Assuming a thermally activated mobility and using the Einstein relation M ≈ D/RT where D is the diffusivity involved in grain boundary migration, one may write for the grain size ¯ t2 − D ¯ 02 = Kt = K0 exp −Q D (2) RT where K = 4 MσV␣ /β. The values of K were derived from plots of ¯ t2 − D ¯ 2 as a function of t, where t is the length of the diffusion D 0 anneal after the quench from the higher temperature ␦-phase and are shown in Fig. 5. These K values for unalloyed Ce samples and Ce–10 wt.% Nd samples for three temperatures at which the grain-growth treatment were carried out are plotted in Fig. 6 as a function of the inverse temperature. The values of the activation energy Q derived from the latter are shown in Table 2. Table 2 Activation energies for diffusion-controlled processes
Fig. 4. Average grain size as a function of the rate of cooling (on a logarithmic scale) through the ␥ → ␦ transformation. The error bars through the experimental points give a measure of the spread of the grain size.
System
Activation energy values reported in the literature
Present study (kJ/mol)
Ce Ce–10Nd alloy
153 [3] 80–105 range [1]
125 ± 20 152 ± 20
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¯ t2 − D ¯ 2 , with D ¯ 2 and D ¯ t2 the average grain Fig. 5. Linear time-dependence of D 0 0 size at the beginning and after a duration t, of the grain growth treatment.
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Fig. 7. Ce–10 wt.% Nd sample after a 2 h heat-treatment at 610 ◦ C in the ␥phase. Average grain size 31.1 ± 20.3 m. Notice that two grains display two perpendicular crack networks.
The experimentally determined activation energies, derived from the grain-growth study, for both unalloyed cerium and the Ce–10 wt.% Nd alloy are of the order of 130 ± 20 kJ/mol which is not inconsistent with the activation energy in the fcc ␥-phase determined from tracer isotope measurements. These values are significantly higher than those reported by Kaiser [1] on the basis of cerium–neodymium diffusion couple studies. In principle such experiments yield chemical diffusion coefficients, which, in the particular case of the nearly ideal cerium–neodymium system, can be expressed as:
that the intrinsic diffusivity of neodymium should by close to 30% be lower than the activation energy for cerium selfdiffusion. The similarity of the activation energy values derived from tracer isotope studies [3] and from the present study, based on grain growth experiments, strongly suggests that the dominant mechanism that underlies grain boundary migration in cerium is bulk rather than grain boundary diffusion.
∗ ∗ ˜ = XNd DCe D + (1 − XNd )DNd
3.2. Epitaxial surface oxide layers
(3)
where the Di∗ are the intrinsic diffusivities of cerium and neodymium, respectively, and XNd are the weight fractions of the two elements. For the 10 wt.% Nd alloy, the intrinsic diffusivity of the neodymium component is the dominant factor that determines the chemical diffusion and the associated activation energy. Considering the similarity in the relevant properties of the two elements, cerium and neodymium, it is unlikely
Fig. 6. Inverse temperature dependence of log(K) derived from grain-growth measurements.
Micrographs of the surface oxidized a 10-wt.% Nd and a 50-wt.% Nd alloy are shown in Figs. 7 and 9, and their X-ray diffraction spectra in Figs. 8 and 10, respectively. According to the diffractogram (Fig. 8), the 10 wt.% sample shown in Fig. 7 consisted essentially of ␥-phase cerium with some minor-
Fig. 8. Diffraction pattern of a Ce–10 wt.% Nd alloy after a 2 h heat treatment at 610 ◦ C. The diffractogram consists essentially of the fcc ␥-phase diffraction peaks, peaks of the surface cerium oxide CeO2 layer and some traces of the dhcp -Ce phase.
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Fig. 9. Micrograph of an as cast, single phase Ce–50 wt.% Nd alloy. Notice the irregular crack network in each grain, in contrast to that observed in the Ce–10 wt.% Nd alloy.
ity -phase (dhcp structure) with a surface CeO2 layer. In the diffractogram (Fig. 10) of the 50 wt.% Nd sample (Fig. 9) only peaks attributable to the -(Ce, Nd) dhcp solid solution are discernable. Auger depth profiling (Fig. 11), performed on the 10 wt.% Nd sample confirmed that the upper-most layers are CeO2 layers. A striking feature of the surface structure, shown in Fig. 7, is the presence of the well-defined nearly parallel and nearly straight lines, which in the majority of the grains, run from border to border in each grain. The straight lines are cracks that developed within the oxide layer, possibly along cleavage planes, and their direction depends on the orientation of the particular grain that underlies the oxide layer. It is relevant to notice that the direction of these crack lines correlates with the color (or hue) of the grain. The color is determined by the thickness of the oxide layer on each particular grain. The thickness varies from grain to grain and depends on the orientation of the grain. In contrast, the cracks appearing in the grains Ce–50 wt.% Nd (Fig. 9) are tortuous, rarely run clearly from border to border. Even in Fig. 1, such crack morphology can be discerned in a few grains pointed at by the surrounding circles. These latter grains are apparently the minority -phase grains in the Ce–10 wt.% Nd alloy. The cracks occur when the thickness of the oxide layer reaches a critical value that depends on the mismatch between the lattice constant of the substrate (the Ce–Nd alloy) and that of the oxide and its elastic constants. Upon reaching the critical value, the oxide layer is unable to withstand the coherency strains and a crack develops, most likely on a cleavage plane of the oxide. This tentative model accounts for the severe cracking apparent in the oxide layer and which appears mostly as crack lines running across the grains. The difference between the crack morphology within the oxide grains shown in Figs. 7 and 9, respectively, can be attributed to the structure of the respective substrates. The 10 wt% Nd has an essentially fcc (␥-Ce) structure with traces of dhcp, -Ce, whereas Ce–50 wt.% Nd has a single phase dhcp structure (Fig. 10). It is not unlikely that cracks
Fig. 10. Diffraction pattern of the as-cast Ce–50 wt.% Nd alloy. The diffractogram consists essentially of the dhcp -phase diffraction peaks. Even though the surface oxide is clearly visible in the micrograph no diffraction peaks of the CeO2 layers sere observed.
along cleavage planes propagate with ease within the epitaxial oxide layer on the highly symmetrical fcc cerium substrate but have difficulties in doing so in the oxide layer grown on the dhcp structure. This difference in the nature of the substrate may be the underlying reason for the tortuous aspect of the crack lines in the oxide grown on the dhcp cerium alloy, as shown in Fig. 9. The depth profiles of cerium and oxygen, shown in Fig. 11 suggest an overall thickness of the oxide of approximately 2000 nm. Over that thickness, the composition and possibly the structure of the oxide varies towards an increasingly Ce-rich sub-oxide in the vicinity of the metal alloy surface. Epitaxial CeO2 layers have been successfully grown on a wide range of substrates that include Al2 O3 , MgO, Si and high Tc compounds [4–7]. To the best of our knowledge the present observation is the first report of such epitaxial layers grown on the parent metal. The lattice mismatch between various oxides on fcc ␥-Ce, for CeO, hex Ce2 O3 and fcc CeO2 is 1.4, 6 and 4.6%, respectively. At this stage of the study it was not possible to determine the succession of intermediate individual oxide lay-
Fig. 11. Auger depth profile of cerium and oxygen through the oxide layer built-up on fcc ␥-cerium.
O. Hachimi et al. / Journal of Alloys and Compounds 427 (2007) 104–109
ers in the surface oxide. The succession of plateaus apparent in the cerium and oxygen concentration profiles shown in Fig. 10 is supporting evidence for the presence of intermediate layers, even though no evidence for such layers was found in the diffraction spectra. 4. Summary The grain size in a Ce–10 wt.% Nd alloy is determined by the rate of cooling through the two-phase g + b region. Grain growth in the upper ␥-phase is a diffusion-controlled process with activation energy close to that associated with self-diffusion in the constituent metals. In the course of spontaneous oxidation, epitaxial CeO2 layers grow on the Ce-alloy surface. Due to the relatively large mismatch between the lattice parameters of the metal substrate and the oxide layer, a network of cracks develops in the oxide layer. The cracks appearing in the oxide grown on fcc ␥-Ce are relatively straight and continuous and cross the grains from border to border. In contrast, the cracks developed within the oxide
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layer grown on single phase dhcp -cerium have an irregular and discontinuous appearance. References [1] D.D. Keiser Jr., Scripta Metall. Mater. 33 (1995) 959–965. [2] K.A. Gschneider, F.W. Calderwood Jr., Alloy Phase Diagr. 3 (1) (1982) 90. [3] M.P. Dariel, D. Dayan, A. Languille, Phys. Rev. B 4 (1971) 4348. [4] T. Inoue, N. Sakamoto, A. Horikawa, H. Takakura, K. Takahashi, M. Ohashi, S. Shida, J. Vac. Sci. Technol., A: Vac., Surf., Films 21 (4) (2003) 1371– 1375. [5] T. Inoue, S. Shida, N. Sakamoto, A. Horikawa, M. Ohashi, Masayuki J. Cryst. Growth 253 (1–4) (2003) 366–373. [6] N. Savvides, A. Thorley, S. Gnanarajan, A. Katsaros, in: CSIRO Telecommunications and Industrial Physics, Sydney, Australia, Thin Solid Films 388 (1–2) (2001) 177–182. [7] A. Thorley, S. Gnanarajan, A. Katsaros, N. Savvides, Layers on MgO, YSZ and sapphire substrates, Epitaxial growth of cerium oxide buffer, Recent developments in oxide and metal epitaxy: theory and experiment, in: Materials Research Society Symposium Proceedings, April 23–26, 2000, vol. 619, San Francisco, CA, USA, 2000, pp. 191–196, ISBN: 1558995277 (Hard cover book).
Microstructural study of Ce–Nd alloys Orly Hachimi a , S. Hayun a , A. Venkert b , M.P. Dariel a,∗ a
Department of Materials Engineering, Ben-Gurion University of the Negev, Beer-Sheva, Israel b Nuclear Research Centre-Negev, P.O. Box 9100, Beer-Sheva, Israel
Received 23 January 2006; received in revised form 22 February 2006; accepted 23 February 2006 Available online 27 April 2006
Abstract The present work is concerned with the grain structure and grain growth in some cerium–neodymium alloys. The grain size in a Ce–10 wt.% Nd alloy is determined by the rate of cooling through the two-phase ␥ + ␦ region. Grain growth in the upper ␥-phase is a diffusion-controlled process with activation energy close to that associated with self-diffusion of cerium. In the course of spontaneous oxidation, epitaxial CeO2 layers grow on the Ce-alloy surface. The presence of such layers has been previously observed on a variety of substrate materials but not on the parent metal cerium. As these layers become thicker, coherency strains give rise to a network of cracks that develop within the oxide layer. The coherence between the cerium–substrate and the oxide layer is maintained even across the initially formed intermediate sub-oxide layers. © 2006 Elsevier B.V. All rights reserved. Keywords: Rare-earth alloys; Microstructure; Oxidation; Grain boundaries
1. Introduction Studies focused on the physical metallurgy of rare-earth metals and intra-rare earth alloy systems are relatively scarce. The paucity of investigations in this field can be attributed to several reasons. Foremost is the limited use of metallic rare-earth metals and alloys in technology, in contrast to their extensive use as more or less minor additions to other metals and in contrast to their usefulness in a plethora of intermetallic compounds displaying interesting and, in some instances, unique physical properties. The limited use of rare-earth based metallic systems is due to their strong tendency to undergo oxidation, their relatively elevated cost on account of difficulties in their preparation at required purity and their poor mechanical properties. On the other hand, the rare-earth metals display interesting features such as the presence of several kinds of allotropic transformations, systematic variations of some of their properties as one goes along the lanthanide series. These features of the rare-earth metals make them propitious candidates for the study of some basic aspects of materials science.
∗
Corresponding author. Tel.: +972 8 6461472; fax: +972 6477148. E-mail address: [email protected] (M.P. Dariel).
0925-8388/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.jallcom.2006.02.050
Recently an interesting feature in some cerium-based alloys has been encountered, namely, the possibility of growing epitaxial oxide layers on cerium and cerium-rich alloys. An example of such oxide layers that reflect the underlying metal structure is shown in Fig. 1. Since it was of interest to further probe this surprising and unexpected observation, it became important to gain control of the grain size of the cerium-based metallic substrate. At room temperature, cerium displays an fcc structure that transforms to bcc at elevated temperature, prior melting. The room temperature grain structure of cerium is determined by the bcc-to-fcc transformation on cooling from the melt. This transformation in pure cerium, in the absence of kinetic barriers, takes place at an invariant temperature. In order to provide some additional degree of freedom for the study, it was advantageous to carry out the investigation on a single-phase binary cerium-rich alloy, in which the bcc-to-fcc transformation takes place over a finite interval of temperatures. The solubility of most non-rare-earth metals in cerium is very restricted, in contrast to intra-rare-earth alloys, which display extensive regions of mutual solubility. One such system is the cerium–neodymium binary, the phase diagram of which is shown in Fig. 2 [1]. Cerium and neodymium are close neighbors in the periodic table (Z = 58 and 60, respectively) with very close atomic radii, at least for the tri-valent form of cerium. As a consequence of the size and chemical similarity, cerium–neodymium alloys display a nearly
O. Hachimi et al. / Journal of Alloys and Compounds 427 (2007) 104–109
105
turned over, remelted several times and finally chill cast in split copper molds to yield 3 cm high, 0.5 cm diameter rods. The Ce–Nd alloys were sliced into 4 mm high discs wrapped in thin Ta foils and sealed within quartz ampoules that had been evacuated to 5 × 10−2 mbar. Heat treatments were carried out in a furnace with the temperature controlled to within 0.5 ◦ C and in which the heating rate and the cooling rate, above 400 ◦ C, could be controlled within a wide range from quenching in water to 0.25 ◦ C/s. The fastest cooling rate through the ␦ → ␥ transformation was achieved by heating the samples, sealed in the quartz capsules to the ␦-phase region at 740 ◦ C and quenching by immersing and crushing the ampoule under water. It is estimated that this procedure allowed attaining a cooling rate of several thousands of degrees per minute. Slower cooling rates were achieved by taking advantage of the temperature control system of the furnace that allowed controlled and accurate cooling.
2.2. Metallographic preparation and image analysis Fig. 1. As cast Ce–10 wt.% Nd alloy. Most grains display a crack network consisting of nearly straight border-to-border cracks in the surface oxide layer. These cracks were formed in the oxide layer built up on ␥-phase fcc cerium substrate grains. In some grains (put in evidence by the black circles) the crack network consists of short, tortuous cracks built in the oxide phase grown on the top of -phase dhcp-Ce grains.
The metallographic preparation of the samples consisted of: (a) mounting the samples in a quick setting resin; (b) pressureless grinding for 20 s on 500 and 1200 grit SiC paper with ethanol cooling; (c) polishing DP-Mol on (Struers) 5–7 m and DP-Nap (Struers) cloth impregnated with 5–7 and 1 m diamond paste, respectively for 2 min each, rinsing with ethanol; (d) gentle swab etching with 2% Nital solution. Image analysis was performed using the ThixometTM picture analysis program to determine the average grain size and its distribution. This program allows collecting and analyzing a large number of contiguous fields of view, thereby improving significantly the statistics of the data collection. Two particular features, characteristic of the etched and oxidized surface of the cerium-alloys hinder a straightforward automatic identification of the grainsize. The first is due to the reactivity of cerium–neodymium alloys and their tendency to undergo oxidation. During the casting and the subsequent annealing treatments, process contaminations and inclusions show up on the surface. Next, the presence of the numerous parallel crack lines, which reflect the strain release in the epitaxial oxide layers render proper grain–boundary identification by the software almost impossible. These drawbacks were overcome by manually drawing the true grain boundaries on transparencies placed upon the original micrographs. An example of the original and the corrected copy are shown in Fig. 3. The digitized corrected copy was fed to the image analysis software whose output yielded histograms based on the measured parameters, namely area, maximum, minimum and average diagonals, aspect ratios of the grains. On examining the data that was obtained, it appeared that choice of the grain surface
Fig. 2. The cerium–neodymium phase diagram according to ref. [2].
ideal solution behavior. The ideal solution behavior finds its expression in the quasi-coincident liquidus and solidus lines in the phase diagram. The two-phase region (␥Ce,Nd) + ␥Ce is drawn only tentatively in the phase diagram but it is reasonable to accept its finite width that provides some latitude in varying the kinetics of the bcc-to-fcc transformation. On the basis of these premises, a study of the grain size in this binary system was initiated as a function of controllable parameters such as cooling rate and grain-growth heat treatments. 2. Experimental 2.1. Sample preparation and heat treatments Cerium and neodymium lumps were purchased from Alfa Aeser and were stated by the supplier to be 99.9% pure with no information regarding the interstitial impurity content. Weighed amounts of the two metals were melted on the hearth of an arc furnace under a 99.5% pure argon atmosphere. The buttons were
Fig. 3. Micrographs of a Ce–10 wt.% Nd, arc-cast alloy. The actual micrograph is shown in the upper figure. Grain boundaries delineated on transparency in the lower figure. Areas in which it was difficult to determine grain boundaries were painted in black.
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area appeared to be the most reliable measure of the grain size. From the surface area of the arbitrary shaped grains as they appeared in the 2-D micrograph, a distribution of the diameters of hypothetical circular grains having the same surface area was derived. The distribution of grain-size deduced from the data and based on the assumption that the hypothetical circular 2-D grains represented the cross section of spherical grains in the bulk of the sample.
2.3. Structural characterization Structural analysis was performed using a Rigaku RINT 2100 diffractometer with a Cu K␣ radiation. The results were analyzed using Atomic Powder Diffraction (APD) and Powder Cell for Windows (PCW) software. The analysis allowed to deconvolute superposed diffraction peaks and to derive the relative fraction of the phases present in the sample and their lattice parameter.
3. Results and discussion 3.1. Grain size A micrograph of an as-cast Ce–10 wt.% Nd alloys is shown in Fig. 3. Attached is also the manually determined grain boundary network that was used in conjunction with the image analysis software for grain size determination. The average grain size and its standard deviation derived from the calculated distribution are shown in Fig. 4 as a function of the cooling rate (on a logarithmic scale) through the ␦ → ␥ phase transition. The figure suggests that the grain size tends to stabilize at constant values, approximately 20 m at high cooling rates, attainable in the experimental set-up, and 80 m at the low cooling rates. It is also noteworthy that the width of the grain size distribution, as is expressed by the standard deviation, is much larger at low cooling rates than at the high ones. Apparently the particular microstructure of the alloy with its inclusions reaches a quasi-equilibrium grain size distribution of 80 m. On the other side, within the range of cooling rates that was available, 15 m was the smallest average grain diameter that was observed. The significant variation of grain size occurs within a change of the cooling rate in the 10–100 ◦ C/min range.
Table 1 Grain-growth treatment parameters Duration of the grain growth treatment (h)
Temperature ◦ C
4, 8 12, 24, 168 1,8,30 12, 24, 168
610 640 660 690
The ␦ → ␥ transformation takes place by nucleation and growth. The high temperature ␦, bcc phase, cannot be retained at room temperature; it is not possible, therefore, to follow by micrographical methods the evolution of the transformation. One can, however, gain some insight in the growth kinetics of the fcc ␥-phase, by carrying out isothermal anneals after a well defined initial structure. This initial structure was that of the arcmelted samples with an average grain size of 23 ± 10 m in a quasi single-phase ␥ structure. The heat-treatment parameters are shown in Table 1. The encapsulated samples after identical treatments in the ␦-phase where removed and quickly inserted into a furnace that had been stabilized at the desired temperature in the ␥-phase. As mentioned previously, there is no significant dependence of the microstructure on the temperature to which the samples were cooled from the ␦-phase. Assuming a diffusion driven normal growth regime of the grain-size, the average ¯ can be derived from the expression: grain size, D, ¯ t2 − D ¯ 02 = 4MσV␣ t D β
(1)
¯ 2 and D ¯ t2 are the average grain size at the beginning and where D 0 after a duration t, of the grain growth treatment, M the mobility of the rare-earth atom in and across the grain boundary, Va its molar volume, σ the pressure difference across a grain boundary and β, a constant dependent on the dispersion of the grain size. Assuming a thermally activated mobility and using the Einstein relation M ≈ D/RT where D is the diffusivity involved in grain boundary migration, one may write for the grain size ¯ t2 − D ¯ 02 = Kt = K0 exp −Q D (2) RT where K = 4 MσV␣ /β. The values of K were derived from plots of ¯ t2 − D ¯ 2 as a function of t, where t is the length of the diffusion D 0 anneal after the quench from the higher temperature ␦-phase and are shown in Fig. 5. These K values for unalloyed Ce samples and Ce–10 wt.% Nd samples for three temperatures at which the grain-growth treatment were carried out are plotted in Fig. 6 as a function of the inverse temperature. The values of the activation energy Q derived from the latter are shown in Table 2. Table 2 Activation energies for diffusion-controlled processes
Fig. 4. Average grain size as a function of the rate of cooling (on a logarithmic scale) through the ␥ → ␦ transformation. The error bars through the experimental points give a measure of the spread of the grain size.
System
Activation energy values reported in the literature
Present study (kJ/mol)
Ce Ce–10Nd alloy
153 [3] 80–105 range [1]
125 ± 20 152 ± 20
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¯ t2 − D ¯ 2 , with D ¯ 2 and D ¯ t2 the average grain Fig. 5. Linear time-dependence of D 0 0 size at the beginning and after a duration t, of the grain growth treatment.
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Fig. 7. Ce–10 wt.% Nd sample after a 2 h heat-treatment at 610 ◦ C in the ␥phase. Average grain size 31.1 ± 20.3 m. Notice that two grains display two perpendicular crack networks.
The experimentally determined activation energies, derived from the grain-growth study, for both unalloyed cerium and the Ce–10 wt.% Nd alloy are of the order of 130 ± 20 kJ/mol which is not inconsistent with the activation energy in the fcc ␥-phase determined from tracer isotope measurements. These values are significantly higher than those reported by Kaiser [1] on the basis of cerium–neodymium diffusion couple studies. In principle such experiments yield chemical diffusion coefficients, which, in the particular case of the nearly ideal cerium–neodymium system, can be expressed as:
that the intrinsic diffusivity of neodymium should by close to 30% be lower than the activation energy for cerium selfdiffusion. The similarity of the activation energy values derived from tracer isotope studies [3] and from the present study, based on grain growth experiments, strongly suggests that the dominant mechanism that underlies grain boundary migration in cerium is bulk rather than grain boundary diffusion.
∗ ∗ ˜ = XNd DCe D + (1 − XNd )DNd
3.2. Epitaxial surface oxide layers
(3)
where the Di∗ are the intrinsic diffusivities of cerium and neodymium, respectively, and XNd are the weight fractions of the two elements. For the 10 wt.% Nd alloy, the intrinsic diffusivity of the neodymium component is the dominant factor that determines the chemical diffusion and the associated activation energy. Considering the similarity in the relevant properties of the two elements, cerium and neodymium, it is unlikely
Fig. 6. Inverse temperature dependence of log(K) derived from grain-growth measurements.
Micrographs of the surface oxidized a 10-wt.% Nd and a 50-wt.% Nd alloy are shown in Figs. 7 and 9, and their X-ray diffraction spectra in Figs. 8 and 10, respectively. According to the diffractogram (Fig. 8), the 10 wt.% sample shown in Fig. 7 consisted essentially of ␥-phase cerium with some minor-
Fig. 8. Diffraction pattern of a Ce–10 wt.% Nd alloy after a 2 h heat treatment at 610 ◦ C. The diffractogram consists essentially of the fcc ␥-phase diffraction peaks, peaks of the surface cerium oxide CeO2 layer and some traces of the dhcp -Ce phase.
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Fig. 9. Micrograph of an as cast, single phase Ce–50 wt.% Nd alloy. Notice the irregular crack network in each grain, in contrast to that observed in the Ce–10 wt.% Nd alloy.
ity -phase (dhcp structure) with a surface CeO2 layer. In the diffractogram (Fig. 10) of the 50 wt.% Nd sample (Fig. 9) only peaks attributable to the -(Ce, Nd) dhcp solid solution are discernable. Auger depth profiling (Fig. 11), performed on the 10 wt.% Nd sample confirmed that the upper-most layers are CeO2 layers. A striking feature of the surface structure, shown in Fig. 7, is the presence of the well-defined nearly parallel and nearly straight lines, which in the majority of the grains, run from border to border in each grain. The straight lines are cracks that developed within the oxide layer, possibly along cleavage planes, and their direction depends on the orientation of the particular grain that underlies the oxide layer. It is relevant to notice that the direction of these crack lines correlates with the color (or hue) of the grain. The color is determined by the thickness of the oxide layer on each particular grain. The thickness varies from grain to grain and depends on the orientation of the grain. In contrast, the cracks appearing in the grains Ce–50 wt.% Nd (Fig. 9) are tortuous, rarely run clearly from border to border. Even in Fig. 1, such crack morphology can be discerned in a few grains pointed at by the surrounding circles. These latter grains are apparently the minority -phase grains in the Ce–10 wt.% Nd alloy. The cracks occur when the thickness of the oxide layer reaches a critical value that depends on the mismatch between the lattice constant of the substrate (the Ce–Nd alloy) and that of the oxide and its elastic constants. Upon reaching the critical value, the oxide layer is unable to withstand the coherency strains and a crack develops, most likely on a cleavage plane of the oxide. This tentative model accounts for the severe cracking apparent in the oxide layer and which appears mostly as crack lines running across the grains. The difference between the crack morphology within the oxide grains shown in Figs. 7 and 9, respectively, can be attributed to the structure of the respective substrates. The 10 wt% Nd has an essentially fcc (␥-Ce) structure with traces of dhcp, -Ce, whereas Ce–50 wt.% Nd has a single phase dhcp structure (Fig. 10). It is not unlikely that cracks
Fig. 10. Diffraction pattern of the as-cast Ce–50 wt.% Nd alloy. The diffractogram consists essentially of the dhcp -phase diffraction peaks. Even though the surface oxide is clearly visible in the micrograph no diffraction peaks of the CeO2 layers sere observed.
along cleavage planes propagate with ease within the epitaxial oxide layer on the highly symmetrical fcc cerium substrate but have difficulties in doing so in the oxide layer grown on the dhcp structure. This difference in the nature of the substrate may be the underlying reason for the tortuous aspect of the crack lines in the oxide grown on the dhcp cerium alloy, as shown in Fig. 9. The depth profiles of cerium and oxygen, shown in Fig. 11 suggest an overall thickness of the oxide of approximately 2000 nm. Over that thickness, the composition and possibly the structure of the oxide varies towards an increasingly Ce-rich sub-oxide in the vicinity of the metal alloy surface. Epitaxial CeO2 layers have been successfully grown on a wide range of substrates that include Al2 O3 , MgO, Si and high Tc compounds [4–7]. To the best of our knowledge the present observation is the first report of such epitaxial layers grown on the parent metal. The lattice mismatch between various oxides on fcc ␥-Ce, for CeO, hex Ce2 O3 and fcc CeO2 is 1.4, 6 and 4.6%, respectively. At this stage of the study it was not possible to determine the succession of intermediate individual oxide lay-
Fig. 11. Auger depth profile of cerium and oxygen through the oxide layer built-up on fcc ␥-cerium.
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ers in the surface oxide. The succession of plateaus apparent in the cerium and oxygen concentration profiles shown in Fig. 10 is supporting evidence for the presence of intermediate layers, even though no evidence for such layers was found in the diffraction spectra. 4. Summary The grain size in a Ce–10 wt.% Nd alloy is determined by the rate of cooling through the two-phase g + b region. Grain growth in the upper ␥-phase is a diffusion-controlled process with activation energy close to that associated with self-diffusion in the constituent metals. In the course of spontaneous oxidation, epitaxial CeO2 layers grow on the Ce-alloy surface. Due to the relatively large mismatch between the lattice parameters of the metal substrate and the oxide layer, a network of cracks develops in the oxide layer. The cracks appearing in the oxide grown on fcc ␥-Ce are relatively straight and continuous and cross the grains from border to border. In contrast, the cracks developed within the oxide
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layer grown on single phase dhcp -cerium have an irregular and discontinuous appearance. References [1] D.D. Keiser Jr., Scripta Metall. Mater. 33 (1995) 959–965. [2] K.A. Gschneider, F.W. Calderwood Jr., Alloy Phase Diagr. 3 (1) (1982) 90. [3] M.P. Dariel, D. Dayan, A. Languille, Phys. Rev. B 4 (1971) 4348. [4] T. Inoue, N. Sakamoto, A. Horikawa, H. Takakura, K. Takahashi, M. Ohashi, S. Shida, J. Vac. Sci. Technol., A: Vac., Surf., Films 21 (4) (2003) 1371– 1375. [5] T. Inoue, S. Shida, N. Sakamoto, A. Horikawa, M. Ohashi, Masayuki J. Cryst. Growth 253 (1–4) (2003) 366–373. [6] N. Savvides, A. Thorley, S. Gnanarajan, A. Katsaros, in: CSIRO Telecommunications and Industrial Physics, Sydney, Australia, Thin Solid Films 388 (1–2) (2001) 177–182. [7] A. Thorley, S. Gnanarajan, A. Katsaros, N. Savvides, Layers on MgO, YSZ and sapphire substrates, Epitaxial growth of cerium oxide buffer, Recent developments in oxide and metal epitaxy: theory and experiment, in: Materials Research Society Symposium Proceedings, April 23–26, 2000, vol. 619, San Francisco, CA, USA, 2000, pp. 191–196, ISBN: 1558995277 (Hard cover book).