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On the formation mechanism of UZr2 phase
Intermetallics 18 (2010) 1707e1712
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Intermetallics journal homepage: www.elsevier.com/locate/intermet
On the formation mechanism of UZr2 phase Chandra Bhanu Basak a, *, N. Prabhu b, Madangopal Krishnan a a b
Materials Science Division, Bhabha Atomic Research Center, Trombay, Mumbai 400 085, India Department of Metallurgical Engineering & Materials Science, Indian Institute of Technology Bombay, Powai, Mumbai 400 076, India
a r t i c l e i n f o
a b s t r a c t
Article history: Received 18 June 2009 Received in revised form 6 February 2010 Accepted 10 May 2010 Available online 19 June 2010
Intermetallic delta phase (UZr2) in UeZr alloy system is known to have hexagonal crystal structure. However, the formation mechanism of delta phase from the parent bcc gamma phase was not investigated before. With an extensive XRD analysis along with the microhardness data the present investigation reveals that gamma to delta transition takes place by the mechanism of omega transformation. Formation of both athermal and isothermal delta phase is also established for UZr2 alloy composition. Ó 2010 Elsevier Ltd. All rights reserved.
Keywords: A. Uranium A. Zirconium F. X-ray Diffraction B. Omega transformation
1. Introduction Non-stoichiometric d-phase (UZr2) is known to be the only intermetallic phase in UeZr system. However, presence of this phase was established only after 1955 and subsequently the stability of this phase was proven beyond doubt [1,2]. Most recent studies on the stability and structure of the d-phase are carried out by Akabori et al. by XRD analysis and subsequently by high resolution neutron diffraction analysis [3,4]. In recent years the UeZr composition around the delta phase region is being considered as a potential candidate for the dispersion fuel application. It is thus important to know the physical metallurgical behaviour of the concerned phase. In U-rich UeZr alloys the d-phase is formed by peritectoid reaction which is extremely sluggish kinetically and hence formation of d-phase could not be confirmed even after long term annealing [5]. Hence, in the present study U-50 wt.% Zr alloy (w72at%Zr) was chosen so that the composition goes directly through the middle of the delta phase field; as can be seen in Fig. 1 [6]. The present study investigates the formation of the intermetallic delta phase from the parent gamma phase. 2. Methodology Vacuum melted uranium ingots and arc melted zirconium bar was used for the alloy preparation. 20 gm of U-50 wt.%Zr alloy was * Corresponding author. Tel.: þ91 22 2559 2932. E-mail address: [email protected] (C.B. Basak). 0966-9795/$ e see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.intermet.2010.05.006
prepared by arc melting under highly purified Ar atmosphere. Melting was carried out for a total six times by turning the alloy button each time. Subsequently, the alloy button was wrapped in 250 mm thick tantalum foil and encapsulated into a quartz capsule under 103 mbar partial pressure of He. The entire capsule was inserted into a graphite crucible which was heated at 1300 C for 4 h in a small vacuum induction furnace. After the furnace cooling the alloy button was copper jacketed and hot-rolled at 750 C in the g-phase region where there is complete solid solubility of the uranium and zirconium. Total thickness reduction of w50% was achieved by three passes with intermediate soaking at 750 C for 5 min. After final pass the samples were soaked at 875 C for 10 min and then water quenched. Total five samples were sliced out by slow speed SiC cut-off wheel. Each of these samples was encapsulated separately into quartz tube under aforementioned condition. Then all these five samples were heated to 875 C for 4 h and one sample was water quenched (after breaking the quartz tube). The temperature of the furnace was then lowered to 720 C, kept there for 4 h and then another sample was water quenched. Once again the temperature was further lowered to 635 C and held there for another 4 h and all three left over samples were water quenched. From the last three samples two samples were aged at 550 C and 300 C for 10 h prior to water quenching. All these temperatures are indicated as dots in the phase diagram (Fig. 1). For the sake of brevity these samples will be identified as 875q, 720q, 635q, 550aq and 300aq; where ‘q’ and ‘aq’ stands for quenched and aged þ quenched respectively. For the conventional metallography 25 mm diameter Teflon mould and quick-set resin was used for cold mounting. Standard
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C.B. Basak et al. / Intermetallics 18 (2010) 1707e1712
Fig. 1. U-rich part of the UeZr phase diagram; vertical dotted line indicates the U50 wt.%Zr composition. The black dots indicate heat treatment temperature (T¼300 C is not shown here).
metallographic procedure was followed for the present study. Electro-polishing was carried out using 50%H3PO4 aqueous solution as electrolyte and SS304 as cathode with a constant potential of 25 V, for delta phase. Chemical etching of gamma phase was carried out by dripping the freshly prepared warm etchant (H2O:HNO3: HF ¼ 5:5:1 v/v) onto the sample surface; it took about 5e10 s to etch the sample. In addition to the metallography; XRD and microhardness analysis were also carried out. XRD was carried out in a qeq goniometer with Cu-Ka radiation (fixed slit) and proportional counter. For microhardness measurement diamond pyramid indenter was used with 100 gm load with a dwell time of 10 s. All the XRD patterns were indexed using GSAS computer program [7] and the intensity profile matching was carried out using peudo-Voigt profile function for phase fraction analysis. Further, the line profile analysis of the individual phases was carried out using WilliamsoneHall method [8]. The equation used for WilliamsoneHall method is well known and for Lorentzian profile it could be written as e
ðbobs: binst: Þcos q ¼
Kl þ 43sin q 10:D
(1)
Fig. 2. Optical micrograph of U-50 wt.%Zr samples. (a) Water quenched from 875 C, under polarized light illumination; original magnification 416. (b) Water quenched from 635 C, under bright field illumination; original magnification 1040.
where, bobs. and binst. stand for observed and instrumental broadening in radian. K is Scherrer constant and l is the wave length of the x-ray in A. D and 3 are size of coherently diffracting domain in nm and non-uniform strain in % respectively. In the present study, bobs. was taken as the FWHM of the peak and the instrumental broadening was found using strain-free standard sample of CeO2 under the same instrumental parameter as was used for the samples.
Except 635q sample, all other samples respond well under polarized light illumination; a typical signature of non-isotropic crystal structure. Fig. 2(a) is the representative microstructure of all these samples revealing equiaxed grains. On the other hand it was observed that the 635q sample was difficult to polish due to its softness. Moreover, 635q does not respond under polarized light illumination indicating an isotropic crystal structure. Fig. 2 (b) is the microstructure of 635q sample under bright field illumination; many etch pits are also visible. Microhardness data of all the samples are presented in Fig. 3. As seen from the Fig. 3, hardness value of 635q sample is almost the average of that pure U and pure Zr. On the other hand it is clearly observed that hardness value is higher in case of aged sample than the quenched samples. The difference in the hardness values
300 aq 550 aq 300
Microhardness (VHN)
3. Experimental results
350
875q 720q
Pure U (orthorhombic- )
250
635q
200
150
Pure Zr (hcp- ) 100 0
50
100
Wt% Zr Fig. 3. Microhardness values of U-50 wt.%Zr samples alongwith the hardness values of a-U and a-Zr. Note that as quenching temperature goes down hardness value also reduces due to the presence of more retained gamma phase.
C.B. Basak et al. / Intermetallics 18 (2010) 1707e1712
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Table 1 Phase, phase fraction and corresponding lattice parameter, lattice volume and microhardness data of U-50 wt.% Zr alloy under different heat-treated conditions. Microhardness (VHN)
Sample history
Phase and Lattice Lattice phase fraction parameter ( A) volume ( A3) a c
Quenched from 875 C Quenched from 720 C Quenched from 635 C Aged at 550 C and quenched Aged at 300 C and quenched
d (w60%) g (w40%) d (w30%) g (w70%) g
5.0429 3.5817 5.0429 3.5784 3.5765
d
5.0419 3.0938 68.1081
320
d
5.0343 3.0938 67.9029
328
3.1052 e 3.1043 e e
68.3862 45.9481 68.3663 45.8212 45.7483
295 270 208
phase. The phase fraction of the retained gamma phase was also calculated out from the XRD patterns. All the lattice parameters and the phase fractions values of the concerned phases are presented in Table 1. Variation in the lattice parameters and lattice volume of d-
a
5.044
Lattice Parameter, a (Å)
5.042
5.040
5.038
5.036
5.034
300
Fig. 4. XRD patterns of U-50 wt.%Zr samples; (a) sample quenched from bcc g-phase field; (b) sample aged in hexagonal d-phase region and quenched.
500
600
700
800
900
800
900
Temperature (°C)
b
3.106
(b)
3.104
Lattice Parameter, c (Å)
between 300aq and 550aq is so small that their standard deviation values overlap. On the other hand higher quenching temperature yields higher hardness, albeit less than the aged samples. The XRD patterns for all these samples are categorized here into two classes depending on the phase field wherefrom they were quenched. The XRD patterns of 875q, 720q and 635q samples quenched from the gamma field are presented in Fig. 4 (a) and (b) represents the same for 550aq and 300aq samples aged in delta phase field. Comparing Fig. 4 (a) and (b) it becomes apparent that except the 635q sample all other samples show similar patterns. However, sample 300aq shows some additional peaks of low intensity. A preliminary investigation reveals that the 2q indexing of the XRD patterns for the 875q, 720q, 550aq and 300aq samples match quite well to that of d-phase with space group P6/mmm (sp. gr. no. 191) having three lattice positions (0,0,0), (1/3, 2/3, 1/2) and (2/3, 1/3, 1/2); same as obtained by Akabori et al. [1,2]. The sample 635q can only be indexed with typical W-prototype bcc structure (Im3m); the structure of parent gamma phase. However, severe intensity mismatch was observed for 875q and 720q samples. Eventually, it was found that intensity of both the XRD patterns can be matched reasonably well with the inclusion of retained gamma
400
3.102
3.100
3.098
3.096
3.094
3.092 300
400
500
600
700
Temperature (°C) Fig. 5. Variation of lattice parameter of d-phase, obtained from the XRD analysis, with respect to the heat treatment temperature; (a) lattice parameter, a and (b) parameter c. The lines are only for visual guide.
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a
a
0.012 0.011
3.582 0.010
) cos inst
0.009 0.008
(2021)
obs
3.579
0.007 (200)
0.006
(1 1 2 2) (220) (211)
0.005
3.578
(00 01)
0.8
1.0
(110)
1.2
1.4
1.6
3.577
650
700
750
800
850
900
b
Quenching Temperature (°C)
2.0
2.2
2.4
2.6
550aq 300aq Linear Fit for 550aq Linear Fit for 300aq
0.010
) cos
0.009
inst
1.0
0.008
(11 22) (11 21)
0.007 (0001) (20 21)
0.006
(
obs
-
0.9
Phase fraction of -phase
1.8
4.sin
3.576 600
b
(2131)
-
3.580
(1 1 21)
(
Lattice Parameter, a (Å)
3.581
875q 720q 635q Linear fit of 875q Linear fit of 720q Linear fit of 635q
0.8
0.005
0.7
0.004 0.8
(2 1 3 1)
1.0
1.2
1.4
0.6
1.6
1.8
2.0
2.2
2.4
4.sin
c
0.5
0.20 60 55
0.4
0.15
50
700
750
800
850
900
c
45
D ( nm)
Quenching Temperature (°C)
720q
40 35
0.10
550aq
300aq
(%)
650
875q
340
30 0.05 25
320
635q Non-uniform strain ( )
Microhardness (VHN)
20
300
Coherently diffracting domain size (D) 15
0.00 300
280
400
500
600
700
800
900
Quenching temperature (°C)
260
Fig. 7. (a) and (b) WilliamsoneHall plot of different heat treated samples showing the used indices by arrows. (c) Plot of coherently scattered domain size (D) and nonuniform strain (3), derived from the WilliamsoneHall plot, against the quenching temperature. The lines in (c) are only for visual guide.
240 220 200 180 300
400
500
600
700
800
900
Heat-treatment temperature (°C) Fig. 6. (a) Variation of lattice parameter of metastable g-phase; (b) corresponding phase fraction as a function of quenching temperature and (c) effect of retained gphase on the microhardness value. The lines are only for visual guide.
phase with respect to the heat treatment temperature is presented in Fig. 5 (aeb). Fig. 6 (a) represents lattice parameter value of metastable g-phase as a function of quenching temperature and corresponding phase fraction is presented in Fig. 6 (b). In fact the effect of g-phase retention is better understood from Fig. 6 (c) where hardness values are plotted against the heat treatment temperature. The line profile analysis results obtained from the XRD patterns are presented in Fig. 7 (aec) using WilliamsoneHall method [8].
C.B. Basak et al. / Intermetallics 18 (2010) 1707e1712
4. Discussions First, it is worthwhile to revisit the crystallography of omega transformation in brief. A volume of work has already been devoted to the study of omega crystallography; mostly in Zr, Hf and Ti systems [9e12]. It will suffice here to mention that there are three modes by which AlB2-prototype omega structure may be generated from the parent bcc phase. The accepted modes of omega transformation can broadly be classified as athermal omega, isothermal omega and irradiation induced omega. However, in all the cases omega is formed by the collapse of alternate (111) planes of the parent bcc phase as depicted in Fig. 8 (aeb). In all the cases a certain orientation relationship (OR) is maintained between the parent bcc and the daughter omega phase. In the present case of parent g and d-phase this OR can be described as e ð111Þg k ð0001Þd and h110ig k h1120id . Also there exists a definite lattice correspondence between the parent and product phase as follows [9e11].
au ¼ cu ¼
pffiffiffi 2a
pffiffiffi g 3 2 ag
(2)
The lattice parameter values of the delta phase calculated from the experimentally obtained lattice parameter of retained g-phase are presented in Table 2. A fair agreement is observed between the calculated and experimental lattice parameter values and lattice volumes for 875q and 720q samples. Clearly one can see that indeed there exists a definite lattice correspondence between the retained gamma phase and the stable delta phase. So, it is likely that in U-50 wt.%Zr alloy the g/d transition, during quenching, takes place by omega transformation mechanism. From Fig. 4 (a) one can see that as quenching temperature goes up the peak width increases. From Fig. 7 (a) is becomes more apparent that the non-uniform strain does not vary much between the 875q, 720q and 635q samples; since the lines are almost parallel to each other. From Fig. 7 (c) it can be seen that the nonuniform strain is very small in these samples. However, size of the crystallite decreases with increasing quenching temperature. Such peak broadening effect is well established in the early stages of omega transformation where the lattice plane collapse is not complete [13,14]. So, in the present case the observed peak broadening is caused due to the formation of the d-phase in the
1711
Table 2 Comparison between experimentally obtained lattice parameters of d-phase and the same calculated from the experimentally obtained lattice parameter of retained bcc g-phase; where, DX ¼ Xexp.Xcalc. Sample ID Lattice parameter Calculated A) parameters of d of retained g ( a ( A) 875q 720q
3.5817 3.5784
c ( A)
V ( A3)
Difference wrt exp. values
Da/aexp. Dc/cexp. DV/Vexp.
5.0653 3.1018 68.9201 0.44% 0.11% 5.0606 3.0990 68.7298 0.35% 0.17%
0.78% 0.53%
sample quenched from higher temperature. As the quenching temperature reduces the driving force required for the (111) plane collapse mechanism g-phase also reduces. In the extreme case, just above the g/d transformation temperature (w613 C), the driving force is too weak to collapse the (111) planes of the gphase; as a result metastable g is obtained as in case of 635q sample. So, with increasing quenching temperature more d-phase is forming, that causes reduction of the coherently diffracting domain size. This manifests by the broadening of the x-ray diffraction peaks. Thus it can be said that quenching from high gamma region results athermal omega formation and less retention of metastable g. Presence of retained g-phase is not only supported by the XRD analysis but also from the microhardness data. As quenching temperature decreases more and more retained g makes the sample softer as revealed in Fig. 6 (c). WilliamsoneHall analysis also supports the fact that presence of d-phase broadens the diffraction peaks due to the lower size of the diffracting crystallites. The aged samples (in d-phase region) initially having metastable g-phase show higher non-uniform strain and crystallite size when compared with the quenched samples. Also, it is unlikely that any of these samples is having any retained g-phase as revealed by the XRD analysis and microhardness data (Fig. 6 (c)). From Fig. 6 (a) it is possible to fit a linear relationship between lattice parameter of g-phase and temperature (in K) and the relationship comes out as follows e
aT ¼ 3:5569 þ 2:16 105 T g
(3)
where, temperature is in K and lattice parameter of g at 0K is 3.5569 A. Now, one can calculate the extrapolated lattice
Fig. 8. (a) Orientation relationship between bcc g-phase and hexagonal d-phase. Dark atoms and bonds represent parent bcc phase and lighter atoms and bonds represent delta phase. The dark planes (triangular shaped) are (111) planes of bcc which collapse themselves to form (0001) planes of d-phase. (b) Arrows indicate the collapse direction of two alternate (111) planes of the parent g-phase.
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C.B. Basak et al. / Intermetallics 18 (2010) 1707e1712
Table 3 Comparison between experimentally obtained lattice parameters of d-phase and the same calculated from the extrapolated lattice parameter values of bcc g-phase at lower temperature; where, DX ¼ Xexp.Xcalc. Sample Extrapolated lattice A) ID parameter of g (
Calculated parameters Difference wrt exp. of d values a ( A)
550aq 300aq
3.5747 3.5693
c ( A)
V ( A3)
Da/ aexp.
Dc/ cexp.
DV/ Vexp.
5.0554 3.0958 68.5168 0.27% 0.06% 0.60% 5.0478 3.0911 68.2068 0.27% 0.09% 0.45%
parameter data of g-phase at 550 C and at 300 C; where, g is thermodynamically metastable. From these data and using Eq. (2) the lattice parameter and lattice volume data of the d-phase can be calculated out at 550 C and at 300 C. These calculated data along with the relative variation with respect to the experimental data are presented in Table 3. Clearly, the close match between the calculated and experimental values suggests that the lattice correspondence between the g-phase and d-phase are well preserved. So it can be concluded that during ageing of the metastable g-phase delta phase is formed by diffusion assisted isothermal omega transformation. However, as can be seen from Fig. 5 (aec), variation in lattice parameter and lattice volume of the athermal omega is little with the temperature of quenching. But in the case of isothermal omega lattice parameter c is more or less same denoting the plane collapse is nearly completed during the ageing treatment; though there is significant variation in the lattice volume due to the large variation in parameter a. As the ageing temperature decreases, between 550aq and 300aq samples, higher non-uniform strain and lower crystallite size could be observed from Fig. 7 (c). At higher ageing temperature growth of the isothermal d-phase would be higher causing higher size of the coherently diffracting phase domain. On the other hand at higher temperature most of the lattice defects associated with the plane collapse mechanism get annihilated and hence the lesser amount of the non-uniform strain remains.
5. Conclusions In U-50 wt.%Zr alloy the g/d transition takes place by omega transformation mechanism; in which the alternate (111) planes of parent g-phase collapse to form AlB2 type hexagonal crystal structure. In the present case g/d omega transformation can take place either athermally or isothermally. Quenching from high gamma field results in athermal d formation with less amount of retained g-phase. Quenching temperature just above the g/d transus causes full retention of metastable g-phase. Metastable gphase is transformed isothermally into d-phase upon ageing in the delta phase region; similar to the diffusion assisted isothermal omega transformation. Acknowledgement Author CBB expresses his sense of gratitude towards Dr. V. Kain, MSD, BARC for the microhardness measurements and to H. S. Kamath, Director, NFG for his enthusiastic support for this work. References [1] Holden AN, Seymour WE. Trans AIME 1957;209:515. [2] Duffey JF, Bruch CA. Trans AIME 1958;212:408. [3] Akabori M, Itoh A, Ogawa T, Kobayashi F, Suzuki Y. J Nucl Mat 1992;188:249e54. [4] Akabori M, Ogawa T, Itoh A, Morii Y. J Phys Condens Mat 1995;7:8249e57. [5] Basak CB, Keswani R, Prasad GJ, Kamath HS, Prabhu N. J Alloys Compd 2009;471(1e2):544e52. [6] Updating Service. In: Okamoto H, editor. ASM metals handbook, binary alloy phase diagram, vol. 3. ASM International; 1992. chap. 2,p. 381. [7] Larson AC, Von Dreele RB. General structure analysis system (GSAS). Los Alamos National Laboratory Report; 2004. LAUR 86748. [8] Williamson GK, Hall WH. Acta Mater 1953;1:22. [9] Sikka SK, Vohra YK, Chidambaram R. Prog Mater Sci 1982;27:245. [10] Dey GK, Tewari R, Banerjee S, Jyoti G, Gupta SC, Joshi KD, et al. Acta Mater 2004;52:5243. [11] Tewari R, Srivastava D, Dey GK, Chakravarty JK, Banerjee S. J Nucl Mat 2008;383:153e71. [12] de Fontaine D. Met Trans A 1988;19A:169. [13] Lavrentiev V, Hammerl C, Auschenbach BR, Pisanenko A, Kukharenko O. Philos Mag A 2001;81(2):511e27. [14] Hayman C, Gerberich WW. Met Trans A 1985;16(2):187.
Contents lists available at ScienceDirect
Intermetallics journal homepage: www.elsevier.com/locate/intermet
On the formation mechanism of UZr2 phase Chandra Bhanu Basak a, *, N. Prabhu b, Madangopal Krishnan a a b
Materials Science Division, Bhabha Atomic Research Center, Trombay, Mumbai 400 085, India Department of Metallurgical Engineering & Materials Science, Indian Institute of Technology Bombay, Powai, Mumbai 400 076, India
a r t i c l e i n f o
a b s t r a c t
Article history: Received 18 June 2009 Received in revised form 6 February 2010 Accepted 10 May 2010 Available online 19 June 2010
Intermetallic delta phase (UZr2) in UeZr alloy system is known to have hexagonal crystal structure. However, the formation mechanism of delta phase from the parent bcc gamma phase was not investigated before. With an extensive XRD analysis along with the microhardness data the present investigation reveals that gamma to delta transition takes place by the mechanism of omega transformation. Formation of both athermal and isothermal delta phase is also established for UZr2 alloy composition. Ó 2010 Elsevier Ltd. All rights reserved.
Keywords: A. Uranium A. Zirconium F. X-ray Diffraction B. Omega transformation
1. Introduction Non-stoichiometric d-phase (UZr2) is known to be the only intermetallic phase in UeZr system. However, presence of this phase was established only after 1955 and subsequently the stability of this phase was proven beyond doubt [1,2]. Most recent studies on the stability and structure of the d-phase are carried out by Akabori et al. by XRD analysis and subsequently by high resolution neutron diffraction analysis [3,4]. In recent years the UeZr composition around the delta phase region is being considered as a potential candidate for the dispersion fuel application. It is thus important to know the physical metallurgical behaviour of the concerned phase. In U-rich UeZr alloys the d-phase is formed by peritectoid reaction which is extremely sluggish kinetically and hence formation of d-phase could not be confirmed even after long term annealing [5]. Hence, in the present study U-50 wt.% Zr alloy (w72at%Zr) was chosen so that the composition goes directly through the middle of the delta phase field; as can be seen in Fig. 1 [6]. The present study investigates the formation of the intermetallic delta phase from the parent gamma phase. 2. Methodology Vacuum melted uranium ingots and arc melted zirconium bar was used for the alloy preparation. 20 gm of U-50 wt.%Zr alloy was * Corresponding author. Tel.: þ91 22 2559 2932. E-mail address: [email protected] (C.B. Basak). 0966-9795/$ e see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.intermet.2010.05.006
prepared by arc melting under highly purified Ar atmosphere. Melting was carried out for a total six times by turning the alloy button each time. Subsequently, the alloy button was wrapped in 250 mm thick tantalum foil and encapsulated into a quartz capsule under 103 mbar partial pressure of He. The entire capsule was inserted into a graphite crucible which was heated at 1300 C for 4 h in a small vacuum induction furnace. After the furnace cooling the alloy button was copper jacketed and hot-rolled at 750 C in the g-phase region where there is complete solid solubility of the uranium and zirconium. Total thickness reduction of w50% was achieved by three passes with intermediate soaking at 750 C for 5 min. After final pass the samples were soaked at 875 C for 10 min and then water quenched. Total five samples were sliced out by slow speed SiC cut-off wheel. Each of these samples was encapsulated separately into quartz tube under aforementioned condition. Then all these five samples were heated to 875 C for 4 h and one sample was water quenched (after breaking the quartz tube). The temperature of the furnace was then lowered to 720 C, kept there for 4 h and then another sample was water quenched. Once again the temperature was further lowered to 635 C and held there for another 4 h and all three left over samples were water quenched. From the last three samples two samples were aged at 550 C and 300 C for 10 h prior to water quenching. All these temperatures are indicated as dots in the phase diagram (Fig. 1). For the sake of brevity these samples will be identified as 875q, 720q, 635q, 550aq and 300aq; where ‘q’ and ‘aq’ stands for quenched and aged þ quenched respectively. For the conventional metallography 25 mm diameter Teflon mould and quick-set resin was used for cold mounting. Standard
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C.B. Basak et al. / Intermetallics 18 (2010) 1707e1712
Fig. 1. U-rich part of the UeZr phase diagram; vertical dotted line indicates the U50 wt.%Zr composition. The black dots indicate heat treatment temperature (T¼300 C is not shown here).
metallographic procedure was followed for the present study. Electro-polishing was carried out using 50%H3PO4 aqueous solution as electrolyte and SS304 as cathode with a constant potential of 25 V, for delta phase. Chemical etching of gamma phase was carried out by dripping the freshly prepared warm etchant (H2O:HNO3: HF ¼ 5:5:1 v/v) onto the sample surface; it took about 5e10 s to etch the sample. In addition to the metallography; XRD and microhardness analysis were also carried out. XRD was carried out in a qeq goniometer with Cu-Ka radiation (fixed slit) and proportional counter. For microhardness measurement diamond pyramid indenter was used with 100 gm load with a dwell time of 10 s. All the XRD patterns were indexed using GSAS computer program [7] and the intensity profile matching was carried out using peudo-Voigt profile function for phase fraction analysis. Further, the line profile analysis of the individual phases was carried out using WilliamsoneHall method [8]. The equation used for WilliamsoneHall method is well known and for Lorentzian profile it could be written as e
ðbobs: binst: Þcos q ¼
Kl þ 43sin q 10:D
(1)
Fig. 2. Optical micrograph of U-50 wt.%Zr samples. (a) Water quenched from 875 C, under polarized light illumination; original magnification 416. (b) Water quenched from 635 C, under bright field illumination; original magnification 1040.
where, bobs. and binst. stand for observed and instrumental broadening in radian. K is Scherrer constant and l is the wave length of the x-ray in A. D and 3 are size of coherently diffracting domain in nm and non-uniform strain in % respectively. In the present study, bobs. was taken as the FWHM of the peak and the instrumental broadening was found using strain-free standard sample of CeO2 under the same instrumental parameter as was used for the samples.
Except 635q sample, all other samples respond well under polarized light illumination; a typical signature of non-isotropic crystal structure. Fig. 2(a) is the representative microstructure of all these samples revealing equiaxed grains. On the other hand it was observed that the 635q sample was difficult to polish due to its softness. Moreover, 635q does not respond under polarized light illumination indicating an isotropic crystal structure. Fig. 2 (b) is the microstructure of 635q sample under bright field illumination; many etch pits are also visible. Microhardness data of all the samples are presented in Fig. 3. As seen from the Fig. 3, hardness value of 635q sample is almost the average of that pure U and pure Zr. On the other hand it is clearly observed that hardness value is higher in case of aged sample than the quenched samples. The difference in the hardness values
300 aq 550 aq 300
Microhardness (VHN)
3. Experimental results
350
875q 720q
Pure U (orthorhombic- )
250
635q
200
150
Pure Zr (hcp- ) 100 0
50
100
Wt% Zr Fig. 3. Microhardness values of U-50 wt.%Zr samples alongwith the hardness values of a-U and a-Zr. Note that as quenching temperature goes down hardness value also reduces due to the presence of more retained gamma phase.
C.B. Basak et al. / Intermetallics 18 (2010) 1707e1712
1709
Table 1 Phase, phase fraction and corresponding lattice parameter, lattice volume and microhardness data of U-50 wt.% Zr alloy under different heat-treated conditions. Microhardness (VHN)
Sample history
Phase and Lattice Lattice phase fraction parameter ( A) volume ( A3) a c
Quenched from 875 C Quenched from 720 C Quenched from 635 C Aged at 550 C and quenched Aged at 300 C and quenched
d (w60%) g (w40%) d (w30%) g (w70%) g
5.0429 3.5817 5.0429 3.5784 3.5765
d
5.0419 3.0938 68.1081
320
d
5.0343 3.0938 67.9029
328
3.1052 e 3.1043 e e
68.3862 45.9481 68.3663 45.8212 45.7483
295 270 208
phase. The phase fraction of the retained gamma phase was also calculated out from the XRD patterns. All the lattice parameters and the phase fractions values of the concerned phases are presented in Table 1. Variation in the lattice parameters and lattice volume of d-
a
5.044
Lattice Parameter, a (Å)
5.042
5.040
5.038
5.036
5.034
300
Fig. 4. XRD patterns of U-50 wt.%Zr samples; (a) sample quenched from bcc g-phase field; (b) sample aged in hexagonal d-phase region and quenched.
500
600
700
800
900
800
900
Temperature (°C)
b
3.106
(b)
3.104
Lattice Parameter, c (Å)
between 300aq and 550aq is so small that their standard deviation values overlap. On the other hand higher quenching temperature yields higher hardness, albeit less than the aged samples. The XRD patterns for all these samples are categorized here into two classes depending on the phase field wherefrom they were quenched. The XRD patterns of 875q, 720q and 635q samples quenched from the gamma field are presented in Fig. 4 (a) and (b) represents the same for 550aq and 300aq samples aged in delta phase field. Comparing Fig. 4 (a) and (b) it becomes apparent that except the 635q sample all other samples show similar patterns. However, sample 300aq shows some additional peaks of low intensity. A preliminary investigation reveals that the 2q indexing of the XRD patterns for the 875q, 720q, 550aq and 300aq samples match quite well to that of d-phase with space group P6/mmm (sp. gr. no. 191) having three lattice positions (0,0,0), (1/3, 2/3, 1/2) and (2/3, 1/3, 1/2); same as obtained by Akabori et al. [1,2]. The sample 635q can only be indexed with typical W-prototype bcc structure (Im3m); the structure of parent gamma phase. However, severe intensity mismatch was observed for 875q and 720q samples. Eventually, it was found that intensity of both the XRD patterns can be matched reasonably well with the inclusion of retained gamma
400
3.102
3.100
3.098
3.096
3.094
3.092 300
400
500
600
700
Temperature (°C) Fig. 5. Variation of lattice parameter of d-phase, obtained from the XRD analysis, with respect to the heat treatment temperature; (a) lattice parameter, a and (b) parameter c. The lines are only for visual guide.
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a
a
0.012 0.011
3.582 0.010
) cos inst
0.009 0.008
(2021)
obs
3.579
0.007 (200)
0.006
(1 1 2 2) (220) (211)
0.005
3.578
(00 01)
0.8
1.0
(110)
1.2
1.4
1.6
3.577
650
700
750
800
850
900
b
Quenching Temperature (°C)
2.0
2.2
2.4
2.6
550aq 300aq Linear Fit for 550aq Linear Fit for 300aq
0.010
) cos
0.009
inst
1.0
0.008
(11 22) (11 21)
0.007 (0001) (20 21)
0.006
(
obs
-
0.9
Phase fraction of -phase
1.8
4.sin
3.576 600
b
(2131)
-
3.580
(1 1 21)
(
Lattice Parameter, a (Å)
3.581
875q 720q 635q Linear fit of 875q Linear fit of 720q Linear fit of 635q
0.8
0.005
0.7
0.004 0.8
(2 1 3 1)
1.0
1.2
1.4
0.6
1.6
1.8
2.0
2.2
2.4
4.sin
c
0.5
0.20 60 55
0.4
0.15
50
700
750
800
850
900
c
45
D ( nm)
Quenching Temperature (°C)
720q
40 35
0.10
550aq
300aq
(%)
650
875q
340
30 0.05 25
320
635q Non-uniform strain ( )
Microhardness (VHN)
20
300
Coherently diffracting domain size (D) 15
0.00 300
280
400
500
600
700
800
900
Quenching temperature (°C)
260
Fig. 7. (a) and (b) WilliamsoneHall plot of different heat treated samples showing the used indices by arrows. (c) Plot of coherently scattered domain size (D) and nonuniform strain (3), derived from the WilliamsoneHall plot, against the quenching temperature. The lines in (c) are only for visual guide.
240 220 200 180 300
400
500
600
700
800
900
Heat-treatment temperature (°C) Fig. 6. (a) Variation of lattice parameter of metastable g-phase; (b) corresponding phase fraction as a function of quenching temperature and (c) effect of retained gphase on the microhardness value. The lines are only for visual guide.
phase with respect to the heat treatment temperature is presented in Fig. 5 (aeb). Fig. 6 (a) represents lattice parameter value of metastable g-phase as a function of quenching temperature and corresponding phase fraction is presented in Fig. 6 (b). In fact the effect of g-phase retention is better understood from Fig. 6 (c) where hardness values are plotted against the heat treatment temperature. The line profile analysis results obtained from the XRD patterns are presented in Fig. 7 (aec) using WilliamsoneHall method [8].
C.B. Basak et al. / Intermetallics 18 (2010) 1707e1712
4. Discussions First, it is worthwhile to revisit the crystallography of omega transformation in brief. A volume of work has already been devoted to the study of omega crystallography; mostly in Zr, Hf and Ti systems [9e12]. It will suffice here to mention that there are three modes by which AlB2-prototype omega structure may be generated from the parent bcc phase. The accepted modes of omega transformation can broadly be classified as athermal omega, isothermal omega and irradiation induced omega. However, in all the cases omega is formed by the collapse of alternate (111) planes of the parent bcc phase as depicted in Fig. 8 (aeb). In all the cases a certain orientation relationship (OR) is maintained between the parent bcc and the daughter omega phase. In the present case of parent g and d-phase this OR can be described as e ð111Þg k ð0001Þd and h110ig k h1120id . Also there exists a definite lattice correspondence between the parent and product phase as follows [9e11].
au ¼ cu ¼
pffiffiffi 2a
pffiffiffi g 3 2 ag
(2)
The lattice parameter values of the delta phase calculated from the experimentally obtained lattice parameter of retained g-phase are presented in Table 2. A fair agreement is observed between the calculated and experimental lattice parameter values and lattice volumes for 875q and 720q samples. Clearly one can see that indeed there exists a definite lattice correspondence between the retained gamma phase and the stable delta phase. So, it is likely that in U-50 wt.%Zr alloy the g/d transition, during quenching, takes place by omega transformation mechanism. From Fig. 4 (a) one can see that as quenching temperature goes up the peak width increases. From Fig. 7 (a) is becomes more apparent that the non-uniform strain does not vary much between the 875q, 720q and 635q samples; since the lines are almost parallel to each other. From Fig. 7 (c) it can be seen that the nonuniform strain is very small in these samples. However, size of the crystallite decreases with increasing quenching temperature. Such peak broadening effect is well established in the early stages of omega transformation where the lattice plane collapse is not complete [13,14]. So, in the present case the observed peak broadening is caused due to the formation of the d-phase in the
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Table 2 Comparison between experimentally obtained lattice parameters of d-phase and the same calculated from the experimentally obtained lattice parameter of retained bcc g-phase; where, DX ¼ Xexp.Xcalc. Sample ID Lattice parameter Calculated A) parameters of d of retained g ( a ( A) 875q 720q
3.5817 3.5784
c ( A)
V ( A3)
Difference wrt exp. values
Da/aexp. Dc/cexp. DV/Vexp.
5.0653 3.1018 68.9201 0.44% 0.11% 5.0606 3.0990 68.7298 0.35% 0.17%
0.78% 0.53%
sample quenched from higher temperature. As the quenching temperature reduces the driving force required for the (111) plane collapse mechanism g-phase also reduces. In the extreme case, just above the g/d transformation temperature (w613 C), the driving force is too weak to collapse the (111) planes of the gphase; as a result metastable g is obtained as in case of 635q sample. So, with increasing quenching temperature more d-phase is forming, that causes reduction of the coherently diffracting domain size. This manifests by the broadening of the x-ray diffraction peaks. Thus it can be said that quenching from high gamma region results athermal omega formation and less retention of metastable g. Presence of retained g-phase is not only supported by the XRD analysis but also from the microhardness data. As quenching temperature decreases more and more retained g makes the sample softer as revealed in Fig. 6 (c). WilliamsoneHall analysis also supports the fact that presence of d-phase broadens the diffraction peaks due to the lower size of the diffracting crystallites. The aged samples (in d-phase region) initially having metastable g-phase show higher non-uniform strain and crystallite size when compared with the quenched samples. Also, it is unlikely that any of these samples is having any retained g-phase as revealed by the XRD analysis and microhardness data (Fig. 6 (c)). From Fig. 6 (a) it is possible to fit a linear relationship between lattice parameter of g-phase and temperature (in K) and the relationship comes out as follows e
aT ¼ 3:5569 þ 2:16 105 T g
(3)
where, temperature is in K and lattice parameter of g at 0K is 3.5569 A. Now, one can calculate the extrapolated lattice
Fig. 8. (a) Orientation relationship between bcc g-phase and hexagonal d-phase. Dark atoms and bonds represent parent bcc phase and lighter atoms and bonds represent delta phase. The dark planes (triangular shaped) are (111) planes of bcc which collapse themselves to form (0001) planes of d-phase. (b) Arrows indicate the collapse direction of two alternate (111) planes of the parent g-phase.
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C.B. Basak et al. / Intermetallics 18 (2010) 1707e1712
Table 3 Comparison between experimentally obtained lattice parameters of d-phase and the same calculated from the extrapolated lattice parameter values of bcc g-phase at lower temperature; where, DX ¼ Xexp.Xcalc. Sample Extrapolated lattice A) ID parameter of g (
Calculated parameters Difference wrt exp. of d values a ( A)
550aq 300aq
3.5747 3.5693
c ( A)
V ( A3)
Da/ aexp.
Dc/ cexp.
DV/ Vexp.
5.0554 3.0958 68.5168 0.27% 0.06% 0.60% 5.0478 3.0911 68.2068 0.27% 0.09% 0.45%
parameter data of g-phase at 550 C and at 300 C; where, g is thermodynamically metastable. From these data and using Eq. (2) the lattice parameter and lattice volume data of the d-phase can be calculated out at 550 C and at 300 C. These calculated data along with the relative variation with respect to the experimental data are presented in Table 3. Clearly, the close match between the calculated and experimental values suggests that the lattice correspondence between the g-phase and d-phase are well preserved. So it can be concluded that during ageing of the metastable g-phase delta phase is formed by diffusion assisted isothermal omega transformation. However, as can be seen from Fig. 5 (aec), variation in lattice parameter and lattice volume of the athermal omega is little with the temperature of quenching. But in the case of isothermal omega lattice parameter c is more or less same denoting the plane collapse is nearly completed during the ageing treatment; though there is significant variation in the lattice volume due to the large variation in parameter a. As the ageing temperature decreases, between 550aq and 300aq samples, higher non-uniform strain and lower crystallite size could be observed from Fig. 7 (c). At higher ageing temperature growth of the isothermal d-phase would be higher causing higher size of the coherently diffracting phase domain. On the other hand at higher temperature most of the lattice defects associated with the plane collapse mechanism get annihilated and hence the lesser amount of the non-uniform strain remains.
5. Conclusions In U-50 wt.%Zr alloy the g/d transition takes place by omega transformation mechanism; in which the alternate (111) planes of parent g-phase collapse to form AlB2 type hexagonal crystal structure. In the present case g/d omega transformation can take place either athermally or isothermally. Quenching from high gamma field results in athermal d formation with less amount of retained g-phase. Quenching temperature just above the g/d transus causes full retention of metastable g-phase. Metastable gphase is transformed isothermally into d-phase upon ageing in the delta phase region; similar to the diffusion assisted isothermal omega transformation. Acknowledgement Author CBB expresses his sense of gratitude towards Dr. V. Kain, MSD, BARC for the microhardness measurements and to H. S. Kamath, Director, NFG for his enthusiastic support for this work. References [1] Holden AN, Seymour WE. Trans AIME 1957;209:515. [2] Duffey JF, Bruch CA. Trans AIME 1958;212:408. [3] Akabori M, Itoh A, Ogawa T, Kobayashi F, Suzuki Y. J Nucl Mat 1992;188:249e54. [4] Akabori M, Ogawa T, Itoh A, Morii Y. J Phys Condens Mat 1995;7:8249e57. [5] Basak CB, Keswani R, Prasad GJ, Kamath HS, Prabhu N. J Alloys Compd 2009;471(1e2):544e52. [6] Updating Service. In: Okamoto H, editor. ASM metals handbook, binary alloy phase diagram, vol. 3. ASM International; 1992. chap. 2,p. 381. [7] Larson AC, Von Dreele RB. General structure analysis system (GSAS). Los Alamos National Laboratory Report; 2004. LAUR 86748. [8] Williamson GK, Hall WH. Acta Mater 1953;1:22. [9] Sikka SK, Vohra YK, Chidambaram R. Prog Mater Sci 1982;27:245. [10] Dey GK, Tewari R, Banerjee S, Jyoti G, Gupta SC, Joshi KD, et al. Acta Mater 2004;52:5243. [11] Tewari R, Srivastava D, Dey GK, Chakravarty JK, Banerjee S. J Nucl Mat 2008;383:153e71. [12] de Fontaine D. Met Trans A 1988;19A:169. [13] Lavrentiev V, Hammerl C, Auschenbach BR, Pisanenko A, Kukharenko O. Philos Mag A 2001;81(2):511e27. [14] Hayman C, Gerberich WW. Met Trans A 1985;16(2):187.