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Precipitation and dissolution peaks of hydride in Zr–2.5Nb during quasistatic thermal cycles
Journal of Alloys and Compounds 310 (2000) 214–218
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Precipitation and dissolution peaks of hydride in Zr–2.5Nb during quasistatic thermal cycles a, b Z.L. Pan *, M.P. Puls b
a Atomic Energy of Canada Ltd., CRL, Chalk River, ON Canada, K0 J 1 J0 Atomic Energy of Canada Ltd., Sheridan Park, Mississauga, ON Canada, L5 K 1 B2
Abstract Two internal friction peaks and corresponding discontinuity (‘knee’) points of elastic modulus have been observed in hydride-forming metals upon heating and cooling, respectively. In the present work, measurements of Young’s modulus as functions of temperature and hold time during a quasistatic thermal cycle were made in Zr–2.5Nb samples containing hydrogen using a composite oscillator technique. The increment of modulus during an isothermal hold is proportional to the decrease in hydrogen concentration in solid solution of the Zr alloy. As a result, elastic modulus measurements provide a means to determine the amount of transformed hydride during the transition. It is confirmed experimentally that the two peaks reflect the variation of the hydride transformation rate during heating or cooling. It is demonstrated by the present work that the maximum-slope point of each peak, on the high temperature side, is coincident with the knee point on the curve of modulus versus temperature and this point provides the most reliable and physically sensible indicator of the end of hydride dissolution during heating, or the beginning of hydride precipitation during cooling. 2000 Published by Elsevier Science S.A. Keywords: Internal friction; Elastic modulus; Zr alloys; Hydrogen solubility; Hydride delayed crack; Phase transformation
1. Introduction The presence of hydrogen and / or deuterium 1 in Zr alloys of nuclear reactor core components could result in local embrittlement when the terminal solid solubility (TSS), or solvus, of hydrogen is exceeded in regions of high tensile stress, such as at flaws. For nuclear engineering applications, an accurate knowledge of the TSS in Zr alloys is crucial to assess the potential for delayed hydride cracking (DHC) [1]. The TSS of hydrogen in Zr and its alloys has been determined by various techniques, such as diffusion, dilatometry, electric resistivity, DHC, differential scanning calorimetry (DSC), neutron diffraction, acoustic emission [2], internal friction [3] and dynamic elastic modulus (DEM) [4]. In some techniques, TSS is detected by a sharp discontinuity (‘knee’) point in curves
*Corresponding author. E-mail addresses: [email protected] (Z.L. Pan), [email protected] (M.P. Puls). 1 For simplicity, both hydrogen and deuterium are referred to as hydrogen in the following.
of elastic modulus versus temperature [4], auto-twisting strain versus temperature (by a pendulum) [5], expansion versus temperature [6] or electric resistivity versus temperature etc. In other techniques, TSS is detected by the maximum slope point in curves of internal friction versus temperature on the high temperature side [7] or differential heat flow versus temperature by DSC [8]. Obviously, some different results are obtained when using these different criteria for detecting the TSS. The question is, how are the knee point and the maximum-slope point interrelated? Whether the peak temperature of the internal friction curve might represent the TSS temperature? Numakura et al. [9] mentioned that ‘the curve of shear modulus vs. temperature shows a marked change at the peak temperature’. Unfortunately, the ‘marked change’ point obtained by [9] in Zr–H was not sufficiently sharp to show the relationship, but the authors’ other work on Ti–H [10] provided a sharp knee point, which was likely close to the maximum slope point, not at the peak, of the internal friction curve. To obtain accurate data of TSS, the consistency of the experimental criteria used to establish the hydrogen solvus by different techniques should be verified. Since the 1960s, the internal friction and dynamic elastic modulus techniques have been employed to study hydro-
0925-8388 / 00 / $ – see front matter 2000 Published by Elsevier Science S.A. PII: S0925-8388( 00 )01028-8
Z.L. Pan, M.P. Puls / Journal of Alloys and Compounds 310 (2000) 214 – 218
gen behavior and to establish the solvus in hydride-forming metals, particularly in Zr alloys [3–5,7]. In the present work, a composite oscillator technique is used to clarify the relationship between the maximum slope point and the knee point by determining the amount of hydride transformed during a quasistatic thermal cycle. The present work identifies that the temperature defined by the maximum slope point on internal friction curves is coincident with the knee point on the modulus curves and best represents the end of hydride dissolution during heating, or the beginning of hydride precipitation during cooling.
2. Experiments Measurements of TSS in three Zr–2.5Nb samples during quasistatic thermal cycling were carried out using the APUCOT (Automated Piezoelectric Ultrasonic Composite Oscillator Technique [4]) at 40 kHz. Two samples were cut from a commercial pressure tube and gaseously doped to hydrogen concentrations of 84 and 45 mg / g. The third sample was obtained from a pressure tube removed from a CANDU 2 nuclear reactor and doped to hydrogen content of 138 mg / g. Each sample was subjected to stepwise heating, followed by stepwise cooling. Both heating and cooling step sizes were 58C ranging over temperatures from 808C to 3808C. At each step, the sample temperature was held constant within 60.18C for 3 or more hours, but an identical hold time was used for a given sample. A low heating and cooling rate of 0.18C / min was applied for the transition between two successive temperature holds. The process of isothermal holds and stepwise heating and cooling at the rate of 0.18C / min is considered as a quasistatic thermal cycling. In addition, each sample was heated and then cooled continuously at 0.18C / min, followed by thermal cycles at 18C / min for multiple runs, being the same as regular tests. During heating and cooling as well as during isothermal holds, internal friction, Q 21 , and Young’s modulus, E, were, simultaneously, monitored as functions of temperature and hold time. The TSSD and TSSP temperatures for hydride dissolution and precipitation can be obtained by determining the knee point on the plot of E versus T during heating and cooling, respectively. Values of TSS determined during quasistatic thermal cycles are termed the quasistatic TSS to distinguish them from the regular TSS values determined at a continuous rate of 1 or 28C / min. Previous work [11] has shown that the increment of hydrogen concentration, CH , in solid solution at a constant temperature is proportional to the decrement of the Young’s modulus and a proportionality factor of 42 wtppm / GPa was determined in Zr–2.5Nb1H alloys. The CH as a function of hold time
2
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can be derived from experimental measurements of E as a function of hold time.
3. Results
3.1. Precipitation and dissolution peaks Fig. 1 shows typical experimental results of hydrogen concentration, CH , in solution as a function of isothermal hold time during quasistatic heating. The CH for the curves at 2798C and 3548C are almost unchanged. This indicates that no significant amounts of hydride are dissolving during the isothermal hold. For curves at 3048C, 3098C and 3148C, the CH tends to increase with hold time. It implies that some amounts of hydrides are being dissolved into solid solution during the isothermal hold, but the increment DCH of hydrogen in solution are various at the different temperatures. Fig. 2 shows a bar chart of DCH , derived from Fig. 1, for each isothermal hold. Using a commercial software package, PeakFit, a fitted curve of the heights of these bars versus the hold temperature is derived and also plotted in Fig. 2. The fitted curve is not an internal friction peak but it may assist us to clearly see the maximum slope point of the DCH versus T occurs at |3318C. In the curve of E versus T, Fig. 3, during the quasistatic heating process there is a knee point at 3318C representing the quasistatic TSSD temperature for this run. This tem-
Fig. 1. Hydrogen concentrations in solution determined as a function of isothermal hold time at various temperatures during heating in a Zr– 2.5Nb184 mg / g H sample.
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Fig. 2. Increments of hydrogen concentration in solution for identical isothermal holds of 3 h, obtained from Fig. 1, as a function of temperature; a curve has been fitted to the heights of the increments.
perature is coincident with the maximum slope point of the fitted curve DCH versus T in Fig. 2, indicated by an arrow, but not coincident with the peak temperature 3148C nor
Fig. 4. Increments of hydrogen concentration in solution for identical isothermal holds of 3 h as a function of temperature; a curve is fitted to the heights of the increments.
with the indistinct peak onset (23508C) of the curve DCH versus T. Similar experimental results during quasistatic cooling from the maximum temperature 3868C for the same Zr– 2.5Nb sample are shown in Fig. 4. A quasistatic TSSP temperature of 2838C was obtained from the knee point on a similar curve of E versus T, as indicated by the arrow on Fig. 4. Again, this TSSP temperature coincides with the maximum slope point on the curve of DCH versus T, but not with the peak temperature of 2758C, nor with the indistinct peak onset of |3008C. These experiments were repeated on the sample of Zr–2.5Nb145 mg / g H and on the irradiated sample of Zr–2.5Nb1138 mg / g H. Similar results were obtained and are presented in Table 1.
3.2. Effect of heating rate on TSS
Fig. 3. Curve of Young’s modulus versus temperature, showing how a knee point is identified which is used to determine the TSS temperature in a Zr–2.5Nb184 mg / g H sample.
The TSSD temperature at 18C / min in Table 1 was the averaged value with a standard deviation 60.58C from more than 10 thermal cycles. From Table 1 the quasistatic TSSD temperature is lower by 1 to 38C than that of TSSD at 18C / min, but this difference does not appear to be statistically significant. The TSSP in Zr–2.5Nb is more complex due to the memory effect of hydride precipitation. Previous studies show [4] that the TSSP temperature sensitively depends on the cooling rate and on the maximum temperature, T max, from which the cooling test starts. Therefore, TSSP1 and TSSP2 were defined as the TSSP obtained during cooling (at the same rate) from the highest and lowest T max , respectively. Two TSSP are presumed to
Z.L. Pan, M.P. Puls / Journal of Alloys and Compounds 310 (2000) 214 – 218
217
Table 1 Comparison between regular TSS and quasistatic TSS (8C) Samples
Zr–2.5Nb184 mg / g H
Zr–2.5Nb145 mg / g H
Zr–2.5Nb1138 mg / g H
TSSD at 18C / min TSSD at 0.18C / min Quasistatic TSSD TSSP1 at 18C / min TSSP2 at 18C / min Quasistatic TSSP
332 331 331 272 (T max 4308C) 290 (T max 3608C) 283 (T max 3868C)
279 278 277 219 (T max 4208C) 242 (T max 3108C) 238 (T max 3508C)
362 360 359 307 (T max 4508C) 328 (T max 3808C) 313 (T max 4028C)
be associated with nucleation and growth of hydride, respectively.
4. Discussion
4.1. Maximum slope point as TSS criterion Fig. 2 indicates that there appear to remain very small amounts of undissolved hydride in the specimen even at the temperature of 3508C. Strictly speaking, the onset point of the peak does not represent the final point for complete dissolution of all hydrides, even though it is much higher than the TSSD temperature of 3318C. The maximum amount of increase in dissolved hydride during each identical isothermal hold of 3 h occurs at the peak temperature of the fitted curve of DCH versus T. This is the temperature of the fastest dissolution of the hydrides, but it is not the end of the hydride dissolution process because significant amounts of hydrides still exist in the sample at the peak temperature. However, at the temperature with the maximum slope of the curve, the total amount of remained hydrides can be, approximately, estimated as producing a concentration of 6 mg / g from Fig. 2. The small amount of remaining hydrides is of the same order of magnitude as the measurement error (from 5% to 10% of total hydrogen) for hydrogen concentration obtained from the hot vacuum extraction technique. Furthermore, the dimensions of the remained hydrides at temperatures higher than the maximum slope point must be very small. It is, thus, practical, and sufficiently conservative, to take the maximum slope point as defining the end of hydride dissolution, i.e., the TSSD temperature. Analogous to the case of hydride dissolution, the peak temperature in Fig. 4 represents the fastest point of hydride precipitation during cooling, but the maximum slope point on this curve at the high temperature side is very close to the beginning of the precipitation process. At the maximum slope point of Fig. 4, the total amount of precipitated hydride may be estimated as a hydrogen content of 7 mg / g, moreover this amount is of the same order of magnitude as the error in the hydrogen analysis. Therefore, it is also reasonable to choose the maximum slope point as representing the beginning of hydride precipitation, i.e., the TSSP temperature.
4.2. Physical mechanism giving rise to hydride precipitation /dissolution peaks In previous work [7], internal friction and Young’s modulus as a function of temperature in a pure Zr sample containing 141 mg / g hydrogen were, simultaneously, measured using a pendulum at the rate of 28C / min and the frequency of 2.2 Hz, as shown in Fig. 5. An internal friction peak was observed during both heating and cooling and there is a knee point indicated by the arrow on both curves of F 2 versus T. Again, the knee points are not located at the peak temperatures nor the terminal points of the peaks, but are coincident with the maximum slope points of the internal friction curves on the high temperature side. It is widely accepted [12] that the internal friction due to phase transformation is proportional to the heating or cooling rate and the vibration period used to measure internal friction, and in turn, this is proportional to the amount of phase transformation per cycle. The peak temperature of Fig. 5 thus represents the fastest point of hydride precipitation or dissolution. In Fig. 5 the precipitation peak is sharper than the dissolution peak, similarly, the peak in Fig. 4 during cooling is also sharper than that peak in Fig. 2 during heating. Peaks of DCH versus T for Zr–2.5Nb in Figs. 2 and 4 are, respectively, equivalent to the two internal friction peaks in Fig. 5, observed in pure Zr. Unfortunately, the hydride precipitation and dissolution peaks in the Zr–2.5Nb containing a similar amount of hydrogen are depressed even at the lower frequency. The physical mechanism that causes this depression of the phase transformation peak in alloys of Zr–2.5Nb1H is not clear at present. It should be valuable that further studies on the difference in microstructure between pure Zr and Zr–2.5Nb could explain the presence or absence of the peak. Hydride dissolution or precipitation is a typical diffusion controlled phase transformation process. During this process, the hydrogen concentration, CH , in solution continuously varies with temperature or with isothermal hold time, as shown in Figs. 1, 2 and 4. Practically, it is not possible to find the exact temperature above which all hydrides would be completely dissolved during heating, or below which all hydrides would, suddenly, commence precipitation during cooling. The maximum slope point on curves of Q 21 versus T and DCH versus T, or the knee point on
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Fig. 5. Internal friction and frequency squared as a function of temperature determined during a thermal cycle at a rate of 28C / min for a pure Zr1141 mg / g H sample using a flexure pendulum at 2.2 Hz.
curves of E versus T, are the most unambiguously identifiable points close to the end of hydride dissolution, or close to the beginning of hydride precipitation. Therefore, these points represent the most feasible and physically reasonable choices to define the TSS temperature.
5. Conclusion 1. The maximum slope point of the precipitation or dissolution peak on curves of Q 21 versus T at the high temperature side is coincident with the knee point of E versus T. This point can be applied for establishing the solvus for hydrogen in Zr alloys. The physical principle forming the basis of the experimental criteria is consistent with that for other techniques. 2. The solubility of hydrogen in Zr–2.5Nb is not significantly different (but slightly higher) when determined using quasistatic heating compared to when determined using the standard heating approach.
Acknowledgements This study was funded by the CANDU Owners Group (COG) under Work Package 2-31-6580.
References [1] R. Dutton, K. Nuttall, M.P. Puls, L.A. Simpson, Metall. Trans. A. 8a (1977) 1553. [2] C.E. Coleman, J.F.R. Ambler, Scripta Metall. 17 (1983) 77. [3] K. Bungardt, H. Preisendanz, Z. Metallkd. 51 (1960) 280. [4] Z.L. Pan, L.G. Ritchie, M.P. Puls, J. Nucl. Mater. 228 (1996) 227–237. [5] I.G. Ritchie, K.W. Sprungmann, J. de Physique C9 (44) (1983) 313. [6] G.F. Slattery, J. Instit. Metals 95 (1967) 43. [7] I.G. Ritchie, Z.L. Pan, ASTM, STP 1169 (1992) 385–395. [8] D. Khatarnian, Z.L. Pan, M.P. Puls, C.D. Cann, J. Alloys Comp. 231 (1995) 488. [9] H. Numakura, T. Ito, M. Koiwa, J. Less-Comm. Met. 141 (1988) 285. [10] H. Numakura, M. Koiwa, Trans. of Japan Institute of Metals 26 (1985) 653. [11] Z.L. Pan, M.P. Puls, I.G. Ritchie, J. Alloys Comp. 211–212 (1994) 245. [12] J. van Humbeeck, J. de Physique C8 (6) (1996) C8–371.
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Precipitation and dissolution peaks of hydride in Zr–2.5Nb during quasistatic thermal cycles a, b Z.L. Pan *, M.P. Puls b
a Atomic Energy of Canada Ltd., CRL, Chalk River, ON Canada, K0 J 1 J0 Atomic Energy of Canada Ltd., Sheridan Park, Mississauga, ON Canada, L5 K 1 B2
Abstract Two internal friction peaks and corresponding discontinuity (‘knee’) points of elastic modulus have been observed in hydride-forming metals upon heating and cooling, respectively. In the present work, measurements of Young’s modulus as functions of temperature and hold time during a quasistatic thermal cycle were made in Zr–2.5Nb samples containing hydrogen using a composite oscillator technique. The increment of modulus during an isothermal hold is proportional to the decrease in hydrogen concentration in solid solution of the Zr alloy. As a result, elastic modulus measurements provide a means to determine the amount of transformed hydride during the transition. It is confirmed experimentally that the two peaks reflect the variation of the hydride transformation rate during heating or cooling. It is demonstrated by the present work that the maximum-slope point of each peak, on the high temperature side, is coincident with the knee point on the curve of modulus versus temperature and this point provides the most reliable and physically sensible indicator of the end of hydride dissolution during heating, or the beginning of hydride precipitation during cooling. 2000 Published by Elsevier Science S.A. Keywords: Internal friction; Elastic modulus; Zr alloys; Hydrogen solubility; Hydride delayed crack; Phase transformation
1. Introduction The presence of hydrogen and / or deuterium 1 in Zr alloys of nuclear reactor core components could result in local embrittlement when the terminal solid solubility (TSS), or solvus, of hydrogen is exceeded in regions of high tensile stress, such as at flaws. For nuclear engineering applications, an accurate knowledge of the TSS in Zr alloys is crucial to assess the potential for delayed hydride cracking (DHC) [1]. The TSS of hydrogen in Zr and its alloys has been determined by various techniques, such as diffusion, dilatometry, electric resistivity, DHC, differential scanning calorimetry (DSC), neutron diffraction, acoustic emission [2], internal friction [3] and dynamic elastic modulus (DEM) [4]. In some techniques, TSS is detected by a sharp discontinuity (‘knee’) point in curves
*Corresponding author. E-mail addresses: [email protected] (Z.L. Pan), [email protected] (M.P. Puls). 1 For simplicity, both hydrogen and deuterium are referred to as hydrogen in the following.
of elastic modulus versus temperature [4], auto-twisting strain versus temperature (by a pendulum) [5], expansion versus temperature [6] or electric resistivity versus temperature etc. In other techniques, TSS is detected by the maximum slope point in curves of internal friction versus temperature on the high temperature side [7] or differential heat flow versus temperature by DSC [8]. Obviously, some different results are obtained when using these different criteria for detecting the TSS. The question is, how are the knee point and the maximum-slope point interrelated? Whether the peak temperature of the internal friction curve might represent the TSS temperature? Numakura et al. [9] mentioned that ‘the curve of shear modulus vs. temperature shows a marked change at the peak temperature’. Unfortunately, the ‘marked change’ point obtained by [9] in Zr–H was not sufficiently sharp to show the relationship, but the authors’ other work on Ti–H [10] provided a sharp knee point, which was likely close to the maximum slope point, not at the peak, of the internal friction curve. To obtain accurate data of TSS, the consistency of the experimental criteria used to establish the hydrogen solvus by different techniques should be verified. Since the 1960s, the internal friction and dynamic elastic modulus techniques have been employed to study hydro-
0925-8388 / 00 / $ – see front matter 2000 Published by Elsevier Science S.A. PII: S0925-8388( 00 )01028-8
Z.L. Pan, M.P. Puls / Journal of Alloys and Compounds 310 (2000) 214 – 218
gen behavior and to establish the solvus in hydride-forming metals, particularly in Zr alloys [3–5,7]. In the present work, a composite oscillator technique is used to clarify the relationship between the maximum slope point and the knee point by determining the amount of hydride transformed during a quasistatic thermal cycle. The present work identifies that the temperature defined by the maximum slope point on internal friction curves is coincident with the knee point on the modulus curves and best represents the end of hydride dissolution during heating, or the beginning of hydride precipitation during cooling.
2. Experiments Measurements of TSS in three Zr–2.5Nb samples during quasistatic thermal cycling were carried out using the APUCOT (Automated Piezoelectric Ultrasonic Composite Oscillator Technique [4]) at 40 kHz. Two samples were cut from a commercial pressure tube and gaseously doped to hydrogen concentrations of 84 and 45 mg / g. The third sample was obtained from a pressure tube removed from a CANDU 2 nuclear reactor and doped to hydrogen content of 138 mg / g. Each sample was subjected to stepwise heating, followed by stepwise cooling. Both heating and cooling step sizes were 58C ranging over temperatures from 808C to 3808C. At each step, the sample temperature was held constant within 60.18C for 3 or more hours, but an identical hold time was used for a given sample. A low heating and cooling rate of 0.18C / min was applied for the transition between two successive temperature holds. The process of isothermal holds and stepwise heating and cooling at the rate of 0.18C / min is considered as a quasistatic thermal cycling. In addition, each sample was heated and then cooled continuously at 0.18C / min, followed by thermal cycles at 18C / min for multiple runs, being the same as regular tests. During heating and cooling as well as during isothermal holds, internal friction, Q 21 , and Young’s modulus, E, were, simultaneously, monitored as functions of temperature and hold time. The TSSD and TSSP temperatures for hydride dissolution and precipitation can be obtained by determining the knee point on the plot of E versus T during heating and cooling, respectively. Values of TSS determined during quasistatic thermal cycles are termed the quasistatic TSS to distinguish them from the regular TSS values determined at a continuous rate of 1 or 28C / min. Previous work [11] has shown that the increment of hydrogen concentration, CH , in solid solution at a constant temperature is proportional to the decrement of the Young’s modulus and a proportionality factor of 42 wtppm / GPa was determined in Zr–2.5Nb1H alloys. The CH as a function of hold time
2
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215
can be derived from experimental measurements of E as a function of hold time.
3. Results
3.1. Precipitation and dissolution peaks Fig. 1 shows typical experimental results of hydrogen concentration, CH , in solution as a function of isothermal hold time during quasistatic heating. The CH for the curves at 2798C and 3548C are almost unchanged. This indicates that no significant amounts of hydride are dissolving during the isothermal hold. For curves at 3048C, 3098C and 3148C, the CH tends to increase with hold time. It implies that some amounts of hydrides are being dissolved into solid solution during the isothermal hold, but the increment DCH of hydrogen in solution are various at the different temperatures. Fig. 2 shows a bar chart of DCH , derived from Fig. 1, for each isothermal hold. Using a commercial software package, PeakFit, a fitted curve of the heights of these bars versus the hold temperature is derived and also plotted in Fig. 2. The fitted curve is not an internal friction peak but it may assist us to clearly see the maximum slope point of the DCH versus T occurs at |3318C. In the curve of E versus T, Fig. 3, during the quasistatic heating process there is a knee point at 3318C representing the quasistatic TSSD temperature for this run. This tem-
Fig. 1. Hydrogen concentrations in solution determined as a function of isothermal hold time at various temperatures during heating in a Zr– 2.5Nb184 mg / g H sample.
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Fig. 2. Increments of hydrogen concentration in solution for identical isothermal holds of 3 h, obtained from Fig. 1, as a function of temperature; a curve has been fitted to the heights of the increments.
perature is coincident with the maximum slope point of the fitted curve DCH versus T in Fig. 2, indicated by an arrow, but not coincident with the peak temperature 3148C nor
Fig. 4. Increments of hydrogen concentration in solution for identical isothermal holds of 3 h as a function of temperature; a curve is fitted to the heights of the increments.
with the indistinct peak onset (23508C) of the curve DCH versus T. Similar experimental results during quasistatic cooling from the maximum temperature 3868C for the same Zr– 2.5Nb sample are shown in Fig. 4. A quasistatic TSSP temperature of 2838C was obtained from the knee point on a similar curve of E versus T, as indicated by the arrow on Fig. 4. Again, this TSSP temperature coincides with the maximum slope point on the curve of DCH versus T, but not with the peak temperature of 2758C, nor with the indistinct peak onset of |3008C. These experiments were repeated on the sample of Zr–2.5Nb145 mg / g H and on the irradiated sample of Zr–2.5Nb1138 mg / g H. Similar results were obtained and are presented in Table 1.
3.2. Effect of heating rate on TSS
Fig. 3. Curve of Young’s modulus versus temperature, showing how a knee point is identified which is used to determine the TSS temperature in a Zr–2.5Nb184 mg / g H sample.
The TSSD temperature at 18C / min in Table 1 was the averaged value with a standard deviation 60.58C from more than 10 thermal cycles. From Table 1 the quasistatic TSSD temperature is lower by 1 to 38C than that of TSSD at 18C / min, but this difference does not appear to be statistically significant. The TSSP in Zr–2.5Nb is more complex due to the memory effect of hydride precipitation. Previous studies show [4] that the TSSP temperature sensitively depends on the cooling rate and on the maximum temperature, T max, from which the cooling test starts. Therefore, TSSP1 and TSSP2 were defined as the TSSP obtained during cooling (at the same rate) from the highest and lowest T max , respectively. Two TSSP are presumed to
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217
Table 1 Comparison between regular TSS and quasistatic TSS (8C) Samples
Zr–2.5Nb184 mg / g H
Zr–2.5Nb145 mg / g H
Zr–2.5Nb1138 mg / g H
TSSD at 18C / min TSSD at 0.18C / min Quasistatic TSSD TSSP1 at 18C / min TSSP2 at 18C / min Quasistatic TSSP
332 331 331 272 (T max 4308C) 290 (T max 3608C) 283 (T max 3868C)
279 278 277 219 (T max 4208C) 242 (T max 3108C) 238 (T max 3508C)
362 360 359 307 (T max 4508C) 328 (T max 3808C) 313 (T max 4028C)
be associated with nucleation and growth of hydride, respectively.
4. Discussion
4.1. Maximum slope point as TSS criterion Fig. 2 indicates that there appear to remain very small amounts of undissolved hydride in the specimen even at the temperature of 3508C. Strictly speaking, the onset point of the peak does not represent the final point for complete dissolution of all hydrides, even though it is much higher than the TSSD temperature of 3318C. The maximum amount of increase in dissolved hydride during each identical isothermal hold of 3 h occurs at the peak temperature of the fitted curve of DCH versus T. This is the temperature of the fastest dissolution of the hydrides, but it is not the end of the hydride dissolution process because significant amounts of hydrides still exist in the sample at the peak temperature. However, at the temperature with the maximum slope of the curve, the total amount of remained hydrides can be, approximately, estimated as producing a concentration of 6 mg / g from Fig. 2. The small amount of remaining hydrides is of the same order of magnitude as the measurement error (from 5% to 10% of total hydrogen) for hydrogen concentration obtained from the hot vacuum extraction technique. Furthermore, the dimensions of the remained hydrides at temperatures higher than the maximum slope point must be very small. It is, thus, practical, and sufficiently conservative, to take the maximum slope point as defining the end of hydride dissolution, i.e., the TSSD temperature. Analogous to the case of hydride dissolution, the peak temperature in Fig. 4 represents the fastest point of hydride precipitation during cooling, but the maximum slope point on this curve at the high temperature side is very close to the beginning of the precipitation process. At the maximum slope point of Fig. 4, the total amount of precipitated hydride may be estimated as a hydrogen content of 7 mg / g, moreover this amount is of the same order of magnitude as the error in the hydrogen analysis. Therefore, it is also reasonable to choose the maximum slope point as representing the beginning of hydride precipitation, i.e., the TSSP temperature.
4.2. Physical mechanism giving rise to hydride precipitation /dissolution peaks In previous work [7], internal friction and Young’s modulus as a function of temperature in a pure Zr sample containing 141 mg / g hydrogen were, simultaneously, measured using a pendulum at the rate of 28C / min and the frequency of 2.2 Hz, as shown in Fig. 5. An internal friction peak was observed during both heating and cooling and there is a knee point indicated by the arrow on both curves of F 2 versus T. Again, the knee points are not located at the peak temperatures nor the terminal points of the peaks, but are coincident with the maximum slope points of the internal friction curves on the high temperature side. It is widely accepted [12] that the internal friction due to phase transformation is proportional to the heating or cooling rate and the vibration period used to measure internal friction, and in turn, this is proportional to the amount of phase transformation per cycle. The peak temperature of Fig. 5 thus represents the fastest point of hydride precipitation or dissolution. In Fig. 5 the precipitation peak is sharper than the dissolution peak, similarly, the peak in Fig. 4 during cooling is also sharper than that peak in Fig. 2 during heating. Peaks of DCH versus T for Zr–2.5Nb in Figs. 2 and 4 are, respectively, equivalent to the two internal friction peaks in Fig. 5, observed in pure Zr. Unfortunately, the hydride precipitation and dissolution peaks in the Zr–2.5Nb containing a similar amount of hydrogen are depressed even at the lower frequency. The physical mechanism that causes this depression of the phase transformation peak in alloys of Zr–2.5Nb1H is not clear at present. It should be valuable that further studies on the difference in microstructure between pure Zr and Zr–2.5Nb could explain the presence or absence of the peak. Hydride dissolution or precipitation is a typical diffusion controlled phase transformation process. During this process, the hydrogen concentration, CH , in solution continuously varies with temperature or with isothermal hold time, as shown in Figs. 1, 2 and 4. Practically, it is not possible to find the exact temperature above which all hydrides would be completely dissolved during heating, or below which all hydrides would, suddenly, commence precipitation during cooling. The maximum slope point on curves of Q 21 versus T and DCH versus T, or the knee point on
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Z.L. Pan, M.P. Puls / Journal of Alloys and Compounds 310 (2000) 214 – 218
Fig. 5. Internal friction and frequency squared as a function of temperature determined during a thermal cycle at a rate of 28C / min for a pure Zr1141 mg / g H sample using a flexure pendulum at 2.2 Hz.
curves of E versus T, are the most unambiguously identifiable points close to the end of hydride dissolution, or close to the beginning of hydride precipitation. Therefore, these points represent the most feasible and physically reasonable choices to define the TSS temperature.
5. Conclusion 1. The maximum slope point of the precipitation or dissolution peak on curves of Q 21 versus T at the high temperature side is coincident with the knee point of E versus T. This point can be applied for establishing the solvus for hydrogen in Zr alloys. The physical principle forming the basis of the experimental criteria is consistent with that for other techniques. 2. The solubility of hydrogen in Zr–2.5Nb is not significantly different (but slightly higher) when determined using quasistatic heating compared to when determined using the standard heating approach.
Acknowledgements This study was funded by the CANDU Owners Group (COG) under Work Package 2-31-6580.
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