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Local strain around hydrogen in amorphous Cu50Zr50 and Cu50Ti50
PII:
Acta mater. Vol. 47, No. 12, pp. 3331±3338, 1999 # 1999 Acta Metallurgica Inc. Published by Elsevier Science Ltd. All rights reserved. Printed in Great Britain S1359-6454(99)00224-4 1359-6454/99 $20.00 + 0.00
LOCAL STRAIN AROUND HYDROGEN IN AMORPHOUS Cu50Zr50 AND Cu50Ti50 H. MIZUBAYASHI{, M. SHIBASAKI{ and S. MURAYAMA Institute of Materials Science, University of Tsukuba, Tsukuba, Ibaraki 305-8573, Japan (Received 9 April 1999; accepted 12 July 1999) AbstractÐThe hydrogen-induced volume expansion, a change in the X-ray diraction ®rst peak due to hydrogen charging and the hydrogen Gorsky eects were measured for amorphous (a-) Cu50Zr50 and Cu50Ti50 and discussed together with the hydrogen Snoek peak reported. The hydrogen-induced volume expansion is similar between a-Cu50Zr50 and a-Cu50Ti50. In contrast, anisotropy of the elastic distortion around hydrogen appears to be much larger in a-Cu50Zr50 than in a-Cu50Ti50. It is surmised that the local atomic structures are more deformable in a-Cu50Zr50 than in a-Cu50Ti50. # 1999 Acta Metallurgica Inc. Published by Elsevier Science Ltd. All rights reserved. Keywords: Melt spinning; X-ray diraction (XRD); Metallic glasses; Internal friction; Hydrogen
1. INTRODUCTION
Amorphous (a-) alloys are potential materials for hydrogen storage because of the absence of disintegration during absorption±desorption cycles re¯ecting no phase separation in the hydrogenated state (see Refs [1, 2] and references therein). On the other hand, a-alloys containing hydrogen reveal an internal friction peak due to stress-induced ordering of hydrogen (the hydrogen Snoek peak, hereafter) [3±10]. The total relaxation strength, St,S, of the hydrogen Snoek peak in a-alloys can be as large as 0.1 because a large amount of hydrogen in solution can contribute to the relaxation, suggesting that aalloys containing hydrogen may be a candidate for a high damping material. For both the items, the local elastic distortion around hydrogen in amorphous alloys plays an important role. When the elastic distortion around hydrogen in amorphous alloys is explained by the strain ellipsoid with the principal values l1, l2 and l3, the hydrogen-induced volume expansion, DV/V, of an a-alloy can be related to the l tensor by DV=V vH =O CH tr l CH
1
where vH denotes the atomic volume of hydrogen, O the atomic volume of host metals and CH the hydrogen concentration. In a-alloys, vH, O and l denote their mean values. As shown in Table 1, vH found in various a-alloys [1, 11] is comparable with vH reported in crystalline metals [2, 12]. In contrast, no hydrogen Snoek peak is found in pure crystal-
line metals, indicating that the symmetry of the lattice strain around hydrogen in pure crystalline metals is the same as that of the host lattice. In other words, the host atomic structure in a-alloys is isotropic in statistical average but each local atomic structure and/or each local elastic distortion around hydrogen in a-alloys may be strongly anisotropic. This issue will be pursued for the late transition metal (LTM) and early transition metal (ETM) aalloys, a-Cu50Zr50 and a-Cu50Ti50, below. In experiments, the value of tr l or the atomic volume of hydrogen vH can be related to a change in the specimen length, DL/L, due to hydrogen charging by DL=L 1=3 vH =O CH 1=3 tr l CH 2 where DL=LW1 is assumed. When the elastic distortion around hydrogen in a-alloys is isotropic, the total relaxation strength, St,G, of the Gorsky eect due to the long range diusion of hydrogen may be given by St,G OE=9kB Tb tr l2 CH
where E denotes the Young's modulus, kB the Boltzmann factor, T temperature and b the number of interstitial sites per host atom [13]. Most interstitial sites for hydrogen in LTM±ETM a-alloys are tetrahedral sites [14] with b 3:7 [15]. When the elastic distortion around hydrogen in amorphous alloys is anisotropic, equation (3) may be rewritten as St,G OE=3kB Tb l21 l22 l23 CH :
{To whom all correspondence should be addressed. {Present address: Toshiba Ltd, Kawasaki, Kanagawa 210-0901, Japan.
3
4
Further, the hydrogen Snoek peak is also expected, where its total relaxation strength, St,S, may be
3331
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MIZUBAYASHI et al.: LOCAL STRAIN AROUND HYDROGEN Table 1. The atomic volume vH of hydrogen in amorphous alloys and crystalline metals
Alloy/metal
H/M
vH/10ÿ3 (nm3)
Reference
a-Cu50Zr50
0±0.15 0.15±0.30 0.30±0.52 0±0.12 0.12±0.30 0.30±0.67 0.67 0.19 0.78 1.40 0.91 1.39 1.72 0.20 0.02 (solution phase)
1.4 1.8 2.0 1.7 1.4 2.2 2.0 2.0 2.0 2.7 2.8 2.6 2.7 4.7 2.7 2.820.3
present
a-Cu50Ti50 a-Cu50Ti50 a-Ni64Zr36 a-Ni40Zr60 a-Ni33Zr67 a-Pd33Zr67 a-Re25Zr75 a-Fe24Zr76 a-Fe89Zr11 a-Pd82Si18 c-Ti, Zr, V, Nb, Ta, Ni, Pd
given by 2
2
St,S OE=9kB T l1 ÿ l2 l2 ÿ l3 l3 ÿ l1 2 CH,S
5
assuming the strain ellipsoid for the elastic distortion around hydrogen [13]. In equation (5), CH,S denotes the hydrogen concentration associated with the hydrogen Snoek peak, where CH,S RCH [6±9]. In the present paper, we measured changes in the specimen length, the Gorsky eects and the ®rst peak in the X-ray diraction due to hydrogen charging, and discussed together with the hydrogen Snoek peak reported. 2. EXPERIMENTAL PROCEDURES
Amorphous Cu50Zr50 and Cu50Ti50 tapes 20 mm thick and 1 mm wide were prepared by melt-spinning in a high-purity Ar gas atmosphere, and stored in a refrigerator. Specimens were cut from asquenched tapes, and mechanically polished in water to remove the surface layer. Hydrogen charging was made electrolytically in 0.1 N H2SO4 at room temperature (RT). The hydrogenated specimens were aged for a few days at RT to homogenize the hydrogen concentration in the specimens. The hydrogen concentration, CH ( H=M in at.%, hereafter), was determined from the hydrogen thermal desorption (see Ref. [9] for details). For a specimen subjected to measurements of the specimen length and the X-ray diraction (XRD), we placed two small markers on a specimen surface using the micro Vickers hardness test machine before hydrogen charging, where the gage length (the specimen length hereafter), L, between the markers was about 20 mm. We measured both the specimen length and the XRD or one of them before and after hydrogen charging, and then subjected the specimen to the hydrogen thermal desorption. The number of data points for the specimen length corresponds with that of the specimens used and so on for the XRD results. For the Gorsky measurements, we separ-
present [1] [1] [11] [1] [1] [1] [1] [1] [1] [2, 12]
ately prepared the hydrogenated specimens and subjected them to the hydrogen thermal desorption after the measurements. The specimen length was measured by an optical microscope with a micrometer stage in the micro Vickers hardness test machine, where a specimen on a glass substrate was fastened at its middle part by a polyimide ®lm avoiding constraint along the specimen length. The measurement accuracy in the optical microscope was 21 mm. Experimental errors for the length change, DL/L, due to hydrogen charging increase with increasing CH because a hydrogenated specimen showed undulation at higher CH. The y±2y scan X-ray diraction (XRD) was made using the Cu Ka radiation. For the XRD apparatus used for a-Cu50Zr50 specimens, the y±2y scan was separately calibrated. For the XRD apparatus used for a-Cu50Ti50 specimens, a specimen and silicon powder were simultaneously subjected to the y±2y scan and the re¯ections from the silicon powder were used as reference. The Gorsky eect was measured as follows. A hydrogenated specimen was clamped at one end to form a reed. The free end of the reed faced an electrode of a displacement meter. The gage length of a specimen was 6±7 mm for a-Cu50Zr50 specimens and about 20 mm for a-Cu50Ti50 specimens because the relaxation strength in a-Cu50Zr50 specimens was much higher than that in a-Cu50Ti50 specimens. The free end of a specimen was bent in the elastic range for a given duration (prestraining) and then the elastic after-eect after unloading was measured, where the specimen temperature was kept at a given temperature within 20:5 K (see Ref. [16] for details). 3. RESULTS AND DISCUSSION
3.1. a-Cu50Zr50 Figure 1 shows changes in the specimen length DL/L due to hydrogen charging observed in aCu50Zr50. In Fig. 1, the hydrogen concentration range for preferential occupation of the Zr4 sites is
MIZUBAYASHI et al.: LOCAL STRAIN AROUND HYDROGEN
3333
Fig. 1. An increase in the specimen length, DL/L, due to hydrogen charging observed in a-Cu50Zr50 is plotted against the hydrogen concentration, CH. The dot and dashed curve a is tentatively ®tted to the data points. See text for the dashed lines 1 and 2.
denoted by the dashed lines 0 and 1, and that for the Zr3Cu1(I) by the dashed lines 1 and 2, which are reported in Ref. [8]. The dot and dashed curve a is tentatively ®tted to the data points, where the increasing rate, d ln L=dCH , is slightly dierent for the hydrogen concentration ranges mentioned above. The atomic volume of hydrogen, vH, determined from the specimen-length data and equation (2) is compiled in Table 1, indicating that the value of vH found in a-Cu50Zr50 is slightly smaller than those reported for other LTM±ETM a-alloys. Figure 2 shows examples of the XRD ®rst peak of a-Cu50Zr50 observed before and after hydrogen charging. The mean atomic distances in a-Cu50Zr50 reported are aCu±Cu 0:254 nm, aCu±Zr 0:275 nm and aZr ±Zr 0:311 nm [17, 18]. As already mentioned, the predominant atomic structure in LTM± ETM a-alloys is the tetrahedron [14, 15], indicating that the representative atomic plane spacing is the perpendicular distance, d, from vertex to the base of the tetrahedron. Then after a rough calculation, the representative atomic plane spacing, D, found in the XRD for a-Cu50Zr50 may be given by D Z2Zr dZr ±Zr 2ZZr ZCu dCu±Zr Z2Cu dCu±Cu = Z2Zr 2ZZr ZCu Z2Cu
6
where ZZr denotes the atomic number of Zr, dCu±Zr 0:817aCu±Zr and so on. Using the values mentioned above, equation (6) gives 2yp 38:99 deg for the Cu Ka radiation, where 2yp denotes 2y at where the intensity of XRD shows a maximum. As will be mentioned below, the XRD ®rst peak observed for a-Cu50Zr50 specimens before hydrogen charging is found around 2yp 38:77 deg which shows good agreement with that estimated using equation (6). In the present work, we suppose that (the wavelength of the Cu Ka radiation)/
Fig. 2. Examples of the XRD ®rst peak of a-Cu50Zr50 observed before and after hydrogen charging.
(2 sin(yp)) monitors the representative atomic plane spacing D in a-Cu50Zr50. We further suppose that for the most part of the ®rst peak, the intensity of XRD, I(y), can be explained by a Gaussian curve I y I0 exp ÿ y ÿ yp =s2
7
re¯ecting that dZr±Zr, dCu±Zr and dCu±Cu are expected to show Gaussian distributions. In Fig. 2, assuming equation (7), dashed curves are ®tted to the XRD ®rst peaks observed before hydrogen charging, where the most part of the ®rst peak can be explained by a Gaussian curve except the higher angle part. For the XRD ®rst peaks observed before hydrogen charging, the mean values, 2yp 38:77 deg and s 3:4 deg, were found. As seen in Fig. 2, the most part of the XRD ®rst peaks observed after hydrogen charging show, in general, shift to lower angle as a whole with increasing CH. At higher CH, the width of the XRD peak (s) tended to increase with increasing CH beyond 30 at.% H, e.g. s 4:1 deg for CH 41:4 at:% H. From 2yp found before and after hydrogen charging and equation (6), we evaluated a change in D due to hydrogen charging, DD, where DD/D may be related to changes in dZr±Zr, dCu±Zr and dCu±Cu due to hydrogen charging, DdZr±Zr, DdCu±Zr and DdCu± Cu, by DD=D Z2Zr DdZr ±Zr 2ZZr ZCu DdCu±Zr Z2Cu DdCu±Cu = Z2Zr dZr±Zr 2ZZr ZCu dCu±Zr Z2Cu dCu±Cu :
8
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MIZUBAYASHI et al.: LOCAL STRAIN AROUND HYDROGEN
Fig. 3. An increase in the representative atomic spacing, DD/D, due to hydrogen charging observed in a-Cu50Zr50 is plotted against CH. The dashed curve b is tentatively ®tted to the data points. The dot and dashed curve a and the dashed lines 1 and 2 shown in Fig. 1 are also depicted.
Figure 3 shows the data for DD/D found in aCu50Zr50, where the dashed curve b is tentatively ®tted to the data points and the dot and dashed line a assumed for the specimen-length data in Fig. 1 is also depicted. In a-Cu50Zr50, DD/D is, in general, larger than DL/L in the present hydrogen concentration range. After a rough approximation, equation (2) for DL/L may be rewritten as DL=L DaZr ±Zr 2DaCu±Zr DaCu±Cu = aZr ±Zr 2aCu±Zr aCu±Cu DdZr ±Zr 2DdCu±Zr DdCu±Cu = dZr ±Zr 2dCu±Zr dCu±Cu :
9
When the hydrogen induced expansion is the same among (Da/a)Zr±Zr, (Da/a)Cu±Zr and (Da/a)Cu±Cu at a given CH, DD=D DL=L is expected. On the other hand, a preferential increase in the atomic spacing for atoms and/or a preferential occupation of interstices with high hydrogen anity is reported in various LTM±ETM a-alloys [19±23]. For the case of Da=aZr ±Zr r Da=aCu±Zr r Da=aCu±Cu r0, the relationship of DD=D > DL=L is expected because of ZZr > ZCu and the ratio, (DD/D)/(DL/L), shows its maximum value of about 1.3 for the case of Da=aZr ±Zr > 0, Da=aCu±Zr 0 and Da=aCu±Cu 0, where equations (8) and (9) with the values, aCu±Cu 0:254 nm, aCu±Zr 0:275 nm, aZr ±Zr 0:311 nm, ZCu 29 and ZZr 40 are assumed. However, (DD/D)/(DL/L) of about 1.3 is, in general, much lower than that found in Fig. 3, suggesting that (Da/a)Cu±Zr and/or (Da/a)Cu±Cu are negative. We suppose that in the hydrogen concentration range below 15 at.% H, hydrogen atoms preferentially occupy the Zr4 sites where aZr±Zr shows expansion and copper atoms around the occupied Zr4 sites relax towards the center of the
Fig. 4. Examples of the elastic after-eects due to the hydrogen Gorsky eect observed in a-Cu50Zr50. Holding time for prestraining is also shown in the ®gure.
occupied sites, giving a decrease in aCu±Zr and/or aCu±Cu. We surmise that the similar topological relaxation takes place for the Zr3Cu1(I) sites and the Zr3Cu1(II) sites [8] for the hydrogen concentration range above 15 at.% H. In other words, in the strain ellipsoid model supposed for equations (1)±(5), the XRD and specimen length data indicate that l1 is positive but l2 and/or l3 are negative. When this is the case, the relaxation strength St,G of the hydrogen Gorsky eect in a-Cu50Zr50 is expected to be much larger than that calculated from equation (3) and the specimen length data. Figure 4 shows examples of the elastic aftereects due to the hydrogen Gorsky eects which were observed in a-Cu50Zr50. For bending of a thintape specimen, the elastic after-eect strain, e(t), due to the hydrogen Gorsky eects may be given by e t=e0 0:81StG exp ÿt=tG 1=32 exp ÿ32 t=tG 1=52 exp ÿ52 t=tG . . .
10
where e0 denotes prestrain. The relaxation time, tG, is given by tG d=p2 =MG
11
where d denotes the thickness of a specimen and MG, the diusion coecient for long range diusion of hydrogen. MG in a-Cu50Zr50 may be given by MG w2 =a n0 exp ÿHG =kB T
12
where w denotes jump length, a a geometrical factor, n0 the attempt frequency and HG the activation enthalpy for long range diusion. For the hydrogen
MIZUBAYASHI et al.: LOCAL STRAIN AROUND HYDROGEN
Fig. 5. Relaxation strength of the hydrogen Gorsky eect observed in a-Cu50Zr50 (the symbols Q) and that calculated from the specimen length data shown in Fig. 1 using equation (3) (the dot and dashed curve c). Relaxation strength of the hydrogen Snoek peak reported in Ref. [8] is also shown. See text for details.
Snoek peak in a-Cu50Zr50, n0 9 1016 =s and the activation enthalpy for the predominant constituent peak, e.g. HS,1 0:80 eV for CH 5 at:% H, have been reported [8]. The very high value found for n0 suggests that the constitutional entropy factor in n0 is considerably high for hydrogen diusion in aCu50Zr50. In Fig. 4, tG found for the specimen 21 mm thick with CH 3:5 at:% H is about 3:6 104 s at 352 K. Application of equations (11) and (12) to the above quantities with assumption of w aZr ±Zr , n0 9 1016 =s and HG 0:80 eV gives a geometrical factor a of about 25, which may be not unreasonable in a rule of thumb estimation. Figure 5 shows the relaxation strength St,G of the hydrogen Gorsky eect observed in a-Cu50Zr50 and the curve c which is calculated from the specimen length data shown in Fig. 1 using equation (3) expected for isotropic strain tensor l1 l2 l3 . In Fig. 5, the relaxation strength St,S of the hydrogen Snoek peak reported is also depicted, where the dashed curves I±III are ®tted to the data points of St,S for the Zr4, Zr3Cu1(I) and Zr3Cu1(II) sites, respectively [8]. As seen in Fig. 5, St,G observed is much higher than that calculated assuming isotropic strain tensor l1 l2 l3 , indicating again that l1 is positive but l2 and/or l3 are negative, where St,G may be explained by equation (4) instead of equation (3). Although the number of data points for St,G is limited, the dependence of St,G on CH appears to be similar to that of the relaxation strength St,S of the hydrogen Snoek peak. These results will be mentioned together with the corresponding results for a-Cu50Ti50 later. 3.2. a-Cu50Ti50 Figure 6 shows changes in the specimen length DL/L due to hydrogen charging observed in a-
3335
Fig. 6. An increase in DL/L due to hydrogen charging observed in a-Cu50Ti50 is plotted against CH. The dot and dashed curve A is tentatively ®tted to the data points. See text for the dashed lines 1 and 2.
Cu50Ti50, where the hydrogen concentration range for the Ti4 sites is denoted by the dashed lines 0 and 1, and that for the Ti3Cu1(I) by the dashed lines 1 and 2, which are reported in Ref. [7]. The dot and dashed curve A is tentatively ®tted to the data points, where the increasing rate d ln L=dCH is slightly dierent among the hydrogen concentration ranges mentioned above. The atomic volume of hydrogen vH determined from the specimen length data and equation (2) is compiled in Table 1. The value of vH found for the hydrogen concentration range between 30 and 67 at.% H shows good agreement with that reported for the comparable hydrogen concentration range in a-Cu50Ti50 [1]. Figure 7 shows examples of the XRD ®rst peak of a-Cu50Ti50 observed before and after hydrogen charging. The weak peak at 2y 44:76 deg and the strong peak at 2y 47:35 deg are the Al(200) re¯ection from an aluminum frame used for the XRD and the Si(220) re¯ection from silicon powders used as reference. In Fig. 7, silicon powders were added for the XRD measurements of the specimens used for 27.4, 49.0 and 73.6 at.% H but not for the specimens used for 3.3 and 13.8 at.% H. The mean atomic distances in a-Cu50Ti50 reported are aCu±Cu 0:245 nm, aCu±Ti 0:275 nm and aTi±Ti 0:300 nm after Ref. [24] or aCu±Cu 0:25 nm, aCu±Ti 0:27 nm and aTi±Ti 0:29 nm after Ref. [23]. For the Cu Ka radiation, equation (6) and the values mentioned above gives 2yp 41:17 deg after Ref. [24] or 2yp 41:55 deg after Ref. [23]. Fitting to the XRD ®rst peak observed before hydrogen charging using equation (7) gives 2yp 41:56 deg and s 2:8 deg, i.e. 2yp observed shows good agreement with the corresponding values mentioned above. Most of the XRD ®rst peak can be explained by a Gaussian function, however, deviations of the observed XRD peak from a Gaussian
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MIZUBAYASHI et al.: LOCAL STRAIN AROUND HYDROGEN
Fig. 8. An increase in DD/D due to hydrogen charging observed in a-Cu50Ti50 is plotted against CH. The dashed curve B is tentatively ®tted to the data points. The dot and dashed curve A and the dashed lines 1 and 2 shown in Fig. 6 are also depicted.
Fig. 7. Examples of the XRD ®rst peak of a-Cu50Ti50 observed before and after hydrogen charging.
function at the lower and higher angle parts are slightly larger in a-Cu50Ti50 than in a-Cu50Zr50. In a-Cu50Ti50, most of the XRD ®rst peaks observed after hydrogen charging show monotonous shift towards lower angle with increasing CH, where s remains almost unchanged for CH below about 30 at.% H and tends to increase for higher CH, e.g. s 3:5 deg for CH 73:6 at:% H. Further, the remaining higher angle part tends to remain unchanged for CH below about 50 at.% H and to shift towards higher angle for CH above about 50 at.% H (see the data for 73.6 at.% H in Fig. 7). The latter observation has been reported for aCu50Ti50 with 77 at.% H [22]. Figure 8 shows the data for DD/D found in aCu50Ti50, which are estimated for the most part of the XRD ®rst peak using equations (7) and (8). In Fig. 8, the dashed curve B is tentatively ®tted to the data points and the dot and dashed line A assumed for the specimen length data in Fig. 6 is also depicted. In a-Cu50Ti50, DD/D is, in general, slightly larger than DL/L for CH below about 50 at.% H and slightly smaller than DL/L for higher CH. In hydrogenated a-Cu50Ti50, a preferential occupation of the Ti4 sites for CH below about 30 at.% H [23] and a preferential increase in aTi±Ti for CH of 77 at.% H [22] are suggested. For the case of Da=aTi±Ti r Da=aCu±Ti r Da=aCu±Cu r0, the relationship of DD=D
Da=aCu±Ti 0 and of Da=aTi±Ti > 0, Da=aCu±Cu 0, where equations (8) and (9) with aCu±Cu, aCu±Ti and aTi±Ti after Ref. [23] or Ref. [24], ZTi 22 and ZCu 29 are assumed. In Fig. 8, DD=D= DL=L of 1±0.8 is found for the hydrogen concentration range beyond 50 at.% H where hydrogen atoms occupy the Ti3Cu1(II) sites [7, 8], suggesting that Da=aTi±Ti r Da=aCu±Ti r Da=aCu±Cu r0 for this CH range. On the other hand, for CH below 50 at.% H, DD/D observed is, in general, slightly larger than DL/L, suggesting that (Da/a)Cu±Ti and/ or (Da/a)Cu±Cu are slightly larger than (Da/a)Ti±Ti. In other words, in the strain ellipsoid model supposed for equations (1)±(5), the dierence among l1, l2 and l3 is not so large, suggesting that the relaxation strength St,G of the hydrogen Gorsky eect in a-Cu50Ti50 is expected to be similar to that calculated from equation (3) and the specimen length data. Figure 9 shows examples of the elastic aftereects due to the hydrogen Gorsky eects observed in a-Cu50Ti50. It is noted that the relaxation
Fig. 9. Examples of the elastic after-eects due to the hydrogen Gorsky eect observed in a-Cu50Ti50. Holding time for prestraining is also shown in the ®gure.
MIZUBAYASHI et al.: LOCAL STRAIN AROUND HYDROGEN
3337
Fig. 11. Redrawing of the curves a (Fig. 1), b (Fig. 3), A (Fig. 6) and B (Fig. 8).
Fig. 10. (a) Relaxation strength of the hydrogen Gorsky eect observed in a-Cu50Ti50 (the symbols q) and that calculated from the specimen length data shown in Fig. 6 using equation (3) (the dot and dashed curve C). (b) Relaxation strength of the hydrogen Snoek peak reported in Ref. [7] is also shown. See text for details.
strength St,G found in a-Cu50Ti50 is about one tenth of St,G observed in a-Cu50Zr50 (see Fig. 4). See Refs [16, 25] for the diusion coecient MG and the activation enthalpy HG in a-Cu50Ti50. Figure 10(a) shows the relaxation strength St,G of the hydrogen Gorsky eect observed in a-Cu50Ti50 [16, 25] and the curve C which is calculated from the specimen length data shown in Fig. 6 using equation (3) expected for isotropic strain tensor l1 l2 l3 . Except for the data found for CH below 1 at.% H [25], the observed data for St,G show good agreement with the curve C, indicating again that the dierence among l1, l2 and l3 is not so large. Figure 10(b) is the dependence of the relaxation strength St,S of the hydrogen Snoek peak on CH observed in a-Cu50Ti50 of various specimen conditions which is redrawn from Fig. 4 reported in Ref. [7]. In the as-quenched state, St,S found in aCu50Ti50 is about one half of that in a-Cu50Zr50 (see Fig. 5), presumably suggesting that the dierence among l1, l2 and l3 in a-Cu50Ti50 is smaller than that in a-Cu50Zr50. In Fig. 11, we compare the specimen length and XRD data found in a-Cu50Zr50 and a-Cu50Ti50, where the tentatively ®tted curves a, b, A and B are depicted. Between a-Cu50Zr50 and a-Cu50Ti50, although the dependence of DL/L on CH is similar to one another, DD/D shows the dierent dependence on CH. On the other hand, it is reported that an amount of decrease in the speci®c volume, DV=V Cry: 0:9%, found after the crystallization of a-Cu50Ti50 [26] is smaller than DV=V Cry:
2:3% found in a-Cu50Zr50 [27]. We surmise that the local atomic structures are more deformable in aCu50Zr50 than in a-Cu50Ti50, resulting in the stronger anisotropy of the hydrogen induced elastic strain in a-Cu50Zr50. To clarify this issue, further work is in progress. 4. CONCLUSION
The hydrogen-induced volume expansion is similar between a-Cu50Zr50 and a-Cu50Ti50. In contrast, anisotropy of the elastic distortion around hydrogen appears to be much larger in a-Cu50Zr50 than in aCu50Ti50. From the combination of the present results with the amounts of decreases in the speci®c volume reported in a-Cu50Zr50 and a-Cu50Ti50, we surmise that the local atomic structures are more deformable in a-Cu50Zr50 than in a-Cu50Ti50. AcknowledgementsÐThe authors would like to thank H. Tanimoto and S. Masuda for their invaluable help on the course of experiments. This work is partly supported by a Grant in Aid for Scienti®c Research from the Ministry of Education, Science, Culture and Sports of Japan, a program of Research for the Future of Japan Society of Promotion of Science, and the University of Tsukuba Research Project.
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6. Mizubayashi, H., Katoh, Y. and Okuda, S., Physica status solidi (a), 1987, 106, 469. 7. Mizubayashi, H., Agari, H. and Okuda, S., Physica status solidi (a), 1990, 122, 221. 8. Mizubayashi, H., Naruse, T. and Okuda, S., Physica status solidi (a), 1992, 132, 79. 9. Matsumoto, M., Mizubayashi, H. and Okuda, S., Acta metall. mater., 1995, 43, 1109. 10. Winter, F., Adam, S. and Sinning, H. R., J. Physique (Paris) IV, 1996, 6(C8), 55. 11. Berry, B. S. and Pritchet, W. C., Mater. Sci. Engng, 1988, 97, 419. 12. Peisl, H., in Topics in Applied Physics Vol. 28; Hydrogen in Metals, ed. G. Alefeld and J. VoÈlkl. Springer-Verlag, Berlin, 1978, p. 53. 13. Nowick, A. S. and Berry, B. S., in Anelastic Relaxation in Crystalline Solids. Academic Press, New York, 1972, p. 301. 14. Harris, J. H., Curtin, W. A. and Tenhover, M. A., Phys. Rev. B, 1987, 36, 5784. 15. Ninomiya, T., in The Structure of Non-Crystalline Materials, ed. P. H. Gaskell, J. M. Parken and E. A. Davis. Taylor & Francis, London, 1982, p. 558. 16. Mizubayashi, H., Odai, S. and Okuda, S., Acta metall. mater., 1994, 42, 561.
17. Waseda, Y., Masumoto, T. and Tamaki, S., Proc. 3rd Int. Conf. on Liquid Metals, Bristol, 1976, Conf. Ser. No. 30. The Inst. Phys., London, 1977, p. 268. 18. Kudo, T., Mizoguchi, T., Watanabe, N., Niimura, N., Misawa, M. and Suzuki, K., J. Phys. Soc. Japan, 1978, 45, 1773. 19. Kai, K., Ikeda, S., Fukunaga, T., Watanabe, N. and Suzuki, K., Physica, 1983, 120B, 342. 20. Suzuki, K., Hayashi, N., Tomizuka, Y., Fukunaga, T., Kai, K. and Watanabe, N., J. Non-Cryst. Solids, 1984, 61/62, 637. 21. Bowman Jr, R. C., Maeland, A. J. and Rhim, W.-K., Phys. Rev. B, 1982, 26, 6362. 22. Grzeta, B., Dini, K., Cowlam, N. and Davies, H. A., J. Phys. F: Met. Phys., 1985, 15, 2069. 23. Rodmacq, B., Mangin, Ph. and Chamberod, A., J. Phys. F: Met. Phys., 1985, 15, 2259. 24. Fukunaga, T., Kai, K., Nakata, M., Watanabe, N. and Suzuki, K., in Proc. 4th Int. Conf. on Rapidly Quenched Metals, 1, ed. T. Masumoto and K. Suzuki. Japan Institute of Metals, Sendai, 1982, p. 347. 25. Mizubayashi, H. and Ishii, T., J. Physique (Paris) IV, 1996, 6(C8), 659. 26. Mizubayashi, H., Hoshina, S. and Okuda, S., J. NonCryst. Solids, 1990, 117/118, 203. 27. Mizubayashi, H., Kaida, M., Otsuka, S. and Okuda, S., Acta metall. mater., 1994, 42, 2099.
Acta mater. Vol. 47, No. 12, pp. 3331±3338, 1999 # 1999 Acta Metallurgica Inc. Published by Elsevier Science Ltd. All rights reserved. Printed in Great Britain S1359-6454(99)00224-4 1359-6454/99 $20.00 + 0.00
LOCAL STRAIN AROUND HYDROGEN IN AMORPHOUS Cu50Zr50 AND Cu50Ti50 H. MIZUBAYASHI{, M. SHIBASAKI{ and S. MURAYAMA Institute of Materials Science, University of Tsukuba, Tsukuba, Ibaraki 305-8573, Japan (Received 9 April 1999; accepted 12 July 1999) AbstractÐThe hydrogen-induced volume expansion, a change in the X-ray diraction ®rst peak due to hydrogen charging and the hydrogen Gorsky eects were measured for amorphous (a-) Cu50Zr50 and Cu50Ti50 and discussed together with the hydrogen Snoek peak reported. The hydrogen-induced volume expansion is similar between a-Cu50Zr50 and a-Cu50Ti50. In contrast, anisotropy of the elastic distortion around hydrogen appears to be much larger in a-Cu50Zr50 than in a-Cu50Ti50. It is surmised that the local atomic structures are more deformable in a-Cu50Zr50 than in a-Cu50Ti50. # 1999 Acta Metallurgica Inc. Published by Elsevier Science Ltd. All rights reserved. Keywords: Melt spinning; X-ray diraction (XRD); Metallic glasses; Internal friction; Hydrogen
1. INTRODUCTION
Amorphous (a-) alloys are potential materials for hydrogen storage because of the absence of disintegration during absorption±desorption cycles re¯ecting no phase separation in the hydrogenated state (see Refs [1, 2] and references therein). On the other hand, a-alloys containing hydrogen reveal an internal friction peak due to stress-induced ordering of hydrogen (the hydrogen Snoek peak, hereafter) [3±10]. The total relaxation strength, St,S, of the hydrogen Snoek peak in a-alloys can be as large as 0.1 because a large amount of hydrogen in solution can contribute to the relaxation, suggesting that aalloys containing hydrogen may be a candidate for a high damping material. For both the items, the local elastic distortion around hydrogen in amorphous alloys plays an important role. When the elastic distortion around hydrogen in amorphous alloys is explained by the strain ellipsoid with the principal values l1, l2 and l3, the hydrogen-induced volume expansion, DV/V, of an a-alloy can be related to the l tensor by DV=V vH =O CH tr l CH
1
where vH denotes the atomic volume of hydrogen, O the atomic volume of host metals and CH the hydrogen concentration. In a-alloys, vH, O and l denote their mean values. As shown in Table 1, vH found in various a-alloys [1, 11] is comparable with vH reported in crystalline metals [2, 12]. In contrast, no hydrogen Snoek peak is found in pure crystal-
line metals, indicating that the symmetry of the lattice strain around hydrogen in pure crystalline metals is the same as that of the host lattice. In other words, the host atomic structure in a-alloys is isotropic in statistical average but each local atomic structure and/or each local elastic distortion around hydrogen in a-alloys may be strongly anisotropic. This issue will be pursued for the late transition metal (LTM) and early transition metal (ETM) aalloys, a-Cu50Zr50 and a-Cu50Ti50, below. In experiments, the value of tr l or the atomic volume of hydrogen vH can be related to a change in the specimen length, DL/L, due to hydrogen charging by DL=L 1=3 vH =O CH 1=3 tr l CH 2 where DL=LW1 is assumed. When the elastic distortion around hydrogen in a-alloys is isotropic, the total relaxation strength, St,G, of the Gorsky eect due to the long range diusion of hydrogen may be given by St,G OE=9kB Tb tr l2 CH
where E denotes the Young's modulus, kB the Boltzmann factor, T temperature and b the number of interstitial sites per host atom [13]. Most interstitial sites for hydrogen in LTM±ETM a-alloys are tetrahedral sites [14] with b 3:7 [15]. When the elastic distortion around hydrogen in amorphous alloys is anisotropic, equation (3) may be rewritten as St,G OE=3kB Tb l21 l22 l23 CH :
{To whom all correspondence should be addressed. {Present address: Toshiba Ltd, Kawasaki, Kanagawa 210-0901, Japan.
3
4
Further, the hydrogen Snoek peak is also expected, where its total relaxation strength, St,S, may be
3331
3332
MIZUBAYASHI et al.: LOCAL STRAIN AROUND HYDROGEN Table 1. The atomic volume vH of hydrogen in amorphous alloys and crystalline metals
Alloy/metal
H/M
vH/10ÿ3 (nm3)
Reference
a-Cu50Zr50
0±0.15 0.15±0.30 0.30±0.52 0±0.12 0.12±0.30 0.30±0.67 0.67 0.19 0.78 1.40 0.91 1.39 1.72 0.20 0.02 (solution phase)
1.4 1.8 2.0 1.7 1.4 2.2 2.0 2.0 2.0 2.7 2.8 2.6 2.7 4.7 2.7 2.820.3
present
a-Cu50Ti50 a-Cu50Ti50 a-Ni64Zr36 a-Ni40Zr60 a-Ni33Zr67 a-Pd33Zr67 a-Re25Zr75 a-Fe24Zr76 a-Fe89Zr11 a-Pd82Si18 c-Ti, Zr, V, Nb, Ta, Ni, Pd
given by 2
2
St,S OE=9kB T l1 ÿ l2 l2 ÿ l3 l3 ÿ l1 2 CH,S
5
assuming the strain ellipsoid for the elastic distortion around hydrogen [13]. In equation (5), CH,S denotes the hydrogen concentration associated with the hydrogen Snoek peak, where CH,S RCH [6±9]. In the present paper, we measured changes in the specimen length, the Gorsky eects and the ®rst peak in the X-ray diraction due to hydrogen charging, and discussed together with the hydrogen Snoek peak reported. 2. EXPERIMENTAL PROCEDURES
Amorphous Cu50Zr50 and Cu50Ti50 tapes 20 mm thick and 1 mm wide were prepared by melt-spinning in a high-purity Ar gas atmosphere, and stored in a refrigerator. Specimens were cut from asquenched tapes, and mechanically polished in water to remove the surface layer. Hydrogen charging was made electrolytically in 0.1 N H2SO4 at room temperature (RT). The hydrogenated specimens were aged for a few days at RT to homogenize the hydrogen concentration in the specimens. The hydrogen concentration, CH ( H=M in at.%, hereafter), was determined from the hydrogen thermal desorption (see Ref. [9] for details). For a specimen subjected to measurements of the specimen length and the X-ray diraction (XRD), we placed two small markers on a specimen surface using the micro Vickers hardness test machine before hydrogen charging, where the gage length (the specimen length hereafter), L, between the markers was about 20 mm. We measured both the specimen length and the XRD or one of them before and after hydrogen charging, and then subjected the specimen to the hydrogen thermal desorption. The number of data points for the specimen length corresponds with that of the specimens used and so on for the XRD results. For the Gorsky measurements, we separ-
present [1] [1] [11] [1] [1] [1] [1] [1] [1] [2, 12]
ately prepared the hydrogenated specimens and subjected them to the hydrogen thermal desorption after the measurements. The specimen length was measured by an optical microscope with a micrometer stage in the micro Vickers hardness test machine, where a specimen on a glass substrate was fastened at its middle part by a polyimide ®lm avoiding constraint along the specimen length. The measurement accuracy in the optical microscope was 21 mm. Experimental errors for the length change, DL/L, due to hydrogen charging increase with increasing CH because a hydrogenated specimen showed undulation at higher CH. The y±2y scan X-ray diraction (XRD) was made using the Cu Ka radiation. For the XRD apparatus used for a-Cu50Zr50 specimens, the y±2y scan was separately calibrated. For the XRD apparatus used for a-Cu50Ti50 specimens, a specimen and silicon powder were simultaneously subjected to the y±2y scan and the re¯ections from the silicon powder were used as reference. The Gorsky eect was measured as follows. A hydrogenated specimen was clamped at one end to form a reed. The free end of the reed faced an electrode of a displacement meter. The gage length of a specimen was 6±7 mm for a-Cu50Zr50 specimens and about 20 mm for a-Cu50Ti50 specimens because the relaxation strength in a-Cu50Zr50 specimens was much higher than that in a-Cu50Ti50 specimens. The free end of a specimen was bent in the elastic range for a given duration (prestraining) and then the elastic after-eect after unloading was measured, where the specimen temperature was kept at a given temperature within 20:5 K (see Ref. [16] for details). 3. RESULTS AND DISCUSSION
3.1. a-Cu50Zr50 Figure 1 shows changes in the specimen length DL/L due to hydrogen charging observed in aCu50Zr50. In Fig. 1, the hydrogen concentration range for preferential occupation of the Zr4 sites is
MIZUBAYASHI et al.: LOCAL STRAIN AROUND HYDROGEN
3333
Fig. 1. An increase in the specimen length, DL/L, due to hydrogen charging observed in a-Cu50Zr50 is plotted against the hydrogen concentration, CH. The dot and dashed curve a is tentatively ®tted to the data points. See text for the dashed lines 1 and 2.
denoted by the dashed lines 0 and 1, and that for the Zr3Cu1(I) by the dashed lines 1 and 2, which are reported in Ref. [8]. The dot and dashed curve a is tentatively ®tted to the data points, where the increasing rate, d ln L=dCH , is slightly dierent for the hydrogen concentration ranges mentioned above. The atomic volume of hydrogen, vH, determined from the specimen-length data and equation (2) is compiled in Table 1, indicating that the value of vH found in a-Cu50Zr50 is slightly smaller than those reported for other LTM±ETM a-alloys. Figure 2 shows examples of the XRD ®rst peak of a-Cu50Zr50 observed before and after hydrogen charging. The mean atomic distances in a-Cu50Zr50 reported are aCu±Cu 0:254 nm, aCu±Zr 0:275 nm and aZr ±Zr 0:311 nm [17, 18]. As already mentioned, the predominant atomic structure in LTM± ETM a-alloys is the tetrahedron [14, 15], indicating that the representative atomic plane spacing is the perpendicular distance, d, from vertex to the base of the tetrahedron. Then after a rough calculation, the representative atomic plane spacing, D, found in the XRD for a-Cu50Zr50 may be given by D Z2Zr dZr ±Zr 2ZZr ZCu dCu±Zr Z2Cu dCu±Cu = Z2Zr 2ZZr ZCu Z2Cu
6
where ZZr denotes the atomic number of Zr, dCu±Zr 0:817aCu±Zr and so on. Using the values mentioned above, equation (6) gives 2yp 38:99 deg for the Cu Ka radiation, where 2yp denotes 2y at where the intensity of XRD shows a maximum. As will be mentioned below, the XRD ®rst peak observed for a-Cu50Zr50 specimens before hydrogen charging is found around 2yp 38:77 deg which shows good agreement with that estimated using equation (6). In the present work, we suppose that (the wavelength of the Cu Ka radiation)/
Fig. 2. Examples of the XRD ®rst peak of a-Cu50Zr50 observed before and after hydrogen charging.
(2 sin(yp)) monitors the representative atomic plane spacing D in a-Cu50Zr50. We further suppose that for the most part of the ®rst peak, the intensity of XRD, I(y), can be explained by a Gaussian curve I y I0 exp ÿ y ÿ yp =s2
7
re¯ecting that dZr±Zr, dCu±Zr and dCu±Cu are expected to show Gaussian distributions. In Fig. 2, assuming equation (7), dashed curves are ®tted to the XRD ®rst peaks observed before hydrogen charging, where the most part of the ®rst peak can be explained by a Gaussian curve except the higher angle part. For the XRD ®rst peaks observed before hydrogen charging, the mean values, 2yp 38:77 deg and s 3:4 deg, were found. As seen in Fig. 2, the most part of the XRD ®rst peaks observed after hydrogen charging show, in general, shift to lower angle as a whole with increasing CH. At higher CH, the width of the XRD peak (s) tended to increase with increasing CH beyond 30 at.% H, e.g. s 4:1 deg for CH 41:4 at:% H. From 2yp found before and after hydrogen charging and equation (6), we evaluated a change in D due to hydrogen charging, DD, where DD/D may be related to changes in dZr±Zr, dCu±Zr and dCu±Cu due to hydrogen charging, DdZr±Zr, DdCu±Zr and DdCu± Cu, by DD=D Z2Zr DdZr ±Zr 2ZZr ZCu DdCu±Zr Z2Cu DdCu±Cu = Z2Zr dZr±Zr 2ZZr ZCu dCu±Zr Z2Cu dCu±Cu :
8
3334
MIZUBAYASHI et al.: LOCAL STRAIN AROUND HYDROGEN
Fig. 3. An increase in the representative atomic spacing, DD/D, due to hydrogen charging observed in a-Cu50Zr50 is plotted against CH. The dashed curve b is tentatively ®tted to the data points. The dot and dashed curve a and the dashed lines 1 and 2 shown in Fig. 1 are also depicted.
Figure 3 shows the data for DD/D found in aCu50Zr50, where the dashed curve b is tentatively ®tted to the data points and the dot and dashed line a assumed for the specimen-length data in Fig. 1 is also depicted. In a-Cu50Zr50, DD/D is, in general, larger than DL/L in the present hydrogen concentration range. After a rough approximation, equation (2) for DL/L may be rewritten as DL=L DaZr ±Zr 2DaCu±Zr DaCu±Cu = aZr ±Zr 2aCu±Zr aCu±Cu DdZr ±Zr 2DdCu±Zr DdCu±Cu = dZr ±Zr 2dCu±Zr dCu±Cu :
9
When the hydrogen induced expansion is the same among (Da/a)Zr±Zr, (Da/a)Cu±Zr and (Da/a)Cu±Cu at a given CH, DD=D DL=L is expected. On the other hand, a preferential increase in the atomic spacing for atoms and/or a preferential occupation of interstices with high hydrogen anity is reported in various LTM±ETM a-alloys [19±23]. For the case of Da=aZr ±Zr r Da=aCu±Zr r Da=aCu±Cu r0, the relationship of DD=D > DL=L is expected because of ZZr > ZCu and the ratio, (DD/D)/(DL/L), shows its maximum value of about 1.3 for the case of Da=aZr ±Zr > 0, Da=aCu±Zr 0 and Da=aCu±Cu 0, where equations (8) and (9) with the values, aCu±Cu 0:254 nm, aCu±Zr 0:275 nm, aZr ±Zr 0:311 nm, ZCu 29 and ZZr 40 are assumed. However, (DD/D)/(DL/L) of about 1.3 is, in general, much lower than that found in Fig. 3, suggesting that (Da/a)Cu±Zr and/or (Da/a)Cu±Cu are negative. We suppose that in the hydrogen concentration range below 15 at.% H, hydrogen atoms preferentially occupy the Zr4 sites where aZr±Zr shows expansion and copper atoms around the occupied Zr4 sites relax towards the center of the
Fig. 4. Examples of the elastic after-eects due to the hydrogen Gorsky eect observed in a-Cu50Zr50. Holding time for prestraining is also shown in the ®gure.
occupied sites, giving a decrease in aCu±Zr and/or aCu±Cu. We surmise that the similar topological relaxation takes place for the Zr3Cu1(I) sites and the Zr3Cu1(II) sites [8] for the hydrogen concentration range above 15 at.% H. In other words, in the strain ellipsoid model supposed for equations (1)±(5), the XRD and specimen length data indicate that l1 is positive but l2 and/or l3 are negative. When this is the case, the relaxation strength St,G of the hydrogen Gorsky eect in a-Cu50Zr50 is expected to be much larger than that calculated from equation (3) and the specimen length data. Figure 4 shows examples of the elastic aftereects due to the hydrogen Gorsky eects which were observed in a-Cu50Zr50. For bending of a thintape specimen, the elastic after-eect strain, e(t), due to the hydrogen Gorsky eects may be given by e t=e0 0:81StG exp ÿt=tG 1=32 exp ÿ32 t=tG 1=52 exp ÿ52 t=tG . . .
10
where e0 denotes prestrain. The relaxation time, tG, is given by tG d=p2 =MG
11
where d denotes the thickness of a specimen and MG, the diusion coecient for long range diusion of hydrogen. MG in a-Cu50Zr50 may be given by MG w2 =a n0 exp ÿHG =kB T
12
where w denotes jump length, a a geometrical factor, n0 the attempt frequency and HG the activation enthalpy for long range diusion. For the hydrogen
MIZUBAYASHI et al.: LOCAL STRAIN AROUND HYDROGEN
Fig. 5. Relaxation strength of the hydrogen Gorsky eect observed in a-Cu50Zr50 (the symbols Q) and that calculated from the specimen length data shown in Fig. 1 using equation (3) (the dot and dashed curve c). Relaxation strength of the hydrogen Snoek peak reported in Ref. [8] is also shown. See text for details.
Snoek peak in a-Cu50Zr50, n0 9 1016 =s and the activation enthalpy for the predominant constituent peak, e.g. HS,1 0:80 eV for CH 5 at:% H, have been reported [8]. The very high value found for n0 suggests that the constitutional entropy factor in n0 is considerably high for hydrogen diusion in aCu50Zr50. In Fig. 4, tG found for the specimen 21 mm thick with CH 3:5 at:% H is about 3:6 104 s at 352 K. Application of equations (11) and (12) to the above quantities with assumption of w aZr ±Zr , n0 9 1016 =s and HG 0:80 eV gives a geometrical factor a of about 25, which may be not unreasonable in a rule of thumb estimation. Figure 5 shows the relaxation strength St,G of the hydrogen Gorsky eect observed in a-Cu50Zr50 and the curve c which is calculated from the specimen length data shown in Fig. 1 using equation (3) expected for isotropic strain tensor l1 l2 l3 . In Fig. 5, the relaxation strength St,S of the hydrogen Snoek peak reported is also depicted, where the dashed curves I±III are ®tted to the data points of St,S for the Zr4, Zr3Cu1(I) and Zr3Cu1(II) sites, respectively [8]. As seen in Fig. 5, St,G observed is much higher than that calculated assuming isotropic strain tensor l1 l2 l3 , indicating again that l1 is positive but l2 and/or l3 are negative, where St,G may be explained by equation (4) instead of equation (3). Although the number of data points for St,G is limited, the dependence of St,G on CH appears to be similar to that of the relaxation strength St,S of the hydrogen Snoek peak. These results will be mentioned together with the corresponding results for a-Cu50Ti50 later. 3.2. a-Cu50Ti50 Figure 6 shows changes in the specimen length DL/L due to hydrogen charging observed in a-
3335
Fig. 6. An increase in DL/L due to hydrogen charging observed in a-Cu50Ti50 is plotted against CH. The dot and dashed curve A is tentatively ®tted to the data points. See text for the dashed lines 1 and 2.
Cu50Ti50, where the hydrogen concentration range for the Ti4 sites is denoted by the dashed lines 0 and 1, and that for the Ti3Cu1(I) by the dashed lines 1 and 2, which are reported in Ref. [7]. The dot and dashed curve A is tentatively ®tted to the data points, where the increasing rate d ln L=dCH is slightly dierent among the hydrogen concentration ranges mentioned above. The atomic volume of hydrogen vH determined from the specimen length data and equation (2) is compiled in Table 1. The value of vH found for the hydrogen concentration range between 30 and 67 at.% H shows good agreement with that reported for the comparable hydrogen concentration range in a-Cu50Ti50 [1]. Figure 7 shows examples of the XRD ®rst peak of a-Cu50Ti50 observed before and after hydrogen charging. The weak peak at 2y 44:76 deg and the strong peak at 2y 47:35 deg are the Al(200) re¯ection from an aluminum frame used for the XRD and the Si(220) re¯ection from silicon powders used as reference. In Fig. 7, silicon powders were added for the XRD measurements of the specimens used for 27.4, 49.0 and 73.6 at.% H but not for the specimens used for 3.3 and 13.8 at.% H. The mean atomic distances in a-Cu50Ti50 reported are aCu±Cu 0:245 nm, aCu±Ti 0:275 nm and aTi±Ti 0:300 nm after Ref. [24] or aCu±Cu 0:25 nm, aCu±Ti 0:27 nm and aTi±Ti 0:29 nm after Ref. [23]. For the Cu Ka radiation, equation (6) and the values mentioned above gives 2yp 41:17 deg after Ref. [24] or 2yp 41:55 deg after Ref. [23]. Fitting to the XRD ®rst peak observed before hydrogen charging using equation (7) gives 2yp 41:56 deg and s 2:8 deg, i.e. 2yp observed shows good agreement with the corresponding values mentioned above. Most of the XRD ®rst peak can be explained by a Gaussian function, however, deviations of the observed XRD peak from a Gaussian
3336
MIZUBAYASHI et al.: LOCAL STRAIN AROUND HYDROGEN
Fig. 8. An increase in DD/D due to hydrogen charging observed in a-Cu50Ti50 is plotted against CH. The dashed curve B is tentatively ®tted to the data points. The dot and dashed curve A and the dashed lines 1 and 2 shown in Fig. 6 are also depicted.
Fig. 7. Examples of the XRD ®rst peak of a-Cu50Ti50 observed before and after hydrogen charging.
function at the lower and higher angle parts are slightly larger in a-Cu50Ti50 than in a-Cu50Zr50. In a-Cu50Ti50, most of the XRD ®rst peaks observed after hydrogen charging show monotonous shift towards lower angle with increasing CH, where s remains almost unchanged for CH below about 30 at.% H and tends to increase for higher CH, e.g. s 3:5 deg for CH 73:6 at:% H. Further, the remaining higher angle part tends to remain unchanged for CH below about 50 at.% H and to shift towards higher angle for CH above about 50 at.% H (see the data for 73.6 at.% H in Fig. 7). The latter observation has been reported for aCu50Ti50 with 77 at.% H [22]. Figure 8 shows the data for DD/D found in aCu50Ti50, which are estimated for the most part of the XRD ®rst peak using equations (7) and (8). In Fig. 8, the dashed curve B is tentatively ®tted to the data points and the dot and dashed line A assumed for the specimen length data in Fig. 6 is also depicted. In a-Cu50Ti50, DD/D is, in general, slightly larger than DL/L for CH below about 50 at.% H and slightly smaller than DL/L for higher CH. In hydrogenated a-Cu50Ti50, a preferential occupation of the Ti4 sites for CH below about 30 at.% H [23] and a preferential increase in aTi±Ti for CH of 77 at.% H [22] are suggested. For the case of Da=aTi±Ti r Da=aCu±Ti r Da=aCu±Cu r0, the relationship of DD=D
Da=aCu±Ti 0 and of Da=aTi±Ti > 0, Da=aCu±Cu 0, where equations (8) and (9) with aCu±Cu, aCu±Ti and aTi±Ti after Ref. [23] or Ref. [24], ZTi 22 and ZCu 29 are assumed. In Fig. 8, DD=D= DL=L of 1±0.8 is found for the hydrogen concentration range beyond 50 at.% H where hydrogen atoms occupy the Ti3Cu1(II) sites [7, 8], suggesting that Da=aTi±Ti r Da=aCu±Ti r Da=aCu±Cu r0 for this CH range. On the other hand, for CH below 50 at.% H, DD/D observed is, in general, slightly larger than DL/L, suggesting that (Da/a)Cu±Ti and/ or (Da/a)Cu±Cu are slightly larger than (Da/a)Ti±Ti. In other words, in the strain ellipsoid model supposed for equations (1)±(5), the dierence among l1, l2 and l3 is not so large, suggesting that the relaxation strength St,G of the hydrogen Gorsky eect in a-Cu50Ti50 is expected to be similar to that calculated from equation (3) and the specimen length data. Figure 9 shows examples of the elastic aftereects due to the hydrogen Gorsky eects observed in a-Cu50Ti50. It is noted that the relaxation
Fig. 9. Examples of the elastic after-eects due to the hydrogen Gorsky eect observed in a-Cu50Ti50. Holding time for prestraining is also shown in the ®gure.
MIZUBAYASHI et al.: LOCAL STRAIN AROUND HYDROGEN
3337
Fig. 11. Redrawing of the curves a (Fig. 1), b (Fig. 3), A (Fig. 6) and B (Fig. 8).
Fig. 10. (a) Relaxation strength of the hydrogen Gorsky eect observed in a-Cu50Ti50 (the symbols q) and that calculated from the specimen length data shown in Fig. 6 using equation (3) (the dot and dashed curve C). (b) Relaxation strength of the hydrogen Snoek peak reported in Ref. [7] is also shown. See text for details.
strength St,G found in a-Cu50Ti50 is about one tenth of St,G observed in a-Cu50Zr50 (see Fig. 4). See Refs [16, 25] for the diusion coecient MG and the activation enthalpy HG in a-Cu50Ti50. Figure 10(a) shows the relaxation strength St,G of the hydrogen Gorsky eect observed in a-Cu50Ti50 [16, 25] and the curve C which is calculated from the specimen length data shown in Fig. 6 using equation (3) expected for isotropic strain tensor l1 l2 l3 . Except for the data found for CH below 1 at.% H [25], the observed data for St,G show good agreement with the curve C, indicating again that the dierence among l1, l2 and l3 is not so large. Figure 10(b) is the dependence of the relaxation strength St,S of the hydrogen Snoek peak on CH observed in a-Cu50Ti50 of various specimen conditions which is redrawn from Fig. 4 reported in Ref. [7]. In the as-quenched state, St,S found in aCu50Ti50 is about one half of that in a-Cu50Zr50 (see Fig. 5), presumably suggesting that the dierence among l1, l2 and l3 in a-Cu50Ti50 is smaller than that in a-Cu50Zr50. In Fig. 11, we compare the specimen length and XRD data found in a-Cu50Zr50 and a-Cu50Ti50, where the tentatively ®tted curves a, b, A and B are depicted. Between a-Cu50Zr50 and a-Cu50Ti50, although the dependence of DL/L on CH is similar to one another, DD/D shows the dierent dependence on CH. On the other hand, it is reported that an amount of decrease in the speci®c volume, DV=V Cry: 0:9%, found after the crystallization of a-Cu50Ti50 [26] is smaller than DV=V Cry:
2:3% found in a-Cu50Zr50 [27]. We surmise that the local atomic structures are more deformable in aCu50Zr50 than in a-Cu50Ti50, resulting in the stronger anisotropy of the hydrogen induced elastic strain in a-Cu50Zr50. To clarify this issue, further work is in progress. 4. CONCLUSION
The hydrogen-induced volume expansion is similar between a-Cu50Zr50 and a-Cu50Ti50. In contrast, anisotropy of the elastic distortion around hydrogen appears to be much larger in a-Cu50Zr50 than in aCu50Ti50. From the combination of the present results with the amounts of decreases in the speci®c volume reported in a-Cu50Zr50 and a-Cu50Ti50, we surmise that the local atomic structures are more deformable in a-Cu50Zr50 than in a-Cu50Ti50. AcknowledgementsÐThe authors would like to thank H. Tanimoto and S. Masuda for their invaluable help on the course of experiments. This work is partly supported by a Grant in Aid for Scienti®c Research from the Ministry of Education, Science, Culture and Sports of Japan, a program of Research for the Future of Japan Society of Promotion of Science, and the University of Tsukuba Research Project.
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