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Ti multilayers
Materials Scienee and Engineering, 97 (1988) 101-104
101
Solid State Amorphization in Ni/Ti Multilayers* J. E. JONGSTE, M. A. HOLLANDERS, B. J. THIJSSE and E. J. MITTEMEIJER
Laboratory ~?fMetallurgy, Delft University of Technology, Rotterdamseweg 137, 2628 AL Delft (The Netherlands)
Abstract
Successive stages in the annealing of a n Ni/Ti multilayer at 523 K were studied by X-ray diffraction analysis. The results appear to indicate diffusion-induced amorphization, although some diffraction phenomena are not understood. An effective diffusion coefficient for the initial stage o f the solid state reaction was determined. Initial stress development is ascribed to differences in molar volume between the crystalline and amorphous phases. Continued annealing led to stress relaxation. I. Introduction
An amorphous metallic alloy may be obtained by interdiffusion in an assembly of polycrystalline components of the individual elements. For example, amorphization can occur in multilayers of alternately stacked layers of gold and lanthanum [1] and of nickel and zirconium [2]. It has been proposed [l] that the formation of such a metastable amorphous phase may be preferred over the stable crystalline state if (i) a large negative enthalpy of mixing occurs in the liquid state, and (ii) one of the elements shows so-called anomalously fast diffusion in a crystal of the other element. Here we report results on the annealing of a Ni/Ti multilayer. This system shows a large negative enthalpy of mixing in the liquid state [3], and anomalously fast diffusion of nickel in ct-Ti (interstitially) has been reported between 900 and 1150 K [4]. The occurrence of amorphization in Ni/Ti multilayers has been claimed earlier [5]. 2. Experimental details
An Ni/Ti multilayer was prepared by magnetron sputtering of alternate nickel and titanium layers onto an Si{100} single-crystal substrate. The multilayer consisted of 20 Ni/Ti bilayers, each approximately 20 nm thick. An amorphous SiO2 layer 200 nm thick *Paper presented at the Sixth International Conference on Rapidly Quenched Metals, Montr6al, August 3-7, 1987. 0025-5416/88/$3.50
was used as a diffusion barrier between the substrate and the multilayer. The sample was annealed at 523 K in progressive stages for up to 16 h in an argonatmosphere. After each step structural changes were analysed by X-ray diffractometry, employing an co diffractometer using Cr Ks and Cu Ks radiation. For more details see ref. 6. 3. The as-prepared samples
The overall composition as determined by electron probe microanalysis was 6 3 . 2 + 0 . 1 a t . % N i and 36.8 ___0.1 at.% Ti, signifying nickel and titanium layers of about equal thickness (52 vol.% and 48 vol.% respectively). According to X-ray diffraction analysis the sample was crystalline, and the nickel and ct-Ti phases exhibited a sharp fibre texture with the closepacked Ni{ 111 } and Ti{001 } planes aligned preferentially parallel to the interfaces, in accordance with previous results for samples with the same bilayer thickness [ 5]. 4. Amorphization
The high angle part of the diffraction pattern is shown for progressive annealing times in Fig. 1: as expected, the integrated intensities of the Ni{ 111 } and Ti{002} reflections decreased with time. Evidently one or more new phases were formed, since the nickel and titanium texture sharpness remained constant during annealing. This was confirmed by tilting the sample in the diffractometer (~o tilting) and then performing a 2,9 0 scan to record the crystal reflections at various angles to the fibre axis. Even for moderate values of _+(o the Bragg peaks vanished, but for the annealed samples an intensity band characteristic of an amorphous phase remained after tilting (Fig. 2), The maximum of the intensity band lies at Q=
4rt sin 0 ~ -30.2nm
1
which is in agreement with the earlier finding (30.1 nm-1 [5]). It also agrees with the main intensity maximum for amorphous melt-spun Ni64Ti36 (30.5 nm 1) [7] and for amorphous mechanically © Elsevier Sequoia/Printed in The Netherlands
102 100OO a
4
800(
3
Iog(]{CpS))
I (cos)
600[
T
400C 200C '
'
42
'
'
'
48
2h
! (cpi~O~ b
16h
Ni-(227)
Ni-(l11)
>
20(deg.)
Fig. 1. The high angle part of the diffraction pattern for several " annealing times at 523 K (CuK~ radiation): (a) 0 ~ h ; (b) 2-16h (insert: the Ni{222} peak and the intensity band at
Q = 60.4nm i). alloyed Ni70Ti30 (30.2 nm 1) [8]. Moreover, the width of the intensity band corresponds to that of ref. 8. An alternative explanation for this band might be the formation of randomly oriented extremely small (1.6 nm) crystallites of an intermetallic compound (e.g. Ni3Ti or NiTi). However, (i) for randomly ori-
Ni-(1111
1 I I', (cps)
I
1 > 20 (deg.) Fig. 3. The low angle part of the diffraction pattern for the as-prepared specimen, showing the (000) satellites up to the 16th order (Cr K~ radiation, logarithmic intensity scale).
20 (deg.)
>
Ti-(O02)
(cleg.)
20
Fig. 2. The high angle part of the diffraction pattern after annealing for 16 h at 523 K (Cr K~ radiation): (a) tilting angle ~o = 0°; (b) tilting angle co = 14° (the absence of sharp crystal reflections should be noted).
ented crystallites several diffraction maxima would be expected, which are not observed, and (ii) the average composition of the new phase is estimated as Ni63Ti37 (see below), which is incompatible with either NiTi or Ni3Ti. In particular, NiTi is unlikely to form as it is not stable below 903 K. The low angle part of the diffraction pattern shows the (000) satellites resulting from the periodic composition modulation (Fig. 3). Bragg peaks up to the 16th order are visible. Here only the positions 2,9m of the maxima are considered. Because of dynamical scattering effects it is necessary to use a modified form of Bragg's law [9] (m2) 2 = 4A2(sin2~m _ 26) where m is the order of the reflection, 2 the X-ray wavelength, A the modulation period and 1 - 8 the real part of the refractive index. A was found to be 2 1 . 7 5 + 0 . 0 2 n m for the as-prepared sample. It decreased on annealing (Fig. 4), consistent with the formation of an amorphous phase, as amorphous NixTil _ x has a smaller molar volume than a mixture of crystalline nickel and titanium (see Section 5). Since no significant change in texture was observed, the amounts of crystalline phases remaining after a certain time t are proportional to the integrated intensities It of the crystal reflections. Figure 4 shows F 2 - {(I0 - 1,)10} 2 and f12 _= {(A, - Ao)/Ao}2 vs. t. In the first part of the process the intensities and A decrease linearly with t 1/2, which is typical of a diffusion-controlled process. However, for the t 1/2 decay of the Ni{ 111 } intensity an incubation time of approximately 1 h is observed. This cannot be attributed to an initial dissolution of titanium in the nickel lattice, since the strain-free lattice parameter of nickel did not change (Section 5). One would expect a 1.0% increase if 10 at.% Ti were to dissolve [ 10]. A possible explanation is initial diffusion of titanium along the nickel grain boundaries, which would leave the intensity of the Ni{ 111 } reflection unaffected.
103 1.0
/
0.8
0.6 04
~J F2T 0.2 O0
,
j
,
]32.104l 2
6
0
> t (h)
, 10
20
Fig. 4. F 2 - {/o - It)/Io} 2 and fiE _={(A, - Ao)/Ao}2 vs. annealing time t at 523 K: ---, parabolic time dependence of the initial annealing stage ~, nickel; 41,, titanium).
An approximate expression can be derived for the effective interdiffusion coefficient /) L in a planar product layer, assuming (i) no solid solution in the parent phases A and B, (ii) a linear concentration profile in the layer, i.e. the molar fraction range Ac of A over the layer is small, and (iii) a constant average composition of the layer [l 1]" 1 - Ac d(FAF,) DL ~ ~ - c zAzB dt where Zn and za are the initial A and B layer thicknesses. This leads to /)L(523 K) ~ 6 . 0 x 10 -22 1 -- ACm2 s l Ac for the initial stage of the reaction. Extrapolation of the data reported for anomalously fast diffusion of nickel in ct-Ti yields D = 8 . 4 x 1 0 2°m2s-~ [4]. Equating this value to /)L would imply (AC)L~0.7at.%, which is probably too small by an order of magnitude. Self-diffusion coefficients of nickel and ct-Ti measured in the ranges I 150-1700 K and 950-1150 K respectively [12, 13] yield DNi = 1.1 × 10-32m2 s - I and DTi = 8.5 × 10 -25 m 2 s I. These values are clearly much smaller than the above value for /)LThe average composition of the amorphous phase can be calculated from the crystal reflection intensities and the initial composition, and it was found to be approximately Ni64Ti36 after 16 h.
Although the occurrence of solid state amorphization in Ni/Ti appears to be indicated by our results, two observations cannot yet be satisfactorily explained. (i) An intensity band with a maximum at Qmax = 60.4 n m - ~was observed in the diffraction pattern (Fig. 1). This band vanishes simultaneously with the Ni{222} peak if the specimen is tilted, which suggests that it originates from an (unidentified) textured crystalline phase. (ii) The small peaks at the low angle side of the Ni{ 111 } reflection (Fig. 1) are interpreted as "Laue" satellites, caused by a uniform small size (perpendicular to the interfaces) of the nickel crystallites. It is not understood why no satellites occur at the other side of the peak. From the satellite positions a size of 9.1 + 0.5 nm was derived, which is not far from the I 1.3 nm layer thickness calculated from the nickel volume fraction. On annealing the satellite intensities decreased, but the positions did not change. This suggests that some crystallites remain unaffected in their columnar length for a considerable time. This seems to contrast with the planar growth of the amorphous phase as observed for Ni/Zr in ref. 14. However, it has been claimed [15] that grain boundary diffusion is necessary to initiate planar growth at later times. The Ti{002} reflection does not show satellites. This may indicate a broad crystallite size distribution for titanium. 5. Volume contraction and stress development The molar volumes of amorphous NiTi alloys are not known. Ignoring densification effects by structural relaxation, a reasonable estimate is 1% above the corresponding crystalline phase (mixture), which has been confirmed for one composition, Ni4oTi6o [16]. Crystalline NisoTiso and Ni75Ti25 have 4.4% and 7.2% smaller molar volumes respectively than those of the corresponding mixtures of nickel and titanium. This would imply for our sample a volume contraction of 4.9% after a complete transition from crystalline nickel and titanium to amorphous Ni64Ti36, and consequently 3.7% after 16 h annealing, when about 75% of the crystalline phases has disappeared. Two limiting cases can be considered for the amorphization. (i) "Coherency" is maintained along the crystalamorphous interfaces (i.e. the number of atoms per unit area interface is the same for the crystalline and the amorphous phases). Then an equilibrium molar volume of the amorphous alloy phase different from those of the adjacent pure element phases will lead to stress development (see below).
104 (ii) No "coherency": in the amorphous phase the equilibrium atomic configuration is realized at all times. Stresses will be absent. It may be assumed that the lateral dimensions of the amorphous product layer match those of the crystalline parent layers during the entire amorphization. Then the relative thickness change of the specimen is obviously equal to the relative macroscopic volume change. Further, if the equilibrium atomic configuration occurs at all annealing times, the relative thickness change will be equal to the relative intrinsic volume change corresponding to the production of the equilibrium amorphous phase. The observed value for the thickness contraction is 2.4% (Fig. 4). This is about two-thirds of the volume contraction predicted above, meaning that the amorphization reaction involves at least partial "coherency" at the interfaces. The Ni{ 111 } and Ti{002} lattice spacings perpendicular to the surface change significantly on annealing (Fig. 5). This can be caused by changes in composition of the crystallites and by stress development. Because of the fibre texture the sin 2¢ method for stress analysis [17] cannot be employed: the Ni{ 111 } and Ti{002} reflections can only be measured in the almost untilted condition of the specimen. However, by tilting, the specimen reflections from other lattice planes from the same crystallites become measurable, here Ni{220} and Ti{103}. Assuming a plane state of stress and ignoring coupling of the crystallites (thus adopting single-crystal values for the elastic bitensor), values for the stress and for the strain-free lattice parameters are obtained [11]. The strain-free lattice parameters, and hence the compositions of the nickel and titanium phases did not change on annealing. Therefore a direct interpretation of the change in the lattice parameter in the untilted condition (Fig. 5) in terms of stress development is possible. In the as-prepared specimen the titanium phase was in a state of high compressive stress, 0.6" 0.3"
°0.1000
•- n
T~I/< 0
-0.3 -0.6 0
~, t (h)
10
20
Fig. 5. Relative change in the lattice spacing with annealing time t at 523 K (d±, spacing perpendicular to the interfaces; do, strain-free spacing).
probably caused by the sputtering process [18], while the nickel phase was nearly stress free. Since the molar volume of amorphous Ni64Ti36 is between those of crystalline nickel and crystalline titanium, interface "coherency" would imply a sudden development of a tensile stress in the nickel layers and a compressive stress in the titanium layers on amorphization. The tensile stress in nickel is indeed found. For titanium the high compressive stress in the as-prepared state possibly precluded the development of a still higher stress. On continued annealing the stresses in the nickel and titanium phases decreased gradually, as a result of relaxation. The largest stress values in the nickel and titanium phases were about + 1000 MPa and - 1100 MPa respectively.
Acknowledgments We are indebted to Dr. Ir. Th. H. de Keijser and Ir. O. B. Loopstra for stimulating discussions. X-ray facilities were provided by Ing. N. M. v.d. Pers and Dr. Ir. Th. H. de Keijser. The Centre for Submicron Technology of Delft University of Technology made availaqale the sputtering facilities. Financial support from the "Stichting voor Fundamenteel Onderzoek der Materie" (Foundation for Fundamental Research of Matter) is gratefully acknowledged.
References 1 R. B. Schwarz and W. L. Johnson, Phys. Rev. Lett., 51
(1983) 415. 2 B. M. Clemens, W. L. Johnson and R. B. Schwarz, J. NonCryst. Solids, 61-62 (1984) 817. 3 A. R. Miedema, Philips Tech. Rev., 36(1976) 217. 4 G. M. Hood and R. J. Schulz, Philos. Mag., 26(1972) 329. 5 B. Clemens, Phys. Rev. B, 33(1986) 7615. 6 M. A. Hollanders and B. J. Thijsse, Int. Conf. on Solid State Amorphizing Transformations, Los Alamos, NM, 1987, in J. Less-Common Met., 140 (1988).
7 K. H. F. Buschow,J. Phys. F, 13(1983) 563. 8 R. B. Schwarz, R. R. Petrich and C. K. Saw, J. Non-Cryst. Solids, 76(1985) 281. 9 P. F. Miceli, D. A. Neumann and H. Zabel, Appl. Phys. Lett., 48 (1986) 24. 10 W. B. Pearson, Handbook of Lattice Spacings and Structures of Metals and Alloys, Pergamon, Oxford, 1958, p. 791. 11 M. A. Hollanders, B. J. Thijsse and E. J. Mittemeijer, to be published. 12 M. Badia and A. Vignes, Acta Metall., 17(1969) 177. 13 F. Dyment and C. M. Libanati, J. Mater. Sci., 3(1968) 349. 14 H. Schrrder, K. Samwerand U. Krster, Phys. Rev. Lett., 54 (1985) 197. 15 A. M. Vredenburg, J. F. M. Westendorp, F. W. Saris, N. M. van der Pers and Th. H. de Keijser, J. Mater. Res., 1 (1986) 774. 16 S. H. Whang, L. T. Kabacoff,D. E. Polk and B. C. Giessen, J. Mater. Sci., 15(1980) 247. 17 V. M. Hauk and E. Macherauch, Adv. X-ray Anal., 27 (1983) 81. 18 J. A. Thornton and D. W. Hoffmann,J. Vac. Sci. Technol., 14(1977) 164.
101
Solid State Amorphization in Ni/Ti Multilayers* J. E. JONGSTE, M. A. HOLLANDERS, B. J. THIJSSE and E. J. MITTEMEIJER
Laboratory ~?fMetallurgy, Delft University of Technology, Rotterdamseweg 137, 2628 AL Delft (The Netherlands)
Abstract
Successive stages in the annealing of a n Ni/Ti multilayer at 523 K were studied by X-ray diffraction analysis. The results appear to indicate diffusion-induced amorphization, although some diffraction phenomena are not understood. An effective diffusion coefficient for the initial stage o f the solid state reaction was determined. Initial stress development is ascribed to differences in molar volume between the crystalline and amorphous phases. Continued annealing led to stress relaxation. I. Introduction
An amorphous metallic alloy may be obtained by interdiffusion in an assembly of polycrystalline components of the individual elements. For example, amorphization can occur in multilayers of alternately stacked layers of gold and lanthanum [1] and of nickel and zirconium [2]. It has been proposed [l] that the formation of such a metastable amorphous phase may be preferred over the stable crystalline state if (i) a large negative enthalpy of mixing occurs in the liquid state, and (ii) one of the elements shows so-called anomalously fast diffusion in a crystal of the other element. Here we report results on the annealing of a Ni/Ti multilayer. This system shows a large negative enthalpy of mixing in the liquid state [3], and anomalously fast diffusion of nickel in ct-Ti (interstitially) has been reported between 900 and 1150 K [4]. The occurrence of amorphization in Ni/Ti multilayers has been claimed earlier [5]. 2. Experimental details
An Ni/Ti multilayer was prepared by magnetron sputtering of alternate nickel and titanium layers onto an Si{100} single-crystal substrate. The multilayer consisted of 20 Ni/Ti bilayers, each approximately 20 nm thick. An amorphous SiO2 layer 200 nm thick *Paper presented at the Sixth International Conference on Rapidly Quenched Metals, Montr6al, August 3-7, 1987. 0025-5416/88/$3.50
was used as a diffusion barrier between the substrate and the multilayer. The sample was annealed at 523 K in progressive stages for up to 16 h in an argonatmosphere. After each step structural changes were analysed by X-ray diffractometry, employing an co diffractometer using Cr Ks and Cu Ks radiation. For more details see ref. 6. 3. The as-prepared samples
The overall composition as determined by electron probe microanalysis was 6 3 . 2 + 0 . 1 a t . % N i and 36.8 ___0.1 at.% Ti, signifying nickel and titanium layers of about equal thickness (52 vol.% and 48 vol.% respectively). According to X-ray diffraction analysis the sample was crystalline, and the nickel and ct-Ti phases exhibited a sharp fibre texture with the closepacked Ni{ 111 } and Ti{001 } planes aligned preferentially parallel to the interfaces, in accordance with previous results for samples with the same bilayer thickness [ 5]. 4. Amorphization
The high angle part of the diffraction pattern is shown for progressive annealing times in Fig. 1: as expected, the integrated intensities of the Ni{ 111 } and Ti{002} reflections decreased with time. Evidently one or more new phases were formed, since the nickel and titanium texture sharpness remained constant during annealing. This was confirmed by tilting the sample in the diffractometer (~o tilting) and then performing a 2,9 0 scan to record the crystal reflections at various angles to the fibre axis. Even for moderate values of _+(o the Bragg peaks vanished, but for the annealed samples an intensity band characteristic of an amorphous phase remained after tilting (Fig. 2), The maximum of the intensity band lies at Q=
4rt sin 0 ~ -30.2nm
1
which is in agreement with the earlier finding (30.1 nm-1 [5]). It also agrees with the main intensity maximum for amorphous melt-spun Ni64Ti36 (30.5 nm 1) [7] and for amorphous mechanically © Elsevier Sequoia/Printed in The Netherlands
102 100OO a
4
800(
3
Iog(]{CpS))
I (cos)
600[
T
400C 200C '
'
42
'
'
'
48
2h
! (cpi~O~ b
16h
Ni-(227)
Ni-(l11)
>
20(deg.)
Fig. 1. The high angle part of the diffraction pattern for several " annealing times at 523 K (CuK~ radiation): (a) 0 ~ h ; (b) 2-16h (insert: the Ni{222} peak and the intensity band at
Q = 60.4nm i). alloyed Ni70Ti30 (30.2 nm 1) [8]. Moreover, the width of the intensity band corresponds to that of ref. 8. An alternative explanation for this band might be the formation of randomly oriented extremely small (1.6 nm) crystallites of an intermetallic compound (e.g. Ni3Ti or NiTi). However, (i) for randomly ori-
Ni-(1111
1 I I', (cps)
I
1 > 20 (deg.) Fig. 3. The low angle part of the diffraction pattern for the as-prepared specimen, showing the (000) satellites up to the 16th order (Cr K~ radiation, logarithmic intensity scale).
20 (deg.)
>
Ti-(O02)
(cleg.)
20
Fig. 2. The high angle part of the diffraction pattern after annealing for 16 h at 523 K (Cr K~ radiation): (a) tilting angle ~o = 0°; (b) tilting angle co = 14° (the absence of sharp crystal reflections should be noted).
ented crystallites several diffraction maxima would be expected, which are not observed, and (ii) the average composition of the new phase is estimated as Ni63Ti37 (see below), which is incompatible with either NiTi or Ni3Ti. In particular, NiTi is unlikely to form as it is not stable below 903 K. The low angle part of the diffraction pattern shows the (000) satellites resulting from the periodic composition modulation (Fig. 3). Bragg peaks up to the 16th order are visible. Here only the positions 2,9m of the maxima are considered. Because of dynamical scattering effects it is necessary to use a modified form of Bragg's law [9] (m2) 2 = 4A2(sin2~m _ 26) where m is the order of the reflection, 2 the X-ray wavelength, A the modulation period and 1 - 8 the real part of the refractive index. A was found to be 2 1 . 7 5 + 0 . 0 2 n m for the as-prepared sample. It decreased on annealing (Fig. 4), consistent with the formation of an amorphous phase, as amorphous NixTil _ x has a smaller molar volume than a mixture of crystalline nickel and titanium (see Section 5). Since no significant change in texture was observed, the amounts of crystalline phases remaining after a certain time t are proportional to the integrated intensities It of the crystal reflections. Figure 4 shows F 2 - {(I0 - 1,)10} 2 and f12 _= {(A, - Ao)/Ao}2 vs. t. In the first part of the process the intensities and A decrease linearly with t 1/2, which is typical of a diffusion-controlled process. However, for the t 1/2 decay of the Ni{ 111 } intensity an incubation time of approximately 1 h is observed. This cannot be attributed to an initial dissolution of titanium in the nickel lattice, since the strain-free lattice parameter of nickel did not change (Section 5). One would expect a 1.0% increase if 10 at.% Ti were to dissolve [ 10]. A possible explanation is initial diffusion of titanium along the nickel grain boundaries, which would leave the intensity of the Ni{ 111 } reflection unaffected.
103 1.0
/
0.8
0.6 04
~J F2T 0.2 O0
,
j
,
]32.104l 2
6
0
> t (h)
, 10
20
Fig. 4. F 2 - {/o - It)/Io} 2 and fiE _={(A, - Ao)/Ao}2 vs. annealing time t at 523 K: ---, parabolic time dependence of the initial annealing stage ~, nickel; 41,, titanium).
An approximate expression can be derived for the effective interdiffusion coefficient /) L in a planar product layer, assuming (i) no solid solution in the parent phases A and B, (ii) a linear concentration profile in the layer, i.e. the molar fraction range Ac of A over the layer is small, and (iii) a constant average composition of the layer [l 1]" 1 - Ac d(FAF,) DL ~ ~ - c zAzB dt where Zn and za are the initial A and B layer thicknesses. This leads to /)L(523 K) ~ 6 . 0 x 10 -22 1 -- ACm2 s l Ac for the initial stage of the reaction. Extrapolation of the data reported for anomalously fast diffusion of nickel in ct-Ti yields D = 8 . 4 x 1 0 2°m2s-~ [4]. Equating this value to /)L would imply (AC)L~0.7at.%, which is probably too small by an order of magnitude. Self-diffusion coefficients of nickel and ct-Ti measured in the ranges I 150-1700 K and 950-1150 K respectively [12, 13] yield DNi = 1.1 × 10-32m2 s - I and DTi = 8.5 × 10 -25 m 2 s I. These values are clearly much smaller than the above value for /)LThe average composition of the amorphous phase can be calculated from the crystal reflection intensities and the initial composition, and it was found to be approximately Ni64Ti36 after 16 h.
Although the occurrence of solid state amorphization in Ni/Ti appears to be indicated by our results, two observations cannot yet be satisfactorily explained. (i) An intensity band with a maximum at Qmax = 60.4 n m - ~was observed in the diffraction pattern (Fig. 1). This band vanishes simultaneously with the Ni{222} peak if the specimen is tilted, which suggests that it originates from an (unidentified) textured crystalline phase. (ii) The small peaks at the low angle side of the Ni{ 111 } reflection (Fig. 1) are interpreted as "Laue" satellites, caused by a uniform small size (perpendicular to the interfaces) of the nickel crystallites. It is not understood why no satellites occur at the other side of the peak. From the satellite positions a size of 9.1 + 0.5 nm was derived, which is not far from the I 1.3 nm layer thickness calculated from the nickel volume fraction. On annealing the satellite intensities decreased, but the positions did not change. This suggests that some crystallites remain unaffected in their columnar length for a considerable time. This seems to contrast with the planar growth of the amorphous phase as observed for Ni/Zr in ref. 14. However, it has been claimed [15] that grain boundary diffusion is necessary to initiate planar growth at later times. The Ti{002} reflection does not show satellites. This may indicate a broad crystallite size distribution for titanium. 5. Volume contraction and stress development The molar volumes of amorphous NiTi alloys are not known. Ignoring densification effects by structural relaxation, a reasonable estimate is 1% above the corresponding crystalline phase (mixture), which has been confirmed for one composition, Ni4oTi6o [16]. Crystalline NisoTiso and Ni75Ti25 have 4.4% and 7.2% smaller molar volumes respectively than those of the corresponding mixtures of nickel and titanium. This would imply for our sample a volume contraction of 4.9% after a complete transition from crystalline nickel and titanium to amorphous Ni64Ti36, and consequently 3.7% after 16 h annealing, when about 75% of the crystalline phases has disappeared. Two limiting cases can be considered for the amorphization. (i) "Coherency" is maintained along the crystalamorphous interfaces (i.e. the number of atoms per unit area interface is the same for the crystalline and the amorphous phases). Then an equilibrium molar volume of the amorphous alloy phase different from those of the adjacent pure element phases will lead to stress development (see below).
104 (ii) No "coherency": in the amorphous phase the equilibrium atomic configuration is realized at all times. Stresses will be absent. It may be assumed that the lateral dimensions of the amorphous product layer match those of the crystalline parent layers during the entire amorphization. Then the relative thickness change of the specimen is obviously equal to the relative macroscopic volume change. Further, if the equilibrium atomic configuration occurs at all annealing times, the relative thickness change will be equal to the relative intrinsic volume change corresponding to the production of the equilibrium amorphous phase. The observed value for the thickness contraction is 2.4% (Fig. 4). This is about two-thirds of the volume contraction predicted above, meaning that the amorphization reaction involves at least partial "coherency" at the interfaces. The Ni{ 111 } and Ti{002} lattice spacings perpendicular to the surface change significantly on annealing (Fig. 5). This can be caused by changes in composition of the crystallites and by stress development. Because of the fibre texture the sin 2¢ method for stress analysis [17] cannot be employed: the Ni{ 111 } and Ti{002} reflections can only be measured in the almost untilted condition of the specimen. However, by tilting, the specimen reflections from other lattice planes from the same crystallites become measurable, here Ni{220} and Ti{103}. Assuming a plane state of stress and ignoring coupling of the crystallites (thus adopting single-crystal values for the elastic bitensor), values for the stress and for the strain-free lattice parameters are obtained [11]. The strain-free lattice parameters, and hence the compositions of the nickel and titanium phases did not change on annealing. Therefore a direct interpretation of the change in the lattice parameter in the untilted condition (Fig. 5) in terms of stress development is possible. In the as-prepared specimen the titanium phase was in a state of high compressive stress, 0.6" 0.3"
°0.1000
•- n
T~I/< 0
-0.3 -0.6 0
~, t (h)
10
20
Fig. 5. Relative change in the lattice spacing with annealing time t at 523 K (d±, spacing perpendicular to the interfaces; do, strain-free spacing).
probably caused by the sputtering process [18], while the nickel phase was nearly stress free. Since the molar volume of amorphous Ni64Ti36 is between those of crystalline nickel and crystalline titanium, interface "coherency" would imply a sudden development of a tensile stress in the nickel layers and a compressive stress in the titanium layers on amorphization. The tensile stress in nickel is indeed found. For titanium the high compressive stress in the as-prepared state possibly precluded the development of a still higher stress. On continued annealing the stresses in the nickel and titanium phases decreased gradually, as a result of relaxation. The largest stress values in the nickel and titanium phases were about + 1000 MPa and - 1100 MPa respectively.
Acknowledgments We are indebted to Dr. Ir. Th. H. de Keijser and Ir. O. B. Loopstra for stimulating discussions. X-ray facilities were provided by Ing. N. M. v.d. Pers and Dr. Ir. Th. H. de Keijser. The Centre for Submicron Technology of Delft University of Technology made availaqale the sputtering facilities. Financial support from the "Stichting voor Fundamenteel Onderzoek der Materie" (Foundation for Fundamental Research of Matter) is gratefully acknowledged.
References 1 R. B. Schwarz and W. L. Johnson, Phys. Rev. Lett., 51
(1983) 415. 2 B. M. Clemens, W. L. Johnson and R. B. Schwarz, J. NonCryst. Solids, 61-62 (1984) 817. 3 A. R. Miedema, Philips Tech. Rev., 36(1976) 217. 4 G. M. Hood and R. J. Schulz, Philos. Mag., 26(1972) 329. 5 B. Clemens, Phys. Rev. B, 33(1986) 7615. 6 M. A. Hollanders and B. J. Thijsse, Int. Conf. on Solid State Amorphizing Transformations, Los Alamos, NM, 1987, in J. Less-Common Met., 140 (1988).
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