- Email: [email protected]
Thermally induced transition from metastable Ni-Nb hexagonal phase to amorphous and its thermodynamic interpretation
Journal of Alloys and Compounds, 196 (1993) 37--40 JALCOM 550
37
Thermally induced transition from metastable Ni-Nb hexagonal phase to amorphous and its thermodynamic interpretation B. X. Liu, H. Y. Bai, Z. J. Z h a n g a n d Q. L. Q i u Department of Materials Science and Engineering, Tsinghua University, Beijing, 100084 (China) (Received July 25, 1992; in final form October 12, 1992)
Abstract In the Ni-Nb system, the free energy curves were calculated for the solid solution, amorphous phase, equilibrium compound and, for the first time, a metastable crystalline (MX) phase, which was formed by ion mixing and identified to be a hexagonal structure with a stoichiometry around Ni75Nb~. In calculating the enthalpy of the MX phase, the structural characteristics and ferromagnetic effect were considered. The constructed Ni-Nb free energy diagram can explain an unusual observation, i.e. the thermally induced vitrification of the MX phase, as well as the glass-forming ability and evolution of ion-mixed amorphous alloys on annealing.
I. Introduction It is known that ion mixing (IM) can produce metastable materials with either amorphous or crystalline (MX) structure. A large number of amorphous alloys have been obtained by IM in some 70 binary metal systems [1] and several empirical models have been proposed to predict the glass-forming ability (GFA) of the metal systems [2, 3]. Thermodynamic calculations have been performed to construct the free energy diagram in order to determine the exact composition range of amorphization by comparing the energetic states of competing phases [4, 5]. However, little attention has been paid to the MX phases obtained by IM, and free energy calculations have not been reported. A structurally similar MX phase has been observed in five binary systems, i.e. Co-Au, Ti-Au, Co-Mo, Ni-Mo and Ni-Nb. These phases exhibit the h.c.p, structure and their lattice sizes are similar [6, 7]. The calculation of the free energy of the MX phase in order to construct a complete free energy diagram of the corresponding system is therefore important. The diagram must include the free energy curves of the solid solution, amorphous phase, equilibrium compound and MX phase. In this paper, we report the construction of the free energy diagram for the Ni-Nb system. The formation of the amorphous alloy and MX phase is explained and the transition from the MX to the amorphous phase on aging is described based on the calculated diagram. 0925-8388/93/$6.00
2. Method of calculation of the free energy diagram First of all, we make some assumptions for the free energy calculation of the MX phase. The Ni-Nb MX phase was formed by IM and identified by X-ray diffraction to be hexagonal with the lattice constants a=3.28 /~, c=5.22 A, c/a=1.59 and a stoichiometry around NivsNb25 [6-8]. The free energy of mixing of the MX phase is given by AGMx = AHMx - TASMx
(1)
where AH~x and ASMx are the enthalpy and entropy of mixing respectively. Since the MX phase is crystalline, ASMx can be neglected (ASMx= 0 at 0 K). The second assumption is that there are elastic and structural contributions to the enthalpy of mixing because the MX phase is unstable. It can be considered as a deformed crystalline structure containing strain energy which leads to elastic and structural terms in the enthalpy of mixing /~k/"/MX = ~ M X
c + /~t/-/MXc "1- ~ ' / M X s
(2)
where fiJ-/MXO, AJ-/ixc and ~¢/UXs are the chemical, elastic and structural contributions to the enthalpy of mixing of the MX phase. 5//MXo is due to the electron redistribution that occurs when the alloy is formed. It has been studied extensively by Miedema and coworkers [9-12] and can be written as Z~-tMXc = I~PlamPxA VA2/3fAB
(3)
where M-/ampis an amplitude concerning the magnitude of the chemical interaction, VA is the atomic volume of metal A in the alloy and lAB is a function which © 1993- Elsevier Sequoia. All rights reserved
B. X. Lm et aL / Transition from metastable crystalline to amorphous phase in Ni-Nb
38
accounts for the degree to which atoms of type A are surrounded by atoms of type B. f,,a3 is given by )cab =XB.[1 + r(XA.XB,)z]
(4)
where XB, is the atomic cell surface area concentration of metal B in the alloy, r is an empirical parameter; for a solid solution, r=0, for an amorphous phase, r = 5 , and for an equilibrium compound, r = 8 [13]. The MX phase of the Ni-Nb system is crystalline with an h.c.p, structure (as identified by X-ray diffraction) and is therefore considered as an ordered compound. Taking this into account, we consider that r = 8. M-/MX° is due to the difference in atomic volume between A and B atoms in the alloy. This term can be computed using classical elasticity theory. M-/MX, takes into account the difference in valence and crystal structure of the two elemental metals and the MX phase. It can be calculated by the formula [14, 15] AHMx. =EMx(Z) --XAE^(ZA)-XBEB(ZB)
(5)
where Z, is the average number of valence electrons per atom (for NbNi3, Z=8.75) and EMX, EA and EB are the lattice stabilities of the MX phase and the pure components respectively. The dependence of the lattice stability on Z for b.e.c., f.c.c, and h.c.p, structures has been derived by Niessen and Miedema [16]. In addition, the correction for ferromagnetic metals has been taken into account in calculating the structure term, since the Ni component is ferromagnetic [17]. According to all these considerations, the free energy of mixing of the MX phase is calculated and obtained. The free energy of mixing of a solid solution is given by
AG,= M-I,- TAS,
(6)
where AH, and AS, are the enthalpy and entropy of mixing respectively. The simplest expression for the entropy is that corresponding to an ideal solution, namely
AS, = -R(XA In XA +XB In XB)
(7)
where R is the gas constant. The enthalpy of mixing of a substitutional solid solution also contains three terms [14, 16, 18] aH, =
+ aHs.
(8)
where &H,o, M-/,, and M-/,, are the chemical, elastic and structural terms respectively. T h e free energy of mixing of the amorphous phase is given by [19]
AG. = M-I, - TAS. +X^AG~(T) +XBAG~-~(T)
(9)
where &Ha and AS. are the enthalpy and entropy of mixing of the amorphous phase. Since the elastic and structural effects can be neglected in the amorphous
phase, AH, contains only the chemical contribution AH, o and the experimental parameter r is taken to be 5. Moreover, it is reasonable to assume that ASa= A&AG~-~ is the difference in Gibbs free energy between the amorphous and crystalline phases of a pure element at room temperature. Turnbull's [20] or Thompson-Spaepen's [21] approximation is applied and we obtain = A H , ( T , - T) 7",
(10)
or
= M-If(Tf- T)2T
Td,Tf+ T)
(11)
where M-/f is the heat of fusion and T¢ is the melting temperature. Turnbull's approximation is suitable for metals of low melting point, while Thompson-Spaepen's approximation is suitable for metals of high melting point. The free energy of mixing of the equilibrium compound is given by AGor ~"Z~-/or
(12)
where M-/o, is the enthalpy of mixing. In the equilibrium compound, ASs=0 at 0 K and is therefore small at higher temperatures. Since there are no elastic and structural effects in the equilibrium compound, M-/or contains only the chemical term M-/o,~, in which r is taken to be 8; AGor is expressed by [9] aGor=aHo
(13)
Hating completed the above calculation, a free energy diagram of the Ni-Nb system was constructed and is shown in Fig. l(b) together with the corresponding equilibrium' phase diagram (Fig. l(a)).
3. Experimental results in the Ni-Nb system and relationship to the free energy diagram
We now turn to the results of the experiments performed in the Ni-Nb system and discuss them in terms of the constructed free energy diagram. Ni-Nb multilayers were prepared by electron-gun evaporation in a vacuum system. Several samples were prepared with various compositions and then irradiated with 300 or 200 keV Xe ÷ ions at room temperature to doses ranging from 3×1014 to 1.7×1016 Xe + c m - L After irradiating to certain doses, amorphous alloys were obtained as shown by the halos in the X-ray diffraction patterns and the increased sheet resistivities [8]; the composition range for IM-induced amorphization extended from 35 to 85 at.% Ni. The recrystallization
39
B. X. Liu et al. / Transition from metastable crystalline to amorphous phase in Ni-Nb
20=0
1600
P (a) 1400 Firmt Halo £
1200fl
Fig. 2. X-Ray diffraction patterns showing the MX+amor1000
(o)
I Nb
I
I
20
IIII
I
40
II I i
60
1
80
Ni
Ni at% +40
phous-o amorphous phase transformation: (a) diffraction pattern of Ni65Nb35multilayers irradiated by 300 keV xenon ions at room temperature to a dose of 5 x 10TMXe ÷ cm -2 showing a mixture of amorphous and h.c.p. MX phase with a = 0.328 nm, c = 0.522 nm and c/a = 1.59; (b) diffraction pattern of the same sample after about 1 month aging showing only amorphous phase remaining. A
bcc
~
MX(hcp) NbNi 3
-40
(b)
L
Nb
20
i
40
I
~
60
P
I
80
I
Ni
Ni at~
Fig. 1. The calculated free energy diagram of the Ni-Nb system (b) and the corresponding equilibrium phase diagram (a).
2 40
temperatures of the ion-mixed amorphous alloys were determined by thermal annealing, and the highest recrystallization temperature was 600--650 °C for an Ni55Nb45 amorphous alloy [8]. The calculated free energy diagram shows that the free energy of the amorphous phase is lower than that of the solid solution over the range 16-85 at.% Ni, and there is a lowest point at Ni53Nb47, indicating that this composition corresponds to the most stable amorphous state. The calculations are in good agreement with the experimental observations within the relevant errors involved in both calculation and experiment. Ni65Nb35 multilayered samples were irradiated to various doses with short intervals to reveal the phase evolution in the multilayers. It was found that a new MX phase of h.c.p, structure was formed together with an amorphous phase at a dose of 5X1014 Xe ÷ cm -2 (lower than the dose inducing uniform mixing and entire amorphization). Figure 2(a) shows an X-ray diffraction pattern revealing a mixture of MX phase and amorphous phase. Interestingly, after 1 month room temperature aging of the sample, the X-ray diffraction pattern showed (Fig. 2(b)) only halos, but no sharp
i
50
I
60
I
70
i
80 Ni Content
i
90
100
at%
Fig. 3. Part of the Ni-Nb free energy diagram (enlarged): A, high-energy state after atomic collision.
diffraction lines, indicating that the MX phase had transformed into the amorphous state. Figure 3 shows a partially enlarged free energy diagram, from which the formation of the MX phase and a possible path of transition from the MX to the amorphous phase can be explained. It can be observed that the free energy curves of the MX and amorphous phases intersect around the composition of 75 at.% Ni and the MX phase may have a higher free energy than that of the amorphous phase. After irradiation to 5 × 1014 Xe ÷ cm -2, the film has not been uniformly mixed and contains a range of compositions, which can probably be represented in Fig. 3 by the points 1 and 1'. After relaxation, two phases are present, i.e. the MX phase and an amorphous phase (points 2 and 2'). As the composition of the MX phase is Ni75Nb~, the amorphous phase should contain more Nb. Room temperature aging causes the MX phase to change into the amorphous
40
B. X. Liu et al. / Transition from metastable crystalline to amorphous phase in Ni-Nb
phase represented by point 3. Thus the amorphous phase seen in the diffraction pattern after aging (Fig. 2(b)) can probably be represented by points 2' and 3 or somewhere in between. The exact average composition of the amorphous phase, although it has not been determined, does not affect the above discussion of the vitrification of the ion-mixed MX phase.
4. Conclusions The free energy of the Ni-Nb MX phase was calculated for the first time and included in a complete free energy diagram of the Ni-Nb system. It is believed that the relative position of the energy curve of the MX phase versus those of the amorphous and equilibrium y' phases is relevant. Firstly, the free energy curve of the MX phase cannot be below that of the 3" phase. Secondly, if the free energy curve of the MX phase was well above that of the amorphous phase (i.e. the two curves would never intersect each other), the observed phase transition would not be possible. The only possible pattern is the result of our calculation, although the accuracy must be improved in the future. On the basis of the constructed diagram, the formation of amorphous alloys and the MX phase and the phase transition from MX to amorphous can be explained satisfactorily.
Acknowledgment This study was supported in part by the National Natural Science Foundation of China.
References
1 B. X. Liu, Vacuum, 42 (1991) 75; B. X. Liu, J. R. Ding, H. B. Zhang and D. Z. Che, Phys. Status Solidi A, 128 (1991) 103; B. X. Liu, D. Z. Che, Z. J. Zhang, S. L. Lai and J. R. Ding, Phys. Status Solidi A, 128 (1991) 345. 2 B. X. Liu, Mater Lea., 5 (1987) 322. 3 J. A. Alonso and J. M. Lopez, Mater. Lett., 4 (1986) 316. 4 S. Simozar and J. A. Alonso, Phys. Status SolidiA, 81 (1984) 55. 5 J. A. Alonso, L. J. Gallego and J. M. Lopez, Philos. Mag., 58 (1988) 79. 6 B. X. Liu, Phys. Status Solidi A, 75 (1983) I(77. 7 B. X. Liu, Nucl. Instrum. Meth., Phys. Rev. B, 7/8 (1985) 547. 8 K. T.-Y. Kung, B. X. Liu and M.-A. Nicolet, Phys. Status Solidi .4, 77 (1983) 355. 9 A. K. Niessen, F. R. de Boer, P. F. de Chatel, W. C. M. Mattens and A. R. Miedema, Calphad, 7 (1983) 51. 10 A. R. Miedema and A. K. Niessen, Calphad, 7 (1983) 27. 11 A. R. Miedema, F. R. de Boer and P. F. de Boer, Z Phys. F, 3 (1983) 1558. 12 A. R. Miedema, P. F. de Chatel and F. R. de Boer, Physica B, 100 (1980) 1. 13 J. M. Lopez, J. A. Alonso and L. J. Gallego, Phys. Rev. B, 36 (1987) 3716. 14 J. M. Lopez and J. A. Alonso, Z. Naturforsch., Teil A, 40 (1985) 1199. 15 P. I. Loeff, A. W. Weeber and A. R. Miedema, Z LessCommon Met., 140 (1988) 299. 16 A.-K. Niessen and A. R. Miedema, Ber. Bunsenges. Phys. Chem., 87 (1983) 717. 17 A. K. Niessen, A. R. Miedema, F. R. de Boer and R. Boom, Physica B, 151 (1988) 401. 18 J. M. Lopez and J. A. Alonso, Phys. Status SolidiA, 76 (1983) 675; 85 (1984) 423. 19 L. J. Gallego, J. A. Somoza, J. A. Alonso and J. M. Lopez, Z Phys. F, 18 (1988) 2149. 20 D. Turnbull, Z Chem. Phys., 20 (1952) 411. 21 C. V. Thompson and F. Spaepen, Acta Metall. F, 27 (1979) 1855.
37
Thermally induced transition from metastable Ni-Nb hexagonal phase to amorphous and its thermodynamic interpretation B. X. Liu, H. Y. Bai, Z. J. Z h a n g a n d Q. L. Q i u Department of Materials Science and Engineering, Tsinghua University, Beijing, 100084 (China) (Received July 25, 1992; in final form October 12, 1992)
Abstract In the Ni-Nb system, the free energy curves were calculated for the solid solution, amorphous phase, equilibrium compound and, for the first time, a metastable crystalline (MX) phase, which was formed by ion mixing and identified to be a hexagonal structure with a stoichiometry around Ni75Nb~. In calculating the enthalpy of the MX phase, the structural characteristics and ferromagnetic effect were considered. The constructed Ni-Nb free energy diagram can explain an unusual observation, i.e. the thermally induced vitrification of the MX phase, as well as the glass-forming ability and evolution of ion-mixed amorphous alloys on annealing.
I. Introduction It is known that ion mixing (IM) can produce metastable materials with either amorphous or crystalline (MX) structure. A large number of amorphous alloys have been obtained by IM in some 70 binary metal systems [1] and several empirical models have been proposed to predict the glass-forming ability (GFA) of the metal systems [2, 3]. Thermodynamic calculations have been performed to construct the free energy diagram in order to determine the exact composition range of amorphization by comparing the energetic states of competing phases [4, 5]. However, little attention has been paid to the MX phases obtained by IM, and free energy calculations have not been reported. A structurally similar MX phase has been observed in five binary systems, i.e. Co-Au, Ti-Au, Co-Mo, Ni-Mo and Ni-Nb. These phases exhibit the h.c.p, structure and their lattice sizes are similar [6, 7]. The calculation of the free energy of the MX phase in order to construct a complete free energy diagram of the corresponding system is therefore important. The diagram must include the free energy curves of the solid solution, amorphous phase, equilibrium compound and MX phase. In this paper, we report the construction of the free energy diagram for the Ni-Nb system. The formation of the amorphous alloy and MX phase is explained and the transition from the MX to the amorphous phase on aging is described based on the calculated diagram. 0925-8388/93/$6.00
2. Method of calculation of the free energy diagram First of all, we make some assumptions for the free energy calculation of the MX phase. The Ni-Nb MX phase was formed by IM and identified by X-ray diffraction to be hexagonal with the lattice constants a=3.28 /~, c=5.22 A, c/a=1.59 and a stoichiometry around NivsNb25 [6-8]. The free energy of mixing of the MX phase is given by AGMx = AHMx - TASMx
(1)
where AH~x and ASMx are the enthalpy and entropy of mixing respectively. Since the MX phase is crystalline, ASMx can be neglected (ASMx= 0 at 0 K). The second assumption is that there are elastic and structural contributions to the enthalpy of mixing because the MX phase is unstable. It can be considered as a deformed crystalline structure containing strain energy which leads to elastic and structural terms in the enthalpy of mixing /~k/"/MX = ~ M X
c + /~t/-/MXc "1- ~ ' / M X s
(2)
where fiJ-/MXO, AJ-/ixc and ~¢/UXs are the chemical, elastic and structural contributions to the enthalpy of mixing of the MX phase. 5//MXo is due to the electron redistribution that occurs when the alloy is formed. It has been studied extensively by Miedema and coworkers [9-12] and can be written as Z~-tMXc = I~PlamPxA VA2/3fAB
(3)
where M-/ampis an amplitude concerning the magnitude of the chemical interaction, VA is the atomic volume of metal A in the alloy and lAB is a function which © 1993- Elsevier Sequoia. All rights reserved
B. X. Lm et aL / Transition from metastable crystalline to amorphous phase in Ni-Nb
38
accounts for the degree to which atoms of type A are surrounded by atoms of type B. f,,a3 is given by )cab =XB.[1 + r(XA.XB,)z]
(4)
where XB, is the atomic cell surface area concentration of metal B in the alloy, r is an empirical parameter; for a solid solution, r=0, for an amorphous phase, r = 5 , and for an equilibrium compound, r = 8 [13]. The MX phase of the Ni-Nb system is crystalline with an h.c.p, structure (as identified by X-ray diffraction) and is therefore considered as an ordered compound. Taking this into account, we consider that r = 8. M-/MX° is due to the difference in atomic volume between A and B atoms in the alloy. This term can be computed using classical elasticity theory. M-/MX, takes into account the difference in valence and crystal structure of the two elemental metals and the MX phase. It can be calculated by the formula [14, 15] AHMx. =EMx(Z) --XAE^(ZA)-XBEB(ZB)
(5)
where Z, is the average number of valence electrons per atom (for NbNi3, Z=8.75) and EMX, EA and EB are the lattice stabilities of the MX phase and the pure components respectively. The dependence of the lattice stability on Z for b.e.c., f.c.c, and h.c.p, structures has been derived by Niessen and Miedema [16]. In addition, the correction for ferromagnetic metals has been taken into account in calculating the structure term, since the Ni component is ferromagnetic [17]. According to all these considerations, the free energy of mixing of the MX phase is calculated and obtained. The free energy of mixing of a solid solution is given by
AG,= M-I,- TAS,
(6)
where AH, and AS, are the enthalpy and entropy of mixing respectively. The simplest expression for the entropy is that corresponding to an ideal solution, namely
AS, = -R(XA In XA +XB In XB)
(7)
where R is the gas constant. The enthalpy of mixing of a substitutional solid solution also contains three terms [14, 16, 18] aH, =
+ aHs.
(8)
where &H,o, M-/,, and M-/,, are the chemical, elastic and structural terms respectively. T h e free energy of mixing of the amorphous phase is given by [19]
AG. = M-I, - TAS. +X^AG~(T) +XBAG~-~(T)
(9)
where &Ha and AS. are the enthalpy and entropy of mixing of the amorphous phase. Since the elastic and structural effects can be neglected in the amorphous
phase, AH, contains only the chemical contribution AH, o and the experimental parameter r is taken to be 5. Moreover, it is reasonable to assume that ASa= A&AG~-~ is the difference in Gibbs free energy between the amorphous and crystalline phases of a pure element at room temperature. Turnbull's [20] or Thompson-Spaepen's [21] approximation is applied and we obtain = A H , ( T , - T) 7",
(10)
or
= M-If(Tf- T)2T
Td,Tf+ T)
(11)
where M-/f is the heat of fusion and T¢ is the melting temperature. Turnbull's approximation is suitable for metals of low melting point, while Thompson-Spaepen's approximation is suitable for metals of high melting point. The free energy of mixing of the equilibrium compound is given by AGor ~"Z~-/or
(12)
where M-/o, is the enthalpy of mixing. In the equilibrium compound, ASs=0 at 0 K and is therefore small at higher temperatures. Since there are no elastic and structural effects in the equilibrium compound, M-/or contains only the chemical term M-/o,~, in which r is taken to be 8; AGor is expressed by [9] aGor=aHo
(13)
Hating completed the above calculation, a free energy diagram of the Ni-Nb system was constructed and is shown in Fig. l(b) together with the corresponding equilibrium' phase diagram (Fig. l(a)).
3. Experimental results in the Ni-Nb system and relationship to the free energy diagram
We now turn to the results of the experiments performed in the Ni-Nb system and discuss them in terms of the constructed free energy diagram. Ni-Nb multilayers were prepared by electron-gun evaporation in a vacuum system. Several samples were prepared with various compositions and then irradiated with 300 or 200 keV Xe ÷ ions at room temperature to doses ranging from 3×1014 to 1.7×1016 Xe + c m - L After irradiating to certain doses, amorphous alloys were obtained as shown by the halos in the X-ray diffraction patterns and the increased sheet resistivities [8]; the composition range for IM-induced amorphization extended from 35 to 85 at.% Ni. The recrystallization
39
B. X. Liu et al. / Transition from metastable crystalline to amorphous phase in Ni-Nb
20=0
1600
P (a) 1400 Firmt Halo £
1200fl
Fig. 2. X-Ray diffraction patterns showing the MX+amor1000
(o)
I Nb
I
I
20
IIII
I
40
II I i
60
1
80
Ni
Ni at% +40
phous-o amorphous phase transformation: (a) diffraction pattern of Ni65Nb35multilayers irradiated by 300 keV xenon ions at room temperature to a dose of 5 x 10TMXe ÷ cm -2 showing a mixture of amorphous and h.c.p. MX phase with a = 0.328 nm, c = 0.522 nm and c/a = 1.59; (b) diffraction pattern of the same sample after about 1 month aging showing only amorphous phase remaining. A
bcc
~
MX(hcp) NbNi 3
-40
(b)
L
Nb
20
i
40
I
~
60
P
I
80
I
Ni
Ni at~
Fig. 1. The calculated free energy diagram of the Ni-Nb system (b) and the corresponding equilibrium phase diagram (a).
2 40
temperatures of the ion-mixed amorphous alloys were determined by thermal annealing, and the highest recrystallization temperature was 600--650 °C for an Ni55Nb45 amorphous alloy [8]. The calculated free energy diagram shows that the free energy of the amorphous phase is lower than that of the solid solution over the range 16-85 at.% Ni, and there is a lowest point at Ni53Nb47, indicating that this composition corresponds to the most stable amorphous state. The calculations are in good agreement with the experimental observations within the relevant errors involved in both calculation and experiment. Ni65Nb35 multilayered samples were irradiated to various doses with short intervals to reveal the phase evolution in the multilayers. It was found that a new MX phase of h.c.p, structure was formed together with an amorphous phase at a dose of 5X1014 Xe ÷ cm -2 (lower than the dose inducing uniform mixing and entire amorphization). Figure 2(a) shows an X-ray diffraction pattern revealing a mixture of MX phase and amorphous phase. Interestingly, after 1 month room temperature aging of the sample, the X-ray diffraction pattern showed (Fig. 2(b)) only halos, but no sharp
i
50
I
60
I
70
i
80 Ni Content
i
90
100
at%
Fig. 3. Part of the Ni-Nb free energy diagram (enlarged): A, high-energy state after atomic collision.
diffraction lines, indicating that the MX phase had transformed into the amorphous state. Figure 3 shows a partially enlarged free energy diagram, from which the formation of the MX phase and a possible path of transition from the MX to the amorphous phase can be explained. It can be observed that the free energy curves of the MX and amorphous phases intersect around the composition of 75 at.% Ni and the MX phase may have a higher free energy than that of the amorphous phase. After irradiation to 5 × 1014 Xe ÷ cm -2, the film has not been uniformly mixed and contains a range of compositions, which can probably be represented in Fig. 3 by the points 1 and 1'. After relaxation, two phases are present, i.e. the MX phase and an amorphous phase (points 2 and 2'). As the composition of the MX phase is Ni75Nb~, the amorphous phase should contain more Nb. Room temperature aging causes the MX phase to change into the amorphous
40
B. X. Liu et al. / Transition from metastable crystalline to amorphous phase in Ni-Nb
phase represented by point 3. Thus the amorphous phase seen in the diffraction pattern after aging (Fig. 2(b)) can probably be represented by points 2' and 3 or somewhere in between. The exact average composition of the amorphous phase, although it has not been determined, does not affect the above discussion of the vitrification of the ion-mixed MX phase.
4. Conclusions The free energy of the Ni-Nb MX phase was calculated for the first time and included in a complete free energy diagram of the Ni-Nb system. It is believed that the relative position of the energy curve of the MX phase versus those of the amorphous and equilibrium y' phases is relevant. Firstly, the free energy curve of the MX phase cannot be below that of the 3" phase. Secondly, if the free energy curve of the MX phase was well above that of the amorphous phase (i.e. the two curves would never intersect each other), the observed phase transition would not be possible. The only possible pattern is the result of our calculation, although the accuracy must be improved in the future. On the basis of the constructed diagram, the formation of amorphous alloys and the MX phase and the phase transition from MX to amorphous can be explained satisfactorily.
Acknowledgment This study was supported in part by the National Natural Science Foundation of China.
References
1 B. X. Liu, Vacuum, 42 (1991) 75; B. X. Liu, J. R. Ding, H. B. Zhang and D. Z. Che, Phys. Status Solidi A, 128 (1991) 103; B. X. Liu, D. Z. Che, Z. J. Zhang, S. L. Lai and J. R. Ding, Phys. Status Solidi A, 128 (1991) 345. 2 B. X. Liu, Mater Lea., 5 (1987) 322. 3 J. A. Alonso and J. M. Lopez, Mater. Lett., 4 (1986) 316. 4 S. Simozar and J. A. Alonso, Phys. Status SolidiA, 81 (1984) 55. 5 J. A. Alonso, L. J. Gallego and J. M. Lopez, Philos. Mag., 58 (1988) 79. 6 B. X. Liu, Phys. Status Solidi A, 75 (1983) I(77. 7 B. X. Liu, Nucl. Instrum. Meth., Phys. Rev. B, 7/8 (1985) 547. 8 K. T.-Y. Kung, B. X. Liu and M.-A. Nicolet, Phys. Status Solidi .4, 77 (1983) 355. 9 A. K. Niessen, F. R. de Boer, P. F. de Chatel, W. C. M. Mattens and A. R. Miedema, Calphad, 7 (1983) 51. 10 A. R. Miedema and A. K. Niessen, Calphad, 7 (1983) 27. 11 A. R. Miedema, F. R. de Boer and P. F. de Boer, Z Phys. F, 3 (1983) 1558. 12 A. R. Miedema, P. F. de Chatel and F. R. de Boer, Physica B, 100 (1980) 1. 13 J. M. Lopez, J. A. Alonso and L. J. Gallego, Phys. Rev. B, 36 (1987) 3716. 14 J. M. Lopez and J. A. Alonso, Z. Naturforsch., Teil A, 40 (1985) 1199. 15 P. I. Loeff, A. W. Weeber and A. R. Miedema, Z LessCommon Met., 140 (1988) 299. 16 A.-K. Niessen and A. R. Miedema, Ber. Bunsenges. Phys. Chem., 87 (1983) 717. 17 A. K. Niessen, A. R. Miedema, F. R. de Boer and R. Boom, Physica B, 151 (1988) 401. 18 J. M. Lopez and J. A. Alonso, Phys. Status SolidiA, 76 (1983) 675; 85 (1984) 423. 19 L. J. Gallego, J. A. Somoza, J. A. Alonso and J. M. Lopez, Z Phys. F, 18 (1988) 2149. 20 D. Turnbull, Z Chem. Phys., 20 (1952) 411. 21 C. V. Thompson and F. Spaepen, Acta Metall. F, 27 (1979) 1855.