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Model of phase formation in ion-mixed binary alloys with positive heats of formation
Journal of the Less-Common
351
MetaO, l60( 1990) 35 I-362
MODEL OF PHASE FORMATION IN ION-MIXED BINARY ALLOYS WITH POSITIVE HEATS OF FORMATION PAOLO M. OSSI Istituto di lngegneria Nucleare-CESNEF-Politecnico (Italy); cINFM di Trento, 38050 Povo-TN (Italy)
di Milano, Via Ponzio 3413-20133 Milan0
(Received October 14, I 989)
Summary The formation of amorphous or crystalline phases in 14 ion-mixed binary systems with large and positive heats of formation is interpreted by an atomistic model based on the development of collision cascades and the related bombardment-induced compositional changes.
1. Introduction Ion mixing has been used during the last 10 years to produce metastable crystalline or amorphous binary alloys. An ample range of constituent metals has been studied over compositions often extending beyond the equilibrium limits. The most impressive class of alloys in this respect are those with large and positive heats of formation AH,, which are immiscible in the solid state and have wide miscibility gaps in the liquid state. The thermodynamic and kinetic regimes not accessible by other techniques, which instead are peculiar to ion mixing, make it possible to explore metastable phase formation in such systems [l-3]. These alloys also allow meaningful tests of the ability of various empirical criteria and theoretical models to predict glass formation by ion mixing. Perhaps the most successful approach is that originally based on the “structural rule” [4], successively refined up to the definition of the maximum possible amorphization range (MPAR) parameter [S]. The evolution of an alloy toward a metastable state is analysed in terms of its properties, extracted from the equilibrium phase diagram. In this paper, a different model, based both on the physics of ion-target interaction and on the surface properties of alloys, which proved to interpret and predict correctly the formation of amorphous or crystalline phases in a large number of ion-mixed systems [6-S], is applied to several alloys with large and positive values of A Hf. 2. The model It is assumed that a dense and well-developed collision cascade is formed around the track of an incoming massive, neutral ion (Fig. 1). This is certainly true 0022-5088/90/$3.50
0 Elsevier Sequoia/Printed
in The Netherlands
352
Fig. I. Schematic diagram of the model. Drop-shaped area: collision cascade; bold solid line: cascade-matrix interface, where segregation occurs. Zigzag line: track of the ion which generates the cascade across an interface between Z and Z’ atom layers: l - displacements of Z atoms; Odisplacements of Z’ atoms.
when targets are composed of heavy (Z> 20) transition metals, as for the alloys considered. Projectile energies of several hundred thousand electronvolts and displacement energies of the order of 25 eV make it likely that matter inside the cascade experiences extreme temperature conditions, typical of a superheated liquid. The following fast energy dissipation via short-range random atomic motions quenches the cascade region with cooling rates of the order of lOI KS-‘. Thus, suitable conditions are provided to nucleate metastable-even glassyphases. It is assumed that in the alloy Z,Z’,, _X), segregation of one of the atomic species takes place at the cascade-matrix interface. Preferential sputtering and/or equilibrium high temperature segregation experiments indicate the segregant species [9]. Segregation induces a local compositional change and consequently a local alteration in the spatial electronic density. The tendency of the system to reequilibrate this alteration is represented by a charge transfer reaction. One electron (e-) is transferred from an atom of the depleted component to an atom of the segregant, according to the scheme
ZZ’
l
ifZ segregates,
(ZZ’)-{(Z+ le-)(Z’- le-)} effective alloy starting alloy
ifz’segregates,
(ZZ’)-{(Zle-)(Z’+ le-)] effective alloy starting alloy
(1)
353
pairs {(Z+ le-)(Z’le-)} and It is assumed that the atom ((Z- le-)(Z’+ le-)} are equivalent to the atom pairs formed by neutral atoms with atomic numbers (Z+ l), (Z’- 1) and (Z- l), (Z’+ 1) respectively. The energy change AE associated with the reaction in eqn. (1) is calculated using electron energies for pure isolated elements [lo]. For example, if Z’ segregates AE=AE(Z-ZAE(Z-Z-
l)+AE(Z’-Z’+ l)=
iE,(Z-
1)
(2)
1)-E,(Z)]
in,(Z - 1) + %ca AE(Z’-Z’+
l)=
{EJZ’ + 1) - E@‘)l i dZ’
+ 1) + 401
(4)
An analogous set of equations should hold for Z segregating. For a given element, E, and n, are the energy and number of valence s electrons respectively. If the elements involved in the charge transfer (both starting and effective alloys) belong to Groups IA and IIA in the periodic table, only s electrons are considered, as in eqns. (3) and (4). In all other cases, A E has a second term, with the same structure as eqns. (3) and (4) which is summed to the part due to s contributions. For elements belonging to Groups IIIA-IIB, this term consists of the difference between the energies of outer shell d electrons, whereas for atoms of Groups BIB-VIIB, the difference between energies of outer shell p electrons is used. The atom pair {(Z - l)(Z’ + l)] is considered to be a nucleus of the effective alloy with the same atomic numbers. Its segregation behaviour is compared with that of the starting alloy (ZZ’). Experimental data indicate that the segregant role coincides with whatever pair of starting and effective alloys is considered. Again following the lower scheme of eqn. ( 1), Z’ segregates into (ZZ’) and (Z’ + 1) segregates into {(Z- l)(Z’+ 1)). Such correspondence of component behaviour is extended to the starting and effective alloys also when segregation data (or theoretical previsions) are lacking. Segregant behaviour is studied by Miedema’s coordinates #* and nwa ‘P [ 1 l] . #* is proportional to the surface energy y of an element; the trend of $* over the Periodic Table follows the trend of elemental surface binding energies [ 121. The difference between component values of $* of an alloy drives segregation through A($*) = 6,1utc - KL,,, = a( Ysolutc - YWIW”t) + bfw
(5)
The term An”-’ -nA&,ve,,t includes size effects and W\= n”j W\.SOIUtC b=
0 0 2 2
N=
2 (4*-o.@ 2
ii’,‘;’
(6)
The barred quantities are averages over component values [ 131. In the present model, we consider the difference between segregant strengths in starting (st) and effective (eff) alloys, which are compared by calculating A(A#*) = A#*cfr - A$*s, = ( Ywlute- YsohcntLf - (Ywl,te - YS”I”B”1 Lt
(7)
f.c.c.-h.c.p.; a
h.c.p.-f.c.c.; a
f.c.c.-b.c.c.; a
f.c.c.-b,c.c.; a
+19
+21
+20
+15
+41
121
VI
[21
1191
1191
a
a
Au&SO; a
Aur&&
Ru,,Au&
f&s+ x,Ws c 20;c
Ag,5Wz; c
f.c.c.-f.c.c.; c
f.c.c.-b.c.c.; a
+20
[ll
Ag,,&,;
a
b.c.c.-h.c.p.; a
+4
[la1
Nb,,,Zr,,,; a
Co,+%;
+8
h.c.p.-f.c.c.; a
Struct. Rule
!I71
mall ’ )
(kJ
Reference A Hj +)
a
Startingalloy
100
100
98
98(“)
98
100
0
74
6; c
6; c
7; c
7;c
6;C
13;a
8; c
13;a
5;a
.5;a
3;c
3;c
2;c
5;a
l;c
2; c
MPAR Size Group. difference difference (> 10:a) (25:a)
Pd
Ag
cu
Au(t)
Au
Au
Ag
Nb
Au
Segr. el.
Co- leAu+ leNb+leZr- leAgf leCr- leAu + leIr - leAu + leOS- leRu - leAu+ leCu+ leW- leAg+leW- le-
Charge transfer
Ag-W
Cu-w
Ru-Au
OS-AU
Ir-Au
Ag-Cr
Zr+Nb
Co-Au
Chase transfer (Paul@)
Experimental data and theoretical predictions on glass formation in ion-mixed binary alloys with positive values of Al”i,
TABLE I
CdTa
ZnTa
TcHg
HgRe
HgOs
CdV
MoY
FeHg
Efl all.
Cd
Zn
Hg
Hg
Hg
Cd
MO
His
-0.095
-0.140
+0.210
+0.270
-26
-31
+2
+ 16
+15
+17
+0.160 +0.250
+31
+ 13
mol- ’ )
A.(AH,) (kJ
+0.10
+0.330
Segr, AE el. (eV)
h.c.p.-f.c.c.; a
f.c.c.-f.c.c.; c
+39
+14
]2,31
PI
%L;s<,Ag4,l:s,,;c
Ag,,,+&h,,,~s,);
86
100
100
100
100
100
7; c
9;c
8;c
6; c
6; c
6; c
2;c
3;c
3;c
5;a
5;a
5;a
Ag(“’
Ag
Ag
Au
Au
Ag
Ag+ leW- leAu+leW- leAu+leW- leRu-leAg+ leOs- leAg+ leAg+leRh- leAg-Rh
Ag-0s
Ag-Ru
W-Au
W-+Au
Ag-W
CdRu
ReCd
TcCd
TaHg
HgTa
TaCd
Cd
Cd
Cd
Hg
Hg
Cd
-0.160
-0.030
-0.120
-0.070
-0.070
-0.095
-12
- 14
-25
-18
-18
-26
a: amorphous. c: crystalline. In column 1 the letter (a or c) indicates the result of the mixing experiments referred to in column 2. + : heats of formation AH, of the starting alloys, calculated for the reported stoichiometry; where various compositions were used, AH, refers to the composition nearest to equiatomic. For the completely immiscible systems AuIr, AgW and AuW, heats of mixing were used. AH, of effective alloys (column 11) are calculated for equiatomic compositions *: phase diagram not available. MPAR is obtained from the reported maximum solid solubilities. In column 8, segregants in starting alloys are deduced from the predictions by different theories (which agree with each other) [ 12, 20, 2 11. For two alloys, experimental data are available (i_:ref. 3; O:ref. 22); these agree with theoretical predictions. Segregants in effective alloys are hypothetical (see text).
c
h.c.p.-f.c.c.; a
+33
]31
Ru,,,Ag,,,; c
b.c.c.-f.c.c.; a
+17
[I91
Wg,,,,,Au IU,U;c
f.c.c.-b.c.c.; a
+17
1191
A~xo:~oWZ,,.&c
b.c.c.-f.c.c.; a
+41
iI91
%.%a,; c
356
and A(An;;‘) = An$-
An;:;‘,,
When A(A#*)> 0, segregation corresponding starting alloy.
(8) is stronger
in the effective
alloy than in the
3. Results In Table 1 we report amorphous (a) and crystalline (c) alloys formed by ion mixing (column 1 ), their heats of formation (column 3), predictions by glassforming ability (GFA) criteria (columns 4-7), and details of the present model. From the table we note that the predictive ability of the listed GFA criteria, which do not take into account the physics of the amorphization process, is poor. We now consider the two major criteria, both of which refer to specific models of the amorphization process, and are based on the calculated heats of formation AH, [ 141 and on the features of the equilibrium phase diagram of the alloy [5]. Alonso’s criterion defines a limiting value of A Hf (or, equivalently, of the heat of mixing AH,,, [ 151) which separates glass-forming alloys from crystalline ones. According to this, all amorphous alloys considered here would turn crystalline on ion mixing. Such a criterion also has difficulty with systems that have slightly negative AH, values, e.g. AuCu and MoNb, which are crystalline, but predicted to turn amorphous. The criterion correctly predicts amorphization only for the class of systems with large and negative AH, values, which correspond to the presence of several intermetallics in the equilibrium diagram, a favourable factor for obtaining glassy phases easily. In Liu’s approach, the MPAR parameter defines the ease with which an alloy amorphizes: the larger the MPAR is, the easier is its amorphization. The value of MPAR is 100 (entire composition range) minus the maximum terminal solid solubilities of alloy components. The model is correct in many cases, but fails for this selection of “thermodynamically pathological” alloys, predicting a crystalline structure for NbZr (which is amorphous) as well as indicating very large MPAR values for all systems that are experimentally found to be crystalline. The remaining columns in Table 1 list segregants in starting alloys, charge transfer scheme, effective alloys, segregants in effective alloys, calculated AE values for the transition from starting to effective alloys, and calculated differences A(AH,) between heats of formation of equiatomic effective alloys and starting alloys with the experimentally found composition [ 161. Comparing columns 9 and 10, we observe that the charge transfer reaction disagrees with charge flux according to Pauling’s electronegativity concept in seven of the 14 cases considered. A E values (column 13) are always positive for amorphous alloys and always negative for crystalline alloys, as has already been found in previous works [6-81. This holds despite the crudeness of the model. Indeed, the energetics of bombardment-induced atomic interactions are included in a purely electronic and local effect, neglecting defect production-migration-recombination processes and atom
357
pair interaction with the surrounding matrix, which is assumed to be unperturbed. Use of electron energies for pure elements, although approximate, is justified by the locality of the model: a single Z atom interacts with a single Z’ atom. Positive AE values mean that charge adjustment by introducing effective alloy atom pairs increases the net energy of the system, destabilizing it. For crystalline alloys, the introduction of effective alloy atom pairs reduces system energy (AE < 0), thus helping to stabilize it.
+.i
Solvent segreg. ( tryst. alloys)
> L =
c
9-
a a --_
_----
Rtig -TcCd
a
-.i
solute (tryst.
segreg. alloys)
Solvent segreg. ( am. alloys)
At An”%,, - I. I -30
-.25
0
nd.u.+~ *
i-25
Fig. 2. Calculated relationship between A(A(*) (variation in the difference between component surface binding energies) and A(Andi;) (variation in the difference between component charge densities at the boundary of the pertinent Wigner-Seitz cell) at the transition from starting to effective alloy. 0, right-hand side: amorphous alloys; p, left-hand side: crystalline alloys.
358
The same type of qualitative conclusion is possible by examining column 14 of Table 1, which lists the differences A(AH,) between heats of formation of effective and starting alloys. Positive values of A( AH,) for amorphous alloys, as well as the negative values found for crystalline alloys, are interpreted in terms of system stabilization, confirming-from the standpoint of a global thermodynamic quantity-the conclusion about the sign of the electronic energy term A E. In Fig. 2, A(A#*) is plotted vs. A(AnLy) for all alloys. The solid line [23] separates the left-hand region where all points refer to crystalline alloys, from the right-hand region, where all points pertain to amorphous alloys. An average value N, = N, = 0.89 is used in eqn. (6). The broken horizontal line divides the regions of amorphous and crystalline alloys into subregions of solvent and solute segregation. For amorphous alloys, positive A(A#*) and A(AniF) values result when solute segregates, whereas solvent segregation coincides with negative values of both parameters. According to eqn. (7), A(A#*) ex p resses the variation in the difference between constituent surface energies y in effective and starting alloys. A(A#*) < 0 corresponds to an increment in surface atomic mobility and thus to a lowering of surface binding energy, when the transition from starting to effective alloy occurs. Many energetically equivalent, spatially uncorrelated local atomic configurations are available to the system. The fast quenching process of cascade solidification favours amorphization. Effective alloy atom pairs play the role of glassy nuclei: they are present in great numbers in amorphous alloys (solvent segregation). They also exist in crystalline alloys (solute segregation), but their density is too low, so they constitute a non-surviving fluctuation. The converse holds for positive A(A$*). Interatomic correlations are reinforced at the transition from starting to effective alloy, and they lower the surface atomic mobility as a consequence of enhanced surface binding energy. Nucleation of a crystalline phase is favoured. In this case, effective alloy atom pairs are crystallization nuclei, which drive crystal formation in alloys turning crystalline (solvent segregation). They are also present in amorphous alloys, when solute segregates, but have a negligible effect compared with amorphization. In the model, surface effects are essential for interpreting phase nucleation and stability. The presence of nucleation centres (effective alloy atom pairs) makes the interface between cascade and matrix incoherent. It is worth noting that amorphous nuclei of atomic dimensions, with compositions different from the average alloy composition, were found in various surface alloys amorphized by ion implantation [24, 251. Heterogeneous nucleation of amorphous phases under electron irradiation [26] supports the hypothesis that amorphous-crystalline nuclei are of atomic dimensions. A linear correlation not expected in principle between surface properties A(A$*) and charge transfer A(E) is reported in Fig. 3. Such regularity has already been observed 16-81. Charge transfer is the fundamental mechanism both in Miedema’s model and in the present one. It is well known that charge redistribution during alloy formation indicates strong chemical bonding, i.e. local ordering in crystals.
359
A +.2 -
; I' .+G < +.I -
O.-
-.1 _
ar~P',~-o.2el-3.lsO~E (tryst. alloys) b.2 -
-.3_
I
1
-.I5
-.I
705
0
+.I
I
I
+.2
+.3
AI (CY ‘1
Fig. 3. Calculated relationship between A(A#*) and electronic energy change AE, at the transition from starting to effective alloy. (The scales for amorphous and crystalline alloys are different.) 0, righthand side: amorphous alloys; q, left-hand side: crystalline alloys.
Turning to nucleation, if the changes suffered by an irradiated alloy can be ascribed to well-developed collision cascades, the description via starting and effective atom pairs agrees with Miedema’s approach. This means that local chemical forces strongly influence irradiation-induced amorphization. In Fig. 4, A(A#*) is plotted VS.A(AH,) for both amorphous and crystalline alloy families. The variation in alloy surface atomic mobility A(A#*) at the transi-
360 A
k.ZS -
\ \
AgRh lil q
cuw
\
AuW q EAgW \
.o-
..25
-
\
\ \
,.50AtAf*k-OA50-O.O18h(AH,b ((xystalline
alloys
:
q
)
A(A~~+o.~s~-~o~sAIAH~~
.?S -
(anorphous
-l.-
I
-40
-30
-20
- 10
alloys
: Q1
4
I
0
+10
+20
+30
*
.
+40
Fig. 4. Calculated relationship between A(A$*) and the difference between heats of formation of effective and starting alloys A( AH,). 0, full line: amorphous alloys; q, chain line: crystalline alloys.
tion from starting to effective alloy is linearly correlated to the difference between the heats of formation of effective and starting alloys. This correlation links the changes in a surface physical property of the alloy (surface binding energy) to the changes in a bulk alloy thermodynamic quantity which reflects the overall stability of that alloy. The correlation supports a recent analysis of mixing experiments, pointing out that thermodynamic forces play a fundamental role in ion mixing: indeed a
361
direct relationship exists between AHm (or AH,} and mixing efficiency 1271. In the low temperature experiments performed with the set of alloys considered, radiation-enhanced delayed diffisional processes are inhibited. Nevertheless, even if such systems are thermodynamically pathological owing to the large and positive AH[ values, the correlations in Fig. 3 show that ion mixing provides conditions which can bring into action local thermodynamic forces, which extend the compositions and ranges over which metastable alloys can be formed.
4. Conclusion The present model, which has already been successfully applied in interpreting phase formation in nearly 100 ion-mixed or ion-bombarded systems [C-8, 28-301, correctly separates glass forming from crystalline alloys and binary alloys with large and positive heats of formation. Segregation at the cascade-matrix interface is connected with local charge transfer events, and glass formation is attributed to a reduction in the difference between surface binding energies of alloy components at the transition from starting to effective alloys.
Acknowledgment This research was supported by the Italian Ministry of Education (MPI). References 1 B.-X. Liu, E. Ma, J. Li and L. J. Huang, Nucf. Znsrrum. Methods B, 19-20( 1987) 682. 2 E. Peiner and K. Kopitzki, Nucl. Znstrum. Methods B, 34 (1988) 173. 3 M. Buchgeister, W. Hiller, K. Kopitzki, G. Mertler, E. Peiner and W. Jager, Mufer. Sci. Eng. A, 215 (1989) 155. 4 B.-X. Liu, W. L. Johnson, M.-A. Nicolet and S. S. Lau, Appl. Phys. Left., 42 (1983) 45. 5 B.-X. Liu, Mater. Lett.. 5( 1987) 322. 6 P. M. Ossi, 2. Pbys. B, 69 ( 1988) 5 11. 7 P. M. Ossi, ~uuva Chim. D, 10 (1988) 395. 8 P. M. Ossi, Radial. Eff: De&c& Solids, 108 ( 1989) 6 1. 9 P.M.Ossi,Su~f:Sci.,201(1988)L519. 10 F. Herman and S. Skillman, Atomic Structure Calculations, Englewood Cliffs, NJ, 1963. I1 A. K. Niessen, F. R. de Boer, P. F. de Chattel, W. C. M. Mattens and A. R. Miedema, Calphad, 7 (1983)51. 12 J. R. Chelikowski, Surf: Sci., 139 (1984) L197. 13 J. C. Hamilton, Whys. Rev. Lett., 42 ( 1979) 989. 14 J. A. Alonso and S. Simozar, SolidState Commun., 48 (1983) 765. 15 J. A. Alonso and J. M. Lopez, Mater. Len., 4 (1986) 3 16. 16 F. R. de Boer, R. Boom, W. C. M. Mattens, A. R. Miedema and A. K. Niessen, Cohesion in Metals: Transition Metal Alloys, North-Holland, Amsterdam, 1989. 17 B. X. Liu, W. L. Johnson and M.-A. Nicolet, Nucl. Instrum. Methods, 209-210 (1983) 229. IX A. Cavalieri, E Giacomozzi, L. Guzman and P. M. Ossi, f. Phys..: Cond. Matt., I(1 989) 6685. I9 W. Hiller. M. Buchgeister, P. Eitner, K. Kopitzki, V. Lilienthal and E. Peiner, Mater. Sci. Eng. A, //5(1989) 1.51.
362 20 A.R.Miedema,Z. Merulfkd.,69(1978)455. 21 J. L. Moran-Lopez and L. M. Falicov, Whys. Rev. B, 18(1978) 2542,2549. 22 J. H. Andersen, P. J. Conn and S. G. Brandenberger, J. Cutal,, I6 (1970) 404. 23 P. M. Ossi, Z. I%y.r. B, 63( 1986) 293. 24 A. Seidel, C. A. Majid and G. Linker, Solid State Commun., 69 ( 1989) 769. 25 L. Thorn&, F. Pons, J. C. Pivin and C. Cohen, Nucl. Instrum. Methods B, I5 (1986) 269. 26 D. E. Luzzi, H. Mori, H. Fujita and M. Meshii, Acta Metall., 34 (1986) 629. 27 Y. T. Cheng, T. W. Warkman, M.-A. Nicolet and W. L. Johnson, Beam solid interactions and transient processes, Mater. Res. Sot. Symp. Proc., 74 ( 1987) 419. 28 P. M. Ossi, Mnter. Sci. Erg., %I( 1987) 55. 29 P. M. Ossi, Muter. Sci. Erg. A, if5 (1989) 107. 30 P. M. Ossi, Z. Phys. B, 77( 1989) 32 1.
351
MetaO, l60( 1990) 35 I-362
MODEL OF PHASE FORMATION IN ION-MIXED BINARY ALLOYS WITH POSITIVE HEATS OF FORMATION PAOLO M. OSSI Istituto di lngegneria Nucleare-CESNEF-Politecnico (Italy); cINFM di Trento, 38050 Povo-TN (Italy)
di Milano, Via Ponzio 3413-20133 Milan0
(Received October 14, I 989)
Summary The formation of amorphous or crystalline phases in 14 ion-mixed binary systems with large and positive heats of formation is interpreted by an atomistic model based on the development of collision cascades and the related bombardment-induced compositional changes.
1. Introduction Ion mixing has been used during the last 10 years to produce metastable crystalline or amorphous binary alloys. An ample range of constituent metals has been studied over compositions often extending beyond the equilibrium limits. The most impressive class of alloys in this respect are those with large and positive heats of formation AH,, which are immiscible in the solid state and have wide miscibility gaps in the liquid state. The thermodynamic and kinetic regimes not accessible by other techniques, which instead are peculiar to ion mixing, make it possible to explore metastable phase formation in such systems [l-3]. These alloys also allow meaningful tests of the ability of various empirical criteria and theoretical models to predict glass formation by ion mixing. Perhaps the most successful approach is that originally based on the “structural rule” [4], successively refined up to the definition of the maximum possible amorphization range (MPAR) parameter [S]. The evolution of an alloy toward a metastable state is analysed in terms of its properties, extracted from the equilibrium phase diagram. In this paper, a different model, based both on the physics of ion-target interaction and on the surface properties of alloys, which proved to interpret and predict correctly the formation of amorphous or crystalline phases in a large number of ion-mixed systems [6-S], is applied to several alloys with large and positive values of A Hf. 2. The model It is assumed that a dense and well-developed collision cascade is formed around the track of an incoming massive, neutral ion (Fig. 1). This is certainly true 0022-5088/90/$3.50
0 Elsevier Sequoia/Printed
in The Netherlands
352
Fig. I. Schematic diagram of the model. Drop-shaped area: collision cascade; bold solid line: cascade-matrix interface, where segregation occurs. Zigzag line: track of the ion which generates the cascade across an interface between Z and Z’ atom layers: l - displacements of Z atoms; Odisplacements of Z’ atoms.
when targets are composed of heavy (Z> 20) transition metals, as for the alloys considered. Projectile energies of several hundred thousand electronvolts and displacement energies of the order of 25 eV make it likely that matter inside the cascade experiences extreme temperature conditions, typical of a superheated liquid. The following fast energy dissipation via short-range random atomic motions quenches the cascade region with cooling rates of the order of lOI KS-‘. Thus, suitable conditions are provided to nucleate metastable-even glassyphases. It is assumed that in the alloy Z,Z’,, _X), segregation of one of the atomic species takes place at the cascade-matrix interface. Preferential sputtering and/or equilibrium high temperature segregation experiments indicate the segregant species [9]. Segregation induces a local compositional change and consequently a local alteration in the spatial electronic density. The tendency of the system to reequilibrate this alteration is represented by a charge transfer reaction. One electron (e-) is transferred from an atom of the depleted component to an atom of the segregant, according to the scheme
ZZ’
l
ifZ segregates,
(ZZ’)-{(Z+ le-)(Z’- le-)} effective alloy starting alloy
ifz’segregates,
(ZZ’)-{(Zle-)(Z’+ le-)] effective alloy starting alloy
(1)
353
pairs {(Z+ le-)(Z’le-)} and It is assumed that the atom ((Z- le-)(Z’+ le-)} are equivalent to the atom pairs formed by neutral atoms with atomic numbers (Z+ l), (Z’- 1) and (Z- l), (Z’+ 1) respectively. The energy change AE associated with the reaction in eqn. (1) is calculated using electron energies for pure isolated elements [lo]. For example, if Z’ segregates AE=AE(Z-ZAE(Z-Z-
l)+AE(Z’-Z’+ l)=
iE,(Z-
1)
(2)
1)-E,(Z)]
in,(Z - 1) + %ca AE(Z’-Z’+
l)=
{EJZ’ + 1) - E@‘)l i dZ’
+ 1) + 401
(4)
An analogous set of equations should hold for Z segregating. For a given element, E, and n, are the energy and number of valence s electrons respectively. If the elements involved in the charge transfer (both starting and effective alloys) belong to Groups IA and IIA in the periodic table, only s electrons are considered, as in eqns. (3) and (4). In all other cases, A E has a second term, with the same structure as eqns. (3) and (4) which is summed to the part due to s contributions. For elements belonging to Groups IIIA-IIB, this term consists of the difference between the energies of outer shell d electrons, whereas for atoms of Groups BIB-VIIB, the difference between energies of outer shell p electrons is used. The atom pair {(Z - l)(Z’ + l)] is considered to be a nucleus of the effective alloy with the same atomic numbers. Its segregation behaviour is compared with that of the starting alloy (ZZ’). Experimental data indicate that the segregant role coincides with whatever pair of starting and effective alloys is considered. Again following the lower scheme of eqn. ( 1), Z’ segregates into (ZZ’) and (Z’ + 1) segregates into {(Z- l)(Z’+ 1)). Such correspondence of component behaviour is extended to the starting and effective alloys also when segregation data (or theoretical previsions) are lacking. Segregant behaviour is studied by Miedema’s coordinates #* and nwa ‘P [ 1 l] . #* is proportional to the surface energy y of an element; the trend of $* over the Periodic Table follows the trend of elemental surface binding energies [ 121. The difference between component values of $* of an alloy drives segregation through A($*) = 6,1utc - KL,,, = a( Ysolutc - YWIW”t) + bfw
(5)
The term An”-’ -nA&,ve,,t includes size effects and W\= n”j W\.SOIUtC b=
0 0 2 2
N=
2 (4*-o.@ 2
ii’,‘;’
(6)
The barred quantities are averages over component values [ 131. In the present model, we consider the difference between segregant strengths in starting (st) and effective (eff) alloys, which are compared by calculating A(A#*) = A#*cfr - A$*s, = ( Ywlute- YsohcntLf - (Ywl,te - YS”I”B”1 Lt
(7)
f.c.c.-h.c.p.; a
h.c.p.-f.c.c.; a
f.c.c.-b.c.c.; a
f.c.c.-b,c.c.; a
+19
+21
+20
+15
+41
121
VI
[21
1191
1191
a
a
Au&SO; a
Aur&&
Ru,,Au&
f&s+ x,Ws c 20;c
Ag,5Wz; c
f.c.c.-f.c.c.; c
f.c.c.-b.c.c.; a
+20
[ll
Ag,,&,;
a
b.c.c.-h.c.p.; a
+4
[la1
Nb,,,Zr,,,; a
Co,+%;
+8
h.c.p.-f.c.c.; a
Struct. Rule
!I71
mall ’ )
(kJ
Reference A Hj +)
a
Startingalloy
100
100
98
98(“)
98
100
0
74
6; c
6; c
7; c
7;c
6;C
13;a
8; c
13;a
5;a
.5;a
3;c
3;c
2;c
5;a
l;c
2; c
MPAR Size Group. difference difference (> 10:a) (25:a)
Pd
Ag
cu
Au(t)
Au
Au
Ag
Nb
Au
Segr. el.
Co- leAu+ leNb+leZr- leAgf leCr- leAu + leIr - leAu + leOS- leRu - leAu+ leCu+ leW- leAg+leW- le-
Charge transfer
Ag-W
Cu-w
Ru-Au
OS-AU
Ir-Au
Ag-Cr
Zr+Nb
Co-Au
Chase transfer (Paul@)
Experimental data and theoretical predictions on glass formation in ion-mixed binary alloys with positive values of Al”i,
TABLE I
CdTa
ZnTa
TcHg
HgRe
HgOs
CdV
MoY
FeHg
Efl all.
Cd
Zn
Hg
Hg
Hg
Cd
MO
His
-0.095
-0.140
+0.210
+0.270
-26
-31
+2
+ 16
+15
+17
+0.160 +0.250
+31
+ 13
mol- ’ )
A.(AH,) (kJ
+0.10
+0.330
Segr, AE el. (eV)
h.c.p.-f.c.c.; a
f.c.c.-f.c.c.; c
+39
+14
]2,31
PI
%L;s<,Ag4,l:s,,;c
Ag,,,+&h,,,~s,);
86
100
100
100
100
100
7; c
9;c
8;c
6; c
6; c
6; c
2;c
3;c
3;c
5;a
5;a
5;a
Ag(“’
Ag
Ag
Au
Au
Ag
Ag+ leW- leAu+leW- leAu+leW- leRu-leAg+ leOs- leAg+ leAg+leRh- leAg-Rh
Ag-0s
Ag-Ru
W-Au
W-+Au
Ag-W
CdRu
ReCd
TcCd
TaHg
HgTa
TaCd
Cd
Cd
Cd
Hg
Hg
Cd
-0.160
-0.030
-0.120
-0.070
-0.070
-0.095
-12
- 14
-25
-18
-18
-26
a: amorphous. c: crystalline. In column 1 the letter (a or c) indicates the result of the mixing experiments referred to in column 2. + : heats of formation AH, of the starting alloys, calculated for the reported stoichiometry; where various compositions were used, AH, refers to the composition nearest to equiatomic. For the completely immiscible systems AuIr, AgW and AuW, heats of mixing were used. AH, of effective alloys (column 11) are calculated for equiatomic compositions *: phase diagram not available. MPAR is obtained from the reported maximum solid solubilities. In column 8, segregants in starting alloys are deduced from the predictions by different theories (which agree with each other) [ 12, 20, 2 11. For two alloys, experimental data are available (i_:ref. 3; O:ref. 22); these agree with theoretical predictions. Segregants in effective alloys are hypothetical (see text).
c
h.c.p.-f.c.c.; a
+33
]31
Ru,,,Ag,,,; c
b.c.c.-f.c.c.; a
+17
[I91
Wg,,,,,Au IU,U;c
f.c.c.-b.c.c.; a
+17
1191
A~xo:~oWZ,,.&c
b.c.c.-f.c.c.; a
+41
iI91
%.%a,; c
356
and A(An;;‘) = An$-
An;:;‘,,
When A(A#*)> 0, segregation corresponding starting alloy.
(8) is stronger
in the effective
alloy than in the
3. Results In Table 1 we report amorphous (a) and crystalline (c) alloys formed by ion mixing (column 1 ), their heats of formation (column 3), predictions by glassforming ability (GFA) criteria (columns 4-7), and details of the present model. From the table we note that the predictive ability of the listed GFA criteria, which do not take into account the physics of the amorphization process, is poor. We now consider the two major criteria, both of which refer to specific models of the amorphization process, and are based on the calculated heats of formation AH, [ 141 and on the features of the equilibrium phase diagram of the alloy [5]. Alonso’s criterion defines a limiting value of A Hf (or, equivalently, of the heat of mixing AH,,, [ 151) which separates glass-forming alloys from crystalline ones. According to this, all amorphous alloys considered here would turn crystalline on ion mixing. Such a criterion also has difficulty with systems that have slightly negative AH, values, e.g. AuCu and MoNb, which are crystalline, but predicted to turn amorphous. The criterion correctly predicts amorphization only for the class of systems with large and negative AH, values, which correspond to the presence of several intermetallics in the equilibrium diagram, a favourable factor for obtaining glassy phases easily. In Liu’s approach, the MPAR parameter defines the ease with which an alloy amorphizes: the larger the MPAR is, the easier is its amorphization. The value of MPAR is 100 (entire composition range) minus the maximum terminal solid solubilities of alloy components. The model is correct in many cases, but fails for this selection of “thermodynamically pathological” alloys, predicting a crystalline structure for NbZr (which is amorphous) as well as indicating very large MPAR values for all systems that are experimentally found to be crystalline. The remaining columns in Table 1 list segregants in starting alloys, charge transfer scheme, effective alloys, segregants in effective alloys, calculated AE values for the transition from starting to effective alloys, and calculated differences A(AH,) between heats of formation of equiatomic effective alloys and starting alloys with the experimentally found composition [ 161. Comparing columns 9 and 10, we observe that the charge transfer reaction disagrees with charge flux according to Pauling’s electronegativity concept in seven of the 14 cases considered. A E values (column 13) are always positive for amorphous alloys and always negative for crystalline alloys, as has already been found in previous works [6-81. This holds despite the crudeness of the model. Indeed, the energetics of bombardment-induced atomic interactions are included in a purely electronic and local effect, neglecting defect production-migration-recombination processes and atom
357
pair interaction with the surrounding matrix, which is assumed to be unperturbed. Use of electron energies for pure elements, although approximate, is justified by the locality of the model: a single Z atom interacts with a single Z’ atom. Positive AE values mean that charge adjustment by introducing effective alloy atom pairs increases the net energy of the system, destabilizing it. For crystalline alloys, the introduction of effective alloy atom pairs reduces system energy (AE < 0), thus helping to stabilize it.
+.i
Solvent segreg. ( tryst. alloys)
> L =
c
9-
a a --_
_----
Rtig -TcCd
a
-.i
solute (tryst.
segreg. alloys)
Solvent segreg. ( am. alloys)
At An”%,, - I. I -30
-.25
0
nd.u.+~ *
i-25
Fig. 2. Calculated relationship between A(A(*) (variation in the difference between component surface binding energies) and A(Andi;) (variation in the difference between component charge densities at the boundary of the pertinent Wigner-Seitz cell) at the transition from starting to effective alloy. 0, right-hand side: amorphous alloys; p, left-hand side: crystalline alloys.
358
The same type of qualitative conclusion is possible by examining column 14 of Table 1, which lists the differences A(AH,) between heats of formation of effective and starting alloys. Positive values of A( AH,) for amorphous alloys, as well as the negative values found for crystalline alloys, are interpreted in terms of system stabilization, confirming-from the standpoint of a global thermodynamic quantity-the conclusion about the sign of the electronic energy term A E. In Fig. 2, A(A#*) is plotted vs. A(AnLy) for all alloys. The solid line [23] separates the left-hand region where all points refer to crystalline alloys, from the right-hand region, where all points pertain to amorphous alloys. An average value N, = N, = 0.89 is used in eqn. (6). The broken horizontal line divides the regions of amorphous and crystalline alloys into subregions of solvent and solute segregation. For amorphous alloys, positive A(A#*) and A(AniF) values result when solute segregates, whereas solvent segregation coincides with negative values of both parameters. According to eqn. (7), A(A#*) ex p resses the variation in the difference between constituent surface energies y in effective and starting alloys. A(A#*) < 0 corresponds to an increment in surface atomic mobility and thus to a lowering of surface binding energy, when the transition from starting to effective alloy occurs. Many energetically equivalent, spatially uncorrelated local atomic configurations are available to the system. The fast quenching process of cascade solidification favours amorphization. Effective alloy atom pairs play the role of glassy nuclei: they are present in great numbers in amorphous alloys (solvent segregation). They also exist in crystalline alloys (solute segregation), but their density is too low, so they constitute a non-surviving fluctuation. The converse holds for positive A(A$*). Interatomic correlations are reinforced at the transition from starting to effective alloy, and they lower the surface atomic mobility as a consequence of enhanced surface binding energy. Nucleation of a crystalline phase is favoured. In this case, effective alloy atom pairs are crystallization nuclei, which drive crystal formation in alloys turning crystalline (solvent segregation). They are also present in amorphous alloys, when solute segregates, but have a negligible effect compared with amorphization. In the model, surface effects are essential for interpreting phase nucleation and stability. The presence of nucleation centres (effective alloy atom pairs) makes the interface between cascade and matrix incoherent. It is worth noting that amorphous nuclei of atomic dimensions, with compositions different from the average alloy composition, were found in various surface alloys amorphized by ion implantation [24, 251. Heterogeneous nucleation of amorphous phases under electron irradiation [26] supports the hypothesis that amorphous-crystalline nuclei are of atomic dimensions. A linear correlation not expected in principle between surface properties A(A$*) and charge transfer A(E) is reported in Fig. 3. Such regularity has already been observed 16-81. Charge transfer is the fundamental mechanism both in Miedema’s model and in the present one. It is well known that charge redistribution during alloy formation indicates strong chemical bonding, i.e. local ordering in crystals.
359
A +.2 -
; I' .+G < +.I -
O.-
-.1 _
ar~P',~-o.2el-3.lsO~E (tryst. alloys) b.2 -
-.3_
I
1
-.I5
-.I
705
0
+.I
I
I
+.2
+.3
AI (CY ‘1
Fig. 3. Calculated relationship between A(A#*) and electronic energy change AE, at the transition from starting to effective alloy. (The scales for amorphous and crystalline alloys are different.) 0, righthand side: amorphous alloys; q, left-hand side: crystalline alloys.
Turning to nucleation, if the changes suffered by an irradiated alloy can be ascribed to well-developed collision cascades, the description via starting and effective atom pairs agrees with Miedema’s approach. This means that local chemical forces strongly influence irradiation-induced amorphization. In Fig. 4, A(A#*) is plotted VS.A(AH,) for both amorphous and crystalline alloy families. The variation in alloy surface atomic mobility A(A#*) at the transi-
360 A
k.ZS -
\ \
AgRh lil q
cuw
\
AuW q EAgW \
.o-
..25
-
\
\ \
,.50AtAf*k-OA50-O.O18h(AH,b ((xystalline
alloys
:
q
)
A(A~~+o.~s~-~o~sAIAH~~
.?S -
(anorphous
-l.-
I
-40
-30
-20
- 10
alloys
: Q1
4
I
0
+10
+20
+30
*
.
+40
Fig. 4. Calculated relationship between A(A$*) and the difference between heats of formation of effective and starting alloys A( AH,). 0, full line: amorphous alloys; q, chain line: crystalline alloys.
tion from starting to effective alloy is linearly correlated to the difference between the heats of formation of effective and starting alloys. This correlation links the changes in a surface physical property of the alloy (surface binding energy) to the changes in a bulk alloy thermodynamic quantity which reflects the overall stability of that alloy. The correlation supports a recent analysis of mixing experiments, pointing out that thermodynamic forces play a fundamental role in ion mixing: indeed a
361
direct relationship exists between AHm (or AH,} and mixing efficiency 1271. In the low temperature experiments performed with the set of alloys considered, radiation-enhanced delayed diffisional processes are inhibited. Nevertheless, even if such systems are thermodynamically pathological owing to the large and positive AH[ values, the correlations in Fig. 3 show that ion mixing provides conditions which can bring into action local thermodynamic forces, which extend the compositions and ranges over which metastable alloys can be formed.
4. Conclusion The present model, which has already been successfully applied in interpreting phase formation in nearly 100 ion-mixed or ion-bombarded systems [C-8, 28-301, correctly separates glass forming from crystalline alloys and binary alloys with large and positive heats of formation. Segregation at the cascade-matrix interface is connected with local charge transfer events, and glass formation is attributed to a reduction in the difference between surface binding energies of alloy components at the transition from starting to effective alloys.
Acknowledgment This research was supported by the Italian Ministry of Education (MPI). References 1 B.-X. Liu, E. Ma, J. Li and L. J. Huang, Nucf. Znsrrum. Methods B, 19-20( 1987) 682. 2 E. Peiner and K. Kopitzki, Nucl. Znstrum. Methods B, 34 (1988) 173. 3 M. Buchgeister, W. Hiller, K. Kopitzki, G. Mertler, E. Peiner and W. Jager, Mufer. Sci. Eng. A, 215 (1989) 155. 4 B.-X. Liu, W. L. Johnson, M.-A. Nicolet and S. S. Lau, Appl. Phys. Left., 42 (1983) 45. 5 B.-X. Liu, Mater. Lett.. 5( 1987) 322. 6 P. M. Ossi, 2. Pbys. B, 69 ( 1988) 5 11. 7 P. M. Ossi, ~uuva Chim. D, 10 (1988) 395. 8 P. M. Ossi, Radial. Eff: De&c& Solids, 108 ( 1989) 6 1. 9 P.M.Ossi,Su~f:Sci.,201(1988)L519. 10 F. Herman and S. Skillman, Atomic Structure Calculations, Englewood Cliffs, NJ, 1963. I1 A. K. Niessen, F. R. de Boer, P. F. de Chattel, W. C. M. Mattens and A. R. Miedema, Calphad, 7 (1983)51. 12 J. R. Chelikowski, Surf: Sci., 139 (1984) L197. 13 J. C. Hamilton, Whys. Rev. Lett., 42 ( 1979) 989. 14 J. A. Alonso and S. Simozar, SolidState Commun., 48 (1983) 765. 15 J. A. Alonso and J. M. Lopez, Mater. Len., 4 (1986) 3 16. 16 F. R. de Boer, R. Boom, W. C. M. Mattens, A. R. Miedema and A. K. Niessen, Cohesion in Metals: Transition Metal Alloys, North-Holland, Amsterdam, 1989. 17 B. X. Liu, W. L. Johnson and M.-A. Nicolet, Nucl. Instrum. Methods, 209-210 (1983) 229. IX A. Cavalieri, E Giacomozzi, L. Guzman and P. M. Ossi, f. Phys..: Cond. Matt., I(1 989) 6685. I9 W. Hiller. M. Buchgeister, P. Eitner, K. Kopitzki, V. Lilienthal and E. Peiner, Mater. Sci. Eng. A, //5(1989) 1.51.
362 20 A.R.Miedema,Z. Merulfkd.,69(1978)455. 21 J. L. Moran-Lopez and L. M. Falicov, Whys. Rev. B, 18(1978) 2542,2549. 22 J. H. Andersen, P. J. Conn and S. G. Brandenberger, J. Cutal,, I6 (1970) 404. 23 P. M. Ossi, Z. I%y.r. B, 63( 1986) 293. 24 A. Seidel, C. A. Majid and G. Linker, Solid State Commun., 69 ( 1989) 769. 25 L. Thorn&, F. Pons, J. C. Pivin and C. Cohen, Nucl. Instrum. Methods B, I5 (1986) 269. 26 D. E. Luzzi, H. Mori, H. Fujita and M. Meshii, Acta Metall., 34 (1986) 629. 27 Y. T. Cheng, T. W. Warkman, M.-A. Nicolet and W. L. Johnson, Beam solid interactions and transient processes, Mater. Res. Sot. Symp. Proc., 74 ( 1987) 419. 28 P. M. Ossi, Mnter. Sci. Erg., %I( 1987) 55. 29 P. M. Ossi, Muter. Sci. Erg. A, if5 (1989) 107. 30 P. M. Ossi, Z. Phys. B, 77( 1989) 32 1.