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Stabilities of binary intermediate phases in transition metal alloy systems
Journal of the Less-Common Merals, 35 (1974) 285-292 (‘8 Elsevier Sequoia S.A., Lausanne Printed in The Netherlands
STABILITIES OF BINARY METAL ALLOY SYSTEMS
INTERMEDIATE
285
PHASES
IN
TRANSITION
G. V. RAYNOR Depcwtnwnt of Physicul Mrrullurgy Birmingham BI5 2TT (Ct. Britain) (Received
October
and Science
of’ Materials,
University
of Birminghum,
Edghuston,
8, 1973)
SUMMARY
The stabilities of the p, x and Cr,Si phases which occur in transition metal alloy systems have been assessed from their temperatures of formation, where sufficient constitutional information exists. The results are assessed with respect to the influences of the atomic size factor, the difference between the group numbers of the components and the electronegativity difference between the components. The three types of intermediate phase show interesting differences. In particular, the evidence suggests that, although they share the same stoichiometry and crystal structure, the Cr,Si phases (A,B phases) in which the B component is a transition metal behave differently from those in which the B component is a non-transition metal, and should possibly be treated as a different class of intermediate phase.
I. INTRODUCTION
In many alloy systems in which a transition metal forms one or both components, it is observed that intermediate phases tend to occur with the same, or similar, crystal structures in different systems. In many cases, the sequence of phases observed, as the number per atom of electrons outside closed shells increases, is as follows: b.c.c. solid solution
+ Cr,Si
--+ g + p
-+ x -+ c.p. hexagonal
-+ f.c.c. solid solution.
In a given system one or more of the phases in this sequence may not occur, but the order of occurrence is maintained with increasing electron concentration. These phases have been briefly discussed by Hume-Rothery, Smallman and Haworth’, and at greater length by Nevitt2 and by Sinha3. These accounts have concentrated on the factors which affect the occurrence and approximate compositions of the individual phases, but have paid little attention to the stabilities of the phases in terms of the temperatures at which they form, either from the liquid or in the solid state. Recently, the melting points and compositions of many of the cr phases were discussed4. For purposes of comparison,
G. V. RAYNOR
an index of stability, I, was defined such that, for a system P-Q, component Q is the higher melting:
in which
I = lo4 T,/looT,+(z---T,)x,
where T, and Tq are the melting points of the components in “K, T, is the maximum temperature in “K at which the 0 phase is stable, and x is the mean composition of the phase in at.% of Q. This is equivalent to expressing the melting point, or temperature of maximum stability of the phase, as a percentage of the temperature characteristic of composition x on the linear interpolation between the melting points of the components. It was concluded that the value of the stability index, I, for the o phases depended in a relatively systematic manner on atomic size factor relationships, and that important influences were exerted by the group numbers of the components and the nature of the B component (a metal of Group VIIA or VIII of the Periodic Table). It appeared of interest, therefore, to examine the stabilities of the Cr,Si, p and x phases in a similar manner, and the present communication summarises the main results of such a study. II. PROCEDURE.
RESULTS
AND DISCUSSION
Information with regard to the compositions of the Cr,Si, p and x phases, and the temperatures at which they are formed, either from the liquid (congruently or by a peritectic reaction) or peritectoidally in the solid state, was sought from the compilations of alloy equilibrium data by Hansen and Anderkos, Elliott6 and Shunk7, and, where appropriate, from original publications. The stability indices were calculated and, as previously4, examined with particular reference to atomic size factors and the differences NB-NA between the group numbers of the components of the phases. In addition the influence of the electronegativity difference between the components was studied. The crystal structures of the p, x and Cr,Si phases are of varying degrees of complexity, but all involve high co-ordination numbers of 12 and above. Consequently, it has been considered better to assess size factors in terms of the Goldschmidt atomic diameters’ corresponding to co-ordination number 12. The atomic size factor values used in the diagrams of this communication are thus the differences dg-~&, expressed as a percentage of dA, The group numbers involved in A$-N’ are defined as the numbers of electrons outside the closed shells of the preceeding inert gas elements in the Periodic Table. The assessment of the electronegativity difference between the components forming a given intermediate phase is a matter of some difficulty. The scale of electronegativities published by Gordy’, though of wide application, contains no values for the important elements of Group VIII of the Periodic Table. Recently, however, a scale of electronegativities based on somewhat different considerations has been published by Miedema’. For elements contained in both lists there is close and satisfactory correlation. In the present work the scale due to Miedema has been chosen, and electronegativity valnes for silicon and germanium, which are not included, have been estimated by graphical comparison of the two scales.
STABILITIES
OF BINARY
INTERMEDIATE
287
PHASES
(a) The p phases
The crystal structure adopted by the p phases is based on the composition A&, where the A component is niobium, molybdenum, tantalum or tungsten, and the B component is iron, cobalt or nickel. The rhombohedral unit cell contains 13 atoms; the smaller (B) atoms are surrounded by twelve atoms in an icosahedral arrangement, while co-ordination numbers around the larger atoms are 14, 15 and 16. Twelve examples are known but sufficient information exists for only eight.. Examination of the available information indicates that the difference between the group numbers of the components N&i” exerts little influence on the stability index, I (Fig. l(a)). The values of I occupy a relatively narrow band of values between 78.6 (MO-Fe) and 71.4 (Nb-Ni), except for the ~1phase in the TaaFe system, for which the peritectic temperature at which the p phase is formed is somewhat uncertain. According to Burlakov and Kogan”, metallographic evidence shows that the phase TaFe is formed peritectically at some temperature near 1400°C and no closer designation is possible.
Fig. 1. Stability
index, I, plottld
I 80-
MO-Fe
a
b,
against
N&V,, for (a) the p phases and (b) the x phases.
MO-CO ‘0
NbdCo
W-,O,\o,
Ta-Nig
70-
w-co \
Mo-Ni
-
O\ Ta -Fe?
60loo-
b
Ti-Re
Nb_~-pG”’
go-
--ifc?RT
TZJ-R.2 -
/
-oZr-Re
,072
m-
/ AI-ReO
/
I
I
I
I
12
14
16
Fig. 2. Stability index, I, plotted against ponent, using Goldschmidt atomic diameters
modulus of size factor with respect to for (a) the 11phavq nnd fhj the x nhases.
the
A com-
288
G. V. RAYNOR
Figure 2(a) shows the calculated values of I plotted against the size factor for the p phases. The indication is that for Nn-NA values of 2 and 3 an increase in the size factor corresponds with a decrease in the stability index. There is also a slight general tendency for an overall decrease in I as the size factor increases. It may be noted that the p phase in the Ta-Fe system corresponds to the largest size factor in the group for which NB-NA is equal to 3; it may be partly for this reason that the corresponding point falls low in Fig. l(a). In Fig. 3(a) the stability index is plotted against the electronegativity difference between the components. The effect of an increase in this difference is slight and unsystematic, but the diagram suggests a tendency for the stability index to decrease.
6o0 I
/
1,
Electronegativity
Fig. 3. Stability 1 phases.
index.
2I
3 1
difference
I, plotted
against
electronegativity
difference
for (a) the
The clearest indication from Figs. l(a), 2(a) and 3(a) is that Nn-NA value, increasing size factor leads to a decrease in 1.
and (b) the
for a given
(6) The x phases The crystal structure of the x phases is that of a-Mn. The A component is from Group IIIA, IVA, VA or VIA of the Periodic Table and the B metal is a transition metal of Group VIIA or VIII. Some seventeen phases are known; according to Hume-Rothery’ they are characterised by electron: atom ratios of 6.2-7.0. The cubic unit cell contains 58 atoms. Of these, 24 have co-ordination 12 (icosahedral packing), 24 have co-ordination 13, and 10 are surrounded by polyhedra of 16 atoms. Figure l(b) shows the stability index plotted against Nn-NA for the x phases for which information is available. Although there is a range of I values for each value of Na-NA, the diagram suggests clearly that the stability of the x phases increases as the value of NB-NA increases from 1 to 3. The available information is insufficient to determine trends at higher NB-NA values. These results contrast with those for the /J phases. As shown in Fig. 2(b), the index of stability for the x phases tends to increase with increasing size factor, irrespective of the value of Na-NA. This is
STABILITIES OF BINARY INTERMEDIATE
PHASES
289
the reverse of the trend for the p phases. A similar reversal of behaviour is indicated by Fig. 3(b), which shows that there is a general tendency for the stability index to increase as the electronegativity difference between the components increases, although ranges of stability exist at a given electronegativity difference. In Fig. 2(b) the points for the Ti-Re and Cr-Mn x phases (size factor approximately 6) fall, respectively, above and below the general trend of variation of I with size factor. The data summarised in Fig. 3(b) suggest that the TiiRe x phase is stabilised by a high value of the electronegativity difference, while the reverse is true for the Cr-Mn phase. In general, the variation of I with size factor and electronegativity difference between components for the x phases is not dissimilar to the behaviour of conventional electron compounds, and supports previous suggestions’ of the importance of the electron:atom ratio in the formation of these phases. (c)
The Cr,Si
phases
A large number of phases with the crystal structure of Cr,Si are known to exist, although reliable constitutional information does not exist for all. The composition is almost invariably A,B, where component A is a transitional metal from Group IV, V, or VI of the Periodic Table and B is either a transition metal of Group VIII or a non-transitional metal. It has been pointed out that the ratio of the sizes of the component atoms in the Cr,Si phases does not differ greatly from unity. The crystal structure is cubic and the unit cell contains eight atoms. The B atoms have twelve equidistant A neighbours at a distance of J5aJ4 where a is the lattice spacing. The A atoms, however, have four B neighbours and ten A neighbours. There are two sets of A-A distances (a/2 and J6a/4), and the structure is remarkable in that one of these distances is considerably shorter than the other. The constitutional data available were initially analysed in the same way as for the p and x phases. No systematic variation of the stability index with NR-NA could be demonstrated; it was, however, immediately apparent that the range of stability index for positive NR-NA values (B = transition metal of Group VIII) was significantly lower than that for negative NB-NA values. Similarly, though there are indications of systematic variation of I with both electronegativity difference and size factor, the overall tendency of phases with a transition metal as B component to correspond with somewhat low I values caused a wide spread of 1 for a given value of either. The preliminary work suggested strongly that, though sharing the same stoichiometry and crystal structure, phases with a transition metal as the B component behaved differently from the other Cr,Si phases in relation to the size factor and electronegativity difference characteristic of the particular alloy systems in which the phases occur. This is emphasised in Fig. 4, where the dependence of the stability index, I, on the size factor is plotted for both types of phase. In the case of non-transitional B components (Fig. 4(a)) there is a clear tendency for the highest I. values to occur for the lower size factors, and the concentration of high values in the region of zero size factor is significant. In the case of Zr,Au, the information
290
G. V. RAYNOR
Nb-Ga
b
Nb-Ge
1 90 Ti_Ir Nb-lL oz-oo-
Nb-Pt
Ti-Pt
’
0, V-Ni
m-
cr-Pto
~-W-L-
8MO-OS
b
---__ ---
2
4
Fig. 4. Stability index, I, plotted against Goldschmidt atomic diameters for Cr,Si (b) transition metal B components.
6
+
8
the size factor with respect phases with (a) non-transition
to the A component, metal B components
using and
given by Shunk’ suggests that the temperature of formation is not below 1100°C but may be higher. For Nb,Ge, a range of homogeneity in the solid state has been observed at 1600°C and the temperature of formation must be above this. The appropriate points in Fig. 4(a) have therefore been distinguished by upward pointing arrows. The position of the point for Nb,Sn and the range of I values for size factors of zero to -2 are referred to below in connection with Fig. 5.
90-
Cr-Pt
Nb-Pt
o-----_
Ti-Pt
---e----Mo-Ir~
Nb-Ir
23
MO-05
so-
b
0 cr.05
70-
v-coo
60N&h cr-RUO
Xl-
I 0
0.5 Electronegativity
1.0
1.5 difference
2.0
Fig. 5. Stability index, f, plotted against electronegativity difference transition metal B components and (b) transition metal B components.
for Cr,Si
phases
with (a) non-
STABILITIES OF BINARY INTERMEDIATE
PHASES
291
As shown in Fig. 4(b) the dependence of I upon size factor is quite different from that in Fig. 4(a); for size factors exceeding that of Nb,Ir (- 7.86) the stability index drops very sharply, whereas the variation is not marked between size factor values from -7.86 to zero. The data are insufficiently critical to define the general trend of I for positive size factor values. Figures 5(a) and (b) show I plotted as a function of the electronegativity difference between the components. The behaviour of phases with non-transition metal and transition metal B components is again quite different. Though in Fig. 5(a) there is a range of I values for a given electronegativity difference, the range is shifted towards lower values as the electronegativity difference increases. It is particularly to be noted that the phase Nb,Sn, which has a high index in spite of a relatively high size factor, corresponds to a negligible electronegativity difference between components, while the progressively decreasing I values in Fig. 4(a) for V,Ga, Zr,Sn and Ti,Au correspond with progressively increasing electronegativity difference. The behaviour of the phase Mo,Ge is not as yet understood. By contrast, the phases for which component B is a transition metal appear to be relatively insensitive to electronegativity differences between values of 1 and 2, but to be unable to form at lower values. It is possible that the low stability index values for Cr,Ru and Cr,Os, in spite of apparently favourable size factors, are due to unfavourable electronegativity differences between the components. It is for this reason that the line approximately representing the dependence of I on the size factor between values for the latter of -8 and +8 has been drawn as shown in Fig. 4(b). The abnormally low point for Nb,Rh in Fig. 5(b) may be attributable to the high size factor value for this phase (Fig. 4(b)). F’g 1 ures 4 and 5 taken together reinforce the impression that different influences are involved in the relative stabilities of the Cr,Si phases for which the B component is, respectively, a transition metal and a nontransition metal. The highest stability indices for the cases where B is a nontransition metal occur for low size-factors and low degrees of electrochemical interaction, suggesting that these two factors predominate. On the other hand, except at high (negative) size factors the stability of the phases with a transition metal B component is relatively insensitive to the electronegativity difference between the components. This in turn suggests that the transition metal clorbitals may be adopting a specific role in the binding forces and hence in the stability index of these phases. It should also be noted that the phases in Fig. 5(b) with the lower values of I (Mo,Os, Cr,Os, V&o, Nb,Rh and Cr,Ru) are all formed in the solid state. In Fig. 5(a) only Zr,Sn is formed in the solid state; the value of I is, nevertheless, not abnormally low. The three classes of intermediate phases occurring in transition metal alloy systems discussed in this communication show interesting differences with regard to the dependence of their stabilities on the more usually considered alloying factors. The Cr,Si phases in which a transition metal forms the B component appear to be in a class by themselves. With regard to the remaining phases, increasing size factor leads to a decrease in the stability index, I, for the Cr,Si phases with non-transitional B components, a decrease in I for p phases with specific NB-NA values, but an increase in I for the x phases. Increasing electronegativity difference leads to a decrease in the I value for Cr,Si phases with
292
G. V. RAYNOR
non-transitional B components, is without marked effect on the p phases but increases the I values for the x phases. Only in the case of the x phases does the NB-NA value appear to have any appreciable influence.
REFERENCES 1 W. Hume-Rothery, R. E. Smallman and C. W. Haworth, The Structure of Metals and Alloys, Monograph and Report Series No. I, Metals and Metallurgy Trust, London, 1969, pp. 239-257. 2 M. V. Nevitt, in J. H. Westbrook (ed.), Intermetallic Compounds, Wiley, New York, 1967, pp. 217-229. 3 A. K. Sinha, Progr. Mater. Sci., 15 (1972) 79. 4 G. V. Raynor, J. Less-Common Metals, 29 (1972) 333. 5 M. Hansen and K. Anderko, Constitution of Binary Alloys, McGraw-Hill, New York, 1958. 6 R. P. Elliott, Constitution of Binary Alloys, First Suppl., McGraw-Hill, New York, 1965. 7 F. A. Shunk, Constitution of Binary Alloys, Second Suppl., McGraw-Hill, New York, 1969. 8 W. Gordy, Phys. Rev., 69 (1946) 604. 9 A. R. Miedema, J. Less-Common Metals, 32 (1973) 117. 10 V. D. Burlakov and V. S. Kogan, Phys. Metal. Metallogr. (USSR), 7 (1959) 67.
STABILITIES OF BINARY METAL ALLOY SYSTEMS
INTERMEDIATE
285
PHASES
IN
TRANSITION
G. V. RAYNOR Depcwtnwnt of Physicul Mrrullurgy Birmingham BI5 2TT (Ct. Britain) (Received
October
and Science
of’ Materials,
University
of Birminghum,
Edghuston,
8, 1973)
SUMMARY
The stabilities of the p, x and Cr,Si phases which occur in transition metal alloy systems have been assessed from their temperatures of formation, where sufficient constitutional information exists. The results are assessed with respect to the influences of the atomic size factor, the difference between the group numbers of the components and the electronegativity difference between the components. The three types of intermediate phase show interesting differences. In particular, the evidence suggests that, although they share the same stoichiometry and crystal structure, the Cr,Si phases (A,B phases) in which the B component is a transition metal behave differently from those in which the B component is a non-transition metal, and should possibly be treated as a different class of intermediate phase.
I. INTRODUCTION
In many alloy systems in which a transition metal forms one or both components, it is observed that intermediate phases tend to occur with the same, or similar, crystal structures in different systems. In many cases, the sequence of phases observed, as the number per atom of electrons outside closed shells increases, is as follows: b.c.c. solid solution
+ Cr,Si
--+ g + p
-+ x -+ c.p. hexagonal
-+ f.c.c. solid solution.
In a given system one or more of the phases in this sequence may not occur, but the order of occurrence is maintained with increasing electron concentration. These phases have been briefly discussed by Hume-Rothery, Smallman and Haworth’, and at greater length by Nevitt2 and by Sinha3. These accounts have concentrated on the factors which affect the occurrence and approximate compositions of the individual phases, but have paid little attention to the stabilities of the phases in terms of the temperatures at which they form, either from the liquid or in the solid state. Recently, the melting points and compositions of many of the cr phases were discussed4. For purposes of comparison,
G. V. RAYNOR
an index of stability, I, was defined such that, for a system P-Q, component Q is the higher melting:
in which
I = lo4 T,/looT,+(z---T,)x,
where T, and Tq are the melting points of the components in “K, T, is the maximum temperature in “K at which the 0 phase is stable, and x is the mean composition of the phase in at.% of Q. This is equivalent to expressing the melting point, or temperature of maximum stability of the phase, as a percentage of the temperature characteristic of composition x on the linear interpolation between the melting points of the components. It was concluded that the value of the stability index, I, for the o phases depended in a relatively systematic manner on atomic size factor relationships, and that important influences were exerted by the group numbers of the components and the nature of the B component (a metal of Group VIIA or VIII of the Periodic Table). It appeared of interest, therefore, to examine the stabilities of the Cr,Si, p and x phases in a similar manner, and the present communication summarises the main results of such a study. II. PROCEDURE.
RESULTS
AND DISCUSSION
Information with regard to the compositions of the Cr,Si, p and x phases, and the temperatures at which they are formed, either from the liquid (congruently or by a peritectic reaction) or peritectoidally in the solid state, was sought from the compilations of alloy equilibrium data by Hansen and Anderkos, Elliott6 and Shunk7, and, where appropriate, from original publications. The stability indices were calculated and, as previously4, examined with particular reference to atomic size factors and the differences NB-NA between the group numbers of the components of the phases. In addition the influence of the electronegativity difference between the components was studied. The crystal structures of the p, x and Cr,Si phases are of varying degrees of complexity, but all involve high co-ordination numbers of 12 and above. Consequently, it has been considered better to assess size factors in terms of the Goldschmidt atomic diameters’ corresponding to co-ordination number 12. The atomic size factor values used in the diagrams of this communication are thus the differences dg-~&, expressed as a percentage of dA, The group numbers involved in A$-N’ are defined as the numbers of electrons outside the closed shells of the preceeding inert gas elements in the Periodic Table. The assessment of the electronegativity difference between the components forming a given intermediate phase is a matter of some difficulty. The scale of electronegativities published by Gordy’, though of wide application, contains no values for the important elements of Group VIII of the Periodic Table. Recently, however, a scale of electronegativities based on somewhat different considerations has been published by Miedema’. For elements contained in both lists there is close and satisfactory correlation. In the present work the scale due to Miedema has been chosen, and electronegativity valnes for silicon and germanium, which are not included, have been estimated by graphical comparison of the two scales.
STABILITIES
OF BINARY
INTERMEDIATE
287
PHASES
(a) The p phases
The crystal structure adopted by the p phases is based on the composition A&, where the A component is niobium, molybdenum, tantalum or tungsten, and the B component is iron, cobalt or nickel. The rhombohedral unit cell contains 13 atoms; the smaller (B) atoms are surrounded by twelve atoms in an icosahedral arrangement, while co-ordination numbers around the larger atoms are 14, 15 and 16. Twelve examples are known but sufficient information exists for only eight.. Examination of the available information indicates that the difference between the group numbers of the components N&i” exerts little influence on the stability index, I (Fig. l(a)). The values of I occupy a relatively narrow band of values between 78.6 (MO-Fe) and 71.4 (Nb-Ni), except for the ~1phase in the TaaFe system, for which the peritectic temperature at which the p phase is formed is somewhat uncertain. According to Burlakov and Kogan”, metallographic evidence shows that the phase TaFe is formed peritectically at some temperature near 1400°C and no closer designation is possible.
Fig. 1. Stability
index, I, plottld
I 80-
MO-Fe
a
b,
against
N&V,, for (a) the p phases and (b) the x phases.
MO-CO ‘0
NbdCo
W-,O,\o,
Ta-Nig
70-
w-co \
Mo-Ni
-
O\ Ta -Fe?
60loo-
b
Ti-Re
Nb_~-pG”’
go-
--ifc?RT
TZJ-R.2 -
/
-oZr-Re
,072
m-
/ AI-ReO
/
I
I
I
I
12
14
16
Fig. 2. Stability index, I, plotted against ponent, using Goldschmidt atomic diameters
modulus of size factor with respect to for (a) the 11phavq nnd fhj the x nhases.
the
A com-
288
G. V. RAYNOR
Figure 2(a) shows the calculated values of I plotted against the size factor for the p phases. The indication is that for Nn-NA values of 2 and 3 an increase in the size factor corresponds with a decrease in the stability index. There is also a slight general tendency for an overall decrease in I as the size factor increases. It may be noted that the p phase in the Ta-Fe system corresponds to the largest size factor in the group for which NB-NA is equal to 3; it may be partly for this reason that the corresponding point falls low in Fig. l(a). In Fig. 3(a) the stability index is plotted against the electronegativity difference between the components. The effect of an increase in this difference is slight and unsystematic, but the diagram suggests a tendency for the stability index to decrease.
6o0 I
/
1,
Electronegativity
Fig. 3. Stability 1 phases.
index.
2I
3 1
difference
I, plotted
against
electronegativity
difference
for (a) the
The clearest indication from Figs. l(a), 2(a) and 3(a) is that Nn-NA value, increasing size factor leads to a decrease in 1.
and (b) the
for a given
(6) The x phases The crystal structure of the x phases is that of a-Mn. The A component is from Group IIIA, IVA, VA or VIA of the Periodic Table and the B metal is a transition metal of Group VIIA or VIII. Some seventeen phases are known; according to Hume-Rothery’ they are characterised by electron: atom ratios of 6.2-7.0. The cubic unit cell contains 58 atoms. Of these, 24 have co-ordination 12 (icosahedral packing), 24 have co-ordination 13, and 10 are surrounded by polyhedra of 16 atoms. Figure l(b) shows the stability index plotted against Nn-NA for the x phases for which information is available. Although there is a range of I values for each value of Na-NA, the diagram suggests clearly that the stability of the x phases increases as the value of NB-NA increases from 1 to 3. The available information is insufficient to determine trends at higher NB-NA values. These results contrast with those for the /J phases. As shown in Fig. 2(b), the index of stability for the x phases tends to increase with increasing size factor, irrespective of the value of Na-NA. This is
STABILITIES OF BINARY INTERMEDIATE
PHASES
289
the reverse of the trend for the p phases. A similar reversal of behaviour is indicated by Fig. 3(b), which shows that there is a general tendency for the stability index to increase as the electronegativity difference between the components increases, although ranges of stability exist at a given electronegativity difference. In Fig. 2(b) the points for the Ti-Re and Cr-Mn x phases (size factor approximately 6) fall, respectively, above and below the general trend of variation of I with size factor. The data summarised in Fig. 3(b) suggest that the TiiRe x phase is stabilised by a high value of the electronegativity difference, while the reverse is true for the Cr-Mn phase. In general, the variation of I with size factor and electronegativity difference between components for the x phases is not dissimilar to the behaviour of conventional electron compounds, and supports previous suggestions’ of the importance of the electron:atom ratio in the formation of these phases. (c)
The Cr,Si
phases
A large number of phases with the crystal structure of Cr,Si are known to exist, although reliable constitutional information does not exist for all. The composition is almost invariably A,B, where component A is a transitional metal from Group IV, V, or VI of the Periodic Table and B is either a transition metal of Group VIII or a non-transitional metal. It has been pointed out that the ratio of the sizes of the component atoms in the Cr,Si phases does not differ greatly from unity. The crystal structure is cubic and the unit cell contains eight atoms. The B atoms have twelve equidistant A neighbours at a distance of J5aJ4 where a is the lattice spacing. The A atoms, however, have four B neighbours and ten A neighbours. There are two sets of A-A distances (a/2 and J6a/4), and the structure is remarkable in that one of these distances is considerably shorter than the other. The constitutional data available were initially analysed in the same way as for the p and x phases. No systematic variation of the stability index with NR-NA could be demonstrated; it was, however, immediately apparent that the range of stability index for positive NR-NA values (B = transition metal of Group VIII) was significantly lower than that for negative NB-NA values. Similarly, though there are indications of systematic variation of I with both electronegativity difference and size factor, the overall tendency of phases with a transition metal as B component to correspond with somewhat low I values caused a wide spread of 1 for a given value of either. The preliminary work suggested strongly that, though sharing the same stoichiometry and crystal structure, phases with a transition metal as the B component behaved differently from the other Cr,Si phases in relation to the size factor and electronegativity difference characteristic of the particular alloy systems in which the phases occur. This is emphasised in Fig. 4, where the dependence of the stability index, I, on the size factor is plotted for both types of phase. In the case of non-transitional B components (Fig. 4(a)) there is a clear tendency for the highest I. values to occur for the lower size factors, and the concentration of high values in the region of zero size factor is significant. In the case of Zr,Au, the information
290
G. V. RAYNOR
Nb-Ga
b
Nb-Ge
1 90 Ti_Ir Nb-lL oz-oo-
Nb-Pt
Ti-Pt
’
0, V-Ni
m-
cr-Pto
~-W-L-
8MO-OS
b
---__ ---
2
4
Fig. 4. Stability index, I, plotted against Goldschmidt atomic diameters for Cr,Si (b) transition metal B components.
6
+
8
the size factor with respect phases with (a) non-transition
to the A component, metal B components
using and
given by Shunk’ suggests that the temperature of formation is not below 1100°C but may be higher. For Nb,Ge, a range of homogeneity in the solid state has been observed at 1600°C and the temperature of formation must be above this. The appropriate points in Fig. 4(a) have therefore been distinguished by upward pointing arrows. The position of the point for Nb,Sn and the range of I values for size factors of zero to -2 are referred to below in connection with Fig. 5.
90-
Cr-Pt
Nb-Pt
o-----_
Ti-Pt
---e----Mo-Ir~
Nb-Ir
23
MO-05
so-
b
0 cr.05
70-
v-coo
60N&h cr-RUO
Xl-
I 0
0.5 Electronegativity
1.0
1.5 difference
2.0
Fig. 5. Stability index, f, plotted against electronegativity difference transition metal B components and (b) transition metal B components.
for Cr,Si
phases
with (a) non-
STABILITIES OF BINARY INTERMEDIATE
PHASES
291
As shown in Fig. 4(b) the dependence of I upon size factor is quite different from that in Fig. 4(a); for size factors exceeding that of Nb,Ir (- 7.86) the stability index drops very sharply, whereas the variation is not marked between size factor values from -7.86 to zero. The data are insufficiently critical to define the general trend of I for positive size factor values. Figures 5(a) and (b) show I plotted as a function of the electronegativity difference between the components. The behaviour of phases with non-transition metal and transition metal B components is again quite different. Though in Fig. 5(a) there is a range of I values for a given electronegativity difference, the range is shifted towards lower values as the electronegativity difference increases. It is particularly to be noted that the phase Nb,Sn, which has a high index in spite of a relatively high size factor, corresponds to a negligible electronegativity difference between components, while the progressively decreasing I values in Fig. 4(a) for V,Ga, Zr,Sn and Ti,Au correspond with progressively increasing electronegativity difference. The behaviour of the phase Mo,Ge is not as yet understood. By contrast, the phases for which component B is a transition metal appear to be relatively insensitive to electronegativity differences between values of 1 and 2, but to be unable to form at lower values. It is possible that the low stability index values for Cr,Ru and Cr,Os, in spite of apparently favourable size factors, are due to unfavourable electronegativity differences between the components. It is for this reason that the line approximately representing the dependence of I on the size factor between values for the latter of -8 and +8 has been drawn as shown in Fig. 4(b). The abnormally low point for Nb,Rh in Fig. 5(b) may be attributable to the high size factor value for this phase (Fig. 4(b)). F’g 1 ures 4 and 5 taken together reinforce the impression that different influences are involved in the relative stabilities of the Cr,Si phases for which the B component is, respectively, a transition metal and a nontransition metal. The highest stability indices for the cases where B is a nontransition metal occur for low size-factors and low degrees of electrochemical interaction, suggesting that these two factors predominate. On the other hand, except at high (negative) size factors the stability of the phases with a transition metal B component is relatively insensitive to the electronegativity difference between the components. This in turn suggests that the transition metal clorbitals may be adopting a specific role in the binding forces and hence in the stability index of these phases. It should also be noted that the phases in Fig. 5(b) with the lower values of I (Mo,Os, Cr,Os, V&o, Nb,Rh and Cr,Ru) are all formed in the solid state. In Fig. 5(a) only Zr,Sn is formed in the solid state; the value of I is, nevertheless, not abnormally low. The three classes of intermediate phases occurring in transition metal alloy systems discussed in this communication show interesting differences with regard to the dependence of their stabilities on the more usually considered alloying factors. The Cr,Si phases in which a transition metal forms the B component appear to be in a class by themselves. With regard to the remaining phases, increasing size factor leads to a decrease in the stability index, I, for the Cr,Si phases with non-transitional B components, a decrease in I for p phases with specific NB-NA values, but an increase in I for the x phases. Increasing electronegativity difference leads to a decrease in the I value for Cr,Si phases with
292
G. V. RAYNOR
non-transitional B components, is without marked effect on the p phases but increases the I values for the x phases. Only in the case of the x phases does the NB-NA value appear to have any appreciable influence.
REFERENCES 1 W. Hume-Rothery, R. E. Smallman and C. W. Haworth, The Structure of Metals and Alloys, Monograph and Report Series No. I, Metals and Metallurgy Trust, London, 1969, pp. 239-257. 2 M. V. Nevitt, in J. H. Westbrook (ed.), Intermetallic Compounds, Wiley, New York, 1967, pp. 217-229. 3 A. K. Sinha, Progr. Mater. Sci., 15 (1972) 79. 4 G. V. Raynor, J. Less-Common Metals, 29 (1972) 333. 5 M. Hansen and K. Anderko, Constitution of Binary Alloys, McGraw-Hill, New York, 1958. 6 R. P. Elliott, Constitution of Binary Alloys, First Suppl., McGraw-Hill, New York, 1965. 7 F. A. Shunk, Constitution of Binary Alloys, Second Suppl., McGraw-Hill, New York, 1969. 8 W. Gordy, Phys. Rev., 69 (1946) 604. 9 A. R. Miedema, J. Less-Common Metals, 32 (1973) 117. 10 V. D. Burlakov and V. S. Kogan, Phys. Metal. Metallogr. (USSR), 7 (1959) 67.