Gupta D. (Ed.). Diffusion Processes in Advanced Technological Materials

Подождите немного. Документ загружается.

222 DIFFUSION PROCESSES IN ADVANCED TECHNOLOGICAL MATERIALS

TiAl and NiAl are the only phases that reveal a nonlinear Arrhenius

behavior of self-diffusion at high temperatures; that is, above 1470 K in

TiAl

[7]

and above 1500 K in NiAl.

[36]

The curvature in the Arrhenius plot

of TiAl is explained by an additional contribution of a specific ASB mech-

anism [Fig. 4.7(b)] and is related to the large concentration of thermal Ti

antistructure atoms at high temperatures, even in the Al-rich TiAl

alloys.

[7, 8]

The observed upward deviation of D

from the otherwise

straight Arrhenius line in NiAl at T  1500 K seems to have another ori-

gin. The concentration of thermal Ni antistructure atoms in NiAl is

notably lower than in TiAl [see Fig. 4.3(b)], which corresponds to a higher

degree of order in NiAl. Moreover, the upward deviation of D

observed in NiAl at about the same temperature, independent of the com-

position.

[36]

These features correlate with recent measurements of the

vacancy concentration in NiAl alloys.

[81]

The regular change of Fe diffusion in the B2 FeAl alloys of different

compositions (Fe

Al, Fe

Al, and FeAl) was related to the change in the

long-range order parameter S.

[92]

Using the long-range order parameter for

the B2 order, which is related to the Al content by the relation S

max

 2X

is the atomic fraction of aluminium), the activation enthalpy of Fe self-

diffusion in the B2 region can be described by the following relation:

[92]

 (220  46 S

max

)kJmol. (13)

In Fig. 4.18, Ti self-diffusion and Ga solute diffusion in different tita-

nium aluminides are compared with respect to the homologous tempera-

ture, T

T. Here T

is the melting temperature of the corresponding stoi-

chiometric compound. Systematic changes in the diffusion behavior of the

Ti aluminides are clearly observed: Ti and Ga diffusion decreases gradu-

ally from pure a-Ti to Ti

Al and finally to TiAl.

This phenomenon most likely originates from: (1) the sublattice dif-

fusion mechanism in these materials, (2) prevailing vacancy concentra-

tions on the transition metal sublattices, and (3) a systematic decrease of

the coordination number of the transition metal sublattice. Figure 4.18

reveals that the self-diffusivity follows the following relationship: D



 D

TiAl

, in a line with the coordination number of the transition

metal sublattices in the corresponding structures: z

 12  z

 8 

TiAl

 4.

Figure 4.3(a) and (b) indicates that the vacancy concentrations on the

transition metal sublattices are similar in Ti

Al and TiAl. The ratio QT

also lies in the common limits of vacancy diffusion: 17.4k for Ti

Al and

17.5k for TiAl. These values are close to that in pure a-Ti, QT

 18.8k.

The main difference in the absolute values of the diffusivities therefore

stems from the pre-exponential factors D

 gfa

exp{S

/k}. Here, f is the

Chapter-04.qxd 11/29/04 6:36 PM Page 222

correlation factor; a is the lattice constant; n

is the attempt frequency; S

is the formation entropy; the numerical factor g reflects the smaller coor-

dination number of the sublattice with respect to the whole lattice: g  1,

23, and 13; f  0.781, 0.467,

[105]

and 0.71;

[80]

and a  2.95, 2.91, and

2.83 Å for the a-Ti, Ti

Al, and TiAl phases, respectively. Comparative

ratios of the products g  gfa

for the three phases are g

DIFFUSION IN INTERMETALLIC COMPOUNDS, HERZIG, DIVINSKI 223

Figure 4.18 Ti and Ga diffusion in a-Ti (solid lines

[68, 77]

), Ti

Al (dashed-dotted

lines

[65, 68]

), and TiAl (dashed lines

[7, 68]

) as functions of the reduced temperature

T.

Chapter-04.qxd 12/2/04 1:50 PM Page 223

TiAl

 5.4:3.2:1. From the actual diffusion measurements shown in Fig. 4.18

and Tables 4.2 and 4.3, the corresponding ratios of 70:5:1 are obtained.

While the ratios g

TiAl

are reasonable, the one for Ti is rather large.

The large discrepancy in a-Ti may be attritubed to the entropy factor,

which should be taken into account, especially for pure Ti. Thus, the

observed systematics alone does not result from the structural limitations,

although the change in D follows the constraints imposed by the given

sublattice structures.

Note that the Ga diffusivity D

in these compounds follows a similar

tendency (Fig. 4.18). Such behavior was also established for the Al diffu-

sion data extracted from the interdiffusion measurements in the Ti alu-

minides.

[68]

This can be explained by the same arguments as for transition

metal self-diffusion and further indicates that the sublattice diffusion

mechanism operates for Ga and Al in the Ti aluminides.

4.6 Grain Boundary Diffusion

Grain boundary (GB) diffusion in intermetallic compounds was

investigated to a much smaller extent than bulk diffusion. Some exper-

imental information is available already for Ni,

[55, 106–108]

Ti,

[109]

and

[110]

aluminides. The primary problem, however, is to improve our

understanding of GB diffusion in intermetallic compounds on the atom-

istic level. For example, diffusion mechanisms in GBs, and the effects

of the order and of structural multiplicity, are still not well under-

stood.

[111]

It is not clear if the local disorder at GBs occurs by the same

mechanism as in the bulk lattice, that is, by means of antistructure

atoms or structural vacancy formation.

[111]

Therefore, in this overview,

experimental results will be described and unresolved problems will be

highlighted.

GB diffusion measurements in intermetallic compounds were per-

formed in the Harrison B-regime conditions.

[112]

Schematically, in such a

case, the tracer atoms diffuse fast along GBs. Then, at some depth, they

penetrate into the bulk of the grains and diffuse further, at a slower rate,

over a distance that is distinctly larger than the GB width d.

[112]

As a result,

the so-called triple product P  sdD

can be determined from the

detected diffusion profile. Here s is the segregation factor and D

is the

GB diffusion coefficient. In GB self-diffusion experiments in pure metals,

s  1 and P represents a double product P  dD

. In intermetallic com-

pounds, especially in off-stoichiometric alloys, we can expect a certain

segregation of a constituent component to the GBs, resulting in s  1. The

total effect, however, is likely to be small and can be neglected in a first

approximation.

224 DIFFUSION PROCESSES IN ADVANCED TECHNOLOGICAL MATERIALS

Chapter-04.qxd 11/29/04 6:36 PM Page 224

4.6.1 Ni

Ni GB diffusion in the Ni

Al phase field was systematically investigated

in the temperature interval 968 to 1190 K.

[55]

Although only a marginal com-

positional dependence of Ni bulk diffusion is observed in this compound, a

distinct V-type dependence of the product P

on the composition is estab-

lished, with a minimum in P

about the stoichiometric composition

[55]

[see

Fig. 4.19(a)]. The resulting activation enthalpies reveal a maximum at about

the stoichiometric composition and decrease on both sides as the Ni content

deviates from stoichiometry [Fig. 4.19(b)]. The Arrhenius parameters of the

GB diffusivity P

in Ni

Al are summarized in Table 4.6.

Zulina et al. studied Ni GB diffusion in near-stoichiometric Ni

Al and

several Ni

Al-based alloys.

[108]

The resulting values of P

are smaller than

those measured by Frank and Herzig

[55]

at the given composition, and the

activation enthalpy of Ni GB diffusion in Ni

74.8

25.2

is larger

[Fig. 4.19(b)]. However, note that Zulina et al. determined the activation

enthalpy Q

by fitting only three experimental points in the Arrhenius

diagram. It thus includes a larger uncertainty.

As shown in Fig. 4.19(a), Cermak et al.

[106]

observed a maximum in

the P

versus composition plot instead of a minimum measured by Frank

and Herzig

[55]

at temperatures 950 K. On the other hand, at T  900 K,

a minimum of P

around stoichiometry was observed, in agreement with

Frank and Herzig.

[55]

The deduced activation enthalpies of Ni GB diffu-

sion

[106]

are remarkably larger than the values determined by Frank and

Herzig.

[55]

This behavior may be explained by GB segregation of residual

impurities in the alloys and/or by the applied experimental procedure.

DIFFUSION IN INTERMETALLIC COMPOUNDS, HERZIG, DIVINSKI 225

Table 4.6. Arrhenius Parameters of Grain Boundary Self-Diffusion in Ni,

Ti, and Fe Aluminides

Composition P

Phase Tracer at.% Al (m

1

) (kJmol) Q

Q

Ref.

Al Ni 26.6 7.3  10

14

153 0.51 55

24.8 4.4  10

14

154 0.51 55

22.4 2.2  10

15

115 0.38 55

NiAl Ni 50.0 4.6  10

15

152 0.53 80

46.5 9.0  10

14

182 0.65 80

Al Ti 25 4.8  10

13

195 0.68 109

33 3.2  10

11

252 0.88 109

TiAl Ti 56 4.6  10

15

123 0.47 109

Al Fe 25 4.0  10

9

227 0.8 110

Chapter-04.qxd 11/29/04 6:36 PM Page 225

73 74

75 76

Composition [at.% Ni]

-22

-21

-20

P [m

-1

]

252627

Composition [at.% Al]

1190 K

1066 K

968 K

1012 K

(a) Triple product P for Ni

Al alloys. Open circles

[55]

and solid

squares

[106]

at T = 1013 and 1073 K, respectivel

73 74

75 76

Composition [at.% Ni]

100

125

150

175

200

225

250

[kJ/mol]

252627

Composition [at.% Al]

Ni in Ni (Frank et al.)

( )

Ni in Ni (Mishin et al.)

(b) Activation enthalpy Q

for Ni

Al alloys. Open circles

are from Frank and Herzig

[55]

; dashed lines represent

activation enthalpy of grain boundary diffusion of Ni in

pure Ni

[55,113]

; the full triangle is from Zulina et al.

[108]

Figure 4.19 The triple product P and the activation enthalpy Q

of Ni GB diffusion in Ni

Al as functions of composition.

226 DIFFUSION PROCESSES IN ADVANCED TECHNOLOGICAL MAT ERIALS

Chapter-04.qxd 11/29/04 6:36 PM Page 226

Frank and Herzig established

[55]

that by increasing the Ni content on

the Ni-rich side of Ni

Al, both P

and Q

values approach the values

measured for pure Ni [see Fig. 4.19(b)]. This can be explained by the seg-

regation of Ni, which was experimentally observed

[114]

at GBs in Ni

Al on

the Ni-rich side. On the other hand, the increase of the P

values and the

decrease in Q

on the Al-rich side can be explained by an excess of Al

segregating to GBs.

[114]

These Al atoms increase the free volume at GBs;

thus the formation enthalpy of the Ni vacancies at the GBs is

decreased.

[115]

These features most likely contribute to the enhancement of

Ni GB diffusion in these compositions.

[55]

Atomistic simulations are nec-

essary to explain the effect of GB segregation on diffusion behavior.

Polycrystalline Ni

Al is well known to reveal grain boundary brittle-

ness, which is successfully suppressed by microalloying with boron.

[116, 117]

The effect of boron addition on Ni GB diffusion in Ni

Al was carefully

studied.

[106, 118]

The doping of Ni

Al with 0.24 at.% B and the segregation

of B decrease Ni GB diffusion by a factor of 2 to 3 and increase the acti-

vation enthalpy Q

slightly with respect to pure Ni

Al.

[55, 118]

This effect is

explained by an increase in GB cohesion and Ni–Ni atom bonding upon

boron alloying.

[118]

Moreover, B segregation is likely to block otherwise

energetically favorable diffusion paths along GBs and increases the

vacancy formation enthalpies in the boundary core.

4.6.2 Ti

Ti GB self-diffusion was studied as a function of composition in Ti

within the temperature interval 940 to 1316 K.

[109]

As shown in Sec. 4.4.2.1,

Ti bulk self-diffusion is practically independent of composition in the

Al phase.

[65]

However, Ti GB self-diffusion reveals a distinct composi-

tional dependence: As the Al content on the Al-rich side of the compound

increases, the P

values systematically decrease [see Fig. 4.20(a)]. This

tendency is opposite to that observed in the other A

B compound investi-

gated, Ni

Al [Fig. 4.19(a)]. With increasing deviation from the stoichio-

metric composition, the GB diffusivity in Ti

Al is decreased and the acti-

vation enthalpy increases to an unusual large value in comparison with

that of bulk diffusion in this compound. In Fig. 4.20(b), the compositional

dependence of the activation enthalpy of Ti GB diffusion in Ti

Al is com-

pared with that of Ti GB diffusion in pure a-Ti.

[109]

in a-Ti is similar

within experimental accuracy to the value of Q

in stoichiometric Ti

Al.

The absolute value of the product P

in a-Ti, however, is larger by one

order of magnitude than that in Ti

[109]

This correlates with the geo-

metric limitations imposed by the particular structure of the Ti sublattice

in GBs of Ti

Al.

[119]

DIFFUSION IN INTERMETALLIC COMPOUNDS, HERZIG, DIVINSKI 227

Chapter-04.qxd 11/29/04 6:36 PM Page 227

7.5

8.5

9.5

-1

[10

-4

-1

]

-23

-22

-21

-20

P [m

-1

]

1300 1200 1100

T [K]

(a) Arrhenius dependence of triple product P in Ti

Al alloys.

Compositions in at.% are marked on each plot.

64 66 68

70 72 74

Composition [at.% Ti]

150

175

200

225

250

275

300

[kJ/mol]

262830323436

Composition [at. % Al]

Ti in α

-Ti

Ti in α-Ti

(b) Activation enthalpy Q

of Ti grain boundary diffusion

in α-Ti and α

-Ti

Al alloys.

[109]

Figure 4.20 Tr iple product P and the activation enthalpy Q

of Ti GB diffusion in a

-Ti

Al.The dashed line is for grain bound-

ary diffusion in a-Ti.

228 DIFFUSION PROCESSES IN ADVANCED TECHNOLOGICAL MATERIALS

Chapter-04.qxd 11/29/04 6:36 PM Page 228

The Arrhenius parameters of Ti GB diffusion in several representative

Al alloys are given in Table 4.6. While in stoichiometric Ti

the

ratio Q

Q

adopts a typical value for GB diffusion, Q

Q

 0.68, this

value increases remarkably in Al-rich compositions. In Ti

, Q

hardly deviates from Q

, the activation enthalpy of Ti bulk self-diffusion

in this alloy. Note that such larger values of Q

Q

were already observed

in other cases: Q

Q

 0.9 for Co diffusion in CoSi

[120]

and Q

Q

 0.8

for Fe diffusion in Fe

Al,

[110]

as discussed in Sec. 4.6.5.

4.6.3 TiAl

Ti GB self-diffusion was recently measured in several TiAl alloys.

[109]

The data suggest negligible compositional dependence of Ti GB diffusion

in TiAl. The Arrhenius dependence of Ti GB diffusion in two representive

compositions of a

-Ti

Al and a-Ti is compared in Fig. 4.21. Ti diffuses

very fast along GBs in TiAl, even in comparison with a-Ti. The ratio

Q

 0.45 for TiAl is typical for pure close-packed metals.

The comparison of the absolute values of Ti GB self-diffusion in

Al and TiAl shows that the GB self-diffusivity in TiAl is larger by

about one order of magnitude than in Ti

Al with stoichiometric composi-

tion, and even larger by two orders of magnitude than P

in Ti

similar temperatures.

Ti diffusion was measured along a

g phase boundaries between a

Al and g-TiAl phases.

[121]

Material, so-called polysynthetically twinned

(PST) single crystals, with a uniformly oriented lamellar structure, was

investigated.

[121]

In Fig. 4.21, these results are compared with Ti GB self-

diffusion in both a

and g phases. Diffusion in a

g phase boundaries is

very slow and is in line with the GB diffusion data in the Al-rich Ti

phase. These low values of Ti GB diffusivity in the a

g interphase

boundaries reflect their compact structure and were explained by vacancy-

mediated nearest neighbor jumps in the Ti sublattice of the phase bound-

ary in correspondence with its special atomic arrangement.

[121]

4.6.4 NiAl

Ni GB self-diffusion in NiAl was measured within the temperature

interval 958 to 1194 K.

[80]

No distinct compositional dependence of Ni GB

self-diffusion has been established in the limited range of compositions

investigated. The results are given in Fig. 4.22. A slight tendency for an

increase of the activation enthalpy for Ni GB diffusion in Ni-rich NiAl

alloys is shown in Fig. 4.22(b). The Arrhenius parameters of Ni GB self-

diffusion in representative NiAl alloys are listed in Table 4.6.

DIFFUSION IN INTERMETALLIC COMPOUNDS, HERZIG, DIVINSKI 229

Chapter-04.qxd 11/29/04 6:36 PM Page 229

230 DIFFUSION PROCESSES IN ADVANCED TECHNOLOGICAL MATERIALS

Figure 4.21 Comparison of grain boundary diffusion in pure a-Ti (solid line),

-Ti

Al (dashed lines), g-TiAl (dotted-dashed line), and TiAl polysynthetically

twinned (PST) interphase boundaries (circles).

[109]

The Al content of the corre-

sponding alloys is indicated in at.%.

Chapter-04.qxd 12/2/04 1:50 PM Page 230

DIFFUSION IN INTERMETALLIC COMPOUNDS, HERZIG, DIVINSKI 231

50 51 52 53 54

Composition [at.% Ni]

-23

-22

-21

P [m

-1

]

464748

5051

Composition [at.% Al]

1194 K

958 K

1004 K

1052 K

1115 K

(a) Triple product P for Ni grain boundary diffusion in NiAl

[80]

50 51 52 53 54

Composition [at.% Ni]

120

140

160

180

200

220

[kJ/mol]

464748

5051

Composition [at.% Al]

(b) Activation enthalpy Q

for Ni grain boundary diffusion in NiAl

[80]

Figure 4.22 Tr iple product P and the activation enthalpy Q

of Ni grain boundary diffusion in NiAl alloys as a function of com-

position.

[80]

Chapter-04.qxd 11/29/04 6:36 PM Page 231