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

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502 DIFFUSION PROCESSES IN ADVANCED TECHNOLOGICAL MATERIALS

observed that long-range Cu diffusion is a difficult process in both the

Cu (1)-O (1) chains and the Cu (2)-O (2) planes. If a certain amount of

thermal vacancies are assumed to exist on the Cu sites, similar to those

commonly observed in the metal and transition-metal oxides,

[20, 21]

diffusion is possible without the mediation of oxygen vacancies or

excursions on the oxygen sublattice. Cu atom migration could then be

thought to take place in all combinations of atomic jumps of the types

110, 301, and 031, as shown in Fig. 10.8. For example, Cu

atoms would diffuse along the Cu (1)-Cu (1) diagonal in the basal

plane, along Cu (2)-Cu (2) diagonals in the Cu-O planes and (001) planes,

and so forth. Note that communication between the chains and planes

is permissible only by the diagonal jumps between Cu (1)-Cu (2) sites.

The alternative Cu (2)-Cu (2) jumps along 001 are somewhat

shorter, but their contribution to diffusion may not be substantial. Since

there would be fewer thermal vacancies in the Cu sites than in the oxy-

gen O (1) sites, and they would be accompanied by longer jumps,

cation diffusion may be expected to be very slow. Therefore, both D

and Q would be larger for cation diffusion compared to anion diffusion

in the YBCO lattice and they may resemble the corresponding values in

closely packed lattices of pure metals, such as Cu.

[22]

The analysis can

be extended to show that cation diffusion in the YBCO lattice resem-

bles self-diffusion in the Cu lattice. From the lattice parameters of the

neutron diffraction studies,

[19]

an average length of 5.5Å for the

Cu (1)-Cu (1), Cu (1)-Cu (2), and the Cu (2)-Cu (2) diagonal jumps (l)

may be estimated. To the first approximation, the pre-exponential term

(cm

/sec) may be written as:

(cm

/sec)  l

n e

(∆S/k )

, (1)

where n is the lattice frequency 7  10

/sec, ∆S is the entropy for dif-

fusion, and k is the Boltzmann constant. Hence the measured value of D

(Table 10.1) for Cu in YBCO leads to the entropy ∆S  5k. The corre-

sponding value for self-diffusion in Cu is ∆S

 3k.

[22]

Considering the

dissimilarities of the lattice and the nature of the nearest neighbors,

entropy as well as the enthalpy for Cu cation diffusion in the YBCO have

values similar to those for Cu self-diffusion in the Cu metal. Note that the

orthorhombic to tetragonal transformation has no effect on cation diffu-

sion kinetics. The Arrhenius plot, shown in Fig. 10.7, remains straight

through the transformation that occurs at 700°C. This is consistent with the

fact that the YBCO cell volume is preserved during this second-order

transformation.

[19]

The cation diffusion processes are, however, expected

to be anisotropic, but the available data are sparse. Considering the diffusion

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DIFFUSION IN SOME PEROVSKITES, GUPTA 503

mechanism proposed above for Cu, we do not expect any significant

anisotropy for Cu diffusion, although it is not ruled out for the Ba and Y

species.

10.2.3.2 Self-Diffusion of Ba and Y in YBCO

As Fig. 10.8 shows, both Ba and Y atoms are deeply embedded in the

YBCO lattice, and their atomic movement is expected to be even more

difficult than Cu. Diffusion of Ba and Y atoms would require excursions

to the Cu sites, which would disturb the thermodynamic equilibrium of

the occupancy of sites. In addition, the chemical environments for Ba and

Y cations are different than that of Cu. Ba resides in Ba-O insulating lay-

ers, while Y is surrounded by Cu (2)-O layers, which have partially free

electrons. Thus the state of defects, the energetics, and the diffusion paths

for Ba and Y may be expected to be vastly different. A long-range diffu-

sive motion may in fact involve cooperative atomic jumps between the Cu

and Ba or Y sites. The activation energies for Ba and Y diffusion are

expected to be much larger than that for Cu, and diffusion is likely to be

highly anisotropic. Table 10.1 shows that the activation energies measured

by Chen et al.

[9]

for Ba and Y species are indeed very large, of the order

of 900 to 1000 kJ/mol, and diffusion of Ba shows an anisotropy of at least

1000. These activation energies are similar to those observed for steady-

state creep in transition metal oxides.

10.2.4 Diffusion of Cation Impurities in YBCO

Bulk and thin-film YBCO specimens described in Sec. 10.2.1 were

used to study diffusion of the

Ni cation

[6, 7]

under an oxygen pressure of

Pa. The corresponding diffusion profiles, plots of the log-specific

activity versus the square of the cumulative penetration distance, are

shown in Fig. 10.9(a) and (b). All

Ni diffusion profiles displayed in

Fig. 10.9, in bulk as well as the epitaxial thin-film specimens, showed ini-

tially high data points and subsequently became linear. Unlike

Cu tracer

(see Fig. 10.6), which should not have had any problems of solubility in

the host YBCO specimens, the

Ni tracer may have exceeded the solubil-

ity limit because

Ni has a half-life of 85 years and a large number of Ni

atoms are required to obtain detectable radioactivity. Therefore, we relied

on the deeper linear (Gaussian) segments of the

Ni profiles to extract the

diffusion coefficients. Thus,

Ni diffusion coefficients have been obtained

by fitting the Gaussian solution of the Fick’s law for an instantaneous

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504 DIFFUSION PROCESSES IN ADVANCED TECHNOLOGICAL MATERIALS

Figure 10.9(a)

Ni radiotracer diffusion penetration profiles in bulk polycrystalline

YBa

7x

specimens.

[7]

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DIFFUSION IN SOME PEROVSKITES, GUPTA 505

Figure 10.9(b)

Ni radiotracer diffusion profiles in YBa

7x

epitaxial thin films

on (100) SrTiO

substrate. Note the scale factor (SF) for the abscissa marked on

each profile.

[6]

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source and semi-infinite boundary conditions to the linear segments in the

profiles shown in Fig. 10.9(a) and (b).

This section compares and contrasts the impurity cation (

Ni) diffu-

sion parameters obtained in polycrystalline bulk and epitaxial films with

similar data in single crystals obtained by Routbort et al.

[8]

Then we exam-

ine diffusion of Co, Cu, Ag, and Zn impurity cations in the polycrystalline

YBa

7–d

specimens listed in Table 10.1. We first discuss the Ni tracer

diffusion, which behaves more or less similarly to the Cu tracer and is

known to substitute for Cu in the YBCO lattice.

10.2.4.1 Ni Tracer Cation Diffusion in YBa

7d

In Fig. 10.10, the Ni diffusion data are plotted for epitaxial,

[6]

poly-

crystalline,

[7]

and single-crystal specimens

[8]

to show the effect of

microstructure and crystal anisotropy. As Table 10.1 shows, the activation

506 DIFFUSION PROCESSES IN ADVANCED TECHNOLOGICAL MATERIALS

Figure 10.10 Arrhenius plots of Ni diffusion in YBa

7x

polycrystalline bulk,

[7]

epitaxial thin films on (100) SrTiO

substrate,

[6]

and single-crystal specimens.

[8]

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DIFFUSION IN SOME PEROVSKITES, GUPTA 507

energy for Ni diffusion in the YBCO specimens (epitaxial thin-film, poly-

crystalline, or single-crystal specimens) is very similar to that for the Cu

tracer between 240 to 260 kJ/mol. This is understandable since both

occupy the same sites and have similar electrical charge.

Figure 10.10 shows that the

Ni radioactive tracer data in the

(100) epitaxial films agree reasonably well with the secondary ion

mass spectroscopy (SIMS) diffusion data of Ni in the c direction of

single crystals of YBa

7x

. The principal difference is in D

for

the

Ni data in polycrystalline bulk specimens due to contributions of

grain boundaries present in the specimens (see Fig. 10.1). The small

difference between the Ni diffusion coefficients in the epitaxial films

and the single crystals seen in Fig. 10.10 may be attributed to the pres-

ence of a higher density of dislocations in the former rather than

anisotropy of the diffusion coefficients, because both were diffused in

the c direction.

10.2.4.2 Cation Impurity Diffusion and Effect of

Charge Imbalance

In Fig. 10.11, impurity cation diffusion for Zn, Ni, Ag, and Co

[6–8]

compared with the Cu self-diffusion data.

[7, 8]

Note that charge may be an

important factor in determining the sites occupied by impurity cations;

consequently, the diffusion kinetics will be affected. It is well recognized

that Zn and Ni in low concentrations, of the order of 0.05%, substitute Cu

in Cu (1) sites,

[23]

but in higher concentrations (≈0.30) they occupy Cu (1)

and Cu (2) sites randomly.

[24]

Ag also replaces Cu on Cu (1) and Cu (2)

sites,

[25]

while Co occupies exclusively the Cu (1) sites.

[26]

For radiotracer

studies that involve very small concentrations, we may consider that Zn,

Ni, and Co all go into Cu (1) sites. Because of their close proximity to

oxygen-ion vacancies, diffusion along Cu (1) sites is much faster than

along Cu (2) sites. Furthermore, the valent states of (a) Cu, Zn, (b) Co, Ni,

and (c) Ag are 2, 2 or 3, and Ag 1, respectively. As Fig. 10.11

shows, that diffusion of Zn in bulk YBCO specimens falls on the Cu self-

diffusion Arrhenius plot. This is not surprising since both Cu and Zn have

2 states and Zn occupies Cu (1) sites. Ni diffusion in the epitaxial films

also come very close to the Cu self-diffusion line, indicating that it is

likely to diffuse in the Cu (1) sites in the Ni

2

state. Ag, on the other hand,

diffuses substantially faster than Cu or Zn. Routbort et al.

[8]

have

advanced an explanation to account for this difference: Ag

1

, being nega-

tively charged with respect to the Cu

2

ion it replaces, may attract oxygen-

ion vacancies for charge compensation, thereby lowering the activation

energy for motion at the saddle point. As a converse corollary, if Co

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occurred in the 3 state, it should repel oxygen-ion vacancies, increase

the saddle-point energy, and slow down its diffusion. This is, in fact,

observed, as shown in Fig. 10.11. It is therefore seen that diffusion of the

cation impurities, which lie close to Cu in the Periodic Table, is very sim-

ilar to Cu self-diffusion, with some perturbations caused by their charge

dissimilarities, if any.

10.2.4.3 Cation Impurity Diffusion in Piezoelectric Perovskites

Besides cation diffusion in YBCO, similar data are also available in

several other perovskites, notably the single crystals of the PbMnNbO

PbTiO

(PMN-PT) system.

[10]

Figure 10.12 compares Ag radiotracer dif-

fusion in the PMN-PT piezoelectric ceramic and the YBCO. It also shows

the Cu self-diffusion in the YBCO. Ag diffusion in the PMN-PT single

crystals compares well with the self-diffusion of Cu in the HTSC YBCO.

508 DIFFUSION PROCESSES IN ADVANCED TECHNOLOGICAL MATERIALS

Figure 10.11 Comparison of diffusion of cation impurities (Ag, Ni, Co, and Zn) with

Cu self-diffusion in YBa

7x

. (Table 10.1 gives the source of the data.) The

arrow indicates the orthorhombic-to-tetragonal transformation.

[8]

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DIFFUSION IN SOME PEROVSKITES, GUPTA 509

The Ag diffusion data in the polycrystalline YBCO, however, are signifi-

cantly higher due to the contribution of the grain boundaries. Nevertheless,

the diffusion process in two perovskites, YBCO and PMN-PT, appears to

be similar and to involve primarily thermal vacancies on Cu or the Pb

sites, respectively.

10.3 Anion Diffusion in Several HTSC

Cuprates

Soon after the discovery of the HTSC cuprates, it was realized that

they were essentially nonstoichiometric compounds and that the deviation

from the stoichiometry (x) is controlled largely by the anion (oxygen)

defect equilibria. The electronic defects, namely the electrons and the

holes, are also related to the defect equilibria. In fact, oxygen stoichiom-

etry turned out to be a critical parameter in determining the supercon-

ducting transition temperature, T

, and the critical current, J

[27]

Diffusion

of anions is also expected to be closely related to the concentration and

Figure 10.12 Arrhenius plots of diffusion of

11 0

Ag in PMN-PT single crystals and

polycrystalline superconducting YBa

7x

Cu self-diffusion in the latter is

also shown for comparison.

[10]

(See Table 10.1)

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mobility of defects and hence to the stoichiometry of the compounds.

Therefore, it is not surprising that the early investigators noted large

changes in the physical properties of the compounds upon heating and

cooling, notably color, electrical resistance, and specific gravity. Some of

these effects became bases of measurements of fast in-and-out diffusion

of oxygen in these compounds, as discussed later in this section. Fast dif-

fusion kinetics of oxygen in a large number of superconducting cuprates

and their defect equilibria have been comprehensively reviewed by

Routbort and Rothman.

[28]

We will discuss here only the salient features of

oxygen diffusion in the HTSC cuprates and the manner in which they may

be related to self-diffusion of the Cu cation, in YBCO in particular.

Bakker et al.

[29]

provide details of the defect equilibria in YBCO in their

excellent paper.

10.3.1 Oxygen Diffusion Data in HTSC Cuprates

In Table 10.2, we have compiled critical data on oxygen diffusion in

a number of HTSC cuprates measured by the SIMS technique using

stable isotope. The data are also displayed in Fig. 10.13. The scatter

among data from material to material is rather large, varying 6 to 10

orders of magnitude. The anion diffusion coefficients are also many

orders of magnitude larger than those for cation species (compare data

in Tables 10.1 and 10.2), although in some cases diffusion kinetics

do come close to each other (for example, in YBa

7d

and

compounds). For rigorous comparison of diffusion data in

dissimilar compounds, a homologous temperature scale should be used;

however, this is not possible because these compounds decompose and

sublime before melting takes place. Figure 10.8 clearly shows that dif-

fusion of oxygen would be quite complex because it occupies five dif-

ferent kinds of sites due to differing environments, state of occupancy,

and, in particular, ordering of oxygen atoms and vacant sites in the basal

planes. Departure from stoichiometry, as measured by x, is the control-

ling parameter, but it is not a fixed quantity. It increases at higher tem-

peratures and decreasing partial pressure of O

. The deviation of the sto-

ichiometry decreases as the occupancy in O (1) and O (4) sites is

reduced and an increase in O (5) sites takes place. The reductions or

increments of occupancy may be neither proportional nor compensatory.

The magnitude of x and its thermodynamic kinetics vary from material

to material. Diffusion of oxygen may also be expected to be anisotropic

by several orders of magnitudes.

[30]

Hence these numerous variables

result in a very large scatter in the diffusion data for oxygen, as seen in

Fig. 10.13. However, meaningful inferences have been drawn from

510 DIFFUSION PROCESSES IN ADVANCED TECHNOLOGICAL MATERIALS

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DIFFUSION IN SOME PEROVSKITES, GUPTA 511

Table 10.2. Oxygen Diffusion in Some HTSC Cuprates

Stoichiometry D

Q Comment

No. Host Technique (x) (cm

s) (kJ/mol) Reference

1La

2x

CuO

0 1.6  10

6

80.0 S [33]

2La

2x

CuO

0.10 0.55  10

6

62.6 P [33]

3La

2x

CuO

SIMS(

0.10 0.2  10

6

77.0 P [34]

4La

2x

CuO

0.10 5.9  10

6

126.2 C [33]

5La

2x

CuO

0.24 12 234.1 P [33]

6 YBa

7x

0 1.36  10

4

93.5 P [31]

7 YBa

7x

Resistance 0.7 3.5  10

2

125.3 P [32]

8 YBa

7x

Calculation 0.1 0.04 125.3 P [35]

9 YBa

7x

0 0.08 200.6 P [36]

10 YBa

7x

075296 C [36]

11 Bi

SIMS (

8 1.7  10

5

89.3 P [37]

12 Bi

8 0.6 212.3 C [37]

13 Bi

6 0.06 203.6 AB plane [38]

14 YBa

7x

Radiotracer 0.1 4.0 255.3 P [6, 7]

Cu Cation

15 YBa

7x

Molecular 0.09 1.4  10

4

94.4 Theory

dynamics [39]

P: polycrystalline; C: c axis or AB plane; S: single crystal; NA: not available

these data; these have been summarized by Routbort and Rothman for

YBCO,

[28]

as follows:

1. The measured oxygen tracer diffusion coefficients (D) are

relatively insensitive to the oxygen partial pressure (P

2. The Arrhenius plot at the fixed partial pressure of 10

Pa is

straight over a large temperature range and remains unbroken

through orthorhombic-tetragonal transformation, similar to

the Cu cation discussed in Sec. 10.2.

3. In single crystals, D

W D

at small values of x obtained at

300°C and P

 10

Pa, but D

≈ D

at higher values of x

obtained at 600°C and P

 2  10

Pa, where the subscripts

a through c refer to a and b directions in the AB plane and c

is the direction normal to it (see Fig. 10.8).

4. D

V D

at low temperatures, and both Qand D

are much larger

in the c direction, indicating that oxygen diffusion is occurring by

individual lattice vacancies far away from the basal planes.

5. In polycrystalline material, D

poly

≈ D

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