Diffusion of 51Cr in Cr-doped MgO

1. Phys. Chm. Solid4 Vol. II, pp. 1355-1359 Pergdmon Press Ltd., 1989. Prinkd in Great Britain

DIFFUSION OF “Cr IN Cr-DOPED MgOt G. W. WEBER. W. R. BITLER and V. S. STUBICAN Department of Materials Science

and Engineering,

The Pennsylvania U.S.A.

State University,

(Received 17 December 1979~ ctccepted in revised form

University

Park, PA 16802,

2 Mug 1980)

Abstract-An arc fusion technique was used to grow single crystals of MgO and Cr-doped MgO. Diffusion coefficients for “Cr in Cr-doped single crystals were measured at three temperatures 1383, 1444 and 1495°C using a high specific activity isotope “Cr. An approximately linear relationship between the concentration of Cr-ions in MgO and diffusion coefficients of “Cr was obtained. It is shown that the activation energy of 19.6 kcal/mole obtained for the doped crystals is the difference between the energy for motion and the energy for association of the Cr-vacancy complexes. Using a previously determined value of 39.9 kcal/mol for the energy of motion, the energy of association for the Cr-vacancy complex is calculated to 20.3 ? 3 kcallmol or 0.88 2 0. I3 eV.

I. INTRODUCTION The substitution requires

of a divalent

the creation

to Lidiard[l]

of one lattice

when an impurity

nearest neighbor

position,

in which, however,

ion in an alkali vacancy.

According

a complex

is formed

with an

energy arising from the electrostatic

tion

departs

which

are considered

from

a simple

separations.

coulombic

Impurities

to exist either

attracform

or as un-

of defects tends towards

value as the impurity

In the same way the diffusion ion, according

to Lidiard’s

then reach a constant

concentration coefficient

theory,

a

increases.

of the impurity

should increase and

value at high impurity

concen-

Hanlon[Z]

observed

diffusion

in Cd-doped

obtained

similar

Mn-doped Similar

silver

saturation

bromide

for

and

the diffusion

Cd2+

Siiptitz[3]

of Mn2+ in

have been conducted

in metal deficient

semiconductors,

amount

of metal vacancies

was varied

oxygen

pressure.

diffusion

conflicting Co,_,0

for

silver bromide and silver chloride. investigations

primarily

apparent

results

Several

of

“Fe

results.

Fe1_,0[4,

The diffusion

in the amount

of metal vacancies

the

diffusion

of an aliovalent

were

Crystals

coefficient

homogeneously is available

in oxides

alternating

current,

Single crystals

M20rM0

from

vertical

with a beryllium-copper

interdiffusion

in

data

couples

arc furnace. from

I pm finish with a piston-in-cylinder

solidified

blocks to

type device having a

machining tolerance of 5 pm. impurities:

Fe

containing

more

analysis indicated 104Oppm than

the following

(IOO-300ppm

0.3 mole

%

major

in specimens

Cr,O,),

Ca

IOO-

300 ppm, Si 200-500 ppm, and Cu l-3 ppmf. Crystal size decreased as the Cr203 concentration increased. Doping levels of 0.3 mole % of Cr203 produced transmission

anneal

crystals

size of 3 x 3 x 5 mm. Electron

maximum

electron

microscopy

Prepared

has not been studied

magnesium

wire saw and were polished

precipitates

on the tracer

precalcined

were removed

often

Comparable

of solute concen-

of MgO and Crz03 powders in an

of 6oCo in

as shown by several

doped single crystals.

only from

grown

51 with

with the increase

solute

the

chromium-

2. EXPERIMENTAL PROCEDURES

43,500 X) of the crystals

authors [6, 71. The influence

to determine

in single crystal

tration and temperature.

have examined

coefficient

was found to increase linearly

in oxides

in which the

by varying

investigators in

was designed

of “Cr

doped magnesium oxide as a function

Spectrographic

trations.

the

study

coefficient

oxide or from mixtures

The degree of association

cation gradient in the MO

at

associated charged defects. saturation

present

diffusion

and vacancies

as complexes

a trivalent

material is present [8,9]. The

ion and vacancy are in a

association

nearest neighbor

halide

with a

microprobe

and

(magnification

to

did not reveal any discernible

or heterogeneities. crystals

were preannealed

temperature

for

at the diffusion

approximately

100% of

diffusion

anneal time to ensure that the dislocation

vacancy

substructures

were

equilibrated

the and

at the tem-

perature of interest. The high specific activity an activity

chromium

isotope used has

of l50m Ci/mg of 5’Cr in a 0.5N HCI solution.

The radiometric

purity

was >99%

with

no detectable

I solution of the isotope and a 0.01m solution of MgSO, . 7H20 were prepared, radioactive

tThis research was part of a thesis submitted by G. W. Weber in partial fulfillment of the requirements for the degree of Doctor of Phisosophy in Ceramic Science. SPpm by weight.

PCS Vol. 41. No. U-E

contamination.

and applied in IOA aliquots evaporation

of water,

A 2:

to the crystal

the sulfates

surface. After

were converted

to

oxides by heating at 1200°C in air for 30 min. The crystal was then annealed face to face with a duplicate uncoated

G. W. WEBER et al.

1356

crystal. The couple was held together with Pt-wire and annealed in a vertical Pt4ORh or molydbenum-resistance furnace which could be controlled to ?l”C. Diffusion annealed crystals were edge- and back-sectioned to a depth of >15 m to eliminate edge effects from vapor transport. The crystal was then mounted to a piston-in-cylinder polishing device and sectioned with diamond paste which was no coarser than 3 pm. The thickness of the section removed from the crystal was determined by a k2.5 pm hand-held micrometer, a dial guage comparator (accuracy kO.5 pm) and the weight loss technique. An analysis of variance performed on the results obtained by the three techniques indicated that there was no statistically significant variation attributable to the different techniques. Counting was done for the 0.320 MeV “Cr y-ray with a heavily shielded Tl doped NaI scintillation crystal and single channel spectrometer. The residual activity in the crystal was counted after a section of specified thickness was removed. To optimize counting statistics only activities larger than five times the background count level were utilized.

RESULTS AND DlSCUSSlON

The residual-penetration diffusion in undoped MgO “tail” was characteristic of study. The solution of the Fick’s

data obtained for the “Cr is shown in Fig. I. A long all profiles measured in this Law for this case is[ IO]:

Q

N(x, t) = 2(rD*t)l~2

2

( 4;*t>

exp --

(1)

where N(x, t) is the activity at a distance x after a diffusion anneal time I, Q is the quantity of diffusing

material, and D* the tracer diffusion coefficient. If a ratio is established between the total initial activity before any section is removed, A(O), and the activity remaining after a thickness x has been removed, A(x), in which activity is the integral of expression (1) over the applicable limits it can be shown that:

where F is the error function and erfc is the complementary error function. If a relatively high energy radiation passes through a material with low absorption and for small distances, the absorption corrections developed by Gruzin[ll] are not required. This could be shown to be true for 0.320 MeV y-radiation in the current experimental situation[lt]. The plot of the inverse complementary error function of A(x)/A(O) vs penetration distance for the data in Fig. 1 is given in Fig. 2. The two distinct regions of diffusion were consistently observed in the results if sufficient activity was available to resolve the curve fully. The first portion of the curve was used to determine the volume diffusion coefficient, D*, and the effect of the second slope (probably due to pipe diffusion) upon the first was mathematically extracted to yield a representative value for the initial slope[ 131. Diffusion was studied at three different temperatures 1383, 1444 and 1495°C using MgO crystals doped with O-O.34 mole % Cr203. Results obtained for the different temperatures are shown on Fig. 3. It is evident that there is an approximately linear relationship between D(Cr*) and the concentration of dopant. According to Lidiard’s model in which the complexes are regarded as diffusing species, the intrinsic diffusion coefficient, D(G), of the impurity is related to diffusion of the complexes as

COUNTS

1,000

1

L

0

20

1

I

40 PENETRATION

Fig. 1. Residual

counts

vs penetration

distance

I

60

for an undoped

60 (MICRONS MgO

I

I

100

120

1

single crystal

at 1490°C for 6.19 x I@ s.

Diffusion of “0

in Cr-doped MgO

PENETRATION

1357

(MICRONS)

vs penetration distance for an undopedMa0 crystalat Fig. 2. Inverse complementary error function of [A(x)/A(O)] 1490°Cfor 6.19~ lo’s

15.

P 1383°c 0 1444oc cl 1495oc

MOLE

PERCENT

Cr203

Fig. 3. Diffusion coefficient of “Cr in Cr-doped MgO single crystals as the function of the concentration of dopant and temperature.

developed an expression for p:

follows:

I/Z D(Cr) = Do [y]

(3)

where & is the diffusion coefficient of the complex, p is the degree of association, c is the total impurity concentration [CrJ expressed as atomic fraction. For diffusion of Cr* tracer in uniformly doped crystals p is constant along the diffusion profile so that: (4)

D(Cr*) = Dep. Perkins

and

Rapp[9]

following

Lidiard’s

theory

p =3/4+&This yields for D(Cr*)

l/16+3+1 4cA

4c2A2

’

(5)

in the limit of low concentration: D(Cr*) = Doy

(6)

Do = const. exp (- E,/kT) where I?,,, = activation energy for motion of the Cr-vacancy complex A = 12 exp (-EJAT)

G. W. WEBER ef

1358

al.

EA = the association energy of the Cr-vacancy complex and c = total Cr ion concentration expressed as atomic fraction. For the above conditions the slope of In D* vs l/T would yield the difference in the energy of association and energy of motion: AE=E,,,-IEp,/

(7)

In the current observations, the diffusion data were well represented as being proportional to c but did not extrapolate to zero as predicted by the model. The extrapolated values for D(Cr*) to zero concentration of Cr3+ were consistent in order of magnitude with the values obtained in measurements on similar but undoped MgO crystals as shown in Figs. 3 and 4. It is postulated that the diffusivity observed in the undoped MgO and the non zero extrapolated values of D(Cr*) for the doped MgO crystals result from the contribution of the background impurities to the diffusivity. Assuming for example that the significant impurity is W+, that at the temperature of interest Si” is sufficiently associated such that it does not effect the Cr ion-vacancy association equilibrium, the contribution of the Si4’ to the observed D(Cr*) would be then independent and additive to the Lidiard expression. The data for the undoped MgO crystals were therefore used to determine a D(Cr*)sit which was subtracted from the measured data for the doped crystals. These corrected data were then analyzed according to the Lidiard model as extended by Perkins and Rapp[9] and are shown in Fig. 5. A computer program (MINITAB) for multiple regression applied to Arrhenius representation of the data, Fig. 6, yielded an average energy of

ATOMIC

5.6

OF

CHROMlUM

(x103)

5.7

5.6

5.9

6.0

104/ T(“K-‘)

Fig. 6. LogD

71

FRACTION

Fig. 5. Corrected values for diffusion coefficient of 5’Cr in Crdoped MgO as the function of the concentration of dopant and temperature.

vs l/T

for the diffusion of J’ in Cr-doped obtained from Fig. 5.

MgO

19.6? 1.7kcal/mol and the overall accuracy is *3 kcal/mol. It is concluded that the observed activation energy in the undoped crystals represents the activation energy of motion for an associated impurity. For the crystals used in this investigation this energy was 74.3 kcallmol and is identified as the energy of motion for the Si-vacancy associate. The activation energy determined from the doped crystals corrected for the background impurity contribution is then the difference between the energy of motion and the energy of association of a Cr-vacancy complex: AE = E,,, - lEAI = 19.6kcallmol

Fig. 4. Log D vs l/T

for the diffusion of s’Cr in the MgO single crystal.

tD(Cr*)si is the tracer diffusion coefficient of Crr’ controlled by the Si’+ impurity concentration.

in MgO

(8)

According to Glass and Searly[l4] the energy for motion of the Cr-vacancy complex in MgO is 39.9 kcal/mol. If we take this value to be correct then according to our results the energy for association of chromium-vacancy pairs is 20.3 -+3 kcal/mol or 0.88 * 0.13 eV.

Diffusion of s1 Cr in Cr-doped MgO Acknowledgements-Experimental part of this work was supported by the Office of Naval Research under contract No. N001467-0385-001 I and the work on the theoretical interpretation of results was supported by the Department of Energy under Contract No. ER-78-S-02-4998.

REFERENCES

I. Lidiard A. B., In Handbuch der Physik (Edited by S. Fluegge), Vol. XX, pp. 298-339. Springer-Verlag, Berlin (1957). 2. Hanlon, J. E., J. Chem. Phys. 32, 1492 (1960). 3. Siiptitz P., Proc. 6th ht. Symp. on Reactivity of Solids, (Edited by J. W. Mitchell, R. C. DeVries, R. W. Roberts and P. Cannon) pp. 39-36. Wiley-Interscience, New York (1%9). 4. Hembre P. and Wanner J. B.. Trans. Met. Sot. AIME 245. 1547 (1%9). 5. Chen W. K., Peterson N. L. and Robinson L. C., In Annual

6. 7. 8. 9. IO. I I.

1359

Review of Materials Science (Edited by R. A. Huggins), Vol. 3, pp. 75-109. Annual Reviews Inc., Palo Alto, California, (1973). Carter R. E. and Richardson F. D., Trans. AIME 200, 1244 (1954). Rahman S. F. and Berard M. F., J. Am. Gem. Sot. 60, 67 (1977). Minford W. J. and Stubican V. S., J. Am. Gem. Sot. 57,363 (1974). Perkins R. A. and Rapp R. A., Met Trans. 4, 193 (1973). Jost W., In D&ion in So/ids, Liquids and Gases, p. 17. Academic Press, New York (l%O). Gruzin P. L., Izvesl. Akad. Nauk SSSR, Ord. Tekhn. Nauk 3,

353 (1953). 12. Weber G. W., Ph.D.

Thesis. The Pennsylvania State University (1974). 13. Harding B. D., Phys. Status Solidi BSO, 135 (1972). 14. Glass A. M. and Searly T. M., J. Chem. Phys. 48, 1420 (1968).