Theory of deformation luminescence in KCl crystal

Theory of deformation luminescence in KCl crystal

Volume 147, number 4 PHYSICS LETI’ERS A 9 July 1990 Theory of deformation luminescence in KC1 crystal Y. Hayashiuchi Osaka Electro-Communication Un...
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Volume 147, number 4

PHYSICS LETI’ERS A

9 July 1990

Theory of deformation luminescence in KC1 crystal Y. Hayashiuchi Osaka Electro-Communication University, Neyagawa, Osaka 572, Japan

T. Hagihara Department ofPhysics, Osaka Kyoiku University, Tennoji, Osaka 543, Japan

and T. Okada Institute ofScientificand IndustrialResearch, Osaka University, 8-1, Mihogaoka, Ibaraki, Osaka 567, Japan Received 8 September 1989; revised manuscript received 13 December 1989; accepted forpublication 14 May 1990 Communicated by J.I. Budnick

A theory ofdeformation luminescence (DL) in KC1 crystal colored by y-irradiation is presented for understanding the characteristics ofthe DL intensity I. The intensity calculated by simple rate equations describing the change in the numbers ofluminescence centers and electrons explains well the deformation rate and temperature dependences of!.

A broad band light-emission from plastically deforming alkali halides colored by X- or y-irradiation has been observed by Pirog and Sujak [1] and was then named deformation luminescence (DL) by Butler [2]. Several workers [3—7]have proposed the dislocation mechanisms for DL. Namely, the dislocations by overcoming the F-centers may ionize the F-center [8], as F—+F~+ e—, where e is the released electron in the conduction band. If the electron recombines radiatively with any luminescence center, we observe this phenomenon as DL. In a previous paper [9], we reported the experimental results on DL at low temperatures in specimens subjected to yirradiation at LNT following warming up to room temperature. Based on the spectrum analysis of DL, we concluded that the V2-center acts as an effective luminescence center in colored KC1 crystals. Several workers [2,9] have found experimentally the characteristic behaviors of the DL intensity I. I increases 2, with the straina rate obeying a power law Iccthe E’ where a takes valueE, of about 0.6— 1. Besides, observed I as a function of temperature fits well an evident Arrhenius plot. The activation energy was 0375-960l/90/$ 03.50 © 1990

—

evaluated to be about 0.06—0.1 eV. There have been, however, only a few comprehensive theories which can explain these behaviors of!. In the following, we show a theory about E and the temperature dependences of !, describing the DL process by a simple rate equation. When the dislocations encounter the point defects, the dislocations interact with them elastically [10] or electrostatically [11,121 and then overcome their barrier with the help of the thermal activation energy. If the point defects are electron centers, such as F- and F—-centers, the trapped electron in the centers will be excited into the conduction band through the interaction with dislocations [8,13]. The free electrons produced in this way are trapped again by some color centers, such as F-, F~-centersand V-type centers. Let us denote the color center of kind X which captures electrons by Xm write theInnumber of Xm by them same symbol Xm and for brevity. case that X is an F-type center, m just equals the number of electrons trapped in the centers and thus X 0, X1 and X2 represent F~-,F- and F—-centers, respectively. If,

Elsevier Science Publishers B.V. (North-Holland)

245

Volume 147, number 4

PHYSICS LETTERS A

however, X is a V-type center, m does not cone-

dXm

spond to the number of electrons trapped in Xm, since the V-type center is a hole center so that free electrons captured in this center annihilate simultaneously. Let the total number of Xm’S be X, i.e., X= ~ ,nXm, where the sum ~ m is taken over the possible values of m for the color center of kind X. In the present system the temperature is not so high that the point defects cannot easily migrate in the crystal. The number X can be then treated as a constant. We also assume that the free electrons in the specimen hardly escape from the surface. The total number of free and trapped electrons is then conserved, i.e.,

dt

9 July 1990

—=x,n_

1x

—1

~X,n+IX

4 XmXm,m4~i

XmXm.m_i.

The solutions of these two equations evidently satisfy the conservation law (2). The electron releaserate Xm,m_j is a constant and depends on the release process due to the dislocation motion as well as the thermal activation. The electron capture-rate Xm,,,, +1 for xm can be written in terms of iC~,,,, the electron capture cross section multiplied by the electron yelocity and C, i.e., (5)

Xmm+iKxmfl.

N+~mX x

=C,

m

where C is a constant, N is the number of free electrons and the sum~xis taken over the kinds ofpoint defects. Since none of the point defects are excited by moving dislocations before the deformation, N equals zero initially. In our system C then equals the number of F-centers before deformation, because Fcenters are unique defects which contain one electron before the deformation. For simplicity, we normalize Xm, Xand Nby C, i.e., XmXm/C, nN/C, x= X/C, respectively. The conservation laws for the numbers of electron capture centers and electrons are then written as .~

n

+

~‘

= .~

—1 ~ mx,~ —

(1) ~ ‘

/

The numbers n and Xm change with time during the deformation process, which can be formulated by the rate equation in the following way. Let us introduce the transition probability x 13 per unit time from the state x to the state xj. For i >1, x1,3 corresponds to the electron release-rate of x and for i
246

Kxm generally depends on the type of the capture center Xm. Because of eqs. (2) and (5), eq. (4) then becomes a nonlinear differential equation for Xm’S. In terms of xm and Xm,m+ ~, the number of photons emitted from xm per unit time ‘xm is expressed by the general form ‘xm = CXmXm m +1, provided that the transition Xm~Xm+ takes place following the emission of a single photon. This can be also written as

(6)

‘x,n = CXmKx,n fl ç

rom eq. In KC1 crystal containing F— and V-type centers, the analytical solution of n can be obtained under some reasonable assumptions. According to the ex3 slab by asingle photomultiperiments [9], DL fromobserved colored KC1 crystal of a 3tube plier x 6 xwhich 8 mmis set at a distance of about 30 cm from the specimen, is l0~—l0~ photons/s. This in.

tensity seems relatively weak, although the crystal contains enough F-centers of C—’ 10 ‘7/cm3 and Vcenters of Cv’--’ lO’6/cm3 [91.The observed DL intensity will depend on the solid angle of the measuring system to the specimen, because the photons are emitted from the specimen in isotropic directions. Even if the DL intensity is corrected with a solid angle 1 0~,however,the DL intensity from the 3 s. This specimen issuggests evaluated to be photons/cm evaluation that n <<108 1 during the deformation. Under this condition, we can obtain the steady state solution for n in an approximate form, 2

=

x

~

~,?

(XmXm.miXmXm,m+i),

(3)

+i

nnilI’XF_FXFF+ \ ICFICF+

Volume 147, number 4

PHYSICS LETTERS A

from eqs. (3) and (4). Here XFF and x~+represent the electron release-rates of F—- and F-centers, respectively, and ICF+ as well as ICF are Kxm in the case of F~-and F-centers, respectively. The transition xm—xm_I for V-type centers is entirely impossible, since m in Xm does not correspond to the number ofelectrons which are trapping in this center. Then, in the steady state, all of the Xm for 0 ~ m ~ M~ 1 vanish, where M~ is the maximum number of electrons which the V-type center can capture. This leads to the result that the DL intensity decreases with time and then approaches zero in the steady state. If, however, the number of V-type centers presumably introduced in the crystal is large and the electron capture cross section is small, the DL intensity decreases with very long decay time and then quasi-constant luminescence after a certain time will be realized. In such a condition the change in Xm for the V-type center is small, so that we can put x0—_C~/Cand Xm0 for m>~1 in the quasi-steady —

state. Hence the DL intensity from the V-type center is given uy ~

I !4’Ky PCF KF+

)

\1/2

(XF_FXFF+)

1/2

(7)

9 July 1990

the order of 10— 8~We assume that the electron release by dislocation takes place just after the dislocation is unpinned from the pinning defect. t~ and t~ are therefore roughly equal to the pinning time r which is of the order of 1 s [15,161. Since the free F-center is thermally stable even at room temperature [17], we find that iF>> t~ ( t). ~ r~is so long that the relation it/iF <


XFF+

1.

Similarly, we have (9) provided that the relation t~_/tF_ <


XF-F~P/’t,

,~ 1/2

/

(

~,

\‘4’1CF+J

t

I~C~,, K’~14’ ~

(10)

.

showing that Its proportional to 1 ft. Hence the strain rate and temperature dependences of I become similar to that of 1 ft. Figs. 1 and 2 are typical experimental data on land lit, as a function of inverse 100

being ~ in eq. (5) for V-type centers. Some of the F-type centers are free from the dislocations, so that XF-F and x~+for such defects are owing only to the thermal activation. Others, however, are interacting with the moving dislocations. We then consider that the electron release process is enhanced further by the dislocation motion. We will introduce the rate ofthe point defects interacting with the dislocations and denote this rate by p. The averaged XF_F and x~+are given by

0

I

iCy

I

i0~

I

K Cl

-

-

1

-

10

0

“~k~ 2

1 ~

10

I

-

~

2

XF-F=p/TF_+(lp)/TF-,

where TF_ and r~are the lifetimes of F—- and F-centers free from the dislocation interaction, respectively, and r~and i~ are that of F—- and F-centers interacting with dislocations, 2p, respectively. candisbe where p isp the given approximately location density and byr p~itr is the effective interaction range between dislocation and point defect. Ifwe assume r—. b and take p = 1 0~cm/cm3 in KC1 crystal plastically deformed by 1% strain, p will become of

I

a.

N.

-

“N

N

N

Oo 100 ~

‘N.., io~ 2

4

E

1

I

I

~

6

‘N I (K—1)

I

8

10

Fig.

1. DL intensity land inverse pinning time 1 /r asa function of mverse temperature lIT.

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Volume 147, number 4

PHYSICS LETTERSA

‘00 I

I

v= v

2

~0

‘

0 exp(

KC~

~ 10-1

-

-

2!

/~—

I

~

io—~

1°~

‘j’

~

~7

~ 1O~a

/0 o,/~

E

100 ~ I

4

io3

io-2

io~ Strain Rate io- (s1)

106

9 July 1990

—

where , and v0 are the average potential that controls the movement of dislocations, the average activation volume for overcoming and a constant, respectively [20]. For a>> kT, this can be approximated by

((

v~v0exp

—

temperature and strain rate. The electron capture cross sections2 of F-centers is of the toorder of [18], which corresponds the size 7.5an x atomic l0’~cm of cross section. Although we have few detailed data on the electron capture cross sections for F~-and V-centers, these will be ofthe order of 10— i5 cm2 [19], since the wave function of these defects is expected to spread in an atomic size. Hence we can put iCy PCF ICF+, and eq. (10) reduces to I—~C’~p/i. If we take the typical values Cy = 101 5 l016 cm3,p= 108 and 100 s [ 15,16], Ibecomes of the order of 107_l08 photons/cm3 s, which is in good agreement with the empirical data. t depends on the dislocation motion against the pinning force caused by the point defects. In addition, this movement of dislocation is also controlled by a thermally activated process. Let us denote by U the potential energy of the obstacle for the dislocation to overcome and denote the activation volume by Q. The depinning probability per unit time 1/i is then given, through general arguments [18], by l0_I6

kT — a\ )‘

so that we have E~E 0exp —

Fig. 2. DL intensity land inverse pinning time I ft as a function ofstrain rate.

/kT) sinh( a/kT)

—

kT

)

because of the relation E = bpv [21]. Eliminating a from 1/i and v, we obtain 1/i as a function of E and T in the form l/i=(l/ro)(E/Eo)aexp(_U~/kT)

where U’ and a are defined as 1 Q\

,

(11)

—

U ~

U)c~~a=—~—,

respectively. Hence, inserting eq. (11) into eq. (10), we have the strain rate and temperature dependences of I in the form IxEaexp(_U~/kT) (12) For U and —SQ, we have a— 1 and U’ .~U. If
l/r=(1/r 0) exp(—U/kT) sinh(Qa/kT) where a is the applied stress and r0 is a constant. This reduces to

1 /r= (1/i0) exp [

[1] M. Pirog and B. Sujak, Acta Phys. Polon. 33 (1968) 865. —

(U— Qa) /kT]

for Qa>> kT. In this expression, a depends strongly

on the deformation rate e under the condition that ~ is kept constant. The average dislocation velocity v is given by a form similar to 1/i, 248

References

[2]C.D. Butler, Phys. Rev. 141 (1966) 750. [3] F,I. Metz, R.N. Schweiger, H.R. Leider and L.A. Girifalco, J.Phys.Chem.6l (1957) 86. [4] H.R. Leider, Phys. Rev. 110 (1958) 990. (5] F.D. Senchukov and S.Z. Schumurak, Soy. Phys. Solid State 12 (1970) 6. [6] S.Z. Schumurak, Soy. Phys. Solid State 10 (1969) 1526.

Volume 147, number 4

PHYSICS LETTERS A

9 July 1990

(7] S.Z. Schumurak and M.B. Eliashberg, Soy. Phys. Solid State 9(1967) 1427. [8] W.W. Tyler, Phys. Rev. 86 (1952) 801. [9] T. Hagihara, Y. Hayashiuchi,Y. Kojima, Y. Yamamoto, S. Ohwaki and T. Okada, Phys. Lett. A 137 (1989) 213. [10] A.M. Stoneham, Theory of defects in solids (Clarendon, Oxford, 1975). [11] R.W. Whitworth, Ady. Phys. 24 (1975) 203. [12] T. Kataoka, L. Colombo and J.C.M. Li, Philos. Mag. ‘~

[15] T. Hagihara, Y. Hayashiuchi and T. Okada, Phys. Lett. A 108 (1985) 263. [16] T. Hagihara, Y. Hayashiuchi and T. Okada, Phys. Lett. A 115 (1986) 385. [17] C.K. Clifford, in: Point defects in solids, Vol. 1 (Plenum, New York, 1972) ch. V, p.291. [18] J.J. Markham, F-Centers in alkali halides (Academic Press, New York, 1966) p. 132. [19] Varley,Y.Nature 174 (1954) 886. [20] J.H.O. T. Hagihara, Hayashiuchi and T. Okada, Cryst. Lattice

(1984) ~ [13] K. Asami, T. Nab and M. Ishiguro, Phys. Rev. B 34 (1986) 5658. [14] A.T. Bharucha-Reid, Elements of the theory of Markov processes and their application (McGraw-Hill, New York, 1960).

Defects Amorph. Mater. 16(1987)105. [21] J.J. Gilman and W.G. Johnston, Solid state physics, Vol. 13 (Academic Press, New York, 1962) p. 147.

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