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Radiation stability of carbon foil microstructure
Nuclear Instruments and Methods North-Holland, Amsterdam
in Physics
RADIATION
OF CARBON
STABILITY
E.A. KOPTELOV,
S.G. LEBEDEV
Research
3 November
239
FOIL MICROSTRUCTURE
and V.N. PANCHENKO
Institute for Nuclear Research of the USSR, Academy Received
B42 (1989) 239-244
of Sciences, Moscow II 7312, USSR
1988 and in revised form 30 January 1989
A problem of a radiation shrinkage of carbon foils due to amorphous-graphite phase transition is considered. The graphitization kinetics under irradiation is shown to be described by chemical rate type equations. Such an approach gives the possibility of estimating the lifetime of amorphous and graphite targets. In conditions when a surface absorption of freely migrating component is negligible compared with the volume reactions of radiation defects the dimensionless equations for hydrocarbon foils graphitization and for clustering of radiation defects in graphite are indentical. This gives an expression for the lifetime ratio. Numerical estimates agree well with the experimental data. The glow discharge foil deposition is assumed to include the following processes: the nucleation, the growth of layers and the graphitization of amorphous layers. Estimations of corresponding characteristic times based on experimental data show that these processes can be considered independently. After the nucleation stage the graphitization develops in slowly growing films and so the above-mentioned kinetical model can be applied. As a result estimations of both the graphite domain size and the amount of bound hydrogen vs glow discharge conditions follows in satisfactory agreement with quoted data.
1. Introduction A carbon stripper target failure under ion beam bombardment [l] led us to model the lifetime of carbon foils in terms of stresses induced by radiation defects. The carbon foil was considered to be in a stable crystalline state like graphite. Glow discharge (GD) cracked foils [2-41 are perhaps in such a state. The GD foil structure depends on the glow discharge potential V. Foils prepared at voltages Vi 2.5 kV are stable but exhibit an enormous rate of shrinkage leading to an early rupture under irradiation and breakage into many pieces [4]. With rising voltages the rate of shrinkage had been found to decrease but no significant differences in the lifetime were observed. Foil lifetime which is discussed was defined in the experiments as the time to reach half beam intensity. Voltages in the range 2.5 < V I 3.5 kV are found to produce satisfactory foils with decreasing shrinkage as compared with foils produced at lower voltages or by the carbon arc (CA) methods. The structure and properties of thin amorphous carbon films have been investigated by a solid-state magnetic resonance method [5]. The corresponding data are shown in table 1. The difference in the properties is probably due to the allotropic nature of the carbon with threefold (sp2) as well as fourfold (sp3) coordinations. The relative importance of these bonding sites on the physical and electronic properties represents a key issue in understanding the behaviour of amorphous carbon. Ignoring the special case of diamond it may be seen that 0168-583X/89/$03.50 0 Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
the film density and fraction of tetrahedral (sp3) bonding correlate with hydrogen content in the films. For the hydrogenated carbon films described here it is proposed that the domains of trigonal (sp2) carbon atoms are separated not by diamond like regions but by hydrogenated tetrahedral (sp3) carbon atoms in grouppings CH,. Thin carbon films prepared by evaporation and deposited at room temperature have been found to be amorphous [6] with a structure composed mainly of randomly linked tetrahedra. The graphite domain regions are separated by tetrahedral carbon atoms or dangling bonds. Under heat treatment progressive graphitization proceeds as the diameters of the domains increases until polycrystalline graphite is produced. Irradiation appears to produce similar changes to those of the pre-graphitization stage of heat treatment [7].
Table 1 The structure
and properties
of thin amorphous
carbon
151 Material
sp2/sp3 (W)
Bound H (at.%)
Density
Diamond rf-anode rf-cathode dc-anode dc-cathode Graphite
O/100 14,‘86 20/80 so/50 60/40 100/O
0 61 58 47 31 0
3.0-3s 1.02 f 0.08 1.17kO.08 1.47+0.01 1.7 *0.01 2.3 k2.7
(g/cm3 )
films
240
E.A. Koptelov et al. / Radiation stability of carbon foil microstructure
The different properties of the glow discharge deposited films can be attributed to differences in the growth environment. In the glow discharge process condensable radicals form an amorphous film whose structure is modified during growth by ion bombardment and other energetic processes. The growth en~ro~ent at the rf anode is characterized by the lowest ion energy, thus favoring hydrogen incorporation and sp3 bond formation. The higher energy at the rf cathode and dc electrode surfaces promote hydrogen loss and sp’ bond formation. It has been suggested that during high-energy surface bombardment weaker bonds are removed from the growing film. Thus the more tightly bonded three or fourfold coordinated carbon atoms will survive over singly bonded hydrogen. Also, since double bond hydrogenation is an exothermic process graphitic bonding is favored over tetrahedral bonding in higher energy growth en~ro~ents. By means of infrared spectroscopy 1’71with low power densities and relatively high gas pressure (1-2 Wcm-zTorr-‘) C-H bonds were observed. As the power density was increased to around 40 Wcm-*Torr-’ the hydrocarbon bonds disappeared although hydrogen was still present. With higher power density there was indication of graphitization and reducing hydrogen content assumed to be caused by heating effects. The samples prepared using a glow discharge in ethylene with 10% argon at “normal” power density have a low content of bound hydrogen - 7 at.% [7] (1 at.% [S]) which indicates the predominance of a graphite-like phase in the foils (table 1). The radiation shrinkage is determined in this case by accommodation of radiation induced defects [l J. On the other hand the degree of sp3 to sp2 transition indicates both the density change and the rate of radiation shrinkage.
2. The graphitization kinetics Fig. 1 shows a graphite-like domain surrounded by a hydrogenated diamond-like region in the configurations of CH,. The microstructure variation is associated with both, disappearance of the sp3 phase and growth of graphitelike regions by means of the displaced sp3 phase carbon atoms accumulation at the edges of graphite domains. The graphitization kinetics equations may be obtained by means of the following assumptions. Under irradiation broken tetrahedra are created as a result of the destruction of sp3 phase bonds. The broken tetrahedra and displaced sp3 phase carbon atoms are homogeneously generated by the ion flux throughout the amorphous phase. The fate of an displaced atom may be any of: (a) recombination with a broken tetrahedron, i.e. regeneration of the CH, cell; (b) trapping by another displaced
0 CARBON * HYDROGEN
ATOM ATUM
Fig. 1. Graphite-like domain su~ound~
by hydrogenated diamond like regions in the ~nfigurations of CH,.
atom and thus forming the nucleus of a graphite domain; (c) annihilation at the edge of a graphite domain, causing the domain to grow. Here we assume that the annihilation at the foil surface can be neglected, implying that the probability of trapping by (a), (b) and (c) dominates. We propose that the sp3 phase displaced atom is situated inside the tetrahedron (see fig. 1). Each broken tetrahedron is surrounded by N sites for trapping displaced atoms where N is equal to the number of CH, grouping tetrahedra. The number of jumps per second to a trapping site is N-‘v, (where u = bv exp( - EJkT) is the displaced atom diffusion speed, b = ( K)-‘/3 _ the hopping distance, K = p/rn,p - the amorphous phase atom number per unit volume, ~1the amorphous phase molar mass, p - the amorphous phase density, m, - the atomic mass unit, Y - the appropriate vibration frequency, Em - the activation energy for displaced atom motion). Thus the rate of an displaced atom recombination with a broken tetrahedron is
Here n,, rra are the amorphous phase broken tetrahedron and displaced atom concentrations per unit volume respectively, SE= 2( K)-2/3. Next we calculate accurately the rate at which the edge of a graphite domain may accumulate the displaced atoms. In order to do this we must calculate the number of sites from which a displaced atom may jump to become attached to the half-plane of an edge and this involves the calculating of the number of appropriate sites per unit length along the edge of a graphite domain. If the atom considered can reach the edge of the graphite domain by a single jump then the ~~~p~ding number of sites
E.A. Koptelov et al. / Radiation stability of carbon foil microstructure
is equal to 2N/3. The graphite bonds number per edge unit length is 4/(fiaa) [9], where a is the graphite space lattice constant. The area per graphite domain lattice atom is 3a2fi/4 and if a graphite domain has a radius r, and hence a total line length of 2ar, the rate at which it grows is: d(nr’) -1 ~ 2-rrr
dt
=
+N-1v)na,-1 $?- ???$
Ap _=_-
dt
If na( r, t) is the domain size distribution function then the total rate of loss of the displaced atoms to graphite domain is: W2=rno(r,
t) drNjNPiU4n,KP’ bPJ5
83 = -nonavD 3a&i
= G - n.n,vQ/2
’
dn t
= G - n,n,v0/2,
dt
-
The amorphous foil material deformation graphitization can be estimated easily from: Al 1 (Ps-P) -i- &= 3p,K’
II II y
= 0,
= (0.2Kl
- 0.14K2)$,
(11)
s
(4)
where No* = nrdm, nr is the graphite domain asymptotic density, t the irradiation time of a foil. The formation of a graphite domain takes place after the nucleation time to e t, - the amorphous foil lifetime as is shown in [lo]. It is easily seen from the solution of eq. (4)-(6) that n a + 0 at t + co. Hence one may consider that all displaced atoms (besides taking part in the (a) and (b) processes) are trapped by the graphite domains and therefore they acquire sp’-coordination. The foil material density may be represented as follows: ii=Pw+Pa(l-K),
(8) density,
nt
s
tV3~V6(
nV=
ps is the graphite
under
where
81 -non,vO 3afi
where G is the displaced atoms creation rate per unit volume per unit time in the amorphous phase. In these relations the derivatives and squares of n, which tends to zero at large times are neglected. The effect of defect formation within the graphite zones has also been neglected. Thus the asymptotic behaviour of the broken tetrahedra concentrations is:
where
K’
PS
Next we calculate the lifetime relation of the amorphous and graphite targets. It is generally accepted for graphite structure foil [l] that
where i is defined by ti o = jFrno(r, r) dr, no being the graphite domain density. The equations describing the graphitization process at large times are dn a
n,
(4-P)
P
dr - = vn,Da/lr.
dt
carbon atoms with the sp3 coordination, p = 0.83 g/cm3, as may be obtained by using the table 1 data. An increment in the foil material density under irradiation is
thus
71a
thus
/0
241
K -
the fraction
of
Q~,)-“~.
k,, k, are textural coefficients [l], complexes asymptotic density, kg number per unit volume. Assuming both the graphite and amorphous of (7), (lo)-(12) gives the lifetime
(12)
Nlm - the interstitial - the graphite
atoms the same strength of foil the combination ratio:
here tg is the graphite target lifetime, Gg - the graphite phase generation rate. In the case where the interstitial complexes are the main defect sinks one can obtain Nm = r213 [lo]. Since K = p/mop this leads to the following estimation: ‘k, =
exp[ (E$ - E,)/6KT] x
[PK+Pg(l-K)]
1 3’2
’
(14)
As E, = kT, [ll], where T, is the melting point of the material, qC seems to be slightly depending on T.
242 3, TIM mkrostructure glow discharge
E.A. Xbptelou et al. / Radiation stability ojcarban foil micrastructure development of c~bon foils in the
Let us consider the foii deposition under glow dischwge ion ~mb~dm~t in detail. The ion energy in a @ow ~scb~ge pTasma such as ~~u~ter~ during deposition of a f&n is a ~s~bnt~ q~~~t~. The energy d~st~b~t~o~ is strongly peaked at - 0.2 V [12] with a t&t extending up to higher energies. In Tait’s experimertts [q the average energy therefore is E = 500-800 cV. The, range of the majority of ions R will be some 30-40 A [13]. Except during the initial stages in film growth the range will be considerably less than the thickness of the film. Consequently the conditions of uniform generation of defects are only achieved in the neax surface of the film and the foil surface probably is the main defect sink. Let us consider the question: how the foil microstructure utiu be ~~sfo~ed under glow discharge ion bomb~~ment~ This is evidently not the case of the modified microstructure domain size to be more than R. In reality the glow discharge foil deposition includes three processes, namely: 1) the nucleation, 2) the growth of amorphous layers and 3) the amorphous layer graphitization under intense intrinsic ion beam bombardment, Let us calculate the corresponding characteristic times of these processes. Assuming the foil deposition rate in T&t’s experiments is about 4 A/s the range time deposition t, = ta will be about 10 s. The nucleation time can be estimated as f, = fG’& + ft~,~‘R)“]-‘~~ = ffF5 s fG* is the totaT displaced atoms creation rate) as is shown in ref. flO]_ The growth time of the graphite domain is estimated ga = Ra/(z&) = 10-s s, As can be seen &he characteristic times are represented by the rdation 1, e t, c I, and these three processes can be regarded independently. Therefore process 3) can be treated in the framework of the graphitization model, which is presented above. Aasurning the graphite crystalline dimension expected to be never more than B let us calculate the amorphous phase fraction and the me&n crystallite size in the growing f&n. fn order to do this we must consider the kinetics rate equators in the near surface gruwing layer of a f&n the thickness of which is never more than R. The surface &spIaced atoms sink number per unit volume pit, will be some (@h)-‘, where St = (K)-2/“, h is the layer thickness, Assuming h = R/2 the mmpbous phase formation kinetics equations may be represented as follows: 2vn* dnx dt=G*-n:n:vL?* =O, tstt,, 05)
Table 2 A comparison of cakulated bound H fraction with th*t experimental data Glow discharge co&lions
Cakxdated atomic % H
EkperimerM
pure ethylene
20
2S.Sf 5.8
30% argon 10% argon, reduced power
0 49
7.5 i 2.1 42 i8.6
atomic
% H 171
Gffw
discharge Glow discharge Glow discharge
where C* is the glow discharge displaced atoms crew tion rate in the growing film (see below), 7* - the mean graphite domain radius, n:, n: - the amorphous phase displaced atoms and broken tetrahedra concentrators per tit volume, respectively_ The third term in the right hand part of eq. (115) is the surface displaced atoms sink intensity obtained by means of an embedding procedure within a uniform lossy medium [14], The main displaced atom flow in this case is trapped by a surface where new layers growth takes place. In Tait’s experiments a glow discharge was performed in a mixture of dried ethylene and 10% argon gas. According to Bondarenko /12] a glow discharge plasma mainly produces singly charged ions. Assuming the displaced atoms creation rate by H ions to be relatively small as compared with Ar md C km displaced atoms creation rates the total displaced atoms creation rate in the growing film may be represented as foUows: P=G,*,“+G,y,
fW
where c;,*,, G$ are the creation rates of the Ar” and Cf ion displaced atoms respectively. The terms in the right hand part of the eq. (18) may be calculated according to the approach of ref. [I] (see table 3). Eq. (15) may be regarded as stationary especMly in view of the h$.& mobility of the displaced atoms. Therefore the solution of the set of equations at time t, may be written as follows: 09)
11:=2 J*
=
IGJt,
cw
$@q&&,
(21)
d ~-$R s
where a = I.6 x 10-s cm is the graphite lattice conistant. The approximation G*QRt, z+ 1 is used which is correct for all practical cases. The sps phase quantity that is transformed in& graphite may be obtained by means of relation (20). The mean graphite domain size which is formed in the
E.A. Koptelov et al. / Radiation stability of carbon foil microstructure
glow discharge foil can be evaluated by means of relation (21). It is obvious that n: is the carbon atoms fraction which acquire the graphite sp2 coordination assuming the initial foil structure has been amorphous. As is shown in ref. [7] the CH, groupings are the predominating coordination of bound hydrogen. Then the middle fraction of bound hydrogen is: f”=
(1+
[2(1-
%)1’)j’.
243
where a is the graphite phase relaxation volume per vacancy. The graphite phase increment due to defect formation is described by the difference between the third and the sixth terms in right hand side of relation (24). Therefore the pure graphite phase deformation can be expressed as:
(22) Thus the graphite foil lifetime may be represented as follows (see eq. (11)):
4. Results and discussion The glow discharge cracking of an ethylene-argon mixture produces carbon films that are more resistant to radiation damage than those prepared in the conventional manner. For example the comparison of glow discharge foils made in 10% argon and standard foils made by carbon arc evaporation show a lifetime enhancement ‘k, = 9 [15] for 1.2 MeV argon ion beam. The same lifetime ratio for glow discharge versus evaporated foil is obtained at Oak Ridge [16] for 10 MeV chlorine ion beam. In the Chalk River experiments the lifetime enhancement, ‘k, = 10-12, is obtained for 10.5 MeV iodine ion beam. Despite a lot of experimental data on the carbon foil behaviour under ion beam bombardment there is as yet no clear understanding of the lifetime enhancement. In this study we have attempted to shed some light onto this problem. The analysis given above indicates that the lower the content of amorphous phase in the foil and the greater the foil graphite phase hence the greater the foil lifetime. From our study the lifetime ratio for pure graphite versus amorphous foils may be obtained as a function of amorphous phase fraction K by means of relation (14). As K + 1 a pure amorphous phase foil is achieved. Assuming G = Gs one can obtain the maximal lifetime ratio: YP c_ = 35.
(23)
On the other hand as K + 0 the foil structure tends to be pure graphite and to check the model the effect of defect formation within the graphite domain must be taken into account. Therefore the increment in the foil material density under irradiation will be the following:
+a& ( -a(1
l-K+
2)$
-,,K-&(1-K) g
-
K)4$, i3
thus
AP _ P
h--p) nt +a>?, P&C
K
K Kg
(25)
The combination of (ll), tion: a = %(0.2K, u
(12) and (27) gives the evalua-
- 0.14K2)2
= 0.144 at. vol.
(28)
For the evaluation of the vacancy relaxation volumes of the other materials a has been taken to be 0.1 at. vol. for MO and 0.05 atomic volume for Al [18]. As a can be regarded as independent of the irradiation conditions one can obtain ‘k, + 1 as K tends to zero. From equation (14) ‘k, seems to be slightly dependent on T. This point needs to be tested experimentally. Because the carbon atoms displacement energy depends on its coordination in the lattice one can see that G/G, # 1 at all. Unfortunately the displaced atoms creation rate data for amorphous carbon foil is not known. As is shown in ref. [7] the arc evaporated amorphous phase fraction K is equal to 0.3. Then ‘k, = 12 may be obtained by means of the relation (14). The corresponding experimental value is ‘k, = 9-10 [19]. The relations (19)-(22) may be useful to study the foil microstructure in view of its fabrication conditions. The fractions of both, graphite and amorphous phases may be obtained as a functions of the fabrication conditions. The results can be compared with the experimental data. Such an analysis of Tait’s [7] experimental data has been made (see table 2). As can be seen a satisfactory agreement with the experimental data has been obtained. The bound hydrogen content has been evaluated with the help of relation (22). Studies of the hydrogen content of glow discharge foils can provide important clues to their structure. For example the comparison of the total hydrogen content determined by a nuclear method with the content of hydrogen bound to carbon determinated by infrared spectroscopy gives an idea of the molecular hydrogen content [7]. For the films made by the carbon arc process the hydrogen content determinated by scattering and infrared techniques are the same within experimental uncertainties. Whilst this agreement may be fortuitous the incorporation of molecular hydrogen in
244
E.A. Koptelov et al. / Radiation stability of carbon foil microstructure
carbon arc foils seems unlikely. This gives an idea of arc foils densification by means of an amorphous-graphite phase transition. Films deposited from vapour onto substrate sufficiently cold to prevent surface diffusion tends to the disordered or amorphous. As the substrate temperature is raised the atoms diffuse to give a polycrystalline or even single crystal films if epitaxy occurs. When the films are deposited with simultaneous ion bombardment as in glow discharge sufficient energy may be given to the atoms in the deposited film to be displaced and to diffuse. The structure of the resulting film is therefore more ordered depending on the exact conditions of bombardment rate and temperature. Therefore the conventional arc evaporated carbon film is likely to be disordered if the substrate is held at room temperature. On the other hand foils prepared by hydrocarbon cracking where intense ion bombardment occurs throughout deposition may give a film with increased ordering. Our results are broadly in line with these observations. The glow discharge ion displaced atoms creation rate G* is defined to be the sum of Ar+ and C+ ion fractions. Our analysis of Tait’s experiments shows that G*l, will be about 6 dpa, which is considerably lower than Tait’s evaluation of 100 dpa [20] where the ion range limitation (R I 40 A) was not taken into account. But it is consistent with Tait’s observation that crystallographic changes take place early in the irradiation lifetime of the glow discharge foils at times comparable to the total lifetime of foils made by evaporation [21]. This gives some idea of the nature of the glow discharge foil preparation stability. It is known that the lower the layer thickness the greater the ultimate strength. Conceivable the glow discharge growing layer failure does not take place because the layer thickness h is too low (h I R). Indeed the mean growing graphite domain size d will be about 15 A according to relation (21). This is consistent with the experimental observations on the glow discharge graphite crystallites 20 A in diameter [20]. The crystallization process is described by fi dependence as can be seen from eq. (21). Such time depenTable 3 Examples of values of parameters used in the calculation Parameter
Value
c (cm/s) b (cm) K (cme3)
2.3 X lo5 exp( -0.3 2.3x10-’ 8 x10*2 5.4x10-‘6 2.1 x 1022 1.9x1022 5 x10-4 10-4
n (cm*) G: (cm-3s-‘) Gzr (cm-3s-1) Z* (A/cm*) Z: (A/cm*)
eV/kT)
dence is obtained for the regrowth kinetics in the graphite basal plane [22]. For readers interested in the numerical results, the numbers entering the calculation are presented in table 3, where Z* and Zr* are the glow discharge currents at a normal and reduced powers respectively. Finally the calculated results are shown to be in good agreement with the experimental data especially in view of the technological parameters variations. The authors wish to thank Professor V.M. Lobashev and Professor Yu.Ya. Stavisskii for helpful discussions.
References [l] E.A. Koptelov, S.G. Lebedev and V.N. Panchenko, Nucl. Instr. and Meth. A256 (1987) 247. [2] B.H. Am&age, J.D.H. Hughes, D.S. WhitmeII, N.R.S. Tait and D.W.L. Tolfree, Nucl. Instr. and Meth. 167 (1979) 25. [3] N.R.S. Tait, D.W.L. Tolfree, B.H. An&age and D.S. Whitmell, Nucl. Instr. and Meth. 167 (1979) 21. [4] B. Huck, E. Jaeschke, W. Kratschmer, R. Repnow and H. Wirth, Nucl. Instr. and Meth. 184 (1981) 215. [5] S. Kaplan, F. Jansen and M. Macho&in, Appl. Phys. Lett. 47 (7) (1985) 750. [6] A. Oberlin, M. Oberlin and M. Maubois, PhiIos. Mag. 32 (1975) 833. [7] N.R.S. Tait, D.W.L. Tolfree, P. John, I.M. Odeh, M.J.K. Thomas, M.J. Tricker, J.I.B. Wilson, J.B.A. England and D. Newton, Nucl. Instr. and Meth. 176 (1980) 433. [8] C.J. Sofield, C.J. Woods, N.E.B. Cowem, L.B. Bridwell, J.M. Butcher and J.M. Freeman, Nucl. Instr. and Meth. 203 (1982) 509. [9] L.M. Brown, A. Kelly and R.M. Maver. _ Philos. Maa. 19 (1969) 721. WI E.A. Koptelov, Radiat. Eff. 45 (1980) 163. WI A. Zeeger, H. Foll and W. Frank, in: Radiation Effects in Semiconductors (Plenum Press, New York, 1975). WI A.W. Bondarenko, Zh. Tekh. Fix. XL111 (1973) 821. P31 M.A. Kumakhov and F.F. Komarov, The Energy Loss and Ion Ranges in Solids (Minsk University Publishing House, Minsk, 1979) in Russian. 1141R. BuIlough, M.R. Hayns and M.H. Wood, J. Nucl. Mater. 90 (1980) 44. [I51N.R.S. Tait, D.W.L. Tolfree and D.W. Whitmell, Nucl. Instr. and Meth. 166 (1979) 333. WI R.L. Auble and D.M. Galbraith, Nucl. Instr. and Meth. 200 (1982) 13. 1171J.L. Gallant, D. Yaraskavitch, N. Bum, A.B. MacDonald and H.R. Andrews, Proc. Arm. Conf. Int. Nuclear Target Development Sot. (1979) p. 17. WI W. Schilling, J. Nucl. Mater. 69/70 (1978) 465. P91 N.R.S. Tait, Nucl. Instr. and Meth. 184 (1981) 203. PO1 N.R.S. Tait, D.W.L. Tolfree, D.S. Whitmell and B.H. Armitage, Nucl. Instr. and Meth. 163 (1979) 1. 1211M. Pickering, N.R.S. Tait and D.W.L. Tolfree, Philos. Mag. 42 (1980) 257. P21 L. SaIamanca-Riba, G. Braunstein, M.S. DresseIhaus, J.M. Gibson and M. Endo, Nucl. Instr. and Meth. B7/8 (1985) 487.
in Physics
RADIATION
OF CARBON
STABILITY
E.A. KOPTELOV,
S.G. LEBEDEV
Research
3 November
239
FOIL MICROSTRUCTURE
and V.N. PANCHENKO
Institute for Nuclear Research of the USSR, Academy Received
B42 (1989) 239-244
of Sciences, Moscow II 7312, USSR
1988 and in revised form 30 January 1989
A problem of a radiation shrinkage of carbon foils due to amorphous-graphite phase transition is considered. The graphitization kinetics under irradiation is shown to be described by chemical rate type equations. Such an approach gives the possibility of estimating the lifetime of amorphous and graphite targets. In conditions when a surface absorption of freely migrating component is negligible compared with the volume reactions of radiation defects the dimensionless equations for hydrocarbon foils graphitization and for clustering of radiation defects in graphite are indentical. This gives an expression for the lifetime ratio. Numerical estimates agree well with the experimental data. The glow discharge foil deposition is assumed to include the following processes: the nucleation, the growth of layers and the graphitization of amorphous layers. Estimations of corresponding characteristic times based on experimental data show that these processes can be considered independently. After the nucleation stage the graphitization develops in slowly growing films and so the above-mentioned kinetical model can be applied. As a result estimations of both the graphite domain size and the amount of bound hydrogen vs glow discharge conditions follows in satisfactory agreement with quoted data.
1. Introduction A carbon stripper target failure under ion beam bombardment [l] led us to model the lifetime of carbon foils in terms of stresses induced by radiation defects. The carbon foil was considered to be in a stable crystalline state like graphite. Glow discharge (GD) cracked foils [2-41 are perhaps in such a state. The GD foil structure depends on the glow discharge potential V. Foils prepared at voltages Vi 2.5 kV are stable but exhibit an enormous rate of shrinkage leading to an early rupture under irradiation and breakage into many pieces [4]. With rising voltages the rate of shrinkage had been found to decrease but no significant differences in the lifetime were observed. Foil lifetime which is discussed was defined in the experiments as the time to reach half beam intensity. Voltages in the range 2.5 < V I 3.5 kV are found to produce satisfactory foils with decreasing shrinkage as compared with foils produced at lower voltages or by the carbon arc (CA) methods. The structure and properties of thin amorphous carbon films have been investigated by a solid-state magnetic resonance method [5]. The corresponding data are shown in table 1. The difference in the properties is probably due to the allotropic nature of the carbon with threefold (sp2) as well as fourfold (sp3) coordinations. The relative importance of these bonding sites on the physical and electronic properties represents a key issue in understanding the behaviour of amorphous carbon. Ignoring the special case of diamond it may be seen that 0168-583X/89/$03.50 0 Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
the film density and fraction of tetrahedral (sp3) bonding correlate with hydrogen content in the films. For the hydrogenated carbon films described here it is proposed that the domains of trigonal (sp2) carbon atoms are separated not by diamond like regions but by hydrogenated tetrahedral (sp3) carbon atoms in grouppings CH,. Thin carbon films prepared by evaporation and deposited at room temperature have been found to be amorphous [6] with a structure composed mainly of randomly linked tetrahedra. The graphite domain regions are separated by tetrahedral carbon atoms or dangling bonds. Under heat treatment progressive graphitization proceeds as the diameters of the domains increases until polycrystalline graphite is produced. Irradiation appears to produce similar changes to those of the pre-graphitization stage of heat treatment [7].
Table 1 The structure
and properties
of thin amorphous
carbon
151 Material
sp2/sp3 (W)
Bound H (at.%)
Density
Diamond rf-anode rf-cathode dc-anode dc-cathode Graphite
O/100 14,‘86 20/80 so/50 60/40 100/O
0 61 58 47 31 0
3.0-3s 1.02 f 0.08 1.17kO.08 1.47+0.01 1.7 *0.01 2.3 k2.7
(g/cm3 )
films
240
E.A. Koptelov et al. / Radiation stability of carbon foil microstructure
The different properties of the glow discharge deposited films can be attributed to differences in the growth environment. In the glow discharge process condensable radicals form an amorphous film whose structure is modified during growth by ion bombardment and other energetic processes. The growth en~ro~ent at the rf anode is characterized by the lowest ion energy, thus favoring hydrogen incorporation and sp3 bond formation. The higher energy at the rf cathode and dc electrode surfaces promote hydrogen loss and sp’ bond formation. It has been suggested that during high-energy surface bombardment weaker bonds are removed from the growing film. Thus the more tightly bonded three or fourfold coordinated carbon atoms will survive over singly bonded hydrogen. Also, since double bond hydrogenation is an exothermic process graphitic bonding is favored over tetrahedral bonding in higher energy growth en~ro~ents. By means of infrared spectroscopy 1’71with low power densities and relatively high gas pressure (1-2 Wcm-zTorr-‘) C-H bonds were observed. As the power density was increased to around 40 Wcm-*Torr-’ the hydrocarbon bonds disappeared although hydrogen was still present. With higher power density there was indication of graphitization and reducing hydrogen content assumed to be caused by heating effects. The samples prepared using a glow discharge in ethylene with 10% argon at “normal” power density have a low content of bound hydrogen - 7 at.% [7] (1 at.% [S]) which indicates the predominance of a graphite-like phase in the foils (table 1). The radiation shrinkage is determined in this case by accommodation of radiation induced defects [l J. On the other hand the degree of sp3 to sp2 transition indicates both the density change and the rate of radiation shrinkage.
2. The graphitization kinetics Fig. 1 shows a graphite-like domain surrounded by a hydrogenated diamond-like region in the configurations of CH,. The microstructure variation is associated with both, disappearance of the sp3 phase and growth of graphitelike regions by means of the displaced sp3 phase carbon atoms accumulation at the edges of graphite domains. The graphitization kinetics equations may be obtained by means of the following assumptions. Under irradiation broken tetrahedra are created as a result of the destruction of sp3 phase bonds. The broken tetrahedra and displaced sp3 phase carbon atoms are homogeneously generated by the ion flux throughout the amorphous phase. The fate of an displaced atom may be any of: (a) recombination with a broken tetrahedron, i.e. regeneration of the CH, cell; (b) trapping by another displaced
0 CARBON * HYDROGEN
ATOM ATUM
Fig. 1. Graphite-like domain su~ound~
by hydrogenated diamond like regions in the ~nfigurations of CH,.
atom and thus forming the nucleus of a graphite domain; (c) annihilation at the edge of a graphite domain, causing the domain to grow. Here we assume that the annihilation at the foil surface can be neglected, implying that the probability of trapping by (a), (b) and (c) dominates. We propose that the sp3 phase displaced atom is situated inside the tetrahedron (see fig. 1). Each broken tetrahedron is surrounded by N sites for trapping displaced atoms where N is equal to the number of CH, grouping tetrahedra. The number of jumps per second to a trapping site is N-‘v, (where u = bv exp( - EJkT) is the displaced atom diffusion speed, b = ( K)-‘/3 _ the hopping distance, K = p/rn,p - the amorphous phase atom number per unit volume, ~1the amorphous phase molar mass, p - the amorphous phase density, m, - the atomic mass unit, Y - the appropriate vibration frequency, Em - the activation energy for displaced atom motion). Thus the rate of an displaced atom recombination with a broken tetrahedron is
Here n,, rra are the amorphous phase broken tetrahedron and displaced atom concentrations per unit volume respectively, SE= 2( K)-2/3. Next we calculate accurately the rate at which the edge of a graphite domain may accumulate the displaced atoms. In order to do this we must calculate the number of sites from which a displaced atom may jump to become attached to the half-plane of an edge and this involves the calculating of the number of appropriate sites per unit length along the edge of a graphite domain. If the atom considered can reach the edge of the graphite domain by a single jump then the ~~~p~ding number of sites
E.A. Koptelov et al. / Radiation stability of carbon foil microstructure
is equal to 2N/3. The graphite bonds number per edge unit length is 4/(fiaa) [9], where a is the graphite space lattice constant. The area per graphite domain lattice atom is 3a2fi/4 and if a graphite domain has a radius r, and hence a total line length of 2ar, the rate at which it grows is: d(nr’) -1 ~ 2-rrr
dt
=
+N-1v)na,-1 $?- ???$
Ap _=_-
dt
If na( r, t) is the domain size distribution function then the total rate of loss of the displaced atoms to graphite domain is: W2=rno(r,
t) drNjNPiU4n,KP’ bPJ5
83 = -nonavD 3a&i
= G - n.n,vQ/2
’
dn t
= G - n,n,v0/2,
dt
-
The amorphous foil material deformation graphitization can be estimated easily from: Al 1 (Ps-P) -i- &= 3p,K’
II II y
= 0,
= (0.2Kl
- 0.14K2)$,
(11)
s
(4)
where No* = nrdm, nr is the graphite domain asymptotic density, t the irradiation time of a foil. The formation of a graphite domain takes place after the nucleation time to e t, - the amorphous foil lifetime as is shown in [lo]. It is easily seen from the solution of eq. (4)-(6) that n a + 0 at t + co. Hence one may consider that all displaced atoms (besides taking part in the (a) and (b) processes) are trapped by the graphite domains and therefore they acquire sp’-coordination. The foil material density may be represented as follows: ii=Pw+Pa(l-K),
(8) density,
nt
s
tV3~V6(
nV=
ps is the graphite
under
where
81 -non,vO 3afi
where G is the displaced atoms creation rate per unit volume per unit time in the amorphous phase. In these relations the derivatives and squares of n, which tends to zero at large times are neglected. The effect of defect formation within the graphite zones has also been neglected. Thus the asymptotic behaviour of the broken tetrahedra concentrations is:
where
K’
PS
Next we calculate the lifetime relation of the amorphous and graphite targets. It is generally accepted for graphite structure foil [l] that
where i is defined by ti o = jFrno(r, r) dr, no being the graphite domain density. The equations describing the graphitization process at large times are dn a
n,
(4-P)
P
dr - = vn,Da/lr.
dt
carbon atoms with the sp3 coordination, p = 0.83 g/cm3, as may be obtained by using the table 1 data. An increment in the foil material density under irradiation is
thus
71a
thus
/0
241
K -
the fraction
of
Q~,)-“~.
k,, k, are textural coefficients [l], complexes asymptotic density, kg number per unit volume. Assuming both the graphite and amorphous of (7), (lo)-(12) gives the lifetime
(12)
Nlm - the interstitial - the graphite
atoms the same strength of foil the combination ratio:
here tg is the graphite target lifetime, Gg - the graphite phase generation rate. In the case where the interstitial complexes are the main defect sinks one can obtain Nm = r213 [lo]. Since K = p/mop this leads to the following estimation: ‘k, =
exp[ (E$ - E,)/6KT] x
[PK+Pg(l-K)]
1 3’2
’
(14)
As E, = kT, [ll], where T, is the melting point of the material, qC seems to be slightly depending on T.
242 3, TIM mkrostructure glow discharge
E.A. Xbptelou et al. / Radiation stability ojcarban foil micrastructure development of c~bon foils in the
Let us consider the foii deposition under glow dischwge ion ~mb~dm~t in detail. The ion energy in a @ow ~scb~ge pTasma such as ~~u~ter~ during deposition of a f&n is a ~s~bnt~ q~~~t~. The energy d~st~b~t~o~ is strongly peaked at - 0.2 V [12] with a t&t extending up to higher energies. In Tait’s experimertts [q the average energy therefore is E = 500-800 cV. The, range of the majority of ions R will be some 30-40 A [13]. Except during the initial stages in film growth the range will be considerably less than the thickness of the film. Consequently the conditions of uniform generation of defects are only achieved in the neax surface of the film and the foil surface probably is the main defect sink. Let us consider the question: how the foil microstructure utiu be ~~sfo~ed under glow discharge ion bomb~~ment~ This is evidently not the case of the modified microstructure domain size to be more than R. In reality the glow discharge foil deposition includes three processes, namely: 1) the nucleation, 2) the growth of amorphous layers and 3) the amorphous layer graphitization under intense intrinsic ion beam bombardment, Let us calculate the corresponding characteristic times of these processes. Assuming the foil deposition rate in T&t’s experiments is about 4 A/s the range time deposition t, = ta will be about 10 s. The nucleation time can be estimated as f, = fG’& + ft~,~‘R)“]-‘~~ = ffF5 s fG* is the totaT displaced atoms creation rate) as is shown in ref. flO]_ The growth time of the graphite domain is estimated ga = Ra/(z&) = 10-s s, As can be seen &he characteristic times are represented by the rdation 1, e t, c I, and these three processes can be regarded independently. Therefore process 3) can be treated in the framework of the graphitization model, which is presented above. Aasurning the graphite crystalline dimension expected to be never more than B let us calculate the amorphous phase fraction and the me&n crystallite size in the growing f&n. fn order to do this we must consider the kinetics rate equators in the near surface gruwing layer of a f&n the thickness of which is never more than R. The surface &spIaced atoms sink number per unit volume pit, will be some (@h)-‘, where St = (K)-2/“, h is the layer thickness, Assuming h = R/2 the mmpbous phase formation kinetics equations may be represented as follows: 2vn* dnx dt=G*-n:n:vL?* =O, tstt,, 05)
Table 2 A comparison of cakulated bound H fraction with th*t experimental data Glow discharge co&lions
Cakxdated atomic % H
EkperimerM
pure ethylene
20
2S.Sf 5.8
30% argon 10% argon, reduced power
0 49
7.5 i 2.1 42 i8.6
atomic
% H 171
Gffw
discharge Glow discharge Glow discharge
where C* is the glow discharge displaced atoms crew tion rate in the growing film (see below), 7* - the mean graphite domain radius, n:, n: - the amorphous phase displaced atoms and broken tetrahedra concentrators per tit volume, respectively_ The third term in the right hand part of eq. (115) is the surface displaced atoms sink intensity obtained by means of an embedding procedure within a uniform lossy medium [14], The main displaced atom flow in this case is trapped by a surface where new layers growth takes place. In Tait’s experiments a glow discharge was performed in a mixture of dried ethylene and 10% argon gas. According to Bondarenko /12] a glow discharge plasma mainly produces singly charged ions. Assuming the displaced atoms creation rate by H ions to be relatively small as compared with Ar md C km displaced atoms creation rates the total displaced atoms creation rate in the growing film may be represented as foUows: P=G,*,“+G,y,
fW
where c;,*,, G$ are the creation rates of the Ar” and Cf ion displaced atoms respectively. The terms in the right hand part of the eq. (18) may be calculated according to the approach of ref. [I] (see table 3). Eq. (15) may be regarded as stationary especMly in view of the h$.& mobility of the displaced atoms. Therefore the solution of the set of equations at time t, may be written as follows: 09)
11:=2 J*
=
IGJt,
cw
$@q&&,
(21)
d ~-$R s
where a = I.6 x 10-s cm is the graphite lattice conistant. The approximation G*QRt, z+ 1 is used which is correct for all practical cases. The sps phase quantity that is transformed in& graphite may be obtained by means of relation (20). The mean graphite domain size which is formed in the
E.A. Koptelov et al. / Radiation stability of carbon foil microstructure
glow discharge foil can be evaluated by means of relation (21). It is obvious that n: is the carbon atoms fraction which acquire the graphite sp2 coordination assuming the initial foil structure has been amorphous. As is shown in ref. [7] the CH, groupings are the predominating coordination of bound hydrogen. Then the middle fraction of bound hydrogen is: f”=
(1+
[2(1-
%)1’)j’.
243
where a is the graphite phase relaxation volume per vacancy. The graphite phase increment due to defect formation is described by the difference between the third and the sixth terms in right hand side of relation (24). Therefore the pure graphite phase deformation can be expressed as:
(22) Thus the graphite foil lifetime may be represented as follows (see eq. (11)):
4. Results and discussion The glow discharge cracking of an ethylene-argon mixture produces carbon films that are more resistant to radiation damage than those prepared in the conventional manner. For example the comparison of glow discharge foils made in 10% argon and standard foils made by carbon arc evaporation show a lifetime enhancement ‘k, = 9 [15] for 1.2 MeV argon ion beam. The same lifetime ratio for glow discharge versus evaporated foil is obtained at Oak Ridge [16] for 10 MeV chlorine ion beam. In the Chalk River experiments the lifetime enhancement, ‘k, = 10-12, is obtained for 10.5 MeV iodine ion beam. Despite a lot of experimental data on the carbon foil behaviour under ion beam bombardment there is as yet no clear understanding of the lifetime enhancement. In this study we have attempted to shed some light onto this problem. The analysis given above indicates that the lower the content of amorphous phase in the foil and the greater the foil graphite phase hence the greater the foil lifetime. From our study the lifetime ratio for pure graphite versus amorphous foils may be obtained as a function of amorphous phase fraction K by means of relation (14). As K + 1 a pure amorphous phase foil is achieved. Assuming G = Gs one can obtain the maximal lifetime ratio: YP c_ = 35.
(23)
On the other hand as K + 0 the foil structure tends to be pure graphite and to check the model the effect of defect formation within the graphite domain must be taken into account. Therefore the increment in the foil material density under irradiation will be the following:
+a& ( -a(1
l-K+
2)$
-,,K-&(1-K) g
-
K)4$, i3
thus
AP _ P
h--p) nt +a>?, P&C
K
K Kg
(25)
The combination of (ll), tion: a = %(0.2K, u
(12) and (27) gives the evalua-
- 0.14K2)2
= 0.144 at. vol.
(28)
For the evaluation of the vacancy relaxation volumes of the other materials a has been taken to be 0.1 at. vol. for MO and 0.05 atomic volume for Al [18]. As a can be regarded as independent of the irradiation conditions one can obtain ‘k, + 1 as K tends to zero. From equation (14) ‘k, seems to be slightly dependent on T. This point needs to be tested experimentally. Because the carbon atoms displacement energy depends on its coordination in the lattice one can see that G/G, # 1 at all. Unfortunately the displaced atoms creation rate data for amorphous carbon foil is not known. As is shown in ref. [7] the arc evaporated amorphous phase fraction K is equal to 0.3. Then ‘k, = 12 may be obtained by means of the relation (14). The corresponding experimental value is ‘k, = 9-10 [19]. The relations (19)-(22) may be useful to study the foil microstructure in view of its fabrication conditions. The fractions of both, graphite and amorphous phases may be obtained as a functions of the fabrication conditions. The results can be compared with the experimental data. Such an analysis of Tait’s [7] experimental data has been made (see table 2). As can be seen a satisfactory agreement with the experimental data has been obtained. The bound hydrogen content has been evaluated with the help of relation (22). Studies of the hydrogen content of glow discharge foils can provide important clues to their structure. For example the comparison of the total hydrogen content determined by a nuclear method with the content of hydrogen bound to carbon determinated by infrared spectroscopy gives an idea of the molecular hydrogen content [7]. For the films made by the carbon arc process the hydrogen content determinated by scattering and infrared techniques are the same within experimental uncertainties. Whilst this agreement may be fortuitous the incorporation of molecular hydrogen in
244
E.A. Koptelov et al. / Radiation stability of carbon foil microstructure
carbon arc foils seems unlikely. This gives an idea of arc foils densification by means of an amorphous-graphite phase transition. Films deposited from vapour onto substrate sufficiently cold to prevent surface diffusion tends to the disordered or amorphous. As the substrate temperature is raised the atoms diffuse to give a polycrystalline or even single crystal films if epitaxy occurs. When the films are deposited with simultaneous ion bombardment as in glow discharge sufficient energy may be given to the atoms in the deposited film to be displaced and to diffuse. The structure of the resulting film is therefore more ordered depending on the exact conditions of bombardment rate and temperature. Therefore the conventional arc evaporated carbon film is likely to be disordered if the substrate is held at room temperature. On the other hand foils prepared by hydrocarbon cracking where intense ion bombardment occurs throughout deposition may give a film with increased ordering. Our results are broadly in line with these observations. The glow discharge ion displaced atoms creation rate G* is defined to be the sum of Ar+ and C+ ion fractions. Our analysis of Tait’s experiments shows that G*l, will be about 6 dpa, which is considerably lower than Tait’s evaluation of 100 dpa [20] where the ion range limitation (R I 40 A) was not taken into account. But it is consistent with Tait’s observation that crystallographic changes take place early in the irradiation lifetime of the glow discharge foils at times comparable to the total lifetime of foils made by evaporation [21]. This gives some idea of the nature of the glow discharge foil preparation stability. It is known that the lower the layer thickness the greater the ultimate strength. Conceivable the glow discharge growing layer failure does not take place because the layer thickness h is too low (h I R). Indeed the mean growing graphite domain size d will be about 15 A according to relation (21). This is consistent with the experimental observations on the glow discharge graphite crystallites 20 A in diameter [20]. The crystallization process is described by fi dependence as can be seen from eq. (21). Such time depenTable 3 Examples of values of parameters used in the calculation Parameter
Value
c (cm/s) b (cm) K (cme3)
2.3 X lo5 exp( -0.3 2.3x10-’ 8 x10*2 5.4x10-‘6 2.1 x 1022 1.9x1022 5 x10-4 10-4
n (cm*) G: (cm-3s-‘) Gzr (cm-3s-1) Z* (A/cm*) Z: (A/cm*)
eV/kT)
dence is obtained for the regrowth kinetics in the graphite basal plane [22]. For readers interested in the numerical results, the numbers entering the calculation are presented in table 3, where Z* and Zr* are the glow discharge currents at a normal and reduced powers respectively. Finally the calculated results are shown to be in good agreement with the experimental data especially in view of the technological parameters variations. The authors wish to thank Professor V.M. Lobashev and Professor Yu.Ya. Stavisskii for helpful discussions.
References [l] E.A. Koptelov, S.G. Lebedev and V.N. Panchenko, Nucl. Instr. and Meth. A256 (1987) 247. [2] B.H. Am&age, J.D.H. Hughes, D.S. WhitmeII, N.R.S. Tait and D.W.L. Tolfree, Nucl. Instr. and Meth. 167 (1979) 25. [3] N.R.S. Tait, D.W.L. Tolfree, B.H. An&age and D.S. Whitmell, Nucl. Instr. and Meth. 167 (1979) 21. [4] B. Huck, E. Jaeschke, W. Kratschmer, R. Repnow and H. Wirth, Nucl. Instr. and Meth. 184 (1981) 215. [5] S. Kaplan, F. Jansen and M. Macho&in, Appl. Phys. Lett. 47 (7) (1985) 750. [6] A. Oberlin, M. Oberlin and M. Maubois, PhiIos. Mag. 32 (1975) 833. [7] N.R.S. Tait, D.W.L. Tolfree, P. John, I.M. Odeh, M.J.K. Thomas, M.J. Tricker, J.I.B. Wilson, J.B.A. England and D. Newton, Nucl. Instr. and Meth. 176 (1980) 433. [8] C.J. Sofield, C.J. Woods, N.E.B. Cowem, L.B. Bridwell, J.M. Butcher and J.M. Freeman, Nucl. Instr. and Meth. 203 (1982) 509. [9] L.M. Brown, A. Kelly and R.M. Maver. _ Philos. Maa. 19 (1969) 721. WI E.A. Koptelov, Radiat. Eff. 45 (1980) 163. WI A. Zeeger, H. Foll and W. Frank, in: Radiation Effects in Semiconductors (Plenum Press, New York, 1975). WI A.W. Bondarenko, Zh. Tekh. Fix. XL111 (1973) 821. P31 M.A. Kumakhov and F.F. Komarov, The Energy Loss and Ion Ranges in Solids (Minsk University Publishing House, Minsk, 1979) in Russian. 1141R. BuIlough, M.R. Hayns and M.H. Wood, J. Nucl. Mater. 90 (1980) 44. [I51N.R.S. Tait, D.W.L. Tolfree and D.W. Whitmell, Nucl. Instr. and Meth. 166 (1979) 333. WI R.L. Auble and D.M. Galbraith, Nucl. Instr. and Meth. 200 (1982) 13. 1171J.L. Gallant, D. Yaraskavitch, N. Bum, A.B. MacDonald and H.R. Andrews, Proc. Arm. Conf. Int. Nuclear Target Development Sot. (1979) p. 17. WI W. Schilling, J. Nucl. Mater. 69/70 (1978) 465. P91 N.R.S. Tait, Nucl. Instr. and Meth. 184 (1981) 203. PO1 N.R.S. Tait, D.W.L. Tolfree, D.S. Whitmell and B.H. Armitage, Nucl. Instr. and Meth. 163 (1979) 1. 1211M. Pickering, N.R.S. Tait and D.W.L. Tolfree, Philos. Mag. 42 (1980) 257. P21 L. SaIamanca-Riba, G. Braunstein, M.S. DresseIhaus, J.M. Gibson and M. Endo, Nucl. Instr. and Meth. B7/8 (1985) 487.