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EPR line shift in carbon due to adsorbed oxygen
EPR LINE
SHIFT IN CARBON ADSORBED OXYGEN
DUE TO
K. ANTONOWICZ, S. ORZESZKO and Js WIECZOREK Department of Physics, Nicholas Copernicus University, Torun, Poland (Received 4 Decembe-r 1968) Abstract-An amorphous carbon deposit was produced on flat glass plates by evaporation of spectroscopically pure carbon rods in an argon atmosphere. Such deposits exhibit a high spin concentration. The electron spin resonance absorption tine shows anistropy in g-value dependent on orientation of the plate relative to the externa1 magnetic field, and which appears to be due to adsorbed molecular oxygen. The results indicate that oxygen is adsorbed on an argon monolayer which tightly covers the carbon. The interaction between carbon and oxygen spins occurs across the argon monolayer. The local field produced by adsorbed oxygen at the site of the carbon spin is dependent upon the orientation of the surface relative to the external magnetic field. The calculated dependence of the local field cm the surface oxygen density is in good agreement with the observed line shift. From the assumed model, the diameters of the argon atom and oxygen molecule can be determined, and are found to be in good agreement with the data given in literature. 1. INTRODUCTION
In a previous paper [l] some properties of electron paramagnetic resonance, (EPR) in highly amorphous carbon were reported. The carbon was produced by evaporation of spectroscopically pure carbon rods in an argon atmosphere. At a suitable pressure of argon a highly amorphous carbon deposit is obtained. For such deposit a g-anistropy was observed which depends on orientation of the sample relative to the external magnetic field [l]. This surprising effect has been studied by us in detail. The study showed that the assumption of some kind of anisotropy of the carbon deposit caused by shrinkage[2] or by epitaxial growth of the crystal nucleus for instance, fails to give a proper explanation of the observed effects. Further progress was made when the dependence of anisotropy on the amount of adsorbed oxygen was found with a complete of anisotropy after out disappearance gassing the sample in a vacuum of the order of lOA7 mm. Hg. In this paper the results of
experimental and theoretical studies of the dependence of the g-anisotropy on the amount of adsorbed oxygen are presented. 2. EXPERIMENTAL
AND RESULTS
An amorphous carbon deposit was collected on flat thin glass plates of a size 2 X 10 mm suitable for mounting in the cavity of the EPR spectrometer. A standard carbon sample, a small grain of sugar char (500°C) sealed off under vacuum in a very fine capillary tube and then heat-treated to 700°C (line width 0.3G , g = gfF,,) was placed in a quartz tube together with the glass plate and the two EPR signals from both samples were recorded together. Due to the larger difference in line width and intensity, the signal of the standard gives only a narrow reference mark relative to which the g-value of the sample was determined. The EPR meastrrements were made using a transmission cavity of 9820 MHz, most of the meas~lrements having been performed at liquid nitrogen The homogeneity of the temperature.
500
K. ANTONOWICZ
magnetic field over the area of the sample was of the order of 10m4G. At room temperature the g-value for the deposit was exactly equal to that of the reference line, irrespective of orientation of the sample relative to the external magnetic field. At liquid nitrogen temperature, in general, the peaks of both lines do not coincide the relative shift being dependent on the orientation of the sample in the magnetic field. After closer examination of this anisotropy two important properties were found which throw light on the matter: (1) the anisotropy disappears in high vacuum (better than lop6 mm Hg); (2) the anisotropy and sometimes reverses after changes repeated cycles of evacuation and admission of air. Both facts indicate that the anisotropy does not depend on the structure of the deposit, but is the result of the conditions of evacuation and/or degree of outgassing of the sample. Small changes in the local field due to adsorbed molecular oxygen, a strongly paramagnetic gas, can be expected. Argon gas, adsorbed by carbon during deposition in the reaction vessel has also a strong influence on the EPR behavior. The EPR line of the carbon as deposited although weak can be easily detected at room temperature, in air, under atmospheric pressure. The line is about 20G wide. On the other hand, once the sample is .well outgassed at elevated temperature, the EPR becomes very sensitive to oxygen. This shows that adsorbed argon protects the carbon from oxygen and that this protecting shield is removed by outgassing[3]. When the carbon was prepared in an argon atmosphere, large amounts of gas are evolved by heating the sample in vacuum at a temperature of about 220°C. The desorbed gas is spectroscopically identified as argon. It seems reasonable to assume that carbon is covered with argon, which protects the spin centers in carbon from oxygen. Oxygen can be adsorbed only as a second layer on top of the argon.
tit al.
To observe the influence of oxygen, EPR measurements were performed in gradually reducing the amount of adsorbed oxygen. A fine control of the amount of oxygen adsorbed on the surface of a small sample at liquid nitrogen temperature, was achieved by use of a special sample holder (Fig. 1). In the quartz tube A at its flattened end B were placed the sample plate and the reference standard. The end B fits into the Dewar vessel of the spectrometer cavity. The capillary tube C reduces the rate of gas diffusion. D is a gas trap filled with activated carbon. The holder can be rotated around the axis AB. The measurements proceed in several steps. (A) After connecting the sample holder to the vacuum system, the sample is cooled to liquid nitrogen temperature, and only then the tube is evacuated, the activated carbon outgassed and the tube sealed off at A. The tube is transferred to the Dewar vessel in the
Fig. 1. Sample holder. A, connection to vacuum system; B, the carbon sample with reference standard; C, a capillary tube; D, activated carbon.
EPR LINE SHIFT
spectrometer cavity and the first measurement made. One finds a broad line overlapped with the sharp reference line at its centre, the relative position of both lines being independent of the orientation relative to the external magnetic field. Next the tube is taken out of the liquid nitrogen, for a few seconds and put back into the cavity Dewar vessel. One can see now an appreciable narrowing of the broad line of the carbon deposit and a small g-shift of the line towards higher field strength for both directions relative to the magnetic field. The first short warming up of the sample has reduced the amount of adsorbed oxygen; one does not know to what extent, but certainly this must have occurred. Such warming up of the sample is then repeated over and over (the number of consecutive operations being indicated on the abscissa in Fig. 2) increasing for a while up to a maximum. Further heating of the sample causes a gradual disappearance of the shift, the effect being
Fig. 2. Experimental results fbr the R-value as obtained for the two directions relative to the magnetic field in the 3 series of experiments in which the coverage with the adsorbed oxygen molecules has been reduced in steps (see text). t, indicates the number of consecutive operations.
IN CARBON
501
associated with an increase in the gas pressure inside of the tube. (Fig. 2(a)) The pressure at which the line shift disappears could not be determined exactly. From the character of the discharge observed one could estimate it to be about lo-” mm Hg. (B) In order to achieve a further reduction in the adsorbed oxygen the sample holder was opened and evacuated to a pressure of lo-‘mm Hg. During evacuation the sample was kept at room temperature and afterwards again cooled down to liquid nitrogen temperature. Then the pressure was decreased to about low6 mm Hg., the activated carbon was outgassed and the tube sealed off. Now the EPR measurement shows at the beginning no anistropy but an equal shift for both directions relative to the magnetic field to smaller g-value than that for the free electron (Fig. 2(b)). After warming the sample a a-anisotropy appears. For perpendicular orientation of the glass plate relative to the magnetic field the line is shifted to a higher field strength, for parallel orientation the line centre coincides with the reference signal. Further outgassing permits to trace a continuous increase in the g-anistropy with the line for parallel orientation remaining closer to that of the free electron. The anisotropy reaches a maximum at some particular coverage, then drops to zero and appears again, but now its character is different. For perpendicular orientation of the glass plate to the magnetic field the line is shifted to a lower magnetic field (opposite shift to that observed before) while for parallel orientation it is shifted to a higher magnetic field. Thus the anisotropy is again high and the shift of both lines is about symmetric on opposite sides of gfree. Once more it reaches a maximum and then at further outgassing decreases. (C) To reduce still further the amount of adsorbed oxygen, the tube is opened again, evacuated at room temperature to lO_” mm Hg., the activated carbon outgassed and then the sample cooled down to liquid nitrogen
502
K. ANTONOWIC~
temperature. For a few minutes the sample is permitted to adsorb oxygen at the low pressure, and the tube is sealed off. Again an anistropy is observed (Fig. 2(c)). This is a case where for perpendicular orientation the line is shifted to a higher field, but for parallel orientation the line is not shifted. On outgassing one can see a decrease in the anisotropy and change in its direction. When outgassing proceeds further high vacuum can be reached by cooling the activated carbon down to liquid nitrogen temperature. In high vacuum the anisotropy as well as the shift of the line from the position for the free electron disappears. A strong narrowing and increase in intensity indicates the complete outgassing of the sample. 3. THEORETICAL
CONSIDERATIONS
The dependence of the g-value on the amount of adsorbed oxygen, seems to be at first sight confusing. Calculations of the local magnetic field produced by the adsorbed oxygen lead to predictions which are in good agreement with experiment however. The following assumptions are made for calculating the contribution of oxygen paramagnetism to the local magnetic field at the carbon spin centers. 1. The surface of the deposited carbon can be approximated by a plane covered with a monolayer or argon. Oxygen is adsorbed on top of the argon layer. The layers are assumed to be parallel to the glass surface on which the carbon is deposited. A random distribu~on of carbon spin centres and irregularity of the carbon surface are taken into account by averaging the distance between oxygen and argon layers. 2. Only carbon-oxygen spin-spin interactions are taken into account. The interactions of similar spins, producing the line width, are neglected. 3. The interaction of two dipoles can be expressed by means of local magnetic fields. It is assumed that the total local magnetic
et d
field produced at a given point in the carbon is given by the sum of contributions from all oxygen molecules. Dipole-dipole interaction produces line broadening in general, but in this case the time variable part of this interaction is less effective than the presence of a static component of the field. This is firstly due to the distribution of both oxygen and carbon spins in form of two parallel layers at a given distance, so that the relative distribution of the spins is not completely random, the time average of the local field produced on the carbon surface being different from zero. Secondly, it is due to the fact that the interacting spins are unlike. When spin are identical the so-called ‘flip-flop’, allows a simultaneous reversal of the interacting spins in opposite directions. If two spins are unlike the rotating field produced by, let us say, ,ul, is off resonance for I_LZand exerts on it a negligible torque, whereas the static field produced by pi at pz is as effective as for like spins. It is easy to show that for unlike spins the flip-flop interaction term does not commute with the Zeeman hamiltonian and can be dropped [4]. The interaction of two magnetic moments 1~~= rltiJ, and ccc.= ycftJc is the well-known dipole-dipole coupling
w,c
=
~6JC_J(J1rlc~~~~rlc)]. (1)
(1) can be written as
where Hlc is the local field produced by spin 1 at the site of spin C. Detailed discussion of (1) is to be found in the literature[4]. In the case of two unlike spins, Hlc is given by H,c = ~1
3cos28-1 &
(3)
EPR LINE
SHWT
where 0 is the angle between J1 and vector T, describing the relative position of the two spins, and p1 is the magnetic moment of the oxygen molecule (spin 1). EItc is the zcomponent of the magnetic field produced by spin 1 at the site of spin C. The instantaneous local field seen by a carbon spiu pc is of the order of hundreds of gauss and the sign depends on the orientation of p, relative to the magnetic field, but there exists between neighboring oxygen molecules an exchange coupling which produces a fast flipping spins. Thus the instantaneous field NIP can be replaced by its time average vaIue
1N CAREOK
503
local fields at different spin sites, so that only the average values of the quantities appearing in (6) are of interest. The summation in (6) can be easily performed. First let us assume a concentration of adsorbed oxygen so small that the contribution to the local magnetic field can be neglected from all but the one closest molecule. The sum in (6) is now reduced to one term, but due to random distribution of both oxygen molecules and carbon spin centres in the planes, as well as to possible two dimensional motion of oxygen molecules the term (3 co? @- f),P must be averaged over all possible 8 and r_ 1. If the external magnetic field is perpendicular to the carbon surface (Fig. 3(a)), then
If after adsorption an oxygen molecule is in its ground state 3C,- the average value (,u} is given in reasonable approximation by Curie’s law
where g =2:2, S = 1, y, is the Bohr magneton, HO is the magnetic field, k is Boltzmann constant and T is the absolute temperature. The time average (j2.) is a very useful concept because we can treat the magnetic moment of each oxygen molecule as being parallel to an external magnetic field of value H,,. Equation (4) gives the local magnetic field produced by one oxygen molecule, The total local field can be assumed to be the sum of contributions from all molecules
Fig. S. A schematic showing how the local magnetic field produced by oxygen molecules of one-zone distributed on the circumference of a circle of radius ~1.d. k, in the plane at distance d is calculated for a carbon spin located at the point A. (a) HO, field perpendicular to the plane: fb)H,, field parallel to the plane.
(3cos20-l)/r3= Due to rapid convergence of the series in equation (6) the extent of the plane and the total number m of 0, molecules can be assumed infinite. The observed local field is an average of a great number of individual
(l/d”)(3cos~8-l)cos”8 (7)
where d is the surface and symmetry (7) The average
mean distance between carbon oxygen layer. Due to axial is independent of the angle CJJ. value of (7) is
504
K. ANTO~OWIC~ et al.
(1/d3)( (3cos20-1)
COSS8),, = (2/T&3)
n/z X
s
(3 co9
0-
1) toss &4e
0 =
+(0*25/d3).
(8)
2. If the external
magnetic field is parallel to the carbon surface (Fig. 3(b)) there is no symmetry and we have to average over angle cp. We note that cos 8’ = (r’/r) cos (o while the average of cos* cpis l/2, so
(a)
’ (b)
Fig. 4. (a) Idealized hexagonal close-packing of
(cos2 @‘)a”.C= ices” 0.
spheres. (b) Two-dimensional distribution of adsorbed molecules. A total magnetic field is
Introducing again d = r . sin 8 and averaging over 6’we have
obtained by summation of contributions from the central molecule and molecules in consecutive zones, 6k molecules in each zone, k assuming values between one and infinity.
((3 cos2 8-
l)/r3) = (2/%-d3) V/2
X
f
(~cos2~-
1)
0
X sin3 0~~
= - ( 0*297/d3).
(9)
By substitution of (8) or (9) into (4) one finds the local magnetic field seen by the carbon spin for two different orientations of the sample relative to the magnetic field. When the external magnetic field is perpendicular to the carbon surface the local magnetic field is positive, when parallel, negative. Let us consider now a higher concentration of adsorbed oxygen molecules, when the contribution of many neighboring molecules to the local magnetic field must be included and let’s assume a hexagonal close-packing of spheres in the plane, Fig. 4(a), (by spheres we understand oxygen molecules adsorbed on the argon layer). Each molecule is surrounded by six neighbours; in the next zone there are 12 molecules, and in the k-th zone 6k molecules. Now we assume the destruction of long range order by random modulation of the lattice parameter. If the average distance between molecules is n.d., where n is a nositivc number. the arrangement of
molecules can be assumed (to a good approximation) tobe like that in Fig. 4(b). Neighbouring molecules are assumed to be in zone with 6k molecules in each zone. This situation is, of course, not correct for a particular molecule at a particular time but for a great number of molecules in a plane the statistical model of one molecule and its surroundings will be approximately just like that in Fig. 4(b). The average local field at the carbon spin is the sum of contributions from the central oxygen molecule and molecules from all other zones. The magnetic field produced by one molecule is averaged over the area of each zone. The contribution from the k-th zone, for perpendicular orientation relative to the magnetic field, is (see Fig. 3(a))
= (pjtik
bM
= -
and the contribution
d3
(S/(1 +k*n%P)) (J2+kZn2d2)3/2
2 - ( 1 +
k2n2 kZ,~~2)5/2
from all zones is
- 1
EPR LINE SHIFT IN CARBON
(W
while for parallel orientation magnetic field (Fig. 3(b))
relative
to the
(11) is obtained. Equation (6) can be rewritten two directions (H,,,),
(ti) = d3(3
co532O- 1) cos3 0)
+6(/-d d”
m k(2-?zW) kzl (1-t &%2)5’2
(CL)
~~~~,)~~=--&(%Cos*$+3(P) 7 The over each large
now for the
(12)
I) sin”@)
m R(2-n2k2) kz (1 +pn*)5/**
(13)
first terms in (12) and (13) are averaged the zeroth zone. In sums for small k term can be calculated separately. For k or 12,when 1 4 k*n* unity is neglected
505
and the simple sum calculated. In (12) and (13) the parameter n depends on the twodimensional density distribution of oxygens in the pIane (n.d. is the average distance between oxygen molecules). The continuous lines in Fig. 5 represent the dependence of the calculated local magnetic field on n and, consequently, on the average distance between the oxygen molecules. 4. DISCUSSION According to the proposed interpretation the g-value for the carbon spin remains constant and equal to gfrree.It is only the local field created by the magnetic polarization of the oxygen layers which varies with the direction of the magnetic field and shifts the position of the EPR Iine as the sample is rotated. Thus it is the variation of the local field and not of the real g-value which is observed. The peculiar changes with the density of coverage of the surface with oxygen molecules can be easily comprehended for the case of the magnetic field perpendicular to the surface if one considers that a local field due to the spin of an oxygen molecule focated exactly across the argon layers has the same direction as the polarizing
0.3 0.2
Fig. 5. Dependence of local field on the average distance between oxygen molecules. Curves are calculated from formulas (12) and (13) of‘ the text X, o, give experimental results for perpendicular and parallel orientation of the sample relative to the magnet.ic field.
506
K. ANTONOWICZ et al.
field, but the local field for more distant position of the molecule has a reversed direction. Since the interaction decreases fast with the distance, for a single molecule moving in the plane at random the first effect prevails after averaging (point E, Fig. 5). As the coverage increased however and the zone diameter decreases, the point is reached when the local field due to molecules of the first zone tips the balance in favor of a reversed local field (Point C). At still higher coverage, the molecules of the first zone move so close to the central molecule (directly across) that their field begins to add a parallel component to the polarizing field. The case of the magnetic field parallel to the surface is somewhat more complicated due to the absence of axial symmetry, but one can see that the field due to the molecule located exactly across the layer and to other more distant but located in the plane perpendicular to the field, opposes the polarizing field, and the field of the more distant molecules and behind this plane is parallel to the polarizing field. Thus a reverse situation develops. The crossing points B and D of the two curves occur below the axis in Fig. 5, because in general the maximum positive contributions to the local field are not as large as the maximum negative ones (what can be seen from the above considerations). Formulas (12) and (13) and Fig. 5 can in principle be compared with experiments (Fig. 2). There is however the difficulty that in the experiments the density of oxygen molecules is not measured directly and only the local field is determined from the position of the lines. However, in our experiments, experimental conditions were realized in which the direction of density changes is known. In vacuum the sample can only lose adsorbed oxygen. When desorption proceeds slowly one can follow the variation of the local field starting from complete coverage of the surface by oxygen to complete outgassing. Because the sequence of alternation in local field follows the dependence shown in Fig. 5,
a correspondence between some experimental and theoretical points can be established. The outstanding identifiable points are those at maximum or at crossing of the two curves; they are marked B-E on Fig. 5. Experimental data corresponding to these points are introduced in Fig. 5. The maximum of anisotropy at the point C can be measured with the highest precision. In the experiments presented in Fig. 2, the difference in local fields at point C was 0.46 G. This difference can be calculated from (12), (13) and Fig. 5.
(4 = 7
* 0.55.
(14)
In (14) the only unknown quantity is d. On evaluation one finds d = 4*4A, the area occupied by one argon atom is 15.2 A[21 which is in good agreement with the value of 14.6 A[21 obtained from other measurements[5]. This agreement is rather surprising, since it indicates that free spins are located only on the surface monolayer of carbon. Another indication of the location of the free spins on the carbon surface follows from the study of line shape. If one assumes a random distribution of the free spins throughout the volume of the carbon sample, one would expect that only a small fraction of spins would be influenced by adsorbed oxygen. The result of that would be a change in line shape. Precise measurements show, however, that the line shape is independent of the sample orientation relative to the magnetic field, the line as a whole together with its wings being shifted on rotation. Of special interest is point B in Fig. 5. This point corresponds to the highest density of oxygen at which our approximation holds. Further reduction in the average distance between oxygen molecules leads to a rapid discrepancy between calculated and experimental data which is clearly seen at the point A. On the other hand, the point B corres-
EPR LINE
SHIFT
ponds to the most stable surface condition investigated. This is why it seems reasonable to assume that point B corresponds to the situation where the surface is completely covered by a single layer oxygen. If this assumption is correct, the molecule diameter of oxygen is calculated to be 3sOOA. The diameter of the O2 molecule as obtained from viscosity measurements is 2.98 A, and from the Van der Waals equation, 2*92A. The agreement is better than one might expect. Higher density than that corresponding to point B represents a multilayer coverage. This was not taken into account in (12) and (13). At point C the ,anisotropy reaches a maximum value. At a perpendicular orientation relative to the magnetic field the line has a smaller apparent g-value than that for a free electron, at a parallel orientation it shows a small shift in the opposite direction. The average area covered by one oxygen molecule at this point is 18.0 A. Further outgassing leads to the disappearance of anisotropy, but both lines are shifted towards smaller g-values. At point D the area covered by one O2 molecule is 69.0 A [2]. Still further outgassing leads to the appearance of a different kind of anisotropy. At perpendicular orientation of the sample relative to the magnetic field, the line is shifted towards higher, at parallel orientation towards smaller, g-values than that for a free electron. The density of oxygen molecules at point E is small, the area covered by one molecule being about 200 A[2]. This configuration is unstable. Usually after a few minutes a complete outgassing of the sample occurs and the anisotropy disappears. In Fig. 5 the experimentally observed point which corresponds to complete outgassing of the sample is not indicated since it is located
507
IN CARBON
at 713 CCI(no anisotropy or any shift of the line). Finally it might be worthwhile to note that an important reason why the experiments have to be carried out under good vacuum conditions is the molecule exchange between the gas and the adsorbed phase, which limits the lifetime of the oxygen molecule in the adsorbed state. Should this lifetime become considerably shorter than the duration of a spin alignment, the time average of the field seen by a carbon spin will tend to zero. 5. CONCLUSIONS 1. The observed g-anistropy in flakes of amorphous carbon produced in an argon atmosphere appears to be due to adsorbed The character of anisotropy is oxygen. dependent upon the degree of surface coverage. 2. There are strong indications that spin centers in highly amorphous carbon are located on the surface of the carbon deposit. 3. The model presented, of a carbon surface covered by argon and on top of it by oxygen, permits to find from EPR measurement the correct values of atomic diameter of argon and of molecule diameter of oxygen and the surface area per molecule of oxygen at various stages of occupation of the carbon surface.
REFERENCES 1. Antonowicz K., Orzeszko S., Rozploch F. and Szczurek T., Carbon 5,261 (1967). 2. Mrozowski S., Proc. fourth Carbon ConJ, p. 271. Pergamon Press, Oxford (1960). 3. Austen D. E. G. and Ingram D. J. E., Chem. Znd. Rev. 981 (1956). 4. Abragam A. In The Principles of Nuclear Magnetism. Clarendon Press, Oxford (1961). 5. Yates D. J. C., Advan. Catalysti 12,265 (1960).
SHIFT IN CARBON ADSORBED OXYGEN
DUE TO
K. ANTONOWICZ, S. ORZESZKO and Js WIECZOREK Department of Physics, Nicholas Copernicus University, Torun, Poland (Received 4 Decembe-r 1968) Abstract-An amorphous carbon deposit was produced on flat glass plates by evaporation of spectroscopically pure carbon rods in an argon atmosphere. Such deposits exhibit a high spin concentration. The electron spin resonance absorption tine shows anistropy in g-value dependent on orientation of the plate relative to the externa1 magnetic field, and which appears to be due to adsorbed molecular oxygen. The results indicate that oxygen is adsorbed on an argon monolayer which tightly covers the carbon. The interaction between carbon and oxygen spins occurs across the argon monolayer. The local field produced by adsorbed oxygen at the site of the carbon spin is dependent upon the orientation of the surface relative to the external magnetic field. The calculated dependence of the local field cm the surface oxygen density is in good agreement with the observed line shift. From the assumed model, the diameters of the argon atom and oxygen molecule can be determined, and are found to be in good agreement with the data given in literature. 1. INTRODUCTION
In a previous paper [l] some properties of electron paramagnetic resonance, (EPR) in highly amorphous carbon were reported. The carbon was produced by evaporation of spectroscopically pure carbon rods in an argon atmosphere. At a suitable pressure of argon a highly amorphous carbon deposit is obtained. For such deposit a g-anistropy was observed which depends on orientation of the sample relative to the external magnetic field [l]. This surprising effect has been studied by us in detail. The study showed that the assumption of some kind of anisotropy of the carbon deposit caused by shrinkage[2] or by epitaxial growth of the crystal nucleus for instance, fails to give a proper explanation of the observed effects. Further progress was made when the dependence of anisotropy on the amount of adsorbed oxygen was found with a complete of anisotropy after out disappearance gassing the sample in a vacuum of the order of lOA7 mm. Hg. In this paper the results of
experimental and theoretical studies of the dependence of the g-anisotropy on the amount of adsorbed oxygen are presented. 2. EXPERIMENTAL
AND RESULTS
An amorphous carbon deposit was collected on flat thin glass plates of a size 2 X 10 mm suitable for mounting in the cavity of the EPR spectrometer. A standard carbon sample, a small grain of sugar char (500°C) sealed off under vacuum in a very fine capillary tube and then heat-treated to 700°C (line width 0.3G , g = gfF,,) was placed in a quartz tube together with the glass plate and the two EPR signals from both samples were recorded together. Due to the larger difference in line width and intensity, the signal of the standard gives only a narrow reference mark relative to which the g-value of the sample was determined. The EPR meastrrements were made using a transmission cavity of 9820 MHz, most of the meas~lrements having been performed at liquid nitrogen The homogeneity of the temperature.
500
K. ANTONOWICZ
magnetic field over the area of the sample was of the order of 10m4G. At room temperature the g-value for the deposit was exactly equal to that of the reference line, irrespective of orientation of the sample relative to the external magnetic field. At liquid nitrogen temperature, in general, the peaks of both lines do not coincide the relative shift being dependent on the orientation of the sample in the magnetic field. After closer examination of this anisotropy two important properties were found which throw light on the matter: (1) the anisotropy disappears in high vacuum (better than lop6 mm Hg); (2) the anisotropy and sometimes reverses after changes repeated cycles of evacuation and admission of air. Both facts indicate that the anisotropy does not depend on the structure of the deposit, but is the result of the conditions of evacuation and/or degree of outgassing of the sample. Small changes in the local field due to adsorbed molecular oxygen, a strongly paramagnetic gas, can be expected. Argon gas, adsorbed by carbon during deposition in the reaction vessel has also a strong influence on the EPR behavior. The EPR line of the carbon as deposited although weak can be easily detected at room temperature, in air, under atmospheric pressure. The line is about 20G wide. On the other hand, once the sample is .well outgassed at elevated temperature, the EPR becomes very sensitive to oxygen. This shows that adsorbed argon protects the carbon from oxygen and that this protecting shield is removed by outgassing[3]. When the carbon was prepared in an argon atmosphere, large amounts of gas are evolved by heating the sample in vacuum at a temperature of about 220°C. The desorbed gas is spectroscopically identified as argon. It seems reasonable to assume that carbon is covered with argon, which protects the spin centers in carbon from oxygen. Oxygen can be adsorbed only as a second layer on top of the argon.
tit al.
To observe the influence of oxygen, EPR measurements were performed in gradually reducing the amount of adsorbed oxygen. A fine control of the amount of oxygen adsorbed on the surface of a small sample at liquid nitrogen temperature, was achieved by use of a special sample holder (Fig. 1). In the quartz tube A at its flattened end B were placed the sample plate and the reference standard. The end B fits into the Dewar vessel of the spectrometer cavity. The capillary tube C reduces the rate of gas diffusion. D is a gas trap filled with activated carbon. The holder can be rotated around the axis AB. The measurements proceed in several steps. (A) After connecting the sample holder to the vacuum system, the sample is cooled to liquid nitrogen temperature, and only then the tube is evacuated, the activated carbon outgassed and the tube sealed off at A. The tube is transferred to the Dewar vessel in the
Fig. 1. Sample holder. A, connection to vacuum system; B, the carbon sample with reference standard; C, a capillary tube; D, activated carbon.
EPR LINE SHIFT
spectrometer cavity and the first measurement made. One finds a broad line overlapped with the sharp reference line at its centre, the relative position of both lines being independent of the orientation relative to the external magnetic field. Next the tube is taken out of the liquid nitrogen, for a few seconds and put back into the cavity Dewar vessel. One can see now an appreciable narrowing of the broad line of the carbon deposit and a small g-shift of the line towards higher field strength for both directions relative to the magnetic field. The first short warming up of the sample has reduced the amount of adsorbed oxygen; one does not know to what extent, but certainly this must have occurred. Such warming up of the sample is then repeated over and over (the number of consecutive operations being indicated on the abscissa in Fig. 2) increasing for a while up to a maximum. Further heating of the sample causes a gradual disappearance of the shift, the effect being
Fig. 2. Experimental results fbr the R-value as obtained for the two directions relative to the magnetic field in the 3 series of experiments in which the coverage with the adsorbed oxygen molecules has been reduced in steps (see text). t, indicates the number of consecutive operations.
IN CARBON
501
associated with an increase in the gas pressure inside of the tube. (Fig. 2(a)) The pressure at which the line shift disappears could not be determined exactly. From the character of the discharge observed one could estimate it to be about lo-” mm Hg. (B) In order to achieve a further reduction in the adsorbed oxygen the sample holder was opened and evacuated to a pressure of lo-‘mm Hg. During evacuation the sample was kept at room temperature and afterwards again cooled down to liquid nitrogen temperature. Then the pressure was decreased to about low6 mm Hg., the activated carbon was outgassed and the tube sealed off. Now the EPR measurement shows at the beginning no anistropy but an equal shift for both directions relative to the magnetic field to smaller g-value than that for the free electron (Fig. 2(b)). After warming the sample a a-anisotropy appears. For perpendicular orientation of the glass plate relative to the magnetic field the line is shifted to a higher field strength, for parallel orientation the line centre coincides with the reference signal. Further outgassing permits to trace a continuous increase in the g-anistropy with the line for parallel orientation remaining closer to that of the free electron. The anisotropy reaches a maximum at some particular coverage, then drops to zero and appears again, but now its character is different. For perpendicular orientation of the glass plate to the magnetic field the line is shifted to a lower magnetic field (opposite shift to that observed before) while for parallel orientation it is shifted to a higher magnetic field. Thus the anisotropy is again high and the shift of both lines is about symmetric on opposite sides of gfree. Once more it reaches a maximum and then at further outgassing decreases. (C) To reduce still further the amount of adsorbed oxygen, the tube is opened again, evacuated at room temperature to lO_” mm Hg., the activated carbon outgassed and then the sample cooled down to liquid nitrogen
502
K. ANTONOWIC~
temperature. For a few minutes the sample is permitted to adsorb oxygen at the low pressure, and the tube is sealed off. Again an anistropy is observed (Fig. 2(c)). This is a case where for perpendicular orientation the line is shifted to a higher field, but for parallel orientation the line is not shifted. On outgassing one can see a decrease in the anisotropy and change in its direction. When outgassing proceeds further high vacuum can be reached by cooling the activated carbon down to liquid nitrogen temperature. In high vacuum the anisotropy as well as the shift of the line from the position for the free electron disappears. A strong narrowing and increase in intensity indicates the complete outgassing of the sample. 3. THEORETICAL
CONSIDERATIONS
The dependence of the g-value on the amount of adsorbed oxygen, seems to be at first sight confusing. Calculations of the local magnetic field produced by the adsorbed oxygen lead to predictions which are in good agreement with experiment however. The following assumptions are made for calculating the contribution of oxygen paramagnetism to the local magnetic field at the carbon spin centers. 1. The surface of the deposited carbon can be approximated by a plane covered with a monolayer or argon. Oxygen is adsorbed on top of the argon layer. The layers are assumed to be parallel to the glass surface on which the carbon is deposited. A random distribu~on of carbon spin centres and irregularity of the carbon surface are taken into account by averaging the distance between oxygen and argon layers. 2. Only carbon-oxygen spin-spin interactions are taken into account. The interactions of similar spins, producing the line width, are neglected. 3. The interaction of two dipoles can be expressed by means of local magnetic fields. It is assumed that the total local magnetic
et d
field produced at a given point in the carbon is given by the sum of contributions from all oxygen molecules. Dipole-dipole interaction produces line broadening in general, but in this case the time variable part of this interaction is less effective than the presence of a static component of the field. This is firstly due to the distribution of both oxygen and carbon spins in form of two parallel layers at a given distance, so that the relative distribution of the spins is not completely random, the time average of the local field produced on the carbon surface being different from zero. Secondly, it is due to the fact that the interacting spins are unlike. When spin are identical the so-called ‘flip-flop’, allows a simultaneous reversal of the interacting spins in opposite directions. If two spins are unlike the rotating field produced by, let us say, ,ul, is off resonance for I_LZand exerts on it a negligible torque, whereas the static field produced by pi at pz is as effective as for like spins. It is easy to show that for unlike spins the flip-flop interaction term does not commute with the Zeeman hamiltonian and can be dropped [4]. The interaction of two magnetic moments 1~~= rltiJ, and ccc.= ycftJc is the well-known dipole-dipole coupling
w,c
=
~6JC_J(J1rlc~~~~rlc)]. (1)
(1) can be written as
where Hlc is the local field produced by spin 1 at the site of spin C. Detailed discussion of (1) is to be found in the literature[4]. In the case of two unlike spins, Hlc is given by H,c = ~1
3cos28-1 &
(3)
EPR LINE
SHWT
where 0 is the angle between J1 and vector T, describing the relative position of the two spins, and p1 is the magnetic moment of the oxygen molecule (spin 1). EItc is the zcomponent of the magnetic field produced by spin 1 at the site of spin C. The instantaneous local field seen by a carbon spiu pc is of the order of hundreds of gauss and the sign depends on the orientation of p, relative to the magnetic field, but there exists between neighboring oxygen molecules an exchange coupling which produces a fast flipping spins. Thus the instantaneous field NIP can be replaced by its time average vaIue
1N CAREOK
503
local fields at different spin sites, so that only the average values of the quantities appearing in (6) are of interest. The summation in (6) can be easily performed. First let us assume a concentration of adsorbed oxygen so small that the contribution to the local magnetic field can be neglected from all but the one closest molecule. The sum in (6) is now reduced to one term, but due to random distribution of both oxygen molecules and carbon spin centres in the planes, as well as to possible two dimensional motion of oxygen molecules the term (3 co? @- f),P must be averaged over all possible 8 and r_ 1. If the external magnetic field is perpendicular to the carbon surface (Fig. 3(a)), then
If after adsorption an oxygen molecule is in its ground state 3C,- the average value (,u} is given in reasonable approximation by Curie’s law
where g =2:2, S = 1, y, is the Bohr magneton, HO is the magnetic field, k is Boltzmann constant and T is the absolute temperature. The time average (j2.) is a very useful concept because we can treat the magnetic moment of each oxygen molecule as being parallel to an external magnetic field of value H,,. Equation (4) gives the local magnetic field produced by one oxygen molecule, The total local field can be assumed to be the sum of contributions from all molecules
Fig. S. A schematic showing how the local magnetic field produced by oxygen molecules of one-zone distributed on the circumference of a circle of radius ~1.d. k, in the plane at distance d is calculated for a carbon spin located at the point A. (a) HO, field perpendicular to the plane: fb)H,, field parallel to the plane.
(3cos20-l)/r3= Due to rapid convergence of the series in equation (6) the extent of the plane and the total number m of 0, molecules can be assumed infinite. The observed local field is an average of a great number of individual
(l/d”)(3cos~8-l)cos”8 (7)
where d is the surface and symmetry (7) The average
mean distance between carbon oxygen layer. Due to axial is independent of the angle CJJ. value of (7) is
504
K. ANTO~OWIC~ et al.
(1/d3)( (3cos20-1)
COSS8),, = (2/T&3)
n/z X
s
(3 co9
0-
1) toss &4e
0 =
+(0*25/d3).
(8)
2. If the external
magnetic field is parallel to the carbon surface (Fig. 3(b)) there is no symmetry and we have to average over angle cp. We note that cos 8’ = (r’/r) cos (o while the average of cos* cpis l/2, so
(a)
’ (b)
Fig. 4. (a) Idealized hexagonal close-packing of
(cos2 @‘)a”.C= ices” 0.
spheres. (b) Two-dimensional distribution of adsorbed molecules. A total magnetic field is
Introducing again d = r . sin 8 and averaging over 6’we have
obtained by summation of contributions from the central molecule and molecules in consecutive zones, 6k molecules in each zone, k assuming values between one and infinity.
((3 cos2 8-
l)/r3) = (2/%-d3) V/2
X
f
(~cos2~-
1)
0
X sin3 0~~
= - ( 0*297/d3).
(9)
By substitution of (8) or (9) into (4) one finds the local magnetic field seen by the carbon spin for two different orientations of the sample relative to the magnetic field. When the external magnetic field is perpendicular to the carbon surface the local magnetic field is positive, when parallel, negative. Let us consider now a higher concentration of adsorbed oxygen molecules, when the contribution of many neighboring molecules to the local magnetic field must be included and let’s assume a hexagonal close-packing of spheres in the plane, Fig. 4(a), (by spheres we understand oxygen molecules adsorbed on the argon layer). Each molecule is surrounded by six neighbours; in the next zone there are 12 molecules, and in the k-th zone 6k molecules. Now we assume the destruction of long range order by random modulation of the lattice parameter. If the average distance between molecules is n.d., where n is a nositivc number. the arrangement of
molecules can be assumed (to a good approximation) tobe like that in Fig. 4(b). Neighbouring molecules are assumed to be in zone with 6k molecules in each zone. This situation is, of course, not correct for a particular molecule at a particular time but for a great number of molecules in a plane the statistical model of one molecule and its surroundings will be approximately just like that in Fig. 4(b). The average local field at the carbon spin is the sum of contributions from the central oxygen molecule and molecules from all other zones. The magnetic field produced by one molecule is averaged over the area of each zone. The contribution from the k-th zone, for perpendicular orientation relative to the magnetic field, is (see Fig. 3(a))
= (pjtik
bM
= -
and the contribution
d3
(S/(1 +k*n%P)) (J2+kZn2d2)3/2
2 - ( 1 +
k2n2 kZ,~~2)5/2
from all zones is
- 1
EPR LINE SHIFT IN CARBON
(W
while for parallel orientation magnetic field (Fig. 3(b))
relative
to the
(11) is obtained. Equation (6) can be rewritten two directions (H,,,),
(ti) = d3(3
co532O- 1) cos3 0)
+6(/-d d”
m k(2-?zW) kzl (1-t &%2)5’2
(CL)
~~~~,)~~=--&(%Cos*$+3(P) 7 The over each large
now for the
(12)
I) sin”@)
m R(2-n2k2) kz (1 +pn*)5/**
(13)
first terms in (12) and (13) are averaged the zeroth zone. In sums for small k term can be calculated separately. For k or 12,when 1 4 k*n* unity is neglected
505
and the simple sum calculated. In (12) and (13) the parameter n depends on the twodimensional density distribution of oxygens in the pIane (n.d. is the average distance between oxygen molecules). The continuous lines in Fig. 5 represent the dependence of the calculated local magnetic field on n and, consequently, on the average distance between the oxygen molecules. 4. DISCUSSION According to the proposed interpretation the g-value for the carbon spin remains constant and equal to gfrree.It is only the local field created by the magnetic polarization of the oxygen layers which varies with the direction of the magnetic field and shifts the position of the EPR Iine as the sample is rotated. Thus it is the variation of the local field and not of the real g-value which is observed. The peculiar changes with the density of coverage of the surface with oxygen molecules can be easily comprehended for the case of the magnetic field perpendicular to the surface if one considers that a local field due to the spin of an oxygen molecule focated exactly across the argon layers has the same direction as the polarizing
0.3 0.2
Fig. 5. Dependence of local field on the average distance between oxygen molecules. Curves are calculated from formulas (12) and (13) of‘ the text X, o, give experimental results for perpendicular and parallel orientation of the sample relative to the magnet.ic field.
506
K. ANTONOWICZ et al.
field, but the local field for more distant position of the molecule has a reversed direction. Since the interaction decreases fast with the distance, for a single molecule moving in the plane at random the first effect prevails after averaging (point E, Fig. 5). As the coverage increased however and the zone diameter decreases, the point is reached when the local field due to molecules of the first zone tips the balance in favor of a reversed local field (Point C). At still higher coverage, the molecules of the first zone move so close to the central molecule (directly across) that their field begins to add a parallel component to the polarizing field. The case of the magnetic field parallel to the surface is somewhat more complicated due to the absence of axial symmetry, but one can see that the field due to the molecule located exactly across the layer and to other more distant but located in the plane perpendicular to the field, opposes the polarizing field, and the field of the more distant molecules and behind this plane is parallel to the polarizing field. Thus a reverse situation develops. The crossing points B and D of the two curves occur below the axis in Fig. 5, because in general the maximum positive contributions to the local field are not as large as the maximum negative ones (what can be seen from the above considerations). Formulas (12) and (13) and Fig. 5 can in principle be compared with experiments (Fig. 2). There is however the difficulty that in the experiments the density of oxygen molecules is not measured directly and only the local field is determined from the position of the lines. However, in our experiments, experimental conditions were realized in which the direction of density changes is known. In vacuum the sample can only lose adsorbed oxygen. When desorption proceeds slowly one can follow the variation of the local field starting from complete coverage of the surface by oxygen to complete outgassing. Because the sequence of alternation in local field follows the dependence shown in Fig. 5,
a correspondence between some experimental and theoretical points can be established. The outstanding identifiable points are those at maximum or at crossing of the two curves; they are marked B-E on Fig. 5. Experimental data corresponding to these points are introduced in Fig. 5. The maximum of anisotropy at the point C can be measured with the highest precision. In the experiments presented in Fig. 2, the difference in local fields at point C was 0.46 G. This difference can be calculated from (12), (13) and Fig. 5.
(4 = 7
* 0.55.
(14)
In (14) the only unknown quantity is d. On evaluation one finds d = 4*4A, the area occupied by one argon atom is 15.2 A[21 which is in good agreement with the value of 14.6 A[21 obtained from other measurements[5]. This agreement is rather surprising, since it indicates that free spins are located only on the surface monolayer of carbon. Another indication of the location of the free spins on the carbon surface follows from the study of line shape. If one assumes a random distribution of the free spins throughout the volume of the carbon sample, one would expect that only a small fraction of spins would be influenced by adsorbed oxygen. The result of that would be a change in line shape. Precise measurements show, however, that the line shape is independent of the sample orientation relative to the magnetic field, the line as a whole together with its wings being shifted on rotation. Of special interest is point B in Fig. 5. This point corresponds to the highest density of oxygen at which our approximation holds. Further reduction in the average distance between oxygen molecules leads to a rapid discrepancy between calculated and experimental data which is clearly seen at the point A. On the other hand, the point B corres-
EPR LINE
SHIFT
ponds to the most stable surface condition investigated. This is why it seems reasonable to assume that point B corresponds to the situation where the surface is completely covered by a single layer oxygen. If this assumption is correct, the molecule diameter of oxygen is calculated to be 3sOOA. The diameter of the O2 molecule as obtained from viscosity measurements is 2.98 A, and from the Van der Waals equation, 2*92A. The agreement is better than one might expect. Higher density than that corresponding to point B represents a multilayer coverage. This was not taken into account in (12) and (13). At point C the ,anisotropy reaches a maximum value. At a perpendicular orientation relative to the magnetic field the line has a smaller apparent g-value than that for a free electron, at a parallel orientation it shows a small shift in the opposite direction. The average area covered by one oxygen molecule at this point is 18.0 A. Further outgassing leads to the disappearance of anisotropy, but both lines are shifted towards smaller g-values. At point D the area covered by one O2 molecule is 69.0 A [2]. Still further outgassing leads to the appearance of a different kind of anisotropy. At perpendicular orientation of the sample relative to the magnetic field, the line is shifted towards higher, at parallel orientation towards smaller, g-values than that for a free electron. The density of oxygen molecules at point E is small, the area covered by one molecule being about 200 A[2]. This configuration is unstable. Usually after a few minutes a complete outgassing of the sample occurs and the anisotropy disappears. In Fig. 5 the experimentally observed point which corresponds to complete outgassing of the sample is not indicated since it is located
507
IN CARBON
at 713 CCI(no anisotropy or any shift of the line). Finally it might be worthwhile to note that an important reason why the experiments have to be carried out under good vacuum conditions is the molecule exchange between the gas and the adsorbed phase, which limits the lifetime of the oxygen molecule in the adsorbed state. Should this lifetime become considerably shorter than the duration of a spin alignment, the time average of the field seen by a carbon spin will tend to zero. 5. CONCLUSIONS 1. The observed g-anistropy in flakes of amorphous carbon produced in an argon atmosphere appears to be due to adsorbed The character of anisotropy is oxygen. dependent upon the degree of surface coverage. 2. There are strong indications that spin centers in highly amorphous carbon are located on the surface of the carbon deposit. 3. The model presented, of a carbon surface covered by argon and on top of it by oxygen, permits to find from EPR measurement the correct values of atomic diameter of argon and of molecule diameter of oxygen and the surface area per molecule of oxygen at various stages of occupation of the carbon surface.
REFERENCES 1. Antonowicz K., Orzeszko S., Rozploch F. and Szczurek T., Carbon 5,261 (1967). 2. Mrozowski S., Proc. fourth Carbon ConJ, p. 271. Pergamon Press, Oxford (1960). 3. Austen D. E. G. and Ingram D. J. E., Chem. Znd. Rev. 981 (1956). 4. Abragam A. In The Principles of Nuclear Magnetism. Clarendon Press, Oxford (1961). 5. Yates D. J. C., Advan. Catalysti 12,265 (1960).