R. H. Herber Rutgers, the State University New Brvnswick, New Jersey
I
Introduction to Miissbauer Spectroscopy
The fundamental principles of spectrescopy are familiar to every chemist. The solution of a wide variety of chemical problems involves a spectroscopio study (either directly or by implication) as part of the evidence marshalled bv the investieator in SUDport of his description of events in the laboratory. i n many spectroscopic studies in which lines or bands are observed-as for examplein IR, visible, UV, NMR, ESR, or mass spectrometry--the excitation of the transition in question is brought about either by using a quantum source with a broad or nearly flat response over a range of energies (e.g., a glohar or incandescent light source), or by scanning a wide range of energies through a continuously variable "window" (e.g., varying magnetic or electric fields in NMR, ESR, or mass spectroscopy). It is only in fluorescence (resonance) spectroscopy that a narrow band of energies emitted by a quantum source exactly matches the transition energy in an absorber material. Because of the considerable success which resonance spectroscopy has enjoyed in optics and atomic physics, a number of attempts were made soon after the discovery- of gamma radiation to extend the techniques of fluorescence spectroscopy to nuclear transitions. Almost all of these early experiments either were inconclusive or led to resonance absorptions which were so small as to be questionable a t best. The reason for these failures in t,he case of nuclear transitions (in contrast to the successes in optical experiments) is readily apparent from a consideration of the line width of the transition as compared to the recoil energy suffered by the source and the absorber as a result of the transition. The width (r)of a spectral line emitted by a source is related to the mean lifetime (7)of the excited state (from which the transition to the ground state originates) by the uncertainty principle.
r7 = h
(1)
so that
-
In optical transitions where T = 10-lo sec, r 7 X 10-8ev. I n the case of fluorescenceexcitation, 7 may be as long as several seconds, in which case r < 10-16 .-BY.
When a nucleus undergoes a transition from state E. to state E. by the emission of a photon, the conservation of momentum requires that the momentum of the atom, (p,), recoiling in one direction, is just equal and opposite to the momentum of the photon (p,) emitted in the Presented in part at the 17th Analytical Summer Symposium, Cornell University, June 24-26, 1964.
180
/
Journal of Chemicol Educofion
opposite direction. The kinetic energy of the recoiling atom is ER, so that for an atom of mass M and velocity v En
=
My2 =
pyP 9M
(3)
Moreover, the momentum of a photon of zero rest mass is related to the energy by E
=
p,c
(4)
so that
Since the two momenta must be equal, it follows that
A consequence of this conservation of momentum is that E, will he less than the transition energy, E, = E. - E., by just En Moreover, the energy required to populate the E. state in an absorber (initially in state E.) will be larger than Et by the same amount En. I n optical transitions, E R is much less than the natural line width so that resonance is readily observed, despite the fact that the emission lineis displaced toward lower energies by 2En from the line required by the ahsorber. This situation is represented schematically in Figure la. A typical value of the ratio of recoil energy to line width En/T for an optical transition is -2 X I n the case of nuclear transitions, on the other hand, the larger transition energy implies a larger recoil energy, and for excited states having the lifetimes of optically excited states, the ratio En/T can become very large. This reduces the overlap between the line emitted by the source and the line required to populate the corresponding transition in the absorber to a negligibly small value, as shown in Figure lb. I t is for this reason that nuclear resonance spectra are difficult to observe. In a recent excellent review, Goldanskii (1) has summarized the pertinent values of En and r for optical and nuclear transitions, and these data (somewhat augmented) are collected in Table 1. I n early attempts to observe gamma ray resonance, a number of experimental methods were devised to provide the 2En of energy by which the emitter and absorber are out of resonance. Most of these methods (2) made use of the fact that an emitter which has a velocity v with respect to the propagation axis of an emitted quantum, imparts to that quantum a Doppler energy EA. -, where
Table 1
A (cm) Energy (ev) En (ev) r (ev) EdII
IR (HC1 vibr.)
Visible (NaD line)
X-ray (Fe K.)
3.46 X lo-' 3.6 X lo-' 1.93X10-* 6.6 X 102.9 X lo-%
5.89 X 2.1 1.13X10-8 6.6 X 101.71XlO-1
1.93 X 6.2 X lo-" 3.3X10-' 6.6 X lo-8 5.OX10-'
The velocity u can be supplied either mechanically or thermally. In the former method the photon source is mounted on a rapidly moving piston or a revolving flywheel and observations are made during those portions of the mechanical cycle during which an appropriate velocity component in the direction of the absorber obtains. Thermal excitation methods are based on the well-known relationship between translational energy and temperature for a monatomic gas.
from which
Since we require Ed = 2ER,we obtain from (7) and (9)
which is the temperature necessary to obtain a root-
----Isomer Fern
transitionSnl1Q
14.4 x 1.9 x 10-3 4.55 X lo-' 4.2 X lo-'
23.8 X 103 2.6 x lo-' 2.4 X 10" 2.8 X l o 6
Gamma ray emmmn FeS7 137 X 10" 6.6 X lo-' 4.6 x lo-' 1.4 X 10'
mean-square velocity which will just give the required Doppler energy to compensate for the recoil energy losses. (It is also possible to impart the required Doppler velocity to the atom undergoing the transition of interest by taking advantage of the recoil effect due to a prior nuclear event such as gamma ray or particle emission. Successful experiments of this kind have indeed been reported-for example in the Eu'S2-Sm'SZ decayhut such strategems are of limited applicability and will not be considered further in the present discussion.) Mossbauer's Discovery
The German physicist R. L. Mijssbauer undertook a study (3, 4) of resonance absorption in Irlal in which the low gamma ray energy (129 Kev) and resultant small recoil energies (0.046 ev) require a Doppler compensation temperature of only about 260°C.' In order to reduce the natural overlap due to thermal excitation which still persists a t room temperature, he cooled his source and absorber materials in a liquid nitrogen bath a t 78°K Instead of finding the expected decrease in the resonance effect, Mossbauer observed instead a marked increase in the resonant absorption by the absorber ("marked increase" here means a change of 3% in transmission !) . Mossbauer realized that the large resonance overlap implied by this decrease in transmission was due to the fact that an appreciable fraction of the emission and absorption events occurred, in fact, without any appreciable recoil energy loss a t all. This situation occun because under the conditions of his experiment, the effective recoiling mass [M in eqn (€41 has become the mass of the whole crystal (or metallic) lattice rather than the mass of an individual atom. In terms of the Debye theory of solids, this implies that the quantum jump does not involve contributions from the phonon spectrum of the matrix material, and such recoil-free transitions are usually referred to as "no-phonon" events. This interpretation provides an immediate link between the fraction of recoil-free events and the Debye temperature of the solid, and this relationship will be discussed in detail below. As in any resonance experiment, the resonance condition is best observed by systematically disturbing the system and noting the influence of this variation in the measurable parameters (i.e., changes in the intensity of the transmitted or scattered radiation). In the case of 1 By equating En with the mean kinetic energy of 8. monatomic gas, the required temperature is T = E&. In the case of Ir"1,
Figure 1. Id Overlap (schematic) of emirdon and absorption liner in o p t i c ~ ltransitions. (bl Absence of overlap lrcharnatic) of emission and absorption liner in nuclear transitions involving atoms which are free b recoil. Drown to scale, the separation between the two lines would b e about 4 X 1 06timesthe width of eoch line a t half maximum.
T
=
4.6 X
ev X 1.60 X lo-" erg ev-' = 5330K (2600C). 1.38 X 10-'' erg deg-I
lo-'
(The usual factor of is ahsent if the overlap of two spectral lines as a. function of translation in one dimension is considered, as the case here.)
Volume 42, Number 4, April 1965
/
181
a nuclear transition having a l i e width r, it is possible to shift the photon energy emitted by the source (or that accepted by the absorber) by r by imparting to the source a Doppler velocity v so that
of greatest interest to a chemist are the magnitude of the resonance effect (E), the line width (r), the isomer shift (IS), the quadrupole splitting (QS), magnetic hyperfine structure (mhfs), line asymmetry, and temperature coefficients of these parameters. We shall now briefly examine these in modest detail.
The Doppler velocity of the relative source-absorber motion which is required to shift the gamma-ray energy by one line width for a number of Mossbauer nuclides is summarized in Table 2. From these data it is seen that the relative sourceabsorber velocity required to shift the two transition lines by one line width is very modesta and (in theory) readily attained by common mechanical or electromechanical devices.
Magnitude of the Resonance Effect (r)
Table 2. Doppler Velocity Equol to M&bouer Nuclides El
Nuclide (Kev) 14.4 SnlLSm 23.8 I 129 Auln 77
t./,
(seo)
r
For Several v = -
r (ev)
1 . 0 ~ 1 0 ' 4.55~10-5 1.9X10-8 2.4X104 3.25 X lo-' 1 . 4 X lO-'O 1.9X10-' 2.4X107
.E ,
(mm sec-')
0.0945 0.303 7.53 0.94
From the preceding section it is seen that to obtain a resonant gamma-ray absorption spectrum it is necessary to relate the transmission intensity to the instantaneous source-absorber velocity. In practice there are a number of methods which can be used to accomplish this, and these can be roughly divided into two groups: those which employ constant velocity drives and those which employ continuously variable velocity drives. The characteristics and advantages of each of these systems have been discussed in detail by Wertheim (5) and elsewhere (6). In the present discussion we shall not explore any of these methods in detail, but will concern ourselves only with the details of the spectra which are obtained. A typical Mossbauer spectrum is shown in Figure 2, which is a characteristic plot of the total number of events (counts) observed as a function of source-absorber velocity (the standard convention is to represent motion of the source toward the absorber by positive velocities and motion of the source away from the absorber by negative velocities). The profile of the resonance maximum obeys (ideally) the Lorentz relationship I (E) =
In most experiments the nuclear transition of interest is accompanied by other radiations which are not resonantly emitted or absorbed. In the case of CoS7(FeS7), for example, in addition to the 14.4-Kev gamma ray of the "Mossbauer line," there is an equal population of 123-Kev precursor events as well as 97" of 137-Kev radiation and numerous low-energy X-rays which arise from both Auger effects and scattering from the environment near the source-detector arrangement. Despite careful energy resolution, some of this radiation will reach the detector and thus contribute to the total counting rate, evenly distributed over the range of Doppler velocities. It is for this reason that absolute values of e are seldom experimentally accessible, since this parameter depends on the fraction of all of the detected events which are resonantly absorbed. Moreover, the magnitude of e depends on the number of absorber nuclei in the optical path. For nuclides such as TmlBg,Ta181, and Aul" which are in each case the only stable nuclide of that element, isotopic enrichment is neither possible nor necessary. In the case of high abundance nuclides such as Erl" (33.4y0), Hf177 (18.5%), WIE2(26.4%), IrlS1(38.5%), and Irlga(61.5%), isotopic enrichment of the absorber is usually not necessary and can a t best increase e by a sniall factor. For low abundance Mossbauer nuclides, such as Few (2.170j0),Zn6' (4.11y0),and Ybl'O (3.03%), a marked increase in e can be achieved by working with absorbers enriched in the resonance nuclide. Indeed in some instances, as in studies of very high molecular weight biological materials, such enrichment is crucial to the obtaining of a measurable resonance effect. In cases where there is some choice of host lattice for the source nuclide available, large resonance effects can be observed by using a single line (see below) emitter in a matrix of high Debye temperature. Such single line sources also facilitate subsequent data analysis. In most cases, trial and error methods are required to indicate a source matrix which will give the largest values of e with a given absorber. For Mossbauer resonance
constant (E - E o ) ~
+
in which Eo is the Doppler energy (in velocity units) a t resonance maximum. Since the resonance line which is observed is a measure of the overlap of two lines of width T, the measured full width a t half maximum is 2
r
=
r.
The parameters of the Mossbauer spectrum which are a The Doppler velocity corraponding to P c / E , for Zn6'k 1.56 X lo-' mm sec-1. According to one of the cognoscenti in this field, this is comparable to the growth rate of a.tomato plant.
182
/
Journol of Chemical Educofion
Figure 2.
Typical M&rbrnuer spectrum.
experiments in iron compounds, Co67diffused into stainless steel, metallic chromium, palladium, platinum, or copper appear to give the largest resonance effects. For tin spectroscopy, Sn119mincorporated in a B203Na2C03ceramic (7) or into Mg2Sn, gives e values of 1 & 4 0 ~ oeven , a t room temperature. Relative values of e, which depend on the probability of recoil-free emission if) and absorption if') as well as on the effective thickness of the absorber, may be strongly temperature-dependent. Measurements of 8 a t various absorber temperatures can be used to calculate Debye temperatures for the absorber and are primarily exploited for this purpose. I n some instances, relative values of e have been used in arriving a t a qualitative estimate of the proportion of various chemical environments present in an absorber. Relative E values are also useful in the study of hyperfine interactions, principally those due to magnetic phenomena. Such studies of magnetic hfs have been reported by a number of inve~t~igators (8-1 1). (P) As we have already noted in the preceding discussion, the width of a nuclear transition (energy level) is given by the Heisenberg uncertainty principle as The Line Width
(In the case of nuclear de-excitation, there are usually two competing processes which depopulate the upper of two energy states: gamma emission and internal conversion. The gamma-ray width T,is related to the tot,al width J? of the excited state by the relationship
in which a is the int,ernal conversion coefficient. The coefficient a is by no means a trivial number for most Mossbauer transitions. Typical values are 15 for FeS7 (14.4 Kev), 7.3 for Snllg (23.8 Kev), and 2.5 for AulW (77 Kev). Since in a Mossbauer experiment two transitions are matched with respect to their energies, the width (that is, the full width a t half maximum) of the resonance line, P, can never be less than twice the n a b ural line width; i.e., P 2 2 r,. I n practice, it is seldom possible to observe resonance lines as narrow as 2 r,, since the finite thickness of both the source and the absorber will tend to broaden the resonance line. I n addition, the limits of velocity resolution of the motion drive, the presence of solid-state defects and impurities, and thermal effects all tend to increase the width of the resonance line. Nonetheless. the resonance line width which is observed with a standard absorber is (in addition to the magnitude of e) the most reliable measure of the quality of a Mossbauer source. As in all optical experiments, the resolution which is attainable is inversely related to the line width, and the maximum amount of data for a given nuclide will be obtained for a source of minimal P. Since P is related to the number of absorber atoms in the optical path, and since the magnitude of the resonance effect also depends on this value, a compromise between a large e and a wide resonance line, and a small E and a smaller value of P has to be made. Since 8 also depends on the
non-resonant absorption of gamma radiation by other (usually high 2) atoms in the optical path, this compromise is usually best arrived at by empirical methods. The Isomer Shift (IS)
The Mossbauer parameter which yields the greatest amount of chemical information is the isomer shift, which is defined as the displacement of the resonance maximum from zero velocity. In the case of spectra with hyperfine structure, the isomer shift refers to the displacement from zero velocity of the center of the resonance spectrum. The origin of the isomer shift was first correctly identified by Kistner and Sunyar (18). A recent review of the applications of this effect to both chemical and nuclear problems has been given by Shirley (13). The isomer shift arises from the fact that the nucleus of an atom occupies a finite volume. For a spherical 1.20 nucleus, this volume is V = 4/3 7rRa, where R X 10-l3 A'". If a uniform nuclear charge distribution is assumed inside the nucleus, the potential due to this charge at a radial distance r from the origin is
-
for r < R and is V(r) = -Ze2/r for r > R. I n anonrelativistic approximation, t,he electron density a t the nucleus is appreciably large only for s electrons and can be approximated by J.,2(0). (Actually for relativistic px/,electrons, this probability term is not zero and cannot be ignored for heavy nuclei. For the present discussion, however, it will suffice to consider only the charge density due to electrons with 1 = 0.) Since nuclear excited and ground states do not have the same radius of equivalent charge distribution [in the case of Feu the ground-state radius is larger than the radius of the a/2 state ( I d ) ] , the s electrons will interact to a different extent with the nuclear charge. Specifically, the perturbation energy due to this interaction is
and the perturbation difference between the excited state and the ground state is
in which 6R = RarCited - Rground.I n practice, a(@) is not measurable by itself, but can be evaluated only with respect to a given source-absorber pair. For such a pair of resonant atoms, the isomer-shift energy is
in which the two s electron wave functions refer to the absorber and source respectively. The isomer-shift energy is observed in a resonance experiment as a D o p pler shift, which occurs a t a velocity
The fractional increase in the nuclear radius, 6R/R, has been calculated for a number of Mossbauer nuclides, for FeS7,1.16 X 10W4 and has the value -1.8 X for Sn119m( l a , and -3 X 10-4for AuIg7(16). Volume 42, Number 4, April 1965
/
183
Since the isomer shift arises from the difference in fiS2(0)between source and absorber, absolute values of
the IS have little significance. Indeed, recent precision measurements have suggested (17) that even nominally identical Mossbauer sources will give rise to different isomer shifts with the same absorber, apparently being dependent on the source preparation history (plating, diffusion, annealing, etc.) in as yet incompletely understood ways. To overcome this difficulty, it has become customary to report isomer shifts observed for a particular source and a reference absorber. In the case of CoS7sources, a convenient reference absorber is Nsa[Fe(CN)5NO].2H20 (18) which is readily available in high purity, is stable, has a narrow line width, and has a large f' (probability of recoil-free absorption of the y quantum) a t room tem~erature.~In the case of Sn119" spectra, reference absorbers of Mg,Sn, or SnOz a t room temperature, or metallic (8)tin a t liquid nitrogen temperature can be used. A number of interesting correlations between chemical properties and IS have been reported. The first systematic interpretation of isomer shifts for iron compounds was that of Walker, Wertheim, and Jaccarino (14). Collins and Pettit (19, $0) have shown that for a number of iron tetracarbonyls the isomer shift is a linear function of the nuclear quadrupole splitting, while the results of other iron organic compound spectra can be interpreted ($1) on the basis of treating the isomer shift as an additive molecular property. The isomer shift systematics for tin absorbers have been reviewed recently (sf?), and can be related to ligand electronegativities. Similar correlations have also been suggested for EulS1and AuLg'. Isomer shifts for a number of I I z P absorbers have been reported by deWaard et al. (23).
0 Z
Q + a u
-
0 Y)
m 4
k"u -
.I.S.-
L W
a s .
-0.4
-Oi
-0;
-0.~1
or
6.1
62
63
d4
VELOCITY IN CM. SEC-I Figure 4. Mbrrbwer spectrum which shows both the isomer (chemical) shift (IS1 and quadrupole splitting (QS) parameters which can be extracted from the d d a .
+
split into (I '/2) components having the same center a t the unsplit level. This splitting is shown schematically in Figure 3. The interaction between a nuclear quadrupole moment Q and the electric field gradient tensor is observed in a Mossbauer spectrumas a splitting (QS) of the resonance line, as shown in Figure 4. The presence of a non-zero field gradient a t the nucleus is determined primarily by the symmetry of the distribution of electrons about the nucleus, which in turn is dependent on the symmetry of the bonding about the atom in question. In general, the presence of two mutually perpendicular axes of threefold4 or higher symmetry will result in a zero field gradient, whereas in lower symmetries, quadrupole interaction will be observed. The field gradient, which is equal to the second derivative of the potential with respect to the coordinate, is usually expressed in terms of b2V/az2 = ep, and the asymmetry parameter
Using this notation, the eigenvalues of the Hamiltonian which give the interaction between Q and the efg tensor are
in which the magnetic quantum number m, has the values I,I - 1, . . . -I.5 When the Mossbauer atom occupies a lattice site which experiences an axially symmetric field, b2V/bx2 = b2V/by2 so that q = 0 aud Figvre 3. The origin of the quadrupole splitting. The energy levels for the 1r.o nuclei ore shown at left. The d.splacement d ~ to s the ikomer khemid l B i f l is shown in the center. The effect of a non-vonirhing electric field gradient ot the Mb5sbouer lottice point i, % h o wot the righr.
Quadrupale Splitfing (QS)
An energy level corresponding to a nuclear spin moment of odd half integral I has an (I I/%)fold d e generacy in a spherically symmetric electric field. I n a non-spherically symmetric electric field (i.e., when the field gradient tensor does not vanish a t the nucleus) this degeneracy will be lifted, and the nuclear level will be
+
a Stainless steel, although convenient, is less suitable as a standard absorber because of the laree T values which are observed.
184
/
Journal o f Chemical Education
AEQ =
eaqQ
U ( 2 1 - 1)
[3m?
- 1(1 + 1)]
=
QS
For nuclei with spin 0 or the term U ( 2 I - 1) vanishes and hence AEQ vanishes. The resultant absence of splitting is of course due to the fact that the nuclear charge distribution is spherical and is independent of the electric field symmetry due to the ligands. For nuclei with I = the term
That is, rotation by 120' will result in a configuration superimposable on the initial configuration. "Since only values of m~'appear in this expression, states of +mr and -mr will he degenerate. This degeneracy can be lifted in the presence of an internal or external magnetic field, and will he discussed below.
has the value I/, for mr = a/2 and -I/, for m, = I/%. Thus the differencein the two eigenvalues of the quadmpole interaction Hamiltonian is
(chemical) symmetry around the tin atom is clearly less than cubic. Magnetic Hyperfine Structure (MHFS)
In an actual chemical compound, the electric field gradient tensor has two major contributions-that from incompletely filled (non-spherically symmetric) electron shells and that arising from charges on the ligand atoms. The effect of these distant charges on the wave functions of the electrons associated with the given atom is usually considerable, and ligauds which are not in cubic or octahedral symmetry will give rise to an enhanced efg, above that due to the unfilled electron shells alone. I n the case of iron compounds, those with octahedral symmetry, e.g. Ka[Fe(CN)6], KIIFe(CN)~],and Fe( a ~ a c )and ~ those with tetrahedral symmetry, e.g. K2Fe04,show zero or very small quadmpole splittings. When this symmetry is destroyed, however, as in Na2 [Fe(CN).JVO].2H20, two well-resolved resonance maxima are observed, corresponding to transitions from the ground state to the two non-degenerate6levels of the first excited state in the nitroprusside absorber. Typical data for K4[Fe(CN)6]and Nap[Fe(CN)~N0]~2Hp0 are shown in Figure 5. In the case of Sn118 compounds, similar observations obtain. Thus (CsH6)i3nwith tetrahedral symmetry shows no quadrupole splitting, while (C6HG),SnCIspectra contain two well-resolved resonance maxima.
180
200
ANALYZER ADDRESS 220 240 260
280
As mentioned briefly in the preceding section, states of both +m, and -m, occur a t the same energy (i.e., they are degenerate) in an asymmetric electric field. This degeneracy can be removed by placing the Mossbauer atom into a magnetic field which arises either internally (in a ferromagnetic material such as metallic iron or FerOa)or which is generated by an external magnet device. Under such conditions, a nuclear Zeeman effect is observed in which each nuclear energy level is split into (21mIl 1) components as in Figure 6. The selection rules (for dipole transitions) which govern allowed transitions between these substrates are Am1 = 0 or 1, so that in an absorber with an excited state of I = 8 / and a ground state of I = '/p, a six-line hyperfine structure spectrum will be observed. Typical data for metallic iron are shown in Figure 7.
+
*
300
Figure 6. Origin of mognetic hyperfine structure. This onorgy level scheme I s opproprlate where the E. rtote spin is '1% and the E. state spin is 1 . More complex rpllttingr occur for stater with higher nuclear spin valuer.
Figwe 5. Miissbauer spectra of on octohcdrolly symmetric complex [ N ~ , F ~ C C N Iond ~ I of o didorled octahedral complex [No?iFe(CNlsNOI. 2H201, %howlngthe effect of o non-vonihinp electric fielo grodicnt ot the Miisrbouer lattice point.
I t is important to recognize that the absence of (resolved) QS does not necessarily imply "chemical" cubic symmetry but only "electric field" cubic symmetry. For example, recent studies (24) of ((CsH6)aSn)z and related binuclear alkyl and aryl tin compounds as well as tris(para fluoro phenyl) tin hydride, show no quadmpole splitting in their resonance spectra, although the ligand Wxcept for magnetic hyperhe splitting.
For the chemist whose major interests are other than those involving magnetic field intensities in materials such as alloys and oxides, the major significance of the MHFS is that it provides a convenient method for calibrating a Mossbauer spectrometer by data obtained by other than Mossbauer methods. The ground state (+I/%, -I/%) splitting in metallic iron has been determined by NMR measurements (36) to be 3.92 mm sec-1. A recent high-precision Mossbauer measure0.008 mm sec-' in ment (26) yields a value of 3.924 good agreement with the NMR data (86)and lends support to the use of an iron-foil absorber to calibrate the velocity scale in a non-constant velocity drive spectrometer. In practice, what is done is to determine the absorption spectrum of a metallic iron absorber using a narrow line, unsplit source. In a spectrum of the type shown in Figure 7 , (recorded by information storage in a multichannel analyzer) the number of channels b e tween peaks 2 and 4 and between peaks 3 and 5 should be equal and the two lines in each pair are separated (at room temperature) by 3.924 mm sec-'.
*
Volume 42, Number 4, April 1965
/
185
Line Asymmetry
A Mossbauer spectrum obtained by using a source showing no hyperfine structure interactions and an absorber in which the resonant absorption again occurs without hyperfine interactions, consists of a line which is symmetric about the resonance maximum. This symmetry is not, however, necessarily obtained with absorbers which show either QS or MHFS interactions. I n the case of a quadrupole split line, two effects can give rise to unequal values of c and/or F for the two resonance lines. The first of these is due to a preferential orientation of the absorber in its mounting so that non-random orientations of a unique crystal axis with respect to the source-detector asis are obtained. This effect was first discussed by Kalvius et al. (27), who noted an asymmetry of unequal e values in the spectrum of Fe(C0)6 in which the two lines are separated by a quadrupole splitting of 2.57 + 0.04 mm sec-1 a t 7S°K. The origin of the non-equivalence of r for the two resonance lines lies in the angular dependence of the line intensity, which will be different for m, = 0 and mr = 1. Specifically, the angular dependencies are for / / I(8) = ( 1 + casa 8 ) I ( e ) = 1 + z/, sinZe / , in which 0 is the angle between the axis of symmetry and the optical axis of the experiment. Wertheim has pointed out (5, 28) three salient features of this angular dependence: (1)I(@)# 0 for either line a t any value of 6;' (2) the maximum difference in I(0) for the two lines occurs when the symmetry axis is parallel to the optical
--
me-
axis; and (3)
I(B)~O is equal for the two quadrupole
. - ""
split lines. An immediate consequence of (3) is that for a finely powdered material, packed into an absorber holder in random orientations, the two lines should be of equal intensity. This conclusion was tested experimentally by Kalvius et al. (27) by rapidly freezing their Fe(C0)6sample and thus producing randomly oriented microcrystalline material which gave lines of equal e and F. A further contribution to line asymmetry for an absorber which has a quadrupole spli
