(a.) Sample Preparation
The samples were made from 99.999% pure host (Pb or Ag) and either Sn
enriched to 84% 
Sn isotope or natural Sn (which contain 
8%
Sn ). The components used were all in the form of small pellets
except for the 
Sn , which was in powder form and had been reduced
from a powder of enriched SnO
. This reduction was done under a H
atmosphere at 1200 K for one hour.
The correct mixture of components were weighed to a total mass between
2.5 and 10 grams and put in a quartz ampule which was then evacuated
by a mechanical pump and sealed. In order to assure that the two
component elements would mix well, the samples were then heated over a
flame until the Sn melted (the Pb host, when used, was also melted)
and mechanically shaken. The samples were held in a furnace at least
50K above the melting temperature of the pure host for 24 hours, and
then quenched into cold water. After inspecting the ampule to
determine that it had not cracked during the heating or quenching, the
ingot was extracted, and cold rolled into a foil. The final thickness
of the foil was determined so that the sample would be about 1
absorption thickness for non-resonant 24KeV x-rays. This foil was
coated with a thin film ( 1000Å) of aluminum to inhibit
oxidation. For the samples with a Ag host, this Al film itself was
oxidized by suspending over boiling water to prevent the Al from
diffusing into the Ag host. The aluminum coating did not need to be
oxidized for the Pb host alloys because Al does not dissolve in Pb.
Alloys with various compositions were made in this way. For the Pb
host, the samples used had enriched Sn concentrations of 0.5, 1.0,
2.0, 3.0, and 5.0 at.% (The room temperature solubility limit for Sn
in Pb is 3 at.%). For the Ag host, the samples used had
enriched Sn concentrations of 1.0, 2.0, 4.0, and 8.0 at.%, and
natural Sn concentration of 4 at.% (The solubility limit for Sn in Ag
is 12 at.%). The relative Sn concentrations of the alloys were
confirmed by XAFS, Auger depth analysis, and EDS (energy dispersive
spectroscopy). XAFS measurements determined that the relative Sn
abundance for the 1.0, 2.0, and 5.0 at.% Sn-Pb had the ratio 1:2:5.
Auger depth analysis gave the ratio for 1, 2, and 4 at.% Sn-Ag as
1:(1.6):(4.7). EDS gave the ratio for 1, 2, and 4 at.% Sn-Ag as
1:(2.1):(3:2).
(b.) Spectroscopy
The Mössbauer measurements were performed with the alloys as the fixed
absorber versus a moving gamma source in a constant acceleration
mode. The source was 
Sn in a calcium stannate (CaSnO
) matrix
with line width 
= 0.382 mm/s. The velocity scale was
determined from the quadrupole splitting[10] of SnF
.
The Pb-Sn alloys were cooled by a flow of liquid nitrogen through a cold finger. The temperature was controlled by a microprocessor within 0.05%. The Ag:Sn samples were heated to desired temperatures and kept stable within 0.5%. It was important to keep the temperature (T) constant for the long run time at each T (up to 3 days) for better statistics caused by the weak intensity that prevailed at high temperatures due to the low Mössbauer fraction coupled with the low isotope content in the sample. To check the apparatus, a 0.1mm thick sample of natural metallic tin supplied by the source manufacturer ( Amersham International) was measured at 80K. The on-resonance dip was as expected from the estimated Mössbauer fractions.
Figure (1) shows a typical set of spectra obtained from Ag 4 at.% Sn at different T's. Figure (2) shows the corresponding information for a Pb 1 at.% Sn sample. Note that the relative decrease in spectral intensity for Pb 1 at.% Sn is much greater between 145K and 150K than that between 140K and 145K. The solid curve through the data points is a result of a Lorentzian best fit using a standard commercial software package. The analyses yield the spectral intensity, line position (shift), and width. The spectral intensity I is the integrated area of the data after subtraction of the background. Attempts to fit more than one Lorentzian resulted in poorer fits.
In order to evaluate the effect of the absorber thickness[11],
we plotted experimental line width 
versus absorber thickness
at room temperature for the Ag alloys. 
initially increases
linearly with thickness and starts to saturate at large thicknesses.
Extrapolation to zero thickness results in an experimental linewidth
of 0.82 mm/s. The absorber line width is 0.44mm/s
(=0.82 - 0.38 mm/s of the source), as compared to the natural line
width of the 24KeV isomer level of 0.32 mm/s. The `zero thickness'
broadening could result from local inhomogeneities of electric field
gradients induced by the long-range Friedel oscillations of the
shielding tails around the tin impurities causing quadrupole
splitting[12]. This interpretation is consistent with the
larger high temperature width for the Ag matrix than the Pb one. The
tails will be much weaker for the Pb matrix which has the same valence
charge as the Sn.
Concomitant with line broadening, excess absorber thickness decreases
the spectral intensity I as checked by comparing the two Ag alloys
of 4% natural Sn and 4% enriched Sn (Fig. (3)). For the
same sample thickness the enriched sample has about 10 times the
resonance absorption as the natural sample. As the temperature
increased above room temperature the enriched sample varied from a
thick to a thin resonance absorber because of the decreased
Mössbauer fraction. At room temperature the enriched sample has a
, where 
is the effective absorber thickness at its
resonance peak[13], while thin absorbers satisfy the
relation 
. The natural sample remained thin throughout this
temperature range as shown by its line width in Fig. (3).
Lining up the 
versus T plots at high temperature, as is
done in Fig. (3), the enriched sample plot falls below the
natural sample as room temperature is approached. To avoid any
spurious variations introduced by this decrease of the spectral
intensity as the resonance thickness increases, the data were analyzed
only in the ``thin" range as monitored by the line width, where
saturation effects were negligible.
(c.) Results
The temperature dependence of the spectral intensity for Ag alloys is shown in Fig. (3) for thin absorbers, and for Pb alloys in Fig. (4).
To increase clarity, each curve has been moved vertically by an
arbitrary amount. Since several factors, such as sample thickness and
Sn concentration, also add a constant to the even when the
effect per atom is a constant, we limit our measurements to the
temperature dependence of the spectral intensity, and ignore the
offset
value.
The varies linearly with T at low temperatures as expected
for harmonic vibrations[14]. As the temperature increases
for the Ag hosts a gradual deviation from linear variation sets in and
at above 900K a more rapid drop occurs. There is a weak concentration
dependence in the temperature dependence of the samples. The Pb
hosted alloys show
a more spectacular concentration and temperature dependence.
As the concentration increases the anomalous drop from the linear
Debye-Waller behavior becomes less precipitous, and occurs at a higher
temperature.
The 3% sample is near the solubility limit at room temperature, and
reversibility checks discussed below show some precipitation at lower
temperatures. The 2, 1 and 1/2% samples are fully dissolved at low
temperatures and yet there is a significant difference between the 2%
and the other two samples. Both the linear slope and the rapid drop
are different. The intensity of the 1/2% sample was too small to
follow up to the temperature 
where the rapid drop occurs.
However, since the 1/2% sample has the same slope as the 1% sample,
as listed in Table ( i), we assume that its full temperature
dependence is the same and infer that interactions between impurities
have a negligible effect on the Mössbauer affect for concentration
of 1% and less. We will discuss the deviations from linearity for the
isolated impurities in the next section but we did an experimental
check to verify that the rapid decrease in intensity was not due to
the onset of a broadened line due to, say, bulk diffusion. To further
test the assumption of only one unbroadened Lorentzian in the Pb 1
at.% Sn data, the background was determined by fitting the shoulders
of the spectra, away from the drop, with a straight line and
determining the total area below this line by adding all the points.
The resulting area agreed with the best fit of a single Lorentzian for
all spectra within the uncertainties of the fits.
Figures (3) and (4) display the linewidth 
versus T dependence for Ag and Pb based alloys, respectively. The line
shifts are shown versus T in Figs. (5) and (6) for
the Ag and Pb based alloys, respectively. Both the line widths and
shifts have the expected behavior for the Pb hosts. However, the 4 and
8% Ag samples have a shift from a linear temperature dependence which
does not occur for the 2% sample. From the disappearance of the
shift at low concentration we infer that the isolated impurity
behavior is linear.
We checked the reversibility of the Mössbauer signal for the 2 and 3
at.% Sn in Pb samples and for the 2, 4 and 8% Sn in Ag samples.
Measurements were performed as the samples were heated and cooled.
The results for are shown in Fig. (3) for the Ag
alloys and in 4(a) for the Pb alloys, while the line shifts of the Ag
alloys are shown in Fig. (5). The Pb alloy line shifts were
verified to be reversible for the 2 at.% sample. The x's in
Figs. (3) and (4) are on cooling and the rest of the
points are on heating. The solid dots in Fig. (5) show the
results for the Ag alloys on heating while the x's are on cooling. The
3% Pb sample was the only one that showed appreciable irreversibility
in its . The 4% and 8% Ag samples displayed
irreversibility in line shift on the initial cycle. The 4% sample was
cycled a second time and the irreversibility disappeared. The
significance of these results are discussed in the next section.