\documentstyle[art10,overcite,titlepage]{article}   %{thesis}
\textwidth=6in
\textheight=8in
\newcommand{\Tc}{T$_{c}$}
\newcommand{\Jc}{J$_{c}$}
\newcommand{\oC}{$^{\circ}$C}
\newcommand{\degre}{$^{\circ}$}
\newcommand{\etal}{et~al.}
\newcommand{\ybc}{YBa$_{2}$Cu$_{3}$O$_{7-\delta}$}
\newcommand{\bittzo}{Bi$_{2}$Sr$_{2}$Cu$_{1}$O$_{6}$}
\newcommand{\bittot}{Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8}$}
\newcommand{\bitttt}{Bi$_{2}$Sr$_{2}$Ca$_{2}$Cu$_{3}$O$_{10}$}
\newcommand{\sccoz}{(Sr,Ca)O}
\newcommand{\sccoo}{(Sr,Ca)CuO$_{2}$}
\newcommand{\sccto}{(Sr,Ca)$_{2}$CuO$_{3}$}
\newcommand{\sccot}{(Sr,Ca)Cu$_{2}$O$_{3}$}
\newcommand{\scc}{(Sr,Ca)$_{x}$Cu$_{y}$O$_{z}$}
%
\title{The Glass-Ceramic Processing of \bittot}
\author{D. P. Matheis, S. Misture and R. L. Snyder}
\date{\today}
%
%\renewcommand{\baselinestretch}{1.5}
\begin{document}
\maketitle

\section{Introduction}

The reluctant glass-forming ability of bismuth oxide 
allows for a very quick and convenient method of producing \bittot\
of high phase purity while avoiding the weak points of other fabrication 
methods.  Glass formation and devitrification to form superconducting 
compounds in the bismuth system has been reported by Zheng and MacKenzie 
\cite{zhen} and
Minami \cite{mina}.  This method is superior to the solid state reaction 
and chemical processing methods that are commonly used.  
In the case of the solid state method, several long heat-treatments 
are necessary, and phase purity is difficult to achieve.  
A number of chemical processing techniques 
have been used to prepare superconductors. \cite{chee90}  The 
disadvantages of any chemical processing method are related to expense 
and complexity.  The glass-ceramic method attains intimate mixing of the 
cations through the fluid melt, and the fast devitrification of the glass 
allows for complete conversion to the crystalline superconductor within 
short heat treatment times.  A thorough understanding of the reactions 
involved in the devitrification is necessary to the effective use of this 
technique.  

Most of the concerns in producing traditional glass-ceramics are 
superfluous in the application of the technique to the formation of the 
bismuth superconductors in the absence of additional glass formers.  Such 
extremely rapid quench rates are necessary 
to form a glass out of the bismuth melt that the glass fractures on cooling
which renders glass forming techniques relatively useless.  Thus, it is not 
possible to take full advantage of the glass-ceramic technique to make 
finished pieces with this material.  There has been work 
\cite{atit,rear90} on 
the addition of other glass formers to the composition to improve the glass 
forming potential of this material to better make use of the full advantages 
of the glass-ceramic process, and it is possible that a stoichiometry 
higher in bismuth may improve the glass's forming 
characteristics.\cite{lebe}  Although 
the full advantages of the glass-ceramic technique cannot be applied to the 
compositions studied in this work, the process of melt quenching and 
devitrifying does function well in the production of phase-pure powder samples 
which is not easily accomplished by other methods.  

The study by Zheng and MacKenzie \cite{zhen} has noted that a glass can 
be made from the 4334 composition, and that after heating the glass at 
800\oC\ a crystalline superconductor with a high-density oriented 
microstructure is produced.  

In an investigation by Oka \etal \cite{oka}, glass was prepared by 
quenching melts of nominal composition 2212 and 4336 into ice water.  These
glasses were analyzed by DTA and high-temperature x-ray diffraction.  The 
DTA analysis showed a sharp exothermic peak at 430\oC\ and a broad exotherm 
above 500\oC\@. In the high-temperature x-ray diffraction patterns the broad
peak of the amorphous phase split into less broad  113, 115 and 200 peaks 
of the Bi-2201 phase.  The crystallization of this phase is complete by 
750\oC, and the Bi-2212 phase forms above 800\oC\@.  

The crystallization of glasses of composition 
Bi$_{x}$SrCaCu$_{2}$O$_{\omega}$ (x=1.5,2.7) has been studied by 
Tatsumisago \etal \cite{tats}.  DSC scans of these glasses as bulk 
samples and as powders have been made to perform a 
Kissinger analysis of crystallization temperature to determine the activation 
energy of crystallization.  The values attained for the activation energy 
of crystallization in this analysis were in the range of 379 to 437 kJ/mol.  
The temperatures of glass transition and crystallization were seen to be 
lower for the higher bismuth stoichiometry glass and the crystallization 
temperature was lower for powder samples than for bulk samples indicating a
surface crystallization mechanism.  

\section{Experimental Procedures}

Samples used in the experiments conducted in this work were prepared by 
the melt quench method.  Samples have been prepared with various Bi:Sr:Ca:Cu 
molar ratios to study solid solution effects.
Samples have been prepared with the stoichiometric ratios 4514, 2212, 4334 
and 2122 to investigate the solid solution effects of varying the calcium to 
strontium ratio in the Bi-2212 phase.  Each of these samples were batched by 
weighing the proper amount of high grade 
Bi$_{2}$O$_{3}$, SrCO$_{3}$, CaCO$_{3}$, and CuO to make 20 gram batches of
the above cation molar ratios, and mixing them in a mortar and pestle.  The
batches were then contained in a platinum crucible and placed in an 
1100\oC\ SiC glow bar furnace at ambient atmosphere for 10 minutes to
develop a fluid homogeneous melt.  The melt was then removed from the 
furnace and quickly poured onto a metal plate that was cooled with liquid 
nitrogen.  The melt was then pressed from above with a metal disk that 
was also liquid nitrogen cooled.  This extremely rapid quenching method 
resulted in thermal stresses that fractured the sample into small pieces.  
These pieces were collected, and some saved to be used as bulk samples while 
the remainder were wet ground with acetone in a mortar and pestle to form a 
powder sample.  

Thermal analysis was used to study the 
reactions of the glass samples during devitrification. Differential 
Scanning Calorimetry (DSC) analysis was performed using a Mettler DSC30 with 
a low temperature accessory 
%Measurements 
%were made in the temperature range of ambient to 550$^{\circ}$C in flowing 
%air, with the samples setting in aluminum pans.  Scans where measured at a 
%heating rate of 10$^{\circ}$C/minute.  During these nucleation studies, 
%samples were heated quickly to a soak temperature in the DSC, held there for 
%3 hours, cooled to ambient, and then scanned.  
and differential thermal analysis measurements have been made using a Harrop 
DTA 
%Scans were performed on 
%glass powder of 2:2:1:2 composition at heating rates of 2, 4, 6, 10, and 
%15\oC\ 
%per minute in ambient atmosphere, for Kissinger analysis of the glass 
%crystallization.
%All samples were contained in platinum crucibles.
while simultaneous differential thermal analysis (DTA) and 
thermogravimetric analysis (TGA) 
were performed using a TAG24 Simultaneous Thermoanalyzer.
%The STA setup for this experiment consists of a DTA 
%apparatus of sample and reference connected to a differential thermocouple
%in a furnace supported by a balance which measures any change in weight of 
%the sample. Samples were contained in a platinum crucible using either 
%oxygen or nitrogen atmosphere during scans with a heating and cooling rate of 
%10\oC.  Scans were from ambient to 1000$^{\circ}$C and back to ambient.
%
%A powder sample of amorphous Bi-2212 was analyzed using transmission 
%electron microscopy.  This analysis was performed on a JEM - 2000FX 
%Electron Microscope, [Japanese Electron Optics Limited, Tokyo Japan]
%Powder x-ray diffraction has been used at ambient temperature to analyze 
%samples quenched from high temperature.  This data collection was performed on 
%a Siemens D500 $\theta - 2\theta$ diffractometer using copper K$_{\alpha}$ 
%radiation.  The diffractometer was configured with a 1$^{\circ}$ divergence
%slit, a 0.05$^{\circ}$ receiving slit and a diffracted beam graphite 
%monochromator.  Samples were wet ground in acetone in a mortar and pestle 
%and mounted using a top loading sample holder or a zero background sample 
%holder and step scanned at a step size of 0.02$^{\circ}$2$\theta$ from 3 to 
%65$^{\circ}$2$\theta$.
%The d-spacing, intensity, and peak widths reported in this study were 
%determined using profile fitting of the diffraction peaks.

In-situ high-temperature powder x-ray diffraction was used to analyze the 
devitrification reactions of the glass samples.  The equipment used in this 
experiment included a Norelco diffractometer equipped with a scanning 
position sensitive proportional counter interfaced through a
Halder multichannel analyzer.
% to a 386 workstation to control data collection 
%with software from G. Zorn \cite{zorn}.  This system uses copper K 
%radiation with a 1$^{\circ}$ divergence slit and a beta filter. The sample 
%is heated by placing it on a metal strip through which an electric current 
%is passed to achieve resistive heating.  Temperature control is achieved by 
%means of a Halder temperature controller also interfaced with the 386 
%workstation.
High-temperature x-ray data was also collected using a Siemens $\theta - 
\theta$ D500 diffractometer with a scanning position sensitive detector 
using a braun graphatized wire.  The diffractometer is outfitted with a Paar
hot stage  assembly.  This data was collected at the Siemens central research 
laboratory in Munich.

\section{Results}

Determination of the temperature of maximum nucleation 
rate has been performed according to the method described by Ray and 
Day \cite{ray90}, by related DSC peak height to the number of nuclei present 
in the glass.  In this study, the DSC is used to 
analyze the initial crystallization of the Bi-2212 glass by means of this 
nucleation analysis method, in addition to determining the enthalpy 
of this crystallization.  DSC analysis of a powdered 
glass with no prior heat treatment indicates a glass transition temperature
of 390 to 400\oC\ and a crystallization exotherm onset at 445\oC\ and peak at
475\oC\@. The enthalpy of the primary crystallization event determined 
from the exotherm area is 22(2) kJ/mol of 2212 glass.  
For the nucleation study, samples were soaked for 3 hours at
300, 350, 400, 410, 420, and 430\oC\@.  
%The 300 and 350\oC\ soaks were to 
%establish a pre-T$_{g}$ nuclei population, while the remaining temperatures
%were used to study the range of temperatures between T$_{g}$ and the 
%crystallization temperature.  
Figure \ref{nuc} shows the peaks heights of 
the primary exotherm for the different soak temperatures plotted with a 
best fit polynomial.  This plot shows that the temperature of maximum 
nucleation rate is $\sim$400\oC\ which, is just above T$_{g}$.

\begin{figure}
\vspace{3.5in}
\caption{Analogous nucleation rate curve for initial crystallization of a 
Bi-2212 glass determined from DSC peak heights for samples soaked at 
various temperatures.}
\label{nuc}
\end{figure}

The activation energy of crystallization of the primary crystallization 
event has been determined using the modified Kissinger equation 
\cite{kiss56,aug} which is independent of the Avrami {\em n}.
\[ln(\frac{\phi}{T_{p}-T_{0}}) = -\frac{E_{a}}{RT_{p}} + constant \]
This equation relates the activation energy $E_{a}$ to the exotherm peak 
temperature $T_{p}$ and the heating rate $\phi$ of the DTA scan.  
Figure \ref{kiss} contains the modified Kissinger plot for a sample of 
Bi-2212 glass powder 
that has not undergone nucleation treatment.  From the slope of this graph 
determined by linear least squares regression, the activation energy is 
calculated to be 395 kJ/mol, with a standard error of regression of .074.
The Avrami {\em n} value can now be calculated from the equation 
\[n = \frac{2.5}{\Delta T} \frac{RT_{p}^{2}}{E_{a}}.\]
The value of {\em n} calculated for this sample is 3.6(9) which indicates a 
bulk crystallization process.

\begin{figure}
\vspace{3.5in}
\caption{Modified Kissinger plot for Bi-2212 glass powder with no 
nucleation treatment.}
\label{kiss}
\end{figure}

Melt-quenched samples were next analyzed by means of simultaneous differential 
thermal and thermogravimetric analysis.  These samples were analyzed 
in oxygen and nitrogen atmosphere with a heating rate of 
10$^{\circ}$/minute from ambient to 1000$^{\circ}$C and cooled back to 
ambient. The first sample to be analyzed was a melt quenched powder sample in 
oxygen atmosphere shown in figure \ref{stamqo}.  On heating, this sample 
exhibited a strong exothermic 
reaction with onset of 450\oC\ followed by weaker exotherms with onsets 
at 490\oC\ and 540\oC\@.  There are also 4 weight gain events in this 
temperature region indicated by inflections in the TGA trace.  The 
initial weight gain corresponds to the 450\oC\ exotherm but there is 
no obvious relation between the remaining weight gain events and the DTA 
trace.  There is a 1.32\% weight gain from 400 to 720\oC, and an 
additional gain to 1.4\% from 720 to 790\oC\ where the weight is maximum. 
Above 790\oC, the weight begins to decrease.  As the temperature 
continues to increase, there are three endothermic reactions present with 
onsets at 860, 930, and 965\oC\@.  The first of these is quite strong with 
the intensity decreasing for the following two reactions.  There are 
three weight loss events that correspond well to the endothermic 
reactions leading to a net weight loss of 0.13\% below the starting 
weight.  Upon cooling from 1000\oC, there is a gradual weight gain to 
0.25\% above the initial weight.  This weight gain ends at 860\oC\ where 
the first of two cooling exotherms occurs.  The second cooling exotherm 
is more intense than the first and it occurs at 750\oC\@.
\begin{figure}
\vspace{3.5in}
\caption{Simultaneous thermal analysis data for a melt quenched Bi-2212 
powder sample scanned in an oxygen atmosphere.}
\label{stamqo}
\end{figure}

Figure \ref{stabgl} shows an STA plot for a bulk Bi-2212 glass sample 
heated in oxygen.  This plot is similar to the powder sample except that 
the weight gain for the bulk sample is significantly less than for the 
powder sample, and there is almost no weight gain during the initial 
devitrification.  The DTA trace of this sample also shows an endothermic 
peak at $\sim$775\oC\ not seen in the powder sample.

\begin{figure}
\vspace{3.5in}
\caption{Simultaneous thermal analysis data for a melt quenched Bi-2212 
bulk sample scanned in an oxygen atmosphere.}
\label{stabgl}
\end{figure}

When a melt-quenched powder sample is treated in a nitrogen 
atmosphere, the results are significantly different as shown in figure 
\ref{stamqn}.  On heating, three exothermic reactions are again present at 
onsets of 450, 490, and 560\oC\ similar to the oxygen run, although the 
first reaction is less intense relative to the second two reactions 
than in the oxygen run.  There is no weight gain in the nitrogen 
atmosphere.  As the temperature continues to increase, there is only one 
endothermic reaction at an onset of 760\oC\ compared to the three 
reactions beginning at 860\oC\ in the oxygen run. There are two weight 
loss events the first of which begins at the endotherm onset, and is 
followed by a gradual weight loss which continues until the 
maximum temperature of 1000\oC\ is reached, resulting in a total weight 
loss of 0.62\%.  On cooling, there is a single exothermic reaction with an 
onset temperature at 760\oC\@.  
\begin{figure}
\vspace{3.5in}
\caption{Simultaneous thermal analysis data for a melt quenched Bi-2212 
powder sample scanned in a nitrogen atmosphere.}
\label{stamqn}
\end{figure}

The data from the simultaneous thermal analysis studies is summarized in 
table \ref{statabg} listing the reaction temperatures 
and weight change trends of the samples analyzed by this method.

\begin{table}
\begin{center}
\caption{Summary of simultaneous differential thermal and thermogravimetric
analysis data for amorphous Bi-2212 samples in oxygen and nitrogen.}
\label{statabg}
\begin{tabular}{||c|c|c|c|c|c||} \hline\hline
 & & \multicolumn{2}{c|}{DTA} & \multicolumn{2}{c||}{TGA} \\ \cline{3-6}
Sample & Atmos. & Temp. \oC\ & heat flow & Temp. \oC\ & weight change net\% \\ 
\hline
glass & O$_{2}$ & 450 & exo & 400-720 & +1.32 \\
powder & & 490 & exo & & \\
 & & 540 & exo & 720-790 & +1.40 \\
 & & 860 & endo & & \\
 & & 930 & endo & 790-1000 & -0.13 \\
 & & 965 & endo & & \\ \hline 
 & & 860 & exo & 1000-860 & +0.25 \\
 & & 750 & exo & & \\ \hline \hline
bulk & O$_{2}$ & 460 & exo & & \\
glass & & 507 & small exo & 400-620 & 0.21\\
 & & 580 & small exo & 620-790 & 0.82 \\
 & & 770 & endo & 790-875 & 1.23 \\
 & & 885 & endo & 875-1005 & 0.43 \\
 & & 930 & endo & & \\ \hline
 & & 885 & exo  & 1005-890 & 0.83 \\
\hline \hline
glass & N$_{2}$ & 450 & exo & & \\
powder & & 490 & exo & & \\
 & & 560 & exo & & \\
 & & 760 & endo & 760-1000 & -0.62 \\ \hline
 & & 760 & exo & & \\ \hline \hline
\end{tabular}
\end{center}
\end{table}

In high-temperature x-ray powder diffraction experiments 
x-ray diffraction patterns were collected every 10\oC\ between 450 and 
500\oC, every 50\oC\ between 500 and 800\oC, and every 10\oC\ between 800 
and 900\oC\ and back down to 750\oC\ in air.  
\begin{figure}
\vspace{3.5in}
\caption{High-temperature x-ray diffraction patterns of Bi-2212 glass 
powder showing the devitrification process.}
\label{417a2}
\end{figure}
The patterns involved in the devitrification reactions are shown as 3-D 
plots in figure \ref{417a2}.  At 450\oC, broad peaks of the 
Bi-2201 phase grow out of the amorphous profile, and small peaks matching 
those of Cu$_{2}$O can also be seen.  In the subsequent x-ray patterns, 
gradual sharpening of the Bi-2201 peaks occurs and some small peaks form by
600\oC\ which can be accounted for by SrCuO$_{2}$ and Ca$_{2}$CuO$_{3}$. 
%The peaks of the 650\oC\ pattern are listed in table \ref{quant} with the 
%standard values for these phases.
%\begin{table}
%\caption{Listing of peaks from the x-ray diffraction pattern of the 
%Bi-2212 glass devitrification treatment at 650\oC.}
%\label{quant}
%\begin{center}
%\begin{tabular}{||rr|rr|rr|rr|rr||}\hline \hline
%\multicolumn{2}{||c|}{Experimental} & \multicolumn{2}{c|}{Bi-2201} &
%\multicolumn{2}{c|}{Cu$_{2}$O} & \multicolumn{2}{c|}{SrCuO$_{2}$} &
%\multicolumn{2}{c||}{Ca$_{2}$CuO$_{3}$} \\
%\multicolumn{2}{||c|}{pattern} & \multicolumn{2}{c|}{PDF 39-283} &
%\multicolumn{2}{c|}{PDF 34-1354} & \multicolumn{2}{c|}{PDF 39-1492} &
%\multicolumn{2}{c||}{PDF 34-282} \\ \hline
%d & I/I$_{0}$ & d & I/I$_{0}$ & d & I/I$_{0}$ & d & I/I$_{0}$ & 
%d & I/I$_{0}$ \\ \hline
%4.104 & 13 & 4.096 & 17 & & & 4.084 & 12 & & \\
%3.777 &  3 & 3.752 &  2 & & & & & & \\
%3.464 & 48 & 3.447 & 64 & & & 3.492 & 19 & & \\
%3.080 & 42 & 3.076 & 26 & & & & & 3.146 & 20 \\
%3.014 & 100 & 3.007 & 100 & 2.978 & 25 & 2.989 & 73 & & \\
%2.833 & 17 & & & & & 2.826 & 71 & & \\
%2.706 & 65 & 2.685 & 68 & & & 2.723 & 10 & 2.771 & 55 \\
%2.608 & 11 & 2.582 &  3 & & & 2.606 & 100 & & \\
%2.583 &  9 & & & & & & & 2.5454 & 80 \\
%2.465 &  7 & 2.461 &  3 & & & & & 2.4669 & 100 \\
%2.424 &  8 & 2.424 & 4 & 2.427 & 100 & & & & \\
%2.258 &  5 & 2.242 & 4 & & & & & & \\
%2.120 &  8 & & & 2.120 & 100 & & & & \\
%2.037 & 26 & 2.023 & 40 & & & 2.0419 & 30 & 2.0386 & 35 \\
%1.932 & 22 & 1.925 & 25 & & & 1.9570 & 40 & 1.9561 & 12 \\
%1.908 & 22 & 1.899 & 32 & & & & & 1.8879 & 20 \\
%1.820 &  7 & 1.811 &  5 & & & 1.7866 & 20 & & \\ 
%1.720 &  7 & 1.6926 & 15 & & & 1.7480 & 34 & & \\
%\hline \hline
%\end{tabular}
%\end{center}
%\end{table}
The sharpening of peaks continues as the temperature increases with no 
significant change in phase composition until 800\oC\ when significant 
peaks of the Bi-2212 phase can be seen starting to grow.  
As the temperature increases to 880\oC, the Bi-2212 phase peaks 
grow at the expense of the other phases.  

In order to monitor the crystallite growth of the superconducting phases, 
the peak widths of the Bi-2201 113 peak and the Bi-2212 115 peak have been 
used to calculate the crystallite size at each temperature during 
devitrification and plotted versus temperature in figure \ref{bi12s}. 
The size of the Bi-2201 crystallites begin small and grow as the temperature 
rises and then diminish as the Bi-2212 formation begins and 
crystallite growth of this phase occurs. 
\begin{figure}
\vspace{3.5in}
\caption{Crystallite size determined from the Bi-2201 113 and Bi-2212 115 
peaks at increasing temperatures indicating crystallite growth of 
these phases.}
\label{bi12s}
\end{figure}
In this plot, the Bi-2201 crystallite size increases between 600 and 
800\oC\ 
showing that growth of this phase occurs in this temperature region. 
Above 800\oC, the crystallite size of the Bi-2212 phase increases quickly.  

To further study the growth of Bi-2201 crystallites, a series of high 
temperature x-ray diffraction measurements were made holding at various 
temperatures. In each run, a new sample of Bi-2212 glass powder was 
heated at 10\oC/second to the soak temperature, and scanned repeatedly 
over a period of one hour.  A new sample was used at each 
temperature to minimize crystallite growth at temperatures below the soak 
temperature.  Crystallite size was determined by the Scherrer method and 
plotted versus time.  Figure \ref{hgrows} contains 
the crystallite size based on the 200 peak width over one hours time at 
temperatures from 450 to 700\oC\@.  
\begin{figure}
\vspace{3.5in}
\caption{Crystallite size change over time at various temperatures based on
the 200 peak width for the Bi-2201 phase.}
\label{hgrows}
\end{figure}
Although there is a great deal of scatter
in the data, the general trends are clear. The slope of the best fit lines 
for temperatures 450, 500 and 550\oC\ are all near zero, indicating very 
little crystallite growth at these temperatures.  Crystallite 
growth does occur at 600, 650 and 700\oC\ at rates of 16, 33 and 23 
\AA/hour, respectively. The fastest growth is indicated at 650\oC\@.
%A similar study was conducted over ten hours time from 650 to 750\oC\@.  
%Crystallite size determined from the 113 peak of the Bi-2201 
%phase is plotted versus time in figure \ref{hgrow}.  
%\begin{figure}
%\vspace{3.5in}
%\caption{Crystallite size change over time at various temperatures based on
%the 113 peak widths of the Bi-2201 phase.}
%\label{hgrow}
%\end{figure}
%The results of the 113 peak is used since this peak has no overlap 
%complication. Over this longer period of time, the growth rate increases with 
%temperature through 750\oC\@.

When Bi-2212 glass powder is heated in nitrogen the main peaks of the Bi-2201 
phase grow out of the amorphous hump above 450\oC\ as in air, however the 
growth of the Bi-2201 peaks is slower in nitrogen and the sample melts by 
800\oC\ so that no Bi-2212 formation is seen.

\section{Discussion}
The activation energy determined in this study for Bi-2212 glass 
crystallization is consistent 
with the results of Tatsumisago \etal \cite{tats}, but the bulk 
crystallization indicated by the large Avrami parameter is in conflict with 
the results of Tatsumisago who reports a surface nucleation mechanism.  
These conflicting conclusions can be 
resolved by analysis of the STA data for Bi-2212 glass samples in oxygen and
nitrogen atmosphere.  There is a large weight gain by the sample in oxygen 
atmosphere which can be attributed to oxygen uptake by the devitrifying 
glass since no weight gain is seen in an identical experiment in nitrogen 
atmosphere.  In the case of the bulk glass sample, the weight gain is less 
than that of the powder sample.  The crystallization exotherm is present in 
both oxygen and nitrogen atmospheres with the same onset temperature but the 
peak is broader and less intense in nitrogen and for the bulk sample than 
for the powder sample in oxygen.  Also of interest is the presence of an 
endotherm in the bulk sample that is not seen in the powder sample in oxygen, 
but which matches the temperature of the endothermic reaction seen in the 
nitrogen sample.  These results indicate that 
although the nucleation and crystallization are a bulk phenomenon, the 
devitrification is a reactive process involving the absorption of oxygen.  
When a powder sample is heated, it can more easily react with the 
oxygen atmosphere than can a bulk sample in which O$_{2}$ will have to diffuse 
over a much further distance.  The 
first crystallization event is the formation of Bi-2201 which is followed 
by the formation of 
Bi-2212 above 800\oC\@.  The lack of an exothermic peak above 800\oC\ 
shows that the Bi-2212 formation is not a crystallization process.

The results of the STA analysis clarify confusing observations made in 
furnace devitrification runs of several Bi-2212 glass samples.  
During furnace devitrification of Bi-2212 glass powder, there was no evidence 
of liquid phase formation at 870\oC\ since the sample was still a loose 
powder after heat treatment.  However, when 
this same heat treatment is applied to bulk samples of glass, the pieces of 
superconductor undergo deformation, and stick together where they come into 
contact, indicating a presence of liquid phase.  This difference in behavior
is the result of the difference of oxygen absorption in the powder and bulk
samples.  The STA analysis of the bulk glass sample shows an endothermic 
reaction at the same temperature as the melting of the powder sample in 
nitrogen.  This result can be interpreted as indicating that the interior of 
the bulk samples, which is not fully oxygenated during the devitrification, 
was melting as the samples in a reducing atmosphere did.  

The high-temperature x-ray diffraction of Bi-2212 glass powder and the 
STA analysis provide consistent 
evidence for the crystallization sequence for the devitrification to 
produce the Bi-2212 phase.  The first crystalline phase formed is the 
Bi-2201 phase at $\sim$450\oC\ with very broad peaks indicating a very 
small crystallite size in the 100\AA\ range.  These peaks sharpen as the 
temperature increases indicating crystallite growth.  By 600\oC, a small 
amount of Cu$_{2}$O has formed and some SrCuO$_{2}$ and Ca$_{2}$CuO$_{3}$ 
are seen by 650\oC\@.  Above 
800\oC, the Bi-2212 phase begins forming at the expense of the other
phases.  The amount of Bi-2212 increases dramatically above 850\oC, and 
after soaking at 870\oC\ for as little as 4 hours, only the Bi-2212 phase 
remains.  By monitoring the peak width's of the Bi-2201, peaks it can be 
seen that crystallite growth is a maximum in the region 750 to 800\oC, and 
then this phase diminishes above 800\oC\ with Bi-2212 growing rapidly above 
850\oC\@.  

The lack of any definite feature in the DTA trace of the Bi-2212 glass 
sample in oxygen in the 800 to 850\oC\ temperature region when Bi-2212 is 
forming opens the question of the nature of the Bi-2201 to Bi-2212 
transformation.  The existence of an endotherm onset at 860\oC\ is also 
curious due to the broad onset shape of the peak and the observation from 
furnace devitrification runs at 870\oC\ that liquid phase is not present at 
this temperature.  In these furnace runs, the sample comes out as a loose 
powder which is inconsistent with the sintering effects expected in the 
presence of a liquid phase.  Also considering the analysis of the Bi-2212 
melting which will be given in a separate paper, one must conclude that 
there is no liquid phase present at 860\oC\ during the glass devitrification.  
This conclusion is confirmed by the high-temperature x-ray diffraction study 
of Bi-2212 glass devitrification in which 
decomposition of the Bi-2212 phase is not seen until 880\oC\@.  Since this is 
the case, it is possible  to relate the rather broad endothermic trend at 
860\oC\ to the formation rather than the melting of the Bi-2212 phase.  
Since the Bi-2212 formation involves an endothermic rather than exothermic 
heat flow, this formation cannot be due to further crystallization of the 
glass.

By comparing the structures of Bi-2201 and Bi-2212, a probable mechanism 
for
the transformation from Bi-2201 to Bi-2212 can be proposed.  In the Bi-2201
structure, there is a single copper oxide plane between two strontium oxide 
planes in a perovskite arrangement.  In the Bi-2212 structure, there are two
copper oxide planes between the strontium oxide layers with a single layer 
of calcium atoms between the two copper oxide planes.  In transforming from
the one layer to the two layer phase, the a-b dimensions of the crystal 
lattice do not change significantly while the c-axis dimension expands to 
accommodate the increased number of layers in the unit cell.  Thus, the 
transformation can be modeled as the diffusion of CaCuO$_{2}$ units into 
the Bi-2201 structure to form the additional layers and force the c-axis 
expansion.  Following this model, the transformation would be a slow 
diffusion controlled process.
So the shape of the DTA trace can be explained as the broad endotherm at 
860\oC\ being due to absorption of heat to feed the diffusion process, and 
then the slope of the trace becomes more sharply negative above 880\oC\ as 
melting occurs.
This model is also consistent with the 
observations made through the x-ray diffraction analysis in which evidence for 
Bi-2212 formation is seen as low as 700\oC\ in quenched samples, and in 
the high-temperature x-ray patterns Bi-2212 is seen to grow at the expense 
of Bi-2201 over the temperature region from 800 to 880\oC, supporting a 
model including a slow transformation. The x-ray diffraction patterns of 
Samples quenched from 800\oC\ show weak reflections of both the Bi-2201 and 
Bi-2212 along with a strong sharp peak for the 200 reflection.  The 200 
reflection of course is only dependent on the arrangement of the 
atoms in the {\bf a}-{\bf b} plane and not on the spacing of the planes in the 
{\bf c}-axis direction which will effect the other reflections in the pattern.  
Thus, the x-ray diffraction patterns of the 800\oC-quenched samples indicate
undisturbed order in the {\bf a}-{\bf b} plane directions with limited order 
in the {\bf c}-axis direction which is consistent with the diffusion model.  

\section{Conclusions}
In a number of studies \cite{byun90,byun91}, the phases present in samples 
of varying nominal composition, prepared by the solid state reaction 
process, have been used to make conclusions about the thermal equilibrium 
of this system rather than about the limitations of the solid state method.
The main conclusion from these studies has been that in order to produce 
phase pure Bi-2212, a nominal composition of 4334 is necessary.  While this 
is undoubtedly true when using the solid state reaction method, this cannot
be taken as an indication of thermal equilibrium since the same thing is 
not true for samples prepared by the glass-ceramic method in this thesis.  
The ability to produce Bi-2212 over a range of Sr/Ca solid solubility by 
the glass-ceramic process has been confirmed by the lattice parameter 
analysis, to be reported elsewhere, showing the expected Vegard's law behavior.

The work analyzing the high-temperature chemistry of Bi-2212 has lead to 
several recommendations for the efficient processing of this material.  The
phase-pure production of this material is best accomplished through the use
of the glass-ceramic process as outlined in this paper.  By quenching a 
melt of bismuth oxide, strontium carbonate, calcium carbonate and copper 
oxide from 1100\oC, a glassy material can be produced which on heat treatment
will result in phase pure Bi-2212.  However, for best results, 
the glass should be ground into a fine
powder to facilitate the oxygen absorption, and be contained in a non-reactive 
crucible, such as magnesia, 
while heated slowly through the temperature region 375--415\oC\ to allow 
for full nucleation of the glass, and then the temperature should be raised 
above 800\oC\ quickly to avoid Bi-2201 growth.  Upon reaching 860--870\oC, 
the sample should be held at temperature to allow complete 
conversion of Bi-2201 and small amounts of Cu$_{2}$O, SrCuO$_{2}$ and 
Ca$_{2}$CuO$_{3}$ to Bi-2212 in four to eight hours.  
Care should be taken in heating to the soak temperature since
overshooting the soak temperature by five to ten degrees could result in 
melting of the superconductor.  The crystallization sequence reported here 
is consistant with that resently reported by Holesinger \etal. \cite{hole92}

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\end{document}
