Poole Ch.P., Jr. Handbook of Superconductivity

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626 Chapter 14: Phase Diagrams

Introduction

Investigation of high-temperature superconductor materials has become an

exciting and extensive research area in the past 10 years. Since the initial

report of the 30 K superconductor by Bednorz and Miiller (1986), a large

number of multicomponent oxide materials have been discovered (Cava, 1995);

most of these compounds exhibit complex chemistry, including nonstoichiometry,

defects, and incommensuracy. International efforts in superconductivity research

have led to many alternative methods of processing as well as novel applications.

The developments of coated conductors utilizing the BazYCu306+ x and

Ba2RCu306+x (R=lanthanides) phases with ion beam assisted deposition

(IBAD) and rolling assisted biaxially textured substrate (RABiTS) techniques

have prompted the intensive investigations of these systems in thin- and thick-

film forms (Goyal

et al.,

1996; Wu

et al.,

1995; Paranthaman

et al.,

1997). In the

BizO3-PbO-SrO-CaO-CuO systems (BSCCO), the Bi-containing materials

were found to show promising superconducting and other properties that are

appropriate for wire and tape applications using the powder-in-tube (PIT)

techniques (Balachandran

et al.,

1994; Sandhage

et al.,

1991; Sato

et al.,

1991; Malosemoff

et al.,

1997; Zhou

et al.,

1995) for fabrication. These novel

processes have brought superconducting technology closer to reality. Presently,

high-quality high-temperature superconducting materials are still relatively diffi-

cult to prepare. Challenging problems have to be overcome for large-scale

commercial processing to be successful (Wong-Ng, 1999). At a more basic

level, the underlying principles governing the superconducting properties are not

totally understood.

Phase diagrams are critical research tools for many scientific disciplines,

including materials science, ceramics, geology, physics, metallurgy, chemical

engineering, and chemistry. These diagrams contain important information for

the development of new materials, control of structure and composition of critical

phases, and improvement of properties of technologically important materials.

Phase diagrams can be thought of as "road maps" for processing; they provide

the theoretical basis for synthesis of high-T c materials. Applications of phase

diagrams range from preparation of high-quality single crystals and single-phase

bulk materials to deliberate precipitation of second phases as flux pinning sites

(Majewski, 1996; Majewski

et al.,

1995a; Tiefel

et al.,

1990) and the formation of

melts. The presence of melts can have a beneficial effect on superconductor

processing. For example, melts were found to be essential during PIT processing

of Bi-2223 and 2212 wires, and during the production of textured or crystal-

lographically aligned material in tapes or thin films (Aksenova

et al.,

1993; Zhang

and Hellstrom, 1993).

The aim of this chapter is to provide experimental phase diagrams of high-

T c superconductors representative of systems undergoing research. Among

B. General Discussion and Scope 627

current systems, the BaO-Y203-CuO (BYC), BaO-R203-CuO (BRC), and

BSCCO systems have been studied most extensively. A brief description of

some of the frequently encountered terms used in phase equilibrium work, as well

as a few experimental techniques involved in determining some of these

diagrams, are also presented prior to the discussion of the diagrams.

In the following description of the multicomponent systems, a numerical

code is used to indicate the stoichiometry of compounds in the order in which the

cations are listed. For example, the symbol 213 (or 2:1:3) is used to represent

the compound BazYCu306+x, and the symbol 2212 (or 2:2:1:2) is used to

represent the compound BizSrzCaCu20 x and its solid solution.

General Discussion and Scope

a. Information Provided

Before any research and development is conducted on material synthesis or

processing, it is logical to first study the relevant phase diagrams to obtain

information about the phase relationships and other characteristics of the material.

Phase diagrams can be used to depict a wide range of information, such as (1)

identity of compounds formed from specific end members, (2) stability range,

composition, and temperature range of a specific phase, (3) the optimum

conditions for synthesis, (4) the impurities likely to be present with a phase

prepared under specific conditions, (5) the region of homogeneity of solid

solutions, (6) polymorphism of a phase, (7) temperature and composition range

suitable for glass formation, (8) melting temperature (or temperature range) of a

compound, (9) primary phase field (crystallization composition field) of a phase,

(10) effect of admixture on the melting point or stability of a phase, (11) effect of

temperature and pressure on processing, and (12) prediction of properties of the

final products, based on the phase assemblage.

b. Key Terms Used

The frequently encountered nomenclature and the general terms discussed in the

following sections are briefly described next. For a more complete set of

definitions and a glossary, refer to Volume 1 of Phase Diagrams for Ceramists

(Levin et al., 1964).

A solidus is the locus of temperature-composition points in a system at

temperatures above which solid and liquid are in equilibrium and below which the

system is completely solid. In binary diagrams without solid solutions, it is a

straight line, or a combination of straight lines representing constant tempera-

628

Chapter

14:

Phase Diagrams

tures, and with solid solutions, it is a curved line or a combination of curved and

straight lines. Likewise, in ternary systems, the solidus is represented by flat

planes or by curved surfaces.

A phase

is any portion, including the whole, of a system that is physically

homogeneous within itself and bounded by a surface that mechanically separates

it from any other portions.

The

components

(of a system) are the smallest number of independently

variable chemical constituents necessary and sufficient to express the composi-

tion of each phase present in any state of equilibrium. Zero and negative

quantities of the components are permissible in expressing the composition of

a phase.

The

phase rule

states that, for a system in equilibrium, the sum of the

number of phases (P) plus a number of degress of freedom (F) must equal the sum

of the number of components (C) plus 2, or P + F = C + 2.

The number of

degrees of freedom

of a system is the number of intensive

variables that can be altered independently or arbitrarily without bringing about

the disappearance of a phase or the formation of a new one. Intensive variables

are those that are independent of mass, such as pressure, temperature, and

composition.

A join

(tie-line) is the region of a phase diagram representing all mixtures

that can be formed from a given number of selected compositions. A join may be

a line (binary), a surface (ternary), etc., depending on the number of selected

compositions, which need not be compounds. Each selected composition,

however, must be incapable of formation from the others.

The

lever rule

(or center of gravity principle) states that when a particular

composition separates into only two phases, the given composition and that of the

two phases are colinear; furthermore, the amounts of the two separated phases are

inversely proportional to their distances from the given composition. Thus, if A

and B represent the compositions of two phases formed from composition C, then

the amount of A times the length AC equals the amount of B times the length BC,

or A/B = BC/AC:

X ...... X .......... X

A C B

The

composition (or compatibility) triangle

in the phase diagram of a

condensed ternary system is the area bounded by three tie-lines (joins) connecting

the composition points of three phases that are in equilibrium within the triangle.

The

composition (or compatibility) tetrahedron

in the phase diagram of a

condensed quaternary system constitutes the four triangular planes connecting the

compositions of four solid phases that can coexist in equilibrium with liquid. The

composition of the liquid is represented by a

quaternary invariant point,

which

may be either a eutectic point within the composition tetrahedron or a peritectic or

reaction point outside the tetrahedron.

B. General Discussion and Scope 629

A solid solution is a single crystalline phase that may be varied

in composition within finite limits without the appearance of an additional

phase.

A liquidus is the locus of temperature-composition points representing the

maximum solubility (saturation) of a solid phase in the liquid phase. In a binary

system, it is a line; in a ternary system, it is a surface, usually curved. At

temperatures above the liquidus, the system is completely liquid. A point on the

liquidus represents equilibrium between liquid and, in general, one crystalline

phase (the primary phase).

The primary phase is the only crystalline phase in equilibrium with a liquid

of a given composition. It is the first crystalline phase to appear on cooling a

composition from the liquid; or conversely, it is the last crystalline phase to

disappear on heating a composition to melting.

The primary phase region (or primary phase field) is the locus of all

compositions in a phase diagram having a common primary phase.

The invariant points are the particular conditions within a system, in terms

of pressure, temperature, and composition, for which the system possesses no

degrees of freedom. An example is the triple point of a gas.

A eutectic represents an invariant (unique temperature, pressure, composi-

tion) point for a system at which the phase reaction on the addition or removal of

heat results in an increase or decrease of the proportion of liquid to solid phases,

without change of temperature. At a eutectic point the composition of the liquid

phase in equilibrium with the solid phases can always be expressed in terms of

positive quantitatives of the solid phases.

The eutectic composition is that combination of components in a simple

system having the lowest melting temperature at any ratio of the components and

is located at the intersection of the two solubility curves in a binary system and of

the three solubility surfaces in a ternary system.

A peritectic point is an invariant point at which the composition of the

liquid phase in equilibrium with the solid phases cannot be expressed in terms of

positive quantities of the solid phases. Whereas the composition of a eutectic

point always lies between or within the composition limits of the solid phases in

equilibrium with the liquid, the composition of a peritectic point always lies

outside the composition limits.

A congruent melting point is a specified pressure and temperature at which

a solid subtance changes to a liquid of identical chemical composition.

An incongruently melting point is a specified pressure and temperature at

which one solid phase transforms into another solid phase plus a liquid phase,

both of different chemical compositions than the original substance.

A boundary line is the intersection of adjoining liquidus surfaces in a

ternary phase diagram. The area enclosed by a series of boundary lines is termed

a primary phase area.

An isothermal section is a phase equilibrium diagram constructed at a given

specific temperature.

630 Chapter 14: Phase Diagrams

Liquid immiscibility

refers to two or more distinct liquid phases coexisting

in equilibrium.

c. Phase Diagram Compilations

Various sources of information are needed for users for pursuing phase diagram

studies. For more than 60 years, a long-standing cooperative effort between NIST

and the American Ceramics Society (ACerS) has resulted in an extensive set of

compilations of Phase Diagrams for Ceramists (PDFC) (NIST,

Phase Diagrams

for Ceramists.

To date, these compilations include 12 volumes of oxides, salts,

and refractory materials, three annual volumes of diagrams published in 1991,

1992 and 1993. In addition, two volumes containing high-temperature super-

conductor data, including diagrams, write-ups and biblographic information, were

also published in 1991 and 1997

(Superconductors,

Vol. I and II) (Whitler and

Roth, 1991; Vanderah

et al.,

1991). These phase diagrams are mostly from the

literature, and the data have been edited by experts in the field. Under this

NIST/ACerS phase diagram effort, technical expertise in the compilation of

phase diagrams is provided by NIST researchers and by various university,

industry, and government collaborations. The ACerS assumes the responsibility

for the production aspects of the work and for all means of data dissemination.

The PDFC series have also been computerized and published in the form of

a CD-ROM database (version 2.1). This database contains more than 13,000

diagrams published in the

Phase Diagrams for Ceramists,

Vol. I through X,

Annuals 1991, 1992, and 1993, and

High-T c Superconductors,

Vol. I. Future

supplements will also include

High-T c Superconductors,

Vol. II. Computer search

capabilities include authors, system components, year of publication, biblio-

graphic reference, and location in the PDFC series. On-screen manipulations of

the diagrams are also possible, which include plotting of the diagrams, magni-

fication of selected regions, conversion from mole fraction (%) to weight % (or

vice versa), lever rule calculations, overlay of related diagrams, display of the

cursor position in real units, reverse function for binary diagrams (permits

switching of left and fight end members), and a curve follow feature to track

curve coordinates.

Computer and software developments have prompted increased applica-

tions of databases for materials analysis. If the phase diagram information of a

specific system is not complete, one can search through other sources of

databases in conjunction with the phase diagram database for providing addi-

tional phase information. These databases include the Powder Diffraction file

(PDF) produced by ICDD, 1 the Crystal Data database (NIST), the Crystal

Structure Series (Wyckoff), the Inorganic Crystal Structural Database (ICSD),

IlCDD, International Center for Diffraction Data, Newton Square; 12 Campus Blvd, Newton Squares,

PA 19073-3273.

C. Experimental Methods 631

Structural Data on Intermetallic Phases (CRYSTMET) (Toth Information

Systems), and the NIST/Sandia/ICDD Electron Diffraction Database (NIST).

ICDD has identified a subtile of high-T c superconductors and related phases

(such as those found in phase diagrams, products of reaction with container

materials, with thin film substrates and conventional superconductors) (Wong-Ng

et al.,

1996).

Experimental Methods

A phase diagram is usually constructed using a combination of methods. For

subsolidus phase diagrams, a number of compositions are prepared in the region

of interest, followed by the determination of the phase assemblages present. Tie-

lines connecting phases in equilibrium are determined in this way. When a new

phase is discovered, the structure can be studied either by using single crystals, or

ab initio

structural determination using the powder sample. The experimental

methods for determining phase diagrams are generally divided into two types:

static and dynamic. In the static methods, the temperature of the sample is held

constant until equilibrium is attained. The most widely used of these is the

quenching method (air quench or quench into a medium such as water bath, oil,

liquid nitrogen cooled helium). Quenching studies in combination with powder

X-ray diffraction and petrographic microscopy for phase identification are

essential for obtaining subsolidus phase diagrams. Liquidus phase diagrams

require further experiments for determining the melting temperatures of phases

or assemblages, and the estimation of liquid compositions. Dynamic techniques,

including differential thermal analysis (DTA) and thermogravimetric analysis

(TGA), are needed to obtain an indication of phase transitions, reactions, and

associated loss of volatiles, such as oxygen. Scanning electron microscopy (SEM)

techniques are used to study the microstructures of the experimental products,

particularly of the primary crystals. Quantitative microanalysis techniques,

including energy dispersive x-ray analysis (EDX) or wavelength dispersive

methods, are used for the determination of the compositions of the residual

grains (primary crystals) and of the quenched liquid.

a. Quenching Methods

For relatively fast quenching, experiments are generally carried out using a

vertical tube furnace. Upon achieving equilibrium, the sample is dropped into the

quenching medium (Wong-Ng and Cook, 1995). The goal of this type of

experiment is to capture the phase assemblages and microstructure by cooling

from high temperature to room temperature in a few seconds. The sample is

632

Chapter 14: Phase Diagrams

contained in a small crucible suspended from the thermocouple assembly by thin

wires (such as Pt). After insertion of the sample, the vertical-tube furnace is

valved off and flushed with desired gas. The sample is then equilibrated in the hot

zone of the furnace in the presence of flowing gas of the desired atmosphere. At

the conclusion of the experiment, current is passed through the thin suspension

wires, causing them to melt. For controlled atmospheric quenching, the sample

drops into a liquid nitrogen (LN2)-cooled copper cold well, with helium flowing

at a rapid rate. This prevents reaction of the sample with atmospheric constituents

during the quench.

b. X-ray Powder Diffraction

X-ray diffraction is a very convenient and nondestructive method for phase

identification. Results can show if the composition is a single phase, a mixture of

phases that correspond to the compositional tie-line of a two-phase system, or an

aggregate of higher component regions. In order to study lattice parameters for

establishing or confirming the formation of solid solution, the powder x-ray

diffraction method can also be used. In these methods instrumental (external) and

internal calibrations can be achieved by using standard reference materials (SRM)

produced by NIST (Hubbard

et al.,

1987; Hubbard, 1982). For atmospherically

sensitive materials, a special cell with an O-ring seal can be employed to avoid

reaction with atmospheric CO2 and H20 during analysis (Ritter, 1988). Signal

absorption can be minimized by employing an X-ray transparent window.

c. Differentiation Thermal Analysis and Thermogravimetric

Analysis

Thermal analysis is a technique that measures a physical property of a substance

as a function of temperature, generally under a controlled temperature program.

In the case of the TGA experiment, the weight of a specimen is measured as a

function of time (or temperature). The changes of the weight before and after the

experiment can be determined. In a DTA experiment, a sample and a reference

material (usually alumina in the high-T c superconductor experiments) are heated

(or cooled) at a uniform rate and the difference in temperature between the two is

plotted as a function of the temperature of the reference sample or furnace

temperature. From the characteristic of the peak observed along the DTA curve,

an exothermic or endothermic event involving the sample can be determined.

C. Experimental Methods

633

d. Scanning Electron Microscopy

During the SEM experiment, a focused electron beam is swept over the surface of

a specimen in a raster pattern, and various resulting emissions from the sample

(backscattered electrons, secondary electrons, or X-rays) are detected. An image

is formed on a cathode ray screen by mapping the intensity of the detected signal

as a function of position. Combining this technique with an X-ray spectrometer

allows chemical analysis of a microvolume of the sample.

e. Determination of Liquid Compositions

In general, after a sample is melted and solidified, the liquid will assume the form

of an amorphous state and one can easily distinguish the amorphous regions from

the primary crystals after melting. In the case of high-temperature superconduct-

ing oxides, often the melts recrystallize instantaneously as crystals. This is

particularly true in Ba-Cu-O and related systems, where relatively large

barium cuprates form and it is difficult to distinguish between primary crystals

and crystals crystallized from liquid. In this situation a wicking technique can be

used (Wong-Ng and Cook, 1995). To capture liquid free of any primary crystal-

line phases for SEM/EDX analysis, a sintered ceramic wick with open porosity

(i.e., MgO) can be placed in the crucible with the appropriate sample. During the

heat treatment, liquid is drawn into the wick by capillary action. Because of the

filtering action of the small (<5-10 l~m) openings in the wick, primary solid

phases do not enter the capillary. During the quench, the liquid is retained in the

wick, thus making a representative sample of the melt available for analysis.

The liquid composition can be obtained most directly by using electron

probe microanalysis. This method measures the intensity of characteristic X-rays

emitted from a specimen and relates this intensity to the concentration of the

elements involved. Standardization using samples of known composition is

essential. Corrections for the atomic number Z, the absorption A, and the

fluorescence F (ZAF method) must be applied to the intensity ratios. A detailed

description of quantitative microanalysis is given by Heinrich and Newbury

(1991). Modem software such as DTSA (Fiori

et al.,

1991) facilitates the

application of these methods.

fi Vapor Pressure Measurements

For the equilibrium study of vapor pressure of T120 in the Tl-containing

superconducting systems, an efficient method is the two-zone technique (Aselege

634 Chapter 14: Phase Diagrams

et al.,

1994), which utilizes a condensed thallium oxide source to supply a

constant partial pressure of T120 vapor through the vaporization reaction

2 T120 x(c) < > 2 T12 O(v) + (x - 1)O

2 (V).

(1)

Using this procedure, the sample, which is in powder form, and the condensed

thallium oxide (T1203) are each held typically in high-purity A1203 boats, and in

turn are held within an A1203 tube. The source boat is held in the closed end and

the sample boat in the open end. The open end is then wrapped tightly with

several layers of thin gold foil.

The equilibrium constant

K(T)

for reaction (1) is expressed by

K(T) = p(T120)22p(O2)(x-1)/a(T120x) 2.

(2)

The activity of T120 x in the denominator of Eq. (2) is unity if the condensed

thallium oxide exists as a pure phase. With source temperature and p(O2) fixed,

p(T120 ) may be determined from the equilibrium constant

K(T).

Representative Phase Diagrams

In the two volumes of

Phase Diagrams for High-T c Superconductors

(Whittler

and Roth, 1991; Vanderah

et al.,

1991), a total of 542 diagrams have been

collected and edited. As superconductor research is a highly active field, many

systems have been investigated extensively in various laboratories. Inevitably,

there are repetitions and inconsistencies. The following is a group of selected

diagrams that represent either the major industrial activities of high-T c systems

today, or systems that have attracted considerable attention. This compilation

emphasizes the BYC, BRC, and the BSCCO systems that contain the actual high-

temperature superconductors, and not the subsystems or systems containing only

related phases.

a. Ba-Y-Cu-O Systems

Extensive international research efforts since 1987 have led to the accumulation

of a large body of information concerning the crystal chemistry and phase

equilibria of the BYC system; this is particularly true for the subsolidus

relationships, as they are essential for the preparation of the high-T c compound

Ba2YCu306+ x in single-phase, crystalline form. Phase diagrams of this high-T c

system vary significantly depending on the annealing atmosphere (and the

presence of CO2).

D. Representative Phase Diagrams 63S

1. Prepared in Air

Roth

et al.,

(1988) were among the first to determine a complete phase diagram of

the BaO(BaCO3)-IY203-CuO system, at ~950~ and it is shown in Fig. 14.1.

YzCu205 is the only binary oxide reported in the I(yzO3)---CuO system. Four

phases were observed in the BaO(BaCO3)--~(Y203) subsystem. Barium rich

Ba4Y207 and Ba2Y205 have been reported to be oxycarbonates, with formulas

of Ba4Y207.CO2 and BazY2Os.2CO2. When pure BaO is used instead of BaCO3,

the Ba4Y207 and BazY205 compounds cannot be prepared. There are a total

of three ternary oxides, including the high-temperature superconductor

BazYCu306+ x (2:1:3) and an ubiquitous impurity phase BaYzCuO 5 (1:2:1)

that is known as the "green phase." Another barium-rich oxycarbonate solid

solution region is known as "the other perovskite phase," and is bounded by the

4:1:2, 5:1:3, and 3 : 1:2 compositions. The Ba2YCu306+ x phase is known to

Fig. 14.1.

BaO (BaC03)

Ba4Y207~..~ P .. ~t Ba2Cu03

Ba2Y205

Ba3Y40g /

BAY204

,,,4:1

,3:2:1

BGCu02

l -/ v v \ v ,v

0 20 40 "-,... 60 80 100

1/2(Y203) Mol ~ Y2Cu20s CuO

Phase diagram of the temary system BaO(BaCO3)-~zY203-CuO at ~950~ (Roth

et al.,

1988). The positions of the

BazYCu306+ x (2"

1"3) superconductor and the green phase

BaY2CuO 5 (1" 2"1) are shown.