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Extra Phase Diagrams of Materials - Phase Diagram Sample Preparation, Lecture notes of Chemistry

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Sample Preparation
Phase Diagram Sample Preparation
By Robert D. Shull
National Bureau of Standards
The procedures by which samples are prepared for phase diagram studies are examined and
critically evaluated. The three key elements that require attention (aHoy purity, homogeneity,
and equilibrium) are separately addressed, and several examples of bad procedure are
presented with information on their past and future consequences. The origin of commonly
confronted problems are described and special procedures are suggested for their circum-
vention. Additionally, new methods for the early detection of some sample problems are
presented, and the usefulness of rapidly solidified materials (as specimens) in phase diagram
studies is illustrated.
Of the many problems that befall phase diagram studies,
one of the most damaging and yet difficult to detect is that
of poor specimen characterization. In most instances that
this problem arises, the cause is found to be due to inatten-
tion to this important aspect of the program because of its
"triviality". Certainly, the most interesting and rewarding
aspect of any investigation is the interpretation of the
measurements performed on the samples. However, it
should not be construed that the preparation of the sam-
ples is by any means an inconsequential prerequisite to
this end. Obviously, the results of a study will depend on
the state of the alloys on which the measurements were
made. ]f carelessness is exercised on the development of
the specimens, especially such that their constitution and
thermomechanical history is not well-characterized, then
the conclusions drawn from their measurement will most
likely be in error.
A clear example of such a situation would be the gross
contamination of an alloy with tungsten by the inadver-
tent touching of the tungsten electrode in an arc furnace
with the alloy during the melting operation. The alloy, if
initially comprised of two elements, becomes a ternary
alloy and (according to the phase rule) allows an extra
degree of freedom for the subsequent establishment of
phase equilibria. The binary phase diagram determined
from such ternary alloys (if for some unknown reason they
were unrecognized as such and still used) is likely to be
quite different from the true diagram. Unfortunately, how-
ever, most instances of improper sample preparation are
much more subtle than this example. It is also unfortunate
that, usually in these more subtle instances, the problem
is found after a great deal of time and effort has already
been expended on using that sample.
This paper is concerned with sample preparation in gen-
eral, especially as it impacts alloy phase diagram studies
specifically. Alloy contamination is only one of three major
areas in this regard that must be addressed. The other two
problem areas are alloy homogeneity and alloy equili-
brium. Homogeneity ensures that all parts of the sample
are equivalent in composition. Consequently, the phase
equilibria attained in one part of the sample will be the
same as those attained in a different part of the sample.
Equilibrium should be ascertained so that the reported
phase diagram could properly be labeled an equilibrium
diagram. Specimens used in its determination should, con-
sequently, be appropriately stabilized. Additionally, if a
sample is truly at equilibrium in a given state, then cer-
tainly it does not matter how that state was achieved. If,
however, the sample is not at equilibrium--a condition
which is more generally the circumstance-- then the state
of the alloy (and, therefore, the measurement value deter-
mining it) will depend on the path by which that state was
reached. Such problems-- those that are directly traceable
to the preparation procedures of the specimens--are not
easily detected. This is doubly true for the reader of the
investigation results, where complete information is un-
available and vague terms such as "standard procedures"
frequently appear. This paper is designed to aid this latter
group of people (in formulating their evaluations of a
particular study) as well as to help the future investigator
(in designing his experimental program) by indicating
the places where problems in the above-listed three areas
are likely to occur and of their possible consequences. In
what follows, each problem area will be dealt with in the
natural order in which it is confronted during the prepara-
tion of the alloy for measurement: i.e., alloy purity, ho-
mogeneity, and equilibrium. Methods for their detection
and suggestions for best circumventing these problems are
then presented.
Alloy Purity
By necessity, alloy purity questions obviously must start
with purity questions of the constituent elements. A phase
diagram study should always begin with an analysis ofth e
beginning materials used in the investigation, if for no
other reason than to ascertain that the or.der of the system
(binary, ternary, quaternary, etc.) being studied matches
that of the alloys being used. At this stage, optical micros-
copy of the starting elements has been found very useful,
by being capable of the quick detection of insoluble con-
taminants. On the other hand, the qualitative detection of
soluble contaminants (including interstitial elements) is
possible by the relatively fast differential thermal anal-
ysis (DTA) method. This very powerful and widely used
phase diagram tool relies on the detection of the heat ab-
sorbed or released during a phase transformation in a
specimen as heat is supplied at a very constant rate to its
adiabatic enclosure. However, its usefulness in validating
elemental purities (especially in regard to the difficult-to-
detect interstitial contents) has not been generally recog-
nized. Figures 1 and 2 are shown to illustrate this novel
capability. In these and later figures herein containing
DTA data, the vertical axis depicts the differential tem-
perature between the sample and an A1203 reference cruci-
ble (the latter having a total heat content close to that of
the specimen and containing no phase transitions in the
temperature range of interest). The horizontal axis (implic-
itly, a time scale) indicates the programmed furnace tem-
perature. Large deviations from a horizontal line indicate
heat released (upward deviations) or absorbed (downward
deviations) during a phase transformation. For a congru-
ent transformation (i.e., the phenomenon of melting or
Bulletin of Alloy Phase Diagrams Vol. 4 No. 1 1983 5
pf3
pf4
pf5
pf8
pf9
pfa

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Download Extra Phase Diagrams of Materials - Phase Diagram Sample Preparation and more Lecture notes Chemistry in PDF only on Docsity!

Sample Preparation

Phase Diagram Sample Preparation

By Robert D. Shull

National Bureau of Standards

The procedures by which samples are prepared for phase diagram studies are examined and critically evaluated. The three key elements that require attention (aHoy purity, homogeneity, and equilibrium) are separately addressed, and several examples of bad procedure are presented with information on their past and future consequences. The origin of commonly confronted problems are described and special procedures are suggested for their circum- vention. Additionally, n e w methods for the early detection of some sample problems are presented, and the usefulness of rapidly solidified materials (as specimens) in phase diagram studies is illustrated.

Of the many problems that befall phase diagram studies, one of the most damaging and yet difficult to detect is that of poor specimen characterization. In most instances that this problem arises, the cause is found to be due to inatten- tion to this important aspect of the program because of its "triviality". Certainly, the most interesting and rewarding aspect of any investigation is the interpretation of the measurements performed on the samples. However, it should not be construed that the preparation of the sam- ples is by any means an inconsequential prerequisite to this end. Obviously, the results of a study will depend on the state of the alloys on which the measurements were made. ]f carelessness is exercised on the development of the specimens, especially such that their constitution and thermomechanical history is not well-characterized, then the conclusions drawn from their measurement will most likely be in error. A clear example of such a situation would be the gross contamination of an alloy with tungsten by the inadver- tent touching of the tungsten electrode in an arc furnace with the alloy during the melting operation. The alloy, if initially comprised of two elements, becomes a ternary alloy and (according to the phase rule) allows an extra degree of freedom for the subsequent establishment of phase equilibria. The binary phase diagram determined from such ternary alloys (if for some unknown reason they were unrecognized as such and still used) is likely to be quite different from the true diagram. Unfortunately, how- ever, most instances of improper sample preparation are much more subtle than this example. It is also unfortunate that, usually in these more subtle instances, the problem is found after a great deal of time and effort has already been expended on using that sample.

This paper is concerned with sample preparation in gen- eral, especially as it impacts alloy phase diagram studies specifically. Alloy contamination is only one of three major areas in this regard that must be addressed. The other two problem areas are alloy homogeneity and alloy equili- brium. Homogeneity ensures that all parts of the sample are equivalent in composition. Consequently, the phase equilibria attained in one part of the sample will be the same as those attained in a different part of the sample.

Equilibrium should be ascertained so that the reported phase diagram could properly be labeled an equilibrium diagram. Specimens used in its determination should, con- sequently, be appropriately stabilized. Additionally, if a sample is truly at equilibrium in a given state, then cer- tainly it does not matter how that state was achieved. If, however, the sample is not at e q u i l i b r i u m - - a condition which is more generally the circumstance-- then the state of the alloy (and, therefore, the measurement value deter-

mining it) will depend on the path by which that state was reached. Such p r o b l e m s - - those that are directly traceable to the preparation procedures of the s p e c i m e n s - - a r e not easily detected. This is doubly true for the reader of the investigation results, where complete information is un- available and vague terms such as "standard procedures" frequently appear. This paper is designed to aid this latter group of people (in formulating their evaluations of a particular study) as well as to help the future investigator (in designing his experimental program) by indicating the places where problems in the above-listed three areas are likely to occur and of their possible consequences. In what follows, each problem area will be dealt with in the natural order in which it is confronted during the prepara- tion of the alloy for measurement: i.e., alloy purity, ho- mogeneity, and equilibrium. Methods for their detection and suggestions for best circumventing these problems are then presented.

Alloy Purity

By necessity, alloy purity questions obviously must start with purity questions of the constituent elements. A phase diagram study should always begin with an analysis ofth e beginning materials used in the investigation, if for no other reason than to ascertain that the or.der of the system (binary, ternary, quaternary, etc.) being studied matches that of the alloys being used. At this stage, optical micros- copy of the starting elements has been found very useful, by being capable of the quick detection of insoluble con- taminants. On the other hand, the qualitative detection of soluble contaminants (including interstitial elements) is possible by the relatively fast differential thermal anal- ysis (DTA) method. This very powerful and widely used phase diagram tool relies on the detection of the heat ab- sorbed or released during a phase transformation in a specimen as heat is supplied at a very constant rate to its adiabatic enclosure. However, its usefulness in validating elemental purities (especially in regard to the difficult-to- detect interstitial contents) has not been generally recog- nized. Figures 1 and 2 are shown to illustrate this novel capability. In these and later figures herein containing DTA data, the vertical axis depicts the differential tem- perature between the sample and an A1203 reference cruci- ble (the latter having a total heat content close to that of the specimen and containing no phase transitions in the temperature range of interest). The horizontal axis (implic- itly, a time scale) indicates the programmed furnace tem- perature. Large deviations from a horizontal line indicate heat released (upward deviations) or absorbed (downward deviations) during a phase transformation. For a congru- ent transformation (i.e., the phenomenon of melting or

R. D. Shull

Fig. 1 Differential S a m p l e Temperature (dT) vs Programmed Furnace Temperature for DTA Mea-

surements on 99.999 wt.% Pure Au

o.o

0 ~'~- 1.o i - -o

lO

P U R E A u

........ ,-~. , - - ~

\ .'

\ ,

........................................... : ............................................. ................... .............................................

\

I I i t

T E M P E R A T U R E ( C ) Measured during heating at a rate of 2.5 ~

Fig. 2 Differential Sample Temperature (dT) vs

P r o g r a m m e d F u r n a c e T e m p e r a t u r e for DTA

Measurements on 99.9 wt.% Pure Ti

2.O f

I CLEAN Ti

\ / / ...................................................... ................. i/ ...........................................................................

\

GASSY Ti o..................................................................................... \

- 2.o ............................................i~.... .. .... ., :

    1. 0 860 880 900 920 TEMPERATURE (C) One piece contained 150 ppm oxygen (top curve) and a similarly pure piece contained 300 ppm oxygen (bottom curve). Both sets of data were measured during heating at a rate of 2.5 ~

that of an allotropic crystal structure change of a pure element), it can be shown 1 that the shape of the DTA curve would be triangular, as is shown in Fig. 1 for the melting of a sample of pure Au. The critical aspects of the curve, insofar as purity is concerned, are the high sharpness of the initial deviation from the horizontal (occurring at the temperature of transformation), the linearity of the sub-

sequent deviation, and the abruptness of the transfor- mation conclusion (indicated by the reduction in devia- tion). The relatively fast exponential decay in d T back to the horizontal also is a result of the high purity of the sample, but is less quantitative. If the sample was not pure, the range in transformation t e m p e r a t u r e s that would consequently result would be reflected by signifi- cant rounding of the DTA curve at the beginning and end- ing points of the transformation as well as the loss of linearity in the central region. The thermal response char- acteristics of the measurement equipment also will con- tribute to a lack of sharpness in the transformation, but the effect is small. Observe, for example, the very slight effect at the beginning and end of the DTA arrest, shown in Fig. 1, fbr the melting of a sample of pure Au. Now, compare this curve with those shown in Fig. 2 for the a(cph) --*/3(bcc) congruent phase transition in two nomi- nally pure pieces of titanium. The top curve is for a sample of as pure a piece of bulk titanium as one is able to obtain. However, it is obvious (primarily from the lack of linearity immediately following the initial deviation in d T from the horizontal) that even this material is not completely pure. In fact, a later chemical analysis confirmed a 99.9% purity, but a content of 150 ppm oxygen and 20 ppm nitrogen (by weight). The bottom curve, however, is for a more typically obtained piece of high-purity t i t a n i u m - - 9 9. 9 % pure (300 ppm oxygen and 30 ppm nitrogen). The DTA analysis shows this sample contains a considerable interstitial con- tent. One might also note the effect of this interstitial contamination in raising the transition temperature for the transformation (i.e., as reflected by the increase in furnace temperature at which the first deviation in d T is detected). In this particular instance, the increase was approximately 3 ~

In general, most investigations pay attention to the purity of the starting materials. Therefore, problems in alloy contamination--for instance, that of the unintentional

R.D. Shull

Conversely, any unduly large (or small) weight losses also

are indicative of something remiss that requires further

checking. The origin of the measured weight gains and

losses (in the absence of any noticeable crucible effects,

such as sticking or discoloration) may be checked by calcu-

lating the expected alloy content under various limiting

assumptions and looking for agreement with the actual

measured value. The limiting case assumptions useful in

this regard include (a) all weight losses being attributed to

the highest vapor pressure element (works well when

there exists a large difference in vapor pressures), (b) the

weight losses of each element being proportional to the

alloy content (used when the vapor pressures of the con-

stituents are equivalent), and (c)the weight gains (if

small) being completely due to gaseous (O, N, H) pickup or

(if gains are large) to tungsten addition.

Contamination of the samples also may occur during

the homogenization and aging heat treatments. Such

contamination generally comes from the surrounding

atmosphere, but may derive from the contact materials.

Atmospheric contamination may again be reduced by

heat treatment in a vacuum or inert-gas surrounding. As

discussed in the melting operation, sealed systems are

preferable. A good practice commonly used in phase dia-

gram studies is the treatment of the sample while it is

sealed inside a fused silica tube. The degree of protection

afforded by such a procedure is proportional to how good a

vacuum the investigator initially achieved in the tubes

before backfilling with inert gas or sealing. For highly

reactive materials (e.g., Ti and Zr) a vacuum of 10 _6 Torr

(1.3 x 10 4 Pa) is required for high-accuracy work. For

very long heat treatments at high temperatures of reactive

metals, it also has been found very useful to double encap-

sulate the sample in two silica tubes. In such a procedure,

the small amount of gas that permeates through the outer

tube does not develop a large enough concentration to

drive any significant diffusion through the inner tube. In

the thin-necked down portions of the tubes where the cap-

sules are sealed off, the permeation of gas into the silica

tubes is most significant, amounting to approximately

10 -3 atoms/s for oxygen and 10 4 atoms/s for nitrogen. ~'

In a recent investigation of the Ti-A1 system, this author

consistently measured a decrease in the oxygen contents of

its alloys by 100 to 200 ppm (by weight) when the extra

precaution of double encapsulation was followed. Extra

protection against contamination by the surrounding at-

mosphere is often provided by a loose wrapping of a get-

tering foil around the sample. This is also a useful practice

if the alloy reacts with the fused silica tube at the treat-

ment temperature. Of course, the choice of the getter ma-

terial should be predicated upon its nonreactivity with the

alloy as well.

A special situation of sample preparation is the treatment

of alloy powders. These samples, required by many mea-

surement techniques, possess a high surface area. Conse-

quently, atmospheric contamination of these materials is

very easy. The effects of such contamination will vary with

the measurement technique: these methods (e.g., DTA,

X-ray diffraction, and magnetic susceptibility), which are

sensitive to the volume of material, will be affected most.

The surface area to volume ratio of these samples is very

high, and the volume percent of contaminated material

will, therefore, be greater for alloys in this form. High-

temperature heat treatment of such samples should be

kept to an absolute minimum. In fact, unless the powders

are prepared just prior to measurement (with only a short

stress-relief anneal in between), the probability of signifi-

cant contamination is great.

Alloy Homogeneity

Phase diagrams are similarly affected by problems in alloy

homogeneity. Due to the importance of composition as a

variable in influencing phase equilibria, its control and

uniformity are essential. The sample begins in a very in-

homogeneous state: that of the separated elements. Uni-

formity is subsequently created by the melting and mixing

of these constituents. Problems in creating such a mixture

(and at the proper composition) are most likely to occur

when the constituent elements possess large differences in

density, melting points, or vapor pressures. Also, for alloys

in systems containing liquid immiscibility regions, the

creation of compositionally different species in the liquid is

thermodynamically favored, and unsatisfactory samples

often will result.

The m a n n e r in which the above problems may be

minimized (or eliminated), in large part, depends on the

method used to melt the alloys. Melting under a vacuum

(e.g., electron-beam melting and vacuum-induction melt-

ing) results in significant losses due to vaporization: the

vaporization is preferential and composition control is dif-

ficult. Evaporative loss of material may be significantly

reduced by heating and melting in the presence of an inert-

gas atmosphere. The inert gas provides a gas layer near

the surface of the metal through which the metal vapor

must diffuse before being swept away by convection cur-

rents. The vaporization of metal possessing a pressure (i.e.,

a concentration) equal to its vapor pressure at the surface

of the metal where equilibrium is attained becomes lim-

ited by the rate at which the metal vapor may diffuse (i.e.,

change its concentration) away from the surface. This dif-

fusion rate is controlled by the mean free path (L) of the

vapor atoms, which is inversely p ~ t i o n a l to the exter-

nal gas pressure (P): L ~ (~?/P) V T / M , with ~ being the

gas viscosity; T, the temperature; and M, the molecular

weight of the gas. 7 Using the example of tungsten at

1000 ~ an order of magnitude reduction in vaporization

rate is observed for an external pressure application of 100

Torr (13 kPa) argon gas.

Electric-arc melting is one method that takes advantage of

the reduced vaporization rate of materials in the presence

of an external gas. Due to its widespread use in phase

diagram studies, this technique requires special attention.

Although the total vaporization during melting is less in

this process, which employs a partial pressure of inert gas

to sustain a plasma conducting the electric current be-

tween the electrode and sample, selective vaporization can

still be a serious problem, especially in the time period

between the initial heating and alloy formation. The vapor

pressure (and, therefore, the pressure scaled vaporization

rate) of an element increases with temperature and with

few exceptions (e.g., Ca, Cr, Mg, Mn, Sr, Ti, and Zn) scales

with its melting point. Consequently, if all the constituent

elements of an alloy were heated evenly in the furnace up

to the melting point of the highest melting element (so

that a single liquid solution was attained), there would be

significant losses of the lower melting elements due to the

long times they were held at high temperatures (and,

therefore, in high vapor pressure states) in their pure

forms. Once an alloy solution is formed, the problem is

Sample Preparation

partially alleviated. A reduction in the vapor pressures of the constituents occurs according to Raoult's law: PA = XAP~ (where PA and P~ are the vapor pressures of element "A", respectively, in the solution and the pure form, and Xa, which is always less than 1.0, is the mole fraction of "A" in the solution). In an electric-arc furnace, the elements may be heated unevenly. In this apparatus, therefore, it is possible to obtain a controlled composition by melting the highest melting element first. Its initial placement on top of the pile of constituents in the arc furnace ensures this condition is realized. On melting, this element flows onto the lower melting elements located underneath it, immediately melting and fusing with them. If performed properly, at no time are the lower melting elements exposed to high temperatures while in their highly volatile pure state.

Once all the elements of an alloy have liquefied, gross alloy homogeneity is obtained by vigorous stirring and mixing, followed by a fast cool. An investigator must be especially careful at this stage when preparing alloys com- prised of elements having wide differences in both melting points and densities. An example of what m a y happen only too easily in these instances is depicted in Fig. 4 for a sample of TigoMolo. During the time the molybdenum (which has the higher melting point, TM = 2610 ~ was heating, the titanium (TM = 1668 ~ on which it was sit- ting in the arc furnace reached its melting point first and liquefied. The molybdenum, also possessing a much higher density (PMo = 10.2 g/cm 3 vs PTi -----4.5 g/cm3), fell to the bottom of the melt and never completely melted. Even

Fig. 4 Optical Macrograph of an Arc-Melted TigoMol0 Alloy Showing an Unmelted Chunk of Mo in the Middle

NOMINAL Ti9oMOlo

(As Cost)

The sample was chemically etched in a solution of 60% lactic

acid, 20% HNO3, and 20% HF.

Fig. 5

u)

I--

Z

O

O

X-ray Energy Dispersive Analysis (EDX) Spectra

M

O

1000

3000

2000

0 0.000 5.

UNMIXED BLOB - - Mo

..... / / / N : M I. N A. L. T ' 9 0 i O l O MATRI.X

10.000 15.000 20.

E N E R G Y ( k e V )

For the unmelted molybdenum chunk (top curve) and the alloy matrix (bottom curve) for the as-cast TigoMoloalloy shown in Fig. 4.

Sample Preparation

Fig. 7 Differential Sample Temperature ( d T ) vs Programmed Furnace Temperature for DTA Measure-

ments on Slowly Solidified CussTi4s

A O

I--

    1. 5
      1. 0
    1. 5
    1. 0

Cu55Ti45 (As Cost)

--------.,,._..~ ................................................ le~ ............................................................................................................

. t l - 9 : "%. ,'- , ~,~ "4 \ / ' ' :.--,.,.;

o

.................................................................... , .............. .~ ............................... 9 ................................. ........

    1. 5 l I I I

T E M P E R A T U R E (C)

Measured during heating at a rate of 5 ~

Fig. 8 Differential Sample Temperature (dT) vs Programmed Furnace Temperature for DTA Measure-

ments o n a n As-Crystallized Sample of CUssTi4s Metallic Glass

    1. 5

o V

"o

    1. 5
    1. 5
    1. 5

Cu55Ti45 (As Crystollized) r , ,. , , i i,,,

........................................................................................... '. ~..................................................................

-4.5 I I I

T E M P E R A T U R E (C)

Measuredduring heating at a rate of 5 ~ These data were obtainedon the same sample as shown in Fig. 7, but measured prior to it.

R.D. Shull

5 ~ The absence in this alloy of any low-tempera-

ture thermal peaks near 880 ~ attests to the fact that the

[3' + ~] and [6 + ~] two-phase fields in this system, con-

trary to Fig. 6, do not extend as far as this alloy com-

position. Consequently, the low-temperature arrests mea-

sured for the alloy in Fig. 7 (slow-cooled) must derive from

portions of the slow-cooled alloy containing compositions

near the eutectic. Figure 8 additionally demonstrates the

usefulness of metallic glasses in providing compositionally

homogeneous alloys for phase diagram studies.

As long as the composition variations created during con-

ventional (slow) solidification do not possess large spatial

extents, they may generally be eliminated by heat treat-

ment of the sample at sufficiently high temperatures,

where the elemental diffusion coefficients are large

enough (>-10 =m crh2/s) to enable mass transport to even

out the composition in reasonable time periods. Of course,

such a treatment should be performed in a single-phase

field if complete homogeneity is desired. Under the ex-

tremely simplified assumption that diffusion occurs by

the random walk of atoms on a simple cubic lattice, one

may easily derive ~~that the root mean square distance (~)

traveled by the atoms is a simple function of time (t) and

diffusivity (D): ~ = ~/2Dt. More elaborate treatments of

this problem 11result in similar relationships that roughly

agree (within a factor of 3 or 4) with this X/2Dt depen-

dence. The spatial extent of the inhomogeneity created in

the solidification process may be estimated by the spacing

between the dendrite arms observed in the optical micro-

graphs of as-cast alloys. For the arc-melted TigoMolo alloy

shown in Fig. 4, this spacing is approximately 100 tzm.

Because the diffusivity (D) is a highly temperature-

dependent parameter, both the proper homogenization

temperature and time must be chosen with care such that

the calculated ~ will be longer than the measured arm

spacing. It should also be remarked that the spatial extent

of the inhomogeneity may also be reduced (resulting in

shorter required heat treatment times) by rapidly solidi-

fying the alloy and also by cold working the as-cast alloy.

The above described homogenization treatment should

always be administered to an alloy following melting. This

is an area where attention has generally been lacking. If

this treatment is not performed, those compositionally

different regions will remain different and local equilibria

(indicative of those compositions) may subsequently de-

velop that will, in general, be quite different from that of

the average alloy content. Phase diagram measurements

made on such alloys would certainly be misleading. Homo-

genization should be performed, if possible, in a single-

phase region of the phase diagram, so there will not be any

thermodynamically forced composition variation via

phase separation. If this criterion cannot l~e satisfied,

the forced homogenization in a multiple-phase field will

still be beneficial by reducing the number of composition

variations to that of the order of the phase field. The re-

duced spatial extent of these variations will also aid in

reducing the times required for any lower temperature

phase equilibration.

Complete alloy homogeneity is a difficult quality to prove.

Because of the obvious infeasibility of completely slicing

up the samples and observing them in their entirety,

effects due to inhomogeneity may become evident during

an investigation (even when great precautions were taken

to avoid them). Consequently, both the reader of the litera-

ture and the phase diagram investigator must not s u m -

marily discount their possibility, even in very careful

work. A very clear example of such an occurrence recently

surfaced in this author's own investigation of Ti-Al alloys.

In this investigation, the boundaries between the ordered

(a2) and disordered (a) hexagonal phases and the high-

temperattwe body-centered cubic (fl) phase were being

determined in the titanium-rich end of the alloy sys-

tem. The DTA data (shown in the bottom curve of Fig. 9)

for a supposedly well-homogenized Ti79A121 sample

indicated the existence of two-phase transitions in the

40 ~ temperature range between 1110 and 1150 ~ Be-

cause the thermal arrest representative of the a ~ a + a

reaction had already been detected at a lower tempera-

ture, the existence of two high-temperature phase reactions

presented the exciting possibility of the existence of a

new high-temperature phase. Similarly measured data,

however, for alloy samples of TislA119 and Ti75A125 were

subsequently found to be inconsistent with these conclu-

sions. Consequently, a second alloy sample of Ti79A121 was

similarly prepared and homogenized, and the DTA data for

it are presented in the top curve of Fig. 9. The absence of

the two thermal arrests at high temperatures attests to

the fact that the original sample was inhomogeneous.

The two peaks observed in the original alloy resulted

from two compositionally distinct regions (unobservable

by optical microscopy) in the material, each giving rise

to a separate a ~ fl phase transition at a temperature

characteristic of its composition. John Cahn ~2 suggested

that such a result could be expected to occur if there

was insufficient homogenization of the as-cast structure.

The as-cast structure may be viewed as possessing a

roughly sinusoidally varying Composition (C) with distance

(X): C(X) = Co + C1 sin(n~rX/L). During homogeniza-

tion, the amplitude (C~) of such an oscillation decreases.

Because the magnitude of the derivative, IdC/dX], is

smaller at the maxima and minima of such a distribution,

there is a greater volume percent of material having com-

positions near the maxima and minima values. Such a

bimodal distribution could then be expected to produce two

DTA peaks as observed rather than a single broadened

thermal arrest.

Alloy Equilibrium

Phase diagrams may be determined experimentally from

samples representing either the equilibrium state or va-

rious degrees of approach to the equilibrium state. If the

former condition applies, then the validity of the equili-

brium assumption must be demonstrated. Measurements

performed on nonequilibrium alloys will certainly lead to

incorrect diagrams if the results of such measurements

are erroneously attributed to the stable, time-invariant

state. The determination of compositions and volume per-

cents of phases is one area which frequently leads to poor

diagrams when the representative samples were indeed

not representative of the equilibrium state. In the Ti-A

system, one of the reasons for the more than four topo-

logically different phase diagrams presently in the liter-

ature for this system is the improper interpretation of

alloy equilibrium.

Proper alloy equilibration, in general, requires long-time

aging heat treatments following homogenization. Usually,

the treatment temperatures are lower than the homoge-

nization temperatures, resulting in diffusivities that are

accordingly much smaller. If a phase transition is favored

at a particular temperature that requires large changes

R. D. Shull

Fig. 10 Dark Field Image Transmission Electron Micrograph for Ti3AI in a Ti79AI21 Alloy

Aged at 1050 ~ for 165 h, followed by an immediate quench into a solution of icy brine.

Fig. 11 Fe-rich End of the Fe-AI Phase Diagram

I I [ i I p~' I i I ' I

700 il~II FeAI -

t

t / "'"

' , , / O~+Fe3A, ,I / F'e3A, i I I r

S ' / , , , , , ,

Atom per cent o l u m i n u m

As determined by Swann, Duff, and Fisher16 (dashed lines) and by Okamoto and Beck '7 (solid lines).

the solid curves of Okamoto and Beck. In evaluating phase

diagrams, it should be noted that coherent (metastable)

boundaries always lie inside incoherent (stable) bound-

aries. If the true equilibrium diagram is desired, then

whenever possible, phase coherency should be broken up

(e.g., by cold work, or possibly by extensive coarsening)

during the sample preparation. It should be noted that for

coherent phase equilibria, the well-known lever rule is not

strictly valid. 19 Consequently, the use of this rule to deter-

mine the compositional extents of multiple phase fields

should not be performed indiscriminately.

The approach to the equilibrium method is equally valid in

phase diagram studies. In this instance, an extrapolation,

appropriate to the particular measurement method, is

used to obtain the equilibrium value. Any dynamic mea-

surement tool (e.g., DTA, heat capacity, or electrical

resistivity) requires the use of this technique: the extrapo-

lation in these instances being to zero heating or cooling

rate. Isothermal anneals for varying lengths of time, fol-

lowed by the measurement of some property, are also

included here. Extrapolations, in these instances, are

then to infinite time. Of course, the accuracy of this tech-

nique depends on the number and spacing of the data and,

especially, on the closeness of the sample to equilibrium

during the last measurement. The further away from equi-

librium the sample is, the greater the range of extrapo-

lation required, and the greater the inaccuracy of the

method. This is particularly true when (as is usually

the circumstance) the proper extrapolation function is not

completely known.

Conclusion

Because of the ease with which a sample may be prepared

in a nonrepresentative state, great care must be exer-

cised in the development of the specimens used in phase

diagram studies. As was shown earlier, even in very care-

ful studies, alloy problems arise, and the existence of

such problems should never be summarily discounted.

The probability of a sample becoming unreliable varies

inversely with the care exercised in its production. Con-

sequently, the authors of phase diagram studies should

always fully describe their sample preparation techniques.

Sample Preparation

The assumption should be made that specimen problems do exist unless proven otherwise. The absence of prepara- tion data (or the presence of very cursory data) implies either inattention or blatant disregard for this factor. Ob- viously, neither attitude is conducive to good samples, and such investigations should be viewed with reservation.

Acknowledgment

The author would like to express his sincere appreciation to Dr. Archie McAlister for measuring much of the DTA data shown in this paper, Dr. Robert Reno for the TEM pictures, and Mr. Charles Brady for the optical metallo- graphy. The author would also like to thank Dr. John Cahn for helping interpret some of the data presented here. Special gratitude is also expressed to Prof. Paul A. Beck at the University of Illinois for initially imparting to the author a few years ago the importance of good alloy prepa- ration technique.

References

  1. A.J. McAlister and R. D. Shull, to be published.
  2. I.A. Popov and N.V. Shiryaeva, Russ. J. Inorg. Chem., 6, 1184 (1961).
  3. C. Allibert, J. Driole, and E. Bonnier, C.R. Acad. Sci., Paris, 268C, 1579 (1969). 4. J.D. Verhoeven and E.D. Gibson, J. Mat. Sci., 13, 1576 (1978). 5. A. Roth, Vacuum Technology, North-Holland Publishing Co., New York, 168 (1976). 6. S. Dushman, Scientific Foundations of Vacuum Technique, John Wiley and Sons, Inc., New York, 531 (1949). 7. S. Dushman, Scientific Foundations of Vacuum Technique, John Wiley and Sons, Inc., New York, 33 (1949). 8. S. Dushman, Scientific Foundations of Vacuum Technique, John Wiley and Sons, Inc., New York, 80 (1949). 9. Metals Handbook, 8th ed., Vol. 8, American Society for Metals, Ohio, 300 (1973).
  4. C.A. Wert and R.M. Thomson, Physics of Solids, McGraw- Hill, Inc., New York, 61 (1970).
  5. G.A. Geiger and D. R. Poirer, Transport Phenomena in Metal- lurgy, Addison-Wesley Publishing Co., Reading, MA 496 (1973).
  6. John W. Cahn, private communication (1983).
  7. T. Sato, Y.C. Huang, and Y. Kondo, Trans. J. Inst. Met., 1, 22 (1959).
  8. E. Ence and H. Margolin, Trans. Met. Soc. AIME, 221, 151 (1961).
  9. I.I. Kornilov, T.T. Nartova, and S.P. Chernyshova, Russ. Met., 6,156 (1976).
  10. P.R. Swann, W. R.Duff, and R. M. Fisher, Trans. TMS-AIME, 245,851 (1969).
  11. H. Okamoto and P.A. Beck, Met. Trans., 2,569 (1971).
  12. S.M. Allen and J. W. Cahn, Acta Met., 23, 1017 (1975).
  13. J.W. Cahn, Acta Met., 10,907 (1962).

Utilization of Phase Diagrams

Phase diagrams are justifiably regarded as an important component of our technological society; the Bulletin will publish examples that illustrate their value in the development of new science, trouble shooting, manufacturing control, and the development of new materials. Readers are invited to share their experiences by submitting items to the Editor, in any area of application.

Phase Diagrams in Dental Metallurgy

All metals used in dentistry must have exceptional corro- sion resistance and high strength. They may be classified according to use into: (a) metals used for direct restora- tions; (b) metals used for casting indirect restorations; and (c) wrought metal wires and appliances used in orthodon- tics and oral surgery.

Gold foil and silver amalgam are compacted directly into a cavity for restoration. Silver-amalgam alloy consists of Ag3Sn, to which has been added copper and sometimes other alloying elements. Particles of this material are agi- tated with mercury and react with it to form a plastic mass that hardens rapidly. The phase relationships in the qua- ternary Ag-Sn-Cu-Hg system involved in this hardening reaction are not yet fully understood. The phases found in dental amalgam are, however, identifiable as phases found in the corresponding binary and ternary systems.

Many of the casting alloys are gold-base, and they are commonly used in the as-cast condition. Platinum, pal- ladium, and silver are used for solid solution strength- ening; iridium and ruthenium, which are nearly insoluble in gold, are used for grain refinement. Sometimes alloys containing 5% or more of copper are age-hardened by pre- cipitation of Au~Cu. In recent years, the high cost of gold has led to the use of alloys at both ends of the silver-

palladium system. These two metals exhibit complete mis- cibility in the solid state. Cobalt-chromium-base alloys have been used for casting for several decades, though the cobalt-chromium phase diagram still has not been fully established. Recently, nickel-chromium alloys have come into wider use. For this system the equilibrium structure for the range of chromium contents normally used is a solid solution of chromium in nickel. The wrought wires used in orthodontics are of austenitic stainless steel, nitinol (TiNi), and ELGILOY ~ alloy.* Phase relationships in these systems are well established. In oral surgery, austenitic stainless steel and alloys in the nickel-chromium and cobalt-chromium systems are used predominately. Overall, it is clear that the evolution of dental alloys has tended to be empirical. In some instances their metallurgy is understood in terms of phase diagrams, but, in others, e.g., ternary and higher-order alloys based on the cobalt- chromium system, basic information needed for such un- derstanding (such as the avoidance of sigma and other embrittling phases) is still missing.

*ELGILOY~is a registered trademark ofthe ElgiloyCo.,Div.ofAmerican Gage and Machine Co.~Elgin, IL 60120.

Contributed by A. A. Johnson and J.A. Von Fraunhofer, University of Louisville, Louisville, KY 40292.