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Structural Properties and Stability of Metastable Phases in
the Zr-Nb System: Part I. Systematics of Quenching-and-
Aging Experiments
G. AURELIO, A. FERNA
´NDEZ GUILLERMET, G.J. CUELLO, and J. CAMPO
An experimental study is presented of the effect of an isothermal treatment (“aging”) at 773 K upon
the structural properties of three metastable phases formed by quenching Zr-Nb alloys from 1273 K,
viz., hcp (
␣
), bcc (

), and ⍀. Using neutron-diffraction (ND) measurements and Rietveld analysis,
the lattice parameters (LPs) and the constitution of Zr-Nb alloys with up to 18 at. pct Nb are determined.
By combining these data with the LP vs at. pct Nb relations previously determined by us on quenched
alloys, an analysis is performed of the composition changes and phase reactions occuring upon aging.
The present results open up the possibility of using quenching-and-aging experiments to gain insight
into the
␣
⫹

metastable equilibrium in the Zr-rich side of the Zr-Nb system.
I. INTRODUCTION A key problem is that the ⍀regions formed upon aging are
too small to be studied by standard metallographic tech-
T
HE
structural properties and the relative stability of the niques. As a consequence, the composition changes that are
phases formed by alloying the elements of Group IV of the expected to occur upon aging (Section V) have previously
Periodic Table (i.e., Ti, Zr, and Hf) with other transition been studied by relying on, e.g., estimates based on LP data
metals (TMs) is a matter of continuous theoretical and practi- from X-ray diffraction experiments.
[15–18]
On the basis of
cal interest. These elements present a high-temperature bcc this indirect information, the possibility of a metastable equi-
(

) phase, which transforms upon cooling into an hcp (
␣
)librium between two phases, viz.,

and ⍀, has been specu-
phase.
[1]
In their alloys with other TMs, the bcc →hcp lated upon by various authors.
[16,19]
However, in order to
transformation occurs upon quenching in a martensitic way, develop a more detailed picture of the actual processes,
when the content of the alloying element is relatively low. additional information is needed, in particular, on the reac-
In more concentrated alloys, an alternative diffusionless tions also involving the
␣
phase. Motivated by such a lack
transformation of the

phase occurs, which originates the of information, we have started a long-term systematic study
so-called “athermal” ⍀phase. This phase has been the sub- of the effects of the aging treatment upon the stability and
ject of various experimental investigations in the past.
[2]
structural properties of the metastable phases that are present
More recently, a systematic study of the ⍀phase and other in quenched Zr-Nb alloys. The distinctive feature of the
metastable phases has been carried out, which includes neu- work is the combination of extensive ND measurements of
tron-diffraction (ND) experiments in the prototype systems the LPs with estimation procedures based on previously
Zr-Nb and Ti-V,
[3–10]
as well as calculations of the electronic established correlations for structural parameters in Zr-Nb
structure in TMs and ordered alloys.
[11,12,13]
In particular, in alloys. Using these LP values, new information on the com-
Zr-Nb alloys quenched from high temperatures, the lattice position of the aged phases is obtained. As a first step, a
parameters (LPs) of the metastable phases,
␣
,

, and ⍀have series of alloys with up to 18 at. pct Nb which were quenched,
been determined as functions of composition.
[7,8]
In this aged at 773 K, and quenched again have been investigated,
way, a database has been developed, using high-quality ND and the results are reported in the present article. Further
measurements performed at the Institut Laue–Langevin in experimental studies of these alloys based on complementary
Grenoble and structure refinements based on the Rietveld characterization techniques are in progress and will be
method.
[14]
reported in forthcoming articles.
The general theme of the present article is the effect of
an isothermal heat treatment, often called “aging,” upon
those metastable phases that form by quenching. Regarding II. EXPERIMENTAL TECHNIQUES
the ⍀phase, it has long been accepted that this phase can
also be formed isothermally in alloys of Ti, Zr, and Hf.
[2]
A. Alloys, Samples, and Heat Treatments
However, the properties and behavior of such “isothermal”
⍀phases have not yet been established as a function of Four Zr-Nb alloys with nominal Nb contents of 5, 6, 10,
and 18 at. pct Nb were used in this work. One alloy (6composition as accurately as those of the athermal ⍀phase. at. pct) was obtained from Teledyne Wah Chang (Albany,
Oregon), and the remaining were prepared by melting Zr
and Nb (99.9 and 99.8 pct purity, respectively) in an arc
G. AURELIO, Graduate Student, and A. FERNA
´NDEZ GUILLERMET,
Professor, are with the Centro Atomico Bariloche and CONICET, Bariloche
furnace, on a water-cooled copper hearth, using nonconsum-
(RN), 8400, Argentina. G.J. CUELLO, Scientist, is with the Institut Laue-
able electrodes under 350 torr of Ar atmosphere. Each alloy
Langevin, F-38042 Grenoble, Cedex 9, France. J. CAMPO, Researcher, is
was remelted at least six times to favor homogeneity. The
with the Instituto de Ciencia de Materiales de Aragon, CSIC-Universidad
global composition of the alloys was determined by wave-
de Zaragoza, 50009 Zaragoza, Spain.
Manuscript submitted October 2, 2000.
dispersive X-ray (WDX) microanalysis, using pure elements
METALLURGICAL AND MATERIALS TRANSACTIONS A VOLUME 32A, AUGUST 2001—1903
as standards, in a PHILIPS* scanning electron microscope
*PHILIPS is a trademark of Philips Electronic Instruments Corp., Mah-
wah, NJ.
operating with a Microspec WDX spectrometer. The mea-
sured Nb contents were 4.7, 5.8, 9.7, and 18.0 at. pct Nb.
However, when discussing the results of the work (Sections
IV through VIII), we will refer to the nominal compositions.
We remark that this WDX technique only allows the determi-
nation of the global composition of the sample, as the volume
analyzed by the electron probe is approximately 1
3
, which
is larger than the monophasic regions in the sample, e.g.,⍀
particles with an average volume of the order of 2 ⫻10
⫺4
3
in the aged Zr-10 at. pct Nb alloy.
[20]
The average content
of O and N in the as-quenched samples is 50 and 1500 wt
ppm, respectively, determined by a fusion method using a
LECO* TC-36 analyzer. The alloys were cut into cubes with
Fig. 1—Neutron diffraction data for the alloy with 10 at. pct Nb. For the
as-quenched state, a Rietveld refinement (line) of the experimental data
*LECO is a trademark of the LECO Corporation, St. Joseph, MI. (symbols) is shown. The difference between the observed and calculated
intensities (line at the bottom), as well as the Bragg reflections of the ⍀
sides measuring about 2 mm in length, wrapped up in Ta
and bcc phases (vertical bars), is also presented. The ND spectra correspond-
foil, encapsulated in quartz under high-purity Ar, annealed
ing to aging times of 10, 40, 120, 180, and 360 min are plotted using lines.
Vertical arrows in the longest aging time spectrum indicate the Bragg
1 hour at 1273 K, and quenched in water at room temperature
reflections of the
␣
phase.
(RT) by breaking the capsule. Each alloy was divided into
six samples of about 10 g, and one of those samples was
measured in the as-quenched condition. The rest were encap- III. PHASES AND STRUCTURES IN
sulated in Vycor* glass and annealed at 773 K for 10, 40, QUENCHED ALLOYS
*Vycor姞is a trademark of Corning Inc., NY.
In this section, we briefly review the key structural infor-
mation about the metastable phases that are detected at RT120, 180, and 360 minutes. These annealings were inter-
rupted by again quenching the samples in water at RT. in quenched(q) Zr-Nb alloys, viz., the hcp formed martensiti-
cally (
␣
q
), the athermal ⍀phase (⍀
q
), and the untransformed
bcc phase (

q
). The
␣
q
phase presents an hcp structure, with
the space group P6
3
/mmc. The composition dependence of
B. Neutron-Diffraction Measurements the LPs of
␣
q
have been established by Benites et al.
[7]
in
alloys with up to 8 at. pct Nb. Their results, described by
The ND experiments were performed with the D1B two-axis the expressions
powder diffractometer at the Institut Laue–Langevin, using a
Ge monochromator (311 reflection) to obtain a wavelength of a
␣
(A
˙)⫽(3.23160 ⫾0.00001) ⫺(0.0033 [1]
1.2830 ⫾0.0005 A
˚. The flux on the sample for this wavelength ⫾0.0001) ⫻(at. pct Nb)
is 0.4 ⫻10
6
ncm
⫺2
s
⫺1
. This diffractometer is equipped with
a
3
He multidetector containing 400 cells, with an angular and
span of 80 deg. The measurements were made at RT using a c
␣
(A
˙)⫽(5.14750 ⫾0.00004) ⫺(0.0030 [2]
vanadium cylinder filled with about 10 g of the cube-shaped
sample and mounted on a rotator device. With the rotation ⫾0.0001) ⫻(at. pct Nb)
of the sample holder around its vertical axis, a very good
approximation to powder spectra was attained, as discussed will be accepted in the present study.
The athermal ⍀
q
phase can be described by a hexagonalelsewhere.
[21]
The present ND data, which amount to 24 spec-
tra, were processed with the full-pattern-analysis Rietveld lattice with three atoms per unit cell. The atomic positions
are (0, 0, 0), (1/3, 2/3, 1/3 ⫹z
⍀
), and (2/3, 1/3, 2/3 ⫺z
⍀
),method, using the program Fullprof.
[22]
The precise value of
the neutron’s wavelength and the zero point of the diffraction where z
⍀
(0 ⱕz
⍀
ⱕ1/6) is a parameter that allows a
continuous description of the bcc →⍀transformation. Inangle 2
were determined using Al
2
O
3
to calibrate. The follow-
ing parameters were determined for each alloy: the LPs of the the so-called “ideal” ⍀phase, z
⍀
⫽1/6 and the inner atoms
collapse into the central atomic plane, which correspondsbcc, hcp, and ⍀phases; the relative amount ( f) of each phase;
and the internal parameter (z
⍀
)ofthe⍀phase,which isdefined to a hexagonal symmetry described by the space group P6/
mmm (Figure 2). This structure is observed in pure Zr andin the next section.
As an example, we present in Figure 1 the ND data obtained Zr-rich alloys.
[8]
However, in more concentrated Zr-Nb
alloys, the collapse of the inner atoms is not complete (0 ⬍for the alloy with 10 at. pct Nb. For the as-quenched state,
we show a Rietveld refinement (line) of the experimental data z
⍀
⬍1/6), and, in such a case, the structure has a trigonal
symmetry which is described with the space group P3m1.(symbols). The difference between the observed and calculated
intensities (line at the bottom), as well as the Bragg reflections The composition dependence of the a
⍀
,c
⍀
, and z
⍀
parame-
ters has been established by Benites and Guillermet,
[8]
andof the ⍀and bcc phases (vertical bars), are also presented.
The ND spectra corresponding to aging times of 10, 40, 120, the reader is referred to their article for a detailed analysis
of the experimental trends.180, and 360 minutes are plotted using lines.
1904—VOLUME 32A, AUGUST 2001 METALLURGICAL AND MATERIALS TRANSACTIONS A
Fig. 2—The unit cell of the hexagonal, so-called ideal ⍀phase.
The LP of the untransformed

phase, i.e.,

q
, as a function
Fig. 3—Phase fractions of the
␣
q
,

q
, and ⍀
q
phases in quenched Zr-Nb
of the Nb content has been determined using ND techniques
alloys, determined by ND measurements as a function of Nb content (open
by Grad et al.
[5]
and Benites et al.
[7]
The composition depen-
symbols). The phase fractions determined by Grad et al.
[6]
in a Zr-9.7 at.
pct Nb alloy using time-of-flight experiments are also shown. The dashed
dence for

q
proposed by Grad et al. and corroborated by
lines are only guides to the eye (cf. Section IV).
Benites et al.,viz.,
␣

(A
˚)⫽(3.5878 ⫾0.0007) ⫺(0.00288 [3]
⫾0.00003) ⫻(at. pct Nb)
will be adopted in the present work.
IV. CONSTITUTION OF QUENCHED ALLOYS
A key step of the present study is to establish the relative
amount of each of the metastable phases as a function of
composition after quenching. These quantities, denoted by
f, will be referred to in the following text as “phase fractions.”
A variety of experimental difficulties usually make the deter-
mination of the phase fractions a nontrivial task, which
explains the general lack of information on these quantities
for the alloys of interest here. In diffraction experiments,
the mass fraction of each phase is related to the relative
intensities of its Bragg reflections. In determining fby ana-
lyzing diffraction data, overlapping peaks must then be sepa-
rated, and various factors must be taken into account which
affect these intensities. The ND measurements in a high-flux
diffractometer and structure refinement with the Rietveld
method
[14]
allowed us to significantly alleviate these diffi-
culties, by accounting for the effect of, e.g., preferred orienta-
tions, correct alignment of the specimen and beam, and
absorption effects.
In Figure 3, we present our results concerning the phase
fraction of
␣
q
,

q
, and ⍀
q
as a function of the Nb content
in a series of quenched alloys, at RT. Three composition
ranges may be distinguished in Figure 3, viz., (1) between
0 and about 6 at. pct Nb, the alloys present mainly the
␣
q
phase, (2) between 6 and 15 at. pct Nb, varying amounts of
⍀
q
are detected, and (3) for at. pct Nb ⬎15, the dominant
Fig. 4—Phase fractions of (a)
␣
,(b)⍀, and (c)

phases in the Zr-Nb
phase is

q
. The dashed lines in Figure 3 are only guides
alloys with 5, 6, and 10 at. pct Nb as a function of aging time, determined
to the eye. The high-Nb part of the curves was drawn in
by ND measurements after quenching, aging at 773 K, and quenching
accord with the expected behavior of the system i.e.,an
again. Open symbols at t⫽0 correspond to the alloys in the as-quenched
increase in the phase fraction of

q
and a decrease in the
state. The lines are only guides to the eye.
amount of ⍀
q
with increasing levels of atomic percent Nb.
[16]
The phase fraction of ⍀
q
shows a maximum at about 9
at. pct Nb, which is in reasonable agreement with indirect good agreement with the present data. For the aging experi-
ments, we selected only four alloys among those showninformation from the hardness measurements by Cometto
et al.
[16]
Finally, in Figure 3, we include the phase fractions in Figure 3, which were considered representative of the
behavior of the system in the interesting composition ranges,determined by Grad et al.
[6]
in a Zr-9.7 at. pct Nb alloy
using time-of-flight ND experiments. Their results are in viz., alloys with 5, 6, 10, and 18 at. pct Nb.
METALLURGICAL AND MATERIALS TRANSACTIONS A VOLUME 32A, AUGUST 2001—1905
Fig. 5—Phase fractions of (a)
␣
,(b)⍀,(c)

, and (d)

2
in the Zr-18 at. pct Nb alloy as a function of aging time, determined by ND measurements after
quenching, aging at 773 K, and quenching again. Open symbols at t⫽0 correspond to the alloy inthe as-quenched state. The lines are only guides to the eye.
V. CONSTITUTION OF THE QUENCHED/ phase fraction of
␣
(Figure 4(a)) remains essentially con-
stant, and the ⍀
q
phase (Figure 4(b)) formed in the firstAGED/QUENCHED ALLOYS quenching step disappears during aging, while some

a
is
A. General Considerations formed (Figure 4(c)). The constitution of the samples aged
for 6 hours and quenched consists of a two-phase state of
It is generally accepted
[16,18,19]
that the aging (a) process
␣
a
⫹

a
.
induces composition changes in the

and ⍀phases. In Upon aging of the alloy with 6 at. pct Nb, some ⍀
a
particular, the ⍀phase formed isothermally at the aging (Figure 4(b)) forms during the initial stages of aging (10
temperature (which in the remainder of this article will be minutes), but disappears after longer aging times. A certain
indicated as ⍀
a
) is expected to have a lower Nb content than amount of

a
phase (Figure 4(c)) also forms and remains
⍀
q
. A key result of the present work is that
␣
q
undergoes, untransformed after quenching. As a consequence, the sam-
on aging, analogous composition changes. Therefore, the ples subjected to the longest aging times (6 hours) and
solute-depleted
␣
phase will be indicated as
␣
a
. These com- quenched show a two-phase state of
␣
a
⫹

a
.
position changes in
␣
and ⍀imply that the Nb content of In the case of the alloy with 10 at. pct Nb, no
␣
q
phase
the

phase should increase, and this enriched

phase will was present in the as-quenched state (Figure 4(a)). The
␣
a
be called

a
.phase is detected in significant amounts in the samples aged
For three of the four alloys studied here, the assumption for 2 hours or longer, as indicated by the new Bragg reflec-
of a homogeneous

a
phase, characterized by a single LP tions, which appear in the ND spectra shown in Figure 1.
value was sufficient to account for the experimental ND The phase fraction of
␣
a
remains nearly constant at the
spectra. The analysis of the Zr-18 at. pct Nb alloy indicated, longest aging times. The ⍀
a
phase (Figure 4(b)) is detected
however, that significant composition differences might be only in the samples aged for 10 and 40 minutes. For these
induced in the

phase by the formation of
␣
a
. The way in two samples, some ⍀
q
is also formed from

a
upon the
which this feature was accounted for phenomenologically final quenching step from 773 K (Figure 4(b)).
in the Rietveld analysis is discussed in detail in Section V–C.
Finally, we remark that in the final quenching step of the
aged alloys, part of the

a
phase might transform athermally C. Phenomenological Account of Composition
into ⍀
q
. As shown subsequently, this is the case of alloys Differences
in which the Nb content of

a
is lower than about 20 at.
pct Nb. On the contrary, no change is expected to occur in Preliminary analyses of the ND spectra corresponding to
the longest aging times, based on including the usual ⍀
q
,the ⍀
a
phase on quenching from the aging temperature to RT.

a
, and
␣
a
phases, did not yield, for the Zr-18 at. pct Nb
alloy, Rietveld fits with the same quality as those for the
B. Effect of Aging Time upon Phase Fractions other alloys. In addition, the LPs of the ⍀
q
phase so obtained
were not consistent with those expected from the composi-In Figure 4, we present the phase fractions as a function
of aging time for the alloys with 5, 6, and 10 at. pct Nb, as tion of the

phase. Systematic comparisons between the
experimental and calculated spectra suggested that the prob-determined after quenching, aging at 773 K, and quenching
again. Concerning the 5 at. pct Nb alloy, we find that the lem was caused by a poor account of the peaks corresponding
1906—VOLUME 32A, AUGUST 2001 METALLURGICAL AND MATERIALS TRANSACTIONS A
to the

a
phase. Furthermore, it was found that the intensity
of the

-phase reflections in the aged alloys could be more
accurately represented by the sum of two almost completely
overlapping peaks for a bcc structure. This was taken as an
indication that significant composition gradients might exist
in the

a
phase of this alloy, which could be represented by
two characteristic Nb contents, viz., a high one, associated
with regions closer to the
␣
a
particles, and a low one, typical
of the rest of the

a
matrix. In line with this tentative picture,
such low-Nb regions were described in the fitting process
by a bcc phase, called

a
2
, whose composition was not ex-
pected to differ significantly from the composition of the
as-quenched

phase, whereas the high-Nb regions were
represented by a

a
phase, as in the other alloys. Since the
analysis performed in this way led to a good agreement
between experimental and calculated spectra, the results to
be presented in the following text correspond to Fullprof
[22]
fits of the Zr-18 at. pct Nb alloy, based on considering that,
in addition to
␣
a
and ⍀
q
, a bcc phase with composition
gradients was present, whose representative Nb contents
were accounted for phenomenologically by those of the

a
and

a
2
regions in the Fullprof calculations. Direct measure-
ments of the Nb contents in the

phase are in progress,
which will allow a critical test of such inferred composition
gradients (Section VIII). In Figure 5, the phase fractions
obtained in the fits are presented. While the fvalue of

a
remains essentially constant in samples aged for more than
120 minutes, the phase fractions of
␣
a
and

a
2
show a monot-
onous increase and decrease with aging time, respectively,
suggesting that this alloy might be approaching a two-phase
state of
␣
a
⫹

a
, like the alloys discussed in Section V–B.
Fig. 6—(a) through (c) The a
␣
and c
␣
LPs and the c
␣
/a
␣
ratio of the
␣
VI. EFFECTS OF AGING UPON THE
phase determined in the quenched/aged/quenched alloys with 5, 6, 10, and
STRUCTURAL PROPERTIES
18 at. pct Nb, as functions of aging time. The values plotted at t⫽0
correspond to the LPs of
␣
in the as-quenched condition. The dashed lines
In Figures 6(a) and (b), we present the LPs of the
␣
phase
represent the LP values of the
␣
phase of Zr.
[24]
The dotted lines are only
determined in the quenched/aged/quenched alloys with 5,
guides to the eye.
6, 10, and 18 at. pct Nb, as functions of the aging time. The
values plotted at t⫽0 correspond to the LPs of
␣
in the
as-quenched condition. The a
␣
and c
␣
parameters increase becomes essentially constant at long aging times. This fea-
with aging time, approaching those of pure-
␣
Zr,
[24]
which ture is illustrated in Figure 1 for the Zr-10 at. pct Nb alloy.
are indicated by the horizontal (dashed) lines. The (1 1 0) bcc peak at 2
⬇30 deg shifts to the right for
In Figures 7(a) through (c), we plot the LPs of the ⍀aging times of 10 and 40 minutes, but remains essentially
phase vs aging time for alloys with 6, 10, and 18 at. pct Nb, fixed for longer aging times.
respectively. The dashed lines in these graphics represent
the LPs of the ⍀phase in pure Zr.
[25]
The phase fraction
of ⍀
a
in the Zr-18 at. pct Nb alloy was very small (Section VII. ESTIMATION OF COMPOSITION
V), and its LPs could not be determined. Therefore, this CHANGES UPON AGING
phase was described in the Fullprof calculations using the
LP values for ⍀
a
obtained in the alloys with 6 and 10 at. In the present section, some indirect information about
the composition changes occurring upon aging will bepct Nb, which were very close to those of ⍀Zr.
[25]
Concern-
ing the z
⍀
parameter, we remark that in all cases where the obtained by an estimation procedure, which is based on
assuming that the LP vs atomic percent Nb relations deter-phase fraction of ⍀
a
was sufficiently high, our analysis did
not show any significant deviation from the z
⍀
⫽1/6 value. mined for
␣
q
and

q
in quenched alloys
[7]
also apply to the
␣
a
and

a
aged phases.Accordingly,values ofthe NbcontentIn Figures 8(a) through (d), we plot the LP of the

phase
determined in the present alloys as a function of aging time. for
␣
and

were obtained by combining the LP vs time
results from Section VI with the LP vs atomic percent NbFor the alloy with 18 at. pct Nb, the composition values
corresponding to the

a
and

a
2
regions (Section V–C) are information presented in Section III.
In Figure 9(a), we plot, using symbols, the estimated Nbpresented. The dashed lines in these graphics represent the
LPs of a

phase with a Nb content equal to the as-quenched content of the

phase of the present alloys as a function
of the aging time. The values for t⫽0 correspond to the

phase. The a

value of the

a
phase is significantly lower
than that of the as-quenched

phase, and the difference

q
phase. At the longest aging times, the

a
compositions
METALLURGICAL AND MATERIALS TRANSACTIONS A VOLUME 32A, AUGUST 2001—1907
Fig. 7—The a
⍀
and c
⍀
LPs and the c
⍀
/a
⍀
ratio of the ⍀phase determined in alloys with (a) 6 at. pct Nb, (b) 10 at. pct Nb, and (c) 18 at. pct Nb, as
functions of aging time. Open symbols correspond to the ⍀
q
phase and filled symbols to the aged ⍀
a
phase determined by ND measurements after
quenching, aging at 773 K, and quenching again. The dashed lines represent the LPs of the ⍀phase in pure Zr.
[25]
The solid lines connecting symbols are
only guides to the eye.
estimated from the LPs of the alloys with 5, 6, and 10 at. estimation of theNbcontent for the ⍀
a
phase will be consid-
ered in the next section.pct Nb are essentially the same. The upper limit of the Nb
content in the

a
regions of the aged

phase in the Zr-18
at. pct Nb alloy also reaches the same value. The lowest
limit, corresponding to what we have called the

a
2
regions VIII. CONCLUDING DISCUSSION AND
in this alloy (Figure 9(b)), is similar to that of the initial

q
REMARKS
phase at the beginning of the aging (dashed line). These The picture of the changes occurring upon aging which
results are consistent with the possible existence of composi- emerges from the present study may be summarized by
tion differences in the aged

phase, which was hypothesized referring to a general reaction involving metastable
in Section V–C. In addition, Figure 9 suggests that such phases, viz.,
differences in the Nb content are slowly decreasing with the
aging time, as expected. New experiments, involving even
␣
q
⫹

q
⫹⍀
q
→
short aging times
␣
a
⫹

a
[4]
longer aging times and other temperatures, will help us to
further test these ideas. ⫹⍀
a
→
long aging times
␣
a
⫹

a
The use of the a
␣
vs atomic percent Nb and c
␣
vs atomic
percent Nb formulae did not yield unique values for the The present results indicate that the Nb content of

a
is
larger than that of

q
, as expected from an analysis basedatomic percent Nb vs aging-time relations of the
␣
a
phase.
As a consequence, in Figure 10, we plot using symbols what on a qualitative Gibbs energy vs composition diagram for
these alloys.
[16]
In addition, we find that the Nb content ofwe considered to be the maximum probable Nb contents in
␣
a
as a function of aging time. These graphics indicate that
␣
a
is significantly lower than that of
␣
q
. In fact,
␣
a
approaches the range of compositions that characterises thethe Nb content in
␣
a
for the alloys with 6 ⱕat. pct Nb ⱕ
18 is lower than about 1 at. pct. This suggests that the
␣
phase in equilibrium with the Zr-rich

phase in the phase
diagram.
[23]
Another interesting observation concerns thecomposition of the
␣
a
phase approaches, upon aging, the
low Nb contents typical of the
␣
phase in equilibrium with composition of the

a
phase coexisting with
␣
a
, in alloys
subjected to the longest aging treatments. According to thethe Zr-rich

phase, in accord with those one would get
by an extrapolation in the Zr-Nb phase diagram.
[23]
The present work, the same composition value is approached
1908—VOLUME 32A, AUGUST 2001 METALLURGICAL AND MATERIALS TRANSACTIONS A
Fig. 8—The LP a

of the

phase determined in alloys with (a) 5 at. pct Nb, (b) 6 at. pct Nb, (c) 10 at. pct Nb, and (d) 18 at. pct Nb, as functions of
aging time. The values plotted at t⫽0 correspond to the LP of

in the as-quenched condition. The dashed lines represent the LP corresponding to a

phase with 5, 6, 10, and 18 at. pct Nb, respectively. The solid lines are only guides to the eye. The constitution of the alloy with 18 at. pct Nb is discussed
in detail in Section V–C.
(Figure 9(a)), in spite of the differences in the initial compo-
sition of the alloy. In view of this fact, it is tempting to
explore the possibility that the
␣
a
and

a
phases might be
approaching metastable equilibrium conditions at 773 K. As
a first step in testing this idea, we made an approximate
calculation of the phase fractions (f
eq
) that one would get
if the metastable
␣
a
/

a
equilibrium condition holds exactly.
Assuming, for the sake of simplicity, that the Nb content of
␣
a
is 1.0 ⫾0.5 at. pct, taking for

a
the average limiting
composition of 32 ⫾1 at. pct Nb from Figure 9(a) and
applying the lever rule, we obtain for the alloys with 5, 6,
and 10 at. pct Nb, f
eq
␣
values of 0.88 ⫾0.09, 0.85 ⫾0.08,
and 0.72 ⫾0.07, respectively. These numbers are to be
compared with those obtained in the present Rietveld analy-
sis of ND data, viz., 0.92 ⫾0.02, 0.77 ⫾0.02, and 0.64 ⫾
0.02, respectively. We conclude that the present results do
not contradict the idea that metastable equilibrium conditions
between
␣
a
and

a
could be approached at 773 K for aging
times longer than 6 hours. This hypothesis is currently being
tested by us.
Finally, we return to the properties of the ⍀
a
phase. In
previous studies in our group,
[3,6]
an attempt was made to
estimate the composition of ⍀
a
by solving a mass-balance
type of relation involving the phase fractions, the composi-
tion of the alloy, and the composition of the

a
phase esti-
mated as in Section VII. However, the results of such a
procedure were considered too uncertain for the present
purpose and were not applied to the present article. Neverthe-
less, we note that the LP results presented in Figure 7 are
consistent with an ⍀
a
phase depleted in Nb, which is in
Fig. 9—(a) The estimated Nb content of the

phase of alloys with 5, 6,
10, and 18 at. pct Nb as a function of aging time. The values plotted at
qualitative agreement with our previous results.
[3,6]
A direct
t⫽0 correspond to the

q
phase. (b) The lowest limit of the Nb content
determination of the ⍀
a
composition in aged alloys and of
for the

a
phase, corresponding to what we have called

a
2
in the Zr-18
the composition gradients in

a
which were inferred from the
at. pct Nb, as a function of aging time. The dashed line represents the
present results is now in progress, using energy-dispersive
composition of the as-quenched

phase. The solid lines are only guides
to the eye.
spectroscopy in a transmission electron microscope.
[20]
METALLURGICAL AND MATERIALS TRANSACTIONS A VOLUME 32A, AUGUST 2001—1909
Fig. 10—The maximum estimated Nb content of the
␣
phase in alloys with (a) 5 at. pct Nb, (b) 6 at. pct Nb, (c) 10 at. pct Nb, and (d) 18 at. pct Nb as
a function of aging time. The dotted lines are only guides to the eye.
8. G.M. Benites and A. Ferna
´ndez Guillermet: J. Alloys Compounds,
ACKNOWLEDGMENTS
2000, vol. 302, p. 192.
9. G. Aurelio and A. Ferna
´ndez Guillermet: Scripta Mater., 2000, vol.
We thank the support of the Spanish Cooperation Research
43 (7), p. 665.
Group, Institut Laue-Langevin, which allowed us to use the
10. G. Aurelio, A. Ferna
´ndez Guillermet, G.J. Cuello, and J. Campo:
D1B neutron diffractometer. We also thank Carlos Ayala and
Centro Ato
´mico Bariloche, Institut Laue-Langevin and Instituto de
Ernesto Aranda (Metallurgy Division, CAB-CNEA) who
Ciencia de Materiales de Arago
´n, Bariloche, unpublished research,
2001.
helped us with the preparation of alloys and samples.
11. J.E. Garce
´s, G.B. Grad, A. Ferna
´ndez Guillermet, and S.J. Sferco: J.
This work is part of a research project supported by Agen-
Alloys Compounds, 1999, vol. 287, p. 6.
cia Nacional de Promocio
´n Cientı
´fica y Tecnolo
´gica (Argen-
12. J.E. Garce
´s, G.B. Grad, A. Ferna
´ndez Guillermet, and S.J. Sferco: J.
tina), under Grant No. 03-00000-00688. One of us (GA)
Alloys Compounds, 1999, vol. 289, p. 1.
acknowledges a grant-in-aid from Sigma Xi, The Scientific
13. G.B. Grad, P. Blaha, J. Luitz, K. Schwarz, A. Ferna
´ndez Guillermet,
and S.J. Sferco: Phys. Rev. B, 2000, vol. 62, p. 12743.
Research Society.
14. The Rietveld Method, R.A. Young, ed., Oxford University Press, New
York, NY, 1995.
15. B.A. Hatt and J.A. Roberts: Acta Metall., 1960, vol. 8, p. 575.
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1910—VOLUME 32A, AUGUST 2001 METALLURGICAL AND MATERIALS TRANSACTIONS A
