THE w-PHASE IN ZIRCONIUM BASE ALLOYS*
B. A. HATT and J. A. ROBERTS?
The metastable o-phase in zirconium base alloys has been found to be truly hexagonal with c/cl -= 0.622 h 0.002. The orientation relationships with respect to the parent p-phase (b.c.c.) are
The interpretation of X-ray data from high solute content alloys quenched from the p-phase indicates
that the w formed during quenching is heavily faulted. The o structure in this state is designated diffuse
w. A model for the @ + o transformationwhich satisfactorily accounts for the observed diffraction effects
is developed. This is based on the gliding of { 112)~ planes in (111 )b directions in a distinct sequenoe. The
magnitude of the glide component is realistically altered to account for intensity differences in the diffractions from diffuse o and bulk w.
LA PHASE w DANS LES ALLIAGES DE ZIRCONIUM
On a montre que la phase metastable w dans des alliages de zirconium Btait hexagonale avec un
rapport c/u = 0,622 + 0,002. Les relations d’orientation avec la phase ,5’ (b.c.c.) sont
(0001)~ 11 (lll)p (ario), 11 (iOl),.
L’interpretation d’essais aux rayons X a partir d’alliages riches en elements en solution trempes a partir de la phase B, indique que la phase w form&e au tours de la trempe contient de nombreuses fautes d’empilement.
La structure o dans cet &tat est indiquee comme phase w diffuse. Un modele pour la transformation /? + o qui satisfait l’ensemble des effets de diffraction observes, a
6ti: developpe. 11 est base SUP le glissement des plans {112}p dans des directions (111)~ suivant une sequence definie.
La grandeur de la composante du glissement peut &tre alteree, ce qui explique les differences
d’intensite 101-s de la diffraction de la phase diffuse w ou de la phase w massive.
DIE o-PHASE IN LEGIERUNGEN rlUF ZIRKON-BASIS
Die metastabile o-Phase van Legierungen auf Zirkon-Basis erwies sich als echt hexagonal mit c/n = 0,622 or 0 002. Die Orientierungsbeziehungen in Bezug auf die P-Phase (kubisch-raumzentriert; aus ihr entsteht die w-Phase) sind
(OOOl), i: (111)~
(2iTO), /i (iOl)fi.
Die Deutung der Rontgenmessungen an Legierungen mit hohem Zusatzgehalt, die van der P-Phase
abgeschreckt wurden, zeigt, da6 die beim Abschrecken gebildete o-Phase sehr fehlerhaft ist. Die w- Struktur wird in diesem Zustand als diffus bezeichnet. Es wird ein Model1 fur die Umwandlung /l - o entwickelt, das die beobachteten Beugungseffekte zur Geniige erklart. Es basiert darauf, da13 {112},-
Ebenen in bestimmter Reihenfolge in (111)~.Richtungen gleiten. Die GrGSe der Gleitkomponente wird der Wirklichkeit so angepa& da13 die Intensitatsdifferenzen der Interferenzen van diffuser und massiver o-Phase erkliirt werden.
INTRODUCTION stages of ageing. This interpretation leads to the The quenched high temperature /?-phase of certain advancement of a possible mechanism for the forma-
titanium and zirconium alloys transforms via an tion of the ru-phase. intermedia,te phase, designated CO, on ageing to the equilibrium state. Under certain conditions the o-
1. THE CRYSTAL STRUCTURE OF THE METASTABLE o-PHASE
phase may be obtained in a state of metastable equilibrium. The first part of this paper concerns a
Previous workers have made crystallographic
detailed crystallographic study of the metastable W- studies of the m-phase as it occurs in titanium base
phase in a Zr-7 at.% vanadium alloy. The second alloys. Austin and Doig(l) suggest that the cu_phase is
part of the paper is devoted to the interpretation of the b.c.c. with side three times that of the basic /I b.c.c.
diffuse co diffractions observed in high solute content cell. Silcock et CL@) and Bagaryatskii et ~2.‘~’ indepen-
alloys in the as-quenched condition and in the early dently proposed a hexagonal structure based on the hexagonal (rhombohedral) unit cell, which is an alter- native unit cell for a b.c.c. lattice.
* Received October 13, 1959. The crystal
t Fulmer Research Institute Limited, Stoke Poges, Bucks. structure of the w-phase in zirconium base alloys to be
ACTA METALLURGICA, VOL. 8, AUGUST 1960 575
576 ACTA METALLURGICA, VOL. 8, 1960
presented here is based on that of Silcock and Bagary-
at&ii and their interpretat.ion is briefly described.
Figure l(a) shows how the three possible unit cells
for a b.c.c. lattice are related. The b.e.c. lattice is out- lined by the tine lines, the heavy lines show the rhom-
bohedral cell and the hatched lines the base of the
hexagonal cell. Fig. l(b) is a projection of the atoms
on to a flllla plane showing the hexagonal cell which
is oriented with respect to the ,8 cell with
(Oool)h,x / / (lll)b.c.c.
(2TTo)hex / 1 (ioi)b.c.c.
thus there are four orientations of the hexagonal cell,
each with a (0001) hex parallel to a (lll),,,~,, of the
8. The cell parameters are related as follows:
a - & ab.c.c. hex -
Chex = id3 ab.c.c.
. * * e/a = &(3/2) = 0,613.
The atomic positions in the hexagonal cell are (O,O,O);
i(%f&. Both Silcock and Bagaryatskii chose the above
hexagonal cell with c/a * 0.613 and proposed new atomic positions:
(O,O,O): Ct($>t,Bf
(O,O,O); &(-&$,0.52)
respectively for the w-phase. These two structures
FIG. 1. (a) Three possible unit cells for a body-caked cubic structure.
---- b.c.c. lattice - Rhombohedral lattice --i-j-i-/ Base of hexagonal lattice
(b) A projection of the atoms in a b.c.c. structure onto
w 0 Atom at 0’00 000 x Atom at 34% %f& + Atom at 384 ff&
The atoms numbered are common to both (a) and (b).
differ in that the atoms near the plane z = 4 lie in the
plane for Silcock’s structure but alternately 0.02 above
and below in Bagar~atskii’s structure.
It can be shown that provided c/a = 0.613 and that
the four hexagonal orientations have developed to the
same extent, then both the cubic and hexagonal inter-
pretations of w will show cubic Laue symmetry. Thus it is only possible to distinguish between the cubic and
hexagonal structures by detailed intensity measure-
ments. However if c/a # 0.613 extra diffractions will
occur which provide an alternative method of dis-
criminating between the two structures.
Preliminary workc4) on polycrystalline material by
the present authors showed that the o ~~ra~tions in
D-base alloys could be best expIained on a hexagonal
cell with c/a > 0.613 and this interpretation has been
verified in detail by the single crystal studies to be
described.
Single crystals were oriented from Laue photo-
graphs with (OOl), coincident with the oscillation
axes and (loo), coincident with the incident X-ray beam. Since (u is oriented with respect to @, a
specimen which is fully transformed to u) still shows
cubic Laue s~rmrnetr~ and can thus be oriented in
terms of the original /3. Oscillation and Weissenberg
photographs were taken with filtered CuKa and mono-
chromatic MoKrx radiation with the (loo), oscil-
lating from 0” to 40” to the direct X-ray beam.
The diffractions recorded in this way did not lie on
straight layer lines as would be expected if m were
cubic or hexagonal with the ideal value of e/a = 0.613.
Since Debye-Scherrer photographs from polycrystal-
line material had indicated a hexagonal cell with
~/a > 0.613 and equal to 0.622 in the metastable state,
the single crystal diffractions were compared with
those which would be obtained from four orientations
of a hexagonal cell with c/a = 0.622. The diffractions
were first indexed on a b.c.c. cell with lattice parameter
three times the ,!Y lattice parameter. These cubic
indices were then transformed to hexagonal indices
corresponding to t,he hexagonal orient~atiolls with
(OOOl), ;; (ill),
(ziio~, i j (ioi ja and
a,=1/2a c, 0’ = @,J%! ap by the matrix
i.-----+ Hexagonal
HATT AND ROBERTS: w-PHASE IN Zr ALLOYS 577
FIG. 2. Oscillation photograph of a single crystal of Zr-7 at. % V with filtered CuKcr radiation. The crvstal oscillated- about (OOl)b with the (100)~ oscillated 0 -+ 46’ to the direct X-ray beam. The crystal was water quenched after 2 hr at 920% and then aged
30 min at 400°C.
These hexagonal indices were then retransformed to
indices corresponding to cubic axes, parallel to the
B axes, but related to the hexagonal cell by
a, = 45 a’ B
e, = 0.622 u’~ # +l/3 as
where aIs is the lattice parameter of a new cubic cell
and the transformation matrix is
,-----+ Cubic
T 1 1.97
i 2 1.97
2 1 1.97 .
The difference between the two sets of cubic indices
indicates the change in the positions of the diffractions
resulting from c/a changing from 0.613 (ideal) to 0.622.
On oscillation photographs about (001 ),, the axial
ratio change shows as small deviations of the dif-
fractions from the straight layer line positions, and
the separation of superimposed diffractions. Fig. 2 is
a film taken with CuKa of a Zr-7.0 at.94 V specimen
aged 8 hr at 400°C and consisting of -98 per cent co.
Table 1 gives the analysis of this 6lm. Here the
(hkl) cubic indices for c/a = 0.613 are compared with
those for c/a = 0.622 together with the observed l-
indices. The agreement between the observed values
and those corresponding to c/a = 0.622 is considered
adequate proof that ,!? transforms to four hexagonal
cells with c/a - 0.622 and oriented with respect to
fi with
(OOOl), /I (ill),
(2iiO), / 1 (TOl),.
Table 1 also gives the P2 values for the atomic
positions
(O,O,O); i (g&B).
Apart from angular factors these values are propor-
tional to the intensities of the diffractions. No detailed
intensity measurements have been made but visual
inspection indicates that the intensities calculated
from these atomic positions give satisfactory agree-
ment with observed intensities. Some idea of the
permissible movements in the c direction of the atoms
in the positions &(I,+,*) as visualized by Bagary-
atskii can be seen from Table 2, where the intensities
of the zero layer diffractions have been calculated for
atomic positions (O,O,O); *($,Q,0.52). Hence the
original (12,0,0), (cubic indices) which consists of the
following two diffractions when c/a = 0.622
2(a), Table 2, (11.92, 0.08, 0.08)
(11.92, 0.08, 0.08)
2(b), Table 2, (11.92, 0.08, 0.08)
(11.92, 0.08, 0.08)
will have zero intensity for atomic positions (O,O,O);
&($,$,+) but will have an intensity proportional to
0.44 for atomic positions (O,O,O); f(g,$,0.52) This
intensity is greater than half the intensity of the
adjacent (4223) diffraction. A very weak single dif-
fraction is recorded near this position on some films
although it has not the above intensity and is not
split. It is thought that this weak diffraction corre-
sponds to a very small amount of p. Thus there is no
evidence to indicate rumpling of the atoms near the
plane z = 4.
The X-ray examination of single crystal specimens
of aged Zr-Nb alloys in the range 8-20 at.% Nb
revealed that the metastable cc)-phase has an identical
crystal structure to that described above for the Zr-7
at. y0 V alloy. The axial ratio was found to be 0.622 &
0.002 but the lattice spacing values are dependent on
alloy composition and ageing temperature.
Additional evidence supporting the hexagonal version of the crystal structure has been obtained from
a Zr-8 at.% Nb single crystal specimen which had
been strained at 400°C while in the metastable cu
condition. On examination at room temperature it
was found that the cu developed on only two of the
four possible orientations.
6-W PP.)
578 ACTA METALLURGICA, VOL. 8, 1960
TABLE 1
--:;:~qzY&:&, 1
_
Zero layer, left-hand side of direct beam
B 3 4
1, 2, 3, and 4
8.94 2.94 0.06 8.96 3.04 , 0.04 0*
G 1
930 930 930 930 370
12,0,0 12,0,0 12,0,0 12,0,0
400 ~___
12,60 12,60 12,so 12,60 420
0 4 0 4 9
:
: 9
--
1 4 1
:
-_- 2.94 0.06 3.04 1 0.04 8.96
__-
11.94 11.94 11.94 11.94
___-
11.91 11.96 11.91 11.96
0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06
Weak diffractions on some films
1 0 25
3 4
1, 2, 3 and 4
5.91 6.04 5.91 6:04
0.09 ~ 0.10
0.04 0.09 1 0.100* 0.04 0
--. 3b 4223
a 4621 e ~ 2243
4621
1
: 4
1, 2, 3and4 I I
1st layer, left-hand side
I 0.94 0.92
0.94 0.94 I 0.92 0.96 0.93 1.06 1.06 -
1.04 1.05 0.94 0.94 0.93
0.91 0.87 1.09 1.09
I /
741 6.94 lO,i,l 9.94 10,&l 9.94 10,5,1 9.96 11,2,1 10.94 ll,~,l 10.94 11,4,1 10.96 13,2,1 12.94 13,2,1 12.94 13,4,1 12.91 11,8,1 10.91
3.s 0.94 0.94 5.04 1194 1.94 4.04
2 2172
2.06 2.06 3.91 7.91
7a ’ 4313 b 4133
i 1
2nd layer, left-hand side
2704 2.04 3.94 2.06 4.91 1.91 0.94 2.06 0.94 2.06
2.04 2.07 1.90
2.02
440T 4 4 I lo,?,2 ~ 9.96 4222 4 10,4,2 9.94
3 3i23 1 1 11,3,2 1
10.91 4 3 13,1,2 12.94
4 x
13,1,2 i 12.94
3rd layer, left-hand side
903 8.94 903 8.94
3 4 903 ; 8.96 4 4 903 8.96
1, 2, 3 and 4 9 301 I
0.06 0.06 0.06 0.06
2.94 2.94 3.04 3.04
2.91 2.94 3.06 3.04 2.94
I 3.00
2.91 3.06 2T94 3.04
2.89 - x : 12,33 12,33 11.91 11.94
3 0 12,33 11.94 4 4 12,33 11.96 1 0 12,33 11.94
: 4 1 12,33 12,33 11.92 11.96 4 0 12,33 11,94
3b I 3033 3522 2352
a ( 5501 b 3252
3303
;4 0557 5322
2.99
2.91 2.89 3.04 2.99
2.94 I -
3.06 2.91 3.04 3.06
- * Mean of two overlapping diffractions with I indices f 0.04 for diffractions with Identity No. la and similarly for diffraction
3a.
HATT AND ROBERTS: w-PHASE IN Zr ALLOYS 579
TABLE 2 ~~~_. ___~
I
Ident. No. hkl cubic hkl cubic c/a = 0.622 F= c/a = 0.613 z = 0.52
Zero layer, left-hand side of direct beam
930 3722 ~ 1 8.92 1 930 3411 2 8.96
930 1232 3 8.92 930 3417 4 8.96 ~
__~. 0.22) 0.22 1 044 .
Zero layer, right-hand side of direct beam
la b a c
2a b a c
I
990 990 990 3630 3 990 3033 4
12,6,0 4261 12,6,0 4223 1 B 12,6,0 2641 3 12,6,0 ) 4223 4
Atomic positions (O,O,O); -+(%,j,z)
9 i 8.88
0 0112
i.12
11.96 11.88 11.96 11.88
I
Rrom the above results it may be concluded that
(1) The metastable w-phase in aged Zr base alloys
has a hexagonal crystal structure with axial ratio
c/a = 0.622 & 0.002 for all alloys examined. The
lattice constants are approximately a, = 5.02 and
G, = 3.00 A, varying slightly with alloy composition
and ageing temperature.
(2) The w-phase is oriented with respect to the /3-
phase according to the relationships
(0001)” /I W),
(2110)” 11 @qP
(3) The original /3 transforms to the four possible
orientations of hexagonal o without showing pre-
ference for a particular orientation, except when the
specimen is subjected to external strain.
(4) In the bulk (metastable) w examined here there is
no evidence for the displacement in the c direction of
atoms in &I$,+,+) positions as suggested by Bagaryat-
skii for LC) in titanium alloys. However in Section 2 it
will be shown that some such displacements can occur
6.04 ~ 5.88 i 6.04
5.88
0.04 0112 0.04 0.12
9 9 1 0.74 9 9 1 0.74
4 4.88 1 0.74 4 4.88 1 0.74
in the diffuse o which precedes the development of the
metastable cc) structure.
2. THE DIFFUSE o-STRUCTURE
Section 1 of this paper has been concerned entirely
with the a+phase in its metastable state. However,
when alloys of increasing solute content are rapidly
quenched from the p-field a characteristic sequence of
structures is observed.(5) At low solute concentrations
complete transformat,ion to the h.c.p. Zr-a phase
cannot be suppressed. On increasing the solute con-
centration the w-phase together with the u-phase is
observed while at slightly higher concentrations it is
possible to obtain almost 100 per cent (r) phase.
Further increase of the solute concentration results in
a certain amount of Zr-,3 phase being retained
together with cc) which does not produce sharp X-ray
diffractions. The a-phase in this state is designated
diffuse W. The diffuseness of the diffractions increases
with increasing solute content although the amount of
diffuse cc) present may still be about 70 per cent of the
total volume.
In certain alloy systems where the solid solubility of
580 ACTA METALLURGICA, VOL. 8, 1960
the P-phase is limited, it is not possible to observe the
complete sequence of as-quenched structures described
and for this reason diffuse w is not observed in the
Zr-Cr and Zr-V systems but is readily detected in the
Zr-Nb and Zr-U systems.
The mode of formation suggests that the a)-phase
occurs by a martensitic type transformation. The term
“martensitic” is taken here to describe the regular
movement of particular lattice planes relative to
adjacent planes of the parent matrix in definite crystal-
lographic directions, the movement resulting in a new
crystallographic structure. The interpretation of the
diffuse w study presented below leads to the formula-
tion of a mechanism, not involving diffusion, which
accounts for the observed diffraction effects and will
also explain the formation of bulk cc).
On ageing alloys which form diffuse o during the
quench, the diffuse diffractions or streaks coalesce and
the characteristic w diffraction pattern becomes
apparent. This coalescence is accompanied by solute
enrichment of the p-phase and impoverishment of the
diffuse w-pha,se.
Experimental results
The diffuse w-phase has been examined by the
single crystal technique using monochromatic radia-
tion from a curved quartz monochromator.
Figure 3 shows a single crystal oscillation photograph from a wai,er quenched Zr-20 at. y0 Nb alloy with the
crystal oscillating about [ liO],. The photograph shows
sharp p diffractions together with areas of diffuse
intensity, the latter being the diffuse LU diffractions;
FIG. 3. Oscillation photograph of a single crystal of Zr-20 at,.% Nb with monochromatic MoKa radiation. The crystal oscillated about (110)~ with the (001)~ oscillated through 0 + 45” to the direct X-ray beam. The crystal was water quenched after 2 hr at 920°C and the photograph shows diffractions from B, diffuse o
and ,!I”.
FIG. 4. Weissenberg photograph of the zero layer perpendicular to (110)~ from the same crystal as used
for Fig. 3.
also present are some weak diffractions from another
phase designated ,!?“. * Fig. 4 is the Weissenberg photo-
graph of t,he zero layer perpendicular to [liO],, and
Fig. 5 is the reciprocal lattice plot of this layer, only
one quadrant being shown since the other three are
symmetrical to this. The diffuse u) diffractions
common to both Fig. 3 and Fig. 4 are labelled and as
can be seen these are elongated both in the (liO),
plane and perpendicular to this plane. In Fig. 5 these
diffractions can be divided into two groups, viz.
(A) Streaks which are elongated in [n2], and hence
perpendicular to [ 11 lla
(B) Streaks which are elongated in [112], and hence
perpendicular to [ 11 lip.
Thus in reciprocal space the diffractions in group (A)
can be interpreted as disks of intensity perpendicular
to [ill], or three rods of intensity perpendicular to
[ill], which due to symmetry make angles of 120”
with each other. Similarly diffractions in group (B)
would correspond to either disks of intensity perpendi-
cular to [ 11 lla or three rods of intensity perpendicular
to [ill],.
Table 3 gives the indices and F2 values for those
bulk o diffractions which can occur in the reciprocal
lattice section shown in Fig. 5. The table shows that
apart from those diffractions which overlap p dif-
fractions only w orientations 2 and 4 diffract in this
section; the reciprocal lattice points corresponding to
these orientations are shown by crosses and dots,
respectively. Thus each of the streaks belonging to
* The @“-phase has a b.c. tetragonal structure with a = 3.52 A and c/a = 1.13 and is orientated to the B-phase having (OO1)b.c.t. I/ (001)~ and (lOO)b.,.t. 11 (100)~. The phase exists in small amounts (less than 5 per cent of the total volume) in high solute content niobium alloys.
HATT AND ROBERTS: o-PHASE IN Zr ALLOYS 5x1
4. However the intensities of the streaks do not agree
with the corresponding bulk CO intensities, but as will
be shown later better agreement is obtained if small
atomic movements are given to the atoms in bulk w to
give a structure intermediate between j3 and bulk CO.
The diffuseness of the diffraction streaks from
diffuse CO as compared with the bulk w diffractions
results from relaxed Laue conditions caused by the
diffracting region either being restricted in size or not
having exact periodicity in three dimensions. Since it
has not been possible to resolve whether the intensity
distribution in reciprocal space is a disk of intensity
perpendicular to (111 )s or three rods perpendicular to
(111 )B both possible interpretations will be developed.
If the intensity distribution corresponds to disks in
reciprocal lattice space those disks associated with cc) in
orientation 2 correspond either to rods of CO in orien-
tation 2 in the crystal where the axes of the rods are
parallel to [ill],, as is shown in Fig. 6(c) or to CO in
orientation 2 with exact periodicity only in the [ill],
direction. A similar argument applies for the disks
FIG. 5. A reciprocal lattice plot of the zero layer perpendicular to (110) reciprocal lattice direction showing the direction of the diffuse o streaks and the position of the corresponding bulk w diffractions.
l 0 orientation 4 X 0 orientation 2
group (A) above can be associated with a diffraction
from bulk o in orientation 2 and those belonging to
group (B) with a diffraction from bulk o in orientation
TABLE 3
Intensity
I I observed P2,.,, I IP,.,,
hlcil
_~ __ ___ _.~__ I
Ident. I
hkl hkil No. 1 cubic hex.
Orient. hlcl
cubic
I Intensity
I ! Orient. (--p,---
observed i P2,,,,, _
-
’ ’
: 4 0
I 4 ~ 9
0 9.0 4 I 1.0 0 0 9 i
4.3 0.6
F20.58 ~-
0 0.6 1.0 1.0 4.3 0.4 7.8
CO.1
_I__- 112 222 442 552 772 882
10,10,2 11,11,2 13.13,2
114 224 444 554 774 884
10,10,4 11,11,4 13,13,4
118 228 448 558 778 888
lO,lO,S l,l,lO 2,2,10 4,4,10 5,5,10 7,7,10 1014 8,8,10 ~ 6061
lOi 0001 202T 1012 3032 2023 4043 3034 50% 1011 2010 0002 3037 1013 4042 2024 5053 3035 3031 2022 4040 1073 5051 0004 6062 3032 4041 2023 5050 _
0 9.0 1 0.6 8,8,10 606i
10,10,10 0006 1 6.9 10,10,10 0005 I
loio 0001 2021 7012 3032 2023 4033 3034 5054 loil 2010 0002 3037 7013 4042 2024 5053 3035 3081
-
2” ; 4 2 4 2 4 2 4 2
: 4 2 4 2 4 2 4 2
; 4 2 4 2 4 2 4 2
* w Will
wm SIll
SIIl
-
w * *
S
VW
S -
S
w * * - - - -
* -
w -
m -
w
112 222 442 552 712 882
10 10 2 _‘_’ 11 112 __‘_-’ 13,13,2
114 224 444 554 774 884 -__
10 10 4 _‘_’ 11,11,4 13,13,4
118 228 448 558 178 888
lO,lO,S
2012 4040 1073 5057 0004 6062
l,l,lO 3032
:::::: 1 4041 2023 5,5,10 5050 7.7.10 lOT4
2 4 2
%
: 4 2 4 2 4 2 4 2 4 2 4 2 4 2 4 2 4 2
; 4 2 4 2 4
* w
wm wm SIII
SITI
-
w * *
s VW
s
S
‘iv *
*
-
-
-
-
*
-
w -
m -
w
0 0 1 0.6 4 1.0 : 4.3 1.0
4 0.4 4 7.8 9 CO.1 0 ~ 9.0 4 1.0 0 I 0 9 4.3 1 0.6
: ; ;:r: 0 9.0 4 4 ~ ::9” 1 0.6
: 1.0 0 4 0.4
: 9
1 6.9
k
1
m
9 ’ 4.3 1 1.0 4 ~ 7.9 0 0
- Not observed. * Oscillation range too small to include this diffraction. There are also o diffractions from all o orientations superimposed on the b diffractions
(llO)B (220)8 (33O)p (44O)p (002)@ (112)J (222)~ (332)~ (442)~ (114)~ (224)~
w Orientation (2) [OOOl], Ij [lll]fi w Orientation (4) [OOOl], 11 [iii],
[2iio], ij [iollB [2irO], II r10118 tiA-(4 PP.)
582 ACTA METALLURGICA, VOL. 8, 1960
REAL SPACE I’ 4 A SINGLE DISC
OF o
b) THREE DISCS OFW
C) A ROD OF o
510 e
t
RECIPROCAL LATTICE REPftESElWiTlCN
A SINGLE ROD
I [I I iJ Rfpmdicular to page and rod.
THREE RODS
A P!_ANE OR 0lS.C
FIG. 6. Representation of w in real and reciprocal lattice spaoe.
associated with orientation 4 but here the axis of the rods of ctt would be parallel to @il],r.
Alternatively if the disks of intensity in reciprocal space are in fact three rods of intensity those associated with LC) in orientation 2 will correspond either to three disks (or more probably ablate spheroids) of w in orientation 2 in the crystal, each disk being parallel to [Ill], but making 120” with each other (Fig. 6b) or three blocks of o with orientation 2 in the crystal, each block having periodicity in two orthogonal directions but not in the third which is perpendicular to [ill],.
The above interpretations may not be very different since both relate to regions of w in the crystal which are structurally perfect in only one direction, for example w with orientation 2 is structurally perfect in only the [ill], direction and any direction perpendi- cular to this will intersect a large number of defects.
The experimental results given above suggest that movement of {112}, planes is involved in the /? -+ LO transformation as is the case for the /? --+ u transforma- tion mechanism proposed by Burger@).
A projection of the atoms in a b.c.c. structure onto a ( liO)B plane is shown in Fig. 7. The packing sequence of the (112), planes is given by 1 2 3 4 5 6 1 2 3 etc. ,,,>,,>,, The w structure can be generated by the {112}@ planes gliding as follows:
P2>s 12345612 345 6
glidecomponent g g 0 g SO g tf0 g S
ctf 1 6Q u.Q 4 Cl&s IQ5 lo+2 Ws2 4 C06” 065
where g is the glide component which glides a (112),
plane by &3/2 * aB in the (1 1 1 >* direction contained in that plane. A gliding sequence occurring on any particular set of {112)@ planes of a particular zone necessarily implies an identical gliding sequence occurring on each of the other two sets of {112)# planes of that zone, Hence bulk w in orientation 2 can be generated by extensive gliding on the (ii2),, (i2Q or (2ii)B planes in a [ill], direction, i.e. g above is in the [f 111, direction. Similarly disks of cu will be produced if glide takes place on a limited number of the above planes. The disks will be parallel to [ill], and perpendicular to [ii2],, [121], and [Zii],. This is shown in Fig. 8 which is a projection of atoms in in b.e.c. structure onto a (liO}, plane.
The disks would degenerate into rods of a parallel to [ill], if the width of disks in the (llO), directions, which lie in the plane of the disks, is restricted to a few atoms while the glide along the (lll>s has occurred for many atoms.
The restriction of the width of the disks in the (llO), directions can be brought about by faulting between the disks. Fig. 9 is a projection of the atoms in a b.c.c. structure onto a (ill), plane, that is a projection at right angles to that of Fig. 8. The three sets of (112j8 planes belonging to the [ill], zone are
FIG. 7. Projection of the atoms in a b.c.c. structure onto a (1101 plane illustrating the (112) packing
4 the gliding of {112}@ planes in different zones. If it is
5 assumed that nucleation of gliding is purely random
6 then the chance of faulting between any two sets of
I 0 I (112}, planes in the same zone is 2 : 1. The case of
2 9 0: interaction of {112}P planes of different zones is
3 is w: complex and will not be developed in detail here but
4 0 4 it does not alter the general conclusions concerning
5 9 0: mechanism.
6 3 0: Table 3 shows that the intensities of the diffuse w
I 0 I streaks do not agree with the intensities of the corre-
sponding bulk u) diffractions. However, a better
correlation is obtained if in diffuse cc) the above
4 glide sequences do not go to completion. When the
5 glide component is 0.087(2/3/2 . aa) instead of
0.167(43/2 . as), the LU produced has atomic positions
Fm. 8. Projection of the atoms in a b.c.c. structure (O,O,O); & ($,+,O.SS) as compared with (O,O,O);
onto a {llO} plane showing the glide sequence to &((Q,$,0.50). P2 values corresponding to these new produce o. positions are shown in Table 3 under F2,,,, and it will
be seen that better agreement with the observed inten-
sities is obtained. Since diffuse o exists as disks on
(1 la}, planes it is probable that coherency strains re-
sulting from transformation prevent the gliding
sequence from going to completion.
Ti-5% Cr alloy. However, since little is known of
Fm. 9. Projection of the atoms in a b.c.c. structure onto a { 11 l} plane illustrating the three (112) planes of
a (111) zone. l Atoms in the plane of projection
x Atoms ‘q above the plane
+ Atoms q above the plane
shown by unprimed numbers for the (112),, primed the gliding sequence suggested is operative during
the formation of bulk o. numbers, l’, 2’, etc., for the (Zii), and doubly primed The mechanism of formation of bulk w from diffuse numbers, l”, 2”, etc., for the (T2i), planes. Faulting
will occur between disks if simultaneous nucleation w, on ageing, is considered to be in part an annealing
out of faults. occurs on non equivalent (112}, planes of the [ll lls
zone as defined by the glide sequence given above in ACKNOWLEDGMENTS
which planes 1, 1’ and 1” have zero glide component. The authors wish to acknowledge the assistance of
If, for example, simultaneous nucleation of 0 occurs D. Stewart, B. Bradford and G. Hansen with the
on planes 3’ and 5”, where plane 3’ glides 0 and plane experimental programme and are also grateful to
5” glides g, a series of faults will develop where the Dr. E. A. Calnan, Dr. G. I. Williams of the Fulmer
disks merge. Research Institute, and Dr. M. B. Waldron and Mr.
Many permutations and combinations of the above B. Butcher of Atomic Energy Research Establishment,
gliding sequence of {112}s planes which could result Harwell, for the many useful discussions.
in faulting are possible when a large number of This work was sponsored by the Atomic Energy
nucleation sites are present. Interaction must be Research Establishment, Harwell, and the authors
considered of each of the three {112}, planes in each are crateful to the Director for nermission to nublish. ~ L I
HATT AND ROBERTS: o-PHASE IN Zr ALLOYS 583
of the four (111 )@ zones and also the interaction of
It is of interest to note that the new atomic positions
reported for the diffuse o structure are similar to
those proposed by Bagaryatskii for bulk o in a
the heat treatment of Bagaryatskii’s alloys it is not
possible to relate the rumpling of the mid plane of
atoms in the w-phase in Ti-5 T/o Cr to coherency strains.
Conclusions
The model proposed for the b -+ w transformation
satisfactorily accounts for the diffraction effects
observed from the diffuse w-phase and implies that
584 ACTA ~ETALLURGICA, VOL. 8, 1960
REFERENCES 3. Yn A. BAIXRYATSKII, G. I. ROSOVA and T. W. SAGANOVA, 1. A. E. AUSTIN and J. R. Dora, J. Met&s, N.Y. 9, 27 l)akE. Akad. Nat& SSSR 105, 1225 (1955).
(1957). 4. B. A. HATT, S. A. ROBERTS and G. I. WILLIAMS, Nature, 2. J. M. Sr-ccoc~, M. H. DAVIES and H. K. HARDY, in Land. 180, 1406 (1957).
Syvqx&~na on the Mechanism of Phase Transform&ions in 5. B. A. HATT and 5. A. ROBERTS, unpublished work. Metals. London, Institute of Metals (1955). 6. W. G. BUROERS, Ph;ysica, &rav. 1, 561 (1934).