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).