Phase transformation, twinning and anelastic phenomenon associated with zirconium dihydride

JOURNAL

OF NUCLEAR

PHASE

MATERIALS

2, No. 4 (1960) 335-340, NORTH-HOLLAND

TRANSFORMATION, ASSOCIATED

TWINNING WITH

AND ANELASTIC

ZIRCONIUM

ROGER

The atom movements tetragonal

and crystallography

transformation

in ZrHz

discussed according to the phenomenological

23 May

and Read.

The large internal absent

Inc., Canoga Park, California,

theories

blement de l’hydrogbne, d’environ

suggests

that

it is Die Atombewegungen

The relaxation

Umwandlung

appears to be controlled

by a diffusion process, presumably an activation

energy

per mole.

changement

et

de

interne trouv6 dans ZrHl,sa (mais absent

ZrH1,6)

sugg&e

que

& un dbplacement

Lieberman

und Read

cette

transformation

de l’interface

die Spannung

de

erscheinung vo~eh~ich

est

diskutiert.

de macle

diirfte

gefunden.

von

Es

ist

mit einer Wande-

zusammenhiingt,

hervorgerufen

die durch

wird. Die Relaxations-

einem

Diffusionsvorg~g,

der Diffusion von Wa~e~toff

etwa 20 kcal/mol

beherrscht von

ermittelt.

indicate that the changes in crystal structure in the Zr-H and Ti-H systems on addition of hydrogen are analogous. With high hydrogen

nature of these materials, which seemingly is intermediate between that of interstitial alloys

content a homogeneous range of cubic phase is observed, which becomes tetragonally distorted near the limiting composition ZrHs and TiHz. The limits of this range do not correspond to a simple stoichiometric ratio between the components. Neutron diffraction investigations have shown that the hydrogen atoms are located in the tetrahedral holes of the near face-centered metal-atom lattice in both ZrHz and TiHz 293). The lattice parameters of TiDl.~s and ZrHl,sz measured by Yakel 4) at various temperatures are reproduced in fig. 1, The critical temperature

and inorganic compounds. This interest has recently been augmented by practical applications of solid hydrogen materials in the field of nuclear engineering as moderators. The crystal structures of the hydride “compounds” which exist at compositions between MH and MHz, where M is a Group IV-A metal, have been studied using X-ray diffraction and neutron diffraction by many investigators. The results of X-ray analysis 1) by the United

Reibung

werden. Kierfiir wurde eine Aktivierungsenergie

Many fundamental studies of solid metallic hydrides have been stimulated by the chemical

This work was supported

inneren

dass dieses Maximum

rung von Zwillingsgrenzen

Introduction

t

bei der

zum tetra-

Theorien von Bowles und MacKenzie

der

naheliegend,

Weehsler,

et Read. La pr&enco du pie important

1.

Maximum

en tenant compte des

et Mackenzie

Lieberman

associ6e

menologischen

du

frottement dans

kubischen

In ZrHl.sz, nicht aber in ZrH1.6 wurde ein ausgepriigtes

des atomes et la cristallographie

Bowles

und die Kristallographie

ZrHa vom

gonalen Gitter wurde studiert und mittals der phiino-

20 000 calories

de phase de ZrHa cubique St ZrHz t&r&-

de

von

und von Wechsler,

gonale sont BtudiBs et discut& th6ories

that of hydrogen,

of about

___.

Les mouvements

avec une 6nergie d’activation

20 000 kcal/mole.

associated with a stress induced twin interface motion.

with

de relaxation

semble contrBl6 par un processus de diffusion, proba-

friction peak found in

in ZrHr.6)

phenomenon

USA

1960

induit par des tensions. Le ph&om&ne

and

of Bowles and MacKenzie and of Wechsler, Lieberman, ZrHI.sp, (but

t

CHANG

of cubic to

are studied

CO., AMSTERDAM

PHENOMENON

DIHYDRIDE

Atomics International, A Division of North American Aviation, Received

PUBLISHING

States

Atomic

335

Energy

Commission.

evaluate the mechanism and atorllmovelllt~tlts it)valved in t’he cubic to tetragonal trallsforlll~btic)lr

52t

in ZrHz. Although

X-ray

the transformation

temperature

carried

studies of ZrH:! tlear

out. the similarity

between

TiHz and t,he microstructural indicate

---

tetragonal

beyond

any

doubt

transformation

have yet to IF ZrHz and

aspect’s of %rHz that

a cubic

to

exists in ZrHe. The

paper discusses also the anelastic

behavior

of

t’etragonal ZrHn. The presence of a relaxation I 4.0

1 -200

1

-100

TOEMPEK&

eoo

300

400

500

(“C)

Fig.

1.

Lattice

parameters

of ‘L’iD~.~~ and

ZrHl.!,z

versus temperatllre.

for the cubic to tetragonal transition in TiD1.98 is 37 f 4’ C. The data for ZrH1.92 suggest definitely a similar cubic to tetragonal transition which cannot be investigated without highpressure and high-temperature X-ray diffraction apparatus. The cause of the distortional transformation in the hydrides is not clear. Ordering of an atomic or magnetic nature is eliminated by the close approach of the compounds to stoichiometric compositions and by the results of neutron diffraction experiments. A ferroelectric ordering process is also unlikely in view of the symmetric positions of the atoms in the tetragonal lattice. There is the possibility of a gradual change in bond character between metal-hydrogen or metal-metal neighbors with decreasing temperature

which might lead to the

observed lattice distortions. An alternate explanation, based on the band bheory of metals rather than a chemical bond theory, may be advanced, The transition from a cubic to a tetragonal lattice would then be considered as arising from an overlapping of Brillouin zone boundaries caused by small variations in electron density with temperature. The cubic to tetragonal transformat)ion in AuCd. AgCd. InTl, etc., has also been interpreted in terms of the zone overlapping hypothesis, especially in view of the fact that small additions of a third component may influence tremendously the transformation behavior. It is the purpose of the present study to

peak in the heavily Owinned tetragonal state and the absence of a similar peak in the cubic: state suggest convincingly that tho relaxation peak is associated with stress induced motion of t,win interfaces in the material.

2.

Crystallography of Transformation and Microstructures of the Transformed Product

The phenomenological theories of the crystallography of cubic to tetragonal transformation have been discussed by Christian 5). It was pointed out that the theories of Bowles and MacKenzie 6) and of Wechsler, Lieberman and Read 7) are essentially equivalent, although they differ in mathematical formulation. The fundamental idea on which the theory is based is that the total transformation distortion is such that at least one plane (the habit plane) is undistorted and unrotated. An undistorted plane is not produced if the total distortion consists solely of the pure lattice distortion. However, the pure lattice distortion may be combined with a slip shear or a twinning shear (over a fraction of the crystal) which does not affect the lattice structure but produces a microscopic change in shape. In the case of cubic to tretagonal transformation in Au-Cd *) and In-T1 9310). the second distortion was invariably shown to be a twinning shear such that the t’etragonal phase is twinned and that for an appropriate ratio of twin thicknesses, the average misfit strain between the twinned tetragonal phase and the cubic phase is zero. An exact calculation by Wechsler, Lieberman and Read 7) yields the following expressions for the habit plane indices (h/cl) referred to the cubic phase:

PHASE

TRANSFORMATION,

TWINNING

AND

ANELASTIC

PHENOMENON

The microstructures (ZrH1.s~) at room

ZrHz

WITH

of a tetragonal

temperature

337

specimen

at 70 x

and

350 x are shown in fig. 2 t. Both the fine twin bands and the gross twin bands are approxi-

! where r,~=ajao and 72 =c/ao, ao, a, and c being lattice parameters of the cubic and tetragonal phases, respectively. The same authors also obtained the following equation for the relative amounts of the two twins (x, 1 -x) :

mately

themselves, the twin interface being the (101) type plane of the tetragonal lattice. 3.

Using the room temperature lattice parameter data of Softina and co-workers 1) for the highhydrogen side of the Zr-H system: ao=4.76

A

a =4.44

A

c =4.97

A

parallel to the (011) type plane of the

high-temperature cubic phase. The X-ray back reflection Laue photogram of a typically twinned region is analyzed and stereographitally plotted in fig. 3, showing the orientation relationship of the twins with respect to

Anelastic Phenomenon Interface Motion

The twin interfaces formed as a result of cubic to tetragonal transformation are very mobile, and their motion requires only very small movements of the atoms. If, for example, the twin interfaces are locked by impurities or defects, applied

motion of these interfaces under an shear stress will be controlled by the

eq. (1) and (2) yield a habit plane of indices

diffusion

(0.067: 1.00, l.lS), which is about 3 degrees from

Furthermore,

twin

j- Similar

invest’igation

(Oil), and 0.51, 0.49 for the relative amounts of the two twins, in agreement with our experimental data.

Fig.

2.

Microstructure

of ZrHl.ss

at room

Associated with Twin

rates

of

the

impurity

interface

both coarse and fine twin

revealed

or

motion the

magnified

in

absence

an of

bands in a cllbic specimen

(ZrR&.

temperature,

defect.

70 and

350 times.

ROGER

CHAN(’

T

figs. 5 and 6. Indeed. a large internal friction peak is present in the hydride ZrH1.92 but. is absent in the hydride very convincing

ZrHl 6. The results aw

that the internal friction peak

in ZrH1.92 is associated motion

with a stress induced

of the twin interfaces

in the material.

The shift of peak temperature yields

an activation

energy

with frequency

of approximately

20 000 calories per mole. -TWIN

Fig.

3. Laue

Stereographic zones

PLANE

projection

of a twinned

ordered two-component

of back

crystal

reflection

(ZrH1.85).

system may require the

synchronized movement of both atom species the rate of which may be controlled by diffusion of one of the two atom species. At low temperatures the motion of the twin interface under dynamic conditions is so slow that no appreciable displacement occurs during a half-cycle of vibration, and the internal friction is low. On

Fig.

internal friction

Phase

diagram

of the Zr-H

system.

Zr HI92

2or

the other hand, the twin interfaces at high temperatures are so mobile that the shear stress is completely relieved at all times, so the intermediate

4.

1

413 CYCLES/set--./

h’!

is again very low. Only in the

temperature

range where both the

displacement and the net shear stress are appreciable, is the internal friction large. The internal friction peak of Cu-Mn alloys (m 90 percent Mn) found by Worrell 11) is thus interpreted by Zener 12) to arise from stress induced movement of the twin interfaces of this alloy. Internal friction measurements were used to study twin interface motion in zirconium hydride. The most recent phase diagram for the Zr-H system is shown in fig. 4 13). At room temperature the material is completely cubic at and completely tetragonal at H/Zr < 1.66 H/Zr > 1.75. The internal friction data of two hydrides ZrH1.92 and ZrHl.6 are reproduced in

4’

Fig.

5.

I 20

I 60 100 TEMPERATURE

I 140 (“C)

I 160

Internal friction versus temperature ZrH1.92 at two frequencies.

2

for

PHASE

TRANSFORMATION,

TWINNING

AND

ANELASTIC

likely

PHENOMENON

WITH

that such movements

synchronized

motion

ZrHs

may require

of both atom

339 the

species. If

twinning is to be described by the shearing of Zr atoms (or ions), the synchronized motion of H atoms (or ions) from tetrahedral hedral and back to tetrahedral and it is not unreasonable interface

motion

hydrogen

40

80

120

160

200

240

TEMPERATURE (“Cl

Fig.

6.

Young’s

modulus and internal friction versus

temperature

4.

for ZrH1.6.

Discussion The

X-ray

diffraction

and

sites is required

to suggest that twin

is controlled

diffusion

A schematic

to octa-

by the rate of

in the lattice.

drawing showing two edge-type

twinning dislocations in a (101) t twin boundary of a face-centered tetragonal lattice is shown in fig. 7 15). The plane of figure is perpendicular to [OlO]. Applying the diagram to ZrHs (the c/a ratio being slightly exaggerated): open circles are Zr atoms (or ions) in the plane of the figure ; filled circles are the projection of the next atomic layer of Zr atoms on this plane; squares are the projection of a layer of H atoms (or ions) located between the two layers of Zr atoms, each H being “tetrahedrally” sur-

metallographic

studies presented here indicate beyond doubt the presence of a cubic to tetragonal distortional transformation in the Zr-H system. Such transformation is indicated by the dotted lines of fig. 4. Further verification of the transformation using high-temperature highpressure X-ray diffraction is needed. An

important

result

of

this

study

is the

internal friction peak associated with stressinduced twin interface motion. The activation energy associated with the relaxation process, m 20 000 calories

per mole, is believed

to be

associated with that for the diffusion of hydrogen in the material. A closer look at the crystal structure of ZrHs suggests that the twin interface cannot be one atomic layer thick and must be composed of arrays of edge or screw type twinning dislocations. The paths taken by atoms during twin interface motion will most likely be defined by the geometry of dislocations or partial dislocations in the lattice in a manner suggested by Kronberg for slip and twinning in sapphire 14). Although the details of atom movements have yet to be worked out, it is

Fig.

I.

Schematic

twinning

drawing showing two edge type

dislocations

of a (101) twin boundary

face-centered t plane;

Numbers

tetragonal

in parentheses

are Miller indices of a

those in square brackets

a direction.

of a

lattice.

are Miller indices of

340

ROGER

rounded

by 4 Zr. The shaded regions are those sites are badly disthe “tetrahedral”

where torted. Two possibilities could

CHANG

(2) the H atoms are relocated unlikely,

tetrahedral

sites:

to nearby inter-

sites. The first possibility

and it is conceivable

second alternative will be impeded

according

that twin boundary

by the relocation

atoms and controlled

is

to the motion

of hydrogen

by the rate of diffusion of

hydrogen. Further studies are needed stantiate the hypothesis.

?

4,

7

C. G. Shull

H.

L. Yakel,

13

micrographs

for

E.

0.

Actn

Wollan,

11 (1958)

Met.

46

84 (1955)

386

dcta

Met.

and J. K. MacKenzie,

A1ME

D. S. Lieberman 197 (1953)

L. C. Chang

2

47

M. W.

Burkart

and

and T. A. Read,

1503

and T. A. Read,

(1951)

Trans.

T. A. Read,

AlME

Trans.

191

AIME

1516

Z. 8. Basinski (1954)

544

129, 224

197 (1953)

)

and

Cry&.

.J. Inst.

1 M. 8. M’echsler,

9

Orlovw,

22

Acta

Jr.,

J. 8. Bowles

Trans.

national,

2).

Rundle,

(1954)

10

ZrH1.85 (fig.

R.

5 (1952)

S.

3 (1959)

D. 11. Zauberis,

607

5) J. W. Christian,

9

and

9 (19.56)

E.

and X.

Physics)

Cry&.

Acta tryst.

9

the

(Soviet.

?) S. S. Sidhu, L. Heaton

The author is grateful to L. L. Bienvenue, Atomics International, who obtained the internal friction data for both ZrH1.g2 and ZrH1.6, and to C. G. Rhodes, Atomics Interobtained

Z. M. Azarkh

CrystaZZogruphy

to sub-

Acknowledgement

who

V. V. Softina,

‘)

exist : (1) the H atoms

stay in the distorted

stitial octahedral

References

and J. A. Christian,

Acta

Met.

2

148

1 F. Worrell, Phys. Rev. 72 (1947) 533 oj Metals 12) C. Zener, Elasticity and Anelasticity 11

(University

)

Report,

14)

of Chicago

G. G. Libowitz,

h’AA-SR-5015

M. L. Kronberg,

15) Z. S. Basinski (1954)

101

Press,

l1.S. Atomic

Commission

(1960)

Acta and

1948) Energy

Met.

J. W.

5 (1957)

Christian,

507 Acta Met.

2