420 O S C I L L A T I O N S D A N S LES D I S T R I B U T I O N S DE T A I L L E S DE P A R T I C U L E S

3. Conclusion

Nous donnons une m6thode pour d6terminer l 'am- plitude a' de la correction a'A sin 7~AM/TrAM; la cor- rection ainsi d6termin6e permet de r6duire la plupart des erreurs autres que celles dues au profil instrumen- tal, qui se superposent aux courbes de distribution de particules. Pour obtenir la valeur de a', nouN prrconi- sons l ' r tude du second moment de la raie de diffraction en fonction de A (courbe de variance). Pour A suffisam- ment grand, cette courbe admet pour asymptote une droite lorsque le fond continu est entire6 correctement (Langford, 1968). Si une telle asymptote n'existe paN, cela prouve que le fond continu est erronr, il est pos- sible de l 'ajuster 5. sa valeur vraie en rendant la courbe de variance aussi rectiligne que possible. L 'asymptote 5. la courbe de variance a une ordonnre ~t l 'origine W0 qui est directement lire ~t a'.

- Wo- L~(O) / I I(X)dX=a'A / I I (X)dX .

Enfin, nous insistons sur l 'existence de points dits sta- t ionnaires dont la position est fix6e par le domaine de mesure et qui lorsque a' ne peut ~tre 6valu6e que gros- si~rement donne une id6e de la distr ibution; l 'ordon- n6e de ces points d6pend encore, mais faiblement, du fond continu.

R6f6rences

BEgTAtrr, E. F. (1949). Th~se, Facult6 des Sciences de l'Universit6 de Grenoble, no. 112.

BERTAUT, E. F. (1950). Acta Cryst. 3, 14. BERTAUT, E. F. (1952). Acta Cryst. 5, 117. BERTALrr, E. F. (1962). International Tables for X-Ray

Crystallography, p. 318, Vol. III. Birmingham: Kynoch Press.

EASTABROOK, J. N. & WILSON, A. J. C. (1952). Proc. Phys. Soc. B 65, 67.

EDWARDS, H. J. & TOMAN, K. (1970). J. Appl. Cryst. 3, 165. LANGFORD, J. I. (1968). J. Appl. Cryst. 1, 48, 131. LOUER, D., WEIGEL, D. & LOUBOUTIN, R. (1969). Acta

Cryst. A25, 335, 338.

g(M)

• \ s " \

"\\ / i i " " ta) cas 1

ol// (v

~ ~ - ~ .._ - 'x "/ tbl cas I1

. . . . . . . . - , - ~ /~ ~ , / ~.~.r ( Ic} cas l l I

(v)

Fig. 6. Distributions obtenues avec un fond continu erron6 (a) A=6°0; (b) A=6°0; (c) A=2°O. Distribution --- origi- nale, - - aprrs correction par la variance (V), - . . . . . aprrs correction g(0) = 0(O)

MERING, J. & TCHOUBAR, D. (1968). J. Appl. Cryst. 1, 153. MERING, J. • TCHOUBAR, D. (1969). J. Appl. Cryst. 2, 128. WILSON, A. J. C. (1962). Proc. Phys. Soc. 80, 286. WILSON, A. J. C. (1965). Proc. Phys. Soc. 85, 807. WILSON, A. J. C. (1970). J. Appl. Cryst. 3, 71. YOUNG, R. A., GERDES, R. J. & WILSON, A. J. C. (1965).

Acta Cryst. 22, 155.

or. AppL Cryst. (1972). 5, 420

A Technique for the Automatic Recording of Phase Transitions in Single Crystals

BY A. M. GLAZER

Cavendish Laboratory, Cambridge, England

(Received 14 July 1972; accepted 14 August 1972)

A simple and automatic technique is described for the continuous recording on X-ray photographs the behaviour of single crystals as a function of temperature, pressure, time etc. With a careful choice of axis and oscillation ranges, a distorted, but recognixable, plot of the phase diagram is obtained in a few hours.

Introduction particularly true when the crystals undergo several transitions between structures that only differ very

Detailed studies of phase transitions in single crystals slightly, as in perovskites and other pseudosymmetric are notoriously difficult and time-consuming. This is materials.

A. M. G L A Z E R 421

During the course of a high-temperature investiga- tion of NaNbO3, it was found useful to construct ap- paratus for the automatic recording of its very com- plex transitions. The apparatus that has been developed is based on the original work of Milledge (1966, 1969) on the improvement of photographic intensity measure- ments and on the study of solid-state reactions (un- published).

In the work described here, the recording of the X-ray reflexions, and therefore the lattice parameters, was carried out as a function of temperature. The same technique could equally well be used to study the effect on the lattice parameters (and on the structures) of time (as in kinetics and ageing studies), pressure, electric fields, stress etc.

Description of Technique

The X-ray camera used in this work is of the Weissen- berg type provided with a back-reflexion film cassette of radius 57.3 mm (manufactured by Stoe & Co.). The crystal (about 0.2 x 0.2 x 0.2 mm in the case of NaNbO3) is set accurately about an axial direction, and an oscillation range is chosen in order to record a high-angle axial reflexion. Weissenberg screens are

used to isolate the zero layer. During the X-ray ex- posure, the film cassette is held stationary for a pre- determined length of time and then translated through a distance of 1 mm parallel to the oscillation axis. This procedure is repeated continuously; the only significant exposure to the film takes place when the cassette is stationary, thus producing a series of steps on the film. The apparatus for performing this operation is ex- tremely simple and is attached to the Weissenberg camera without making any alterations to it.

Fig. 1 shows the equipment assembled on the camera. The timer A (Crouzet, Type 113G) repeatedly provides a 15 sec mains pulse after preset time intervals be- tween 2½ and 60 min. The 4 r.p.m, synchronous motor B drives a 1 mm pitch screw C, which passes into a brass yoke D fitted around the film-cassette carriage. Therefore, whenever the timer produces its 15 see pulse, the film cassette is displaced through a distance of 1 mm. E is a microswitch which halts the motor after the film cassette has travelled through its maximum permissible distance.

In the experiments on NaNbOa, the temperature was raised and lowered smoothly and continuously during the exposure. Full details concerning the high-tem- perature equipment will be the subject of a separate

B C ' D F G

A E

Fig. 1. Photograph of the equipment used. A timer, B synchronous motor, C 1 mm pitch screw, D yoke for film cassette carriage, E microswitch, F high-temperature furnace, G film cassette.

J A C 5 - 3

422 A U T O M A T I C R E C O R D I N G O F P H A S E T R A N S I T I O N S I N S I N G L E C R Y S T A L S

publication (Bett & Glazer, 1972); for the moment only an outline description will be given. This ap- paratus consists of a miniature furnace, F in Fig. I, a three-term temperature controller and a programme- drive unit. The crystal is mounted on the tip of a chromel/alumel thermocouple with alumina cement and the furnace is placed around it. The controller permits temperatures up to 900 °C to be held steady to within + ¼°C and the programme-drive unit produces linear changes of temperature at a number of different rates, from 2.5°C per hr to 1.6°C per see.

Results

In Fig. 2 are shown some X-ray photographs of NaNbO~ taken with the apparatus described above; only a small part of the originals is shown, the high- angle part (0 = 75 to 87°). The photographs have been deliberately oriented in the Figure so that 0=75 ° is at the top. Fig. 2(a) is a composite of four photographs taken with the temperature increasing. In Fig. 2(b) the crystal has been turned through an angle of 90 ° in order to observe the other axes; in this case the tem- perature was decreased from 690°C. For both sets of

photographs the temperature was changed smoothly and continuously at a rate of ¼°C per min, and the exposure time for each step was 5 min i.e. spanning a temperature range of 3.75°C. The reflexions shown are the Cu Koq-Ko~z doublets of 500, 050, 005, and the Cu K0q reflexion of 501 and 105, using indices relative to the pseudocubic subcell. The line drawings below the photographs serve to indicate the major features.

A number of observations can be made: (1) The phase transitions can easily be seen as abrupt

changes in lattice parameter and can be located to within 5-10°C.

(2) Since 0 decreases towards the top of the Figure, lattice parameter increases in this direction. Because the reflexions are of the axial type, 500, 050 and 005, a direct comparison can be made with the phase dia- gram which is shown in Fig. 3. The lattice parameters in this Figure were obtained from an independent study using conventional oscillation photographs (Glazer & Megaw, in preparation). It is clear that there is a close similarity between this diagram and the photographs. The occurrence of twinning at some tem- peratures enables more than one axis to be seen on the same photograph and if the line drawings of Fig. 2

2 ~ ) ' C i 373 "C i 5 2 0 " C i 575°C 641°C 6 9 0 " ~ I

I

• f l r ~ i

"i 0O5

500 I 500 500 . . . . . . . . . . . ' - - 500"050 "" "686" o50

0 = 7 5 °

= 1

= 2

= 87 °

(_b)

; 105

• " ' t ¢ " " . . . ' . . . . | 9 t *~ , , ' , . : .

0 0 5 0 0 5 , 0 0 5 0 0 5

• '" 0 5 0 , - . . . . . - O S 6 . . . . ; . . . . . 6 ~ . . . . . . . . " 6 , ~ . . . .

105 ~ o . . o ° . o ° o - ' ~

501 . • ~ . . . . . . . . .

---i 0 = 7 5 °

= 2

,._. 0 = 8 7 °

~ t 1

i

i

Fig. 2. Photographs of NaNbO3 taken with the device shown in Fig. 1 (a) Compos i te of four pho tographs between 0 = 75 ° and 0 = 87 °. The tempera ture was raised at a rate of ¼ °C per min. (b) Compos i t e of three pho tographs with the tempera ture lowered at a rate of ¼°C per min. Cu K= unfiltered radiat ion. Incremental exposure 5 min. The line drawings show the variat ion in the =, componen t s of the reflexions. Note the close similarity with the phase d iagram of Fig. 3.

A. M. G L A Z E R 423

are superimposed on one another a distorted, but recognisable, likeness to the phase diagram is ob- tained.*

(3) The slopes of the curves drawn through the re- flexions at once indicate the different thermal expan- sions.

(4) Because the technique used here is incremental,

* The methods of obtaining lattice parameters to high precision using back-reflexion oscillation photographs have been fully described by nume lous authors (for example: Edmunds , Lipson & Steeple, 1960; Buerger, 1966).

the reflexions can be examined at each step for the effects of gross multi-domain structures. It is possible to see when one end of the crystal consists of one domain and the other end consists of another e .g . in Fig. 2(a) between 520 and 575 °C each step shows the 050 reflexion positioned slightly towards the left rela- tive to the 500 reflexion.

(5) Coexistence of phases can be seen, as in the transi- tion at 373 °C in Fig. 2(a).

C o n c l u s i o n s

The technique described here is essentially very simple . . . . ~ . . . . ~ . . . . ~ . . . . ~ . . . . ~ . . . . J . . . . ~ . . . . t , . but is capable of providing very sensitive results in the

- study of phase transitions. It can be applied both to / , . ~ single crystals and to polycrystalline samples, and can

3.95 _ be used in the study of thermal expansion, kinetics, .~~,,=b=c ! twinning etc . It should be particularly useful in the

~,J _ rapid characterization of phase transitions as a 3"94 pre- Y " - a=b : liminary to more detailed work, and it therefore forms A

"g - a natural adjunct to conventional thermal techniques, 3"93 - a '~ b - such differential thermal analysis (D.T.A.). as

. C

392 a s i n ~ ~ b ~ The author is indebted to Dr Helen D. Megaw for 8 3 91 ~ " - ' - ' - /" J introducing him to the subject of sodium niobate. In

addition, thanks are also due to the Science Research ~ Council for providing a grant to enable this work to

g I be carried out. 3"90

~. References

I In the press. 3"88 BUERGER, M. J. (1966). X - r a y Crys ta l lography , pp. 364-465.

1 New York: Wiley. EDMUNDS, I. G., LIPSON, H. & STEEPLE, H. (1960). X - r a y

, , , , I , , , , I . . . . I . . . . I . . . . I . . . . I . . . . r . . . . t , Di f f rac t ion by Polycrys ta l l ine Mater ia l s . Edited by H. S. 100 200 300 400 500 600 700 800

PEISER, H. P. RooKsBv & A. J. C. WILSON, pp. 366-394. Temperature (°C) London : Chapman & Hall.

Fig. 3. The variation of pseudocubic lattice parameters in MILLED(3E, H. J. (1966). M o s c o w Abs tr . VIIth. Int. Congr. NaNbO3 as a function of temperature (Glazer & Megaw, in Crystal logr. A220. preparation). MILLEDGE, H. J. (1969). A c t a Cryst . A25, 173.

J. A p p L Cryst . (1972). 5, 423

A Re-Assessment of the Monoteetaid Loop (p-Nb + II-Zr) in the Niobium-Zirconium System

BY P. E. J. FLEWITT

M e t a l l u r g y D i v & i o n , C e n t r a l E l e c t r i c i t y G e n e r a t i n g B o a r d , S o u t h E a s t e r n R e g i o n , C o c k f o s t e r s , H e r t f o r d s h i r e , E n g l a n d

(Rece ived 12 M a y 1972; accep ted 11 Ju ly 1972)

The shape of the two phase, fl-Nb +fl-Zr, monotectoid loop in the niobium-zirconium phase diagram has been re-investigated by X-ray analysis for alloys with controlled content of interstitial impurities.

Several experimental investigations have been con- ducted to establish the phase diagram for the binary niobium-zirconium alloy system (Anderson, Hayes, Robertson & Kroll, 1950; Litton, 1951; Pfeil, 1952; Rogers & Atkins, 1954; Bychkov, Rozanov and Sko-

zov, 1957; Knapton, 1960; Berghout, 1962; Rokosti- kin, 1965). The most acceptable diagram to date comes from the systematic study by Rogers & Atkins (1954). However, argument still centres on the monotectoid loop. At high temperatures niobium and zirconium

JAC 5 - 3*