Fresenius J Anal Chem (1994) 349:91 96 Fresenius' Joumal of

© Springer-Verlag 1994

X-Ray diffraction at high temperatures N. Mattern ~, W. Pi tschke 1, A. D a n z i g I, S. Doy le 2

I Institute of Solid State and Materials Research Dresden, Postfach, D-01171 Dresden, Germany 2Technical High School Darmstadt, Department of Materials Science, D-64295 Darmstadt, Germany

Received: 25 June 1993/Accepted: 25 October 1993

Abstract. Experimental equipment for X-ray diffraction at high temperatures is introduced and the possibility to directly observe the evolution of the atomic (geometric) structure as a function of temperature is discussed. Re- cent results on crystallization investigations of amor- phous iron-based alloys and on the structural develop- ment in thin molybdenum sulphide films are given. The kinetics of the process was followed by means of time re- solved experiments in both cases.

sion and Debye temperatures can also be estimated by this method.

In this paper recent results are reported of high tem- perature X-ray diffraction investigation of two classes of materials. The formation of crystalline phases from the amorphous iron-based metallic alloys has been studied. The second example is the investigation of the structure and the structural development in thin molybdenum sul- phide films. Time resolved experiments in both systems have been used to follow the kinetics of the process.

1 Introduction

X-ray diffraction is a well established method for investi- gating the atomic (geometric) structure of matter [1]. It has successfully been used to determine the (ideal) crystal structure, to extract parameters describing the real struc- ture, and to characterize the orientation distribution for single crystalline and polycrystalline materials. As an routine analytical method, X-ray diffraction has been ap- plied to qualitative and quantitative phase analysis [2].

During their production, materials are often subject- ed to heat treatments which determine their microstruc- ture and properties. The development of materials with optimized physical properties requires knowledge of the structural and chemical events occuring in the process of manufacturing. X-ray diffraction at high temperatures offers the possibility to directly observe the evolution of structure as a function of the heat treatment. Such mea- surements permit the investigation of solid state reactions and phase transformations in the material. Details of a special part of the phase diagram can be studied. By means of X-ray diffraction the temperature and time de- pendence of phase reactions and phase transformation can be investigated and conclusions as to the reaction ve- locities and to mechanisms of phase formation can be ob- tained. Thermal properties such as coefficients of expan-

Correspondence to: N. Mattern

2 Experimental

The requirements for in situ observation of X-ray pat- terns at high temperatures can be met today by commer- cially available diffractometers connected to a heat cham- ber. Essential progress in recent years in the field of high temperature diffraction was reached by:

- the development of complete computer-controlled high temperature diffractometers which allow auto- matic measurements with a chosen temperature pro- gram;

- the availability of position-sensitive detectors and the use of intense synchrotron radiation to reduce the measuring time per diagram especially for time re- solved observation of phase transformations

- reaction chambers which facilitate realistic production conditions in the X-ray diffractometer.

Figure 1 a shows schematically the experimental system of a Bragg-Brentano-diffractometer with a high temperature chamber. In this case the heater is a current-carrying met- al ribbon. The samples, either as powder or compacts, are mounted in direct contact with the heater. Temperature measurement is by means of a W/Re thermocouple di- rectly spotwelded onto the rear surface of the combined sample stage/heater element. Calibration of the tempera- ture scale can be carried out by reference to the known phase transitions of a number of powders. Such equip- ment, consisting of a XPERT diffractometer PW3020

92

" "- , /Focus ing c l r c t e Counter t u b e I Dwergence ~ ~-.~

/

b

Fig. 1. a Schematic presentation of the Bragg-Brentano high tempera- ture diffractometer, b Bragg-Brentano diffractometer XPERT PW 3020 with high temperature chamber HTK 2.3

(Fa. Philips) with a high temperature chamber HTK 2.3 (Fa. Bahler) is shown in Fig. 1 b. With this high tempera- ture chamber, temperatures up to 2700 °C in vacuum, up to 2000°C in an inert gas atmosphere and up to 1600°C in air can be reached. The measuring time per diagram at a given temperature takes 15 -100 min depending on the angle range. Typical measuring programs with about 10 temperature steps last about 24 h.

The measuring time per diagram can be reduced in a conventional diffractometer down to several minutes by means of position-sensitive detectors. To observe fast transformations, more intense X-ray sources are neces- sary. Diagrams with a measuring time of the order of ms [3] or ns [4] can be obtained by the use of synchrotron radiation. Figure 2a shows, schematically, the arrange- ment of a high temperature diffractometer at the DORIS storage ring in Hamburg.

The monochromat ic X-ray beam encounters the sam- ple in the heat chamber. The elastically scattered intensity is registered by means of a position-sensitive detector. Figure 2b shows the set up at B2 at DORIS. The detector used, CPS 120 (Fa. Enraf /Nonius) enables the simulta-

CPS 120

i

/ / ~ =zl. 7775

/ HTK 2.3

b

Fig. 2. a Schematic presentation of the equipment for time-resolved X- ray diffraction at high temperatures, b The powder diffractometer at B 2 of HASYLAB with high temperature chamber HTK 2.3 and position sensitive detector CPSI20

neous registration of the diffraction diagram over a Bragg angle range of 120°C. With this arrangement measure- ment times of the order of seconds are possible. The limitating factor is the dead time of the detector, so that the power of the synchrotron radiation cannot be exploit- ed. Solid state detectors can work with higher count rates, but the angle range is limited to several degrees in 2 0 .

3 Results and discussion

3.1 Crystallization of metallic glasses

Metallic glasses are metallic alloys in an amorphous state obtained by rapid quenching techniques. The amorphous state is metastable and thermal treatments initiate order- ing processes such as structural relaxation and crystalliza- tion [5].

The investigation of the crystallization is essential for the estimation of the stability of metallic glasses but also to understand the short range order of the amorphous al- loy. Furthermore, special microstructures can be obtained from the amorphous state which are impossible to obtain by another way. An actual example is the development of nanocrystalline, soft magnetic materials [6]. Figure 3 shows the X-ray diffraction patterns of an amorphous Fe75BI4SiTCulNb 3 alloy at different temperatures. The amorphous state, indicated by diffuse maxima, is main-

[counts]

14000

12000

10000

8000

6 0 0 0

4000

2000

0 . 0 -

656"C 616"C 575"C 535"C

?o ' 2o ~ ~o-- ' do '

93

Fig. 3. X-ray diffraction patterns of amorphous FejsB/4Si7Cu~Nb 3 at high temperatures (CoK a radiation)

rained up to T a = 450°C. At temperatures above T a = 450°C, crystalline reflections arise. The crystalliza- tion takes place in three steps. In the first stage of the crystallization b.c.c. Fe(Si) is formed primarily in the amorphous matrix. In the second stage at about 600°C, iron boride phases, in this case Fe2B, are formed. At a temperature of about T a = 700 °C recrystallization of the microstructure is observed. The crystallization is a ther- mally activated process depending on temperature and time. Figure 4 shows the time dependence of the X-ray diffraction patterns of amorphous Fe74.sBvSils.~CuINb2.5 at T a = 500°C. The measuring time was 10s per dia- gram. After 230 s crystallization starts. From such tem- perature and time dependence measurements tempera- ture-time-transition (TTT) diagrams can be obtained. The TTT diagram of amorphous Fe79B/4Si 7 is shown in Fig. 5. The lines indicate the beginning of the phase trans- formation. In the two phase region the volume part of the Fe(Si) phase increases with time and temperature. Small

additions of Cu and Nb change the crystallization behav- iour and the microstructure of the phases formed [6, 71. The TTT diagram of amorphous Fe75B14SiTCulNb 3 is shown in Fig. 6. The region of coexistence of the amor- phous phase and b.c.c. Fe(Si) is enhanced remarkably. The microstructure consists of Fe(Si) grains with 10 nm diameter due to the addition of Cu and Nb. This nanocrystalline microstructure is the reason for the excel- lent soft magnetic properties of this material. The time dependence of the formation of the crystalline phase is usually analyzed by the Johnson-Mehl-Avrami (JMA) equation [8]. The volume part V of the transformed phase is given by:

V = 1 - exp (kt) n (1)

with k = temperature dependent rate function, t = time, n = JMA-exponent. The JMA-exponent n is correlated to the mechanism of the phase transformation. In the case of a three dimensional isotropic growth of a fixed nuclei

2 .10

7 $ 6 _ / /

1.8~

O. I 35.00

~ 7 56

1 89

lO~ O0 I I I I I

5 5 O0 7 5 0 0 9 5 . 0 0

Fig. 4. X-ray diffraction patterns of amorphous Fe74.5B7Si15.5CulNb2.5 at 500°C after 100, 200, 320, 460, 664, 990, 1220, 1980 s (Synchrotron radia- tion, 2 = 1.777 A)

94

T [°C]

800 -

700 -

600

500

400

Fe(Si)

+ Fe2B

amorphous ~ ~-~ o - ~ amorphous + Fe(Si)

1'0 5~3 100' 560 - -

Fig. 5. Temperature-Time-Transition diagram of amorphous Fe79BI4Si 7

0.0

-1.0

< ~' -E.0

-3.0

- 4 . 0

4 . 5

Fig. 7. Johnson-Mehl-Avrami Fe75BlaSiTCu~Nb3

+ . ÷ /

÷

÷ ÷ ÷ ÷ + n : l . 1

ooooo n : O . 6

/ 4

/ /

/

/

/ /

/ /

/

/

i i i i r i i i , ] 1 i r r i i i i i i i i i r i i i i i i i i i i i i i i i i i i i i i i , 1 ~ ] 1 i i i i ~ i , 1 1 i i i i i 1 ~

5.0 5.5 6.0 6.5 7.0 7.5 8.0 I n ( t / s e e )

plot of amorphous Fe79B14Si 7 and

T [°C]

800 •

700 •

600 •

500

400-

• Ee(Si) "~- '~-~-- - -~ . ._~ + Ee2B - - ~ • " ~ - ~ 4 X

" ~ - ~ . a m o r p h o u s --~- ~ .

o "~'~ + Fe(Si)'~-'- e amorphous "-.-I +Fe2B o + Fe(Si) o "~-~

amorphous o o ~---.

1'0 5'0 100 500 t [min]

Fig. 6. Temperature-Time-Transition diagram of amorphous Fe75BI4SiTCuINb 3

there are two values of special interest: n = 3 corresponds to the interfacially limited behaviour, where the rate limiting step is the addition of a further a tom to the growing particle; n = 3/2 is, on the other hand, charac- teristic of a diffusion limited behaviour where the rate limiting step is the long range diffusion of the atoms (i. e. a compositional separation in the matrix). Figure 7 shows the JMA-plot for two metallic glasses where the slope gives n. The value of n = 1.1 for Fe-B-Si without Cu and Nb is near to n = 3/2 expected for the diffusion con- trolled crystal growth with a I/t-law [9]. As can be seen in Fig. 9 the alloy with Cu and Nb has a JMA-exponent of n -- 0.6 indicating a changed mechanism due to the ad- ditions. To clarify the role of Cu and Nb, systematic in- vestigations by variation of the amounts of Cu and Nb on the microstructure and kinetics are under way.

3.2 Molybdenum sulphide thin films

Molybdenum sulphide (MoS2) in the form of a thin film is widely used as a lubricant for metallic surfaces in envi-

ronments where hydrocarbon or other fluid-based lubri- cants are unsuitable. It has found widespread application in space technology where its low coefficent of friction in vacuum is of particular use [10]. The inital state of films deposited by sputtering is to believed to either micro- crystalline or amorphous, since the X-ray diffraction pat- tern is observed to consist of one or two diffuse maxima. Although the crystalline structure is known to influence the lubricant properties, no systematic measurements of these structural transformations appear to have been car- ried out.

Thin films of MoS2 were produced by HF magnetron sputtering in argon at a pressure of 10 -2 Pa from a MoS 2 target onto unheated single crystal silicon wafers cut in the (001) direction. The films studied had thicknesses of 150, 300, 450, and 600 nm. Chemical analysis gave a com- position of MoSI 85 and an oxygen content of 5 at.%. To investigate the structural development, diffraction pat- terns were measured from room temperature up to 900 °C. Figure 8 shows the results obtained for a 450 nm film as a function of temperature. Other film thicknesses showed similar behaviour. The most obvious feature is the continuous change in the first diffuse maximum as a function of temperature. With increasing temperature the maximum intensity increases, the position of the maxi- mum shifts, and the reflection narrows. The diffuse maxi- mum gradually transforms into the largest peak, the (002) reflection from hexagonal MoS 2 (P6/3m); this corre- sponds to half the c lattice parameter. At a temperature of about 750 *C further reflections of MoS 2 become visi- ble, as well as weak reflections due to the formation of metallic molybdenum. Figure 9 shows the relationship between temperature and position of the first maximum for all samples studied. With increasing °temperature the lattice spacing d(002 ) decreases from 7.0 A to 6.4 A after annealing at 900°C. The thinnest (150nm) film shows the largest d value, while at higher temperatures all samples approach an effectively equal value. The figure also shows the change in lattice parameter as the sample is subsequently cooled; from this data a thermal expan- sion coefficent, a = 1 .2xI0 -SK ~, has been calculated. The observed (002) lattice spacing is much greater than

[ c o u n t s ] ~

3oooJ !

2 5 0 0 1

2000!

1500!

10(}0

50(}

0.0 ~o Jo J(} ' do ~o c'~el

3500 I I

95

Fig. 8. X-ray diffraction patterns of 450 nm MoS 2 film at T = 35 (lower), 100, 200, 300, 400, 500, 600, 700, 800, 9 0 0 ° C (upper) (CoK a radiation)

that in bulk crystalline MoS2, indicating that even after high temperature annealing, the structure does not have full crystalline order. Figure l0 shows the dependence of the reflection width (FWHM) on temperature. There is a dramatic change in FWHM from approximately 7 ° to less than 0.7 °, (the instrumental broadening is 0.3 °), over the range of sample thicknesses, again with the 150 nm film showing the largest FWHM value prior to heat treat- ment. With increasing temperature the difference in FWHM between the different films becomes less and less significant. The continuous change of the diffraction pat- terns with the temperature indicates that there is a growth of existing microcrystals in the films rather than crystalli- zation from an amorphous state. The analysis of the ob- served (001) reflections verify that the broadening is mainly due to grain size effects. The mean grain size D can be estimated from the FWHM, after correction for the instumental effect by the Scherrer formula [2]:

7.5

65

5,5

4.5

3.5

25

1.5

0.6

.0

I ] [ • i

0 [3

D~O00

0 A

• 1 6 ~30

1 . 8 o

+ + ++ t 200 400 6oo ~oo

Fig. 10. Dependence of the full value of the half width of the first maxi- mum of MoS 2 f i lms on temperature

O

0 o o

Iooo 12o0

16.1 '~

15.6

14.6

I F

A~Ai ° i H J A ~ O

MR ~ 000 0

| ,+,

I o i o o

Io

0

2o0 400 600 8o0 lOOO 12oo

Fig. 9. Dependence of the position of the first maximum of the diffrac- tion curve on temperature

3.5

~ 2 . 5

2.0

1.5

1.0 T=[?50 °C 4

0 100 200 300 400 50(} 6(}(} Time / r a i n

Fig. 11. Dependence of the full value of the half width of the first maxi- mum of MoS 2 at 550°C and 7 5 0 ° C on time

96

~ I 0 3

3 . 5 0

. 7 5

0 . 0 0 ] [ - - - -

7 , 5 0 1 1 . 5 0 1 5 . 5 0 1 9 5 0

T - ¸ ] r ; i

5 0

. 7 5

Jo,oo

Fig. 12. Changes in diffraction patterns of 450 nm MoS 2 with temperature during heating with T = 100 K/rain (Synchrotron radiation 2 = 1.777 A)

W H M / ° 2 ¢ ~ 150 r im, 20 K / r a i n

1 5 , 0 0 . . . . . 150 n m , 50 K / m i n . . . . . 150 n m , 100 K / r a i n . . . . . . . 4 5 0 r im , 20 K / m i n

/ N N . . . . . . 450 n m , 50 K / r a i n ~ " ~ / i ~ . . . . . 450 n m I 0 0 K / r a i n

5 . 0 0

0 . O0 O. O0 2 0 0 T. 0 0 ~ . . . . ~ ~ - ' . . . . . ~ . . . . . . . . . 400 0 0 . 6 0 0 . 0 0 8 0 0 . 0 0 1000 . OL

Temperature / °C

Fig. 13. Dependence of the full value of the half width of the first maxi- mum of MoS 2 films on temperature during heating

neous kinetics at a given temperature, measurements with synchrotron radiation and a position sensitive detector were performed. The structural development with tem- perature and time were followed by experiments at dif- ferent heating rates (20 K/rain, 50 K/rain, 100 K/min) with a measuring time of 30 s. Figure 12 shows the dif- fraction patterns of the 450 nm layer at various tempera- tures during the heating at 100K/rain. The diagrams show the increase in the maximum intensity, the shift of the peak position, and the sharpening of the (002) reflec- tion. The values obtained for the F W H M of the 150 nm and the 450 nm film are compared in Fig. 13; these are in- dependent of the heating rate within the error limit. The structural changes are thermally determined. With in- creasing order the activation energy necessary for a fur- ther improvement also increases and the crystallization process slows down.

Acknowledgement. This work was supported by the Federal Ministry of Research and Technology under contract number 05 5BLCAB1.

D = k/(cos 0 x FWHM) (2)

which gives a grain size of about 2 nm for the as-prepared state and about 20 nm after 900 °C heat treatment. Trans- mission electron microscopy investigations of the as- prepared state and after annealing at 900 °C confirm the existence of microcrystals with an extension as found by the diffraction results [11].

The structural development at a given temperature was investigated by means of time resolved X-ray diffrac- tion in a conventional diffractometer 0 5 min measuring time per diagram). Figure 11 shows the behaviour of the F W H M with time for two isothermal measurements, at 550 and 750°C. It can be seen that the F W H M depends strongly on the temperature but the reduction of F W H M is only about 10% after 7h. To measure the instanta-

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