X-RAY STUDY OF THE COMPRESSIO?i OF THE ALLOY MgIn

HXROSHL IW_-ISAICI

fhr Research Institute for Iron. Steel and Other Xfrtals. Tohoku t’niversit:. Send&. Jqmn

Abstract-A prssurs dependence of the lattice parameters of Sfgln haking the trtragonal Ll,-type structure has been measured by S-ray diffraction method using a diamond anvil-type squeezer up to i-1 CPa. The rate of decrease in the (1 parameter is larger rhan that of the c parameter and. consequently, the axial ratio c u increases from the v3iue 0.957 at atmospheric pressure to 0.97 at about 8 GPa. On further increasing pressure, howrvc:. it remains almost constant. Change in the volume can be described by a Birch-Murnaghan equation with an initial bulk modulus of 33 GPa. Experimental results are discussed taking into account the theory of lattice stability of the allo> dsvsl- npzd by Mrosan. John and Eschrig.

RCsumi--On ;t mesd par diffraction de rayons X la variation en fonction de la pression des paramhtres rtticulaires de MgIn, qui prtsente la structure quadrarique de type Ll,; on utiiisait jusqu.8 IlGPa enciron une prrsse Q enclume losange. Lz param&re a d&xoit plus vite que 12 paramitre c, de sorte que lr rapport c a passe de 0.957 & la pression atmosphtriyue 3 0.97 A 3 GPa envizm. II reste alors &want. si I’on continur d’augmenter la pression. On peit d&ire le changernent de volume par une Cauation de Birch et IrIurnaehan. avec un module de comoressibilit6 initial de 35 CiPa. On discuts les reiultats exp2rimrntauu en t&nr comptc de la thtorie di la stabilitC du rtseau de I’alliape due B Mrosan. John et Eschria.

Zusammenfassuog--Die Dru~kab~ng~gk~it drs Gitterparametcrs x-on MgIn rtrtragonale Struktur votn Typ Ll,) wurdc mit Rijntgenbeugung und einsm Diamantstempel bis zu II GPa gemessen. Der Par- ameter u nimmt rascher ab als c und daher sttigt das .Achsenverh~ltnis c u \-on 0,957 bei .Atmosph:irrn- druok auf 0,97 bei ungefZhr 8 GPa an. Es bleibt sllerdiq mit %-eiterem Druckanstieg nahezu konstant. Die Volumen;inderung kann mit einer Birch-Murnaghan-Gleichung mit einem anfSnglichen Modul van 33 GPa beschriebrn werden. Die Experimente werden unter Beriicksichtigung der Theorie van Mrosan. John und Eschrig iiber die Gitterstabiiit~t dieser Lcgierung diskutiert.

I. IYfl?QDI_XZT10~

In a magnesium-indium system the alloy with the

equiacomic composition has a face-centered cubic structure at high temperatures. Below 33O’C atomic

ordering takes place and the structure of the alloy becomes a tetragonal L10 (CU.&I &type one, which can be regarded as a layered structure consisting of alternate magnesium and indium (002) atomic planes.

An axiai ratio c,a oi the structure is a little smaIter than unity [ 11.

Formation of the ordered structure in this alioy

consisting of the polvvalent metals was theoretically

studied by Mrosan er al. [2] and Kogachi [3] apply- ing the pseudo-potential method. Both these

researchers formulated a structure dependent energy of MyIn. Interesting are the results of the stud>- by bfrosan r’c ~tl.. who expressed the energy as a function of the axial ratio and found that a part of the energy associated with an electronic band structure is lower at c LI = 1.0. bvhereas that part of the energy associ- ated with an electrostatic interaction shows a mini- mum at c it = 0.707. Since a decrease of the axial ratio of the LI,,-t>-pe structure from 1.0 to

0.707 = 1 IL 2 corresponds to a transition into the

BZ(CsCI)-type structure. their results imply that there are two competing terms in the total energy making

favorable different types of the structures. However. a towering in the ener_gy associated with the electronic band structure is somewhat larger and the minimum

in the total energy appears at the axial ratio close to unity, which is in an agreement with what is

actually observed. If the volume of the alloy is reduced by compres-

sion_ some change is expected to be induced into the electronic band structure and, therefore. there may

be a change in the relative contribution to the total

energy from the two different parts of the structure dependent energy. The aim of the present work is

to investigate by X-ray diffraction method ho\% the

axial ratio varies with decreasing volume. In our earlier publication [4] it ~‘a.s shown that

pressure induces a change in the stacking sequence

of the close-packed planes in Sly&. In !vigIn of the L 1 &pe structure. the close-packed planes are t 1 I I i and it is also the aim of the present ~vork co see

ii the stacking sequence of these pianes is ckanged or not.

a-

2. EXPERtMENTAL PROCEDCRES

The alloy was prepared by melting appropriate amounts of magnesium (99.9!Y; pure) and indium i99.99:; pure) metals under argon gas atmosphere in a graphite crucible placed in a high frequency induc- tion furnace. Chemical analysis showed the composi- tion of the alloy thus prepared to be Mg-50.7 at.?; In. After being homogenized the altoy ingot was filed to obtain fine powders, which were then sealed in an evacuated silica tube and anneaied at 250°C for 100 h. The heat-tr~dtment gave strong sharp X-ray diffraction lines of rhe Ll&pe structure. The Iattice parameters were determined using CuKr radiation to be a = 0.45SS & 0.0003mn and c = 0.4391 + 0.0003 nm. with cj:t = 0.957 i: 0.001. These values are in fair agreement with those reported by Ino er nl. [l].

High pressure equipment used was of a diamond anvil-type originaIIy developed by Bassett et al. [S]

and modified in our laboratory. A couple of anvils, one with a face of f.4mm and the other with a face of 0.5 or 0.7 mm in diameter, were used with an In- cannel gasket between them. X sealed-off fine focus tube with a moIybdenum target was empioyed to gen- erate X-rays. After being filtered by zirconium foil the radiation was collimated to produce a beam of 0.1 mm or, at lower pressures, O.Zmm in its diameter, which irradiated an intimate mixture of the powders of MgIn and NaCl squeezed between the anvils. Dif- fracted rays were recorded on a Aat film placed at a distance 70mm from the sample. It took two days to obtain X-ray photographs useful for the sub- sequent analysis, but at higher pressures much longer rime of exposure was necessary. Pressure generated at the sample was estimated by measuring the lattice parameter of NaCl and referring to Decker’s new scale [63_ The maximum pressure attained in the present work was 14 GPa.

DifTraction lines tied for the derermination of the lattice parameters of MgIn were 001, 110, 1 llr ZOO, 002, 220 and 202. A set of a and c values fitting to the &values of &he observed fines were found by a least-squaxs method. With increasing pressure back- ground inttnsity increased and it became difficult to read with a fair accuracy the positions on the fiim of Iines Rith higher indices.

Enor in the iattice parameter determination arising from a shrinkage of the film was corrected by measur- ing the distance between the shadow edges of the fihn cassette. There might be an error a&ins from a sample displacement, but the magnitude of the dis- placement was very small as compared with the large sample-to-film distance 70 mm adopted in the present work and its effect on the fattice parameter deter- mination was considered to be not serious. The accu- racy in the u and c values measured is estimated to be ~O.l-O.?~ at pressures lower than 6GPa and ~0.3-0.P. at higher pressures. For SaCI diffraction lines 200, 120 and 722 were used. The error in the pressure determinatton due to that involved in the measured lattice parameter of NaCI is estimated to be 0.1-0.1 GPa. At higher pressures. it has increased to 0.3-0.5 GPa.

Three separate runs of the high pressure experi- ment were carried out. In some cases, a quality of the diffraction pattern was not high and the lattice parameters could not be determined with the accu- racy menrioned above. The data obtained from such tims have been omitted in the subsequent analysis.

3. EXPERIMENTAL RESULTS

Figure I shows X-ray diffraction photographs of MgIn at 2.5. 5.0 and 9.5 GPa. As was mentioned in

5.0 GPa

9.5 GPa

Fig. 1. X-ray diffraction photographs of MgIn at 2.5. 5.0 a& 9.5 GPa. Fiitered MoKz radiation. Di&action lines are: l-001. Z-110. 3-111, J-I%Q 5-002. 6-220. f-203. Those of NaCi are: 5-200, Q-220,

10-2’.

IWASAKI: STUDY OF COMPRESSION OF MgIn 649

Pressure, GPa

095 I, , , , , !

Fig. 2. Pressure dependence of the lattice parameters and axial ratio of higIn. o0 = 0.4588 nm and c0 = 0.4391 nm.

2, background intensity increases with increasing pressure and therefore it is difficult to distinguish the diffraction lines with weak intensity from the back- ground at higher pressure. No significant change has been observed in the diffraction patterns throughout the experiment, indicating that the stacking sequence

of the close-packed planes remains the same and the

Ll,-type structure of MgIn is stable up to 14 GPa. The pressure dependence of the lattice parameters n and c is shown in Fig. 2, where they are normalized

to their respective values at atmospheric pressure. a,, = 0.4558 nm and c0 = 0.4391 nrn. The compressi- bility of the a-axis is seen to be larger than that Of the c-axis: for instance, at 3.5 GPa

a = 0.4478 + 0.0008 nm with u/o,, = 0.976, while c = 0.4316 + O.ooO8 nm with cjcO = 0.983. At

8.2 GPa, a = 0.438s + 0.001 j nm with a/a,, = 0.956 and c = 0.425 i: 0.0015 nm with c/c0 = 0.968. Since the Ll,-type structure can be regarded as a layered

structure, the results shown in Fig. 2 mean that a

resistance to contraction of the distance between atoms on the same layer is smaller than that between atoms on the neighboring layers.

As a result of the anisotropy in the compressibility the axial ratio c/a gradually increases with increasing pressure as shown at the bottom of Fig. 2. c/a is 0.957 at atmospheric pressure and it increases to 0.97 at about 8 GPa. On further compression the axial ratio

does not increase nor decrease but appears to remain constant.

In Fig. 3, the volume of the alloy is shown as a

function of pressure. Although there is a scatter in

the datum points, the pressure-volume relation can be described by a well-known Birch-Murnaghan equation

with K0 (bulk modulus at 0 GPa) = 38 GPa and < = -4.4. The solid line in Fig. 3 represents P-Y rela- tion based on this equation. Drickamer er al. [7]

reported K0 values of some of metals and alloys

obtained by X-ray measurements. According to them K, = 30.3, 32.3 and 47.6 GPa for magnesium, Mg-2at.%In and indium, respectively. K, of MgIn

is in between the values of the constituent metals.

0ee*

0.84.

o.eo-

Fig. 3. Pressure dependence of the volume of MgIn. Solid line represents a plot of the Birch-Murna_ehan equation with an initial bulk modulus of 38 GPa.

650 IWASAKI: STUDY OF COMPRESSION OF M&I

4. DISCUSSION

The increase, but not decrease, of the axial ratio observed for bfgln on compression can be interpreted in the following way : Since the energy associated with electrostatic interaction always has its minimum at C’U = l/‘, 2 irrespective of the unit cell volume for our alloy containing metallic ions of different valences, the shift of an equilibrium axial ratio to the value much closer to unity is due to the increased contribution to the total energy from that part of the energy associated with electronic band structure. If it were possible to obtain the MgIn alloy with an expanded volume, it would have an Ll,-type struc- ture with the c/n value much deviated from unity. Calculation of the band structure energy at reduced and expanded volume will confirm the situation above mentioned, although a lack of the information on the form factors relevant to these cases may make the calculation difficult.

Above 8 GPa, the axial ratio does not increase but remains almost constant. In this connection notable is a dependence of c/a on the indium content of the alloy. According to fno et al. [l] c/a gradually in- creases as the composition deviates from the stoichi- ometry and it has the largest value, 0.97, at 39 at.% In. This indium content corresponds to the minimum one below which the phase having the Ll,-type structure is no longer stable. Although a change in the alloy composition gives rise to an effect other than the compression effect, it is of interest to note that the same limiting value of the axial ratio has been observed for the ordered phase of MgIn on reducing volume and on reducing electron-atom ratio.

In their lattice stability theory of MgIn, Mrosan

et al. QJ pointed out that a long period superlattice having the CuAuII type structure becomes stable if the axial ratio increases. One of the possible ways to increase c!a of MgIn without changing electron- atom ratio is, as has been seen above, the compres- sion of the alloy. A direct indication of the formation of the long-period superlattice is a splitting of X-ray diffraction lines with the particular indices. For in- stance, the line 110 of MgIn will split into two peaks, while 001 and 111 remain as single peak. A careful inspection of the X-ray photographs taken in the present work, however, has failed to reveal any clear evidence of the formation of the long period superlat- tice. This might be partly due to an insufficient acti- vation of atom diffusion and high pressure-high tem- perature experiment could give a definitive conclu- sion.

~C~~Q~iedge~enr-The assistance by Dr. Y. Watanabe in preparing samples is greatly acknowledged.

REFERENCES

1. N. Ino. M. Hirabayashi and S. Ogawa, Trans. Japan Inst. Merds 6, 171 (19651.

2. E. Mrosan. W. John and H. Eschrig, Phys. Status Solidi (b) 51, 793 (1972).

3. M. Kogachi, J. Ph~s. Chem. Solids 34. 67 (1973). 1. H. Iwasaki, Y. Watanabe and S. Ogawa, J. appl. Crysr.

7, 611 (1974). 5. W. A. Bassett. T. Takahashi and P. W. Stook. Rec.

scient. Insrrum. 38. 37 (1967). 6. D. L. Decker, J. appl. Phys. 42, 3239 (1971). 7. H. G. Drickamer, R. W. Lynch, R. L. Clendenen and

E. A. Perez-Albuerne, in Solid Scare Physics (edited by F. Seitz and D. Turnbull), p. 135. Academic Press, New York (1966).