Formation of amorphous AlCr and AlMn alloy films by rf sputtering

Journal of Non-Crystalline Solids 124 (1990) 121-130 North-Holland

121

Formation of amorphous A1-Cr and A1-Mn alloy films by rf sputtering K. Masui, H. N a k a m o t o , S. M a r u n o , T. K a w a g u c h i a n d S. S a k a k i b a r a Nagoya Institute of Technology, Showa-ku, Nagoya, Japan 466

Received 14 September 1989 Revised manuscript received 2 April 1990

A new type of amorphous alloy, formed in the limited composition range of about 80-90 at.% AI (AI-Cr) and 70-90 at.% A1 (AI-Mn) was produced by rf sputtering under Ar atmosphere. The existence of the amorphous phase was confirmed by X-ray diffraction, transmission electron microscopy and differential scanning calorimetry. The formation of the amorphous phase is discussed in association with the intermetallic compounds (CrAI7, Mn4AI11, MnAI6, etc.) having crystallograpkically complex structure, which have nearly the same composition as the amorphous phase. A weak X-ray scattering halo is observed at the diffraction angle lower than that of the strongest halo which characterizes the amorphous structure. The weak scattering halo, which is generated by an X-ray interference effect, is considered to be correlated to the small clusters in which a transition metal atom coordinates several AI atoms. The crystallization temperatures of the amorphous alloys are about 400 and 370 °C for A1-Cr and A1-Mn samples, respectively.

1. Introduction In general, physical vapor deposition (PVD) processes (sputtering, vacuum evaporation, ionimplantation, etc.)offer some advantages to yield metastable phases, such as amorphous solids [110], supersaturated solid-solution [11], quasicrystals [10,12] and disordered superlattices [11]. Although various kinds of amorphous alloys have been obtained with vapor and melt quenching techniques, only a few papers have been published on Al-based amorphous alloys [4,6,8,10,13] and a systematic study has not been reported. We reported a new type of Al-transition metal (TM; Fe, Co and Ni) binary amorphous alloy, and discussed the prerequisite for amorphous phase formation in these alloy materials [14]. We found that it is necessary to satisfy the following three conditions to form an amorphous solid in A1-TM binary materials: (1) the amorphous phase is formed in the limited composition range of about 75-90 at.% A1; (2) in such a composition range, there exist several intermetallic compounds having

a crystallographically complex structure in the equilibrium state; (3) each T M atom in these compounds coordinates 9 to 11 A1 atom neighbors and forms a polyhedron cluster. It is of interest to study further the prerequisites for amorphous phase formation in A1-Cr and A 1 - M n binary alloys, since these alloy systems were recently noted as systems likely to form a 'quasi-crystal' which has five-fold symmetry [15]. The ideal composition of the quasi-crystal is now believed to be near 80 at.% A1 [16], and this composition is approximately the same as the amorphous phase. The arrangement of atoms in the quasi-crystal is the same as that of the equilibrium phase [15]. It is thought that the quasicrystal is one of the metastable phases formed in a sequence of relaxation process from the amorphous phase to a stable phase in these alloy systems. In this report, as-sputtered and thermally treated samples were examined using X-ray diffraction (XRD), transmission electron microscopy (TEM) and differential scanning calorimetry (DSC).

0022-3093/90/$03.50 © 1990 - Elsevier Science Publishers B.V. (North-Holland)

122

K. Masui et al. / Formation of amorphous A l- Cr and A l- Mn alloy films

2. Experimental procedures

Table 1

Film samples with different thicknesses w e r e deposited onto various substrates suited to each experimental purpose: freshly cleaved NaC1 crystals for electron microscopy ( - 0 . 1 ~m in thickness), A1 foils for calorimetry (3-5 ~m) and

Sputtering power density: Arpressure: Deposition rate:

5×10 3 Torr

Substratetemperature: Target to substrate distance:

-150°C 25-28 mm

Sputtering conditions

'

0.8-1.0 ~m/h

Frequency:

Ni plates for X-ray diffraction (8-10 ~tm). The sputtering conditions are listed in table 1. As shown in the inset of fig. 1, segmented sputter targets were made up of two single sections of A1 plate (99.99%) and TM plate (99.9%), and these were designed so that the A1-TM binary systems could be investigated over a wide composition range. Some compositional profiles of samples normal to chord separating the A1 and T M segments as a function of substrate position are shown in fig. 1. Since the sputtering yield for A1 (1.24) is lower than that for Cr (1.30) in the case of an accelerated Ar + ion of 600 eV [17], the Cr concentration is higher in sputtered samples for a given A1/Cr area ratio of the target. In the case of the A I - M n system, the Mn concentration was also higher. Six kinds of alloy targets (AI-10 wt% Mn, A1-20% Mn, A1-14% Cr, etc.), which were fabricated in a vacuum induction furnace, were used in order to avoid a steep compositional gradient in a sample, 100

-6 W/cm 2

13.56 M H z

The composition of the samples were determined with an electron probe microanalyzer. Two kinds of X-ray diffraction measurements were carried out corresponding to the experimental purposes: (1) a continuous scanning method over a wide range of diffraction angles to identify the phases of the samples; (2) a step scanning method over a narrow range of the angle in a step width of 0.1 ° to measure a weak halo of scattered X-rays. The films deposited onto NaC1 crystals were removed from the substrate in distilled water and floated onto a tungsten mesh. The samples, wrapped with Zr foil, were heat-treated under a high vacuum of 1 0 - 6 Torr. The thermal behavior of amorphous samples was studied with DSC at a heating rate of 20 o C / m i n .

. . . . . . .

[ b. . . . . . . .

~ 8o-

~. 6o target

40

C 0

o

2O

~

. target

[argel t

0

1

I

2

i

3

~

4

5ubstrate

i

5

i

6

I

7

Position

i

8

i

1

~

2

i

3

i

Z,

5ubstrate

L

5

;

i

6

7

8

Position

Fig. 1. Variations of (a) A1 and Cr or (b) A1 and M n contents in a sample on substrate placed along a diameter of the target normal to the interface between the segments.

123

K. Masui et aL / Formation of amorphous A 1- Cr and A l-Mn alloy films 3. R e s u l t s

(o)

Figure 2 shows typical XRD patterns from the as-sputtered samples. The patterns change markedly depending on the A1 content, similar to the cases ofA1-Fe, A1-Co and A1-Ni systems [14]. The pattern for a pure A1 sample is assigned to a fcc crystal. In the case of A1-Cr system (fig. 2(a)), there are only three phases observable: fcc-A1 (90-100 at.% A1); a non-crystalline phase (80-90% AI) for which the peak of the halo is at about 64 o; and bcc-Cr (0-75% A1). In the case of the A1-Mn system (fig. 2(b)), five phases are observed with decrease in A1 content: fcc-A1 (90-100% A1); non-crystalline phase (7090% AI) for which the peak of the halo is at about 65°; disordered MnA1 (30-65% A1); fl-Mn (1545% A1); and a-Mn (0-15% A1). The results of XRD measurement show that the stable phases of superlattices (CrzA1, CrsAI8,

A[ -

(a)

it

'

c~-9°~'~'°A~ Cr-g2at?loAI , Mn-86at:l.A[

Mn-82at~'loAl

1~0

200

3~0 T• rn p e r a t

ur e

400 s00 (°C)

Fig. 3. Typical DSC traces of amorphous alloys in the different AI-TM binary systems.

Cr4A19, y2-MnA1) and intermetallic compounds (CrA14, Cr2A1]], CrAI7, Mn4AItl , MnA14, MnA16) expected from the equilibrium phase diagrams [18,19], were not formed under the sputteringconditions. AI-

A1(220) _ ~

Mn

Pure AI

95at.%AI 95 at. I.AI~\ .

,

AI(III) Ai(200) [(200)_

~AI

•

, I

AIlll I) Pure Al.

'

- ,J- \~ , ~

~tl'(b)

(b)

Cr

A

.

.

.

90 at.%AI

AI At _ ~

82 at. "/.AI 90-at"/'AL~'~'~

61"IAlat.,t ' 47 at. "I.A[

~

*

-

"'___~Mn At)*

.

.

bcc(Cr)

18ati:llA' -

4b

'

j~ 60

"~'~

.

.

.

- ~-

~1

15 at. "I, AI

ccCr(110)

13 at.%AI

....

8b

2e (Cr-K~)

Cr(200) ~

a~

a-Mn

a

11 at. "/.At

6o

8o

2e (Cr-K~)

Fig. 2. X-ray diffraction patterns of RF-sputtered films with different contents of (a) AI-Cr and (b) A I - M n alloys. The asterisks ( * ) indicate the disordered state in superlattice.

124

K. Masui et al. / Formation of amorphous A l- Cr and A l-Mn alloy films

The thermal behavior of samples were examined with DSC and TEM to confirm the presence of the above mentioned non-crystalline phases. Figure 3 shows typical DSC curves from (a) A1-Cr and (b) A1-Mn samples. The former exhibits a single exothermic peak appearing at a temperature of about 400 °C. In the latter case, three broad exothermic peaks are observed which shift to higher temperatures with decreasing A1 contents,

~as~

tered

I

°C

(¢

,'~DU'K,

i~ Fig. 4. Transmission electron micrographs and electron diffraction patterns of sputtered Cr-87% AI alloy film under the condition of (a) as-sputtered and heat-treated to (b) 4 0 0 ° C and (c) 450 ° C at a rate of 20 ° C / m i n .

Figure 4 represents a sequence of steps in a heat-induced structural transformation of the sputtered Cr 87% A1 alloy film. The bright-field image of the as-sputtered film appears ambiguous and featureless even at a magnification of 20 000, and the diffraction pattern gives a broad halo-ring (fig. 4(a)). The bright-field image of the sample heated to 400 ° C (fig. 4(b)) shows the distribution of crystals heterogeneously nucleated with a characteristic oblong shape of about 1 ~m in length, which are randomly scattered within the matrix. The diffraction pattern was attributed to a monoclinic CrA1 v. The samples heated up to 450 °C has a fully crystallized structure as seen in fig. 4(c), and the electron diffraction pattern can be indexed as CrAI7. Figure 5 also provides a sequence of steps of a structural transformation in the Mn-82% A1 alloy film. The bright-field image of the as-sputtered film appears featureless similar to that of the A1-Cr sample, and the diffraction pattern gives a broad halo-ring of amorphous solids. When heattreated at a temperature of 400 o C, higher than the first exotherm peak (360 ° C) of the DSC curve, fine crystallites of a size < 100 A precipitate homogeneously as shown in fig. 5(b). The values of d-spacing calculated from the Debye-ring of the crystallites were d = 3.85, 2.06, 1.48, 1.26 and 1.08 A. These d-values are not matched with those for any of the intermetallic compounds of MnA14, MnA16 and G-phase (MnA112) [19,20]. The values of d-spacing are almost in accord with those of the 'quasi-crystal' of A1 12% Mn alloy reported by Bancel et al. [21]. A more detailed crystallographic study will be necessary to determine the structure of the crystallites. These unknown crystallites are thermally stable even at a temperature of 500 ° C. The bright-field image of the sample heated to 430°C manifests the course of crystallization as seen in fig. 5(c). The oval-shaped crystal is an orthorhombic MnA16. The structure of the fully crystallized sample is shown in fig. 5(d). It can be seen that that large grains of 2 4 ~m in size are formed. The corresponding diffraction patterns from the grain consist of a strong net pattern and weak Debye-rings, which can be indexed a s M n A 1 6 crystals with a small amount of unknown crystallites.

K. Masui et al. / Formation of amorphous AI-Cr and A l-Mn alloy films

125

? ??;'

Fig. 5. Transmission electron micrographs and electron diffraction patterns of sputtered Mn-82% AI alloy film under the condition of (a) as-sputtered and heat-treated to (b) 400 ° C, (c) 430 o C and (d) 550 o C, respectively.

The results of XRD, TEM and DSC observations indicate that an amorphous phase is formed in the limited composition range of about 75 to 90% AI, and the crystallization temperature of the amorphous alloys is about 400 and 360°C for A1-Cr and AI-Mn alloys, respectively,

4. Discussion The experimental results prove that the amorphous phase is formed in a limited composition range for A1-Cr and A1-Mn sputtered binary alloy systems. The structure of the as-sputtered phase in these alloys is shown in the lower part of fig. 6 with the equilibrium phase diagrams of A1-Mn and A1-Cr alloys. The following characteristics have been noted for these samples. First, the number of phases of the as-sputtered samples is considerably smaller in comparison with that of the equilibrium phases. In the composition range of 100-50 at.% A1, only three phases of fcc-A1,

amorphous and bcc-crystal, are observed. Second, the amorphous phase is always observed in the Al-rich composition range. Third, there are many intermetallic compounds (CrA14, Cr2A111, CrAI 7, MnaAlll , MnA14, MnA16) in the composition range in which the amorphous phase is formed. Fourth, various superlattice phases cannot be formed under the sputtering condition but simple bcc crystals (disordered superlattice) appear. This is similar to the results found in the A1-Fe, - C o and - N i binary systems [14]. This similarity may suggest that the vapor quenching process induced by sputtering is too fast to form a superlattice, for which a long-range ordering of atoms is needed. It has been reported, based on structural investigations of various amorphous alloys [22-24], that the short-range order (SRO) of the amorphous phase is similar to that of the stable crystal. From this point of view, we discuss the characteristics of atomic arrangement in the corresponding intermetallic compounds. Figure 7 shows a summary of the crystallographic data on these compounds

126

K. Masui et al. / Formation of amorphous AI-Cr and A I - M n alloy films

[25-28]. The datum of TM-A112 (TM; Cr and Mn) crystal called G-phase [27] is also given as a reference. The structure of the G-phase has a primitive simple fcc-lattice same as that of pure A1, when the structure is in a disordered state, The relations between A1 concentration and the unit-cell volume of the intermetallic compounds and disordered superlattice phases are shown in fig. 8. We point out some remarkable features with respect to the compounds existing in the limited composition range in which the amorphous phase is formed. (1) These compounds have a crystallographically complex structure such as monoclinic, triclinic, etc. (2) These compounds have a large unit-cell volume. (3) Each TM atom coordinates 10 to 12 A1 atoms to form a polyhedron cluster, Since vapor quenching by sputtering is thought to be an atomic process, these intermetallic compounds must be only formed through the rearrangement of surface atoms by thermal relaxa-

1800 . ( a ) " , ~ ' .

tion effects. On the other hand, the structure of these compounds, with many coordinated polyhedron clusters, is so complex that direct formation of of a stable crystalline phase is difficult during deposition. In consequence, it is assumed that the formation of an amorphous phase by sputtering in the limited composition range is closely associated with the existence of the intermetallic compounds having a crystallographically complex structure. The XRD measurement over an intermediate angle region which is suited for the study of the configuration of clusters [29] was undertaken to confirm the presence of coordinated polyhedron clusters in the amorphous solid. Figure 9 shows the typical XRD patterns from as-sputtered and heat-treated alloys. The strong halo between 50 and 80 °, labeled 'main halo', is caused by interatomic correlations in the amorphous state [23]. The main halo from the as-sputtered samples indi-

Cr - AI ,

..

.(b)

Mn-AI

L

%,. 'j "

lZ,00

~ O ,. j

L

~ ~

z <

-

,

1000

~-

~,

600

b~C~

\

.Mo

,/ ,

IlJ

"' ii I Ill III .

as-sputtered p ha s e

.

.

.

.

.

.

.

.

i I

.

II / A m_.

_

J

fccAlJ

60 At

80

:

I

I

b c c (Cr)

0--' 20 4'0 Atomic %

! (MnA,I ~

II ~l"

III 200

#

100 0

~

I i

,

I

',,

t i

II ii

I Ii

,

,,

,

:',,

~ -Mn

I3_M n disorder

Am. MnAI {bcc)*

20 40 60 Atomic °Io A[

.fc o A f

80

100

Fig. 6. A comparison of equilibrium phase diagrams of A1-Cr [181 and A1-Mn [19] systems (upper part) and as-sputtered phases made in this experiment(lowerpart).

127

K. Masui et aL / F o r m a t i o n o f a m o r p h o u s A l - C r a n d A I - M n alloyfilms

ntermetallic

Number of

compound and crystal structure

atoms in a

Mn4Alll (triclinic) a:5092A

Mn=8~ AI=22j 30

b=8.862~

unit-cell

Unit-cell volume

cluster around one TM atom O ;AI :~ ;Mn or Cr

Shape of coordinated polyhedron

Numberof clusters in a unit-cell

MnAIIo (16hedron)

8

~5]

MnAII0 (16hedron)

4

[26

435A3

2

127]

430A3

Ref.

"

c=5.047A m= 85"19' B=I00"24' ¥=I05°20 ' " MnAI6 (orthorhombic) [ a=6.4978~ ] b=75518~ c=88703A

Mn:4

TM.A112" (TM;Mn,Cr)

TM=2 ~ Al=24J26

423A3

TM.A112 (20hedron)

Cr=141 AI=90J104

1630A3

CrAll2 (20hedron)

}28 AI=24

(body-centered cubic, bcc)

[ a=7.507A ] CrAI 7 (monoclinic) a=25.196A ' b= 7.574~ c=I0.949A B=128o43,

Cr2All7

~

6

~8] I0

~

4

(30hedron)

*;metastable phase

Fig.7. Summary of crystallographic

data of the intermetallic compounds in A1-TM(TM;Cr, Mn) systems.

cates that the alloys have no periodic configuration of atoms. It is more noticeable that the weak halo (shaded part), labeled 'sub-halo', appears between 20 and 40 o. Sharp diffraction lines from the crystal phase were observed after heating to a temperature of 440 o C for A1-Cr and 500 o C for A1-Mn. These diffraction lines correspond to the compound CrA17 (fig. 9(a)) and Mnml 4 + MnA16 (fig. 9(b)), and the sub-halo disappears, Here, we discuss the origin of the sub-halo related to the X-ray correlation between polyhedron dusters in which several AI atoms surround one TM atom. Thermodynamical and crystallographical investigations [30,31] on the A1-TM (TM; Cr, Mn, Fe, Co and Ni) intermetallic compounds have pointed out the following characteristics. (1) The heat of formation of the Al-rich compounds has a high negative value and a strong interaction between the A1 and TM atom is present. (2) In the case of an A1 content higher than 70 at.%, each TM atom in these compounds is surrounded by 9 to 12 A1 atoms to form a poly-

hedron cluster. (3) The TM-A1 distances can be classified into two groups having shorter and larger values as shown in table 2. The shorter values of A1-TM distances are less than the total value of the Goldschmitt's atomic radius (A1, 1.43 ,~; Cr, 1.29 ,~; and Mn, 1.37 A). It is thought that several A1 atoms have strong interaction with the TM atom, leading to the formation of small primitive clusters such as TM-4A1. On the contrary, the structure of TM • Al12 (G-phase) is quite different. The TM atom in the G-phase is surrounded by 12 A1 atoms at an equal distance to form a regular icosahedron cluster. Hence the crystal does not form any primitive small clusters such as TM-4A1. As reported through the structural investigation on various amorphous alloys [22-24], the shortrange order (SRO) of the amorphous phase is similar to that of the stable crystal. If the concept is acceptable in the case of A1-TM systems, it is suggested that the SRO of the amorphous phase is almost the same as that of the corresponding compound, and that the small primitive cluster

128

K. Masui et al. / Formation of amorphous Al-Cr and AI-Mn alloy films

crAI,

may show the X-ray scattering halo (sub-halo) through the intercluster interference effect [32]. When the diffraction angle is lower than 35 o (20, Cr-Ka), the fine structure of the electron-density distribution within the cluster the size of which is smaller than about 7 ,~ can be ignored by adopting the sampling theorem of X-ray diffraction [32]. Consequently, if the cluster size is less than about 7 ,~, we can apply the Ehrenfest model [32] to the sub-halo caused by the inter-cluster interference effect of X-ray scattering. Here, the nearest neighbor distance between the clusters, R, which is assumed to be the cluster size, can be estimated using the Ehrenfest relation

150C -e-e-Mn-AI -o-o-Cr-AI 2x v E 100(1 >-~

/ ~-,~pr~ ~ /

~lJ

~

j

50(-\

R = • / E sin O,

~'~\2~'n

It ,

\ \

~~- * . ~// ~ ~ bccCr ~ d CJ _ ~ _ ~r~Al~ _ ~ ~.... 20 40 60 80 100 Atomic % AI Relationships betweenAI concentration and a unit-cell

Fig. 8. volume of the intermetaUic compounds and the superlattice presented in the AI-TM (TM; Cr, Mn) binary systems. The asterisks ( * ) indicate the value of disordered state in superlattice,

such as TM-4A1 can exist in the amorphous phase, The amorphous solid consists of dense random packing (DRP) of these primitive clusters, and it

where E is 1.62 when the packing of the cluster is fcc-like packing, and 20 is the X-ray diffraction angle at which maximum X-ray intensity is observed. The peaks of the sub-halo are at about 33 ° (A1-Cr) and 36 ° (A1-Mn) of 20. The nearest neighbor distance R is calculated as 5.2 ,~ and 5.0 ,~ for A1-Cr and A1-Mn alloys, respectively. These values are nearly in accord with those of the sizes of the primitive clusters calculated with the crystal data of the compounds as shown in table 2. It is thought that these A1-TM amorphous alloys are composed of the dense random packing of the primitive clusters, such as TM-4A1. The existence of a similar weak scattering halo of this type below the angle of the main interatomic halo was also reported for the Sm-Co amorphous alloy [5] and As-S glass [29] as evidence of medium range

Table 2 Interatomic distance and size of the primitive cluster of the intermetallic compounds Compound

Mean distance of shorter TM - 4AI bond (,~)

Mean distance of total bond (]k)

Mn4Alll MnA16 TM.AI12 (G-phase) CrA17

Mn-4A1 Mn-4A1

2.50 2.49

Mn-10AI Mn-10AI

2.61 2.56

a) Cr-4AI

2.55

TM-12AI Cr-12A1

2.7 2.68

a) all TM-AI bond distances are identical.

Sum of Goldschmitt's radius

Size of primitive TM - 4AI cluster

Ref.

(A)

(A)

2.80 2.80

5.00 4.98

[25] [26]

2.72-2.80 2.72

a) 5.11

[27] [28]

K. Masui et al. / Formation of amorphous A 1- Cr and A l-Mn alloy films

(a)

O r - 8 7 clt*/, AI

ic~A''

CrAI~

4~0°c

•-

r-

CrAI7

.A.

360"C

A ~

~

as-spu ttered I

I

T

i

I

I

,

I

I

i

(b) Mn-82at*/,AI

>"

129

o

•

/IJ

<

o 0

>,

500"C

~n E

300"C ~

0

0

/

o

~

C --

as-sputtered I

0

10

20.

~..,-,-,-zr//7~

I

I

20

30

degree

/ t

z.o

(Cr-Ka

t

[

I

50

6o

70

80

)

Fig. 9. X-ray diffraction patterns of sputtered films in the range of lower diffraction angle.

order of small clusters within an amorphous matrix.

5. Conclusion (1) The phases in the as-sputtered samples are less numerous than those found in the equilibrium phase diagram of the A I - T M binary system. (2) An amorphous phase is synthesized only in the limited composition range of about 80-90 at.% A1 (A1-Cr) and 70-90% A1 (AI-Mn). (3) The formation of the amorphous phase in such a limited composition range is closely associated with the existence of several intermetallic compounds having crystallographically complex structures.

(4) The T M atom in an amorphous phase coordinates A1 atom neighbors to form a primitive cluster such as T M - 4 A I , and the amorphous solid

seems to be composed of dense random packing of these primitive clusters. One of the authors (K.M.) wishes to thank Dr S. Prakash of University of California of Los Angeles for his comments during the preparation of the manuscript.

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Solids 81 (1986) 155. [5] s.s. Nandra and P.J. Grundy, Phys. Status Solidi A41 (1977) 65.

130

1(. Masui et al. / Formation of amorphous A I - C r and A l - M n alloy films

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[18] F.A. Shunk, Constitution of Binary Alloys, 2nd Suppl. (McGraw-Hill, New York, 1969) p. 21. [19] T. Gedecke and W. Koster, Z. Metallkd. 62 (1971) 727. [20] G.V. Raynor and K. Little, J. Inst. Met. 71 (1945) 493. [21] P.A. Bancel, P.A. Heiney, P.W. Stephens, A.I. Goldman and P.M. Horn, Phys. Rev. Lett. 54 (1985) 2422. [22] K.H.J. Buschow, J. Non-Cryst. Solids 85 (1982) 221. [23] R.P. Messmer and J. Wong, J. Non-Cryst. Solids 45 (1981) 1. [24] M. Sakata, N. Cowlam and H.A. Davies, J. Non-Cryst. Solids 46 (1981) 329. [25] J.A. Bland, Acta Crystallogr. 11 (1958) 236. [26] A.D.I. Nicol, Acta Crystallogr. 6 (1953) 285. [27] J. Adam and J.B. Rich, Acta Crystallogr. 7 (1954) 813. [28] M.J. Cooper, Acta Crystallogr. 13 (1960) 257. [29] J.C. Phillips, J. Non-Cryst. Solids 43 (1981) 37. [30] O. Kubaschewski and G. Heymer, Trans. Faraday Soc. 56 (1960) 473. [31] A. Pasturel and P. Hicter, J. Less-Common Met. 86 (1982) 181. [32] A. Guinier and G. Fournet, Small-Angle Scattering of X-Rays (Wiley, New York, 1955) pp. 14l, 265.