Mater. Trans. - J

Materials Transactions, Vol. 46, No. 12 (2005) pp. 2893 to 2897
Special Issue on Materials Science of Bulk Metallic Glasses
#2005 The Japan Institute of Metals
Effect of Al on Local Structures of Zr–Ni and Zr–Cu Metallic Glasses
Shigeo Sato1 , Takashi Sanada1 , Junji Saida2 , Muneyuki Imafuku3 ,
Eiichiro Matsubara4 and Akihisa Inoue5
1
NISSAN ARC, LTD., Yokosuka 237-0061, Japan
Center for Interdisciplinary Research, Tohoku University, Sendai 980-8578, Japan
3
Materials Characterization Center, Nippon Steel Technoresearch Co., Futtsu 293-0011, Japan
4
Faculty of Engineering, Kyoto University, Kyoto 606-8511, Japan
5
Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan
2
In order to investigate the role of Al on the thermal stability of supercooled liquid state, the local structures of Zr70 M30 and Zr70 M20 Al10
(M ¼ Ni, Cu) metallic glasses have been studied by the X-ray diffraction and EXAFS measurements. It is found that the different effect of Al
substitution on the local structures around Cu and Ni elements is exhibited. No characteristic change is observed in the local structure in the Zr–
Cu metallic glass by Al substitution, whereas a drastic change in the environment around Ni atom can be confirmed in the Zr–Ni metallic glass.
That is, the coordination number of Zr around Ni decreases significantly by substitution of Al in the Zr–Ni metallic glass. This would be caused
by the preferential correlation between Al and Zr. This result suggests that Al plays a dominant role on the formation of novel local structure with
a decomposition of the tetragonal Zr2 Ni-like local environment in the Zr–Ni binary alloy. We conclude that the novel local structure contributes
to the stability of the supercooled liquid state in the Zr–Al–Ni metallic glass.
(Received July 19, 2005; Accepted September 26, 2005; Published December 15, 2005)
Keywords: zirconium-based metallic glass, radial distribution function, extended X-ray absorption fine structure, local structure
1.
Introduction
Various multi-component metallic glasses with high glassforming ability (GFA) have been found so far.1–3) They show
a glass transition temperature and following supercooled
liquid region before crystallization in the transformation
process, which are quite important indexes of a thermal
stability for a glassy state. In order to explain the origin of the
thermal stability in the metallic glasses, the presence of
strong bonding among the constituent elements4–6) and highly
dense random packed atomic configurations4,5) have been
suggested. Since such features would bring characteristic
local structures, several studies of local structures for the
metallic glasses have been reported by the X-ray diffraction
and the anomalous X-rays scattering and methods.7–10) For
example, the local structures of Fe70 (Zr, Nb)10 B20 metallic
glasses have been explained with the packed connections of
trigonal prisms centering B atom.7,8) Matsubara et al. have
previously discussed the origin of a wide supercooled liquid
region of La–Al–Ni and Zr–(Y)–Ni–Al metallic glasses with
the structural data obtained by the anomalous X-ray scattering method.9,10) However, it has not been fully understood
how each constituent element acts on its partial structure.
Recently, the authors have reported the local structural
studies with a novel approaches of the consideration of
transformation behavior especially quasicrystallization in the
Zr70 Ni30 and Zr70 Cu30 binary alloys.11) In spite of the similar
atomic radii of Ni and Cu and of having the strong chemical
affinity with Zr predicted by the large negative mixing
enthalpies of Zr–Ni and Zr–Cu pairs, they have a quite
different thermal stability of the supercooled liquid state. The
Zr70 Cu30 alloy exhibits glass transition, whereas no glass
transition is observed in the Zr70 Ni30 alloy at the heating rate
of 0.67 Ks1 . The difference of thermal properties between
the two metallic glasses has been discussed by the comparison of the local structures in the glassy and initial crystalline
phases.11,12) The Zr70 Ni30 metallic glass has a similar local
structure with that of the initial crystalline phase of tetragonal
Zr2 Ni, while no significant similarity of the local structures
between the glassy and crystalline states has been confirmed
in the Zr70 Cu30 alloy. It is well known that the thermal
stability of the supercooled liquid state in the Zr–(Ni,Cu)based binary metallic glasses can be improved by the
addition of Al.5,13) Particularly, Al substitution in the Zr–Ni
alloy system brings the remarkable effect with an appearance
of a wide supercooled liquid region. This phenomenon
suggests that the Al element would be likely to be effective
on the formation of novel short-range order especially in the
Zr–Ni-based alloy system. However, the effect of Al on the
local structures of Zr-based metallic glasses has not been
analyzed hitherto.
In this study, we intend to investigate the effect of Al on
the local structure and the thermal stability of the supercooled
liquid state in the Zr70 M30 (M ¼ Ni, Cu) metallic glasses by
employing the radial distribution function (RDF) analysis
using the X-ray diffraction and the extended X-ray absorption
fine structure (EXAFS) measurements. The former method is
indispensable to derive the atomic distance and coordination
number of each atomic pair, and the latter method is very
excellent in evaluating the distribution of the atomic distance.
Then, the role of Al element for the thermal stability of the
supercooled liquid state is investigated in relation with the
viewpoint of the local structures.
2.
Experimental
Melt-spun Zr70 M30 binary and Zr70 M20 Al10 (M ¼ Ni or
Cu) ternary alloys were produced from master ingots
prepared by arc melting high-purity metals of 99.9 mass%
Zr, 99.9 mass% Ni, 99.999 mass% Cu and 99.999 mass% Al.
The sample preparation was carried out in a purified argon
atmosphere. Thermal properties were measured by differ-
S. Sato et al.
ential scanning calorimetry (DSC) at a heating rate of
0.67 Ks1 . The initial crystalline phases were investigated by
X-ray diffraction with Cu-K radiation. The crystallized
samples were prepared in the DSC apparatus annealed at the
onset temperature of the exothermic peak in each DSC curve
for 120 s.
Local atomic structures of melt-spun alloys were studied
by the ordinary X-ray diffraction with Ag-K radiation
operated at 50 kV–40 mA. The observed diffraction profiles
were corrected by air scattering, polarization, absorption and
Compton scattering, and converted to electron units per atom
by the Krogh–Moe–Norman method14) to obtain an interference function, QiðQÞ estimated from the coherent scattering
intensity in absolute units. The ordinary RDF, 2r 2 ðrÞ was
led by Fourier transformation of the QiðQÞ. The coordination
number, N and interatomic distance, r between the constituent elements are calculated by fitting the QiðQÞ and RDF
with non-linear least square fitting method. EXAFS measurements of the Zr K-edge were performed at the beam line
BL12C with a double Si(111) monochromator in the Photon
Factory of KEK, Tsukuba. All measurements were done in
transmission geometry at room temperature. Measured
spectra were analyzed, using the program REX2000 (Rigaku
Corp.). The mean-square fluctuation parameter, 2 appearing
in the Debye-Waller (DW) factor, expð2k2 2 Þ in the
EXAFS formula,15) which indicates the atomic-distance
disorder, was obtained from least square fitting in k-space,
using the structural parameters r and N obtained by the RDF
analyses and theoretical phase shifts and back scattered
amplitude functions calculated by the FEFF-8 code.16)
3.
Results and Discussions
Figure 1 shows DSC curves of the Zr70 M30 and
Zr70 M20 Al10 (M ¼ Ni, Cu) melt-spun ribbons. The onset
temperatures of the glass transition, Tg and the exothermic
peak, Tx are summarized in Table 1. The Zr70 Cu30 and
Zr70 Cu20 Al10 alloys transform into the tetragonal Zr2 Cu
phase through the supercooled liquid state upon annealing,
where the similar Tg and Tx values are observed in these
alloys. On the other hand, the Zr70 Ni30 alloy does not exhibit
a glass transition, while a wide supercooled region appears in
the Zr70 Ni20 Al10 alloy. Namely, Al element acts on the
thermal property in different manner in the Zr–Ni and Zr–Cu
metallic glasses.
Figure 2 shows the X-ray diffraction profiles for the initial
crystalline phases measured by Cu-K radiation. The
identified crystalline phases are summarized in Table 1.
The tetragonal Zr2 Ni appears in the Zr70 Ni30 alloy, and the
different crystalline phase of Zr6 NiAl2 precipitates in the
Zr70 Ni20 Al10 alloy. It is implied that the precipitation of
Zr6 NiAl2 in the Zr70 Ni20 Al10 alloy is due to the new strong
correlations of Al–Zr and Al–Ni pairs. In contrast, the
crystalline phase of the tetragonal Zr2 Cu remains in the
Zr70 Cu20 Al10 alloys. The peak position assigned to Zr2 Cu in
the Zr70 Cu20 Al10 alloy is slightly shifted from that in the
Zr70 Cu30 alloy, indicating that a certain amount of Al atom
dissolves in the Zr2 Cu structure. It is deduced that the initial
crystalline phase would have a close relation with the local
structure of the glassy state. Therefore, it is suggested that the
0.67 K/s
Zr70Ni30
Tx
Tg
Exothermic (a.u.)
2894
Zr70Ni20Al10
Tx
Tg
Zr70Cu30
Tx
Zr70Cu20Al10
Tg
Tx
550
600
650
700
750
800
850
Temperature, T / K
Fig. 1 DSC curves of the Zr70 Ni30 , Zr70 Ni20 Al10 , Zr70 Cu30 and
Zr70 Cu20 Al10 melt-spun ribbons.
Table 1 Glass transition temperature Tg , crystallization temperature Tx and
the initial crystalline phases in the Zr70 Ni30 , Zr70 Ni20 Al10 , Zr70 Cu30 and
Zr70 Cu20 Al10 metallic glasses.
Tg /K
Tx /K
Zr70 Ni30
—
656
Tetragonal Zr2 Ni
Zr70 Ni20 Al10
636
702
Zr6 NiAl2
Zr70 Cu30
612
653
Tetragonal Zr2 Cu
Zr70 Cu20 Al10
635
672
Tetragonal Zr2 Cu
Alloys
Crystalline phase
Al element in the Zr–Cu glassy alloy system might not affect
the significant local structure change.
Figure 3 shows interference functions, QiðQÞs for the meltspun Zr70 M30 and Zr70 M20 Al10 (M ¼ Ni or Cu) alloys. The
QiðQÞs of all the metallic glasses are mostly similar in spite of
the difference of M element or Al substitution. The
corresponding RDFs calculated by the Fourier transformation
of the QiðQÞs are shown in Fig. 4. The components of Zr–Zr
and Zr–Cu pairs in the RDF of Zr70 Cu30 metallic glass are
obscure, while those of Zr70 Ni30 metallic glass are clearly
discriminated. This is likely to be caused by the different
distribution of atomic distances between the constituent
elements. The calculation fit to the QiðQÞs and RDFs were
carried out in consideration of Zr–Al and M–M pairs in
addition to Zr–Zr and Zr–M pairs. The M–M, M–Al and Al–
Al pairs for the ternary alloys are ignored in the calculation
because their weighting factors for the X-ray scattering are
negligibly small. The atomic distances, r and coordination
Effect of Al on Local Structures of Zr–Ni and Zr–Cu Metallic Glasses
Zr2Ni
80
Zr2Cu
Zr6NiAl2
2895
Zr70Ni30
40
0
Zr70Ni30
80
Zr70Ni20Al10
Zr70Ni20Al10
Qi(Q) / nm-1
Intensity (a.u.)
40
0
80
Zr70Cu30
40
0
Zr70Cu30
80
Zr70Cu20Al10
40
0
0
Zr70Cu20Al10
50
100
150
Scattering vector, Q / nm
30
40
50
60
2θ / deg
70
Fig. 3 Interference functions, QiðQÞs of the Zr70 Ni30 , Zr70 Ni20 Al10 ,
Zr70 Cu30 and Zr70 Cu20 Al10 metallic glasses. Solid and dotted lines denote
experimental and calculation curves, respectively.
Fig. 2 X-ray diffraction patterns of the initial crystalline phases in the
Zr70 Ni30 , Zr70 Ni20 Al10 , Zr70 Cu30 and Zr70 Cu20 Al10 metallic glasses.
Zr-Zr
1000 Zr70Ni30
Zr-Ni
500
0
Zr-Zr
1000 Zr70Ni20Al10
2π2rρ r / nm-2
number, N are summarized in Table 2. The atomic distances
of Zr–Ni and Zr–Cu pairs of Zr70 M30 and Zr70 M20 Al10
metallic glasses are much shorter than the sum of atomic radii
estimated from Goldschmidt radii (2:84 101 nm for Zr–Ni
and 2:88 101 nm for Zr–Cu). The almost same atomic
distances of Zr–M pairs have been reported also in the
previous structural studies made for the binary Zr–Ni and Zr–
Cu metallic glasses.17,18) The tendency is significantly
observed in Zr–Ni pair rather than Zr–Cu pair, which
indicates stronger correlation is formed in Zr–Ni pair. For
the ternary alloy systems, the coordination number of Zr–M
pair decreases owing to the effect of Al substitution for M
element. In the Zr70 Cu20 Al10 metallic glass, the decrease is
simply equivalent to the change of the composition ratio of
Cu. Thus, no peculiar change in local structure accompanied
with the Al substitution is characterized by the structural
parameter. Considering the same initial crystalline phase in
the Zr70 Cu30 and Zr70 Cu20 Al10 metallic glasses, the substitution of Al element in the Zr–Cu metallic glass would not
form any novel local structure. In contrast, the coordination
number of Zr–Ni pair of the Zr70 Ni20 Al10 metallic glass is
much smaller than the value of 1.8, which is expected from
the change of composition ratio of Ni. Thus, the local
structure of the Zr–Ni metallic glass is likely to be affected by
Al element, which might be related to the precipitation of the
-1
500
Zr-Ni
0
1000 Zr70Cu30
500
Zr-Zr
Zr-Cu
0
Zr-Zr
1000 Zr70Cu20Al10
500
0
0.1
Zr-Cu
0.2
0.3
0.4
0.5
0.6
r / nm
Fig. 4 Radial distribution functions of the Zr70 Ni30 , Zr70 Ni20 Al10 ,
Zr70 Cu30 and Zr70 Cu20 Al10 metallic glasses. Solid and dotted lines denote
experimental and calculation curves, respectively.
2896
S. Sato et al.
Table 2 Structural parameters N, r and of the Zr70 Ni30 , Zr70 Ni20 Al10 ,
Zr70 Cu30 and Zr70 Cu20 Al10 metallic glasses.
Zr70 Ni20 Al10
Zr70 Cu30
Zr70 Cu20 Al10
Pairs
r/nm
N
/nm
Ni–Ni
0.248
1.3
—
Zr–Ni
Zr–Zr
0.270
0.319
2.6
9.4
0.0127
0.0136
Zr–Ni
0.265
1.3
0.0127
Zr–Al
Zr–Zr
0.300
0.319
1.3
9.5
0.0105
0.0157
Cu–Cu
0.256
1.3
—
Zr–Cu
Zr–Zr
0.279
0.317
2.5
9.0
0.0139
0.0154
Zr–Cu
0.280
1.7
0.0143
Zr–Al
Zr–Zr
0.299
0.318
1.0
9.3
0.0101
0.0156
Zr70Ni30
Zr70Ni20Al10
1.6
Zr70Ni30
Zr70Ni20Al10
1.2
Magnitude of Fourier transform, |F(r)|
Alloys
Zr70 Ni30
Zr-Ni
Zr-Zr
0.8
0.4
0.0
Zr70Cu30
Zr70Cu20Al10
1.2
Zr-Cu
Zr-Zr
0.8
0.4
0.8
0.0
0.0
0.2
0.3
0.4
0.5
0.6
0.7
Fig. 6 Radial structure functions around Zr atoms obtained from Fourier
transform of the EXAFS spectra shown in Fig. 5 of the Zr70 Ni30 ,
Zr70 Ni20 Al10 , Zr70 Cu30 and Zr70 Cu20 Al10 metallic glasses.
-0.8
k3χ (k)
0.1
r / nm
0.0
1.6
Zr70Cu30
Zr70Cu20Al10
0.8
0.0
-0.8
0
50
100
-1
k / nm
Fig. 5 k3 -weighted Zr K-edge EXAFS functions of the Zr70 Ni30 ,
Zr70 Ni20 Al10 , Zr70 Cu30 and Zr70 Cu20 Al10 metallic glasses.
different crystalline phases in the primary stage in the
Zr70 Ni30 and Zr70 Ni20 Al10 alloys.
Figure 5 shows the k3 weighted Zr K-edge EXAFS spectra
for the Zr70 Ni30 , Zr70 Ni20 Al10 , Zr70 Cu30 and Zr70 Cu20 Al10
metallic glasses. Comparing EXAFS spectra for the Zr70 Ni30
and Zr70 Ni20 Al10 metallic glasses, the former one has
different periodic oscillation around 70 nm1 , which indicates the existence of the difference in the local structure
between the two metallic glasses. On the other hand, no
peculiar difference is observed in EXAFS spectra for the
Zr70 Cu30 and Zr70 Cu20 Al10 metallic glasses. Radial structure
functions (RSFs) around Zr atom obtained from Fourier
transforms of these EXAFS spectra are shown in Fig. 6.
Since the phase shift of EXAFS function is not corrected for
these RSFs, the peak positions of atomic pairs assigned in
Fig. 6 do not directly correspond to the proper distance of
atomic correlations.
Here, the in the DW factor was calculated by following
procedure. The shell in the range of about 0.15 to 0.35 nm
was transformed back to k-space. The shell consists of two or
three subshells of Zr–Zr, Zr–M and Zr–Al. Using the
structural parameters of r and N for each atomic pair in
Table 2, the was obtained by fitting the reversed Fourier
filtered signals. The values of the atomic pairs in the
present alloys are summarized in Table 2. Each of Zr–Ni
pair in the Zr70 Ni30 and Zr70 Ni20 Al10 metallic glasses is
smaller than that of Zr–Zr pair. Considering that the smaller
value of means more ordered structure, this result suggests
that Zr atom bonds to Ni atom firmly, which would be based
on the strong chemical affinity between Zr and Ni atoms, with
a heat of mixing of H ¼ 49 kJ/mol. This is consistent
with the investigation of the RDF analysis. The of Zr–Zr
pair for the Zr70 Ni20 Al10 metallic glass is clearly larger than
that for the Zr70 Ni30 alloy, suggesting that the Zr–Zr
correlation for Zr70 Ni20 Al10 is disordered more than that
for Zr70 Ni30 . The increase of the of Zr–Zr pair for the
Zr70 Ni20 Al10 metallic glass would be brought by the
following procedure. Al has a strong chemical affinity with
Zr, of which mixing enthalpy is 44 kJ/mol. This value is
almost equivalent to that of Zr–Ni pair (49 kJ/mol). As
Effect of Al on Local Structures of Zr–Ni and Zr–Cu Metallic Glasses
described in RDF analysis, number of Zr–Ni strong pair
significantly decreases by the Al addition. It is presumably
attributed to the size effect of corresponding elements. The
atomic radius of Al is 1:43 101 nm, which is in the middle
of those of Zr (1:60 101 nm) and Ni (1:24 101 nm).
We suggest that Al–Zr pair can be formed easily rather than
that for Ni–Zr pair under the dense random packed Zr–Al–Ni
supercooled liquid. Consequently, the strong Zr–Ni pair has
to decompose by Al more than the consideration of these
contents in the alloy. Simultaneously, it should be also noted
that there is no significant difference between the of Zr–Ni
pairs for Zr70 Ni30 and Zr70 Ni20 Al10 metallic glasses. This
feature reveals that the strong Zr–Ni bond is still preserved
after the formation of Zr–Al pair. Therefore, two kind of
strong pairs of Zr–Al and Zr–Ni lead to the variety of the
local environment of Zr around Zr due to the different pair
distance, resulting in the increase of of Zr–Zr pair. It is also
pointed out that the Al–Ni has a negative heat of mixing of
22 kJ/mol. It indicates the possibility of the formation of
Al–Ni pair, which might bring the effect on various local
environments of Zr around Zr. It is suggested that such
disordered structure could improve a thermal stability of the
supercooled liquid state and/or the glassy state by preventing
from the rearrangement of the atoms for crystallization.
Comparing with the of Zr–Ni and Zr–Cu pairs, the latter
one is larger. It means that Cu atom does not attract Zr atom
as firmly as Ni atom does, which could be interpreted as a
weak correlation of Zr–Cu pair compared with that of Zr–Ni
pair. It is also predicted from the considerably smaller mixing
enthalpy of Zr–Cu of 23 kJ/mol. As expected from the
quite similar shape of RSFs of the Zr70 Cu30 and Zr70 Cu20 Al10
metallic glasses, the obtained of Zr–Cu and Zr–Zr pairs of
the two metallic glasses could be regarded to be identical.
Namely, the disorder of Zr–Cu metallic glass is not so
affected by Al substitution. Considering that the same
crystalline phase was formed from the two metallic glasses,
it is concluded that the Al atom would not produce
distinguished change in the local structure based on the
binary Zr–Cu metallic glass. In these studies, we can clarify
the different effect of Al on the local structure and stability of
supercooled liquid state in the Zr–Ni and Zr–Cu-based
metallic glasses. In the Zr–Ni-based alloy, it is noted that Al
plays a dominant role for the novel local structure, which
brings a drastic enhancement of the stability of supercooled
liquid state.
4.
Concluding Remarks
The local structures for the Zr70 Ni30 , Zr70 Ni20 Al10 ,
Zr70 Cu30 and Zr70 Cu20 Al10 metallic glasses have been
2897
characterized by RDF analyses and EXAFS method. Contrastive effect of Al substitution on the local structure is
confirmed in the Zr–Ni and Zr–Cu metallic glasses. No
characteristic change is confirmed in the local structure for
the Zr–Cu metallic glass by substituting Al. In contrast, by
substituting Al in the Zr–Ni metallic glass, the coordination
number of Zr–Ni decreases clearly, and the for Zr–Zr
increases. These changes would result from the disruption of
the strong Zr–Ni correlation and the formation of novel
strong correlation of Zr–Al. Al atom would preferentially
correlate to Zr atom. As a result, two kind of strong pairs are
formed, which leads to the variety of local environment of Zr
around Zr. Thus, the Al-induced disordered local environment accompanying with the formation of novel local
structure of Zr–Al and decomposition of that of Zr–Ni would
improve effectively thermal stability of the Zr–Ni–Al metallic glass. In contrast, no significant effect of change in local
structure is observed by Al addition in the Zr–Cu-based
metallic glass. We suggest that the Al plays an only
topological role for stabilizing the supercooled liquid state.
REFERENCES
1) A. Inoue and A. Takeuchi: Mater. Sci. Eng. A 375–377 (2004) 16–30.
2) W. H. Wang, C. Dong and C. H. Shek: Mater. Sci. Eng. R 44 (2004)
45–89.
3) J. F. Löffler: Intermetallics 11 (2003) 529–540.
4) A. Inoue, T. Zhang and T. Masumoto: Mater. Trans., JIM 30 (1989)
965–972.
5) A. Inoue, T. Zhang and T. Masumoto: Mater. Trans., JIM 31 (1990)
177–183.
6) A. Inoue, H. Yamaguchi, T. Zhang and T. Masumoto: Mater. Trans.,
JIM 31 (1990) 104–109.
7) E. Matsubara, S. Sato, M. Imafuku, T. Nakamura, H. Koshiba, A. Inoue
and Y. Waseda: Mater. Sci. Eng. A 312 (2001) 136–144.
8) M. Imafuku, S. Sato, E. Matsubara and A. Inoue: J. Non-Cryst. Solids
312–314 (2000) 589–593.
9) E. Matsubara, T. Tamura, Y. Waseda, A. Inoue, T. Zhang and
T. Masumoto: Mater. Trans., JIM 33 (1992) 873–878.
10) E. Matsubara and Y. Waseda: Mater. Trans., JIM 36 (1995) 883–889.
11) J. Saida, M. Kasai, E. Matsubara and A. Inoue: Ann. Chim. Sci. Mater.
27 (2002) 77–89.
12) K. Saksl, H. Franz, P. Jóvóri, K. Klementiev, E. Welter, A. Ehnes, J.
Saida, A. Inoue and J. Z. Jiang: Appl. Phys. Lett. 83 (2003) 3294–3296.
13) L. Q. Xing, P. Ochin and J. Bigot: J. Non-Cryst. Solids 205–207 (1996)
637–640.
14) C. N. J. Wagner, H. Ocken and M. L. Joshi: Zeit. Naturforsch. 20a
(1965) 325–335.
15) A. V. Poiarkova and J. J. Rehr: Phys. Rev. B 59 (1999) 948–957.
16) A. L. Ankudinov, B. Ravel, J. J. Rehr and S. D. Conradson: Phys. Rev.
B 58 (1998) 7565–7576.
17) H. S. Chen and Y. Waseda: Phys. Status Solidi A 51 (1979) 593–599.
18) A. Lee, G. Etherington and C. N. J. Wagner: J. Non-Cryst. Solids
61&62 (1984) 349–354.