A single-crystal neutron-diffraction investigation of spodumene at 54 K

Abstract

A single-crystal investigation of spodumene from a granitic pegmatite in Minas Gerais, Brazil, was undertaken using neutron (54 K) and X-ray diffraction (room temperature) (R all = 2.8% and 1.9%, respectively). In both refinements, space group C2/c was assigned; the presence of several reflections violating the c glide plane in the low-temperature neutron-diffraction data set is attributed to multiple scattering. An asymmetric density of scattering at the Li site was observed in both refinements, and is related to dynamic disorder. In spodumene, a C2/c fully relaxed low-temperature structure is therefore present, in contrast to LiCrSi 2 O 6 , LiFeSi 2 O 6 , and LiGaSi 2 O 6 pyroxenes, for which it is P2 1 /c. The main geometrical difference between spodumene and LiFeSi 2 O 6 is the flexibility with temperature of the chain of S-rotated tetrahedra in spodumene. It enables spodumene to cope with the variation in octahedron size, in comparison with the stiffness of the completely extended chain of tetrahedra in LiFeSi 2 O 6 . SOMMAIRE Nous décrivons les résultats d'une étude sur cristal unique de spodumène provenant d'une pegmatite granitique de Minas Gerais, au Brésil, par diffraction de neutrons à 54 K et par diffraction X à température ambiante (R all = 2.8% et 1.9%, respectivement). Dans les deux cas, nous adoptons le groupe spatial C2/c; la présence de plusieurs réflexions en violation du plan de glissement c dans les données provenant de la diffraction de neutrons à basse température est attribuable à la dispersion multiple. Une répartition asymétrique de la dispersion associée au site Li a été observée dans les deux affinements, et serait due à un désordre dynamique. Dans le spodumène, une structure C2/c pleinement décontractée est donc présente à basse température, contrairement aux cas des pyroxènes LiCrSi 2 O 6 , LiFeSi 2 O 6 , et LiGaSi 2 O 6 , dans lesquels il s'agit d'une structure P2 1 /c. La différence géométrique principale entre le spodumène et LiFeSi 2 O 6 porte sur la flexibilité selon la température de la chaîne de tétraèdres à rotation S dans le spodumène. C'est ce qui permet au spodumène de se conformer aux variations dans la taille des octaèdres, par rapport à l'inflexibilité dans les chaînes de tétraèdres complètement distendues dans le composé LiFeSi 2 O 6 . (Traduit par la Rédaction) Mots-clés: spodumène, diffraction X, diffraction de neutrons, pyroxène lithinique, dispersion multiple.

Full text

Page 1

521
§
E-mail addresses: mario.tribaudino@.unito.it, fabrizio.nestola@unito.it, mauro.prencipe@unito.it, rundlof@studsvik.uu.se
The Canadian Mineralogist
Vol. 41, pp. 521-527 (2003)
A SINGLE-CRYSTAL NEUTRON-DIFFRACTION INVESTIGATION
OF SPODUMENE AT 54 K
MARIO TRIBAUDINO§, FABRIZIO NESTOLA§ AND MAURO PRENCIPE§
Dipartimento di Scienze Mineralogiche e Petrologiche, Università di Torino, Via Valperga Caluso 35, I-10125 Torino, Italy
HÅKAN RUNDLOF§
Studsvik Neutron Research Laboratory, Studsvik, S-61182 Nykoping, Sweden
ABSTRACT
A single-crystal investigation of spodumene from a granitic pegmatite in Minas Gerais, Brazil, was undertaken using neutron
(54 K) and X-ray diffraction (room temperature) (Rall = 2.8% and 1.9%, respectively). In both refinements, space group C2/c was
assigned; the presence of several reflections violating the c glide plane in the low-temperature neutron-diffraction data set is
attributed to multiple scattering. An asymmetric density of scattering at the Li site was observed in both refinements, and is
related to dynamic disorder. In spodumene, a C2/c fully relaxed low-temperature structure is therefore present, in contrast to
LiCrSi2O6, LiFeSi2O6, and LiGaSi2O6 pyroxenes, for which it is P21/c. The main geometrical difference between spodumene and
LiFeSi2O6 is the flexibility with temperature of the chain of S-rotated tetrahedra in spodumene. It enables spodumene to cope
with the variation in octahedron size, in comparison with the stiffness of the completely extended chain of tetrahedra in LiFeSi2O6.
Keywords: spodumene, X-ray diffraction, neutron diffraction, Li pyroxene, multiple scattering.
SOMMAIRE
Nous décrivons les résultats d’une étude sur cristal unique de spodumène provenant d’une pegmatite granitique de Minas
Gerais, au Brésil, par diffraction de neutrons à 54 K et par diffraction X à température ambiante (Rall = 2.8% et 1.9%,
respectivement). Dans les deux cas, nous adoptons le groupe spatial C2/c; la présence de plusieurs réflexions en violation du plan
de glissement c dans les données provenant de la diffraction de neutrons à basse température est attribuable à la dispersion
multiple. Une répartition asymétrique de la dispersion associée au site Li a été observée dans les deux affinements, et serait due
à un désordre dynamique. Dans le spodumène, une structure C2/c pleinement décontractée est donc présente à basse température,
contrairement aux cas des pyroxènes LiCrSi2O6, LiFeSi2O6, et LiGaSi2O6, dans lesquels il s’agit d’une structure P21/c. La
différence géométrique principale entre le spodumène et LiFeSi2O6 porte sur la flexibilité selon la température de la chaîne de
tétraèdres à rotation S dans le spodumène. C’est ce qui permet au spodumène de se conformer aux variations dans la taille des
octaèdres, par rapport à l’inflexibilité dans les chaînes de tétraèdres complètement distendues dans le composé LiFeSi2O6.
(Traduit par la Rédaction)
Mots-clés: spodumène, diffraction X, diffraction de neutrons, pyroxène lithinique, dispersion multiple.
INTRODUCTION
Several investigations have been undertaken to
clarify the structural behavior and the phase transitions
of Li-bearing pyroxenes. In the pyroxene structure, Li
occupies the M2 site via a coupled substitution with a
trivalent cation at M1. In natural pyroxenes, the substi-
tuting trivalent cation is Al, forming the mineral spo-
dumene (Clark et al. 1969, Sasaki et al. 1980,
Kuntzinger & Ghermani 1999). However, pyroxenes
with trivalent Fe, Cr, Ni, In, V, Sc, Ti and Ga at the M1
site have also been synthesized (Hawthorne & Grundy
1977, Grotepaß et al. 1983, Behruzi et al. 1984, Baum
et al. 1988, Ohashi & Osawa 1988, Sato et al. 1994,
1995, Satto et al.1997, Lottermoser et al. 1998,
Redhammer et al. 2001). Structure refinements of the
end members containing the above trivalent cations
were performed at ambient conditions and at high tem-

Page 2

522
THE CANADIAN MINERALOGIST
perature (Cameron et al. 1973, Redhammer et al. 2001)
and high pressure (Arlt & Angel 2000). In general, a
structure in space group C2/c with a chain arrangement
similar to that of high-T (temperature) pigeonite is stable
at high temperature. A phase transition from C2/c to a
P21/c structure, similar to that of high-T to low-T pi-
geonite (Smyth 1974, Brown et al. 1972, Tribaudino et
al. 2002), occurs in the Cr3+ (Behruzi et al. 1984), Fe3+
(Lottermoser et al. 1998, Redhammer et al. 2001) and
Ga end-members (Sato et al. 1994, 1995), at 343, 228
and 285 K, respectively. At high pressure, a phase tran-
sition to a P21/c structure was observed in spodumene
and LiScSi2O6 at P = 3.6 and 0.6 GPa, respectively (Arlt
& Angel 2000). For all Li-bearing pyroxenes, and by
analogy with ZnSiO3, Arlt & Angel (2002) predicted a
second phase-transition to a high-pressure C2/c struc-
ture, similar to the high-pressure C2/c structure found
in clinoenstatite (Angel et al. 1992). Arlt & Angel
(2000) have shown that smaller cations at the M1 site
favor the P21/c structure at ambient conditions. An ex-
ception is spodumene, which displays a C2/c structure
at room temperature (Sasaki et al. 1980, 1981), despite
the fact that Al has the smallest radius of all possible
M1 cations. They explained this exception by the pres-
ence of chains of S-rotated tetrahedra in spodumene, but
structural details were not provided.
The behavior of Li within the M2 cavity in spo-
dumene is also interesting, as Li has the largest displace-
ment parameters in pyroxenes (Cameron et al. 1973).
Rietveld analysis of preliminary data from low-T neu-
tron powder-diffraction (Knight & Schofield 2000) has
shown evidence for positional disorder of Li off the diad
axis and of possible violations of a centric space-group.
These violations could originate because of a phase tran-
sition below room temperature.
In the present work, data from an investigation of
neutron scattering at T = 54 K are reported and com-
pared with a high-resolution X-ray measurement at 298
K. The aim is to verify the low-temperature structure of
spodumene and to compare the structural changes oc-
curring with temperature in spodumene to those in other
Li-bearing pyroxenes. Moreover, in this work, we docu-
ment a severe case of multiple diffraction in a neutron-
diffraction single-crystal investigation.
This paper focuses on structural features. In a forth-
coming paper, the results of quantum mechanical ab
initio calculations and multipolar refinements will be
reported.
EXPERIMENTAL
A transparent and colorless gem-quality crystal of
spodumene from Minas Gerais, Brazil, was used for the
diffraction studies. The composition was verified by
energy-dispersion analysis, using a Cambridge S 360
scanning electron microscope, equipped with Link Ana-
lytical QX 2000 energy-dispersion spectrometer (EDS).
The analyses were performed using relatively long
counting-times (500 s), in order to improve the detec-
tion of elements at low concentrations. Apart from Al
and Si, only Na and Fe were found in significant con-
centrations. Assuming Li to be present in stoichiomet-
ric amounts, the following formula based on six atoms
of oxygen was obtained: LiNa0.012(1)Fe0.004(2)Al0.98(1)
Si2.01(1)O6.
Two crystals were separated, one to be used for neu-
tron (6 ? 4 ? 2 mm3) and the other for X-ray diffrac-
tion (300 ? 150 ? 100 ?m3). Both show sharp
extinction and no evidence of twinning upon examina-
tion under crossed nicols.
Collection of X-ray and neutron data
X-ray-diffraction intensity data were collected at
room temperature using a Siemens P4 four-circle
diffractometer, operating at 50 kV and 20 mA, with
MoK? radiation (? = 0.71069 Å) monochromatized with
a flat graphite crystal. Cell parameters were measured
using 25 reflections over the 2? interval of 15 and 30°.
Diffraction intensities were collected in the ?–2? scan
mode; the reciprocal lattice sphere was explored up to
2? = 100°, i.e., at a resolution of 0.46 Å, with a scan-
ning speed of 2°/min. All equivalent reflections were
collected in a full sphere. An empirical absorption-cor-
rection based on the ?-scan method (North et al. 1968)
was done. A total of 1960 unique reflections were used
in the refinement.
The collection of neutron data was performed at NFL
(NeutronForskningsLaboratoriet, Studsvik, Sweden)
research reactor, using the single-crystal SXD HUBER
four-circle goniometer, positioned at H8, one of the ra-
dial neutron channels at the R2 reactor. The primary
beam was monochromatized by two copper (220) crys-
tals, one of which is focusing, creating the neutron
wavelength ? of 1.202 Å. The crystal was mounted with
[001] approximately parallel to the ? axis of the instru-
ment and was cooled to 54 K using a close-cycle refrig-
erator. The diffracted beams were measured with a
single 3He detector. The data collection was performed
up to a 2? of 104°, corresponding to a resolution of 0.76
Å. All measurable reflections with indices ± h + k ± l,
constituting half of the reflection sphere, were collected.
A set of 455 unique reflections was obtained after merg-
ing symmetry-equivalents. The intensities were cor-
rected for absorption (? = 1.07 mm–1) using a
laboratory-supplied routine.
Data refinement
Weighted full-matrix least-squares anisotropic re-
finements for both neutron and X-ray data were com-
pleted using SHELX–97 (Sheldrick 1997), the space
group C2/c and starting atom-coordinates of spodumene
(Sasaki et al. 1980). Atomic scattering curves and neu-
tron scattering lengths were taken from the International
Tables for X-Ray Crystallography (Ibers & Hamilton

Page 3

A NEUTRON-DIFFRACTION INVESTIGATION OF SPODUMENE
523
1974). Only the scattering curves of Li and Al were used
to refine the atom positions at the M2 and M1 sites, re-
spectively. The extinction was corrected according to
Larson’s (1970) model, as implemented in SHELX–97.
A fixed weighting scheme was used [1/?(Fo)2].
Cell parameters, agreement factors, fractional coor-
dinates, polyhedron bond-lengths and mean square-root
amplitudes of the atomic displacement ellipsoids (ADP)
are reported in Tables 1, 2 , 3 and 4. A table of structure
factors is available at the Depository of Unpublished
Data, CISTI, National Research Council, Ottawa,
Ontario K1A 0S2, Canada.
RESULTS AND DISCUSSION
Space group at room and low temperature
A set of 302 h + k = 2n + 1 reflections was collected
at 54 K, to check for possible violations of the C-cen-
tering. None of these reflections was found to have I >
3?, and the subsequent full collection of data was per-
formed in the C-centered lattice. The collection of neu-
tron data at 54 K and at room temperature revealed
instead several h0l reflections with l = 2n + 1 (average
I/? = 9.2) violating the c glide plane of the C2/c space
group. In the X-ray data collection, only a few such re-
flections were significant. Violations of the c glide plane
were reported in the literature for X-ray data on spo-
dumene (Clark et al. 1969), and interpreted as evidence
of the acentric space-group C2. However, further inves-
tigations (Sasaki et al. 1981) showed that the c glide
violations in the intensity data of spodumene are due to
multiple diffraction. Multiple diffraction occurs when a
strong diffracted beam in the crystal acts as an incident
beam for further diffraction by the crystal. In low-tem-
perature neutron diffraction, it was decided to test for
the actual presence of these violations, as they could
provide evidence of a transition to an acentric space-
group.
An indication on the presence of the center of sym-
metry can be obtained by the distribution of the normal-
ized structure-factors (| E |; Viterbo 1992) and by the
related mean value of the | E*E – 1 | function. Such dis-

Page 4

524
THE CANADIAN MINERALOGIST
tribution can be calculated theoretically, independently
of the complexity of the structure. The centric distribu-
tion yields a higher percentage of reflections with ex-
treme intensity, whereas in the acentric one, there is a
maximum corresponding to intermediate values of the
intensities. The theoretical values of the average of the
| E*E – 1 | distribution are 0.960 in the centrosymmet-
ric case and 0.738 in the non-centrosymmetric case. In
this work, the X-ray data confirm the presence of a cen-
ter of symmetry at room temperature (< | E*E – 1 | > is
0.980), but the low-T neutron-diffraction data give an
anomalous value (< | E*E – 1 | > is 0.620).
The possible presence of multiple diffraction induc-
ing glide-plane violations was tested by performing ?-
scans on selected h0l reflections with l = 2n + 1, with
X-rays as well as neutrons. In the X-ray experiment, the
intensity of violating reflections was found not to be
significant, other than for specific ? angles, in agree-
ment with the findings of Sasaki et al. (1981). The ob-
served violations were therefore attributed to multiple
diffraction. The neutron data, on the other hand, show
an intensity of the violating reflections much higher than
the observed standard deviation for any ? angle also at
room temperature. However, the intensities shows sharp
changes as a function of ? angle. Such changes are not
due to experimental fluctuations: the ? scan was re-
peated twice, at steps of 0.2 and 0.5°, and the intensity
changes are very similar. Also, these changes cannot be
due to absorption, since the crystal has a regular shape,
and only minor anisotropic absorption was observed. A
likely interpretation is that in the large gem-quality crys-
tal used for neutron diffraction, multiple scattering is so
widespread that owing to overlap of multiple diffrac-
tion, the intensity does not decrease below significance.
This would also explain the anomalous statistics of the
intensities: strong multiple diffraction and extinction
would increase the intensity of weaker reflections and
decrease that of the stronger ones. As a consequence,
the presence of violating reflections cannot be used as
evidence of the lack of an inversion center at low tem-
perature.
Refinement with the alternative non-centrosymmet-
ric space-groups C2 and Cc were attempted on the 54 K
neutron data to verify the actual space-group. In both
cases, the results yielded worse agreement-factors (R =
3.3%) than those of the C2/c refinement. In addition,
errors associated with the bond lengths increased, and
the anisotropic displacement parameters became non-
positive definite. Also, no significant decrease of the
large displacement parameters for Li, nor of any other
atoms, was observed. Therefore a C2/c model was cho-
sen also for the low-T neutron data.
This result indicates that no phase transition occurs
down to 54 K in spodumene, although further investi-
gations at lower T would be useful to finalize the issue.
Displacement parameters and zero-point motion
The displacement parameter observed for Li in spo-
dumene (e.g., Cameron et al. 1973) is significantly
larger than that at M2 in other pyroxenes. Moreover, the
possible presence of site splitting was suggested by
Knight & Schofield (2000). Dynamic and static disor-
der can be distinguished by an analysis of the evolution
of the displacement parameters with temperature. In the
case of negligible positional disorder, the relation be-
tween the displacement parameters and temperature
should be asymptotically approximated by a straight line
passing through the origin at 0 K. Such dependence is

Page 5

A NEUTRON-DIFFRACTION INVESTIGATION OF SPODUMENE
525
no longer linear at low temperature. As previously
shown (e.g., Benna et al. 1990, Pavese et al. 1995, Pilati
et al. 1996, Prencipe et al. 2000), a positive intercept
for a linear extrapolation of the high-temperature data
at 0 K can provide an indication of the presence of po-
sitional disorder. As shown in Figure 1, an extrapola-
tion of the Beq (equivalent to isotropic displacement
parameters) from data for spodumene over the interval
298 to 1033 K (this work, Cameron et al. 1973) to 0 K
shows no significant residual for any atom. The Beq are
significant (about 60% of the room-temperature data)
also in the neutron datum at 54 K; this value is related
to 0 K point motion, but possibly also to extinction ef-
fects that are not fully corrected for. The presence of
significant zero-point motion is in agreement with pre-
vious theoretical (Pilati et al. 1996) and experimental
findings (Prencipe et al. 2000) on the structurally re-
lated diopside, for which the zero-point contribution is
about 40% of the room-temperature Beq.
Effect of M1 cations
on the P21/c – C2/c phase transition
As discussed in the introduction, Li-bearing
clinopyroxenes have P21/c or C2/c symmetry. In Fig-
ure 2, the radius of the M1 cation is plotted as a func-
tion of the temperature of data collection. The transition
temperature for LiCrSi2O6, LiFeSi2O6, and LiGaSi2O6
also is shown. As observed by Arlt & Angel (2000), the
C2/c structure is present in Li clinopyroxenes hosting a
relatively large M1 cation (Fig. 2), whereas the P21/c
structure is adopted in those with a smaller M1 cation.
This observation is closely followed where the M1 cat-
ion is a transition metal or Ga. However, from Figure 2,
spodumene could be predicted to be P21/c up to high
temperature, whereas experimental evidence shows that
the C2/c structure is retained down to 54 K: in spo-
dumene, a fully relaxed C2/c structure is observed,
whereas in LiCrSi2O6, LiFeSi2O6 and LiGaSi2O6 py-
roxenes, the ground structure has P21/c symmetry. An
explanation for this behavior requires additional data on
the high- and low-T behavior of Li pyroxenes, at present
available only for spodumene and LiFeSi2O6 (Cameron
et al. 1973, Redhammer et al. 2001). A comparison be-
tween the C2/c structures of spodumene and LiFeSi2O6
at the different temperatures is nevertheless interesting,
to outline the geometrical behavior of Li pyroxenes with
and without the phase transition. As shown in Figure 3,
in spodumene all the M2–O bond lengths decrease with
temperature continuously and at a similar rate. In
LiFeSi2O6, with decreasing temperature, the M2–O1
distances undergo a significant decrease, whereas the
M2–O3 distances increase (Fig. 3). At the critical tem-
perature, one of the two M2–O3 bond lengths is re-
leased. At the same time, in the C2/c structure of
LiFeSi2O6, Li moves along the diad axis by as much as
2.6 ? 10–4 Å/K, whereas in spodumene it does so by
only 0.2 ? 10–-4 Å/K (Cameron et al. 1973, Redhammer
et al. 2001). Another difference lies in chain rotation
among the tetrahedra (Fig. 4). In pyroxenes, the chain
angle extends with increasing temperature (Cameron et
al. 1973, Benna et al. 1990, Tribaudino 1996), as a
consequence of the stiffness of the tetrahedron with re-
spect to the expansion of the M1 octahedra, which are
linked to the tetrahedra via the common O1 and O2
oxygen atoms (Cameron et al. 1973). The extension in
the chain of tetrahedra with temperature is not possible
in the Fe end-member, which has the chains already
fully elongated at room temperature, as shown in Fig-
ure 4 for LiFeSi2O6. In spodumene, by contrast, the
chain can extend with temperature, approaching, but not
reaching, the fully extended situation at higher tempera-
ture.
ACKNOWLEDGEMENTS
The authors acknowledge the reviews of Franklin F.
Foit Jr., Ross Angel and Günther Redhammer. This
work was supported by EC Access to Research Infra-
structure action of the Improving Human Potential
Programme, contract HPRI-CT-1999-00061, by CNR
and by MIUR, in the framework of the national project:
“Transformations, reactions, ordering in minerals”.
FIG. 1. Equivalent B factors (Beq = 8?2Ueq) for spodumene
as a function of temperature: data at 54 and 298 K are from
this work; data at 573, 733 and 1033 K are taken from
Cameron et al. (1973). The plot for Si is between those for
O1 and Al. The Beq for Li from the refinement by Sasaki et
al. (1980) is reported as an open triangle. The fit was calcu-
lated without the 54 K datum.

Page 6

526
THE CANADIAN MINERALOGIST
REFERENCES
ANGEL, R.J., CHOPELAS, A. & ROSS, N.L. (1992): Stability of
high-density clinoenstatite at upper mantle pressures. Na-
ture 358, 322-324.
ARLT, T. & ANGEL, R.J. (2000): Displacive phase transitions in
C-centered clinopyroxenes: spodumene, LiScSi2O6 and
ZnSiO3. Phys. Chem. Minerals 27, 719-731.
BAUM, E., TREUTMANN, W., BEHRUZI, M., LOTTERMOSER, W. &
AMTHAUER, G. (1988): Structural and magnetic properties
of the clinopyroxenes NaFeSi2O6 and LiFeSi2O6. Z.
Kristallogr. 183, 273-284.
BEHRUZI, M., HAHN, T., PREWITT, C.T. & BALDWIN, K. (1984):
Low and high temperature crystal structures of LiFeGe2O6,
LiFeSi2O6 and LiCrSi2O6. Acta Crystallogr. A40, suppl.
C-247.
FIG. 3.
M2–O bond lengths versus T in spodumene (full tri-
angles) and LiFeSi2O6 (diamonds). Data as in Figure 2.
FIG. 4.O3–O3–O3 kinking angle as a function of T in
spodumene (full triangles), in LiFeSi2O6 (diamonds), in
LiGaSi2O6 (cross), and in LiCrSi2O6 (circle). Data as in
Figure 2.
FIG. 2.
P21/c (open triangles) and C2/c (full triangles) structures for LiM1Si2O6
clinopyroxenes in a plot of T versus M1cation radius. The transition temperatures for
Cr, Ga and Fe end members are given and linked. Only room-temperature data are
reported. The data are taken from this work for LiAlSi2O6, Ohashi & Osawa (1988) for
LiNiSi2O6, Redhammer et al. (2001) for LiFeSi2O6, Behruzi et al. (1984) for LiCrSi2O6,
Sato et al. (1994, 1995) for LiGaSi2O6, Hawthorne & Grundy (1977) for LiScSi2O6,
Grotenpaß et al. (1983) for LiInSi2O6, and Satto et al. (1997) for LiVSi2O6.

Page 7

A NEUTRON-DIFFRACTION INVESTIGATION OF SPODUMENE
527
BENNA, P., TRIBAUDINO, M., ZANINI, G. & BRUNO, E. (1990):
The crystal structure of Ca0.8Mg1.2Si2O6 clinopyroxene
(Di80En20) at T = –130°, 25°, 400° and 700°C. Z.
Kristallogr. 192, 183-199.
BROWN, G.E., PREWITT, C.T., PAPIKE, J.J. & SUENO, S. (1972):
A comparison of the structures of high and low pigeonite.
J. Geophys. Res. 77, 5778-5789.
BURNHAM, C.W., CLARK, J.R., PAPIKE, J.J. & PREWITT, C.T.
(1967): A proposed crystallographic nomenclature for
clinopyroxene structure. Z. Kristallogr. 125, 109-119.
CAMERON, M., SUENO, S., PREWITT, C.T.& PAPIKE, J.J. (1973):
High-temperature crystal chemistry of acmite, diopside,
hedenbergite, jadeite, spodumene, and ureyite. Am. Min-
eral. 58, 594-618.
CLARK, J.R., APPLEMAN, D.E.& PAPIKE, J.J. (1969): Crystal
chemical characterization of clinopyroxenes based on eight
new structure refinements. Mineral. Soc. Am., Spec. Pap.
2, 31-50.
GROTENPAß, M., BEHRUZI, M. & HAHN, T. (1983): Strukturen,
Polymorphie und Mischkristallbildung im System LiScSi2
O6 – LiInSi2O6 – LiScGe2O6 – LiInGe2O6. Z. Kristallogr.
162, 90-91.
HAWTHORNE, F.C. & GRUNDY, H.D. (1977): Refinement of the
crystal structure of LiScSi2O6 and structural variations in
alkali pyroxenes. Can. Mineral. 15, 50-58.
IBERS, J.A. & HAMILTON, W.C., eds. (1974): International Ta-
bles for X-Ray Crystallography IV. Kynoch Press, Bir-
mingham, U.K. (99-101).
KNIGHT, K.S. & SCHOFIELD, P.F. (2000): Structural basis for
the negative eigenvalue in the thermal expansion tensor of
spodumene. ISIS Experimental Rep. 10782.
KUNTZINGER, S. & GHERMANI, N.E. (1999): Electron density
distribution and Madelung potential in ?-spodumene,
LiAl(SiO3)2 from two-wavelength high-resolution X-ray
diffraction data. Acta Crystallogr. B55, 273-284.
LARSON, A.C. (1970): The inclusion of secondary extinction in
least-squares refinement of crystal structures. In Crystallo-
graphic Computing (F.R. Ahmed, ed.). Munksgaard, Co-
penhagen, Denmark (291-294).
LOTTERMOSER, W., REDHAMMER, G., FORCHER, K. & AMTHAUER,
G. (1998): Single-crystal Mössbauer and neutron powder
diffraction measurements on the synthetic clinopyroxene
Li-acmite LiFeSi2O6. Z. Kristallogr. 213, 101-107.
NORTH, A.C.T., PHILLIPS, D.C. & MATHEWS, F.S. (1968): A
semi-empirical method of absorption correction. Acta
Crystalogr. A24, 351-359.
OHASHI, H. & OSAWA, T. (1988): Synthesis of LiNiSi2O6 and
LiTiSi2O6 spodumenes. J. Japan. Mineral. Petrogr. Econ.
Geol. 83, 308-310.
PAVESE, A., ARTIOLI, G. & PRENCIPE, M. (1995): X-ray single
crystal diffraction study of pyrope in the temperature range
30–973 K. Am. Mineral. 80, 457-464.
PILATI, T., DEMARTIN, F. & GRAMACCIOLI, C.M. (1996): Lat-
tice-dynamical evaluation of atomic displacement param-
eters of minerals and its implications: the example of
diopside. Am. Mineral. 81, 811-821.
PRENCIPE M., TRIBAUDINO M., PAVESE A., HOSER A. & REEHUIS
M. (2000): A single-crystal neutron diffraction investiga-
tion on diopside at 10 K. Can. Mineral. 38, 183-189.
REDHAMMER, G.J., ROTH, G., PAULUS, W., ANDRÉ, G.,
LOTTERMOSER, W., AMTHAUER, G., TREUTMANN, W. &
KOPPELHUBER-BITSCHNAU, B. (2001): The crystal and mag-
netic structure of Li-aegirine LiFe3+Si2O6: a temperature-
dependent study. Phys. Chem. Minerals 28, 337-346.
SASAKI, S., FUJINO, K., TAKÉUCHI, Y. & SADANAGA, R. (1980):
On the estimation of atomic charges by the X-ray method
for some oxides and silicates. Acta Crystallogr. A36, 904-
915.
________, MATSUMOTO, T. & SAWADA, C. (1981): The influ-
ence of multiple diffraction on the space group determina-
tion of orthopyroxenes, spodumene, low omphacite and
pigeonite. Phys. Chem. Minerals 7, 260-267.
SATO, A., OSAWA, T. & OHASHI, H. (1994): LiGaSi2O6. Acta
Crystallogr. C50, 487-488.
________, ________ & ________ (1995) Low-temperature
form of LiGaSi2O6. Acta Crystallogr. C51, 1959-1960.
SATTO, C., MILLET, P. & GALY, J. (1997): Lithium vanadium
metasilicate, LiVSi2O6. Acta Crystallogr. C53, 1727-1728.
SHELDRICK, G.M. (1997): SHELXL–97. Program for Crystal
Structure Refinement. University of Göttingen, Göttingen,
Germany.
SMYTH, J.R. (1974): The high temperature crystal chemistry of
clinohypersthene. Am. Mineral. 59, 1069-1082.
TRIBAUDINO, M. (1996): High-temperature crystal chemistry of
C2/c clinopyroxenes along the join CaMgSi2O6 –
CaAl2SiO6. Eur. J. Mineral. 8, 273-279.
________, NESTOLA, F., CÁMARA, F. & DOMENEGHETTI, M.C.
(2002): The high temperature P21/c – C2/c phase transition
in Fe-free pyroxene (Ca0.15Mg1.85Si2O6): structural and
thermodynamic behavior. Am. Mineral. 87, 648-657.
VITERBO, D. (1992): Solution and refinement of crystal struc-
tures. In Fundamentals of Crystallography (C. Giacovazzo,
ed.). Oxford University Press, Oxford, U.K. (319-401).
Received November 3, 2002, revised manuscript accepted
February 19, 2003.