American Mineralogist, Volume 70, pages 365-374, 1985

A high temperature transition in MgGeO, from clinopyroxene (Ap) f;peto orthopyroxene (Pbca) type

TAx,c.Nrrrsu Y,c,I,tA.NA.rA,. M.l,S.lrnnO Hln,c,NO l,tro YOSHO T.ArEucHt

Mineralogical Institute, Faculty of ScienceUniuersity of Tokyo, Hongo, Tokyo I l3 Japan

Abstract

X-ray diffraction studies of the transition of MgGeO, from monoclinic to orthorhombicsymmetry at elevated temperatures have been conducted by precession photography onsingle-crystals of the polymorphs, which were synthesized by the flux method. The transitionoccurs rapidly as a topotactic transformation and obeys the following orientation relations ofthe orthorhombic (o) with respect to the monoclinic (c): t,lla!, bJlb" and c,/c". Thesestructures are very similar to those ofhigh-clinopyroxene (Cpx) and orthopyroxene (Opx), butthe stability relation of the clino-form (low temperature) to the ortho-form (high temperature)is reversed in the germanate compared to the silicate pyroxenps. Both monoclinic(a :9.6O5(2\, b : 8.940(2), c : 5.16(l)A, f :100.95(1f, Czlc) and orthorhombic(d : 18.829(3), b : 8.92A{4, c : fia1()L, Pbca) MgGeO. structures were refined at temper-atures up to 1100'C. At room temperature the clino-MgGeO. among M2*GeO3 (M'* :Mg, Mn, Fe, Co) most closely approximates an ideal clinopyroxene structure, based on thecubic closest packing (CCP) of oxygen atoms, having alc: JlU3, clb: J3l3 andfl : 100..025'. Increasing temperature gradually deforms this ideal structure. Under thermalexpansion, bond distances vary inversely with ionic strength, and the volume expansion ofMgl and Mg2 octahedra forces the chain of GeOn-tetrahedra to straighten and tilt. Apossible slip model of oxygen layers in the clino-to-ortho transition of MgGeO3 is proposedfor the topotactic transformation.

Introduction

The polymorphism of enstatite MgSiO, has been sum-marized by Smith (1969), and the aspects of the structuretransition have been discussed by Sadanaga et al. (1969),Papike et al. (1973), Smyth (1974) and Murakami et al.(1982). Moreover studies on the phase relations of ger-manate pyroxenes have attracted attention owing to theanalogy of these structures to those of silicate pyroxenes.Roth (1955) first reported the isotypism of MgGeO. withorthoenstatite. Robbins and Levin (1959) found anotherpolymorph of MgGeO., analogous to clinoenstatite, butstable at higher temperature than ortho-MgGeO..Pyroxene-type polymorphs of other germanates, MnGeO.,CoGeO, and FeGeO., have also been reported (Tauber etal., 1963; Tauber and Kohn, 1965; Royan and Forwerg,1963; Grebenshchikov et al., L976).

Ringwood and Seabrook (1963) and Ozima and Aki-moto (1983) stated, in their study of high pressure andtemperature phase transformation in MgGeO., thatclino-MgGeO, is stable at higher pressure and lower tem-perature than ortho-MgGeO.. This observation is at vari-ence with the stability relation reported by Robbins andLevin (1959).

Peacor (1968) was the first to investigate the structure ofCoGeO., which he found to be quite similar to that ofhigh-clinoenstatite (Cpx), stating that the arrangement ofoxygen atoms approximates a cub.ic closest packing (CCP).0003-{04xl85/030,1-O365$02.00 365

The structure of orthorhombic MgGeOr, refined by Fanget al. (1969), proved to be isostructural with orthoenstatite,and Hirano et al. (1980) found monoclinic MnGeO. to beisostructural with CoGeO, (Peacor, 1968).

We have synthesized single-crystals of both monoclinicand orthorhombic MgGeO, and refined their structures.We have also found, in our high temperature X-ray-diffraction studies, that the monoclinic phase (Cpx) withspace group C2fc transforms to the orthorhombic phase(Opx) with space group Pbca at about 900"C by topotactictransformation. This type of clino-to-ortho transition atelevated temperatures has not been found in silicate pyrox-enes. This paper presents refined structures of both clino-and ortho-MgGeO. at various temperatures up to 1100'C,discusses structural variations as a function of temperatureand suggests a possible mechanism for the newly foundtransition in the pyroxene-type structures.

Preparation of single-crystals of clino- andortho-MgGeO.

Single-crystals of clino- and ortho-MgGeOr having stoi-chiometric composition were prepared from a mixture ofreagent-grade powders of MgCO3, MgF, and GeO2 blend-ed in the ratios 1:2:3. MgFr acts as a flux. Ortho-MgGeO.was prepared by keeping the mixture at 1550'C for 20 hrsbefore quenching it to room temperature. The crystals thusobtained ate transparent and prismatic, up to

366 YAMANAKA ET AL.: HIGH TEMPERATURE TRANSITION IN MgGeO3

Fig. l. The ft01 precession photographs (MoKc unfiltered, p : l0) of the MgGeO. crystal, showing the process of the topotacticfrom clino- to ortho-phase. (A) Diffraction pattern of the twinned clino-phase at 800'C. (B) After heating the sample at 900"C for 30 min,showing patterns of the twinned clino-phase and the ortho-phase with common a* axis. (C) After further heating for one hour, exhibitingthe single pattern ofthe inverted ortho-phase.

0.3 x 0.1 x 0.1 mm in size. They are commonly euhedraland elongated parallel to c. Crystals of clino-Mgceo3were synthesized with the starting mixture heated at1360'C and then slowly cooled to 800"C at the rate of4"Clhr; they usually grow to approximately the same sizeas those of ortho-MgGeO. and are likewise euhedral. Toinsure homogeneity and stoichiometry, both samples weretested with EPMA. A few stacking faults were detected inthe ortho-phase by means of TEM lattice images.

Observation of the topotactic transition ofclino-MgGeO.

The clino-to-ortho transition in MgGeO. was investi-gated by means of X-ray-precession photographs at elev-ated temperatures. A fragment of a clino-MgGeO. crystalwas set on the head of a thermocouple, mounted on thegoniometer head, and the sample was heated to the desiredtemperatures by electric micro-heater and gas flame heater(Yamanaka et al., 1981). The methods to measure the tem-perature, by both thermocouple and optical pyrometer, aredescribed elsewhere (Murakami et al., 1982).

Precession photographs were taken (MoKa, 140 mA, 50kV, p: 10") after each 3O-minute heating period. All thetested samples of the clino-phase showed a twinned patternwith twin-and-composition plane (100) (Fig. 1A). Nochanges in the diffraction pattern of /r0/ of the clino-phasewere observed at temperature up to 800"C. After heatingthe sample for 30 minutes at 900'C, reciprocal lattice row

ft02 showed both clino and ortho patterns (Fig. 1B). Thisfact and additional photographs prove that the clino-phase(C2lc\ is transformed to the ortho-phase (Pbca) and thatthe transition is topotactic obeying the following relations:a"lla!, b"llb", c"f fc.. The ft02 reflections of the clino-phaseshow diffuse streaks parallel to a*, indicating the existenceof a disordered stacking sequence parallel to [00]. Afterheating for another 30 minutes at same temperature, nei-ther clino-phase reflections nor diffuse streaks were seen onthe photograph: only the sharp reflections of the ortho-phase were observed (Fig. 1C). These observations indicatethat the clino-phase first changes from its ordered stackingsequence to the disordered one during the transition, afterwhich it is transformed to the ortho-phase, having a wellordered sequence, different from that of the clino-phase. At1000"C the clino-phase is rapidly transformed into theortho-phase. No observation above 1200'C could be per-formed, because of the sublimation of the specimen. Thus,the existence of other possible polymorphs, similar in struc-ture to protoenstatite, could be confirmed.

After heating a crystal of ortho-MgGeO. for 24 hours at700"C in order to induce the reverse transformation fromortho- to clino-phase, we found that the diffraction patternof the ortho-phase remained unchanged. This observationdemonstrates that the reverse transformation proceedssluggishly, if at all, at the annealing temperture. The pres-ent in situ experiment of the transformation at elevatedtemperatures could not establish the exact transition tem-

perature, but it did confirm the stability relation of the twopolymorphs: the clino-phase is the low temperature formand the ortho-phase the high temperature form. None ofthe silicate pyroxenes reported to date have shown thistype of transition.

Refinement of the structuresA fragment of the clino-MgGeO. crystal 0.20 x 0.08 x

0.08 mm in size, was used for the structure refinements.Unit-cell dimensions at elevated temperatures were deter-mined by least squares refinement from 20 values of 25reflections within the range 40" <20 < 55' (Table 1). Thedetermination was made on a RTcAKU-rtFcS diffractometerwith graphite-monochromated MoKa radiation (1 :0.71069A) from a rotating anode generator (160 mA, 50kV). Diffraction-intensity measurements were made at 20,2lO, 420, 620 and 750'C for clino-MgGeO3 and at 20, 950and 1100'C for ortho-MgGeO., with a micro-electricheater set on the X-circle and gas-flame heater. X-ray-diffraction intensities were measured by employing thea-20 scanning mode; the scanning speed was 10" lmin in 20and the scanning width, 1.2 + 0.5' tan 0. The intensitiesgreater than 3olFl were corrected for Lorentz and polariza-tion factors and a transmission factor. The full matrix least-squares refinements, including anisotropic temperature fac-tors and isotropic extinction parameter, were conducted bymeans of the program LrNUs (Coppence and Hamilton,1970). Atomic scattering factors and anomalous dispersionparameters were taken from the International Table forX-ray Crystallography, VoL III (197$. The structure pa-rameters obtained from the refinement at each temperatureare presented in Table 2. The number of reflections ob-served and used and the final residuals (R and R.,) of eachrefinement are listed in Table 1.

Since all the samples of clino-MgGeO, that were testedby precession photography turned out to be twins, thespecimen chosen for the refinement was the one having the

367

largest volume ratio of the two individual crystals in thetwin. Only ft/<O reflections within the 70" range in 20(MoKa) were superposed by the twinned crystals. Conse-quently, the reflections were divided into two groups: lrft0reflections and other-than-hk0 reflections. Two differentscale factors were then employed in the least squares refine-ment. An average intensity ratio of 25 reflection pairshaving the same indices was adopted as an initial value ofthe scale factor. The volume ratio of the individual crystalsin the twin was estimated to be 26.7:1 from the convergedscale factors of the two sets of the intensities obtained atroom temperature. The structure refinements at high tem-peratures were conducted in the same manner as that atroom temperature described above.

Structures of clino- and ortho-i\,IgGeO3 at roomtemperature

Clino-MgGeO3

The structure of clino-MgGeO. (Table 3a) was found tobe analogous to that of clino-CoGeO, (Peacor, 1968). Thearrangement of the oxygen atoms approximates a cubicclosest packing (CCP), as reported by Peacor (1968), andtetrahedra and octahedra formed by the oxygen atoms areclose to regular polyhedra (Fig. 2). Unit-cell parameters(Table 4) prove that, in comparison to clino-phases ofCoGeO., MnGeO3 and FeGeO., clino-MgGeO3 moreclosely approximates CCP of oxygen atoms. In this idealstructure composed of CCP oxygen, if r denotes the ionicradius of oxygen, the unit-cJll parameters are expressed bya : 2J llr, b : 6r, c : 2J3r, and p : 100.025'.

Silicate pyroxenes such as diopside-type clinopyroxeneand high-clinopyroxene having space group C2lc, showconsiderable distortion from CCP. Compared with the ger-manate pyroxenes, the smaller tetrahedral chain bridgingthe octahedral bands in the silicate pyroxenes requireslarger cations such as Ca or Na in the M2 sites, whereas

YAMANAKA ET AL.: HIGH TEMPERATURE TRANSITION IN MgGeO,

Table l. Unit-cell parameters and factors of refinements

Cl i no-M9Ge0,

2l 0'c 420"c 620.c

0rtho-MgGe03

20"c 950"c il00'c

r 8 . 8 2 e ( 3 ) . 1 9 . o i l ( 5 ) r e . 0 3 r ( 7 )

albc/b

v(As1Dx ( g/cmr )

emax ( ' )N obs .N usedR ( % )Rwt (% )

2 \ A A ( O 1 r \2\ e .474(212 \ A 0 0 t 1 2 \' r ) 5 . r 8 0 ( r )' r ) r0] .23( r )

1 .07420. 576',I

) 44 ] . 3 ( l )4 . 36 r

8.952(2)s . 3 4 7 ( r )

' r .991 6

0.5972

e 0 1 . 3 ( 3 )4 . 271

s . 6 8 6 ( l ) s . i 0 6 ( 3 )9 . 4 9 6 ( r ) e . s o e ( 3 )9.024(21 e.040( 3 )5 .1e2 ( r ) 5 . 202 (1 )' r o1

. 38 ( ' , r ) r o ] . 55 (3 )' l

. 0733 1 .07370 .5753 0 .5754

4 4 4 . e ( r ) 4 4 7 . r ( 3 )4 .326 4 .304

60 60649 653499 500

5 . 2 1 3 . 7 66 . 2 7 4 . 5 4

9 . 6 0 s ( 2 ) 9 . 6 4 0 (e . 4 3 1 ( 2 ) 9 . 4 5 8 (8 . s40 (2 ) 8 .978 (s . r 6 0 ( l ) s . ' 1 7 3 (' r 0 0 . e s ( 1 )

1 0 r . r 4 (

1 .0744 1 .07370 .5772 0 .5762

4 3 s . ' , r ( r ) 4 3 e . 2 ( l4 . 424 4 .38?

70 60959 645826 545

3 . 5 8 4 . 6 53 . 9 ? 5 . 9 5

"(fi)as inBb(a)c (A )

B

9 . 0 8 4 ( 2 ) e . 1 r 0 ( 3 )5 .415 (2 ) 5 .428 (4 )

2.0928 2.08910 .5961 0 .5975

e 3 5 . 2 ( 5 ) 9 4 ] . 0 ( 8 )4 . I 1 6 4 . 0 9 0

]00 s53716 I 1 44'1838 5895 . 2 1 I r . 5 56 . 2 5 r 2 . 6 0

O Uof,z

4 . 9 66 . 03

Parentheslzed f lgures lepresent the est l@ced stadard deviat lon (esd) and refer to the last decl@lplace. Thls notat lon for esd ls used consistent ly throughout thls work.

36E YAMANAKA ET AL.: HIGH TEMPERATURE TR,4NS/TION IN MgGCO,

Table 2a. Atornic coordinates of clino-MgGeO. Table 2b. Atomic coordinates of ortho-Mgceo3

2l 0.c 420"C 620'C

0 .1237 (7 ). 3647 ( 16 ). 3565 (24 )

t . o o l a a I

Mgl xv

Biso

Mg2 xv

Eiso

G e A xv

Biso

n 1 t 1 ) ( 2 \

. 3440( 3 )? 4 n 1 / q \

. 5 5 ( 6 )

. 377 4 (3 )

. 48e0 (5 )

. 3443 (9 )

. 5 1 ( 7 )

.2709(1)

.3454(2)

.0408( 2 )

. 3 5 ( r )

. 47?2 ( t )

. 3393 (2 )q n q q a 2 \

. 3 7 ( r )

. r 7 8 7 ( 4 )

.3409( ' , I3)

. 0 r 8 8 ( r 4 )

. 3 7 ( e )

. 3 i l 9 ( 5 )

. 5 r32 ( ' , I 0 )

.0382 ( r 8)

. 6 3 ( r r )

. 3 0 7 1 ( 5 )

. 2 r 0 4 ( i l )

. d J J / ( | / , |

. 8 0 ( r 5 )

. 5 b J b ( 4 , ,

. 3 3 6 2 ( 1 3 )

.8 r47( r6 )

.56( i l )

.4299(4)

.4863( r r )

.6689( r 9)

. 6 0 ( 1 2 )

. 4455 (4 )

. r 7e4 (8 )A 2 q q / I 6 \

.34( i l )

.3776(7 )

. 4874 ( r 6 )

. 3532 (28 )? .97 (25 )

.2710(17)

. 3450( 39 )

.0422(64)r . s 6 ( 5 )

. 4729 (2 )

. 3387 (4 )

.8035( 6 )r . 7 4 ( 5 )

. r 7 7 ] ( i l )

.3347 (?7 )

.0250 ( 44 )2.04(41)

. 3093 ( 1 3 )

. s l 50 (31 )

. 0437 (56 )3 .04 ( 54 )

. 3069 ( r 4 )

. 2141 (30 )

. 8324 (60 )J . J Z ( J O , ,

. 5667 ( r 3 )

. 3 4 r 5 ( 3 2 )

.8090( 55 )3 .07 (49 )

0 . 0 0 . 0 0 . 0 0 . 0 0 . 0e071 (3 ) . e068 (s ) . e062 (s ) . 9062 (6 ) 9047 (6 )

. 2 5 . 2 5 . 2 5 . 2 5 . 2 5

.0012(2) .0030(4) .0039(5) .0052(6) .0057(4)

. 0012 (2 ) . 0028 (5 ) . 0028 (s ) . 0045 (6 ) . 0057 (4 )

. 0 0 5 0 ( 6 ) . 0 r 0 2 ( r 5 ) . 0 r 0 6 ( 1 5 ) . 0 1 s 6 ( r 8 ) . 0 r 5 5 ( r 3 )- . 0002 (3 ) - . 0003 (6 ) - . 0002 (6 ) - . 0004 (8 ) . 0003 (6 )0 . 0 0 . 0 0 . 0 0 . 0 0 . 0.2700(3) .2704(5) .270s(5) .2709(6) .2700(5). 2 s . 2 5 . 2 5 . 2 5 . 2 5.00 r4 (2 ) . 003s (5 ) . 0044 (s ) . 0061 (6 ) . 0068 (5 ). 00 r4 (2 ) . 003 r (5 ) . 0034 (5 ) . 004s (6 ) . 00s8 (5 ). 0044 (6 ) . o i l 0 ( r 6 ) . 0 r08 ( r6 ) . 0 ' 167 (20 ) . 0128 ( t 7 )

- . 0005 (3 ) - . 0004 (7 ) . 0002 (7 ) - . 0011 (e ) . 0001 (6 ). 3 0 0 2 ( r ) . 2 9 s e ( r ) . 2 s s 7 ( 1 \ . 2 9 e 4 ( 1 \ . 2 9 9 3 ( t ). 0945 ( r ) . 0e44 ( i ) . 0944 ( r ) . 0e44 ( t ) . 0e44 ( l ). 2 1 0 8 ( r ) . 2 1 r 7 ( r ) . 2 1 2 ' t ( 2 \ . 2 1 2 7 ( 1 \ . 2 1 2 7 ( 2 ). 0009 ( r ) . 002 r ( r ) . 0027 ( r ) . 0035 (1 ) . 0035 (1 ). 00 r0 ( r ) . 002 t ( r ) . 0027 ( r ) . 0041 ( l ) . 0046 (1 ). 0039 (3 ) . 0104 (4 ) . 0094 (4 ) . 0151 (2 ) . 0129 (2 \

- . 000 r ( r ) - . 000 r ( r ) - . 000 r ( r ) - . 000 r ( l ) - . 000 t ( t )- . 0 0 0 7 ( r ) - . 0 0 0 2 ( 1 ) . 0 0 0 1 ( 1 ) - . 0 0 0 3 ( l ) . 0 0 1 5 ( t )- . 0000 ( r ) - 000 (2 ) - . 000 r (2 ) - . 000 r (2 ) . 000 r (2 ). r 1 6 0 ( 3 ) . r ' 1 6 6 ( 6 ) . 1 1 6 4 ( 7 ) 1 1 6 6 ( 8 ) . 1 1 5 7 ( 5 ). 0e0e (4 ) 0906 (7 ) . 09n (8 ) . 0s06 (e ) . 0s23 (8 ). r 3 2 5 ( 6 ) . r 3 2 4 ( r 3 ) . i 3 3 7 ( r 3 ) . r 3 1 e ( ' , r 6 ) . r 3 3 2 ( 1 r ). 0033 (2 ) . 0024 (6 ) . 0030 (6 ) . 0038 (8 ) 0041 ( s ). 00 r3 (3 ) . 0038 (7 ) . 0034 (7 ) . 0060 ( r0 ) . 0062 (7 ).0065(10) .0100(r2) .o '146(22\ .0220(27] | .0165(20)

- . 0001 (2 ) - . 000 r (6 ) - . 0003 (6 ) . 000 r (5 ) - . 00 r2 (6 )- . 0006 (4 ) - . 0010 (10 ) - . 0006 ( r2 ) - . 000e ( i l ) . 0011 (8 ). 000s (s ) . 000 ( r 2 ) - . 0002 ( i l ) - . 0002 ( r5 ) - . 0026 (1 r )

. 3826 (3 ) . 3828 (7 ) . 3831 (7 ) . 3833 (8 ) . 3813 (6 )

.2435(4) .2427(7) .2421(8) .24r8(9) .2418(7)

. 38 r4 (6 ) . 3806 ( i l ) . 38 r7 ( r3 ) . 38 r4 ( r6 ) . 383e ( i l )

. 0012 (3 ) . 0036 (7 ) . 0043 (7 ) . 0053 (9 ) . 0065 (7 )

.00r3(3) .0029(7) .0036(8) .0047(9) .0042(7)

. 0049 (9 ) . 0 r ' r s (24 ) . 0098 (22 ) . 0 r85 (29 ) . o ' , r 5 r (20 )- . 0005 (2 ) - . 001 r (6 ) - . 0012 (6 ) - . 0014 (7 ) - . 0013 (5 )- . 0006 (4 ) - . 0026 (6 ) - . 002 r ( r 0 ) - . 00 r7 (13 ) . 0004 ( r0 )- . 0 0 0 r ( 4 ) - . 0 0 1 2 ( i l ) - . 0 0 r 3 ( r 0 ) - . 0 0 1 7 ( 1 3 ) - . 0 0 0 1 ( 1 0 )

. 360 r (3 ) - 360 r ( i ) . 35s9 (7 ) . 3s88 (8 ) . 3673 (7 )

.0688(3) .0682(7) .0686(7) .0677(8) .0680(7)

. 9034 (6 ) . sos7 (14 ) . e050 ( r3 ) . e088 (16 ) . 9091 ( r 2 )

. 00 r6 (3 ) . 0025 (6 ) . 0029 (6 ) . 0047 (8 ) . 0060 (7 )

. 00 r4 (3 ) . 0027 (7 ) . 0033 (7 ) . 0046 (s ) . 0075 (s )

.0040(9) .0t4s(26) .0r44(24) .0201 (20) .018t (22)- . 0006 (2 ) - . 0008 (6 ) - . 0008 (6 ) - . 00 r6 (7 ) - . 001 r ( 6 )

. 0001 (4 ) . 0007 ( r0 ) . 00 r4 ( r0 ) . 00 r0 ( r3 ) . 0036 ( r0 )- . 0 0 0 8 ( 4 ) - . 0 0 r 7 ( r 0 ) - . 0 0 r 7 ( i l ) - . 0 0 2 r ( r 4 ) - . 0 0 3 0 ( l l )

M92

0l

03

x

vz

B r r9 z z

B r r

z

B r r

z8 r r

B tz

zB r r

B e e

xvz

B r rB z z

Bzzxvz

B r r

.4289(12)

.4852(27 |

. 679 r ( 53 )2 .32 (45 ] ,

. 448 r ( r 0 )

.1745(23)

.6290(37)r . 0 8 ( 3 4 )

xvz

Bieo

xvz

Bieo

xv

Biso

Xv

Bieo

xIz

Bdeo

X

Bieo

x

vz

Biso

G e B

0 t A

0 2 A

0 3 A

0 l B

0 2 8

0 3 8

the Ml site generally contains a smaller cation than M2.The distortion from CCP results from the size differencebetween M1 and M2 sites. In the clino-MgGeO. structure,large Ge-tetrahedral chains conform to CCP of oyxgenatoms and result in the ideal octahedra in M1 and M2sites, which correspond to Mgl and Mg2, respectively.

The O3'-O3-O3" angle has been discussed as a parame-ter of the chain geometry, particularly its "straightness" orits "kink", because 03 is the bridging oxygen atom of adja-cent tetrahedra. This angle is closer to the ideal value of120' in MgGeO3 (129.03) than in other germanate pyrox-enes: 133.4" in CoGeO. (Peacor, 1968), 135.f in MnGeO3(Hirano et al., 1980); and considerably more so than insilicate pyroxenes: diopside (L66.4"), jadeite (174.6") (Ca-meron et al., 1973). The angle of Ge-O3-Ge' inclino-MgGeO. is 117.95', which is similar to the idealangle of 109.47',.rs compared to Si-O3-Si' in the silicatetetrahedral chain. Two bridging bonds, Ge-O3 (1.S01A)and Ge-O3'(1.7984) are significantly longer than two non-bridging bonds; Ge-Ol (1.7384)and Ge-O2 (1.7064). Theacentric location of Ge ions in the tetrahedron is caused bv

the effect of the electrostatic valency differences in oxygenatoms. One way in which clino-Mgceo3 differs from sili-cate pyroxenes is that its structure shows no shared edgesbetween octahedra and tetrahedra. The above featuresdemonstrate that Ge-O bonds have a stronger ionic (lesscovalent) character than Si-O bonds.

Ortho-MgGeO,

The lattice parameters obtained from single crystals ofortho-MgGeOr (Table 4) are similar to those derived frompowder data (Roth, 1955); they arc all a little larger thanthose of orthoenstatite (Smith, 1969) but smaller than thoseof other germanate orthopyroxenes, MnGeO3 (Fang et al.,1969) and CoGeOr (Tauber et al., 1965).

Interatomic distances and angles of ortho-MgGeo3 at20"C (Table 3) indicate that its structure is very similar tothat of ortho-MgGeO, (Fang et al., 1969). The structure(Fig. 3) is made up of four pairs of alternating tetrahedraland octahedral layers parallel to (100). There are two crys-tallographically distinct tetrahedral chains, the A chain and

YAMANAKA ET AL.: HIGH TEMPERATURE TRANSITION IN MgGeo,

Table 3a. Interatomic distances, volumes ofthe polyhedra and tetrahedral chain angles

369

Atoms

CI i no-Mgce03

20'c 210.c 420"c

0rtho-MgGe03

750"C 20"c 950"C620"C

l 4 q l - 0 l A ( A ) ,- 0 1 B r

0 l A ' ]0 l B '0 2 A 10 2 8

llean

o

v t i3 l

Mean

o

V ( A " )

2 . r 3 7 ( 3 ) 2 . ' , I s 0 ( 8 )

2 .074 (3 ) 2 .078 (6 )

2 . 0 4 0 ( 4 ) 2 . 0 4 9 ( 8 )

2 . 0 8 4 ( 3 ) 2 . 0 s 2 ( 7 )

0.0402 0.0425

11 . 776 11 .921

2 . 1 0 4 ( 3 ) 2 . 1 2 2 ( 7 \

2 .023 (3 ) 2 .027 (7 )

2 .217 (3 ) 2 .233 (7 )

2 . l l s ( 3 ) 2 . 1 2 7 ( 7 )

0 .0796 0 .0842

1 2 . 3 9 3 1 2 . 6 1 0

2 . l s e ( 8 ) 2 . 1 6 7 ( 9 )

2.084 ( 6) 2.080(7)

2 . 0 5 5 ( 8 ) 2 . 0 6 r ( 9 )

2 .099 (8 ) 2 .102 (8 )

0 .0438 0 .0461

12 .022 r2 .089

2.057(8) 2.215(32)2 .1s4 ( i l ) 2 . 141 (28 )2 . 1 s 4 ( l l ) 2 . r t 2 ( 3 ? l2 t l q / o \ ? n . ( q l 2 7 \

2.033( r0) 2 .06r (2s)z . v o t \ t t . , z . u l 5 ( J t ,

2 .096 (10 ) 2 .108 (29 )

0 .0478 0 .0569

' t 2 .048 i 2 . 159

2 .075 ( r3 ) 2 .077 (38 )2 .099 (14 ) 2 . r 3s (34 )1 . e 9 7 ( r 3 ) 2 . 0 r 6 ( 3 e )2 . 0 6 r ( 1 3 ) 2 . r 3 5 ( 3 e )2 .223 (14 ) 2 . 33 ' , I ( 32 )2 .2s8 ( r2 ) 2 .273 (36 )

2 . ' , r 2s ( r3 ) 2 . r6 r (36 )0 . I 026 0 . I 087

I 2. I 80 12.669

1 . 7 2 3 ( 8 ) 1 . 7 8 4 ( 2 6 )' r . 702 (9 ) r . 7 ' , n ( 28 )

r . 7 9 6 ( 8 ) r . 8 2 8 ( 2 0 )r . 7s3 (8 ) 1 .827 (2 r )

l . / c J ( d J t . r 6 6 l t J )

0 . 041 7 0. 04761

2 .753 2 .901

1 .741 (6 ) 1 .789 (22 )r . 68s (s ) I . 708 (28 )r . 7 7 5 ( r 0 ) r . 7 8 1 ( 3 0 )r . 7 7 s ( 9 ) 1 . 7 s 6 ( 3 2 \

r . 746 (9 ) 1 .768 (281

0 .0351 0 .0353

2 .644 2 .754

102.20 102.26' l I L00 112 .23

126.40 127.70120 .49 1 1 9 .07

1 5 0 . 3 2 1 5 2 . 9 3129,37 126.29

2 . r 86 (8 )

2 . 0 8 3 ( 5 )

2 .074 (7 )

2 . r 5 ( 7 )

0 .0508

r 2 . ?85

M 9 2 - 0 l A l0 l B0 2 A ]0 2 80 3 A0 3 B J

2 . r ' l e ( 7 ) 2 . r 3 e ( 8 ) 2 . 1 1 7 ( 7 1

2 .022 (71 2 .02s (8 ) 2 .022 (5 )

2 .234 (7 ) 2 .262 (8 ) 2 .282 (7 )

2 . 1 2 s ( 7 ) ? . 1 4 2 ( 8 ) 2 . 1 4 0 ( 6 )

0. 0867 0.0967 0. I 074

12 .577 12 .862 12 .848

G e - 0 1 IGeB 02 B

0 3 80 3 B '

Mean

o

V ( A " )

Mean

o

V (A " )

Tetrahedral bond angles0 3 A - G e A - 0 3 A ' ( ' )0 3 8 - c e B - 0 3 8 ' 1 0 5 . 1 5

G e A - 0 3 A - G e A 'G e B - 0 3 8 - c e B ' 1 1 i . 9 5

03 A' , - 03 A - 03 A, '0 3 B ' - 0 3 B - 0 3 B , ' 1 2 9 . 0 3

r . 7 3 9 ( 3 ) 1 . 7 3 s ( 6 ) 1 . 7 3 8 ( 7 ) 1 . 7 3 8 ( 7 ) 1 . 7 4 6 ( s )r . 7 0 6 ( 3 ) 1 . 7 0 4 ( 6 ) 1 . 7 0 5 ( 7 ) ' , I . 7 0 8 ( 8 ) 1 . 7 0 8 ( 6 )1 . 7 9 8 ( 3 ) 1 . 8 0 3 ( 7 ) 1 . 8 0 6 ( 7 ) I . 8 1 0 ( 8 ) 1 . 8 1 3 ( 6 )' 1 . 8 0 1 ( 3 ) r . 8 0 4 ( 8 ) 1 . 8 1 2 ( a ) t . 7 s e ( e ) 1 . 7 9 6 ( 7 )

r . 7 6 1 ( 3 ) 1 . 7 6 2 ( 7 ) 1 . 7 6 s ( i ) 1 . 7 6 4 ( 8 ) 1 . 7 6 6 ( 6 )0 .0402 0 .0434 0 .0454 0 .0423 0 .041 6

2 .735 2 .736 2 .753 2 .741 2 .753

G e A - 0 l A0 2 A0 3 A03 A '

' r 0s .02 I 04 .94 I 05 . 3 l

l I 8 . 0 5 1 1 7 . 7 8 1 1 8 . 7 l

r 29. 30 129 .07 I 29 . 59

' 105 .74

l l 9 . l ' l

129.40

the B chain, both of which have an O rotation (Thompson,1970). The A chain looks a little more stretched than thb Bchain, as a result of a large O3A'-O3A-O3A" angle(150.32'). Each tetrahedron in the A chain shares one edgewith the M2 octahedron. The B chain in ortho-MgGeO, islittle ditrerent from the chain in clino-MgGeO3. As to theangles O3B'-O3B-O38" and GeBO3B-GeB'; they are129.37" and 120.49', respectively, in ortho-MgGeo3 versus120.37" and 117.95" in clino-MgGeO.. The GeB tetra-

hedron is larger and more regular than the GeA tetra-hedron.

As mentioned above, the M2 octahedron shares an edgewith the GeA-tetrahedron. It follows that the octahedron isextremely distorted. Mg2-O3A and Mg2-O3B bond lengthsare more extended than the four other bonds in the M2sit€. The volume of the M2 octahedron is a little largerthan that of M1. The above features closely resemble thoseobserved in orthoenstatite.

370 YAMANAKA ET AL.: HIGH TEMPERATIIRE ?R,4NSITION IN MgGeO'

Table 3b. Lengths ofedges in the polyhedra

20 'c

Cl i no-IleGeO3

21 0"c 420"c 620"c

0rtho -l lgGe0,

20"c 950'c750.C

O t A - 0 l A 'O t B - 0 l B 'O t A - 0 1 8 '0 1 A - 0 t B0 l A ' - 0 l B 'o tA - 0280 l B ' - 0 2 A0 t A ' - 0280 l B ' - 0 2 A0' l A ' - 02A0 lB - 02802A - 028

Mean

o

0 l A - 0 t B0 lA - 0280 lB - 02A0 lA - 02A0 lB - 0280 lA - 03Ao t B - 0 3 B02A - 03A028 - 03802A - 038028 - 03A03A - 03B

Mean

o

Ge (GeB) s i t e

o tB - 02Bo tB - 038o t B - 0 3 8 '02B - 038028 - 038 '038 - 038 '

Mean

o

GeA s i t e

O tA - 02A0 lA - 03Ao tA - 03A '02A - 03A02A - 03A'03A - 03A' ,

!'lean

o

3 . 0 4 e ( s ) 3 . 0 5 6 ( e )

2 .732 (5 ) 2 .756 (10 \

2 . 8 8 s ( 4 ) ? . 8 e 7 ( e )

3 . r 0 7 ( 4 ) 3 . r 2 4 ( r o )

3 . 0 3 e ( 5 ) 3 . 0 4 7 ( r o )

2 . 7 9 2 ( 4 ) 2 . 8 0 8 ( e )

2 . 8 4 4 ( 5 ) 2 . 8 4 7 ( i l )? . s 4 4 ( 4 ) 2 . 9 5 5 ( 9 )

0 . ' t ? 6 6 0 . 1 2 7 9

1 . t J . l J ) Z . / l O t t u /

2 . 9 1 0 ( 5 ) 2 . e 2 e ( 1 0 )

? .792 (4 ) ? .807 (9 )

3 . 0 5 9 ( 4 ) 3 . 0 8 0 ( e )

? aE7 ( t \ 2 q^n ro \

3 . r 5 7 ( 5 ) 3 . r 8 0 ( 1 0 )

3 . 3 6 e ( 5 ) 3 . 3 e 8 ( r ' r )

2 . e88 (4 ) 3 .005 ( l o )

0 . I 754 0 . I 786

2 . s 6 e ( 4 ) ? . e 7 1 ( e )2 .871 (4 ) ? .874 (9 )? . 8 ? 6 ( 5 \ 2 . 8 2 6 ( r 0 )2 . 8 0 5 ( 4 ) 2 . 8 0 s ( e )2 . 8e2 (4 ) 2 . 886 ( I 0 )2 . 8 s 8 ( 4 ) 2 . 8 6 2 ( r 0 )

2 . 8 5 8 ( 4 ) 2 . 8 7 1 ( r 0 )

0 .0528 0 .0525

2 . 8 0 7 ( l l ) 2 . 7 7 2 ( 3 6 )2 .687 (12 ) 3 .078 (40 )2 . 8 1 7 ( r 3 ) 2 . 9 5 4 ( 3 8 )2 . 8 8 8 ( r 3 ) 2 . 8 r 0 ( 3 7 )3 . 0 3 7 ( r 4 ) 2 . 7 2 s ( 3 3 )3 . 4 6 5 ( r s ) 3 . 0 5 7 ( 3 6 )3 . 0 9 3 ( r 4 ) 3 . 6 1 4 ( 3 8 )2 .552 (14 ) 3 . r 39 (33 )3 .274 (13 ) 3 .488 (38 )3 .086 ( r2 ) 2 .604 (41 )3 . 4 1 5 ( r 3 ) 3 . 3 3 4 ( 3 4 )2 .847 ( r2 ) 2 .e23 (33 )2 a a T r t ? \ 1 n L 2 ( 1 , 7 \

0 . 2715 0 .2978

z , Y a o \ t a l J , u r J ( J f , . /2 .817 ( r 2 l 2 . 847 (33 )2 .780 (12 ) 2 .887 (33 )2 . 7 7 3 ( 1 2 ) 2 . 8 5 e ( 3 4 )2 .873 ( r3 ) 2 .859 (32 )2 .766(13) 3 .035 ( 29 )2 . 8 3 8 ( 1 2 ) 2 . e 1 7 ( 3 3 )

0 .0765 0 .2978

2 . s46 (12 ) 3 . oo r ( 35 )? .861 (12) 2 .895 ( 36 )2 .982 (12 ) 3 .oo r ( 36 )? .924 (14 ) 2 .e63 (4 r )2 .552 (14 ) 2 .604 (41 ] .2.766(13) 2.186(46')

2 .834 ( r 3 ) 2 .876 (3e )

0 . 1 4 5 6 0 . 1 4 3 7

3.065(10) 3 .068(1r ) 3 .0e0(e) 3 :13?[ ]3 i2 . 7 5 0 ( r 0 ) 3 . 0 6 8 ( i l ) 3 . 0 e 0 ( e ) 2 . 8 0 7 ( 1 0 )

2 . s 0 7 ( s t 2 . e 0 4 ( r 0 ) 2 . e r 6 ( 8 ) i : 3 3 3 [ ] i i3 . r 4 0 0 0 ) 3 . r 4 8 ( r ) 3 . r 2 0 ( 1 0 ) 3 : l 9 i i l i i3 .063( r0) 3 .064( i l ) 3 .085(e) t l?? ' l i l2.80e(e) 2.815(i l ) 2.815(8) t2l1l i " \2 . 8 s 8 ( f ) 2 . 8 6 r ( r 3 ) 2 . 9 2 2 ( 9 ) 2 . e 8 2 ( 1 3 )

2 . 9 6 5 ( l 0 ) 2 . 9 6 e ( r ) 2 . e 8 6 ( s ) 2 . 9 5 9 ( 1 ? )

0 . 1 3 3 5 0 . 1 3 1 2 0 . ' ] 3 9 2 0 . 1 4 5 6

3 .177 (42 ] ,3 . l r 4 ( 3 4 )a . t t t \ J o l2 .788 ( 36 )2 . 7 8 8 ( 3 6 )3 . 2 3 8 ( 3 8 12 .s18(37 |3 . 1 8 9 ( 4 0 )3 . r 34 ( 38 )2 . 8 1 0 ( 3 7 )? .725 (33 )3 . 0 2 2 ( 3 7 )2 . e 7 3 ( 3 7 )0 . I 841

2.750( r0) ? .775( r1) 2 .76018)2 9 2 1 ( 1 0 \ 2 . 9 4 5 ( 1 1 \ ? . 9 ? 1 ( 9 \

2 . 8 0 s ( e ) 2 . 8 r 5 ( r 0 ) 2 . 8 1 5 ( 8 )

3 . 0 7 8 ( r 0 ) 3 . r 0 3 ( i l ) 3 . 0 9 3 ( 1 0 )

2 . 9 5 8 ( r o ) 3 . r 0 3 ( i l ) 3 . 0 9 3 ( r 0 )

3 . r 7 3 ( r o ) 3 . 2 0 6 ( 1 2 ) 3 . 2 0 0 ( r o )3 . 4 0 4 ( r 0 ) 3 . 4 6 0 ( r 2 ) 3 . 5 0 0 ( 1 0 )3 . 0 0 3 ( r o ) 3 . 0 2 6 ( r 1 ) 3 . 0 2 6 ( s )0 . 1 7 9 3 0 . 1 9 0 8 0 . 1 9 9 7

2 9 7 2 ( 9 \ 2 9 R ? ( 1 0 \ ? 9 7 n ( A \2 . 8 7 8 ( 9 ) 2 . 8 7 7 ( 1 0 ) 2 . 8 8 3 ( 9 )2 . 8 3 e ( l r ) 2 . 8 2 1 ( 1 2 ) 2 . 8 2 8 ( 8 )2 . 8 0 7 ( r o ) 2 . 8 0 9 ( r ' r ) 2 . 8 r s ( e )2 .8e2 (10 ) 2 .884 (12 ) 2 .897 (e )2 .86e ( ' , l 0 ) 2 .86e (1? ) 2 .877 (e )

2 .867 (10 ) 2 .874 (1 r ) 2 .878 (e )

0 .051 2 0 . 0559 0 . 0505

High temperature crystal chemistry of MgGeO,

A series of refinements at elevated temperatures revealdistinctive high-temperature behaviors of germanate pyrox-ene structures and provide insight into the behavior ofanalogous silicate pyroxenes.

Lattice parameters determined at high temperatures(Table 1) are plotted as a function of temperature in Figure4. The cell edges, ao, b.and co of the clino-phase, increase

linearly within the stable temperature range, with nearlyequal thermal expansion coeflicients. The p-angle function,however, is not linear: it has a positive curvature as tem-perature exceeds 500"C. The distance a" sin 0, which ismeasured perpendicular to the octahedral bands, and has avalue of abofi aJ2 of the ortho-phase, varies linearly.Values ofa", b"and c.change discontinuously to the corre-sponding ao, bo arnd co of the ortho-phase near 900"C, asthe structure transition from clino- to ortho-phase takes

YAMANAKA ET AL.: HIGH TEMPERATURE

Clino MgGeO3 rczk) 2oT

TRANSITION IN MgGeO,

Ortho lvlgGeO3 (Pbca) 20t

371

.Fig. 2. to, "t,nool""*[. **J of MgGeo, at zo"c

viewed along a*.

place. The value ofc" abruptly increases to that ofco, whilethat of a" sin 0 contracts to that of aJ2, at the transitiontemperature. The remarkable expansion of co results fromthe great extension of the A chain in the ortho-phase. Acomparison with the ideal values of alb, clb and p, of thevalues observed in the clino-structure at the various tem-peratures suggests that the oxygen atoms in the structuregradually depart from CCP as the temperature increases.

Interatomic distances and volumes of the cation tetra-hedra and octahedra as a function of temperature (Table3a) and lengths of O-O edges in the polyhedra (Table 3b)indicate the thermal effects on the clino- andortho-MgGeO3 structures. Mean distances of Mgl-O and

Table 4. Unit-cell parameters of germanate pyroxenes

Fig. 3. First and second layers of the orthopyroxene-typestructure of MgGeO. at 20'C viewed along a*.

Mg2-O in the clino-structure (Fig. 5) increase linearly withtemperature; the former is smaller than the latter, but theirthermal expansion coefficients are almost equal. Thevolume increments of the Mgl and Mg2 octahedra are alsonearly equal. In contrast, the increment of the mean Ge-Odistance and especially that of the volume of the tetra-hedron are so small as to be within experimental errors.These thermal changes are consistent with those of silicateclinopyroxenes (Cameron et al., 1973).

The thermal expansion of the octahedra results in: (1)straightening of tbe tetrahedral chain; (2) tilting of thetetrahedra against the plane of the octahedral bands; (3)rotation of the tetrahedra. Since the bridging oxygen 03 inthe tetrahedral chain links the Mg2 octahedron to thechain (Fig. 2), the extreme expansion of Mg2-O3 bringsabout the straightening of the chain by causing the angle ofO3'-O3-O3" to increase with temperature.

The standard deviation o of the interatomic distance.expressed by o:E(x -fzln, is regarded as a measure ofthe deformation of the regular polyhedron. The values of oof Mgl-O, Mg2-O and O-O increase with temperature(Table 3a and Table 3b), suggesting a gradual deformationfrom the ideal structure. This feature is consistent with thevariation of the unit-cell parameters with temperature.

The oxygen atom 01 being tetrahedrally coordinatedwith two Mgl's, Mg2, and Ge, has a valence sum of 2.0.Both 02 and 03 have coplanar three-fold coordinations,the former is coordinated by Mgl, Mg2, and Ge and the

Cl inopyroxene (C2lc)

t '1qceo,1' coceo,z' receo,3' l4nceor4' iaeat (r . I :a i)5'

, ( l ) e 6 o s { 2 ) s 6 s 2 ( 4 ) 9 7 e 8 ( l )D { t ) 8 . e 4 0 ( 2 ) e . 0 r 8 ( 3 ) s 1 5 0 ( l )

" \ A ) 5 . 1 6 0 ( l ) 5 t 8 l ( 2 ) 5 1 9 6 ( t )

B r 0 0 . 3 4 ( r ) " t o l 2 ( t ) " t 0 t . 8 4 ( t ) .

a / b 1 0 7 4 3 1 0 7 4 7 1 0 7 0 8

c / b 0 5 7 7 2 0 5 7 4 5 0 5 6 7 9

v ( i 3 ) 4 3 5 8 8 ( r 4 ) 4 4 4 . 0 0 ( 2 5 ) 4 5 5 . s z \ t z )

D x ( g / c m 3 ) 4 . 4 2 4 5 . 3 7 0 5 . t 4 0

0rthopyroxene (Pbca)

ugceo,T/ coceo,6/ Feceo3

" ( l ) t 8 8 2 e ( 3 ) t 8 7 7

b ( , 3 ) I e 5 2 ( 2 ) 8 e e

r ( A ) 5 . 3 4 7 ( l ) s . 3 5

a / b 1 . 9 9 1 6 2 0 8 7 9

e/b 0.5972 0 59sl

t ' ( i 3 ) e o r . 2 6 ( 3 ) s o z . 7 7

Dx(g/cn3) 4 271 5.283

9 e 2 0 4 ( 9 ) 2 / 1 1 r . 9 1 5 4

9 2 7 7 9 \ 6 ) 6 r = 8 2 8 0

5 2765151 26 r = 4-781

1 0 1 . 7 4 ( t ) " t 0 0 . 0 2 5 "

I 0693 r 'TTl3 = ] tO55

0 5687 1//7 = 0-5774

4 7 5 5 O ( 7 ) 9 6 € 1 3 = 3 5 6 . 8 0

4 . 9 0 3

M n G e o r T / i d e a t ( r = 1 m i ) 5 )

19 267(6) 16,6 r /3 - 18 028

9 2 4 8 ( 3 ) 6 r = 8 2 8 0

5 477(2) 2/ i r = 4,78r|

2 0833 32/6/6. 2 177

0.5922 -t l6 = 0.5774

975 89 192O 13 = 713 6A

4 7 7 8

7, p lesent sork . 2 , Peacor (1968) . 3 , f rob our sEruc ture aDa lys ls wh ichw i l l b e p u b l i s h e d e l s e w h e r e . 4 l H i r a n o e t a l . ( t 9 8 0 ) . 5 . / r l n d i c a l e sthe io f , i c rad ius o f oxygen and rhe va lue o f r i s f ron shannon (1976) .6 , r T a u b e r e r a r . ( 1 9 6 5 ) , ? ) F a n a e t a 1 . ( 1 9 6 9 ) .

372 YAMANAKA ET AL.: HIGH TEMPERA,|URE TRANSITION IN MgGCO'

460

450

140

9.

).00

3.85

5.20

5. r5

0r.0

vo/z

Vc

Ac

acsinB

--6-

200 400 600 E00 l0o0 'c

Temperature

Fig. 4. Variation with temperature of the cell parameters andvolume of clinopyroxene-type and orthopyroxene-type structuresof MgGeOr, marked by subscripts c and o, respectively.

latter by Mg2 and two Ge's. The valence sum of theseoxygens is 1f and 2{, respectively. The diflerent valencesums of these three oxygens are the cause of the diflerentthermal expansion of the cation-oxygen bonds. The meanbond distances around the overcharged 03 atom show thelargest thermal expansion and those around the undersatu-rated 02 have the smallest ones.

Bond strength is related to the force constant, which isderived from the frequency of the stretching mode of thethermal vibration. An anharmonic thermal vibration caus-ing the thermal expansion is intensified by higher temper-atures (Yamanaka et al,, 1984). As a consequence, weakerbonds are easily excited, even by a small thermal energy,and they have the larger thermal expansion coellicient withincreasing temperature. The above features of the thermalexpansion were also found (by Smyth, 1973) in the ortho-pyroxene at high temperature up to 850'C.

The structure of ortho-MgGeo3 at 950'C, in compari-son with one quenched to room temperature, exhibits the

following characteristics: Both mean distances GeA-O andGeB-O are slightly increased and so are the volumes of thecorresponding tetrahedra of GeA and GeB. These featuresare more extr€me in the B chain than in the A chain. Theoctahedral volume and bond distances show larger ex-pansions for Mg2 than for Mgl. The O3A'-O3A-O3A"angle in the A chain increases at high temperatures in thestable region, indicating a lessening of the kink in thechain; the expansion of the Mg2 octahedron stretches theA chain due to the presence of a shared edge O2-O3 be-tween the Mg2 octahedron and the GeA tetrahedron. Onthe other hand, the O3B'-O3B-O3B" angle of the B chain,which is similar to the chain in clino-MgGeO3, does notchange significantly with temperature.

Our attempts to perform structure analyses ofortho-MgGeO3 at temperature higher than 1000'C wereunsuccessful due to the sublimation of the sample duringdiffraction-intensity measurement.

The clino'to-ortbo transition in MgGeO3

In the field of silicate-pyroxene polymorphs, several pos-sible models for the ortho-to-clino transition in pyroxenehave been proposed by Brown et al. (1961), Sadanaga et al.(1969), Coe (1970), and Smyth (1974). Recently Sueno and

i 3

3.0

!

t2 .-o

11 .6 0

B r +A A

V(Ge)l -l a'-

600 800Temperature ('C)

Fig. 5. Variation with temp€rature of mean bond lengths andpolyhedral volumes of Mgl and Mg2 octahedra and GeOn tetra-hedron. Circlets and triangles, if solid, refer to the clinopyroxene-type structure; if open, to the orthopyroxene-typ€ structure. Verti-cal line segments indicate the errors in the mean bond lengfihs.

. r0

r28

tz416

!12.2 2

)t2.0 &

oil.8 5

5 2 .1olcat

qt

Ea

3 0 6

z8

c.6o2

YAMANAKA ET AL.: HIGH TEMPERATURE TRINSITION IN MgGeO,

a

tsAa

BA

cB

373

Clinopyroxene

F---ia-............-r , D .,

Fig. 6. Schematic diagrams of the clinopyroxene and ortho_pyroxene structures. Upper and lower figures are projectionsdown b and c, respectively. Letters A, B and C denote the oxygenstacking layers. Symbols (+) and (-), afier papike et al. (1973),show orientation relationship between the basal trianeles of thesilicate tetrahedra and those of the octahedra to which-the tetra-hedra are attached.

Prewitt (1984) reviewed these models and presonted a newone for the transition from orthoferrosilite to high-clinoferrosilite. Many papers have discussed the ortho-to-clino transition in enstatite caused by shear stress on (100)in the [001] direction, from observation made by electronmicroscopy (Coe and Miiller, I97 3 ; Kirby, 197 6).

In this paper we have presented a new type of transitionin pyroxene-type structures, viz. a clino-to-ortho transitionat elevated temperature. This transition is the reverse ofthat observed in silicate pyroxenes. In both clino- andortho-MgGeO3 structures, tetrahedral and octahedrallayers are alternately stacked along the a axis (Figs. 2 and3). The clino-to-ortho transition requires the following re-arrangements: (l) The octahedral stacking sequence, in thenotation of Papike et al. (1973), changes from (* *)- inthe clino to (+ + - -)_ in the ortho; (2) The runningdirection of the basal triangle of the tetrahedra changesfrom (+ -)- to (+ + - -)_ in the order of the tetra-hedral stacking layers along [100]; (3) The stacking layersin the clino, composed of oxygen atoms in CCp, (ABCABC...) shift to (ABCABACB)- in the ortho by slip of oxygenlayers with a magnitude of cl3 or -2c13 (Fig.6).

All oxygens are shared with silicate chains and octa-

hedra. Since Ge-O bonds have greater strength than M-Obonds, the GeOn tetrahedron can be regarded as a rigidbody. Therefore Ge-O bonds do not break during the tran-sition, while M-O bonds are broken by the shifting of theoxygen layers. The Ml and M2 octahedra in both theclino- and the ortho-MgGeO. are occupied by Mg; theirvolumes, therefore, are not extremely different in eitherstructure. Consequently, a transition model including thecation movement may adequately represent the MgGeO.transition. The relationship between polymorphs is thesame as in MgSiO. or FeSiO., whose structures have samecations in the Ml and M2 sites. The transition model inthese structures was proposed by Brown et al. (1961), Sada-naga et al. (1969), Smyth (1974) and Sueno and Prewitt(1984).

Since the transition under consideration is topotacticand does not alter the crystal shape, the structural changescan result from a cooperative slip of oxygen layers by ther-mal shear stress, such as the one demonstrated byTak6uchi and Haga (1971).

We do not yet understand why the temperature depen-dence of MgGeO, polymorphs is different from that ofsilicate pyroxenes. Thermodynamic data on the stabilityrelations between the two polymorphs of MgGeOr, con-trasting with those of silicate pyroxenes, would greatly en-hance our comprehension of the transition mechanism andalso increase our understanding of the pyroxene poly-morphs.

AcknowledgmentsThe authors are greatful to Prof. J. D. H. Donnay, of McGill

University, for his critical reading of our manuscript and valuablesuggestions for its preparation during his stay in our institute.They would also like to thank Prof. S. Sueno, of University ofTsukuba in Japan, for useful discussion.

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Cameron, M., Sueno, S., Prewitt, C. T., and Papike, J. J. (1973)High temperature crystal chemistry of acrnite, diopside, heden-bergite, jadeite, spodumene and ureyite. American Mineralogist,58, 5911-618.

Coe, R. S. (1970) The thermodynamic effects of shear stress on theortho-clino inversion in enstatite and other coherent phasetransition characterized by a finite simple shear. Contributionto Mineralogy and Petrology, 26,247-2@.

Coe, R. S. and Miiller, W. F. (1973) Crystallographic orientarionof clinoenstatite produced by deformation of orthoenstatite. Sci-ence. 180.64-56.

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B

I10,l@

F

0rthopyroxene

t D . ,

374 YAMANAKA ET AL,: HIGH TEMPERATURE TRANSITION IN MgGCO,

Hirano, M., Tokonami, M., and Morimoto, N. (1980) Crystal-chernistry of MnGeO. polymorphs. Journal of MineralogicalSociety of Japan, 14, 158-164.

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Manuscript receiueil, March 8, 1984;

acceptedfor publication, October 3, 1984.