American Mineralogist, Volume 71, pages 977-984, 1986
High-pressurecrystal chemistry of beryl (BerAlrSi.Otr) and euclase(BeAlSiO4OH)
Rosnnr M. HaznN, ANonpw Y. Au, Llnnv W. FrNcnn GeophysicalLaboratory, CarnegieInstitution of Washington, 2801 Upton Street,N.W., Washington, D.C. 20008
Ansrnlcr Compressibilities and high-pressurecrystal structures of beryl and euclasehave beon determined by X-ray methods at severalpressures. Beryl (hexagonal,space group P6/mcc) has nearly isotropic compressibility; linear compressibilitiesperpendicular and parallel to the c axis ateB':1.72 + 0.04 x l0-a kbar-'and B,:2.10 + 0.09 x 10-akbar-'. The correspondingbulk modulus is 1.70 + 0.05 Mbar if the pressurederivative of the bulk modulus K'is assumedto be 4. Euclase(monoclinic, spacegroup P2r/a)has anisotropic compression,with maximum compressibrlity of 2.44 + 0.05 x l0-a kbar-l parallel to the unique monoclinic b axis, and minimum compressibility of 1.50 + 0.03 x 10-a kbar-' approximately parallel to [01]. The intermediate axis of compressionhas a magnitude of 1.96 + 0.05 x lO-akbar-'in the a-c plane.The bulk modulus of euclaseis 1.59 t 0.03 Mbar if K' is assumedto be 4. The bulk moduli ofBe, Al, and Si cation coordination polyhedrain beryl are all consistent with 1.7 Mbar, which is the crystal bulk modulus. Beryl compressionoccurs primarily by shorteningof cation-anion bond distances.In euclase,the 2.3-Mbar polyhedral bulk moduli are significantly greater than the observed 1.6-Mbar crystal modulus. Compression in euclase,particularly along the b crystallographicaxis, results from a combination of poly- hedral compressionand changesin interpolyhedral angles.
INrnooucrroN calculations for the oxides of Be, Al, and Si by modified Among the more fundamental goals of mineralogy and electron-gasmethods. petrologyisthepredictionofphysicalpropertiesandphase The crystal structure of beryl [BerAlrSiuO,r:hexagonal equilibria from a knowledgeof structureand bonding. The P6/ mcc, Z : 2l has been reported by Gibbs et al. ( I 968) study of minerals must proceed on a broad front of ex- and Morosin (1972). It is characterizedby six-member periment and theory if microscopic structural character- rings of Si tetrahedra, crossJinked by Be tetrahedra and istics are to be related to macroscopicmineral behavior. Al octahedra (Fig. la). The tetrahedral rings lie in the One promising approach is the characteization and ra- (0001)planeandaresuperimposedtoformchannelsalong tionalization of properties-structural, thermochemical, the c axis. Though often classifiedas a ring-silicate, beryl elastic,and vibrational-for a group of closely related canalsobedescribed(Zoltai,1960)asathree-dimensional minerals. The system BeO-AlrOr-SiOr-HrO provides an framework of Be and Si tetrahedra (Fig. lb). ideal suite of large, well-formed, stoichiometric, and or- The structure of euclase [BeAlSiO.(OH): monoclinic dered crystalline phasesin a variety of structuretypes. All P2r/a, Z: 4l was described by Mrose and Appleman atoms are of low atomic number and are thus amenable (1962). Euclasehas a-axis chains of three-member rings to the proceduresof computational quantum chemistry. formed by interconnectedBe and Si tetrahedra (Fig. 2a), Only three types of cation coordination polyhedra-Be crossJinked by Al octahedra (Fig. 2b). Although techni- and Si tetrahedra and Al octahedra-provide the struc- cally an orthosilicate with isolated Si tetrahedra, euclase tural building blocks for most of the phases,thus facili- can be interpreted equally well in terms of chains of Be tating tests of the "polyhedral approach" for modeling and Si tetrahedra. mineral properties (Hazen, 1985). Recent studies, com- The principal objectives of this high-pressureresearch pleted as part of this integratedeffort, include vibrational on beryl and euclaseare (l) to determine pressure-volume spectroscopy (Hoering and Hofmeister, 1985), elastic equation-of-stateparameters and compression anisotro- moduli (Au and Hazen, 1985; Yeganeh-Haeriand Weid- pies by measuringthe pressurevariation of unit-cell di- ner, 1986), thermochemistry (Barton, 1986), and com- mensions, (2) to calculate polyhedral bulk moduli from parative crystal chemistry (Hazen and Au, 1986).Also in high-pressurestructure data in order to test the effectsof progress are modeling of Be polyhedral clusters by ab structure on these moduli, (3) to identifu geometrical initio molecular orbital proceduresand lattice dynamic changesin the beryl and euclasestructures that result in
0003-004x/86/0708-o977$02.00 977 978 HAZEN ET AL.: BERYL-EUCLASE HIGH-PRESSURE CRYSTAL CHEMISTRY
Table l. Unit-cell parametersof beryl and euclaseat several Table 2. Beryl refinement conditions and refined atomrc pressures parameters
BERYL 1 bar 19 kbar 36 kbar 57 kbar
N@ber of obs (I>2o) 299 100 701 94 P(kbar) range c/a a(A) c( A) v(E3) R(z)t 3.1 3,5 3.8 4.r weishred R(Z)+ 2.6 2-8 3.0 Extinicion, .* (*ro5) e.;(z)* r.4(7) 5(1) 1.4(8) 0,001 45-55 9.214(1)* 9.194(1) 676.0(1) 0.99?8 1.001 6 0.001 25 9.208(3) (3) 9.188(3) 674 .7 0.9978 1 .0000 ParaDeter 15 25 9.183(3) 9.159(3) 669.1(3) a,99',t4 0.9918 1B 25 9.179(2) 9.157(3) 668.2(3) 0.99?6 0.9904 0.5 0.5 0.5 0.5 (5) 30 25 9.153(10) 9.13r 663.5(11)0.9965 0.9835 0 0 0 0 33 25 v 9.155(3) 9.118(2) 661.6(3) 0.9960 0.9806 z 0.25 025 0.25 o.25 36 25 9.153(3) 9.119(1) 661.6(3) 0.9960 0.9806 B 0.s1 (7) 0.3(2) 0.4(3) 0.8(4) 40 25 9.r38(ro) r.rr3fi ) 659.2(5) 0.9973 o.9771 43 25 9.135(6) 9.103(2) 657,9(7) 0.9964 o.9752 7/3 7/3 7/3 713 \7 9.r34(4) 657.0(3) 9.096(2) 0.9958 0.9238 2/3 2/3 2/3 2/3 57 14 9.127(3) 652.4(15)0.9931 v 9.064(r5) 0.9670 o.25 o.25 o.25 0.25 B o.sr(3) 0.9(1) 1.1(1) 1.0(1) EUCLASE 0.3876(1) 0-3882(3) 0,3883(3) 0.3893(4) v 0.1159(1) 0.1ls5(3) 0.1161(3) 0.1166(4) P(kbar) a(A) b(a) c( A) v(E3) 0000 B 0.44(3) 0.68(8) 0.87(8) 0.95(10)
0.3103(3) 0.3122(6) 0.3111(6) 0.3107(8) 0.001 4.7800(3) 14.322(1) 4,6335(2) 1oo.31o(5) 312.30(3) 1.0000 0.2369(3) O.2376(7) 0 .2377(6) 0. 2366(8) 21 \.759(1) t\.255(6) 4.612(r) 1o0.24(1t J07.89(10) 0.9859 v 0000 22 4.761(1) 14.254(4) 4.610(1) r00./7(1) J07.85(15) 0.9859 0.82(5) 0.58(13) 1.06(14) 0.30(17) 42 4.746(1) 14.189(|) 4.599(1) roo.r8(2) 304.82(26) 0.9760 B rl9 4.739(1 ) 14.1 58 (3 ) 4.589(1) r00.15(1) 303.11(1r)0.97a7 0.4985(2) 0.4987(4) 0.4984(5) O.4992(6) 62 4.730(1) r4.136(9) 4.580(1) 100.16(2) 3A1.\A(22) 0.9651 v o.74s6(2) 0.1459(4) 0.1450(4) 0.7452(s) z 0.14s3(1) 0.1449(5) 0.L447(5\ 0.1470(6) * Parenthesized figures represenl esd's. B 0.68(3) 0.78(10) 0.98(10) 0.72(72) + Measured unit-cel1 parafreLers nay depend systemabically on the range of 2e used in lheir determinalion (Swansonet a1., 1985). * Parenthesized figures represent esd's Only 25. data were used in equation-of-state deierminations, + ! = rtlrol-lFcll/:Fo weishted R = [tw(lI L-lF.l)2/:"F^zl!/2 compression, and (4) to relate structural changes in beryl pressure at high to the elastic moduli determined by Yoon Lehmann and I-arsen (1974) with an option for manual inter- and Newnham (1973). vention. Refinementconditions and refinedstructural parameters for beryl and euclaseappear in Tables 2 and 3, respectively. ExpnnrvrnxrAr METHoDS Refined anisotropic temperatureparameters and the magnitudes Specimendescription and orientation of thermal vibration ellipsoids for both minerals room appear in Tables 4 and 5.1 Crystals of synthetic beryl (variety emerald) were provided by at conditions Richard (Vacuum Ventures, M. Mandle Inc.). This material con- Data collection at high pressure forms to the ideal beryl composition, with the exception of 0.37 platelike were mount- wt9oCr, correspondingto 1.3olooccupancy ofCr at the AI octa- Flat, crystals approximately 40 ;rm thick pressure for X-ray with hedral site. The synthetic material was dehydrated at 800'C for ed in a diamond-anvil cell ditrraction, 4 h, yielding a sample with less than 0.3 moleculesof HrO per an alcohol mixture of 4:1 methanol: ethanol as the hydrostatic formula unit. pressuremedium and 5-10-pm chips of ruby as the internal pressure Crystalsofnatural euclasefrom Minas Gerais,Brazil (National calibrant. Pressure-celldesign, loading, operation, and (1 Museum of Natural History, Smithsonian Institution, specimen calibration wereas described by Hazen and Finger 982). Special gasket parts no. #121350),were provided by John White. Chemical analysis care was taken to avoid X-ray shielding by the of gasket pm of this colorless,gem-quality material by Barton (1986) showed the diamond cell. Large holes of400 were used, and pm no impurities. Crystal fragments of dimensions approximately the 100 crystals were well centered in the diamond cell 100 x 100 x 40 pm were used for X-ray diffraction studies at throughout the experiments. room and high pressure. Lattice constants of the two Be aluminosilicates were deter- mined at severalpressures. From 12 to 20 reflectionswere mea- Data collection at room pressure sured by the method of Hamilton (1974), as modified by King (1979), Room-temperaturelattice parametersfor both minerals were and Finger in order to correct for errors in crystal cen- as well as diffractometer alignment. refined from diffractometer anglesoftwenty reflections,each of tering on the diffractometer was refined without the which was measuredin eight equivalent positions,by the method Each set ofangular data constraint, and with of King and Finger (1979). Unit-cell parametersrefined without resultant "triclinic" cell was examined for conformity ex- pected symmetry constraints (i.e., as triclinic) are consistentvdth hex- hexagonaland monoclinic symmetries of beryl and eu- These were met within agonal and monoclinic symmetry, respectively, for beryl and clase,respectively. symmetry conditions pressures euclase(Table l). two standard deviations at all studied. High-pressure parameters Table l. Intensities ofall reflections in a hemispherewith (sin d)/I < unit-cell are recorded in 0.7 were measuredby an automated, four-circle diffractometer graphite with monochromatized. MoKa radiation. Omega step ' To obtain copiesofTables 4, 5, and 6a to 6h, order Document scanswith 0.025'step incrementsand 4-s counting time per step AM-86-310 from the BusinessOffce, Mineralogical Society of were used.Digitized data were converted to graphical form, and America, 1625I Street,N.W., Suite414, Washington,D.C. 20006. integrated peak intensities were determined by the method of Pleaseremit $5.00 in advancefor the microfiche. HAZEN ET AL.: BERYL-EUCLASE HIGH-PRESSURE CRYSTAL CHEMISTRY 979
Table 3. Euclaserefinement conditions and refined atomic parameters
21 kbar 42 kbar 62 kbar
Numberof Obs. (I>2o) 745 2O4 191 I97 R (z)+ 4.7 4.2 4.8 4.0 weighEedR (z)+ 2.6 3.3 3.8 3.2 ExtincEion r* (x105) 1.7(3)* 1.2(8) 6.4(8) 3.2(5)
AEom Parameter
0 r7152(I3) 0-L184(4) 0.1784(5) 0.r793(3) 0 10027(s) 0.1002(4) 0.1007(5) 0.r0o2(4) 0 53639(14)0.s3s9(4) 0.5364(s) 0.5359(4) 0.39(1) 0.s8(5) 0.14(6) 0.64(s)
o.24a77(r4) 0.2417(4) 0.2481(5) 0.2481(4) 0.4447o(5) o.444r(4) 0.4433(6) 0.4428(4) Silicon 0.9s708(1s)0.9s16(4) 0.9s73(5) 0.9s82(4) ffi tetrahedra 0.45(r) 0.70(5) o.80 (6) 0.68(5)
0.1741(6) 0.1707(19)0.7697(21) 0.1719(16) Beryllium o.3006(2) o.2985(20) 0.3038(24) 0.3029(18) firj-n tetrahedra 0.4571(7) 0.4573(19)o.4s5o(22) 0.4524(79) 0.60(s) 1.0(2) 0.9(2) 0.9(2) Aluminum ml @tahedra 0.3818(3) 0.3831(9) 0.3818(10) 0.3840(8) 0,0324(1) 0.0324(8) 0.0323(10) 0.0320(8) 0.7630(3) 0.7592(9) 0,761r(11) 0.7609(9) o.s2(3) 0.69(10) 0.0r(12) 0.94(10)
0 3800(3) 0.3790(10)0.37.s4(11)0.37s8(E) 0.3770(1) 0.3712(8) 0.3783(10) 0.3780(8) 0.6s21(3) 0.6489(9) 0.6487(11) 0.6484(9) 0.50(3) 0.67(9) 0.16(12) 0.75(9)
0.3431(3) 0.344s(9) 0.3439(10) 0.3463(8) 0.1998(r) 0.1966(9) 0.1984(11) 0.1990(9) o.5248(6) 0.5291(9) 0.s303(10) 0.s3r3(9) 0.53(3) 0.65(10) 0.67(11) 0.65(9)
0.1006(3) 0.1010(8) 0.1031(10) 0.1042(8) 0.0531 (1) 0.0542(9) 0.0s43(11) 0.0563(8) 0.21r3(3) 0.2096(8) 0.2101(]0) o.2o14(8) 0.so(3) 0.67(9) 0.79(11) 0.70(9) Fig. 1. The crystal structureof beryl (after Gibbs et a1.,I 968). 0.1s96(4) 0.1586(9) 0.1562(11) 0.1ss8(8) (A) The c-axis projection shows the six-member tetrahedral rings 0.3320(1) 0.3297(8) 0.3295(10) 0.32s6(7) of Si, which are crossJinked by Be tetrahedra and Al octahedra. 0.1206(4) 0.11s6(9) 0.117s(1r) 0.1144(9) 0.71(3) 0.81(10) 0.91(12) O.t4(9\ (B) The arrangement of Si and Be tetrahedra results in a contin-
0.063(9) Not Refined uous three-dimensionalframework. 0.302(3) 0.01i( 9) 2.4( rO * ParenEheslzed figures represent esd's
+ --oR=tllrl- F l/tF The four Si-O bonds in the Si tetrahedron (point sym- - welghted R = t:w(lFol lr.l)2/r"ro21172 metry m) rangefrom 1.595to 1.619A, with an average value of 1.608 A fiable 7). The Si tetrahedron is nearly regular, with O-Si-O angles deviating by no more than 1.5"from the ideal 109.5'tetrahedral angle.All six Al-O Intensity data for three-dimensional structure refinements were Al octahedron(point symmetry 32) are sym- collected on all reflections accessiblewithin the region (sin 0)/I = bonds in the 0.7. Omega increments of 0.02' and long counting times of 8 metrically equivalent, with length 1.908 A; however, this to l0 s per increment were used to optimize the number of polyhedron is significantly elongated parallel to c, with observedreflections and the precisionofthe intensities.Observed O-AI-O anglesranging from 76.5 to 96.8". and calculated structure factors at four pressures for both beryl The beryl Be tetrahedron (point symmetry 222) is one and euclaseare recordedin Tables 6a to 6h (seefootnote 1). The of the most distorted cation polyhedra in any Be mineral fixed-@mode of data collection @ingerand King, 1978)was used (Table 8), with a quadratic elongationof 1.09and an angle to maximize reflection accessibility and minimize attenuation by varianceof 327 (Hazenand Finger, 1982).All Be-O bonds I-orentz the diamond cell, and corrections were made for and are symmetrically equivalent (1.657 A;, but O-Be-O an- polarization effects, crystal absorption and X-ray absorption by glesrange from 9l to 131'compared to the ideal 109.5" the diamond and Be components of the pressure cell (Hazen and resulting tetrahedron is both flattened and Finger, 1982). Conditions of high-pressurerefinements, refined value. The isotropic extinction coefrcients (Zachariasen,I 967), atomic po- elongatedin the (001) plane. These distortions may be sitional parameters, and isotropic thermal parameters are re- explained,in part, by the shortenedshared edges between corded in Tables 2 and 3. Be and Al polyhedra (Gibbs et al., 1968). factors of beryl atoms are in Rrsur,rs Anisotropic temperature qualitative agreement with those reported by Morosin Room-pressurerefinements (1972), though absolute values of isotropic and aniso- Refined atomic coordinatesof beryl are in close agree- tropic thermal parameters are somewhat larger than in mentwith thoseofcibbs et al. (1968)and Morosin (1972). previous studies. Extinction (Table 2), which is a large 980 HAZEN ET AL.: BERYL-EUCLASE HIGH.PRESSURE CRYSTAL CHEMISTRY
ffi siti"on tetrahedra
lilll,r-il BerylIiu m tetrahedra FIfi,I ntu.inum octahedra Fig.2. The crystal structure of euclase.(A) The double tetrahedralstrip parallel to a (after Mrose and Appleman, 1962).(B) The a-axis projection showscross-linkages ofBe and Si tetrahedral chains by Al octahedra. efect in most Be minerals and which is inversely corre- The shortestoctahedral O-O distancecorresponds to the lated with thermal parameters,may contribute to these sharededge between Al octahedra. differences.The Ol oxygen, which links adjacent tetra- A three-dimensional difference Fourier synthesisshowed hedra in the six-member ring, displaysthe largestthermal no significantfeatures except for a maximum near the 05 anisotropy.Its motion is describedby a flattened spheroid (hydroxyl) position, which was refined as H. This position with major axesperpendicular to the Si-O-Si direction. is consistent with that found by Hanisch and Zemann Refined positional parametersof euclaseare identical (1966) from infrared pleochroism. The H atom lies near within estimated errors to those reported by Mrose and the Al-Os-Be plane, with an O-H distance of 0.76 A. Appleman ( I 962). EuclaseBe and Si tetrahedra(both with The anions with the greatestthermal vibration anisot- point symmetry l) are nearly regular(Table 8), with mean ropiesare planar three-coordinated02, 03, and 05, which Si4 and Be-O distancesof 1.633 and 1.643A, respec- have maximum vibration amplitude perpendicularto the tively (Table 9). The Al octahedron (point symmetry 1) planes of cation-anion bonding. is lessregular, with Al-O distancesfrom 1.85 to 1.99 A (mean 1.903 A), and O-AI-O anglesfrom 79.8 to 99.3". Linear compressibilitiesand bulk moduli Unit-cell parametersat severalpressures (Table l) were used to calculate linear compressibilities and pressure- Table7. Berylselected bond distances and angles volume equation-of-stateparameters. Unit-cell edgesand the B angle ofeuclase were describedwith the expression Bond/Ang1e 1 bar 18 kbar 16 kbar s7 kbar a: 40 - dP + d2P2, Be-02 [4]+ 1.657(1)* 1.6s4(3) t-.644(3) 7.626 (.4) 02-Be-O212) 91.0(r) 90.9(3) 91 3(2) 90.2(3) 02-Be-02[21 r09.0(1) 108.9(3) r08.s(3) 109.7(3) where ao is the value of the cell parameter at room pres- O2-Be-02I2l 131.2 ( 1) 13r.3(2) 131.3(3) 131.4(3) sure, and d, and d, are fitted parameters. The d, param- A1-02 [6] r.908(1) r.900(4) r.9oo(4) 1.882(s) etersare not significant for any of the parametersin beryl 02-l.r-02 16l e6.8(1) 96.6(2) 96.7 (2) 91.4(2) 02-A1-02[3] 90.6(1) 90.7(2) 90.9(2) 90.6(3) and euclase. 02-A1-02[3] 76.5(r) 76.7(2) 16 .4 (2) 75.5(3) Beryl compressibility (Table l0) is nearly isotropic, with si-01 1-.s95(2) 1.s89(s) 1.s84(s) 1.583( 7) the c axis approximately 20o/omore compressiblethan a, si-01 r 597<2) 1.s9s(5) r,592(4) 1.596(6) si-02 l2l 1.619(1) 1.608(4) 1.600(4) 1.613(s) and a correspondingsmall decreasein c/awith increasing Mean Si-0 1.608 1.600 1.594 1,601 01-s1-01 108.4(2) 109.0(4) r08.4(4) 107.7(5) pressure(Table l). Monoclinic euclase(Table l0), on the 01-si-02 [2] 108.4(1) 108.4(2) 108.2(2) 108.1(2) hand, is 01-si-02 [2] 110.3(1) 109.8(2) 110.4(2) 110.4( 2) other characterizedby significant compression 02-si-02 111.1(1) 111.3(3) 11r.1(3) 112.0(4 ) anisotropy, which is best representedby a strain ellipsoid 01-si r. s95(2) 1.589(5) 1.584(5) 1 583(7) (Hazen and Finger, 1982). One axis of the ellipsoid is 0t--si r.s97(2) 1.s9s(5) L.592(4) 1.596(6) si-01-si 1-68.4(2) 169.0(4) 168.4(4) 161.7 constrainedby symmetry to coincide with the b axis, but principal plane. 02-Be 1.6s7(1) r 654(3) 1.644(3) r.626(4) the other two axesneed lie only in the a-c 02-A1 1.908(1) 1.900(4) 1.900(4) 1.882(5) The compression strain ellipsoid for euclasewas deter- 02-si 1.619(1) 1.608(4) 1.600(4) 1.613(5) Be-02-A1 96.3(1) 96.2(2) 96.r(2) 97-2(2) mined with program srRArN(Ohashi, 1982). Maximum Be-02-Si 727.0(r) 126.8<2) 121.4(2) 127.0(3) 41-02-Si 136. 7(1) L31.O(2) 136.4(2) r35.7( 3) compression(2.44 + 0.05 x l0-o kbar-') is parallel to the b axis, whereas the axis of minimum compressibility * Parenthesized figures represent esd's. (1.50 + 0.03 x l0-a kbar-') is approximately35'from a, + BrackeEed figures represent bond and angle nultiplicities. near [01]. Note that this minimum compressionaxis is HAZEN ET AL.: BERYL-EUCLASE HIGH-PRESSURE CRYSTAL CHEMISTRY 981 thus subparallel to the tetrahedral chain, which is com- Table 8. Polyhedral volumes (43) and distortion parameters pressures posed of rigid Be-Be-Si three-memberrings. The axis of for beryl and euclase at several intermediatecompression (1.96 + 0.05 x l0-a kbar-r) BERYL lies in the a-c plane at right anglesto the major and minor q7 ellipsoid axes. Axial compression ratios for euclaseare Atom I bar 19 t Table 9. Euclaseselected bond distancesand angles Bond/Angle 1 bar 21 kba! 42 kbar 62 kbat Bond/Angle 1 bar 2l tJ>ar 42 kbat 62 kbar Silicon retrahedron O1 (continued) e9 s(3) 100.1(4) 100.4(3) s1-01 L.623(2) 1 608(8) r.609 (10) 1 605(8) Af-01-A1 100 2(1) 12s,1(3) 72s 7(3) 125,2(2) si 02 1.640(2) 1.634(s) 1.639(6) 1.638(5) A1-01 si 125.4(l) 728.3(7) 727 4(8\ 127,4(6) si-01 1 637(2) 1.s89(r2) 1.596(16) 1.607(12) A1-01-si 128.0(1) si-04 7.632(2) r,623(1) r 620(9) 1.608(6) O2 (3-coordinated) MeanSi-o I 633 1 614 | 616 l-61l 02-Si I.640(2) 7-646(22) 1.639(6) 1.638(5) 0t-si-02 rlI 3(1) rr2 2(3) rrr 6(4) r12.0(3) 02-A1 I 910(2) 1.909(8) 1.880(9) r.876(7) 0r-si-03 r07 7(r) 106.6(4) 107.1(s) 706 7(4) o2_Be 1 633(3) I 634(s) 1.s99(26) 1.599( 19) 01-si-04 r11 0(r) r11.:l(6) 111.0( 7) rr2 2(s) 02-si-03 r06.9(r) tol ,5(6) 108 0(7) 107 5(5) si-O2-At 124 r(1) r24 0(6) r24,s(1) 724-2(5\ 02-si-04 r08.6(1) 108 0(3) r07 7(3) t07 8(2' si_02_Be 115.1(1) 116.r(5) 115 3(6) r15.1(5) 03-si-04 11r.2(r) rrr 3(4) r11.s(s) 110.5(4 ) A1-02-Be 120.3(t) LL9.1 (4) 119 9(5) 12O.4(4) o3 (3-coordinaied) Aluminum Octahedron 03-si r $7e) 1, s89(r2) 1 s96(16) r.607(r2) A1-01 | 852(2) 1.843(5) 844(6) r 833(5) 03-Be 1.658(3) 1. 645( r0) r,644(11) 1.643(9' 41-01 1 985(2) 1,991(9) 983(12) r.980(8) 03-Be r 661(3) r,61 5(28) r 7r4(3s) r.693(26) A7-02 r 910(2) 1.909(8) 880(9) 1.8j6(7) A1-04 1 873(2) r.867(4) 871(s) r.861(4) Si-oj-Be t/l.q(t) r22 I(rr) r22 7(1) r22-4(5) 41-04 r.934(2) L 942(12) 940(15) 1.956(.0r si-0J-Be Io.o,t) r2r 6(6) 118 1(14) 118.1 ( 10) Ar-0s 1.866(2) 1 866(12) 1.858(14 ) ,.aasiio, Be-o3-Be tt4 5(r) 112 0(9) 114 4(10) 114.1(7) uean A1-0 1.903 1.903 1 896 w (3-coordina;ed) Beryllium Tetrahedron 04 1.620(9) 1.608(6) Be-02 I.633(3) L,646(22) L,s99(26) 1.599(19) o4-si :'6^2?:(?) r 623(1\ t 6t tt ) (4) 1 871(5) 1.86t(4) Be-03 1.658(3) r 645(10) I 644(11) 1.643(9) n/,-^l I 867 1.e3412l L 940(14) 1.9s6(r0) Be-03 1.667(3) r,675(10) 1,714( 35) r,693(26) il_;i r 942(12) Be-05 r.612(4) t,628(r2) r.585(13) 1.5 79(11) 131.4(6) 130.1(4) Uean Be-o 7 643 | 644 1 634 1.629 si-04-A1 l:1':t1l 131 0(5) 72t.r(s) 126.5(6) 126-1(4) 02_Be_03 104.8(2) 104.8(6) r03.8(7) r03.s(12) oi_oa_oi e6.7rr) 96.9(4) 96 9(s) e6 6(4) 02-Be-03 113.4(2) 11r.3(12) 113 6(r3) r12.s(9) 02-Be-05 105 4(2) 104.3(1l) r08.0(16) r08 6(12) o5 (3-coordinated) 03-Be-03 114 1(2) 1r6.6(14) rr2,2 (L6) r12.3(12) (6) 1.866(2) 1 855(12) 1 858(14) 1.849(10) 03-Be-05 I07.8(2) 108.1(7) r09.5( 7) 109.6 05-41 (10) I.612(4) | 628(12) 1. s8s(13) 1.579(11) 03_Be_05 lrr-2(2) rr1.1 (10) 109.5(13) 110 2 Os-Be o5-H o 16(4\ 01 (3-coordinated) 130.2(11) 128.1(14) 727 3(r0) 01-si r-623(2' r.608 (8) 1.609(r0) r.605(8) Ar-o5-Be | ]j:1f" 01-A1 1.8s2(2) 1.843(5) 1.844(6) iilil1 0t-Al r 985(2) 1.991(9) 1.981(11) i:33313if:-3;-H * PalenLhesized figures represent esd's High-pressurecrystal structure of euclase minimum compression axis of euclasein the a-c plane The three cation polyhedra that are found in beryl also and indicates that structural changesin this direction are form the euclasestructure. All three polyhedral bulk mod- controlled by changesin polyhedral volumes. The signif- uli in euclaseare approximately 2.3 + 0.7 Mbar. The icantly greatercompressibility of euclaseperpendicular to relatively large percentageerrors on theseand other poly- this direction is a consequenceof cation-oxygen a = 9.02810.001- 0.0015810,00003P (81 = t.z2ao.olxto-ukbar-l) and octahedral strips all undergo some decreasewith in- - 'kbar ') c = 9.188i0.003 0.0019310.00007P (8/ = 2.1010.09x10 creasingpressure, particularly the Al-O4-Si angle,which changesfrom 132to 130', and the Al-O5-Be angle,which EUCLASE decreasesfrom l3l to 127'. These significant changesin - I q = rr 779710,000? o.ooo82ro.oooo3l (8" = 1 .7210.06x10-\kbar ) interpolyhedral anglesresult in the observed anisotropic - b = 1{.33210.001 0.O035OrO.O0OO?! (BU = 2.44iO.O5xtO-qkbar-1) compressionof the euclaseunit cell. ') c = rl,6334r0.0006 - 0.0008810.00003P (Bc = "kbar t.9ttO,O6xtO DrscussroN B = 100.3210.02- 0.0032J0.0006P Cornparisonof beryl and euclasewith Be Axes a,9, and c are unit-ce]l edge tengths in A and B is the unil-cett orthosilicatesat high pressure angfe of eucfase in degrees, whereas g's wilh subscripts represent finear Hazen and Au (1986) have described high-pressure conpresslbrfiiies. Pressure is in kbar. structure data for phenakite (BerSiOo)and bertrandite HAZEN ET AL.: BERYLEUCLASE HIGH-PRESSURE CRYSTAL CHEMISTRY 983 [BeoSirOr(OH)],which may be representedby continuous, the six-member ring in beryl often display thermal con- three-dimensional frameworks of Be and Si tetrahedra. traction as a result ofincreased bridging-oxygenvibration Polyhedral bulk moduli in these two orthosilicates are amplitudes while Si-O distancesremain constant (Hazen similar to those recorded here for beryl and euclase.All and Finger, 1982). Be tetrahedra, on the other hand, are four symmetrically distinct Be tetrahedrain phenakiteand expectedto undergoa moderatelinear expansionofabout bertrandite have bulk moduli of approximately 2 Mbar, lO-s 'C-', on the basis of the observed relationship be- which is the same value observed in bromellite (BeO). tweenbond thermal expansionand Paulingbond strength The 2.3 + 0.7 Mbar Be tetrahedral modulus in euclaseis (Hazen and Finger, 1982). In the (001) plane in beryl, consistentwith this value, although the 1.4 + 0.4 Mbar thermal expansion is constrained by the "shrinking" Si modulus ofberyl's very distorted Be tetrahedronis slightly tetrahedralrings, but modestexpansion is possibleparallel lower than other observedvalues. to c becauseof the expansionof Be tetrahedra.Work now Si tetrahedralbulk moduli in beryl and euclaseare both in progresson Be silicate structures at high temperatwe greater than 2 Mbar, consistent with tl;re2.7 + 0.4 and should clarifu the relative magnitudesof polyhedral ther- 1.8 + 0.5 Mbar values for phenakite and bertrandite, mal expansionin these minerals. respectively.With the exception of the distorted Be tet- rahedron in beryl, all Be, Al, and Si polyhedra in these Elasticity of beryl and euclase minerals from the systemBeO-AlrO3-SiOr-HrO have bulk Yoon andNewnham (1973)reported single-crystalelas- moduli consistent with 2 Mbar or greater. These poly- tic stiffnessesof beryl. They observedsmall compression hedra are significantly lesscompressible than monovalent anisotropies, similar to those determined in this study, or divalent cations in six or gtreatercoordination (Hazen with B, > 8,,.Newnham and Yoon (1973) presenteda and Finger, 1982). simple mechanical model to rationalize observed com- It is evident from the severalBe silicatesthat compres- pressional stiffnessesin beryl and other silicates on the sion anisotropies are closely related to polyhedral link- basisof structural geometry.They observedthat the least- ages.The most rigid structural element in theseminerals compressibledirections generally conform to directions is the three-memberBe-Be-Si ring, which occursin phen- of linked Si tetrahedra.Axes of tetrahedral chains in am- akite, bertrandite, and euclase.These rings do not bend phiboles and pyroxenes and planes of tetrahedral sheets with increasingpressure, and their compressibility is thus and rings in layer silicatesand beryl are thus expectedto that of the constituentpolyhedra-approximately 2Mbar be the least-compressibledirections in these minerals. (correspondingto a linear compressibility of about 1.6 x Be tetrahedra and Al octahedra are, on average,only l0-a kbar-'). Thesethree-member rings control compres- slightly more compressiblethan Si tetrahedra in the Be sion along the phenakite c axis and the euclasea axis. aluminosilicatesstudied, and one must considerthe com- Four-member rings of two Be and two Si tetrahedraoccur plete Be-Al-Si polyhedral framework, therefore,when ap- in phenakite, bertrandite, and beryl; they are also rela- plying a structural model such as that of Newnham and tively rigid, limiting compressionin the (001) planes of Yoon. The c-axis compression of beryl, for example, is hexagonalphenakite and beryl. Six-member tetrahedral only 200/ogeater than that of the a axis, in spite of the rings with hexagonalsymmetry, asin phenakiteand beryl, planar configuration ofrigid Si tetrahedra. The three-di- also do not deform, acting as rigid structural units. Sig- mensional polyhedral framework (Fig. l) gives the struc- nificant compressionoccurs in Be silicatesonly when an- ture rigidity alongboth a and c. In euclasethe Si tetrahedra glesbetween adjacent cornerJinked polyhedra are free to are not linked to each other, and no axis of minimum bend. This situation occurs in both bertrandite and eu- compressioncan be inferred by consideration ofSi tetra- clase,which are the most compressibleof the Be minerals hedra alone. Recognition ofthe Be-Si tetrahedral chains studied. (Fig. 2a) and cross-linking octahedral chains (Fig. 2b) as rigid structural elementsis the key to understandingthe High-temperature versushigh-pressure behavior of beryl anisotropic compressionof euclase. Morosin (1972) determined thermal expansion coeffi- Although the mechanicalmodel ofNewnham andYoon cientsfor beryl from -200 to 800"C.The c axis undergoes was applied only to compressionalmoduli, a similar ap- moderate expansion of about 2 x 10-6"C-t, whereasthe proach may be used to rationalize shear moduli on the a axis shows only slight expansion over this range and basisof structure (e.g.,Vaughan and Weidner, 1978; kv- actually contracts with increasing temperature below about ien et al., 1980;Weidner and Vaughan, 1982; Bassand 200"C.At first sight,this extremeanisotropy in beryl ther- Weidner, 1984).Three-member rings of tetrahedra, such mal expansionmight seeminconsistent with the relatively as the Be-Be-Si rings common to many Be silicates,be- isotropic compressionbehavior. However, the expansion have as rigid structural units that are difrcult to deform. anisotropy is not surprising consideringthe very different When these rings form continuous strips or layers, as in thermal expansion behavior of Be and Si tetrahedra, as phenakite or euclase,then unusually large shear moduli opposedto the very similar compressionbehavior. In all occur in the associatedplanes. The Cooelastic stiftress silicate structuresdetermined at high temperatures,the Si coefficient of phenakite (correspondingto pure shear in tetrahedralvolume is unchangedwith increasingtemper- the a-c plane of the hexagonalmineral) is approximately ature. Furthefinore, rigid groups ofSi tetrahedra such as I Mbar, compared with the 0.6-Mbar stiffnessestypical 984 HAZEN ET AL.: BERYL-EUCLASE HIGH-PRESSURE CRYSTAL CHEMISTRY of shear moduli in beryl. A similar large shear stiffness Finger, L.W., and King, H.E. (1978) A revised method of op- should be associatedwith the a-b plane ofeuclasebecause eration of the single-crystal diamond cell and refinement of the structureof NaCl at 32 kbar. American Mineralogist, 63,337- of the rigid plane. (The tetrahedral chains lying in this 342. elastic moduli of euclasehave not been determined.) Gibbs, G.V., Breck, D.W., and Meagher, E.P. (1968) Structural Shearing in Be silicates should be particularly easy in refinement of hydrous and anhydrous synthetic beryl, planes with interpolyhedral anglesthat are free to bend. AlrBerSiuO,,and emerald, Al, ,Cro ,BerSiuOrr.Lithos, l, 275- Observed changesin anglesbetween tetrahedral and oc- 285. Hamilton, W.C. (1974) Angle settingsfor four-circle ditrractom- tahedral strips of euclase at high pressure suggest that eters.In International tablesfor X-ray crystallography,4,273- shearstiffnesses associated with the b-c plane will be un- 284. Kynoch Press,Birmingham, England. usually small. Let Cru Crr, and C,, representeuclase elas- Hanisch, K., and Zemann, J. (1966) Messungdes (Jltrarot-Pleo- tic moduli of pure compressionin the a, b, and c* direc- chroismus von Mineralen. VII. Der Pleochroismusder OH- Streckfrequenz in Euklas. Neus Jahrbuch fiir Mineralogie, tions, respectively. It follows from compressibility Monatshefte 1966, 346-348. observationsof the presentstudy that Crr) C*) C* Hazen,R.M. (1985)Comparative crystal chemistry and the poly- On the basis of the structural arrangement of rigid Be- hedral approach.Reviews in Mineralogy, 14,317-346. Be-Si tetrahedralrings and flexible interpolyhedral angles, Hazen, R.M., and Au, A.Y. (1986) High-pressurecrystal chem- phenakite (BerSiOJ (BeoSLO'(OH)r). we predict that C66> Cr, ) Coo(the pure shearstiffnesses istry of and bertrandite Physicsand Chemistry of Minerals, 13,69-78. associatedwith the a-b, a-c*, and b-c* planes, respec- Hazen, R.M., and Finger, L.W. (1982) Comparative crystal tively). Hence, euclaseshould have shearas well as com- chemistry. Wiley, New York. pressionalanisotropies. - (1985)Crystals at high pressure.Scientific Ameic.an,252, I 10-117. Sulrrrrlnv Hoering, T.C., and Hofmeister, A.M. (1985) Spectroscopicmod- eling of C, for Be-Al-Si minerals. (abs.)EOS (American Geo- Polyhedral properties,including size,shape, compress- physical Union Transactions),66, 357. ibility, thermal expansivity, and elasticcharacter, are sim- King, H.8., and Finger, L.w. (1979) Diffracted beam crystal cen- ilar for a given type of polyhedron in different structures. tering and its application to high-pressure crystallography. Thus the Be tetrahedral bulk modulus is approximately Journal of Applied Crystallography, 12, 374-378. Lehmann, M.S., and Larsen, F.K. (1974) A method for location 2 Mbar in bromellite, phenakite,chrysoberyl, bertrandite, of the peaks in step-scan-measuredBragg reflections. Acta and euclase.Only in beryl, with a severely distorted Be Crystallographica,A30, 580-5 84. tetrahedron,is a smaller Be polyhedral bulk modulus ob- Levien, L., Prewitt, C.T., and Weidner, D.J. (1980) Structureand served. elasticproperties of quartz at pressure.American Mineralogist, groups 65.920-930. StudiesofBe silicates have also shown that of Morosin, Bruno. (1972) Structureand thermal expansionof ber- polyhedra, such as the three-member Be-Be-Si tetrahe- yl. Acta Crystallographica,B28, 1899-1903. dral ring, may behave similarly from structure to struc- Mrose, M.E., and Appleman, D.E. (1962) The crystal structures ture. Compressionanisotropies and shearmoduli of sev- and crystal chemistry of viiyrynenite, (Mn,Fe)Be(PO"XOH), Zeitschrift fiir Kristallographie, eral Be minerals seemto be controlled by the distribution and euclase,AIBe(SiO.XOH). lI7, t6-36. of these rings. These argumentsthus provide a practical Newnham, R.E., and Yoon, H.S. (1973) Elastic anisotropy in and intuitive method to relate mineral structures and minerals. Mineralogical Maga:zine, 39, 7 8-84. physical properties.Further experimentsnow in progress Ohashi, Yoshikazu. (1982) A program to calculate the strain on the structuresand propertiesof minerals in the system tensor from two sets of unit-cell parameters.In R.M. Hazen and L.W. Finger, Eds. Comparative crystal chemistry,92-102. BeO-AlrOr-SiOr-H2O,combined with ab initio molecular Wiley, New York. orbital calculationson characteristicBe-Al-Si po$edral Robinson,K., Gibbs, G.V., and Ribbe, P.H. (1971) Quadratic clusters,will help to define the potential and limitations elongation: A quantitative measure of distortion in coordi- of the polyhedral approach. nation polyhedra. Science,17 2, 567-570. Swanson,D.K., Weidner, D.J., Prewitt, C.T., and Kandelin, J.J. AcxNowr.rncMENTS (1985) Single crystal compression of t-Mg,SiOo. (abs.) EOS (American GeophysicalUnion Transactions),66, 370. The authorsgratefully acknowledge the constructivereviews Vaughan, M.T., and Weidner, D.J. (1978) The relationship of of F. Chayes,J. W. Downs,F. C. Hawthorne,R. E. Newnham, elasticity and crystal structure in andalusite and sillimanite. and H. S. Yoder,Jr. This researchwas supportedin part by Physicsand Chemistry of Minerals, 3, 133-144. NationalScience Foundation grants EAR83-19209 and EAR84- Weidner, D.J., and Vaughan,M.T. (1982)Elasticity ofpyroxenes: 19982. Efects of composition versuscrystal structure.Journal of Geo- physical Research,87, 9349-9354. Yeganeh-Haeri,A., and Weidner, D.J. (1986) Singlecrystal elas- RnrnnnNcns tic moduli of a beryllium silicate: Phenakite BerSiOo.Physics Au, A.Y., and Hazen,R.M. (1985)Polyhedral modeling of the and Chemistry of Minerals, in press. elasticproperties of corundum (a-AlrO3)and chrysoberyl Yoon, H.S., and Newnham, R.E. (1973) The elastic properties (Al.BeOo).Geophysical Research Irtters, 12,7 25-7 28. of beryl. Acta Crystallographica,429,507-509. Barton,M.D. (1986)Phase equilibria and thermodynamic prop- Z,achaiaseg W.H. (1967) A generaltheory of X-ray diffraction ertiesof mineralsin theBeO-A1,O3-SiO,-H,O (BASI{) system, in crystals.Acta Crystallographica,23, 5 58-564. vdthpetrologic applications. American Mineralogist, 7 I, 277 - Zoltai, Tibor. (1960)Classification ofsilicates and other minerals 300. vdth tetraledral structures.American Mineralogist, 45, 960- Bass,J.D., and Weidner,D.J. (1984)Elasticity of single-crystal 973. orthoferrosilite.Journal of GeophysicalResearch, 89, 4359 - Mexuscnrpr RECETvEDAucusr 7, 1985 437l. MeNuscnrpr AccEprEDM.q.ncH 18. 1986