Transmission electron microscopy of experimentally deformed chalcopyrite single crystals

Two crystals of natural chalcopyrite, CuFeS₂, experimentally deformed at 200° C have been studied by means of transmission electron microscopy (TEM). The activated glide planes are (001) and {112}. The dislocations in (001) have the Burgers vector [110] and a predominating edge character. They are split into two colinear partials b=1/2[110] and can cross split into {112}. The dislocations in {112} consist of straight segments along low index lattice lines. They are often arranged in dipoles generating trails of loops. Few dislocations with b=1/2[ \(\overline {11} \) 1] and [1 \(\bar 1\) 0] are present and dislocations with b=[0 \(\bar 2\) 1] occur in low angle subgrain boundaries. From weak beam contrasts it is presumed that most of the dislocations gliding in {112} have b=1/2〈3 \(\overline {11} \) 〉. They are dissociated into up to four partials. Microtwins and different types of stacking faults in {112} also occur. Models of the dissociation of dislocations are discussed.     

Room temperature microplasticity of a spodumene LiAlSi2O6

As uniaxial compression tests of α spodumene LiAlSi₂O₆ at various temperatures and strain rates systematically led to brittle fracture, room-temperature microindentations have been performed with a view to characterizing the glide systems. Transmission electron microscopy (TEM) investigations show that only the [010] (100) glide system is activated. The resulting dislocations are widely dissociated (up to 3,000 Å) following the reaction [010]→[0 1/2 1/6]+[0 1/2 \(\bar 1\) /6]. In contrast, in naturally deformed spodumene the activated glide systems found in TEM studies are [001] {110} and 1/2〈110〉{1 \(\bar 1\) 0} and the corresponding dislocations are not dissociated. Such a difference in mechanical behaviour is interpreted in considering the necessary impingement of the oxygen atoms during dislocation glide. It is shown that only the dissociated b dislocations can glide with a moderate lattice friction at room temperature. The proposed model is supported by the first exploratory deformation runs performed under confining pressure.     

Exsolution of Ca-clinopyroxene from orthopyroxene aided by deformation

Monoclinic calcium-poor shear-transformation lamellae and calcium-rich exsolution lamellae occur parallel to (100) in orthopyroxene. The formation of both structures from an orthopyroxene host involves a shear on (100) parallel to [001], with additional cation exchange in the exsolution case. The shear transformation involves a macroscopic simple shear angle of 13.3° (shear strain of 0.236) and produces a specific a-axis orientation with respect to the sense of shear; we have found that this orientation dominates in exsolution lamellae in kinked orthopyroxene, where the sense of shear is known. In undeformed orthopyroxene, there is generally no preferred sense of orientation of the monoclinic a axes. We advance a specific model for exsolution involving nucleation and growth by shear transformation combined with cation exchange, thus circumventing the classical nucleation barrier and permitting exsolution at lower solute supersaturations.     

Dislocation strain energy in the Al2SiO5 polymorphs

Molar elastic strain energy arising from dislocations in andalusite and sillimanite were calculated using equations derived from a non-core, linear elasticity model. For perfect (unit) c screw dislocations in these polymorphs, minimum dislocation densities of about 10¹⁰/cm² are necessary to significantly perturb the andalusite=sillimanite equilibrium boundary in P-T space. Compared to unit c dislocations, smaller energy perturbations arise from dissociated c screw dislocations, which are commonly observed in kyanite and sillimanite. A low computed value of stacking fault energy (～30 ergs/cm²) in these polymorphs is compatible with the large separations of dissociated dislocations in these phases. Dislocation densities in naturally occurring Al₂SiO₅ polymorphs are typically <10⁸/cm². Assuming that these densities are representative of those existing during metamorphism, as is supported by the lack of microtextures indicative of strong recovery, it is concluded that molar strain energies corresponding to observed dislocation densities (<10⁸/cm²) result in insignificant perturbation of P-T phase equilibrium boundaries of the Al₂SiO₅ polymorphs.     

Structural investigations,high temperature behavior and phase transition of Na6Ca4(SO4)6F2

Polycrystalline material of a sulfate apatite with chemical composition Na₆Ca₄(SO₄)₆F₂ or (Na₂Ca₄)Na₄(SO₄)₆F₂ has been synthesized by solid state reactions. Basic crystallographic data are as follows: hexagonal symmetry, a?=?9.3976(1) Å, c?=?6.8956(1) Å, V?=?527.39(1) ų, Z?=?1, space group P6₃/m. For structural investigations the Rietveld method was employed. Thermal expansion has been studied between 25 and 600 °C. High temperature (HT) powder diffraction data as well as thermal analysis indicate that the apatite-type compound undergoes a reconstructive phase transition in the range between 610 and 630 °C. Single-crystals of the HT-polymorph were directly grown from the melt. Structural investigations based on single-crystal diffraction data of the quenched crystals performed at ?100 °C showed orthorhombic symmetry (space group Pna2₁) with a?=?12.7560(8) Å, b?=?8.6930(4) Å, c?=?9.8980(5) Å, V?=?1097.57(10) ų and Z?=?2. Unit cell parameters for a quenched polycrystalline sample of the HT-form obtained at ambient conditions from a LeBail-fit are as follows: a?=?12.7875(1) Å, b?=?8.7255(1) Å, c?=?9.9261(1) Å, V?=?1107.53(2) ų. The lattice parameters of both modifications are related by the following approximate relationships: a _HT?≈?2c _RT, b _HT?≈?-(½a _RT?+?b _RT), c _HT?≈?a _RT. The HT-modification is isotypic with the corresponding potassium compound K₆Ca₄(SO₄)₆F₂. The pronounced disorder of the sulphate group even at low temperatures has been studied by maximum entropy calculations. Despite the first-order character of the transformation clusters of sulfate groups surrounding the fluorine anions can be identified in both polymorphs. Each of the three next neighbor SO₄-tetrahedra within a cluster is in turn surrounded by 8–9 M-cations (M: Na,Ca) defining cage-like units. However, in the apatite structure the corresponding three tricapped trigonal prisms are symmetry equivalent. Furthermore, the central fluorine atom of each cluster is coordinated by three next M-neighbors (FM₃-triangles), whereas in the HT-polymorph a four-fold coordination is observed (FM₄-tetrahedra).     

Formation mechanism of pigeonite lamellae in skaergaard augite

Fine textures of exsolution lamellae and interface boundaries between augite and pigeonite in augite crystals from Skaergaard ferrogabbro 4430 have been studied by high resolution electron microscopy and X-ray methods. Thick pigeonite lamellae have higher densities of (100) stacking faults than thin lamellae. The displacement vector of the faults has been determined as 5/6c from the measured density of faults and the relative rotation of the augite and pigeonite lattices. The augite and pigeonite lattices are apparently coherent, and no growth ledges were observed at the interfaces. The stacking faults are often combined with the antiphase boundary of pigeonite resulting in a total displacement vector of 1/2(a+b)+5/6c. The observation of thick and thin pigeonite lamellae indicated that the thickening of (001) pigeonite lamellae was controlled by coherency strains accumulated at the interfaces between augite and pigeonite.     

Analysis of high-voltage,high-resolution images of lattice defects in experimentally-deformed dolomite

Deformation-induced stacking defects in dolomite have been characterised following examination at the cation sublattice level using high-resolution electron microscopy at 500kV. Slip on c (≡{0001}) is observed to produce stacking faults, often de-localised laterally, which are terminated by partial dislocations with Burgers vectors of the form 1/3 [1 \(\overline 1 \) 00]: a model for the faulted dolomite lattice has been constructed which agrees with the image appearance. Slip on f (≡{10 \(\overline 1 \) 2}) produces long planar faults which are established as not being stacking faults, in the normal sense, since there appear to be no offsets of the cation sublattice across the faults, nor any general indication of any terminating partial dislocations: it is proposed that the contrast arises from rotational disorder in CO₃ groups which has resulted from the prior passage of partial dislocations during deformation.     

Deformation of shock-loaded andalusite studied with X-ray diffraction techniques

The structural deformation of an andalusite single crystal, shockloaded up to 400 kb with shock wave direction approximately parallel to c, was investigated by means of X-ray powder (Guinier) and single crystal techniques (Weissenberg, precession). Exposure to the dynamic pressure revealed a fracturing of the crystal into lattice blocks, with a mean size >1,000 Å. No change of the lattice constants could be observed after pressure release. From the streaks of X-ray reflection spots measured within the hk0, h0l, 0kl, and hhl planes the shock-induced lattice deformation is interpreted in terms of rotational gliding and/or microfracturing. The distortion mode is highly structure controlled. It follows preferrably two different structural motion systems: (1) Gliding parallel to (001) occurs, which produces lamellae parallel to (001), mainly arranged in two sublattices with common c-axis. The stacking sequence of lamellae along c is irregular. The lamellae-type structure may also result from an orientated transformation into a high pressure phase of lower symmetry and subsequent inversion into the original phase after pressure release. (2) Gliding parallel to (100) occurs. In this case the deformation mode is asymmetrical with respect to the undistorted crystal. The common direction b of the (001) and (100) deformation planes is probably the main direction of the shock-induced lattice deformation.     

Crystal chemistry of selenates with mineral-like structures: V. Crystal structures of (H3O)2[(UO2)(SeO4)2(H2O)](H2O)2 and (H3O)2[(UO2)(SeO4)2(H2O)](H2O), new compounds with rhomboclase and goldichite topology

The crystal structures of two new compounds (H₃O)₂[(UO₂)(SeO₄)₂(H₂O)](H₂O)₂ (1, orthorhombic, Pnma, a = 14.0328(18), b = 11.6412(13), c = 8.2146(13) Å, V = 134.9(3) ų) and (H₃O)₂[(UO₂)(SeO₄)₂(H₂O)](H₂O) (2, monoclinic, P2₁/c, a = 7.8670(12), b = 7.5357(7), c = 21.386(3) Å, β = 101.484(12)°, V = 1242.5(3) ų) have been solved by direct methods and refined to R ₁ = 0.076 and 0.080, respectively. The structures of both compounds contain sheet complexes [(UO₂)(SeO₄)₂]^2? formed by cornershared [(UO₂)O₄(H₂O)] bipyramids and SeO₄ tetrahedrons. The sheets are parallel to the (100) plane in structure 1 and to (?102) in structure 2. The [(UO₂)(SeO₄)₂(H₂O)]^2? layers are linked by hydrogen bonds via interlayer groups H₂O and H₃O⁺. The sheet topologies in structures 1 and 2 are different and correspond to the topologies of octahedral and tetrahedral complexes in rhomboclase (H₂O₂)⁺[Fe(SO₄)₂(H₂O)₂] and goldichite K[Fe(SO₄)₂(H₂O)₂](H₂O)₂, respectively.     

Mechanical twinning in diopside Ca(Mg,Fe)Si2O6: Structural mechanism and associated crystal defects

Diopside twins mechanically on two planes, (100) and (001), and the associated macroscopic twinning strains are identical (Raleigh and Talbot, 1967). An analysis based on crystal structural arguments predicts that both twin mechanisms involve shearing of the (100) octahedral layers (containing Ca²⁺, Mg²⁺ and Fe²⁺ ions) by a magnitude of c/2. Small adjustments or shuffles occur in the adjacent layers containing the [SiO₄]^4? tetrahedral chains. While the (100) twins are conventional with shear parallel to the composition plane, this analysis predicts that (001) twins form by a mechanism closely related to kinking. A polycrystalline diopside specimen was compressed 8% at a temperature of 400° C, a pressure of 16 kilobars, and a compressive strain rate of about 10^?4/s. Transmission electron microscopy on this specimen has revealed four basic lamellar features:

1. (100) mechanical twin lamellae;
2. (100) glide bands containing unit dislocations;
3. (001) twin lamellae;
4. (101) lamellar features, not as yet identified.

The (001) twins often contain remnant (100) lamellae of untwinned host. Twinning dislocations occur in these (100) lamellae and in the (001) twin boundaries with very high densities. Diffraction contrast experiments indicate that the twinning dislocations associated with both twin laws glide on (100) with Burgers vector b=X [001] where X is probably equal to 1/2 on the basis of the structural analysis. Parallels are drawn between mechanical twinning in clinopyroxenes and clinoamphiboles. The exclusive natural occurrence of basal twins in shock-loaded clinopyroxenes and of analogous ( \(\bar 1\) 01) twins in clinoamphiboles is given a simple explanation in terms of the relative difficulty of the “kinking” mechanism as compared to direct glide parallel to the composition plane.     

Observation of lattice defects in orthorhombic iron disulfide (marcasite)

Different types of lattice defects have been studied by transmission electron microscopy (TEM) at 100 and 200 kV in a sample of natural marcasite. The most frequently occurring Burgers vectors are b=[001], [100] and 〈101〉. Dislocations with large Burgers vectors (b=〈110〉 and 〈111〉) have also been characterized: these are possibly split. Interactions between the different dislocations result in a build-up of dislocation networks. Dislocation structures show that the sample has undergone a strong recovery. These observations are confirmed by metallographic and scanning electron microscopy (SEM) observations after chemical etching.     

Antigorite equation of state and anomalous softening at 6 GPa: an in situ single-crystal X-ray diffraction study

The compressibility of antigorite has been determined up to 8.826(8) GPa, for the first time by single crystal X-ray diffraction in a diamond anvil cell, on a specimen from Cerro del Almirez. Fifteen pressure–volume data, up to 5.910(6) GPa, have been fit by a third-order Birch–Murnaghan equation of state, yielding V ₀ = 2,914.07(23) Å³, K _T0 = 62.9(4) GPa, with K′ = 6.1(2). The compression of antigorite is very anisotropic with axial compressibilities in the ratio 1.11:1.00:3.22 along a, b and c, respectively. The new equation of state leads to an estimation of the upper stability limit of antigorite that is intermediate with respect to existing values, and in better agreement with experiments. At pressures in excess of 6 GPa antigorite displays a significant volume softening that may be relevant for very cold subducting slabs.     

Clinopyroxenes from mantle-related xenocrysts in alkaline basalts from Hannuoba (China): augite–pigeonite exsolutions and their thermal significance

Optically homogeneous augite xenocrysts, closely associated with spinel–peridotite nodules, occur in alkali basalts from Hannuoba (Hebei province, China). They were studied by electron and X-ray diffraction to define the occurrence and significance of pigeonite exsolution microtextures. Sub-calcic augite (Wo₃₄) exsolved into En_62–62Fs_25–21Wo_13–17 pigeonite and En_46–45Fs_14–14Wo_40–42 augite, as revealed by TEM through diffuse coarser (001) lamellae (100–300 Å) and only incipient (100) thinner ones (<70 Å). C2/c augite and P2₁/c pigeonite lattices, measured by CCD-XRD, relate through a(Aug)?a(Pgt), b(Aug)?b(Pgt), c(Aug)≠c(Pgt) [5.278(1) vs 5.189(1)Å] and β(Aug)≠β(Pgt) [106.55(1) vs 108.55(2)°]. Cell and site volumes strongly support the hypothesis that the augite xenocrysts crystallised at mantle depth from alkaline melts. After the augite xenocrysts entered the magma, (001) lamellae first formed by spinodal decomposition at a T_min of about 1,100 °C, and coarsened during very rapid transport to the surface; in a later phase, possibly on cooling, incipient (100) lamellae then formed.     

Magnetic structure and cation distribution in (Fe,Mn)2SiO4 (olivine) by neutron diffraction

The cation distribution in the synthetic samples of olivine-type structure with composition (Fe _x Mn_1?x )₂SiO₄ was determined at room temperature and confirms previous Mössbauer results. At low temperature an antiferromagnetic ordering is observed. The magnetic structures can be described in the crystallographic cell (i.e. k=0). They are interpreted on the basis of the irreducible representations (modes) of the symmetry groups which are compatible with Pnma. The dominant modes observed for all compounds, including Fe₂SiO₄ and Mn₂SiO₄, only differ in their direction. The main direction of magnetization is dominated by the Fe²⁺ single-ion anisotropy. At 4.2K, for x=0.29, it is parallel to the c-axis, whereas for x=0.76 the direction is parallel to the b-axis. The anisotropy of the M1-sites dominates in the first case, whereas M2-anisotropy dominates in the second case. The influence of temperature is demonstrated for x=0.50 where c is the main direction at 4.2K, when it is b at 38K.     

The origin of space group violations in a lunar orthopyroxene

The space group of an orthopyroxene (En₈₆) from a deep crustal lunar rock (sample 76535) that was previously reported as having space group P2₁ ca has been re-examined on an automated X-ray diffractometer. In addition to diffractions violating the b-glide of the conventional space group, Pbca (0kl,k-odd) reported in the earlier study, diffractions violating the a-glide of Pbca are also present. Careful examination of both the a-glide- and b-glide-violations shows them to be sharp, with no evidence of diffuse streaks parallel to a ^*, and with consistent intensities at several rotations about ψ. Diffractions violating the b-glide are in registry with the host, however, those violating the a-glide appear to be out of registry and result from a cell with a slightly longer a of about 18.4 Å, consistent with previous electron diffraction studies. The most reasonable explanation for the observed space group violations is that both the a- and b-glide violations result from ordering of Ca into (100) Guinier-Preston (G-P) zones that possess orthopyroxene topology, but have space group P2₁/c and a cell of a=18.4 Å, b=8.83 Å, c=5.18 Å, and β=90.0°; whereas the Cadepleted host has space group Pbca and a cell of a= 18.230(6) Å, b = 8.828(2) Å, and c=5.1946(9) Å. In addition to the G-P zones which may compose 12% or more of the sample, the crystal contains (100) lamellae of pigeonite, and other samples from the same rock contain lamellae of augite.     

Magnetic properties of the clinopyroxenes aegirine and hedenbergite: a magnetic susceptibility study on single crystals

Two natural clinopyroxene single crystals were investigated, an aegirine-augite (AEG) and a magnesian hedenbergite (HED). Both samples were carefully characterized by electron microprobe, X-ray diffraction, and Mössbauer spectroscopy. Magnetic susceptibility measurements of powdered samples reveal low temperature antiferromagnetic coupling and Curie-Weiss behaviour with T _N =7.5(5)?K, Θ _P =?19(1)?K for AEG, and T _N =31(1)?K, Θ _P =+21(1)?K for HED, respectively. Low temperature Mössbauer spectra exhibit relaxation phenomena. Magnetic susceptibility measurements of the single crystals show the direction of the magnetic moments to be lying within the a/c plane for both samples: 50(±2)° from a and 57(±2)° from c in AEG, and 45(±2)° from a and 60(±2)° from c in HED, respectively. The antiferromagnetic interchain interaction competes with the ferromagnetic intrachain interaction in both pyroxenes. In the magnesian hedenbergite a field induced magnetic transition is found. Its dependence on temperature, magnetic field and crystallographic direction is investigated and described.     

Electronic absorption spectra of Cr3+ ions in natural clinopyroxenes

The polarized (E‖a′, E‖b and E‖c) electronic absorption spectra of five natural chromium-containing clinopyroxenes with compositions close to chromdiopside, omphacite, ureyite-jadeite (12.8% Cr₂O₃), jadeite, and spodumene (hiddenite) were studied. The polarization dependence of the intensities of the Cr³⁺ bands in the clinopyroxene spectra cannot be explained by the selection rules for the point groups C ₂ or C _2v but can be accounted for satisfactorily with the help of the higher order pseudosymmetry model, i.e. with selection rules for the point symmetry group C _3v. The trigonal axis of the pseudosymmetry crystal field forms an angle of 20.5° with the crystallographic direction c in the (010) plane. D _q increases from diopside (1542 cm^?1) through omphacite (1552 cm^?1), jadeite (1574 cm^?1) to spodumene (1592 cm^?1). The parameter B which is a measure of covalency for Cr³⁺-O bonds at M1 sites in clinopyroxene depends on the Cr³⁺ concentration and the cations at M2 sites.     

Growth defects in metamorphic biotite

Metamorphic biotites examined by transmission electron microscopy contain planar defects on the (001) plane, superlattices, twins and a microstructure causing streaking of k≠3n rows. Analysis of the fringe contrast shows that the fault vectors associated with the planar defects are either R ₁=±1/3 [010], R ₂=±1/6 [310] or R ₃=±1/6 [3 \(\bar 1\) 0]. Structural considerations indicate that a stacking fault R ₁, R ₂ or R ₃ is most likely to exist in the octahedral layer rather than the potassium layer. The result of such a fault on a unit layer of mica is effectively to rotate it through ±120° about c* (equivalent to the common mica twin law). These stacking faults can provide the mechanism for producing the ±120° rotations associated with the common mica polytypes. Furthermore, many of the observed microstructures can be generated by these stacking faults.     

Polarized electronic absorption spectra of Cr2SiO4 single crystals

Polarized electronic absorption spectra, E∥a(∥X), E∥b(∥Y) and E∥c(∥Z), in the energy range 3000–5000?cm^–1 were obtained for the orthorhombic thenardite-type phase Cr₂SiO₄, unique in its Cr²⁺-allocation suggesting some metal-metal bonding in Cr²⁺Cr²⁺ pairs with Cr-Cr distance 2.75?Å along [001]. The spectra were scanned at 273 and 120?K on single crystal platelets ∥(100), containing optical Y and Z, and ∥(010), containing optical X and Z, with thicknesses 12.3 and 15.6?μm, respectively. Microscope-spectrometric techniques with a spatial resolution of 20?μm and 1?nm spectral resolution were used. The orientations were obtained by means of X-ray precession photographs. The xenomorphic, strongly pleochroic crystal fragments (X deeply greenish-blue, Y faint blue almost colourless, Z deeply purple almost opaque) were extracted from polycrystalline Cr₂SiO₄, synthesized at 35?kbar, above 1440?°C from high purity Cr₂O₃, Cr (10% excess) and SiO₂ in chromium capsules. The Cr₂SiO₄-phase was identified by X-ray diffraction (XRD). Four strongly polarized bands, at about 13500 (I), 15700 (II), 18700 (III) and 19700 (IV) cm^–1, in the absorption spectra of Cr₂SiO₄ single crystals show properties (temperature behaviour of linear and integral absorption coefficients, polarization behaviour, molar absorptivities) which are compatible with an assignment to localized spin-allowed transitions of Cr²⁺ in a distorted square planar coordination of point symmetry C₂. The crystal field parameter of Cr²⁺ is estimated to be 10?Dq?10700?cm^–1. A relatively intense, sharp band at 18400?cm^–1 and three other minor features can, from their small half widths, be assigned to spin-forbidden dd-transitions of Cr²⁺. The intensity of such bands strongly decreases on decreasing temperature. The large half widths, near 5000?cm^–1 of band III are indicative of some Cr-Cr interactions, i.e. δ-δ* transitions of Cr₂ ⁴⁺, whereas the latter alone would be in conflict with the strong polarization of bands I and II parallel [100]. Therefore, it is concluded that the spectra obtained can best be interpreted assuming both dd-transitions of localized d-electrons at Cr²⁺ as well as δ-δ* transitions of Cr₂ ⁴⁺ pairs with metal-metal interaction. To explain this, a dynamic exchange process 2 Cr_loc ²⁺?Cr_{2, cpl} ⁴⁺ is suggested wherein the half life times of the ground states of both exchanging species are significantly longer than those of the respective optically excited states, such that the spectra show both dd- and δ-δ*-transitions.