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1.
Transmission electron microscopy on natural calcium metatitanate perovskite (dysanalyte) reveals the following twin laws in the orthorhombic (space group Pbnm) phase: reflection twins on the {110} and {112} planes, and 90° rotation twins about the [001] axis (referred to as [001]90° twin). Single crystals that were heattreated and quenched from above 1585 K exhibit a dramatic change in domain structure compared with the starting material and specimens quenched from T < 1470=" k.=" mutually=" perpendicular=" {110}=" and=">90° twins are observed throughout the crystal, forming a cross-hatched domain texture. 1/2[001] antiphase domains, which are very rarely observed in the starting material, also become dominant in the crystal. This change in domain structure is interpreted as due to a structural phase transition in perovskite at a temperature below 1585 K. From the point symmetry elements that describe the twin laws and the translational elements that relate the antiphase domains, the most likely phase near 1585 K is tetragonal with space group P4/mbm. These results are consistent with high-temperature powder X-ray diffraction study. On the other hand, density of the {112} twins is increased significantly in the crystal quenched from 1673 K. Twin domains are either bound by mutually perpendicular {110} and (001) walls, or by {112} walls with {110} twin domains within the polygonal {112} domains. Both twin density variation and domain morphology suggest that the crystal may be cubic at this temperature. Microstructure of a single crystal deformed at 1273 K and 3.5 GPa (within the orthorhombic stability field) is morphologically quite distinct from that of the heat-treated specimens. Dislocations dominate the microstructure and often interact with twin domain boundaries.A National Science Foundation Science and Technology Center 相似文献
2.
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:
- (100) mechanical twin lamellae;
- (100) glide bands containing unit dislocations;
- (001) twin lamellae;
- (101) lamellar features, not as yet identified.
3.
W. F. Müller 《Physics and Chemistry of Minerals》1977,1(1):71-82
Phase transitions and associated domains of BaAl2Si2O8-hexacelsian were studied by means of transmission electron microscopy combined with energy-dispersive X-ray microanalysis. Two polymorphs were found: a hexagonal with space group P63/mcm and a pseudohexagonal orthorhombic one with space group Immm. P63/mcm-hexacelsian displays antiphase domains with the displacement vector 1/2 c and Immm-hexacelsian contains twin domains with the three-fold twin axis parallel z and antiphase domains with the displacement vector 1/2 c. When P63/mcm-hexacelsian is heated above ～ 300°C it inverts to Immm-hexacelsian. The reversible and rapid transition and the associated formation of domains was studied by in situ experiments using a heating holder. P63/mcm and Immm are not connected among each other by a group-subgroup relationship, but both are subgroups of P6/mmm. The occurrence of twin and/or antiphase domains respectively in the polymorphs agrees with the symmetry reductions. 相似文献
4.
David C. Palmer Ekhard K. H. Salje Wolfgang W. Schmahl 《Physics and Chemistry of Minerals》1989,16(7):714-719
Lattice parameters, and intensities of selected X-ray reflexions, have been measured as a function of temperature for natural leucite, to characterise the phase transformation behaviour. At low temperatures leucite has a large ferroelastic distortion, but the temperature evolution of lattice parameters cannot be explained in terms of a purely ferroelastic phase transition; in particular, the considerable change in volume with temperature implies an additional transition mechanism, which we correlate with off-centring of K-ions in the low-temperature phase, and a collapse of the 111 structural channels. The transition behavior can therefore be rationalised in terms of two competing mechanisms: (I) Ferroelastic (consistent with the change m3m 4/mmm); (II) Volume-changing (consistent with m3m 4/m). Coupling of the two order parameters QI, and QII gives rise to the intermediate 4/mmm tetragonal phase.Our results confirm the existence of an I4
1/aI4
1/acd transition, but the non-disappearance of the 200 reflexion at high temperatures implies that the expected transition from I41/acd to Ia3d (cubic) symmetry does not occur. We attribute this to a residual strain field conjugated to the order parameter, due to defects (with possible Al/Si order). Nevertheless, within our experimental resolution, the lattice becomes metrically cubic at 665° C. 相似文献
5.
Nina Daneu Aleksander Rečnik Takashi Yamazaki Tadej Dolenec 《Physics and Chemistry of Minerals》2007,34(4):233-247
The atomic scale structure and chemistry of (111) twins in MgAl2O4 spinel crystals from the Pinpyit locality near Mogok (Myanmar, formerly Burma) were analysed using complementary methods
of transmission electron microscopy (TEM). To obtain a three-dimensional information on the atomic structure, the twin boundaries
were investigated in crystallographic projections
and
Using conventional electron diffraction and high-resolution TEM (HRTEM) analysis we have shown that (111) twins in spinel
can be crystallographically described by 180° rotation of the oxygen sublattice normal to the twin composition plane. This
operation generates a local hcp stacking in otherwise ccp lattice and maintains a regular sequence of kagome and mixed layers. In addition to rotation, no other translations are present
in (111) twins in these spinel crystals. Chemical analysis of the twin boundary was performed by energy-dispersive X-ray spectroscopy
(EDS) using a variable beam diameter (VBD) technique, which is perfectly suited for analysing chemical composition of twin
boundaries on a sub-nm scale. The VBD/EDS measurements indicated that (111) twin boundary in spinel is Mg-deficient. Quantitative
analyses of HRTEM (phase contrast) and HAADF-STEM (Z-contrast) images of (111) twin boundary have confirmed that Mg2+ ions are replaced with Be2+ ions in boundary tetrahedral sites. The Be-rich twin boundary structure is closely related to BeAl2O4 (chrysoberyl) and BeMg3Al8O16 (taaffeite) group of intermediate polysomatic minerals. Based on these results, we conclude that the formation of (111) twins
in spinel is a preparatory stage of polytype/polysome formation (taaffeite) and is a result of thermodynamically favourable
formation of hcp stacking due to Be incorporation on the {111} planes of the spinel structure in the nucleation stage of crystal growth. The
twin structure grows as long as the surrounding geochemical conditions allow its formation. The incorporation of Be induces
a 2D-anisotropy and exaggerated growth of the crystal along the (111) twin boundary. 相似文献
6.
Phase-transformation-induced twins in pressureless-sintered lanthanum gallate (LaGaO3) ceramics have been analysed using the transmission electron microscopy (TEM). Twins are induced by solid state phase transformation upon cooling from the rhombohedral
to orthorhombic (o, Pnma) symmetry at ∼145°C. Three types of transformation twins {101}
o
, {121}
o
, and {123}
o
were found in grains containing multiple domains that represent orientation variants. Three orthorhombic orientation variants were distinguished from the transformation domains converged into a triple junction. These twins are the reflection type as confirmed by tilting experiment in the microscope. Although not related by group–subgroup relation, the transformation twins generated by phase transition from rhombohedral to orthorhombic are consistent with those derived from taking cubic
aristotype of the lowest common supergroup symmetry as an intermediate metastable structure. The r→ o phase transition of first order in nature may have occurred by a diffusionless, martensitic-type or discontinuous nucleation and growth mechanism. 相似文献
7.
G. Agrosì G. C. Capitani E. Scandale G. Tempesta 《Physics and Chemistry of Minerals》2011,38(2):101-109
Transmission Electron Microscopy (TEM) and High Resolution TEM (HRTEM) investigations were used to study a complex micro-structure
of twin-related lamellae of 15R SiC polytype, in syntactic coalescence with 6H-SiC. The analysis of the local stacking microstructure by means of HRTEM revealed that the perfect structure of 15R polytype, (23)3 was locally interrupted by numerous adjoining stacking faults parallel to (0001) with stacking of the coupled (22) and (33)
bilayers superimposed on the twin boundaries. HR images taken exactly across both the twin boundaries showed a zig-zag pattern
(23) that switched to (32) by a twin coherent interfaces or, alternatively, a zig-zag pattern (32) which passed to (23) through
an isolated (33), 6H like sequence. The selected area electron diffraction (SAED) patterns taken exactly above both the twin interfaces indicate
classifying of the twin found in this study as a “Friedelian” reticular merohedric twinning. However, two indistinguishable
twin operations matched the observed features: a reflection through rational plane (0001), and 180°-rotation around [0001].
Since individual Si and C atoms and even the SiC bilayer polarity could not be established from these HR images, the real
twin law was deduced by taking into account that the coherent structural match at the interface could be guaranteed only by
a 180°-rotation around [0001]. In order to explain the origin of the planar defects found in this sample, the growth mechanism
and the influence of the low-energy stacking faults were considered. 相似文献
8.
Domains of triclinic Na-feldspar which are a direct consequence of structural strain are investigated theoretically. The following conclusions are arrived at. Only two types of twin walls are created by spontaneous strain, namely the Albite- and Pericline twin walls. If intersections occur, rounded corners are predicted. Any third domain wall close to such an intersection must bend into an S-shape. Narrow domains between two twin walls tend to become needle-shaped close to the intersection with a further, perpendicular, twin wall. The combination of the elastic stiffness coefficients c 44 c 66-c 46 2 is expected to become small at temperatures near to the transition temperature. In the same temperature interval elastic fluctuations occur; their amplitudes and propagation directions are given. 相似文献
9.
Phase transitions and associated domains of meteoritic troilite (FeS) have been studied by means of transmission electron microscopy (TEM). Three polymorphs have been found, two of which can be described by superstructures of the NiAs-type structure (A, C subcell). The P \(\overline 6\) 2c (√3A, 2C) polymorph, stable at room temperature, displays antiphase domains with the displacement vector 1/3< \(\overline {\text{1}}\) 10>. In situ heating experiments showed that the P \(\overline 6\) 2c polymorph changes at temperatures of 115°–150° C into an orthorhombic pseudohexagonal transitional phase with the probable space group Pmcn (A,√3A, C). It contains antiphase domains with the displacement vector 1/2 [110] and twins with a threefold twin-axis parallel c. When heated above 210° C the transitional phase transforms into the high-temperature modification with NiAs structure (P6 3/mmc). All observed phase transitions are reversible. The occurrence of antiphase and twin domains, respectively, agrees with the symmetry reductions involved in the subsolidus phase transitions. This is demonstrated by group-subgroup relationships among the space groups P6 3/mmc, Pmcn, and P \(\overline 6\) 2c. 相似文献
10.
Mechanical twins on both the Albite and Pericline laws are well developed on an optical scale in basic plagioclase from the Harris meta-anorthosite where the rock is affected by closely spaced shear fractures associated with pseudotachylite formation. In some cases the twinning is accompanied by kinking or intracrystalline fractures. The twins may be periodic and form a ladder structure and sometimes appear to intersect on an optical scale showing structures which very closely resemble those seen in microcline.Both Albite and Pericline twins are lenticular as observed by TEM, but isolated twin tips were rarely seen. No dislocations are associated with the twin tips. The twins in the optically observed ladder structure (when thicker than 2m), have themselves a very fine secondary ladder structure, consisting of periodic (200–600 nm) lenticular twins which impinge on the perpendicular twin wall. Intersecting twins were also observed and where two sets of equally thick twins intersect, M-twinning develops as shown by selected-area diffraction.The twin formation is analyzed in terms of the plagioclase structure and a coherent model for twin nucleation proposed. True twins can develop in plagioclase only if the Al/Si distribution is unchanged or nearly so after deformation. Mechanical twinning is quite easy in low plagio-clases between An100 and about An30 which have P¯1 or I¯1 lattices or domains with I¯1-type structures. Only one kind of nucleus can develop coherently in a single crystal, but it may grow to give either an Albite or a Pericline twin. Periodic nucleation and growth give complex textures. The qualitative variation of the twin energy as a function of the obliquity is given for different twin shapes and degrees of Al/Si order. M-twinning arises mechanically by coherent growth and interference of the strain fields. 相似文献
11.
W. A. Dollase 《Physics and Chemistry of Minerals》1998,25(5):389-392
The effects of composition and of temperature on the orthorhombic, Pca2
1
to cubic, F4ˉ3m transition of the stuffed cristobalite structure are reported. A distorton index which measures the departure of the orthorhombic
unit cell from a metrically cubic cell shows that at room temperature, distortion increases in the progression K2CdSiO4 <K2MgSiO4 <K2ZnSiO4≈K2CoSiO4. High temperature X-ray powder measurements document an apparently discontinuous transition to a structure of F4ˉ3m symmetry. Differential scanning calorimetry shows a sharp, reversible, first order transition to the high temperature phase
at about 500–600 °C for these compounds. Measured transformation enthalpies in the range of 7 to 16 J/g correlate roughly
with the distortion index. The transformation involves tetrahedral rotation to an orientationally disordered cubic structure
which retains an ordered M2+/Si distribution.
Received: 8 November 1996 / Revised, accepted: 14 October 1997 相似文献
12.
In calcic plagioclase (Ca, Na) [(Al, Si) AlSi2O8] Al-Si ordering produces superstructures with periodic and non periodic antiphase boundaries (APB's). Crystals growing at high temperature close to the melting point and cooling fairly rapidly order by nucleation of ordered domains which grow, resulting in an irregular pattern of curved APB's (b plagioclase). A modulated structure with periodic APB's forms by continuous ordering at large undercooling below the critical ordering temperature (e plagioclase). During annealing APB's are eliminated by pairwise recombination of adjacent APB's to reduce strain energy along the boundaries thereby transforming nonstable e plagioclase into stable b plagioclase without change in chemical composition. This process is often accompanied by a chemical phase separation with APB's providing favorable surfaces for diffusion. Transformations are documented by transmission electron microscopy (TEM) micrographs illustrating the variation in morphology of APB patterns in igneous and metamorphic plagioclase. They are in agreement with Korekawa et al.'s (1978) model of intermediate plagioclase which relies on periodic stacking of basic units rather than wavelike modulations. The paper includes observations of a new type of satellite in Stillwater bytownite (‘h’ satellites) which are due to fine lamellar exsolution. 相似文献
13.
Turner's (1953) technique of locating the compression (C) and tension (T) axes from the known orientations of C-axis and twin pole ([022̄1] in dolomite and [011̄2] in calcite) for each grain yields the orientation of the unique stress system when a great majority of the grains in the rock shows only singlet twins. However, since it assumes the highest possible value for the coefficient of resolved shear stress s0 (= 0.5), application of the technique to rocks in which a large number of grains show doublet and triplet twins results in great dispersion of the C- and T-axes. In such cases the unique stress system can be established by preparing separate C-axes fabric diagrams for the untwinned grains, grains with singlet twins, grains with doublet twins and grains with triplet twins; measurement of the orientations of the twin planes becomes unnecessary. 相似文献
14.
Dorian M. Hatch Subrata Ghose John L. Bjorkstam 《Physics and Chemistry of Minerals》1994,21(1-2):67-77
Despite their crystallographic differences, the mechanisms of the α-β phase transitions in the cristobalite phases of SiO2 and AlPO4 are very similar. The β→α transition in AlPO4 cristobalite is from cubic ( $\left( {F\bar 43m} \right)$ ) to orthorhombic (C2221), whereas that in SiO2 cristobalite is from cubic ( $\left( {Fd\bar 3m} \right)$ ) to tetragonal (P43212 or P41212). These crystallographic differences stem from the fact that there are two distinct cation positions in AlPO4 cristobalite as opposed to one in SiO2 cristobalite and the ordered (Al,P) distribution is retained through the phase transition. As a result, there are significant differences in their crystal structures, domain configurations resulting from the phase transition and Landau free energy expressions. A symmetry analysis of the “improper ferroelastic” transition from $F\bar 43m \to C222_1$ in AlPO4 cristobalite has been carried out based on the Landau formalism and the projection operator methods. The six-component order parameter, η driving the phase transition transforms as the X5 representation of $F\bar 43m$ and corresponds to the simultaneous translation and rotation of the [AlO4] and [PO4] tetrahedra coupled along 110. The Landau free energy expression contains a third order invariant, the minimization of which requires a first-order transition, consistent with experimental results. The tetrahedral configurations of twelve α phase domains resulting from the β→α transition in AlPO4 cristobalite are of two types: (1) transformation twins from a loss of the 3-fold axis, and (2) antiphase domains from the loss of the translation vectors 1/2[101] and 1/2[011] (F→C). In contrast to α-SiO2 cristobalite, the α-AlPO4 cristobalite (C2221) does not have chiral elements (43, 41) and hence, enantiomorphous domains are absent. These transformation domains are essentially macroscopic and static in the α phase and microscopic and dynamic in the β phase. The order parameter, η couples with the strain components, which initiates the structural fluctuations causing the domain configurations to dynamically interchange in the β phase. An analysis of the MAS NMR data (29Si, 17O, 27Al) on the α α-β transitions in SiO2 and AlPO4 cristobalites (Spearing et al. 1992, Phillips et al. 1993) essentially confirms the dynamical model proposed earlier for SiO2 cristobalite (Hatch and Ghose 1991) and yields a detailed picture of the transition dynamics. In both cases, small atomic clusters with the configuration of the low temperature α phase persist considerably above the transition temperature, T0. The NMR data on the β phases above T0 cannot be explained by a softening of the tetrahedral rotational and translational modes alone, but require the onset of an order-disorder mechanism resulting in a dynamic averaging due to rapidly changing domain configurations considerably below T0. 相似文献
15.
In-situ powder diffraction measurements between 90 and 935?K on four anorthite-rich plagioclase samples (An100, An96Ab4, An89Ab11 and An78Ab22) were used to determine the detailed evolution of these samples through the $I \overline{1} $ – $P \overline{1} $ phase transition. The c-type reflections indicative of $P \overline{1} $ symmetry were detected only in An100, An96Ab4, whereas deviations in the evolution of the unit-cell parameters with temperature were observed in all samples, most prominently in the β unit-cell angle. The c-type reflections disappear at ~510 and ~425?K in An100 and An96Ab4 respectively, and their intensity decreases according to a tricritical trend $ I^{2} \propto \left( {T - T_{\text{c}} } \right) $ . The cell parameter changes were used to determine the spontaneous strains arising from the transition which were modelled with Landau theory, allowing for low-temperature quantum saturation, in order to determine the thermodynamic behaviour. In An100 tricritical behaviour was observed [T c?=?512.7(4)?K; θs?=?394(4)] in good agreement with previous studies, and the c-type superlattice reflections indicative of $P \overline{1} $ symmetry persist up to the T c determined from the spontaneous strain, and then disappear. The evolution of the spontaneous strain in An96Ab4 is tricritical at low temperatures [T c?=?459(1) K, θs?=?396(5)] up to the temperature of disappearance of c-type reflections, but becomes second order beyond ~440?K. In An89Ab11 the strain displays second-order behaviour throughout [T c?=?500(1) and θs?=?212(5)], and the c-type reflections are not detected in the powder diffraction patterns at any temperature. The apparent discrepancy between the absence of c-type reflections in temperature ranges where the cell parameters display significant spontaneous strain is resolved through consideration of the sizes of the anti-phase domains within the crystals. It is deduced that the tricritical phase transition occurs in well-ordered crystals with large domains in which the behavior of individual domains is dominant (i.e. in pure anorthite) or where the $P \overline{1} $ distortions within the domains are large enough to dominate the structural coherency strains between the domains. When both the magnitude of the $P \overline{1} $ pattern of displacements of the tetrahedral framework become smaller and the influence of the structural coherency between anti-phase domains becomes significant, the thermodynamic behavior becomes 2nd-order in character, the c-type reflections disappear, and the orientation of the spontaneous strain changes. 相似文献
16.
The characteristic lamellar-twinning of the right-handed (R) and left-handed (L) structures in the major rhombohedral growth sectors of amethyst quartz has been studied by optical techniques, X-ray topography and transmission electron microscopy (TEM). The TEM observations show that the region of each Brewster fringe consists of fine-scale Brazil twin lamellae parallel to one of the r, z{10 \(\overline {\text{1}} \) 1} planes, and structural considerations suggest that it is one of the r-planes. The twin boundary corresponding to a Brewster fringe has the form of a zig-zag structure consisting of Brazil twin boundaries on two r{10 \(\overline {\text{1}} \) 1} planes, with one predominating. The Brewster fringes appear black between crossed polarizers because light travelling along the optic axis [001] passes through almost equal distances of R and L quartz, giving essentially zero optical rotation. From the visibility of the Brazil twin boundaries in electron micrographs and the visibility of the Brewster fringes in X-ray topographs, the fault vector R and the corresponding composition plane of the major Brazil twin associated with each Brewster fringe has been determined. The streaking of the Brewster fringes observed optically and in the X-ray topographs appears to be due to the stair-rod dislocations at the intersections of the Brazil twin boundaries. Experiments in which synthetic quartz was grown hydrothermally on untwinned seeds and on twinned amethyst seeds showed that the initiation of Brazil twins and the development of Brewster fringes was dependent upon the presence of iron in the growth solution. 相似文献
17.
18.
Cryptoperthites from the Klokken layered syenite intrusion were examined by TEM to determine the role of exsolution, ordering and twinning in the development of the coherent microtextures during slow cooling, the stratigraphic position of the samples in the layered series giving an independent variable in determining their evolution. Both periodicity (primary and secondary) and morphology change with distance from the top of the series. Most samples contain low microcline in the diagonal association.Partial ordering occurred before exsolution, which was followed by Albite-twin formation in the albite lamellae. The twin periodicity depends on the average lamellar thickness (or on the primary lamellar periodicity,
1) and no longer changes during subsequent morphological evolution. In the Or-rich lamellae long-period Albite twins develop before waves form in the lamellar interface. The interfaces rotate with increasing order to give parallel-sided zig-zag lamellae of low microcline with Albite twinned lamellae of low albite, which may pinch and swell. Where the albite lamellae are discontinuous, adjacent microcline lamellae coalesce giving oblique lamellae and Pericline or M-type twins. Thickening of some oblique lamellae gives a distinct secondary periodicity,
2, which outlines lozenge-shaped areas with relics of the primary periodicity and, if coarse enough, is responsible for optically-visible braid microperthite. Coherency, demonstrated by high resolution images, is maintained through all stages of the coarsening.A time-temperature-transformation diagram for continuous cooling is presented and can be used to interpret the kinetics and morphological evolution of cryptoperthites from rocks with very different cooling rates (dykes and lavas to very large plutons), which have, however, similar primary lamellar periodicities. The finest periodicities are only slightly larger than the supposed initial periodicities (
o) for spinodal decomposition and little coarsening can have occurred. Coarsening at cooling rates slow enough to produce significant ordering may be much slower than coarsening in disordered feldspars. Primary coarsening may be stopped by the development of Albite twins in the Abrich phase, which will require reversal of the order-antiorder sense of parts of the framework. Coarsening may also be slowed if the phases at intermediate temperatures order at different rates or have different equilibrium degrees of Al-Si order. Secondary coarsening can develop at much lower temperatures (<400° C) on the formation of low microcline, when both phases have the same framework order. 相似文献
19.
I. Choe R. Ingalls J. M. Brown Y. Sato-Sorensen 《Physics and Chemistry of Minerals》1992,19(4):236-239
We have measured in situ Mössbauer transmission spectra of iron silicate spinel (γ-Fe2SiO4) in a diamond anvil cell at room temperature and pressures up to 16 GPa. The observed spectra show a doublet characteristic of the paramagnetic state. The isomer shift and quadrupole splitting at atmospheric pressure are 1.10 and 2.63 mm/s, respectively, which are smaller than those of fayalite (α-Fe2SiO4). Both the isomer shift and quadrupole splitting decrease linearly with pressure with slope of ?0.003(1) and ?0.020(1) mm/sec · GPa, respectively. This simple linear trend suggests that no electronic or polymorphic transitions occur under 16 GPa except for those due to the small and continuous changes of volume and local symmetry under pressure. On the basis of a crystalline field calculation, the negative pressure derivative of the quadrupole splitting is associated with a trend towards an ideal cubic symmetry of the oxygen sublattice. 相似文献
20.
Both natural and synthetic crystals of whewellite (CaC2O4·H2O, sp.g. P21/c) occur commonly as twins. The geometrical, reticular and structural features of the most important twin law, twin plane (100), and the dubious law ( \(\overline {\text{1}} \) 01) were investigated. The strict application of the periodic bond chain (PBC) theory (Hartman and Perdok 1955) makes possible the identification of original composition planes (OCP). Following the OCP analysis it has been deduced that the energy necessary to produce a (100) twin is very low. This is evidenced by the easy reciprocal arrangement of the two crystal structures which can be shown in two slightly different ways, i.e., by a (100) reflection with a mean [0, 1/2, ?a 0cosβ] translation and a weak relaxation (from 0.1 to 0.25 Å) of the common interface. In OCP an important role is played by water molecules. With regard to ( \(\overline {\text{1}} \) 01) twinning, the geometrical and reticular agreement is not matched by the structural situation. The structural and growth approach to the twin laws of whewellite therefore justifies the very common occurrence only of (100) twinned crystals. 相似文献