D. Nihtianova 1, Jixue Li 2 and U. Kolb 3

1 Central Laboratory of Mineralogy and Crystallography, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., bl. 107, 1113 Sofia, Bulgaria. 2,3Institute of Physical Chemistry, Johannes Gutenberg-University, Welderweg 11, 55099 Mainz, Germany.

Minerals are generally regarded as naturally occurring crystalline phases defined on the basis of their macroscopic physical properties [1]. As phases, or more specifically bulk phases in the “Gibbsian” or classical equilibrium thermodynamic sense, a mineral is said to be homogeneous with respect to its macroscopic physical properties and separable from other so-called phases (and external surroundings) by a physically distinct or discontinuous boundary. Minerals have definite chemical compositions when analyzed at the macroscopic scale, but as exemplified by solid solutions, the local chemical composition may vary within fixed limits. As crystalline phases, whether chemical end members or solid solutions, minerals have internal atomic structures said to possess long-range order on average in three dimensions. The average structure is defined at the microscopic (near atomic) scale and represented by a unit cell that when repeated over an essentially infinite number of atomic distances generates microscopic crystallites, which in turn comprise macroscopic single crystals, polycrystalline aggregates, or powders. The two most fundamental macroscopic properties of a mineral are its chemical composition and crystallographic symmetry. Together these serve as the basis for naming and classifying minerals. Other macroscopic properties (e. g., optical, electrical, magnetic, thermal, mechanical, etc.) can be considered manifestations of a mineral’s average structure. In practice, minerals are defined using so-called conventional methods to analyze their chemical compositions and determine their crystallographic properties. Chemical composition refers to the relative concentrations of different elements making up a mineral from which an average stoichiometry can be derived and expressed as a formula unit. Depending on the method used, a compositional analysis may also include a determination of oxidation states and/or atomic coordination environments. Crystallographic properties include the point group and space group symmetry of a mineral, its unit cell parameters, number of formula units per cell, average structure, etc.

1. Mineral definition at the macroscopic scale

A variety of instrumental methods apart from classical wet chemical methods, are available for analyzing a mineral’s chemical composition. Probably the most common methods today are x-ray fluorescence analysis and electron probe microanalysis. Crystallographic properties are generally determined with x-ray diffraction (XRD) or neutron diffraction, using both powder and single crystal methods. It is common practice and generally a good idea to assess the “homogeneity” of a mineral specimen using some form of optical microscopy (e. g., reflected light or polarized transmitted light) before it is chemically analyzed or examined by powder or single crystal diffraction methods.

There are over 3,500 recognized mineral species and countless mineral varieties that have been classified as crystalline phases using the conventional methods listed above. Guidelines for naming minerals have been published by the Commission on New Minerals and Mineral Names (CNMMN) of the International Mineralogical Association (IMA).

Minerals are generally regarded as crystalline phases formed as a result of geological processes. As a (bulk) crystalline phase in the classical sense, a mineral must satisfy the conditions of long-range structural order in three dimensions, and homogeneity with respect to its macroscopic physical and chemical properties.

Presently, conventional microscopy, diffraction, and analytical methods can be used to study minerals as crystalline phases in the classical sense as long as a macroscopic specimen exists. Macroscopic refers to the quantity of material available, expressed in terms of either the size of a single crystal, mass (volume) of material as a polycrystalline aggregate or powder, number of crystallites, and so on. To put things into perspective, the unaided human eye can resolve objects as small as 10-100m, which serves as a practical lower limit for the macroscopic scale with respect to the size of a specimen. A petrographic microscope and electron microprobe can be used to examine small grains (single crystals or crystal fragments) or small regions in a larger crystal with a diameter of a few micrometers, but generally a macroscopic quantity (statistically significant number) of grains or regions are sampled.

For conventional powder XRD, using a flat-plate, or capillary specimen, at least 1 mg of crystalline material is needed to obtain measurable diffracted intensity (1 g using a synchrotron source). For single-crystal XRD, a suitable crystal must be in the order of 100 m (10 m with a rotating anode or synchrotron source). Crystallites comprising a powder or single crystal specimen must consist of at least six unit cells in three dimensions to act as a coherent scattering domain. Depending on the unit cell size and scattering power of the atoms in the cell, coherent domains as small as 2 to 20 nm across can be detected by XRD if present in sufficient quantities. Coherent domains in minerals are more often in the order of 100 to 1000 nm (0.1 – 1 m) and represent literally millions to billions of unit cells.

2. Mineral definition using HRTEM High resolution transmission electron microscopy (HRTEM) offers the unique ability to observe minerals (or any solid material) directly in real space at or close to the atomic scale, i. e. the scale at which they are ultimately defined. Whereas conventional methods provide information about the average macroscopic structural and chemical properties of a mineral specimen, HRTEM can be used to describe the microstructural and microchemical properties. It combines various modes of imaging, electron diffraction, and chemical microanalysis in a manner that complements the conventional methods of optical microscopy, x-ray and neutron diffraction, and instrumental chemical analysis. With modern HRTEM instruments, lattice or structure images of very small crystals (crystallites) or very small regions in larger crystals can be obtained with 0.2 – 0.3 nm (2 – 3 Å) resolution (less than 0.2 nm with dedicated intermediate – or high-voltage HRTEM instruments). Diffraction patterns (SAED, CBED) and chemical analyses (EDS, EELS) can be taken from areas of a few micrometers to a few nanometers across (and less than 1 nm on dedicated STEM instruments).

Basically two types of HRTEM studies involving minerals have been reported in literature. One type may be considered as “microcrystallographic” in nature, dealing preferably with mineral properties, another as “micropetrographic”, focussing on mineral behavior. HRTEM and associated TEM methods have been used to confirm and refine existing structure models of known minerals, to propose new structure models, to define new minerals, and even to discredit minerals. HRTEM information becomes even more useful when combined with data from other sources. Expect to see more HRTEM studies combined with Rietveld powder x-ray diffraction studies and synchrotron powder diffraction studies involving small volumes of sample or small single crystals (1 – 10 m across). Minerals are often fine-grained, exist in small quantities, and are insufficiently ordered. The two nanocrystalline examples (aerinite (Ca5.1Na0.5)(Fe3+AlFe2+

1.7Mg0.3)(Al5.1Mg0.7)[Si12O36(OH)12H]

[(CO3)1.2(H2O)12] and Pb5MoO8) which are discussed below represent ideal samples for HRTEM

studies [1].

3. Cell parameter determination on aeriniteAerinite, a blue fibrous aluminosilicate mineral associated with the alteration of ophitic rocks, is found in the southern Pyrenees or Marocco and was commonly used as a blue pigment in most catalanic roman paintings between the XI – XV centuries. It was first described in 1876 and added to the mineralogical tables in 1898. Structure solution of aerinite is complicated due to its extremely small crystal size which makes it impossible to isolate single crystals for structural studies. Furthermore, aerinite is always found in mixtures with some other minerals and obtaining pure specimens is extremely difficult. Early attempts to analyse the structure lead to a proposal of a monoclinic unit cell (a = 14.690, b = 16.872, c = 5.170 Å, = 94.45°, Z=2) with (Ca4.0Na0.2)

(Fe3+1.7Fe2+

0.9Mg1.5Al6.1)=10 (Si1.6P0.2Al0.3)=12 O36(OH)1212 H2O + CO2] for aerinite from Saint-Pandelon

(France) [2]. The sample used for the present study is found in Camporrells – Estopanyà area (Huesca – Lleida, Spain) and consists of long bright blue fibres of a diameter of ~ 0.2 – 0.4 m as shown in Fig. 1. For preparation fibres were preselected by a light microscope, crushed in a mortar and dispersed in water via ultrasonic treatment.

Fig. 1: TEM image of an aerinite fibre on quantifoil support (scale bar 0.5 µm).

Based on lab x-ray powder diffraction Rius et.al.determined cell parameters as a = b = 16.872(1) Å, c = 5.2256(5) Å, ==90°, =120° with the most likely space group of P3c1 (No. 158) [3]. In order to investigate the structure of aerinite via TEM we performed electron diffraction using a FEI Tecnai F30 ST at 300 kV with a beam diameter of approx. 20 nm in nanodiffraction mode and 1k x 1k CCD camera. To allow the highest possible movement we used a double tilt–rotation holder and performed a tilt around two axes of the crystal [4]. For strong scatterers like inorganics we can observe often the high order Laue (HOLZ) reflections (see Fig 2. right hand side) and use those as a guide to the next zone. Therefore, it is as well convenient for inorganic samples to use a double-tilt holder. Starting from the initial zone [100], given in Fig. 2 (left hand side), diffraction patterns were taken through tilts around the axes b* and c*; distances and angles were calculated by ELD and are given in Table 1 [5].

tilt in-zone angle[o] angle[o] c[Å] b’[Å] h b[Å] a*[Å-1] k [o] a[Å] zone 33.0 89.9 5.205 4.060 4 17.008 0.0522 -3 59.6 16.565 [430] 30.0 89.8 5.209 2.341 7 16.910 0.0490 -5 59.9 16.820 [750] 28.0 89.8 5.169 5.488 3 16.850 0.0468 -2 60.2 16.414 [320] 23.0 89.9 5.221 3.345 5 16.861 0.0415 -3 60.1 16.674 [530] 17.0 89.9 5.220 8.404 2 16.812 0.0353 -1 60.4 16.358 [210] 10.0 89.9 5.232 3.346 5 16.814 0.0280 -2 60.4 16.495 [520] 6.0 89.9 5.231 5.507 3 16.761 0.0237 -1 60.8 16.216 [310] 0.0 89.9 5.223 4.051 4 16.833 0.0172 -1 60.2 16.757 [410] -14.0 89.9 5.222 14.612 0 16.824 0.0000 1 [100] -28.0 89.9 5.229 4.064 3 16.868 0.0228 1 60.7 16.893 [3-10] -33.0 90.0 5.223 5.533 2 16.772 0.0340 1 60.0 16.971 [2-10] -38.0 90.0 5.215 3.350 3 16.982 0.0463 2 61.0 16.613 [3-20] 89.9 5.217 16.858 60.3 16.616

Table 1. Data for tilt series of aerinite: Tilt about c*

tilt in-zone angle[o] angle[o] b[Å] c’[Å] h c[Å] a*[Å-1] l [0] a[Å] zone 25.0 85.5 16.951 2.369 2 5.133 0.0895 -3 89.0 16.771 [203] 22.0 96.4 17.029 1.615 3 5.126 0.0778 -4 88.3 17.141 [304] 17.0 90.2 16.884 4.995 1 5.172 0.0585 -1 88.8 17.091 [101] 12.0 96.7 17.070 1.710 3 5.174 0.0408 -2 87.6 16.330 [302] 9.0 95.2 16.989 2.583 2 5.184 0.0305 -1 86.8 16.428 [201] 6.0 93.5 16.943 1.731 3 5.196 0.0202 -1 85.4 16.487 [301] 0.0 90.0 16.896 2.628 1 5.259 0.0000 1 [100] -9.0 95.2 16.946 2.586 2 5.246 0.0304 1 87.2 16.453 [20-1] -17.0 90.1 16.869 4.993 1 5.279 0.0586 1 88.8 17.083 [10-1] -25.0 94.8 17.155 2.400 2 5.366 0.0884 3 89.5 16.986 [20-3] -32.0 90.3 17.097 4.500 1 5.425 0.1178 2 89.1 16.991 [10-2] 16.985 5.233 87.9 16.777

Table 2. Data for tilt series of aerinite: tilt about b*

Calculation given for tilt about b*:

*'

sinarcsin

ac 90cos*' cc

2

'cos

'0

12

'sin*

ccca where is the tilt angle. 

with

and

Due to the high flexibility of the rotation-double tilt sample holder it was possible to collect 24 zones in a reasonable orientation. In addition the use of a small C2 aperture of 10 nm diameter delivered an intensity low enough to avoid significant beam damage so that all diffraction patterns could be collected from one crystal.

Due to the high flexibility of the rotation-double tilt sample holder it was possible to collect 24 zones in a reasonable orientation. In addition the use of a small C2 aperture of 10 nm diameter delivered an intensity low enough to avoid significant beam damage so that all diffraction patterns could be collected from one crystal. During the tilt around c* the in-zone angle stayed 90° indicating that b must be 90° as well whereas the in-zone angle through the b* tilt changes leaving different from 90° (compare Fig. 2 and 3). At this point we do not need to know in advance which reflections to use for the correct definition of the zone axes, which can be quite problematic. The in-zone angle can be calculated in later for correct indexing of the reflections.

b*

c*

(1-40)*

b*

Fig. 2: Initial zone [100] of aerinite (left hand side) with 1/b* = 14.612 Å / = 90° and 1/c* = 2.611 Å * 2 = 5.222 Å where every odd line in c* direction is extincted; Zone [410] at tilt about c* of 14° (right hand side) exhibits “ghost reflections” indicated by black arrows.

(102)*

b*

[20-1]-9°

(201)*

b*

[10-2]-32°

Fig. 3: Zone [20-1] of aerinite with an in-zone angle of 87° (left hand side) the “ghost reflections” are indicated by black arrows; Zone [10-2] with an in- zone angle of 73° (middle) and a scheme of the reciprocal space view down titl axis b* (right hand side).

The next step was to identify the zones correctly. For this task one can use “ghost reflections”. Due to the thin specimen the reflections are no sharp spots but elongated in the direction of the beam. This is the reason that we find some weak reflections, which do not belong to the actual but to adjacent zones. For example, zone [410] (Fig.2, right hand side) exhibits 3 weak reflections between the allowed ones indicating an index of h=4. More striking is the comparison of the zones [20-1] and [10-2] given in Fig. 3. Due to the ratio of the cell axes a/c (long/short) the zone [20-1] passes adjacent reflections closer than zone [10-2]. Please note the difference between an extinction in zone [100], where every odd line in c* direction is missing and no ghost reflections are found (first reflection is indexed as (002)), and zone [20-1] where we find one “ghost line” (first strong reflection is indexed as (102)).

To test the indexing, one should allways produce a Vainshtein diagram by plotting the changing reciprocal distance along the axis defined by the tilt angle [6]. It will lead to a regular pattern of reflections and the projected unit will be visible as given in Fig. 4.

0,0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

-0,2 -0,2 -0,1 -0,1 0,0 0,1 0,1 0,2 0,2 0,3 0,3

c*

=90°

l=1

l=2

l=3

a*0,0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

-0,2 -0,2 -0,1 -0,1 0,0 0,1 0,1 0,2 0,2 0,3 0,3

c*

=90°

l=1

l=2

l=3

a*0,0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

-0,2 -0,2 -0,1 -0,1 0,0 0,1 0,1 0,2 0,2 0,3 0,3

c*

=90°

l=1

l=2

l=3

a*

Fig. 4: Vainshtein drawing for view down tilt axis b* (left hand side) and tilt axis c* (right hand side) for aerinite; the projected unit cells are highlighted with black lines.

0,0

0,1

0,1

0,2

0,2

0,3

0,3

0,4

-0,2 -0,1 0,0 0,1 0,2 0,3 0,4

b*

a*

=60°0,0

0,1

0,1

0,2

0,2

0,3

0,3

0,4

-0,2 -0,1 0,0 0,1 0,2 0,3 0,4

b*

a*

=60°

The Vainshtein diagram is the geometrical basis of the calculations used to produce table 1, 2 and delivers the missing values of a and as well. Please note the assymetric indizes of zones for the tilt about c* ( ≠ 90°). As an example we can compare the zones [410]/[3-10], [310]/[2-10] and [520]/[3-20] which have comparable tilt angle resp. d-values and show the same pattern.

The comparison of our results (a = 16.70 Å, b = 16.92(1) Å, c = 5.22 Å, ==90°, =119.7°) with the former cell determination of Rius and a recent one refined by him from synchrotron x-ray powder diffraction (a = b = 16.8820(9) Å, c = 5.2251(3) Å, ==90°, =120°) [7] is quite satisfying. Due to the spike function and some possible misalignment the uncertainty in tilt angle determination is at least ± 0.5°. Therefore, electron diffraction data will never be as accurate as x-ray powder data. Assuming a correct alignment of the eucentric height we still find an inaccuracy of minimum ±0.2 Å for direct measured values and of at least ±0.5 Å for calculated cell distances.

Only zone [100] exhibited extinctions (h-h0l: l=2n) leaving over still four possible space groups (P3c1, Pc1, P63cm, P63mcm). Unfortunately, due to the high beam sensitivity it was not possible to

determine the existence of a centre of symmetry or a 63 screw axis by convergent beam electron

diffraction. Recently, Rius et al. [7] have determined the crystal structure in space group P3c1 (No. 158) by applying the direct methods modulus sum function to synchrotron powder diffraction data. As shown in Fig. 5, the framework of aerinite is formed by units of three pyroxene chains (Si2O6

4-)

placed around one three-fold rotation axis, laterally linked through [001] chains of edge-sharing AlO6 octahedra to other similar units. In each unit, the apical O atoms of the three pyroxene chains

point inwards thus coordinating Fe, Al and Mg atoms, and giving rise to columns of face-sharing octahedra. Two neighbouring units, i. e., two units connected by Al chains, are not symmetry-related: called units A and B. In fact, both are mutually shifted by 0.93 Å along c. The large [001]-channel formed by the pyroxene and AlO6 chains are filled with Ca, H2O and CO3 groups. The

carbonate group is on the third three-fold axis. The framework of aerinite also contains zigzag chains of edge-sharing AlO6 octahedra that join the cylindrical units A and B. Each AlO6 octahedron

consists of four hydroxyl groups (OHA, OHA’, OHB, OHB’) and of the two unshared basal O atoms of the next pyroxene chains (02A and 02B). Ca (also occupied by a small amount of Na+ and some vacancies) is at the centre of a distorted O octahedron. The atomic arrangement formed by one zigzag chain of AlO6 octahedra and the adjacent Ca coordination polyhedra may be described as

forming a four-row wide slab of a brucite-like layer.

The two inner octahedra are filled with Al (and Mg) atoms and the two outer with Ca (and Na). The internal O atoms of the brucite-like layer are hydroxyl groups, the intermediate are unshared basal O atoms of the neighbouring pyroxene chains, while the external ones are water molecules forming relatively strong H-bridges with the partially disordered CO3 groups.

Presumably, the hydroxyl groups in the brucite-like layer also form H-bridges with the apical O atoms of the neighbouring pyroxene chains to compensate for the defect of charge caused by the presence of divalent cations in the face-sharing octahedra.

Fig. 5: Crystal structure of aerinite view down c (left hand side) and corresponding HRTEM [001] image (right hand side).

In addition, from ultrathin slices of the embedded material HRTEM images were obtained in different crystallographic orientations ([001] (see Fig.5), [101], [110], [-111], [102], [120], [201], [122], [203], [301], [1-19], [-124]). Using the stucture model of Rius et al. the comparison of kinematically electron diffraction patterns have been compared with experimental data (Cerius 4.2 [8]) as shown in Fig. 6. The basic course of intensity is distinguishable but clearly the patterns deviate from each other. For quantitative analysis significantly thinner crystals are needed.

Fig. 6: Zone [210] of aerinite from tilt about c* (left hand side and the kinematically calculated data for comparison.

[210]31° C*

4. Structure investigation of Pb5MoO8

single crystals by selected area electron diffraction.

Doyle and Forbes [9] have been the first who show that a new compound Pb5MoO8 is

formed in the PbO – MoO3 system. Pb5MoO8 single crystals were obtained from the

melt under slow cooling using Pt-wire and were investigated by single crystal structure analysis (CAD – 4) and the unit cell parameters were confirmed through x-ray powder data by Mentzen et al. [10] (PDF 37-1086: a = 15.316(4) Å, b = 11.827(1) Å, c = 11.6387(3) Å, = 90.200o, Z = 8, SG P21/c. A partial determination of the structure of

the isomorphous compound Pb5SO8 was performed by Sahl [11]. Despite the

disordered structure and the high degree of X-ray absorption of heavy Pb atoms he succeeded to determine the Pb atomic positions. We try to solve this problem by the use of transmission electron microscopy (EM 420 – T/EDAX, Philips at 120 kV) because the electron diffraction allows us to distinguish more precisely the superstructural details. Six ([100], [010], [001], [011], [101], [110]) selected area electron diffraction (SAED) patterns and two ([001], [021]) HREM images from several particles were obtained and analysed. The diffraction patterns have been photographed on AGFA EM films (6.5 x 9 cm) with exposure times in the interval between 0.1 s and 99 s. The negatives were digitised by Bosch video-camera of high linearity, connected to the specialised image processing system of Kontron – elektroniks group. The system is linked to a PC/486 computer, where the calculations have been performed.

Since the diffraction patterns consist of strong - PbO reflections and essentially weaker superstructure reflections, which contain the main information of the Pb5MoO8 superstructure,

the dynamical range of the electron beam intensities incident on the photoplate is extremely wide and overpasses the linear region of the sensitivity of the photographic material. To overcome this problem a multi-exposure technique was used. The diffraction patterns were photographed in a broad interval of exposure times (0.1 s, 0.2 s, 0.5 s, 1.0 s, 2.0 s, 5.0 s, 10.0 s, 20.0 s, 50.0 s, 99.0 s), so that all of the reflections lie in the linear region of a photoplate of a certain exposure time. Collecting the intensity data at all exposure times, a map of the relative intensities of the reflections is obtained for each EDP. After a detailed analysis of the measured diffraction intensities a principle structure model of the positions of the heavy Pb and Mo atoms of Pb5MoO8 was constructed and tested by a comparison

between the theoretical intensities, calculated by multislice dynamic calculations [12], and the observed ones in all six measured EDP. HREM image simulations were performed in [001] and [021] zone axes and compared to the experimental ones.

The SAED patterns consist of an intense base set of - PbO subcell reflections and weak superstructure reflections h’/4, k’/3, l’/2 referring to the - PbO cell due to a modulation of the structure. To determine the Pb and Mo positions in Pb5MoO8 on the base of the relative

intensities of the SAED reflections a multislice dynamic calculation [12] was performed. The calculations were performed separately for each of the 6th experimental microdiffraction patterns. The thickness of the specimen was determined independently for each of the patterns. The performed procedure is close to the published idea by Bing – Dong et al. [13].

Fig. 7a. Six experimental [100], [010], [001], [110], [011], [101] selected area electron diffraction patterns of Pb5MoO8 single crystals.

Fig. 7b. Multislice calculated [100], [010], [001], [110], [011], [101] SAED patterns of Pb5MoO8 structure.

The most effective starting model happens to be the one presented by Sahl [11] for Pb5SO8, the

modulation of which is changed from 2 : 3 : 2 to 4 : 3 : 2 by doubling the a-parameter of the cell. The procedure of comparison was first applied to the zones [001], [010] and [011] where the (100) reflection appears because of the quadrupole modulation of structure along the a-direction. The best similarity for [001], [010], [011] zone is obtained when Mo atoms replaces 2/3 of Pb atoms in one of four sectional layers perpendicular to the a-axis and forming the fourfold superstructure along the a-direction. The 2/3 Mo substitution in the Mo – Pb layer is responsible for the threefold superstucture along the b-direction. The presented data in this work is not enough to explain the doubling of the c-axis. It only confirms the existence of such twofold modulation along c. Another possibility for the Mo-substitution of Pb atoms is that Mo atoms replace 1/3 of Pb atoms in one of two sectional layers perpendicular to the a-axis forming a twofold superstructure along the a-direction. In this case the observed fourfold superstructure must be due to some disturbances of one of two Mo – Pb layers or Pb – Pb layers. The analysis of the structure types give essentially less intensities for (2h + 1, 0, 0) reflections compared to (2h, 0, 0) reflections than the measured in all directions of [001], [010], [011].

Anyway, due to the limited precision of the EDP – intensity measurement, especially for the (100) reflection, which is too close to the central beam - this argument is not very strong and cannot reject the 1/3 substitution at all. To confirm the hypotheses of the proposed 2/3 substitution HREM observation in [001] and [021] zones were performed in parallel with multislice calculations, based on the 2/3 substitution. These projections are used because the fourfold modulation due to the Mo atoms is well expressed in them. The observed images are enhanced by a Fourier filter with Bragg mask to eliminate the noise frequencies.

The determination of y and z coordinates of Pb and Mo atoms in the layer distinguished by its Mo – content is made by a fit of the [100] zone intensities, which give the best information about the [100] Mo – Pb layer projection. Two other zones [101] and [110] were also used to verify the atomic positions.

The dynamic calculations include all beams with interplanar distances dhkl larger than 0.75 Å at

120 kV acceleration voltage and thickness between 100 Å and 300 Å for the different zones. The structure factors have been calculated on the basis of the relativistic Hartree – Fock electron scattering factors [14]. The thermal diffuse scattering is calculated with the Debye temperature of -PbO: 481 K [15] at 293 K with mean-square vibrational amplitude < > = 0.0013 Å2 following the techniques of Radi [16]. The inelastic scattering due to single-electron excitation (SEE) is introduced on the base of real space SEE atomic absorption potentials [17]. All calculations are carried out in zero order Laue zone approximation (ZOLZ).

U2s

HREM image simulations are performed using the optical parameters of EM 420-T/EDAX Philips microscope with CS = 1.0 mm at Scherzer defocus = -57.6 nm at a thickness of 23.3 Å

along [001] direction and 105.4 Å along [021] direction. The structural peculiarities of the whole class of isomorphous compounds Pb5AO8 (A = S, Se,

Cr) are up to now investigated only by single crystal and powder X-ray methods. Thus two types of superstructures obtained are: 4 : 3 : 2 from single crystal diffractometry and 2 : 3 : 2 from powder diffractometry. This contradiction between the two methods can be solved by using the SAED method as it is done here with Pb5MoO8. SAED investigations undoubtedly confirmed that

4 : 3 : 2 superstructure of deformed -PbO is more probable to this class of compounds [18].

Fig. 8. HREM image from [001] orientation of the Pb5MoO8 crystal particle. The thickness of the particle is 23.3 Å.a) experimental HREM image;b) Fourier transform of experimental HREM image. The size of the used aperture;c) enhanced HREM image after Fourier filter with Bragg mask constructed in accordance with Fourier image (b);d) calculated HREM image in this orientation by multislice method;

Fig. 9. SAED and HREM images from [021] orientation of the Pb5MoO8 crystal particle. The thickness of the particle is 105.4 Å.a) experimental SAED pattern in [021] zone;b) the size of the used aperture;c) enhanced HREM image after Fourier filter with Bragg mask; d) calculated HREM image in this orientation by multislice method;

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