Pecharsky V.K., Zavalij P.Y. Fundamentals of Powder Diffraction and Structural Characterization of Materials

Подождите немного. Документ загружается.

562 Chapter

specimen was prepared by filling a 1 mm deep cavity of a sample holder

without applying any pressure (see section 3.5) to minimize preferred

orientation effects.

Regardless of all precautions in the sample preparation, the pattern

(Figure 6.26) contains two distinct Bragg peaks, which are substantially

stronger than all others. The first peak at

-9.4O

9.308 A) is shown at one

fourth of its height, and the second at -19.1"

4.640 A) has intensity -4

times lower than the first, yet it is -3 times higher than any other Bragg

reflection. The intensities of the remaining Bragg reflections are below 10%

of the strongest. The d-spacing ratio for the two strongest peaks is 2.006,

which clearly indicates that they belong to the same zone, for example, 001

and 002 in the 001 zone. Combined with the markedly planar shape of the

crystallites (inset in

Figure 6.26), these features strongly suggest the

presence of a substantial preferred orientation, which may create problems in

solving the structure and in refining structural and profile parameters. On the

other hand, the fact that the two strongest reflections belong to the same

zone can be used to correct the observed peak positions for the sample

displacement or zero shift errors during the ab initio indexing, as was

actually done in the original

work.]

Semi-manual profile fitting was conducted using WinCSD (see the

footnote on page 515). The first 41 peaks in the range below

39" were

indexed using the IT0 program in a monoclinic unit cell

(Mzo

37),

which

was the best and the only solution with all peaks indexed. The unit cell

refinement resulted in a

18.453 A,

6.560 A,

8.437 A,

91.12O,

and

1021.1 A3. Analysis of the systematic absences results in h

for h01 reflections and 1

2n for 001 reflections, which unambiguously points

out to P2Jn (P2Jc in standard setting) as the only possible space group

symmetry. Moreover,

P2,Ic is one of the most common groups observed

among natural and man-made materials.

Due to the complexity of the pattern, multiple overlaps (e.g, about 90

Bragg reflections are possible in the range of the first 40 observed peaks

below

40") and the relatively broad peaks, the pattern decomposition

was carried out using a semi-manual profile fitting. For each group of Bragg

reflections, located within the manually selected ranges of the powder

This example can be used to illustrate an interesting approach that may be helpful in the

indexing from first principles. Assume that two patterns were collected from the same

powder. The first, using a specimen with minimum or no preferred orientation, and the

second with artificially induced strong texture. Provided the texture axis coincides with

one of the principal crystallographic directions

(e.g. [OOl], [OlO], or [OOl]), the

comparison of two patterns may provide critical information about the indices of certain

peaks, whose intensity was affected (increased or reduced) the most. Once their indices are

determined by analyzing the ratios between the corresponding d-spacings, the problem of

finding the remaining lattice parameters is simplified by eliminating one unknown.

Crystal structure solution

563

diffraction pattern as described in the footnote on page 554, the least squares

profile fitting was conducted by refining the individual 28 position and

integrated intensity of each peak. Common for each range were parabolic

background, full width at half maximum, and the mixing and asymmetry

parameters of the pseudo-Voigt function. The average

was

-2.5%.

When

28 exceeds 35O, peak widths increase over 0.15O. Together with the

increasing density of peaks, this makes it quite difficult to refine both profile

and positional parameters independently. Therefore, full widths at half

maximum were linearly extrapolated from previous ranges

(Figure

6.27)

and

only individual intensities and positions of Bragg peaks were included as

free least squares parameters.

This type of profile fitting is actually a modification of the Pawley

decomposition technique performed without restricting peak positions by

unit cell dimensions, and in small ranges instead of a full pattern. The

observed intensities of 236 individual peaks up to

69" were determined

in this way with a total of 425 Bragg reflections possible in this range of

Bragg angles. Unobserved reflections were assigned small intensity values

(equal to about

of the intensity of the nearest observed peaks) to improve

the chances of solving the structure using direct methods. Experimental data

are found on the CD in the following files:

GSAS

and tabular

(XY)

formats,

files Ch6ExO6-CuKa.raw and Ch6Ex06-CuKa.xy, respectively; the

indexed list of the individual structure factors

IFobs(

is in the file

Ch6Ex06.hk1, and relevant crystal data are in the file Ch6Ex06.ins. The two

latter files are in

SHELX

for&at.

10 20 30 40 50 60

Bragg angle,

(deg.)

Figure

6.27.

Full width at half maximum as a function of Bragg angle observed (below

35')

and linearly interpolated (above

35")

in the powder diffraction pattern of

tmaV3O7

shown in

Figure

6.26.

5 64 Chapter

Chemical composition of the powder was established from the following

data: thermogravimetric analysis in an oxygen atmosphere shows a

-4

weight gain around 200•‹C and then a sharp weight loss (19.2

at -320•‹C.

The orange product, obtained after the TGA, was identified from a powder

diffraction pattern using the Powder Diffraction File as vanadium

pentaoxide,

V2O5. The decomposition temperature, as detected from the

weight loss, is typical for the loss of tetramethylammonium. Thus, the

chemical composition of the residue, temperature and weight changes were

used to deduct a possible formula of the material, the simplest of which is

tmaV3O7, giving a calculated weight loss of 19.5 wt.

The latter is in good

agreement with the experimentally observed 19.2

The oxidation states of

vanadium in [v307]- are 4+ for two vanadium atoms and

for the third one.

A weight gain of 4

in an O2 atmosphere can be explained by the oxidation

of all vanadium to

v5+

and by the formation of tmaV308. The theoretical

weight gain of

4.7

is slightly higher than that observed experimentally (4

because the oxidation reaction was not completed before the

decomposition began.

The gravimetric density was not measured but assuming

4, which is

reasonable for the P21/n space group symmetry where the multiplicity of the

general site position is 4, the calculated density is 2.20 g/cm3. Other

values

either do not agree with site multiplicities (e.g.

3 or 5) or they result in

the unrealistically high density (e.g.

8).

Thus, the final chemical

composition, tmaV307, appears to be the only feasible choice, and it was

employed in the structure determination by using direct phase recovery

methods.

As mentioned above, pattern decomposition resulted in 236

distinguishable observed peaks and, therefore, there is a substantial number

of unresolved Bragg reflections, which is partially due to a significant peak

broadening.' Furthermore, there are 12 light atoms (C,

and 0, not

counting 12 hydrogen atoms) per

vanadium atoms in the formula unit. The

ratio of light to relatively heavy atoms is 4:l.

fraction of electrons in the

heavy atoms is 41

which may be insufficient to recover the whole

structure from the phase angles calculated using only the V atoms positions,

especially taking into account relatively poor resolution of the diffraction

data. Therefore, it is highly unlikely that the Patterson method is suitable in

this case, even though it is less sensitive to the data quality. Thus, this

structure solution case is far from trivial. All things considered, direct phase

determination methods should be employed to find a more significant

portion of the model than just the three independent vanadium atoms.

Structure amplitudes of unresolved Bragg reflections were determined by dividing the

total intensity among all overlapped reflections equally.

Crystal structure solution 565

The structure was solved using SHELXS-90 based on the extracted

structure amplitudes of

425

possible reflections below

70". The direct

phase determination with

E~,

1.1 resulted in the E-map containing an

acceptable model with three "heavy" peaks (Table 6.38) that were

automatically assigned to vanadium. The distances from the vanadium atoms

to all but one from the list of nine strongest peaks are a good match for

V-0

bonds. The only exception is 44, which is too far from all V atoms and too

close to 46 (1.32 A). The 44-46 distance is not listed in Table 6.38.

Since the 46 distance to V3 is nearly ideal (1 239 A), the Q6 but not the

44 peak was included into the trial model. One of the peaks, Q5, is not in

contact with vanadium or oxygen atoms, and it was treated as nitrogen.

Peaks following Q9 have conflicting distances with the first 12 strongest

maxima. The analysis of bond angles and coordination polyhedra confirms

the reasonableness of this model. Its composition,

V3O7 plus one isolated

light atom (presumably nitrogen from the tetramethylammonium molecule),

agrees well with the TGA data, symmetry restrictions and estimated density.

Table

6.38.

Maxima localized from the E-map refined for the best solution obtained by

SHELXS-90 using 425 reflections data below 70" 29; Emi,=l. 1.

Atom/

uid

Bond distances,

Peak

Height

Via

V2a V3a

commentsb

0.794 0.176 0.019 429.9

0.722

0.683

0.069 342.8

0.785 -0.112 -0.252 281.2

0.797 0.189 -0.211 178.5 1.94 2.01 Ola

0.736 0.482 -0.031 151.7 2.31 1.59 1.96 02a

0.892 0.192 0.068 137.1 1.85 03a

0.664 0.019 -0.193 133.3 2.46 Deleted

1.040 0.270 -0.308 132.3 N5a

0.862 -0.295 -0.284 124.2 1.89 06a

0.815 -0.129 0.037 121.1 2.05 2.15 07a

0.760 0.263 0.242 116.8 2.07 1.71

08a

d9 0.685 0.1 18 0.040 114.7 2.06 09a

This column lists the distances to the indicated atom in

The names assigned to atoms consist of the chemical symbol of the element, E-map or

Fourier map peak number, and a letter (if any), which indicates the sequential number of

the calculated Fourier map: a

corresponds to the first iteration, b

second, and so on.

The least squares refinement of this model using SHELXL-97 yields

as shown in Table 6.39. All oxygen atoms and the isolated nitrogen

atom look reasonable because their distances to the vanadium atoms are

within acceptable limits. What is not shown in Table 6.39 is that the

coordination polyhedra of V atoms make both chemical and physical sense:

vanadium oxide forms a layer, composed of V05 pyramids and tetrahedral

V04, as illustrated in Figure 6.28. This layer is similar to layers known for

Chapter

other vanadates. Thus, the model shown in

Table

6.39

may be considered as

a good approximation for the following Rietveld refinement, which will be

discussed in section

7.8.

Since the difference Fourier map was calculated,

analysis of the existing maxima leads to a conclusion that four peaks (not all

are the strongest) can be interpreted as carbon atoms: they have reasonable

bond distances and form a distorted tetrahedral surrounding of the already

found nitrogen atom, which is expected for the tetramethylammonium

[N(CH&]+ cation.

The result of structure refinement after including carbon atoms is shown

Table

6.40.

Neither the residual nor the distances improve, and one carbon

atom, C8b, moves too far away from the nitrogen. The inconsistency in the

location of C8b can be detected even without the refinement from a careful

analysis of the nitrogen environment and or from C-N-C bond angles. Yet

again, this example emphasizes the importance of chemical, physical and

geometrical criteria in the process of solving and refining crystal structures

when quality, resolution andlor completeness of the data are limited by the

technique or by the properties of the specimen.

Figure

6.28.

Metal oxide layer, shown in two different orientations, in the crystal structure of

tmaV307,

which contains

V05

pyramids and

V04

tetrahedra.

Crystal structure solution 567

Table

6.39

Coordinates of atoms after structure refinement using SHELX and peaks found on

the difference Fourier map, which may correspond to possible locations of carbon atoms. All

data below

70' were used; RF

Atom/

Uisol

Bond distances,

Height Vla V2a V3a N5a

Comments

Peak

V1 0.791 0.178 1.015 0.016

Ola

02a

03 a

O6a

07a

08a

09a

N5a

Qll -0.001 0.072 0.736 2.1 1.34 Cl

This column lists the distances to the indicated atom in

Table

6.40

Results of structure refinement by using SHELX; RF

Coordinates of all

atoms were shifted by a vector (-1/2,0, -112) when Eompared to

Table

6.39.

Atom1 Uisol Bond distances,

Comments

Peak

Height Vla V2a V3a N5aa

V1 0.292 0.182 0.513 0.011

Ola

02a

03 a

06a

07a

08a

09a

NSa

C3b

C8b

C9b

1.05

1 .go Incorrect

1.17

Cllb -0.508 0.078 0.226 0.000 1.3

This column lists the distances to the indicated atom in

The high value of

and poor convergence of the model (for example,

the

C-N

and 06a-V3 bond distances are getting worse instead of improving)

are due to both the low resolution and the suspected strong preferred

orientation, which was discussed at the beginning of this section but not

568 Chapter

confirmed at this point. Actually, in the original paper (see the footnote on

page

561),

an arbitrary scale factor of 213 was applied to the intensities of all

hOO reflections in order to reduce preferred orientation effects.

Chapter 7

we will see that the preferred orientation here is quite strong. No correction

has been applied in this example, yet the model of the crystal structure is

reasonable. Geometrical, chemical and physical considerations play a far

more important role in this conclusion than the residual at this stage of the

crystal structure determination process.

6.15

Crystal structure

of ma2M070221

white crystalline powder, prepared by hydrothermal treatment at 200•‹C

of a mixture of molybdic acid, H2Mo04, and methylammonium

(ma)

chloride, CH3NH3Cl, taken in a 1:2 molar ratio and acidified with

hydrochloric acid, HC1, to pH

3.5, resulted in a complex powder

diffraction pattern shown in

Figure

6.29. It was indexed in the monoclinic

crystal system as was discussed in section 5.12.2. The space group C2Ic (or

its acentric subgroup Cc) was established from the analysis of the systematic

absences, and the unit cell dimensions were refined using 120 resolved

reflections below 29

60': a

23.0648(6) A,

5.5134(2) A,

19.5609(5) A,

122.931(1)O, and the sample displacement

-0.098(3)

mm for a 250 mm goniometer radius. The unit cell volume is 2087.8 A3.

The Powder Diffraction File search was unsuccessful and therefore,

further analysis and a structure solution were undertaken.

Thermogravimetric analysis in an oxygen atmosphere reveals sharp 7.3

wt.

weight loss at 300•‹C and the powder diffraction pattern, collected

from a solid residue after the TGA, confirms the formation of molybdenum

oxide, Moo3. Assuming the following decomposition reaction:

it can be shown that the observed weight loss nearly precisely corresponds to

m:n ratio 2:7 and k

m/2

1. The latter ratio also follows from the white

color of the substance under investigation, which implies that Mo is in the

oxidation state. Thus, the chemical composition of the material is

(CH3m3)2M07022.

relatively large volume of the monoclinic unit cell translates into a

considerable complexity of the diffraction pattern even in the case of a base-

centered lattice, as can be seen from

Figure

6.29. There are -10 reflections

per degree at 28

50' and about 20 reflections per degree at 29

100".

P.Y.

Zavalij and

MS.

Whittingham, The crystal structure of layered methylammonium

molybdate (CH3NH3)2M07022 from X-ray powder data, Acta Cryst.

C53,

1374 (1997).

Crystal structure solution

Bragg angle,

(deg.)

10 20 30 40 50 60 70 80 90

Bragg angle,

(deg.)

Figure

6.29.

Powder diffraction pattern collected from a ground rna2M07022 powder using Cu

radiation on a Scintag XDS2000 diffractometer in a step scan mode with a step 0.02'. The

counting time was 30 seclstep in the range 7

67' and 60 seclstep for 67

98'.

The counting time was increased at high Bragg angles to improve the counting statistics for a

large number of weak Bragg peaks possible in this range. To ensure consistency of intensity

measurements, the high Bragg angle part of the diffraction pattern has been scaled to 30

seclstep counting time for further processing. The vertical bars indicate calculated positions of

the

Ka,

components of all possible Bragg reflections. The inset shows the expanded view

from

GO0

to 65.7', which contains 76 possible reflections.

The total number of possible Bragg reflections below

98'

1032.

Therefore, before attempting a structure solution from first principles, a

more thorough search of the relevant databases was performed.

based on the unit cell dimensions and volume produced no results, but after

searching the

ICSD

database for a matching stoichiometry of the molybdate

anion,' two compounds, both with the space group symmetry C2/c, were

found and they are listed together with the title compound in

Table

6.41.

First, 1174 compounds containing Mo and

were found. Second, the list was narrowed to

15 1

structures that have monoclinic base-centered or body-centered lattices. Third,

"Mo7022)' text in the chemical formula was searched. Searching all ICSD records for a

specific text would be very slow.

Chapter

Table

6.41.

Unit cell dimensions for Mo7OZ2-containing compounds present in the ICSD

database.

Compound a,

ICSD Ref.

Cs2M0702, 21.54(1) 5.537(3) 18.91(1) 122.71(3) 1897.7 1887

T1zMo7022 20.5 12(6) 5.526(2) 19.460(6) 125.20(3) 1802.4 343

rna2M07022 23.0648(6) 5.5134(2) 19.5609(5) 122.93 l(1) 2087.8

Considering the unit cell dimensions listed in

Table

6.41, the title

compound is likely to have a structure, which is closely related to both

cesium and thallium heptamolybdates. Perhaps they are isostructural to the

extent where methylammonium substitutes for metal cations in the crystal

lattice. A thallium compound can be also found in the Powder Diffraction

File, record No. 30-1349. It is clear why all powder pattern and unit cell

dimensions searches failed: unit cell volumes are quite different due to the

differences in

The latter is not surprising taking into account that methyl

ammonium ions should occupy larger cavities both due to their size and

weaker interactions of a hydrophobic methyl group with oxygen atoms. In

view of the expected similarity among the three crystal structures listed in

Table

6.41, the atomic coordinates of the Mo7022 layer from the T1

compound were used as the initial model of the metal-oxygen framework for

the methylammonium compound

(Table

6.42 and

Figure

6.30).

Table

6.42.

Coordinates of Mo and

atoms in the unit cell of mazMo7022 as assumed from

the model of the crystal structure of Tl2Mo7OZ2. The space group symmetry is C21c.

Atom Site

Mo 1 4(e) 1 I2 0.1375 1 I4

Mo2 8(f) 0.4081 0.0553 0.475

Mo3 Wf) 0.3732 0.5000 0.0935

Mo4 8(f) 0.0533 0.1061 0.1378

01 8(f) 0.3140 0.0880 0.3882

02 8(f) 0.1496 0.1560 0.2199

8(f) 0.0779 0.1750 0.4549

04 8(f) 0.3995 0.1770 0.0266

05 8(f) 0.3906 0.2330 0.1641

06 8(f) 0.0393 0.3870 0.0677

07 8(f) 0.0234 0.4480 0.1977

8(f) 0.4960 0.4500 0.3 196

09 8(f) 0.4361 0.3800 0.4157

010 8(f) 0.1395 0.2290 0.3577

01 1 8(f) 0.2820 0.4630 0.0033

B.M. Gatehouse and B.K. Miskin, The crystal structures of cesium pentamolybdate,

and cesium heptamolybdate, CS~MO~O~~, Acta Cryst.

31,

1293 (1975).

TolCdano, M. Touboul, and

Herpin, Structure crystalline de I'heptamolybdate de

thallium(I), TI2Mo7Oz2, Acta Cryst.

B32,

1859 (1976).

Crystal structure solution

571

Figure

6.30.

Metal oxide layer in the crystal structure of maMo7OZ2, shown in two different

orientations. The Mo atoms are shown as large dark grey spheres, and the

atoms as small

grey spheres.

If our hypothesis about the relationship between the crystal structures of

T12Mo7022 and mazMo7Oz2 is correct, refining relevant atomic parameters

and completing the model, i.e. finding the coordinates of missing

methylammonium groups should be easier done after the Rietveld

refinement, which will de described in the next chapter, section

7.9.

Experimental data are found on the

in the data files

Ch6Ex07-CuKa.xy

and

Ch6Ex07-CuKa.raw.

6.16

Crystal structure

Mn7(OH)3(V04)41

A diffi-action pattern (Figure 6.31) collected using a powder prepared

from brown rod-like hollow crystals produced hydrothermally2 (Figure 6.31,

Idealized composition without vacancies;

Zhang,

P.Y.

Zavalij, and MS. Whittingham,

Synthesis and characterization of a pipe-structure manganese vanadium oxide

hydrothermal reaction,

Mater. Chem., 9,3137 (1999).

The material was prepared by hydrothermal treatment of V2O5, Mn(CH3C00)2 and

N(CH3)&I taken in

molar ratio at

165

"C for

days.