Autoradiography as a tool for studying iron segregation and related defects in KH2PO4 single crystals

Journal of Crystal Growth

29

(1975)

109—120

0 North-Holland Publishing Co.

AUTORADIOGRAPHY AS A TOOL FOR STUDYING IRON SEGREGATION AND RELATED DEFECTS IN KH2PO4 SINGLE CRYSTALS C. BELOUET

and M.

MONNIER

Laboratoires d’Electronique et de Physique Appliquée, 94450 Limeil-Brévannes, France and J. C. VERPLANKE

Philips Research Laboratories, Eindhoven, Netherlands

Received 18 December 1974; revised manuscript received 20 January 1975 59Fesingle tracer. The iron the crystal perfection respectively A dihydrogen phosphate crystal wassegregation grown by and the temperature decrease were method from a investimother liquor gated by doped means withofthe autoradiography and X-ray topography. The iron segregation in the prismatic facets could be related to growth parameters and a good correlation could be established between the X-ray topographs and the autoradiographs. The implication of the iron segregation in generating crystallographic defects and influencinggrowth kinetics was clearly recognized.

1. Introduction

tion of the solution was achieved by means of a stirrer designed so that the dynamics of the solution past the

The prerequisites for the use of KH 2(j _X)D2XP04 single crystals as targets in solid-state lightand valves 1) are (i) that x be close to unity (ii) such that as Titus their electrical resistivity be high and homogeneous across the target. Departures from the second item were previously ascribed to grown-defects2), and this was confirmed in our own experiments. In addition, the occurrence of these defects was found to be strongly bound to that of impurities in the mother liquor and, among these, the trivalent impurities played a major role3). It was then decided to study the interplay of growth conditions and iron segregation on the occur rence of crystallographic defects using 59Fe as a tracer. Since the growth of deuterated and non-deuterated single crystals are similar in many respects, this experiment was conducted with a non-deuterated crystal. A comparative study of the crystal perfection was achieved by means of both X-ray topography and autoradiography. This article is aimed at presenting an overall view of all the results obtained thus far. More detailed treatments will be given separately in future works.

crystal was mostly controlled by the rotation of the crystal. The which seed was a tetragonal pyramid x 2.5 cm2 section) pointed downwards; it was(2.5 mounted on a methylmetacrylate holder submitted to an adjustable rotation rate. After some growth had already proceeded, a 0.1 N hydrochloric solution of the radioactive iron isotope 59Fe (12 x 10 3Curie) was added into ~F

1

ABLE

of predominant impurities in the mother liquor (given in ~igper g of KDP) prior to the addition ofthe radioactive tracer Content

Impunty

Content

Impurity

Content

7.7

Fe

0.053

cc

3.2

Rb

15 O:003 2.0

-__________________________________________

Ba Zn Sb

the mother liquor. Then, the pH of the solution (see also impurity content in table 1) was readjusted at 4.49 (pH values were measured at room temperature from 0.05 M solutions). During the growth in the radioactive solution, which took place between 324 and 321 °K,the rotation rate of the crystal and the supersaturation were varied in

2. Experimental A KH 2PO4 single crystal was grown using the tem- order to investigate their effects on the iron segregaperature decrease method in an 4). apparatus similar to every tion. The total length the crystal The wascrystal measured The homogenizaday by means of a of cathetometer. thus that already described elsewhere 109

110

C. BELOUET, M. MONNIER AND J. C. VERPLANKE

obtained was sliced and the (001) slices, 2 mm thick, were numbered and selected for the different means of investigation according to the sequence, as shown in fig. 1. Since the decay of 59Fe, of relevance for auto-

fl~ _____________

X MP 4

to

MP

x

was reduced to 50 ~tmin order to allow a good resolution. The exposure time depended on the growth sectors4). Three days were sufficient for revealing the prismatic sectors (fig. 2) whereas three months were required to obtain reasonable information about the pyramidal sectors (during this period of time about 80 % of the decay was collected). The films used were Kodak strips (SO 410, 21 DIN for visible light). Separate exposures were also conducted with 1 mm thick slices, noted M.P. in fig. 1, in order to study the pyramidal sectors. The investigation of the iron content in the prismatic sectors was completed by scanning the films using a microdensitometer operating with a 20 ~im step. The X-ray transmission topographs were carried out either on the slices noted X or M.P. (after the exposures).

Fig. 1 Schematic representation of a (100) cross-section of the crystal which shows the sequence of the studies made on the (001) slices. X is for X-ray topography, A for autoradiography and MP for multi-purpose. The angle a is the tapering angle and the arrow indicates the numbering of the slices.

3. Results

radiography, consists of f3 particles of relatively high energies (53 at % 0.47 MeV and 46 at % 0.27 MeV), the thickness of the slices submitted to autoradiography

respect to the pyramidal and prismatic sectors, already recognized by means of wet chemical analyses4), was dramatically confirmed by the autoradiographs as il-

3. 1.

GENERAL FEATURES

The large difference of the iron segregation with

Fig. 2. Autoradiograph ofslice 42(50 ~xmthick; exposure time: 3 days). Observe the high valUes and the large fluctuations of the iron content in the prismatic sectors (white outer frame) as opposed to the pyramidal sectors where~nocontrast shows up..

ill

AUTORADIOGRAPHY AS A TOOL FOR STUDYING IRON SEGREGATION

lustrated by an example in fig. 2. The iron content later noted [Fe] was found to differ sometimes by as much as a few orders of magnitude for the two types of sectors. The [Fe] variations with growth parameters were found to be relatively large in the prismatic sectors (fig. 2) as opposed to those in the pyramidal sectors. However, the iron content in both sectors was far from homogeneous across the growth front, which resulted in growth habit modifications as can be seen for the prismatic sectors in fig. 2. In all cases where autoradiographs and X-ray topographs of the same or neighbourlng slices were available, a close relationship was often found to occur between the location of the contrasts revealed by both techniques the iron distribution is revealed in the X-ray topographs because changes in the iron incorporation induce lattice strains which,in turn, modify the integrated diffracted intensity (intensity contrast). Consequently, hereafter the iron distribution will often be discussed in close relation to the contrasts which have been revealed by X-ray topographs3) and which are referred to as dislocations, in-

clusions, growth bands, growth ghost, parasiticgrowth ghosts and diffused strains. The following results are separately presented for the different growth sectors, a b ‘ W

1100] d Fe Fig. 3. The diagramme (right-hand side) represents the characteristic shape of the prismatic growth front in a (001) plane. The direction of the rotation co is also given. The graph (left-hand side) shows the variation ofthe iron content across the prismatic growth front (along a (100] direction).

—

and the last section is devoted to particular aspects of growth kinetics. 3.2. PRISMATIC SECTORS X-ray topographs reveal contrasted bands whichwere previously ascribed3) to the segregation of trivalent cations such as iron and chromium. In that study, neither

r59F1

___ b

Prismatic growth

.,,u~ distance

-

Fig. 4. [Fe] variations (linear relative scale) through the prismatic growth front (along the [010] direction), as measured from autoradiograph of slice 32. The scannings (origin at the outer growth front) were made as shown in the X-ray topograph of a neighbouring slice 34. The arrows point out the iron content at the transition from pyramidal to prismatic growth.

112

C. BELOUET, M. MONNIER AND I. C. VERPLANKE

[59~

[~~F~1

200-1015

/

~Cr ~

~Cr =0.03

ACr ‘ijOO3~ ~Cr <<0.03

150

0

5 10rpm

-

r/~f~

~

Prismatic growth [100] Fig. 5. (Fel variations (linear relative scale) through the prismatic growth front (scanning b, fig. 4) versus relative supersaturation AC, at constant co value, right-hand side, and versus rotation rate co at ACr 0.034, left-hand side. The iron concentration in the associated pyramidal sector (extreme right-hand side of the graph) is far too small to appear on this graph.

100 500 000 i.im Fig. 6. Characteristic [Fe] variations (linear relative scale) through the prismatic growth front (measured as in fig. 4) in slices 44, 36 and 22. The rotation rate at the various stages of the growth is given on top (see also fig. 5).

the nature of the incorporated iron possibly a hydro- tion rate. The importance of the morphology modificalysed ion nor its ionization state were investigated as tion around b decreases as the iron concentration dewas the case for ADP5’6). In the same work, this segre- creases in the growth front and vanishes at low [Fe] gation was shown to largely depend on growth para- values. meters. The present study is concerned with two of Fig. 5 gives a general insight into the [Fe] variations these: (1) the relative supersaturation AS!Seq* of the with respect to both the relative supersaturation and solute, noted AC,, and (ii) the stirring of the solution the rotation rate of the crystal. The iron distribution past the crystal. across the growth front as well as the successive bands The autoradiographs and the measurements of the along the growth axis have their direct replicas in the relative 59Fe content along the growth axis made from topographs (e.g. fig. 4). The variations of the contrast (001) slices, as described in the experimental section, in the topographs were actually found to match very showed that the iron distribution in the prismatic well those of the iron content in the autoradiographs. growth front behaves as schematically drawn in fig. 3. A tentative was made to relate, at a constant AC, value, The graph (fig. 3) clearly delineates three regions. The the iron segregation to specific characteristics of the ab and cd regions are characterized by a rapidly vary- stirring, i.e. the rotation rate to and the crystal dimening iron content as opposed to the bc region. In the sions. Due to the particular geometry of the stirring of latter, the average iron content was found to be fairly the solution, the crystal dimension of relevance was closely bound to the growth parameters and was thus chosen in a (001) cross-section. Since this cross-section taken as a reference to Iepresent the iron content in was nearly a square, its diagonal d was then taken as relation to growth parameters. The cross-over in b, the dimension parameter. A simultaneous study of the which is associated to the largest departure from flat- to and d effects on the iron segregation could be easily ness of the growth front always corresponds to the conducted by taking advantage of the tapering of the highest iron content (fig. 4). Its location and distance crystal which caused the dimension d of the slices to from the corners (intersections between two prismatic decrease along the c axis. The relative height of corsectors) is dependent upon (i) the orientation of the responding iron bands measured in slices 22, 36, and rotation, as shown in fig. 3, and (ii) the rotation rate, 44 (fig. 6) decreases when to increases with the excepb moving towards a at decreasing values of the rota- tion of the to 15 rpm band in slice 22. In addition, [Fe] at least for to = 5 rpm and to = 10 rpm de—

—

—

*

—

S,,, concentration at the equilibrium is given in g KH 2PO4 per

100 g solution,

creases when d decreases (from slice 22 to 44). The

113

AUTORADIOGRAPHY AS A TOOL FOR STUDYING IRON SEGREGATION

49

37.4

2~2

10

I 20

99.9

77.8

~n

r

15 and 10AC, rpm. Then, [Fe]order also of decreases at increasing values (fig.since 5), the [Fe] values in table 2 is well expected. These results show that, at a given supersaturation and a working temperature, the incorporation of the iron into the prismatic facets varies in relation to the wd2 quantity, noted F [the viscosity effect which strictly depends on the temperature7) was not studied]. It is

20

10 8

I 30

40I slice runber

587

424

(a) 124

FFe~1

5C

I

‘

I

-

-

seen from figs. 7a, b, that [Fe] is presumably controlled by the two different processes. At F > ~ [Fe] depends on both F and AC,; [Fe] decreases at increasing F values, and given F, decreases at increasing ACr values. This suggests that [Fe] is diffusion- controlled8). the diffusion occurring through a nearly-steady boundary layer against the interface (whose thickness c5 is expected to be a reciprocal function of F and to vary across the growth front as indicated by the iron distribution in fig. 3). At F > ~ [Fe] is little influenced by F. This suggests that [Fe] is no longer diffusion-controlled but rather kinetically-controlled at the crystal surface. In

C 0

stce

number

(b) Fig. 7. Average Fe variations on a linear relative scale (refer to the b—c region in fig. 3), versus the slice number (bottom) and the stirring parameter r (top). Rotation rates were 5 rpm (a) and 10 rpm (b). AC, was 0.034.

this situation and at a given temperature, [Fe] is indeed found to depend mostly on ACr; it can further be anticipated, assuming the iron segregation mechanism to be indicative of that of the growth mechanism, that at F > F0~~ the growth rate along the [100]axis, noted vi,, is diffusion-controlled, whereas at F > F0~~ it is kine-

results of further investigations of the iron content in tically controlled at the surface. In the latter case, v~, particular bands (selected because they were assumed should mostly be a function of ACr at a constant ternto be associated with a nearly steady-state) at AC,’-.~ perature. A precise experimental verification of this 0.034 are plotted in figs. 7a, b. The existence of an statement could not be carried out because of the inoptimal dimension d0~~ associated with a given rotaaccuracy of the measurements of vi,, but it was at least 2 tion to clearly appears. It was also found that the tod 0~~ observed for crystals grown at pH values —~4.5 and at product noted F0~~ was almost constant, as well as the low tapering angles (cc < 2) that v~,was nearly indepeniron segregation associated with it (as shown in table 2). dent of the stirring at high F values whereas it was Departures from a constant [Fe] value at F0~~ may be rapidly decreasing when F came below the cross-over ascribed partly to the fact that ACr very slowly in- ~ creased with the sequence of the experiments to = ~, A further complication arises at F F0~1,since then massive incorporation of iron inhibits corn4). For the sake of completeness, growth the study of 2 entrance of the iron in the Results of the stirring effect TABLE upon the pletely the evolution of F 0~1with ACr still has to be performed. prismatic growth front; the rotation rate is given in revolutions per minute However, on the basis of the above interpretation, the opt ‘.‘.“°opt opt 59Fe content value of the ratio AC,/5 attached to the cross-over from ~

number Slice

(rpm) co

(cm2) d 2

3 28 38

5 10 15

12.40 6.25 4.40

(cm22 rpm) = f’

..1

62 62.50 66.00

relative unit

the diffusion-controlled to the kinetically-controlled

100 70 80

process is expected to be little affected at a given ternperature by a change ofAC,. Thus, when AC, decreases, the rotation rate should be increased.

114

C. BELOUET, M. MONNIER AND J. C. VERPLANKE

For markedly rectangular (001) cross-sections of the crystals (a case which was not studied because of the nearly square cross-section of the crystal), th~stirring may differ for the growth facets, and the tod2 product

_____

is no longer expected to represent the stirring situation

for the two types of facets. However, it was found in other experiments not described here, that a flat prismatic growth front i.e. presenting a nearly homogeneous iron distribution could be obtained regardless of the shape of the cross-section (this can be well understood if for both facets F > F 0~~). Consequently, the necessity of using a reverse rotation rate system for the stirring of the crystal in order to provide an homogeneous9).iron across the growth front vanThisdistribution means a large simplification of the growth ishes apparatus. Another interesting result was that the iron segregation slightly differed (by at least a few percent) for the couples Of facets which were not equivalent in the crystal point-group symmetry 42m. Simultaneously, the average tapering angle cc corresponding to the outer 10 rpm iron band differed for each couple (6°and 7.5°), the highest value being associated with the highest iron content. The latter finding well agrees with the general observation that ccincreases with [Fe]4) (see also growth ghost section). Finally, it is remembered (i) that the large drift of the iron towards the crystal surface was ascribed to the occurrence of an electrostatic barrier at the solid—liquid interface and that (ii) the iron incorporation in the prismatic facets was responsible for the tapering of the crystals3~4). —

—

3 .3.

PYRAMIDAL SECTORS

The most typical contrasts exhibited by the autoradiographs are presented in figs. 8 to 11. Figs. 8a, b show a remarkable combination of all these contrasts. We note (i) the non-uniform iron distribution in different sectors and in a single sector (see also fig. 9a); (ii) two types of growth bands continuous across the growth front (fig. lOa) and discontinuous (fig. 1 la). As already mentioned above, the iron distribution will be presented in close relation with the contrasts observed in the X-ray topographs. —

(a) .

-

2 -r~

GB...

-

GB~

\

‘-.—

—

—

. -.

(b) Fig. 8. (a) Autoradiograph of slice 28 (50 ~im thick). The contrasts in the pyramidal sectors are explained in the diagramme in (b). In this diagramme, dotted lines indicate the position of the [1111 unions which are not revealed in (a). Arrows show the inclusions.

location lines have little or no influence on the local iron segregation. This result is consistent with the observation of the decay of stored pictures displayed by the Titus solid-state light-valve which uses D-KDP targets’ 0), In these experiments, the dislocation-rich area of the target does not show any modified decay, which indicates a normal impurity segregation.

3.3.1. Dislocations

3.3.2. Growth bands The generally accepted statement that growth bands

The dislocation-rich areas are not revealed in the autoradiographs (figs. l0a, b). This suggests that dis-

are due to fluctuations of the impurity content which, in turn, induce growth parameter fluctuations was

AUTORADIOGRAPHY AS A TOOL FOR STUDYING IRON SEGREGATION

115

(a) (a)

(b) Fig. 9. (a) Autoradiograph of slice 32 (50 fim thick). Observe the inhomogeneous distribution of the iron content. Bracket I delineates a region exhibiting an enhanced iron concentration. Its location in the growth sector (along a [111] union) and appearance match very well those of diffused strains as they appear in 3). Arrow H locates the position X-ray transmission of a parasitic growthtopographs ghost. (b) X-ray topograph of a neighbour slice (No. 34). The contrast along the (111] union has almost completely vanished after the parasitic growth ghost (arrow II) has occurred (bottom right). Diffused strains did not appear with the diffraction vector used for this topograph. Compare the occurrence of these defects with the diagramme in fig. 12.

(b) Fig. 10. (a) Autoradiograph of slice 40 (1 mm thick, contrasts are opposite with respect to those of the other autoradiograph), and (b) X-ray transmission topograph ofthe same slice. Observe I, a continuous growth band and II, the absence of contrast in the autoradiograph in a dislocation-rich area.

verified (see for example figs. 8a, b and figs. lOa, b), but the actual situation was found to be highly more complicated. Growth bands recognized as 59Fe bands .

in the present autoradlographs, may not simultane-

116

C. BELOUET, M. MONNIER AND I. C. VERPLANKE

ously develop in the four pyramidal sectors and are not necessarilyhomogeneous or even continuous across a single sector. The response ofthe iron content to changes of growth

-,

_______

conditions is illustrated in figs. 8a, b. The presence of inclusions (which generate veils on the macroscopic

if

(a)

(b)

Fig. 11. (a) Autoradiograph of slice 21 (1 mm thick, exposure time 3 months) which shows a discontinuous growth band in a single pyramidal sector. Arrows I delineate the growth band both in the autoradiograph and in the X-ray transmission topograph (b) (MoAgcc 1 200 reflection) of the same slice. Arrows II indicate a crack. Observe in (b) the fringe network and its location with respect to the growth band.

scale) in sector 4 only is consecutive to a large voluntary supersaturation change over a relatively short penod of time (—‘4 hr). In these experiments, AC, was abruptly dropped from 0.038 to about 0.020 and after a few hours reset at 0.038. During this short period of time, inclusions noted I in fig. 8b developed in sector 4 alone. this finally perturbation, maintamed Following at 0.038 and droppedAC~was to 0.033. At AC, = 0.038, two bands developed in sectors 3 and 4 only (GB,) in fig. 8b), whereas sectors 1 and 2 appeared to be unaffected. At the same time, the growth habit clearly showed up. At AC, = 0.033, all sectors exhi-

bited about the same iron content and simultaneously the trace of the growth habit vanished. That growth bands do not simultaneously occur in all sectors and further do not show a homogeneous iron content across a single growth front results from the interplay of at least three recognized phenomena, i.e.: (1) since4),the it iron segregation coefficient is smaller than unity increases with the growth rate of the sector, e.g. fig. 8a and fig. 1 la, but the growth rates of the different sectors may significantly differ under given growth conditions; (ii) the growth rate across a single sector may vary locally depending on the iron distribution in the

117

AUTORADIOGRAPHY AS A TOOL FOR STUDYING IRON SEGREGATION

associated prismatic sector; and (iii) ~heiron segregation and more generally the impurity segregation may be largely influenced, even at large distances along the growth axis, by preexisting strains in a facet. The two first items are discussed in the next section. The last one, because of its importance will be treated in more detail in a future work. In crystals grown from very pure mother liquors and at very low tapering angles (cc < 2), all these effects vanish, and very homogeneous growth bands simultaneously appear in each sector. An interesting finding concerning the origin of fringes previously observed in X-ray topographs was obtained from the study of discontinuous growth bands by both X-ray transmission topographs and autoradiographs (figs. 1 Ia, b). Besides the correlation between the techniques, fig. 1 lb shows successive fringe networks which are superimposed to the iron growth band and stretch at large distances from this band in a region of the sector which is obviously determined by the location of the band. The fringe spacing, when regular and measurable, was found to be about 54 jsm (MoKec,, radiation this topograph is not reproduced here). This result strongly suggests that these fringe networks are due to planar defects lying in the growth front since the corresponding theoretical interfringe is within 50 to 55 jim”). A preliminary interpretation of the occurrence of these defects far from the band might be that the strain induced by the band (the main component of its fault vector lies in the growth front along a [101] direction) is very progressively relaxed by the occurrence of planar faults. —

—

latter effect may be the result of a differentiated segregation in the 42m symmetry since direct “Fe titrations in neighbouring sectors exhibit different values. A direct consequence of this finding is that the overall irnpurity content in the mother liquor should be made as low as possible if homogeneous (001) slices are required.

3.3.3. Growth ghost The growth ghost, defined as the contrast which appears in the X-ray topographs at the union between sectors, can also be traced in the autoradiographs. More information on the origin of the growth ghost may be obtained by using double crystal X-ray topography12). However, the autoradiographs show that it is associated with significant changes of the iron content on either side of the union, as illustrated in figs. 8a, 9a, b, and lOa, b. It is found to appear also between neighbouring sectors grown at the same speed. The contrast is then very weak, but it can still be interpreted as

3.3.4. Diffused strains and parasitic growth ghost These defects, which were previously observed in X-ray topographs3), appear to originate from the interaction between neighbouring sectors along the [Ill] union. Diffused strains were ascribed to fluctuations of the impurity content across the growth front. The present study confirmed this statement as far as the iron segregation is concerned. Fig. 9a shows an example of a localized enhancement of the iron content intwo growth sectors (though the region delineated by arrow I in fig. 9a does not show up entirely in the particular X-ray topograph presented in fig. 9b, its occurrence is definitely suggested by the strong contrast at the [Ill] union, see also ref. 3). Generally, their occurrence could not be correlated with either the rotation direction or the facet size. Electroding experiments2’1 0) have shown that these defects also occur in non-tapered crystals grown from very pure solutions if growth parameters are made to fluctuate. Their geometry is not well defined, but they are systematically found to occur at the union between sectors and they lie in the fastest growing sector. Along the [111] union, [Fe] is always maximum whereas it decreases slowly across the growth front. The parasitic growth ghosts (fig. 9b) also require a particular study because (i) the regions they delimit with the growth ghost exhibit very different impurity contents (e.g. figs. 9a, b) and a lower or higher electrical resistivity as was found from electroding experiments’ 0), and (ii) they are very often present in the highly deuterated crystals (of interest for solid-state light-valves) regardless of the purity of the motherliquor (see also their effect on growth kinetics next section). These faults, too, are created at the union between neighbouring sectors, but they generally stretch in the sector having the lowest growth rate

resulting from a distortion of the lattice because of different iron contents on either side of the union. This

(fig. 9b). In non-deuterated crystals they rarely occur at intermediate tapering angles (cc = 2 to 6°)pro-

—

—

118

C. BELOUET, M. MONNIER AND J. C. VERPLANKE

vided growth conditions are regular, and they are never found in non-tapered crystals. When present, the sharpness and geometry of the contrast in the topographs depend on the difference of growth rate between the two sectors involved, and their occurrence is more probable when the iron content in the mother liquor increases. The autoradiographs show (fig. 9a) that they occur where [Fe] across the [111] union shows a rather large change (generally they accompany growth bands, figs. 9a, b). On the basis of these results, both types of defects appear to be associated with differences of: (i) growth rates and (ii) iron content in neighbouring sectors. Considering the lattice deformation introduced

ments for the detection of electrical resistivity inhomogeneity’ O) In practice, both these defects can be eliminated if (i) the iron content of the solution is low, (ii) crystals do not taper, and (iii) the growth is very

I

I

I

<

‘u45

~~7~’r ~ I

o.<~u16I c<’~10 ~~~i2rp;

PRISMATIC GROWTH Fig. 12. Schematic diagramme of defects as they appear at [111] unions in X-ray transmission topographs. Arrow I locates the diffused strains, Arrow II, the parasitic growth ghost. The dotted line indicates that the contrast referred to as growth ghost disappears once defect I has occurred.

by the iron3) (magneto-striction type), when a sector develops faster than its neighbour, strains develop in the growth front which may be expected to differ in the two sectors involved. In the fast-growing facet noted F (fig. 12), the strain at the union is due simply to the lateral misfit between the merging growth facets, whereas in the slow-growing facet noted S the distortion is more important. In this case indeed, in addition to the lateral misfit at the union, the spreading of the S facet onto the lattice of the F facet causes another type of strain to occur resulting of the different strain situation3) in the newly grown layers (S facet) and in the sub-layers (F facet). The lateral strain in the F facet can eventually be relaxed by an abnormal impurity segregation which should be highest at the union as was observed, whereas in the F facet larger strains should develop causing the lattice faults observed. it is also generally noted that the contrast at the [111] union decreases when a parasitic growth ghost has occurred(see fig. 9b, bottom right). This descriptive interpretation serves as a basic for more detailed studies which are being conducted using double crystal X-ray topography for strain mapping and electroding experi-

4 039

I I

321

323

I

325 3°K~1 1 10

T

Fig. 13. The growth rate ~ (noted v,) to relative molar supersaturation ratio versus reciprocal temperature. Note the large dependence of the growth rate upon the tapering angle a.

regular. In the case of highly deuterated crystals, similar conclusions can be drawn though even if the first item is fully satisfied the defects under study can still be present. This is ascribed to the hydrogen’3) which then behaves as a major impurity with a segregation coefficient largely exceeding unity, i.e. sensitive to growth rate changes. In addition, the a lattice parameter significantly varies with the hydrogen content; as a result, the role of the hydrogen in highly deuterated crystals is somewhat similar to that of iron for non-deuterated crystals. ~

GROWTH KINETICS

In a previous work4) the growth rate ofthe pyramidal sectors v, was found to be well represented, at least for slightly tapered crystals (cc < 4°),by the relation v

=

A (Ac/c) exp E/kT),

(1)

where A is a constant for a given mother liquor, Ac/c is the relative molar supersaturation, E is an activation energy of about 20 kcal mole~’and the other quantities have their usual meaning. In addition, v,/(Ac/c) was found to depend on the tapering angle, i.e. on the

119

AUTORADIOGRAPHY AS A TOOl. FOR STUDYING IRON SEGREGATION

eq ms1

~

I

I

I

autoradiographs (for evaluating the iron content in the prismatic growth front). Results are given in table 3. I

Furthermore, v~,was found to vary across a pyramidal sector which caused departures from flatness of the growth easily evidenced by the aspect of the growth bands in the X-ray topographs. This was particularly

~ B I~ 11

clear when large [Fe] variations developed across the associated (100) prismatic sector. At low tapering angles (cc <2°), other experiments showed that v,~,given a mother liquor, was not significantly dependent on cc, but non-crystallographically equivalent sectors still ex-

-

TABLE

C -8 0307 Fig. 14.

I

308

309

I

3.10

I

3.11 1/Tb3 ‘K4

3

The relative iron content in the prismatic sectors and the associated growthrate ofthe pyramidal appear on a horizontal line; on a same line, growth rates sectors are classed (from 1 to 4) by order ofdecreasing magnitude; finally, growth rates ofequivalent

The growth rate v

101 (noted v,) to relative molar supersaturation ratio versus reciprocal temperature. Note the sudden v, drop after B associated with the network of so-called parasitic growth ghosts (see X-ray topographs I prior to B and II after B).

iron content in the prismatic growth front (fig.con13) 4)]. Present experiments [see also Mullin et al.’ firmed the latter finding. In a narrow range of large values of the tapering angle (6 to 8°),v,~of each particular pyramidal sector was found to decrease at increasing [Fe] values in the associated prismatic sector. This correlation was established from X-ray topographs for evaluating the relative growth of the pyramidal sectors and micro-densitometer measurements from —

—

sectors (same a values) are separated a = 6 Fe [100] 189 208 206

v [101] 1 32

Fe [TOO] 200 199 201

208

2

199

Fe [010]

? ?

a = 7.5 v [011] Fe [OTO]

2 2

v

[Toll 2 21 1

v [Oil]

214

4

216 214

3 3

120

C. BELOUET, M. MONNIER AND J. C. VERPLANKE

hibited slightly different growth rates. However, at a given cc, the factor A in eq (1) was found to depend on the iron content in the mother liquor, A being relatively smaller at low iron contents, at least in the range 1 5 to 15 ppm If this effect was confirmed, it would imply a rather low growth rate from very pure solutions. Finally, it was found that v~,was strain dependent. The occurrence of parasitic growth ghosts, fig 14, generated in all sectors by severe supersaturation changes at relatively large tapering angles (cc 6.5°).cornpletely inhibited the growth, as shown in fig 14 Under

It is concluded that reproducible growth of perfect crystals can be obtained only if the conditions below are simultaneously satisfied, assunui~igthat good seeds are available (i) very pure starting material, (ii) optimal stirring and (in) very regular growth rate Itis then thought that the most pertinent growth methods to be selected are the transport15) or evaporation methods

which can operate at constant temperature and super-

saturation Such growth set-ups using the stirring systern already described are now being studied, especially

for the growth of highly deuterated crystals. Reports of this activity will be given in a near future

less severe conditions, the presence of these crystallographic defects in a single facet often results in a slower Acknowledgements growth rate of the facet. This circumstance is a visual The authors wish to thank Dr. J. M. Nieuwenhuizen indication to the crystal grower of the occurrence of a

for assisting with autoradiographs, M L Verheijke for

parasitic growth ghost in that facet.

his fruitful comments and J. G. de Brain for processing the slices.

4. Discussion On the basis of these preliminary results, the autoradiography technique proves to be a powerful tool for -

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investigating the relationship between the iron segre-

References 1) G. Marie J. Donjon, R. Le Pape and B. Monod, Onde Electrique 54 (1974) 121.

gation and the growth parameters as well as the role of the iron in generating crystallographic defects, when combined with the X-ray topography technique. The role of the iron segregation in the generation of crys-

2) C. J. Salvo, Trans. IEEE ED-18 (1971) 748.

tallographic defects, including the so-called parasitic

89. 6) K. Niimori, T. Kawano, K. Hukuda and N. Fujita, J. Phys. Soc. Japan 28 (1970) 801.

growth ghost, is very important since it influences both the perfection of the crystal and its growth kinetics. It was already recognized that a prerequisite for obtain~

ing defect-free crystals was that crystals do not taper ~ The present work shows that such a condition can be achieved only if the stirring of the solution past the crystal is well controlled regardless of the iron content

of the mother liquor. In addition, the expected dependence of the stirring on the supersaturation still corn-

plicates the situation, especially at low supersaturation values.

3) C. Belouet, E. Dunia and J. F. Petroff, J. Crystal Growth 4) C. Belouet,Acta Electron. 16 (1973) 339. 5) R. J. Davey and J. W. Mullin, J. Crystal Growth 23 (1974)

7) J.

W.

Mullin and A. Amatavivadhana, J. App!. Chem. 17

(1967) 151. 8) J. C. Brice, The Growth of Crystals from Liquids (NorthHolland, Amsterdam, 1973). 9) J. L. Torgesen, A. T. Horton and C. P. Saylor, 5. Res. NBS 67C (1963) 1. 10) C. Belouet and M. Monnier, Acta Electron. 18 (1975). 11) A. Authier, Phys. Status Solidi 27 (1968) 77. 12) W. Stacy, M. Monnier and C. Belouet, to be published. 13) C. Belouet, R. Crouzier and M. Monnier, to be published. 14) 1. W. Mullin, A. Amatavivadhana and M. Chakraborty, ~. App!. Chem. 20 (1970) 153. 15) V. F. Parvov, Soviet Phys.-Cryst. 12 (1967) 324.