The optical character of the orthorhombic principal planes of YBa₂Cu₃O_7-d in visible reflected light

Article

Reference

The optical character of the orthorhombic principal planes of YBa

₂

Cu

₃

O

_7-d

in visible reflected light

RABE, Heiko, et al.

RABE, Heiko, et al . The optical character of the orthorhombic principal planes of YBa

₂

Cu

₃

O

_7-d

in visible reflected light. Scientific and Technical Information , 1993, vol. 10, no. 5, p. 174-182

Available at:

http://archive-ouverte.unige.ch/unige:35799

Disclaimer: layout of this document may differ from the published version.

1 / 1

The optical Character of the Orthorhombic Principal Planes of YBa ₂ Cu ₃ 0 _{7_ 8} in visible Reflected Light

by H. Rabe, J.-P. Rivera, E. Burkhardt and H. Schmid

Universite de Geneve, Oepartement de Chimie Minerale, Analytique et Appliquee Geneve/Switzerland

To Max Berek, pioneer of ellipsometry by reflected polarized-light microscopy

Introduction

A nearly rectangular crystal plate of twinned, ortho- rhombic Y BCO with mostly idiomorphic low index growth faces of (00 I )-pinacoids. (I 00)-and (0 I 0)-prisms wa. prepared for optical investigation in the vi ible, polarized and reflected light. It belongs to, eries or typical tiny plates of orthorhombic crystals which were found on the surface of a solidified flux and rhus had apparently formed under reduced stress condition.

rt

lOne of these YBCO crystals comained a relatively large triangular single domain, which has been studied in det<til in this work (Fig. I a). The cry tal plate was mounted on a spindle stage of a polarized-light microscope (Leitz ORTHO- PLAN-POL) to allow a precise positjoning of the object.

The optical oriemation of the domain depends on the reference system of the microscope. For the following experiments the uniradial reflectivities or the crystal R; •.

Rt>.R<arealways aligned parallel to the diagonals I and 2, which divide the cro. sed polars by 45° (Fig. lb). ln accordance with the orthorhombic symmetry R,, Rb and Rca.re in .line with the crystallographic axis a. b, and c.

The optical properties of the morphologically dominating (001) face are described elsewhere 1161 and there eems evidence that almost R0 > R •. As for the optical symmetry planes on (I 00) and (0 I 0) the discussion of anisotropy in the visible does not go into detail and informations about elliptical vibration constants are scarcely added. The published values need to be completed, but till now it is djfficult to get crystal faces which w·e useful for optical measurements in the vi. ible. Relics of flux and mostly unknown microinhomogeneities often disturb specular reflection on (I 00)-and (0 I 0)-prism [aces. That is why an optical coupling of immersion-oil between crystal surface and objective of the micro. cope was adopted to diminish those effects. Immersion-oil improves bire1lectance and anisotropy contrast at crossed polars and suppresses the innuence of scauering and absorption in tran parem layers of flux and hydrates. Thi. demonstrates the phase

differe·nce St.~ between R,, Rb on the (00 I )-face, which depends clear! y from the refractive index n₀ of the optical coupling m.edium (normally air or, in this case. immer- sion-oil with n

=

1.52) [201. 1221.

Optical criterion of single-and polydomains A measurement describing the optical properties of an ani otropic crystal face must ensure that there is no superpo ·ing influence of mimetic twinning or other mis- guiding intergrowth. Furthermore, when executing re- flectivity and ellipsometric measurements by means of a

polarized-light microscope, a series of particular pre- cautions concerning parasitic images, glare erfects etc. (see at ref. I 0. chapter 12) has to be respected. In case 6f the above mentioned single domain (Fig. I a) it has been insmed both on (00 1 )-, (0 10)-and (I 00)-faces. that the field stop of the microphotorneter (Leitz MPV I), wa<:>

placed far enough away from differently oriented do- mains and flux nodules. Colour plate 2 a, band Figure 2 a, b show the (00 I)-face of the triangular single domain of Figure I a at a higher magnification with some more details. The inglc domain is limited by (1001-waJls traversing the whole thickne s of the crystal and by the right angled edges along 11001 and [010], forming a nearly isosceles triangle in the (00 I )-plane. Inserting the Laves- Ernst-compensator creates uniform compensation co- lours as a sign of optical homogeneity [211: i.e. for Z//P, sgn(cr) = -1 we find a typical orange-yell.ow subtraction colour over the whole triangle. Z//P means: in start po- sition the angle 0 of the Lctves-Ernsr-compensator is zero and the higher index. n₁ofthe A-plate (first-order red) runs parallel to Lhe vibration direction of the po.larizer P. For more details see at ref. [7] and [8].

From the justructions for use of the Utl'es-Ernst-com- pensator

171,

18]. the sign of the phase difference

O u

=

o,.

8₂• expressed by sgn (KcK₁₎ with K = -arctan(S) and its correlation with the crystallographic axis is determined:

500)Jm

ftg 1 a Crystal piau~ of orthorhombic YBCO: objectiVe 3.2x :N A 0.12/alf· crossed polaruers (N I. bottom right hand. marked b'('f' mangle of a smg/e domam retlecung wtth a maximum oTtmenslly m diagonal postttOtl. R Ill R,/12. Poll/{110}.

e.g. for the (a. b)- plane K₁<K₁ and K .. <K_11• The indices I and 2 refer to the fixed reference system of the microscope (see colour platt! I and 2). The observed correspondence of the trace,<, of the domain walls on the (00 I) and (00 I) surrnce together with the narrow transition width ofT, of crystals of the same batch indicates that the platelet i,<, emircly orthorhombic and rather homogeneous through- out the thickness [17].

A quantitative characterisation of the inglc domain area· appearing optically homogeneous consists in the mea- :.urement of orientation and form of the vibration cllip:.e

30JJm

Crystal Single Domains

2

Ftg 1 b. Onenrauon of the umradial reflectwlttes R, R. of tile mangle smgle domam in ftgure Ia. corresponding to rile reference svsrem of polanter P. analyter A and diagonals I 2 01 the microscope

ol'the renected polarized light. The polarizers are eros ed at monochromatic light and the uniradial reflcctivitie R₁₁•

Rn are set in the diagonal position as shown in Figure 2a.

Then the phase-difference 8,, ~ i cancelled out by means of a tilting compensator (here: a plate of MgF₂• 4 orders.

n.₁ //2. Leica-Wetzlar. Germany). Moving the analyzer from the crossed posirion (cp.,

=

^{90° = N+) by ~cp,.,. rhe}

linearly polarized vibration extinguishes. the ingle do- main area becomes dark and fades away in the isoLropic background (Fig. 2b).

Figure 3 ·how the corresponding vibration ellipse and

f1g. 2a.IJ. Smgle liomam of fig 1 a ar htgl1er magniftcarion and same area as shown i11 colour plate 2b: objec/lve. 50x/N.A

=

0 85/0!I·immerslon, monochromatiC light. A.= 480 nm

la Crossed polartlers (N' 1: no cornpel)saror 111sarted. R,. R" m diagonal position. all domams on (00 I) show a max1mum of mtensity corrJParable to colour plare 7 a

2b.ldem Fig. 2a, bllt tiltmg compensator mserted; tho elltpt1cal vibratton IS converted intoali11earone. wluch is extmgUishedaltormovmg 1/leanaly;er·angle<p, from N' (<p,,

=90•) to<p, = 97°(see Fig. 3).

175

Fig. 3: Orientation of tile vtbration elltpse tn rile single domain of F1g. 2a.

the optical reference system of the microscope:

The ratio of the sides of the rectangle circumscribing the vibration ell ipse corresponds to the ratio of the square root of the uniradial reflectivities "'R/ R₁ (compare also the vibration ellipse::. of Figure 9a. 9b and 13). The para- meters of the vibration ellipse refer to Berek's fundamen- tal experiments of microellipsometry from 1937 [J 9]: The azimuth 11 between the plane of polarizer P and the semi- majors axi of the vibration ellipse; the ellipticity 0, where tan 0 = b/a;

x

=arctan "'R/ R₁ and ~q>A: rotation of the analyzer [rom Lhe posiLion of crossed polarizer (N') to the position of extinction of the linearly polarized vibration, obtained after compensation.

Anisotropy of (100)-and (010)-faces

As a consequence ofrhe usually plate like habit ofYBCO crystals, the pseudotetragonal prism faces ( 1 00) and (0 l 0) are rather nan·ow grown along [00 ll By mounting the crystal on a spindle stage, accurate perpendicular specular rellection was achieved by rotating the crystal around [100]-and [010]-zones. A zone stands for a direction of the cutting edge between two crystal faces. whose terms are enclosed by brackets like !uvw!. The prism faces usually show a imple domain pattern: mostly pru·allel stripes of alternately changing (a.c) = (0 I 0)-and (b,c) = ( l 00)-domains [21, [6j, !9lln case or a very high density of [J 10}-walb d1e stripes are not resolved and a single domain is mimicked. Measurement of reflectivity on these domains are difficult to perform, especially in air, because .impurities li.ke flux nodules, which prevem an undisturbed renection from the crystal surface, seem to stick more frequently to ( l 00)- and (0 I 0)- than on (00 1 )- faces. lmensiries of the reflected light by adjusting rhe crystallographic axis a,c and b.c successively parallel to

the polarizer are only given in arbitrary units [3].

The use of immersion-oi I as a coupling medium between crystal and objective diminishes the influence or surface impurities on the rellectance of the crystal face. which is given by the structure and chemical composition or YBCO. Figure 4 hows the reflecrivity in o/c as a function

Fig 4 Reflectivity in %as a functwn of wavelength calibrated by means of a SIC· and a glass prism·

standard (Leica Werzlar).

curves I and 2. measured m air. curves 3-15 measured in tmmersion·od mdices a b, c refer to the umradtaf reflecuvities parallel {I 00}.

{010] and {001/ respective- ly; curve I: RtfwJ. curve 2:

RjaJr). curve 3-6. R,(oJI}.

curve 7-10: Rrfoil}, curve 11-15 Rjo1l}.

12-

IOJ Rb - - -··(1)

~ 1 a ~·(2)

c: Ra

~ 8 ... ....,.·. -···- · - · · - · --(3)

>- , / I ..--(7)

.-:: 61

f ,-·

.;""·-Rc- · -·- -.,....:-(4)(8)

> •

E ....

^~

...

^===--r9l

=

o

.,...,.. ----

...-__ _

. ·-

··-·:;...r'.

-

~..-; ~.1-(51 ~ r

E

4 1' ::-:- - •-

;f::--r; ^{- sJ}

Q; ~ ~-----_:-R :.-_.,... _....-(10)

~ ₂

l ...

^--~ _{R c;} ^{.J bl} _: ^,..₁₁₌ ^-- _I ^-111),(12) ₍₁₃₁

o• :::::(14)

1-...--~~-.---~.----,--(IS)

436 480 542 589 643

A[nm]

of wavelength, calibrated by means of a SIC- and a glass- prism standard (Leica Wetzlar). Curve::. l and 2 represent the measurements in air. curves 3-15 the measurements in immersion-oi I. Reliable re1lectivities ofR, are only avail- able in oil as mentioned before. The curves refer to approximate values. because even on a single face a great scattering of reflectivity values is found. Due ro layers of hydrates and experimental problems, so called "glare- effects"of parasitic. scatLered 1 ight [I 0

J.

the precision of lhi method is restricted here to 2-3% only. In spite of these restrictions we can say that R< > Rn> R,, where R₁^, and Rccome closer to one another when passing from blue to red. R. and R, practically show no dispersion in the visible, whibt Rb increases from blue to red. as observed already earlier !4!. Contrary to the measurement of abso- lute values, the ratio of the uniradial reflectivities R/ R₁ are more reproducible.

Figures 5 and 6 show the ratio R/ R1, determined QY photomultiplier current. The measurements on ( l 00) and (0 10) are only made in immersion-oil (Fig. 5). the mea ·u- rements on (00 I) enable a comparison of Rt!Ra, deter- mined in air and oil (Pig. 6). The enh<ulcemem of RJR., between blue and red after changing the coupling medium from air to oil points to the increasing bircflcctance in immersion-oil:

RJR:,on (0.10)> R1/R. on (00 I)> RJR~>on (100). RJR.and R,/R,, increase. RJR₀ decreases from blue to red. Compared with immersion-oil, these tendencies are less noliceable in air.

Further informations are given at eros ed polars by use ol' the Laves-Emst-compensator (see colour plate la-f and 2a,b). In colour plate Ja-r the ( J 00)- and (0 1 0)-prism faces are folded along the [0 1 0]-and [I 00 ]-zone into the plane oft he (00 1 )-pinacoid. lf no com pen. at or modulates t.he intensjties of twin domains on (001 ). the symmetry of twinning leads to equicoloured stripes // { 110}-walls (colour plate I a). By following the traces of the

f

II 0}- walls from the (001)- to the ( 100)- and (010)-facets. we observe a remarkable contrast between ( 1 00)- and (0 I 0)- clomains (colour plate I c):

The (0 I 0)

=

(a,c)-domains appear very dark for any cry tal orientation at crossed polar .. Particularly when

Crystal Single Domains

0 5 ^rr.·

q ~

⁶

~

_cr

- 1

^{... n!} _·~ ^"'

*~

"' _{~ }4} ^-~ 3 p \1)

~¹¹¹ (911101 0

~ ~

~ u

~~1n1

^~ e

~ ~ Z-

: : ; : ;'141

0 2

, J.si I

~---~;,;~~gg~(l51 ^-o

0 ~

-5 ⁰

* ^{< \\\}

^{c ::0 1 01( - t 4 )}

~ ' l

'? ^{p ' cal 0 ~ 0}

^---·

!:! ₄^I _{36 480} ^I _542-^I ₅₈₉ ^I ₆₄₃ ' 436 480 542. ~ Gq3

A-[nm] t.{nfll]

Fig. 5 and 6 Ratto of umradtal reflecrivtrtes R .JR .. (lererrnmed by phoromuluplter currenr 5·

measurements in oil. curve 1-4 R IR .. on iO I OJ. curve 5-8 RJR, on (700}. curve 9--11 R.IR. on (001/. 6 comparison of Rt!R, derermined m air (curve 41 and moil (curve 1-3) on (001), where R,l!R and RJ!R,.

ljJ 1 (deg) 0 10 2.0 "30 40 40 30 20 10 0 s

b,C 45 O,C

Ftg 7 lntenstly of ret!ecred light as a tunc/ton of rhe rotat10n angle 'If~ of the crysraf on the mtcroscope stage for differe/lt wavelengllls. objective: 50x/NA = 0.85/oil·nnmorswn; crossed polarizers I <!I"= 90•= N· ). compaoson between (100} = (b.c}- and (0/0)=(a,c)-faces. Measured pomts for w,= 45° only, cominuous curves are calcufilled J11e great cJrfference of intenstties between adjacent domams gwes tile wsual!llus,on, that (0 10) be/1aves ISatropJcal/y

c//2. c//2.

b//1 0//1

reviewed in air these domains seem to be nearly isotropic.

where as the ^(I 00)

=

(h.c)-domains are very bright in the diagonal position and show a good extinction in the normal position. The behaviour of the (01 0)-domains bas been interpreted as quasi-isotropic f2], [61. However. the photometric measurements with crossed polars of the present study (Fig. 7) how anisotropic reflectance on both (I 00)- and (0 I 0)-domains in i mmersion-oi I. The visually observed isotropic behaviour of (0 I 0) is the result or a phy. iological illusion [IIJ, due to the high intensity ratio L,₁"11

/l

11ll 01 of light tran mined through the analyzer. The weak intensity of (0 I 0)-reflectance follows approximately a cos²(\j!.,)-law (Fig. 7), where \j!~, repre- sents the angle of the object-stage, and simulates an isotropy next to the strong reflectance of Lhe adjoining (I 00)-domains.

The LctFes-Emst-compensation as shown in plate lb, ld and I e can be explained as follows:

Plate lb: if Z//P and sgn(o')

=

-1 (cr

=

-45°¹ ident cr

=

+45°²), lbe domain on (00 I) show altematively ''blue"

addition and '·yellow'' subtraction colours l7], L9]. Plate I d: When turning the crystal for 90° around a [I 001- or [010[-zone, tJ1e (b.c)-domains on (100) show similar

"blue·· addition, whereas the (a,c)-domains on (0 I 0) show a '·reddish'' subtraction colour.

Plate le: if Z/!P and sgn(cr)

=

^{+l(cr = +45°1 ident cr =}

+315°²), the compensation colour of the (b.c)-domains change from "blue'' Lo "yellow··. Comparing the com-

pensation colour of (I 00)-, (0 1 0)-and (001 )-domain!> the change of colour on the (0 I 0)

=

(a.c)-clomains is difficult to perceive with the bare eye, but can be proved photo- metrically. The anisotropy is weak and agrees wirh the

mall phase difference of (0 I 0) in Figure 12a. When the Laves-Enzst-compensatorturns tocr=+45°.lhecolours of compensation on crystal-facets witJ1 low pha e-diJferen- ce agree with those of a Lambda-retarder (first-order red) [ 15].

El/ipsometric results

Additional ellipsometric measurements have been made to control Ll1e observed and photographical.ly registered differences between ferroelastic domains. Reflected po- larized light is characterised by size and orientation of a vibration ellipse relative to the fixed ystem of the micro- , cope (polarizers and their two bisects I and 2). Suitable domains giving reliable ellipsometric results must be selected by aid of the LaPes-Emst-compensator. The appearing colour of compen ation verifies where the conditions of optical homogeneity are realised.

As an example, two adjacent (100)-and (010)-domains

rt'fi'ti'Jtrrs H.\lt'IH for cr (U'C'III'tllllr.: to ,,~,~ t•owll.\ prnl!l~t· (nt•gatt~'t.'), I{,., of lilt~

C<Jmpl'nsaior UtnJs clocku·ise (t:omue,·~clocku·t.'i('}

! IUJrnmlt:-t,d n1en:mce f\'Sr£'11L' f'Otmtrtu~;:ativc (posit ire). ij Uyo[tht' < ampNt.'ili/OrtunH dnd .. :wl.w! (r'Oltltler·clock\\ is~ I

1

-

77

1 b. scale for all f•gures. ~

PlaTe Ia to 11. nearly equidistonr Widths of

I

sr11pe domams.

1c.

1e. Loves- Ernst- comp.

,/~r.;<;...:<--=--.--0

"'<""&'~---::-b

r-'--~M--0 r-"T~~-b

Plate lc to If domams on (100)- and (010)-prism faces;

1d.

1f.

The fl 00}-and (01 OJ-planes have been folded mto the (001 }-plarre. where the enclosed Cf'/Stal edge follows a/tematefy the a- and b-axis of tile domams The excel/em comc1dence of the {110}-domam walls on both (001/ and (100} respectively (010) emphasises the uaversmg character of the ferroefasttc twmnmg.(

Plate le: idem plate /d. but noww1th theLaves-Ernsr-compensaro1 wrningclockwise lsgn(a}= +I. (a= 315~}. both domams change tile" colour of compensauon (1 00) from

"blue addition· to "yellow substracuon", (010) non perceptible with the bare eye

2o

~g ~

I

^Ro,b

Plate Ia. lb:domamson(OOI}·Pif'IBCOJdS.

Plate Ia, I c. no compensator tire symmetry of crossed polars slwws onlv eqUireflectmg domams on (00 I J in plate I a ;usc as m figure 2a, being separated by the dark reflecting domam walls Contraf'/ to th1s result lhe (100}-and (010}-domams generate m1ense comrast as shown 111 pla1e 1 c. on (I 00) With bnght and on (0 I 0) wllh low reflect1on Plate I b, I d. 1dem plate I a, I c. but now w1th Laves-Emst-compensator mserred; Z"ll Polarizer, sgn(cr) ~ ·1 (lhe 'A.-plate turns am,.

clockwise, cr = +45u}. the colours of compen- sauon are descnbed as follows. (001)-pma- coid (plate 1 b). che (a. b)-domams show "blue additwn· if R.lll and R,/!2 and "yellow subtractwn",lf R,/12 and R.!/1 (100)- and (010}-prrsm faces (plaie ld)" tile (b.c}-do- mams show "blue add11ion if R. 1!2 and RJ/1 and the (a,c)-domams show a "reddish subtraction",ifR,//2andR/II 'Zdofinedac

/81" 1rf olche 'A.-plaie

Plate If idem plate J e. but msteadof the Laves-Ems/-a Le11zciltmg-compensator rype B. IS mserted. whose fr( varies/12 as a functron of the tiltrng angle. The stage of the microscope has been wmed by 90" m order to obtain the "keyboard" pattem of phase shifted compensation colours Now the 551 nm-isochromacic curve moves II c-axis of the crystal plate Funller deta11s see f1gures 72 and 13

All photomicrographs shown 1n the colour plates I a to 1 f and 2a, 2b Polaozed-/1ght lnJcroscope (LeitZ ORTHOPLAN-POLJ. objecuve 50x!N A = 0,85/oi/-Jmmersion.

crossed polaozers (q>. = 90"= N'}. unrrad1al reflectivities R, (i =a, b. c) m diagonal posrtrons parallel 1 and 2 of t11e m1croscope reference system

Plate 2a and 2b Smgle domam area of a (001 }·pmacoid (plaie 2a} and 11s OPfiDSI/e s1de (OO]}(plate 2b). the Laves-Ernst-compensator is msertelf on both s1des Z!!P. sgn(a) =-1 (rrt of tf1o /,-plate rums anti-clockwise ro cr = +30°}, both single domam areas shows a

"yellow subtraction· colour. The companson

of the(OOI /-and (00 n-pmacoJd demonstrates perfect correspondence of tile domam walls on both s1des of the Cf'/Stal The edge and vertices of the single domam form a tnangu- lar prism. lhe umlorm "yellow subrraccion·

colour of which proves optical homogeneav.

The large smg/e domain prea of colour plate 2b is also shown in f1gure 2a,b Ill comrast of monochromatiC l1ght

Remark:

colour p/are 2a and 2b had to be composed or three phocograp!Js. Thelf different dept/Is of colours (saturation of "yellow subtraction"}

espec1ally on place 2b rs due to automated development of colour ponts

are measured at monochromatic light (Fig. 8a and 8b).

The corresponding vibration ellipses in Figures 9a and 9b explain the different behaviour of compensation and extinction

on

(100) and (010). The light, which i re- flected from (0 I 0) practically does not need a com- pensator to be extinguished. because the ellipticity is very small and the ellipse strongly elongated (Fig. 9a). Con- trary to the (01 0)-, the (1 00)-domain does not extinguish without compensation of its phase difference (Fig. 9b).

The vibration ellipse of the rel'lected light can be mea- sured following the rules and abbreviations of Berek [ 19].

If the phase-difference

8d Fig.

12a. as measured with a tilting compensator) and the angle ~<pA of lhe rotating analyzer comply with the conditions of null-ellipsometry [ 12], all further parameters as the azimuth 11 (fig. 12b), the ellipticity 8 (Fig. 12c), Lhe "characteristic angle 1:" (Fig.

12d) and the ratio of the uniradiaJ reflectivities R/R₁ (Fig.

I 0 and II) are calculated.

The phase-difference 81.2 increases from blue to red and the values in oil are significantly greater than in air [5J.

The measurements on (00 I) enable a comparison ofR₁/R •.

which are determined both in air and oil as well by photometric and ellipsomet1ic methods (Fig. 6 and II).

The curves are similar concerning the dependence on the wavelength, but the values of the ratio Ri R1, calculated from ellipsometric measurements, arc greater than those which are directly measured by photomultiplier current.

On (0 1 0) the curve 2 and 3 differ remarkably from each other, when measured at different points on the same prism face of the crystal plate.

The azimuth 11 is tl'Ongly related to the biretlectance and ratio R2/R1 and particularly well distinguishable in im- mersion-oil (Fig. 12b): 11(0 I 0)>11(100), whereby the dif- ference increases from blue to red. 11( 1 00) decreases from blue (==l 0°) to values <5° in the red. i.e.

R c

(red) ap- proaches Rt, (red) as shown in Figure 4. The resulting vibration ellip e looks very. imilar to those oftransmilled light (Fig. 13): a remarkably strong ellipticity, the half- axis of which tend to lie pru·aiJel P respectively A (11== 0).

is different from all experience of ore-microscopy in reflected light as tabulated in

I

13]. The colours of com- pensation due to bire!lectance may be confused with those or transrniued light. if a Lambda-plate (first-order red=

t ^t

Crystal Single Domains

551 nm) is used for phase-shifting

I

14]. But compared with opaque minerals the extremely large e.llipticity of YBCO is primarily caused by the dispersi.on of absorp- tion.

The characteristic angle 1: (Fig. 12d) proves to be a sensitive test for orthorhombic symmetry.

rr

the three differently oriented principal planes of an anisotropic crystal show obviou ly different vaJues of 't, then an uniaxial symmetry of the repre entation ovaloid of the reflected light can be excluded.

The phase shift between ( 1 00)-and (0 I 0)-domai ns can be directly seen, if a tilting compensator is inserted which cause a continuous phase shirt within the object field. In white light a ·'keyboard·· of coloured domains (colour plate If) and in monochromatic light nearly equidistant stripes of alternating bright and dark (extinguished (I 00)- and (010)-domnins are visible (Fig. 14a).

The domain pattern in monochromatic light can be ex-

I

plained by Figure 14b, those in white light (colour plate lf) schematically in Figure 15: if the 551 om-isochroma- tic curve ("first-order red .. ) of the lilting compensator passes below field diagonal 1 (area Il). then the (0 10)- domain with it ve1y low phase difference nearly how the same colour of compensation. Following the ascend- ing path ctifference of the lilting compensator from area II to area 1 the colour of compensation changes from "first- order red'' to "'blue·· adclitjon similar to Michel-Levy's colour table for transmitted light. Contrary to this the adjoining (100)-domain reduces the phase shift of the tilting compensator by irs negative phase difference of about-70 nm. Hence the domain colour in areal changes from '·blue"= 620 nm to ·'first-order red" and in area II from "first-order red" to "orange'·= 480 nm. The colour of area II following the 551 nm-isochromatic curve of the tilting compensator is imilar to that of the LaPes-Emst- compensator in colour plate I e. whose actual path difference equaL 562 nm (manufactured by Halle in Berlin, Germany).

Using monochromatic light (Fig. 14b), all domains with ''first-order red" are extinguished. A a consequence o.f the different phase shifts in (I 00)- and (0 I 0)-clomains extinction occurs alternately in area J for ( 1 00)- and in area 11 for (010)-domains.

t

^{I 30JJm I}

Fig Ba,b. (100)· and (010)-stnpe domams m extmc11on posirwns

Ba extmction of "black· (010)-stripes, Bb. exvnction of -black· (I 00)-stripes, objective. 50X/N.A. : 0,85/oil-immersion, monochromatic light {A

=

^{480 nm).}

- - - - - - -

179

Rg 9a

_ ,,

4 36 480 542 589

J\[nml

Ftg 10 r.ompanson of RIR, for (001 }, (0 10) and (I 00) in oil, curve I R,!IR;. R,/!R,, curve 2.3. RJ/R7, RJ!R,, curve 4, 5. RJ!R,. R,,//ff,.

Fig 12a to 12d Phasedifferenceo ,(a). azimuthfl (b).

e/lipttcttye lc!andcharacteristtcanglet (d), measured moil, on(OO I): R.,!/R .. R.!IR_1; on ( 1 00}: R,/!R,, R, 1/R,:

on 1010}: RJ/R,., R,I!R,, In Ftgs 12a anrl 12c some curves are dolled tor better readabilicy.

d> 80

Q)

'0

.s 60

<0

Q) 40

(.) c

£

~ ²⁰ '6

I

Q) 0

"'

^a

"' "

.<::

a.

-20

436 460 542 569 643

A.(nmJ

Fig 12<!

F1g. 9a

·(I)

-:;.1

436 480 542. 589 64·3

J\[nm)

F1g. II comparison of the ratio R/R,. for measurements m air(curve 2} and oil(curve 1) on (00 I). computed from rand t.\j)A as in figure 10.

Rg. 12b

436 480 542 589 643

A(nml

Ftg. 9a.b: Figure 9a corresponds with Rg. Ba. n1e elongated vibration ellipse I= low elliPtiCity) of (a. c) =

(010) enables practrcally extinctton 011 rurning the ana- lyzer alone Without retardattan by a compensator Rgu- re 9b corresponds with Fig. Bb In contrast to 10 I 0) the wtbratwn elltpse of (b,c)

=

(100) enables no extmct1on without compensation of t11e phase difference (0, . = 35D).

Fig 7 0 to 12. El/ipsomerric parameters cafculaced fiorn zhe measured path difference rand analyzer angle tl.tf!~

for conduions of null·ellipsometry /12/.

F1g. 10. 11: Calculated ratioofumradial refleciiVilies R/

R, versus wavelength

d>

Q) 'U -~

0 _...

.D

c ⁴⁰

0

~ ₃₀

0

co II

~ 20 o>

c a

~ 10

~ g

Q) 436 460 542 569 643

A[nm]

Fig 12c

d>

Q)

'0

!: ¹⁰⁰ _Oir

1- eo

Q)

0, c a ⁶⁰

(.)

+=

"'

c ⁴⁰ 2

(.) 20

~ a

.<::

<.J

436 480 542 569 6:43

A.[nm]

Fig. 72d

F!g. 13 Vibratton elltpse of (I 00}

=

(b,c)·plane. "A = 643 nm in oil. exrremely SI/ong ellipticity

r e

= 33"1 and phase dtfference (OJ. =

65"}, bur low btreflectance and az1muth (q<5"1 exp- -::::::3aJb.,_:~-~~==:::=i::lKin p.d'. lams a compensarwn ef-

.,cp fecc Stmt'lar co condicwns in

lransmJI!ed ligltr /

2

Conclusions

SuperconcluctiJ1g crystals ofYBCO are usually composed of polysynthetic lamella twin domains. The polarized- light microscope enable in situ studies of the domain wall dynamic!> in order to visualise the ferroclastic wall move- ments 124J. Mechanical detwinning performed under vi- sual control of polari:.:ing micro copy reveals a suitable method for transfom1ing polydomains into single domain crystals [5][16.1 [ 18]. Single domain following the real symmetry of the orthorhombic lattice structure are found out from polydomain material by means of the Lal"es- Ernsl-compen. ator. They are characterised by homo- geneOu!> colours of compen. ation and can be isolated from polydomains for further investigations. The pheno- menon of ··puzzle-domains·· as described elsewhere 19J [25] can easily be distinguished from the true ortho- rhombic ferroelastic domains by different compensation methods. In any case an oil-immersed coupling between sample and objective lens enhances the image contra L. It diminishes the influence of light scattering flux residuals on the crystal surface where the increasing refractive index of the coupling medium (n₀⁾ enhance~ rhe saturation of compen~ation col.ours. This can be explained by the phase term K =arctan (2n₀kln²+k²+n₀^), which changes its value by an increasing ⁿ0 in such ^a way that the resulting colour coordinates are shifted to higher values of colour saturation 121 ]. Measurements of ani otropic properti.es must ensure that there exists no kind of mimetic twinning, the external symmetry of which is higher than that of a single domain or twin component 123]. Otherwise the result of an optical investigation may be inconsistent with the structural status of the crystal. For example, a high density of { 110}-walls masks the real triaxial symmetry (compare colour plate 2a.b: there exist orne areas show- ing the ·'first-order red'", where the { l I 0 }-walls remain under the limit of optical resolution). The polmized-light microscope and its different mode. of application like micro-ellipsometry or Differential Interference Contrast or Nomarski 1171 give us a quick answer concerning these problems of the real crystal symmetry.

Crystal Single Domains

---

A

b

a

Fig. 14· A "keyboard'" of bngltt and dark domains m monocllromalic light (A= 551 nm}

due ro dtfferent phase slufts m adjacent (100}-and (010/-domams. /4a. m1crophoro:

ObJeCtive. 50X/N A. =0,85/0f!.tmmersion. LE/Tltiltmgcompensator. typeBwtthMgF.-- p!EJte. d= 1.52mm, ayi/2. 14b: Schematic i/lusl!auon of the domam-keyboard in figUJe

14a

f1J blue

1m

red1.0.

llli!l

^orange

A

l beyond field OioQCI!l<ll1 rM;F, ·62ollln

n: bolo-.. l~<ld diaoonal 1 r~r.·5514'1m

Fig. 15: Scttematlcrepresentation of the colour sh1h due to compensation on (1 00)· and (0 1 0)-damams as exempldted m colour plate If (see text).

---~

181

Abstract

The uniradial renecti\'ities¹ R, (i = a. b. c) or an ortho- rhombic single domain or YBa₁Cu₁0H

=

(YBCO) and their properties in polarized light are reviewed. Wherea.

the (00 1 )-pinacoidl> or YBCO single crystal~ are thought to be best known. there o;;eems less invc ti!?:ated about the optical character of (hkO)-prisms. lt is e;ident, that de- finite resulll> on (hkO)-pri. ms are only available, if an oil- immersed optical between crystal

anu

objective is used.

dt'fllwtl II\· \1. Bt.'rt.'~ J /1)/ mu/ua/1\· prrprmlkula,. \•ihrutiiiJJ tlirt•rtru/1.\ t~(an "f'tit'u/1\·

an;,,·nfl·opic· metlwm purnllel It) rlw .\\tlllll('(r)'tJXesu{tlte rrprt~sentatimr twnloit/t~l Iltl.!

rt'/lt•r·u·tf f!OIIll'l~l'ri b~/11

Ackflowledgemefll

Tlw autlwr~ are grtue.fu/Jo R. Cnn .for Jerlmica/ help umllo /he S11·i.1 1

lliUiimwf .'kiellr•• hl/lmlmion {or (immcial .IIIJIJ>IIrl.

Authors' address (corresponding address)'

Dr. Heiko Rabe. c/o Departemenr de Chimie Minerale Analyttque et Appliquee de /'Universite, Section de Cl1imie-Sciences II. 30 Quai Emest·Ansermet. CH-7217 Geneve 4/Switzerland: resp. Dr. Heiko Rabe, Ekensunder Weg 1 8, 1000 [12305} Berlin/Germany.

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