Electron Microscopy

34 Electron Microscopy MASAKI TSUJI Kyoto University, 34.1

Japan

GENERAL INTRODUCTION

785

34.2 TRANSMISSION ELECTRON MICROSCOPY OF POLYMERS 34.2.1 Image Formation in TEM 34.2.2 Amplitude Contrast 34.2.2.1 Diffraction contrast 34.2.2.2 Mass thickness contrast 34.2.3 Phase Contrast

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34.3 HIGH RESOLUTION TRANSMISSION ELECTRON MICROSCOPY 34.3.1 Scattering of Electrons by an Object 34.3.2 Image Formation in High Resolution TEM 34.3.3 Some Factors Limiting Resolution in High Resolution TEM 34.3.3.1 Resolution-limiting factors relating to the microscope 34.3.3.2 Resolution-limiting factors relating to the specimens 34.3.4 Some Aspects of Image Processing in High Resolution TEM 34.3.4.1 The analog processing system (optical filtering) 34.3.4.2 The digital processing system 34.3.4.3 Theoretical treatment of image processing

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34.4

SCANNING ELECTRON MICROSCOPY AND SCANNING TRANSMISSION ELECTRON MICROSCOPY 34.4.1 Scanning Electron Microscopy (SEM) 34.4.2 Scanning TEM (STEM) 34.4.3 Scanning Tunneling Microscopy (STM) THE APPLICATION OF ELECTRON MICROSCOPY TO THE STUDY OF POLYMER SOLIDS 34.5.1 Solution-grown Crystals of Polymers 34.5.1.1 Poly(p-xylylene) (PPX) 34.5.1.2 Poly(p-phenylene sulfide) (PPS) 34.5.1.3 Other polymers 34.5.2 Thin Films of Polymers 34.5.2.1 Isotactic polystyrene (isotactic PS) 34.5.2.2 Polyethylene (PE) 34.5.2.3 Other polymers 34.5.3 Fiber Structure 34.5.3.1 Poly(p-phenylene terephthalamide) (PPTA) 34.5.3.2 Polymeric sulfur nitride USNJJ 34.5.3.3 PE fibers and others 34.5.4 Natural Polymers

811 812 812 813

34.5

34.6

REFERENCES

813 813 813 821 824 824 825 829 830 832 832 834 834 834 835

34.1 GENERAL INTRODUCTION In 1955 Jaccodine reported thin, spirally grown, lozenge-shaped lamellar crystals, namely single crystals, of a low molecular weight linear polyethylene (PE) from dilute benzene and xylene solutions.1 This work was extended to high molecular weights, independently, by Till,2 Keller3 and Fischer.4 These authors observed the morphology of PE single crystals under a transmission electron microscope (TEM). Keller, especially, clarified that molecular chains which are much longer 785

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Microscopy

than the lamellar thickness (~ 10 nm) must fold back and forth at the surface of the lamella.3 This suggestion had already been made as early as 1938 by Storks 5,6 but had passed unheeded. This epochal concept of chain folding was squarely opposed to the traditional, so-called 'fringed micelle' model by Herrmann et al.,1 which had been the working hypothesis to explain the structure of gelatin. However, since Fischer8 and Kobayashi et al.9 independently discovered that with TEM the melt-grown spherulites which had been regarded to have the fringed micelle structure were also composed of single-crystal-like lamellae, then lamellar crystals with chain folding have been considered as the basic structural constituents of crystalline polymer solids. The solid structures of various polymers, including single crystals, have been studied with TEM. However, the application of TEM was limited to morphological investigations of polymer solids, not only because TEM did not have sufficient resolving power to resolve the individual atoms or molecules comprising the polymer solids, but also because polymer molecules are easily destroyed by electron irradiation. Consequently one observed the morphology of specimens, for example, by imaging them at low magnifications and/or investigating them by selected area electron diffraction (ED). In these cases, a small amount of irradiation ought to suffice. It is well known that TEM is designed to make a magnified image of an object or its ED pattern by slightly changing the focal length of the intermediate lens, namely by changing an electric current of the lens. That is to say, when the lenses, such as the intermediate lens and the projector lens which are below the objective lens, are focused on the image made by the objective lens, then the magnified image of the object is observed on the fluorescent screen; if their focal length is changed so that they are focused on the diffraction pattern made by the objective lens at its back focal plane, then the magnified ED pattern

Figure 1 (a) High resolution darkfieldTEM image of the /J-form of a PPX single crystal showing 1.8 nm 100 lattice fringes, (b) In the ED pattern, the circle shows the position and size of the objective aperture

Electron Microscopy

787

will be observed on the screen. When an aperture, the so-called selected area aperture, is introduced in the image plane of the objective lens then the ED pattern from a corresponding domain of the specimen can be obtained. This method is called the selected area ED. The shadow-casting method, replication method or staining method (negative or positive) can improve considerably the radiation resistivity, and therefore these are the methods used to investigate the morphology of polymer solids with high contrast, as shown in the following section. Resolution beyond a couple of nm should not be expected with these methods because of effects such as granularity of shadowing or staining materials. The first success of high resolution electron microscopy in the field of polymer science was the dark field image (Section 34.2.2.1) showing 1.8 nm lattice fringes taken from the /?-form of a poly(p-xylylene) (PPX) single crystal, which was reported in 1969.10 Figure 1(a) shows ED from the j8-form of a PPX single crystal (see Figure 3, where the circle indicates the size and position of the objective aperture). The bright area in the 400 dark field image (Figure lb) is not uniform, and corresponds to the domain that satisfies the Bragg condition sufficiently to give a 40.0 reflection with an intensity larger than its surroundings. This demonstrates well the mosaic nature of the single crystal. Owing to the interference effect between the 40.0 reflection and its satellites, 1.8 nm lattice fringes in two directions are recognized in the same area and intersect each other at an angle of 60°. Later, there have been published several reports concerning high resolution TEM of polymers, for example lattice images of rigid polymers such as poly(p-phenylene terephthalamide) (PPTA), 1 1 - 1 3 the molecular image of PPX 1 4 and so on. Nevertheless, even now the main purpose of TEM is the observation of morphologies of polymer solids at low to medium magnifications. Ever since Bragg 15 reported the optical analogy of X-ray diffraction patterns in 1939, the optical transform method has been much developed in the field of structure analysis using X-ray or electron diffraction. 16'17 On the basis of this principle, Klug et a/.18 established the so-called optical filtering method for image processing of electron micrographs, after the method already used in the field of information science.19 On the other hand, with the advent of the space age, digital image processing for pictures which are transmitted over great distances from far ranging space probes has been rapidly advanced. 20 Such image processing techniques have become indispensable for the high resolution electron microscopy. The author uses mainly TEM, in particular high resolution TEM, for the investigation of polymer solids. There are some recent reviews concerning the morphological observations of polymer solids by TEM and scanning electron microscopy (SEM), including sample preparation. 21 " 25 These are worth reading not only for beginners but also for specialists of TEM in the field of polymer science. There are also some reviews about high resolution TEM of polymers. 3 0 ' 1 0 0 , 1 3 3 ' 3 4 5 In this chapter, the high resolution TEM of polymers will be discussed in some detail, while other techniques will only be mentioned briefly.

34.2 TRANSMISSION ELECTRON MICROSCOPY OF POLYMERS 34.2.1

Image Formation in TEM

Provided a light microscope has an ideal objective lens in which all kinds of aberrations are corrected almost perfectly, the resolution limit of the microscope with illumination parallel to the optical axis is given by Abbe's theory 2 6 " 2 8 as dD

=

KX/sina,

(1)

where dD is the minimum distance between two light-absorbing particles that can be recognized as separated points in the image, k is the wavelength of the light, a is the aperture angle of the objective lens and K is a constant (K = 0.61 for incoherent illumination, or K = 0.77 for coherent illumi­ nation). Since a < n/2, then dD > KL Therefore the resolution of a microscope never exceeds about half the wavelength of the light used. In electron optics the relation between aperture angle and resolving power is more complicated. Electron lenses used as an objective lens cannot be corrected spherically, though they can be stigmated almost correctly by the stigmator. Electron waves passing through the outer zones of the lens miss the Gaussian image point. The resolution limit due only to spherical aberration is given by <*s =

cy

(2)

where Cs is the spherical aberration coefficient. The intensity distribution in the image plane

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Microscopy

correspondng to a point object may be considered as a Gaussian distribution whose half-breadth corresponds to the 'resolution limit'. Therefore the resolving power d of TEM may be approximately estimated from both equations (1) and (2) using the following equation dl

(3)

Since a is considered sufficiently small, the optimum aperture angle aopt and the resolution limit dopt are given as follows (for K = 0.61) =

0.77 (A/C,)*

(4a)

=

0.91 (P Cs)*

(4b)

For 200 keV (1 ev = 1.6 x 10" 1 9 J) {k = 0.00251 nm) and Cs = 2.8 mm, dopt = 0.42 nm. This simple estimation is applicable to the amplitude contrast due to the so-called 'absorption' effect of a specimen. As is mentioned in Section 34.3, the resolution limit in high resolution TEM, owing to phase contrast, is better than the estimation here. The contrast in TEM can be classified roughly into two types; amplitude contrast and phase contrast. Amplitude contrast is classified further into mass thickness contrast and diffraction contrast. The word 'diffraction contrast' is used for crystalline specimens, although the term 'Bragg contrast' is also used in some cases.29 There is almost no absorption of high energy electrons when they pass through the specimen. By introducing a small opening (objective aperture) at the back focal plane of the objective lens, electrons scattered by the specimen outside of the opening will be trapped. Thus this 'absorption' effect induces amplitude contrast.

34.2.2 34.2.2.1

Amplitude Contrast Diffraction contrast

There are two ways of introducing an objective aperture: a bright field (BF) mode in which an aperture is set to introduce the unscattered primary beam into the aperture; and a dark field (DF) mode in which one is set to cut the primary beam off and to make images with electrons scattered in a certain direction. Figure 2 schematically shows the effect of an objective aperture in amplitude contrast. 30 By comparing (b) with (c), it can be seen that in TEM a crystallite that gives some Bragg reflections appears as a darker area in BF and as a brighter area in DF, on the fluorescent screen. Figure 3 shows (b) D F and (c) BF images of the /?-form of a PPX single crystal. The size and position of the objective aperture is indicated with circles in Figure 3(a) for both cases. Many radial stripes due to diffraction contrast are clearly seen, suggesting the existence of six (10.0) sectors in the crystal. The (40.0) D F image (Figure 3b) also shows such a sectorization and a mosaic nature of the crystal. It is considered that sectorization of a polymer single crystal comes from chain folding.31 The shape and contrast of bright areas are slightly different from sector to sector. These may be due to the collapse of the crystal on the supporting film, though it has the tent-like or hollow pyramidal

Incident beam

i

Object Objective lens Aperture

Mass thickness contrast

Figure 2

Diffraction contrast (Bright field)

Diffraction contrast (Dark field)

Effect of an objective aperture in amplitude contrast

Electron Microscopy

789

(C)

^

i

;i Figure 3

2

^m

r

Dark field (b) and bright field (c) images of the /i-form of a PPX single crystal. The circles in ED (a) of the crystal show the size and positions of the objective aperture used to obtain (b) and (c)

structure in solution. 32 In the DF mode, tilted illumination with an objective aperture set sym­ metrically on the optic axis may be better, in taking the effect of spherical and chromatic aberrations into account. 33 In present day TEMs, the DF mode using tilted illumination is naturally installed. Therefore, once the direction and angle of beam tilt are set, it is easy and simple to change the mode from BF to DF or DF to BF by conveniently pushing the mode selector. It should be noted, however, that tilted illumination changes the Bragg condition. As a special technique, multiple dark field imaging is frequently used. 34 If the intermediate lens is strongly excited at the mode of selected area diffraction, a bright field image and many dark field images are observable at the same time, but are rather out of focus. This technique is convenient to investigate the crystallographic orientation of the specimen.

34.2.2.2

Mass thickness contrast

Negative staining with uranyl acetate or phosphotungstic acid (which is a familiar method in the biological research field), staining with O s 0 4 or R u 0 4 , and shadowing with heavy metals such as a

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Microscopy

Pt-Pd alloy will enhance mass thickness contrast, viz. amplitude contrast.23 For negative staining, hydrophobicity of support film surface is harmful because it prevents uniform spreading of the specimen and/or negative stain on the support film surface, if they are in water. To suppress this effect, supporting films which are freshly made are recommended. In the literature there have been several methods reported for recovering the hydrophobicity of specimen supports, such as: adding some chemicals;35'36 adding detergents such as Bacitracin as wetting agents;36'37 irradiating the support surface with UV;38 or using a glow discharge. 39-43 Figure 4 shows ribbon-like fibrils of bacterial cellulose negatively stained with uranyl sulfate348 and clearly demonstrates the influence of hydrophobicity and the effectiveness of ion bombardment in a glow discharge.44 In the photograph (Figure 4b and c), as a result of successful staining it can be seen that a ribbon-like fibril consists of finer microfibrils. In the case of synthetic polymers, Os0 4 is used for the staining of the copolymer, where the component with double bonds is selectively oxidized with Os0 4 . 2 3 The Ag2S insertion technique for the morphological observation of PPTAfibersis also considered as one of the staining techniques.269 Kanig introduced negative staining for PE with uranyl acetate, after treatment with chlorosulfonic acid.45 Voigt-Martin used this technique to estimate the distribution of lamellar

Figure 4 The effectiveness of hydrophilization of a specimen support film by ion bombardment in a grow discharge for negative staining. The specimen (ultrasonically disintegrated protofibrils of bacterial cellulose) was negatively stained with uranyl sulfate: (a, b) typical examples of uneven spreading of a negative stain due to the hydrophobicity of specimen support film (without glow discharging); and (c, d) examples of uniform spreading of a negative stain after hydrophilization by glow discharging

Electron Microscopy

791

thicknesses in melt-crystallized PE. 348 The stacked lamellar structure of crystalline polyalkenes, like PE, is well observed with this technique, but finer structure is not recognized. Staining of synthetic polymers is extensively reviewed by Grubb.23 Figure 5 is a micrograph of a crystalline thin film of isotactic polystyrene (isotactic PS) shadowed with Pt-Pd at an angle of tan - 1 (1/4)46 It shows the existence of edge-on lamellae composed of two-dimensional and immature spherulites. Some regions, indicated by white arrows, are possibly flat-on lamellae. In the encircled area, parallel stacked lamellae have the appearance of a shish kebab. Three typical methods of metal shadowing are well known and shown schematically in Figure 6: (a) with W basket for almost all metals; (b) with W filament for some metal wires such as Au and Ag; and (c) for Pt with C. The physical properties of shadowing some metals are shown in Table l.47 The mass m needed for desired thickness t of evaporated layer is roughly estimated as m =

4nr2dt/sin6

(5)

where d, r and 6 are the density, the distance between the source of evaporation and the specimen, and the shadowing angle, respectively. Several metals such as Cr, Au and Ag are used for increasing image contrast and also as a reference to measure lattice spacing corresponding to Bragg reflection which appears in the ED pattern from a crystalline specimen. Al is also frequently used as a reference. For example, lattice spacings of 111 and 200 are as follows: 0.234 nm (111), 0.202 nm (200) for Al, and 0.235 nm (111), 0.204 nm (200) for Au. The best material for high resolution shadowing is W.21 The evaporation of W, however, is not easy because of its high vaporization temperature, and thus needs a special installation with a static high voltage.47'270 Anyhow, the shadowing method is useful for enhancing

Figure 5 A thin film of isotactic PS annealed and crystallized at 165 °C for 10 min, and Pt-Pd shadowed at an angle of tan" 1 (1/4) CPC—z*

792

Microscopy Pt-Pd, Cr

Tungsten basket

(a)

Tungsten filament

Au

_*

(b)

(C)

Carbon rod

z^c:

Carbon rod

Figure 6 Three typical methods of metal shadowing

Table 1 Physical Properties of some Metals for Shadowing and of Carbon47 Material Density at 20°C (gem" 3 ) Melting temperature (°C) Evaporation temperature (°C) at 10" 5 Torr

Al

Au

Pt

Ag

W

Cr

Pt-Pd (80:20)

C

2.70 660 996

19.3 1063 1465

21.4 1774 2090

10.50 961 1005

19.1 3382 3309

7.20 1903 1205

19.4

2.25 >3500 2681

— —

the image contrast due to the topographical unevenness of the specimen surface,48'49 but it is helpless against the inner structure of specimens with smooth surfaces. For bulk polymers, replication combined with metal shadowing is useful to examine the surface topography.50 If the specimen itself is soluble in a certain solvent, then single-stage replication is applicable. Two-stage replication with a thermoplastic resin-like collodion is used for a specimen which has no suitable solvent, and also for observing the so-called 'extraction replica', namely a tiny fraction of the bulk polymer. Procedures are illustrated in Figure 7 for single- and two-stage replication. Kbbayashi et al using the ED of an extraction replica from a PE melt-grown spherulite demonstrated that the spherulite is made up of single-crystal-like lamellae.9 Shadowing is applicable to the determination of the thickness of a specimen, using the shadow angle and shadow length.21 As one of the metal-coating methods, Au decoration is sometimes used.21 For specimens having very small steps in their surfaces, the shadowing technique is not applicable because the surface perturbations are too small. When the specimen, which is thinly coated with evaporated Au, is heated slightly, Au migrates to such steps and nucleates there.51 Shimamura introduced this technique to investigate the fiber structure of PE, combined with the optical diffraction/filtering technique of its electron micrograph.52 Whilst some incident electrons are scattered elastically in all directions after passing through a specimen, others pass through without a change of direction. The scattering angle (twice the Bragg angle for a crystalline specimen) of electrons is related to the spatial frequency distribution of the inner potential of the specimen;48,53 the larger the angle, the higher the spatial frequency, namely the finer the structure.54 Therefore, in amplitude contrast, such a high resolution is not expected because electrons passing through a small aperture hole will make images. Figure 8 demonstrates well the effect of the size of the objective aperture in an axial BF mode, using optical filtering apparatus (see Section 34.3.4.1 and also ref. 55). If one requires an image containing information about the molecular arrangement in a crystal, then a fairly large opening must be used as the objective aperture.

793

Electron Microscopy (a)

(b)

Specimen

Heat and press Metal shadowing 1-5%

collodion solution in amyl acetate

To peel collodion replica from the specimen

Carbon coating

/

/

/

Metal shadowing

To dissolve the specimen

Carbon coating

To dissolve collodion

Figure 7 Procedures of two types of replication: (a) single-stage replica; and (b) two-stage replica

34.2.3

Phase Contrast

Phase contrast is related to high resolution observation at an atomic or molecular scale. The electron waves passing through a specimen are modulated in their amplitude and phase. 53 When the modulation of the amplitude is small and a large opening is used as an objective aperture, a sufficient contrast is not expected in just the focus image, namely the Gaussian image. A proper amount of defocus brings forth the optimum phase difference between the transmitted wave and the wave scattered elastically by the specimen, and gives contrast to the image, i.e. phase contrast. 5 3 ' 5 6 , 4 9 Applications of the phase contrast technique were first introduced by Petermann et al. to study the morphology of polymer solids, especially their fiber structure. 57 This technique is called 'defocus

794

Microscopy

Figure 8 Optical analogy of the effect of the size of objective aperture in an axial bright field mode on image details: (a) model object was constructed on the basis of the projection of the /}-form of a PPX crystal on the afe-plane along the chain axis (c-axis), with its optical diffraction pattern (see Section 34.5.1.2); (b) though reflections up to 400 were used to make the image, orientations and mutual positions of the individual ellipses are not recognized (it was confirmed that if reflections up to 440 are used, orientations and mutual positions of ellipses can be recognized in the image), (c) reflections upto 210 were used, resulting in the ellipses of the corresponding individual molecules not being resolved; and (d) using reflections up to 200

contrast'. Examples are shown in Figures 9 and 33 for an annealed thin film of isotactic PS, and in Figure 39(a) for a stretched and annealed thin film of PE. These were taken at a considerably large amount of defocus; ~ 40 /xm underfocus at 200 kv. 298,350 In Figure 9, immature spherulites with a sheaf-like appearance are seen, as in the case of shadowing (see Figure 5). Lamellae stacked in the stretching direction (fiber axis) are clearly recognized in Figure 39(a), and the averaged sequence, namely the long period, is about 30 nm. More detailed discussions for these materials will be given later (Sections 34.5.2.1 for isotactic-PS and 34.5.2.2 for PE). . : .: 1 liK ■

. r * ^ * . "

"

.

■

:

'

Rvj'

Z-:.?t ' ■-■■■■

■

'

'

'

■

■

■

'

■

■

'

■

.

'

.

.

,

-

-

'

•** If 1 frlnfln3

■ *

ll

/im

Figure 9 Defocused bright field image of a thin film of isotactic PS annealed and crystallized at about 170°C (taken at ~ 40 /an underfocus at 200 kV)

Electron Microscopy

795

34.3 HIGH RESOLUTION TRANSMISSION ELECTRON MICROSCOPY In high resolution electron microscopy, very thin specimens which can be treated as phase objects are observed using a fairly high accelerating voltage (at least 100 kV). In this case, the resolution limit should be estimated from the standpoint of the phase contrast based on Scherzer's treatment.58 The image contrast of phase objects ought to be very weak on Gaussian image plane. Therefore, as described by Scherzer, a small amount of defocusing is beneficial to the contrast, and the amount of optimum defocus, namely 'Scherzer focus', is related to the spherical aberration coefficient, Cs. The true resolving power is inherently limited by the wavelength, maximum aperture angle, illuminating angle and defocus spread, as well as by C s . 56,59 In this section, the theory of image formation in high resolution TEM on an atomic or molecular level will be briefly described, together with some practical problems to obtain high resolution electron micrographs of polymer solids, especially polymer crystals. 34.3.1 Scattering of Electrons by an Object If a periodic object (of thickness R) consists of stacked thin slices, each of which is expressed by a one-dimensional transmission function cos(2nx/d) with a period of d, the phase difference between the wave \//1 which was scattered by the first slice and propagated for a distance JR, and the wave \j/2 scattered for the first time by the last slice is given by nRk/d2.60 This phase difference must be within 7i/2 according to Cowley's criterion to avoid negative interference of the waves.60 Then, in order to resolve a distance dmin9 the specimen thickness must not exceed approximately61'62 d2mJ2X

Kmax =

(6)

This equation is derived by considering the effect of Fresnel diffraction. For k = 0.00251 nm (200 kV electrons), equation (6) gives # max = 8.0 nm for dmin = 0.2 nm, and Kmax= 50 nm for dmin = 0.5 nm. When a specimen is sufficiently thin in relation to the TEM resolution, then the specimen is considered as a two-dimensional object according to the criterion mentioned above. Its effect on the electron beam is represented by changes of phase and amplitude which are considered to take place on a single plane. Thus the scattering from this object can be treated kinematically. Here the timerelated term is neglected, and only the spatial component will be discussed in the following treatment. The spatial component of the incident wave function, which is assumed to be coherent and of unit amplitude, will be multiplied by the two-dimensional transmission function of this planar object, and can be written as q(xQ)

=

Qxp{-i(7(j)(x0)

-

n(xQ)}

(7)

j32)1/2}

(8)

Here a is the interaction constant63 as a

=

2n/kE{l

+

(1

-

where E is the accelerating voltage In equation (7), (j>{x0) and fi(xQ) are the projections in the beam direction of the three-dimensional potential distribution 0(x o ,z) and an effective absorption function fi(xQ9 z) of the specimen, respectively, so that *(*o) = J*(*o.*)
P)

H{x0)

(10)

and =

L(jc0,z)dz

For a particularly thin object and/or sufficiently high accelerating voltage with a fairly large size of objective aperture, JU(JC0) can be neglected and the specimen can be treated as a pure phase object. If the specimen is composed of light atoms, (JC0) is sufficiently small, and only the first order term is significant in the expansion of the exponential in equation (7) q(*o)

=

1

-

iu(x0)

(11)

In this case, the object is called a 'weak phase object'. The first term of equation (11) represents the

796

Microscopy

unscattered incident wave and the second one the scattered wave. The Fourier transform Q, of the function q, is given by

l q( *°

Q(«)

)exp(27rii#jt0)dx0

=

S(u) —

io{u)

(12)

where (13)

•(.) = (j)(x0)Qxp(2niux0)dx0

or for periodic objects O(ii)

=

(XloY¥(Kk)

=

Wff)£fi(fcfk)cxp{2irf(fac6

+

kyQ)}

(14)

(where h, k are Miller indices; fj(h, k) is the atomic scattering factor of the;th atom for electrons; and *o> yo a r e fractional coordinates.)

34.3.2

Image Formation in High Resolution TEM

The objective lens of TEM transfers the electron wave, after it has been transmitted through the object, to form its diffraction pattern (viz. spatial frequency distribution spectrum of the object) at the back focal plane, and then to form its inverted real image at the Gaussian image plane, as shown in textbooks of ordinary physical optics. 26 ' 27 The total process is interpreted in terms of two successive Fourier transforms. The amplitude transmittance of an object corresponds to the wave function of electrons transmitted through the object, as described in the previous section. With the coordinates assigned as in Figure 10, the amplitude A(jcf) (at the back focal plane of the objective lens) of the electron wave transmitted through an object will be given by the following equation 6 4 - 6 7 A(xf) = (iMflexp {-!*(/ + dx

A/)

ik(xjllf)(\

-

dJffiQMXfiaipi-ik-Af'XJ/lWilS)

where A/is the amount of defocusing (being positive for underfocusing) and k = 2n/L The last factor in equation (15) is the wave aberration due to the defocussing A / (distances d2 and (dl — A/) in Figure 10 are fixed in TEM, where d^ and d2 are a pair of conjugate distances with respect to the objective lens). The diffraction intensity at the back focal plane is given by |A(jcf)|2. Then from equation (15) |A(*f)|2 = (iM 2 / 2 HQ(*f/W (16) Including the effects due to spherical aberration and defocusing, the aberration function x is defined as follows58 Xixt/kf)

nX-Af-(xf/X2f2)

-

(7r/2)CsA3-(jcf2M2/2)2

(17)

l Object

Object plane

Back focal plane

Figure 10 Image formation by an objective lens in TEM: amax= maximum aperture angle;/= focal length of the lens; and A/= amount of defocus (positive for underfocus)

Electron Microscopy

797

Thus equation (15) can be modified as A(x f )

=

(i/A/)exp{-ifc(/

+

dx

-

A/)

-

ik(xf/2f)(l

-

dt/f)}Q(xt/Xf)aLp{-ix(xt/Xf)}

(18)

The amplitude ^(JCJ) at the image plane is given by the diffraction integral, namely the Fresnel diffraction, of A(x{)P{xi/Xf\ where P is the aperture function. Therefore ¥(*,)

=

(-l/M)exp{-*7c(/

+

d,

-

Q(n)exp { - ix(u)} P(«)exp {Inixp/M}

A/)

-

ikxf/2(d2

-

du

/)} x (19)

where M is the magnification (cf. M = d2/d1) and «(= xf/Xf) is the spatial frequency. The intensity I(JCJ) of the image is given by I(x t )

|V(x,)| 2

=

=

|*P(x,)|2/M2

(20)

where *(*i)

=

Q(«)exp{-iz(«)}P(«)exp{27rijc i n/M}dii

(21)

If we use a circular objective aperture and an aberration function with cylindrical symmetry, both functions for u = \u\ are as follows 1 for u

-

P(II)

0

for u

< >

wmax wmax

(22)

and X(u)

nX-Afu2

=

-

(7t/2)CsA3u4

(23)

where wmax « amax/A and amax is the maximum aperture angle of the objective lens. Noting that the potential function
«

(1/M 2 ){1

-

2L70(tt)sin^(u)P(w)exp{27ciJcIn/M}dii}

(24)

where sin#(w) is called the 'phase contrast' transfer function. 68-70 This equation indicates that the image intensity l(xt) is greatly affected by defocusing through sin x{u) in the case of phase contrast. If sin^(w) = 1 (or — 1) and P(M) = 1 for all M, then l(x.)

=

(l/M2)[l

T

2<7(-*i/M)]

(25)

and we thus obtain the magnified and inverted real image which is to reflect the potential distribution , viz. the true structure of the object. Under actual circumstances, sin/(w) oscillates and here we define u0 as the smallest value of u (except u = 0) given by sin x(u) = 0. For high resolution electron microscopy, we must operate TEM at the 'optimum defocus' which gives |sin%(u)\ its maximum value of 1 over as wide a range of u as possible. The amount of this optimum defocus, namely the Scherzer focus, is calculated as 6 2 AX = UW)CM1'2

(26)

Figure 11 shows several solid curves which illustrate the defocus dependence of sin#(w) for Cs = 1.06 mm and X = 0.00142 nm (500 keV where 1 eV = 1.6 x 10" 1 9 J). (The effect of defocus on the image contrast will be demonstrated in Figure 27(b) in Section 34.5.1.2.ii.) The value of Afs for this microscope is estimated as 45 nm using equation (26). The aperture size umax should be selected under the optimum defocus condition so as to cut-off all the scattering waves in the higher spatial frequency range where sin %(M) oscillates violently. It may be best to select u0 at the optimum defocus as wmax(see Figure lie). Then l/u max corresponds to the resolving power. The resolution limit at optimum defocus is defined by equation (27) for axial illumination. d

=

0.66(C S A 3 ) 1/4

(27)

Various criterions have been proposed to determine the optimum defocus condition, and the

798

Microscopy 5 0 0 keV (a)

Cs = 1.06 mm

l h A f = -45nm

(b)

(c)

1 A f = 90nm (d)

2

4

\ \

L_

y

I |

V v-V

" ^ -

~~~- \

6

8

\

i/ (nm-1)

Figure 11 The defocus dependence of the phase contrast transfer functions sin x (solid curves) and D F • sin x (dashed curves) of JEOL JEM-500 (Cs = 1.06 mm, X = 0.00142 nm, ft = 2 x 10" 4 rad, A = 10 nm). In (c) A / = 45 nm corresponds to Scherzer focus of this TEM, and see Section 34.3.3.l.ii for ft and A

resulting resolution limits differ slightly. 5 8 ' 7 1 - 7 3 The overall process of image formation in high resolution TEM is shown in Figure 12, where D F (M) means the damping factor to sin^(w), and this will be described in the next section. The effect of DF(w) on sinx(u) is shown in Figure 11, using dashed curves.

exp{-io(X)}

qW

A(ii)

=

s

io(t>(X)

1

Q(M)-exp{-iz(M)}-D F (ii) Q(u) X(u) D F (II)

= =

^lq(X)1 nXAfu2

= -

2

S(u)

-

iaO(ii)

lcsX3u4

Aperture Beam divergence Chromatic aberration

l(X) Figure 12

s

1

2<7^- 1 [0>(w)-sinx(w)-D F (M)]

Overall process of image formation in high resolution TEM, where, & and & ~ * represent the Fourier and inverse Fourier transforms, respectively

Electron Microscopy

799

34.3.3 Some Factors Limiting Resolution in High Resolution TEM In the previous section, the phase contrast image formation and the resolution limit in high resolution TEM were described. In this section, some problems in obtaining high resolution micrographs of polymer crystals will be discussed. There are many factors which restrict the resolution limit of TEM. 7 4 The average distance between polymer chains in crystals is assumed to be 0.5 through 1 nm. To obtain information on molecular arrangement in the crystal, however, 0.2-0.3 nm resolution may be needed. Principal factors affecting the resolution of TEM imaging are summarized in Sections 34.3.3.1 and 34.3.3.2.

34.3.3.1

Resolution-limiting factors relating to the microscope

(i) Spherical aberration of the objective lens The effect of this aberration was described in Sections 34.2.1 and 34.3.2. Electron micrographs should be taken under the optimum defocus condition (the so-called Scherzer condition), in order to obtain the image which reflects the true structure of the object, as shown in Section 34.3.2. For 200 kV TEM, the relationship between Afs and Cs (equation 26) and that between the resolution limit d and Cs (equation 27) suggests that, in order to clear 0.2 nm as the resolution limit, Cs needs to be smaller than 0.5 mm, and A^ = 41 nm underfocused for Cs = 0.5 mm. Several methods were proposed to estimate C s . 7 4 ' 7 6 (ii) Defocus spread and illuminating angle The illuminating angle (relating to beam divergence) and the defocus spread (relating to chromatic aberration) modify the phase contrast transfer function sin/(u); 5 6 the function is multiplied by two envelope functions S(u) and E(u) which are expressed in terms of the illuminating angle and the parameter for defocus spread as 7 7 S(u) =

expi-Knfr/XyiC^ut-Af-m2}

(28)

and E(M)

=

exp{-[(7C/lM 2 /2)-(C c -(5£/2£ N /ln2)] 2 }

=

exp{ - [(TT2A-M 2 /2)] 2

(29)

where ft is the illuminating angle, Af the defocus, C c the chromatic aberration constant, SE/E the fluctuation of accelerating voltage, and A the parameter for the defocus spread. The combined effect of these two envelope functions on sin/(w) is shown in Figure 11 using dashed curves. Since two envelope functions dampen |sin/(i/)| to a considerably small value at u > wmax[wmaxis given from Scherzer's limit in equation (27)] as shown in Figure 11, practically we need not use the objective aperture. There have been some methods to measure f}{ and/or A. 5 9 ' 7 4 ' 7 8 Table 2 shows the properties of modern electron sources at 100 kV. 2 5 ' 3 3 ' 5 6 To get small ft and A, a field emission gun (FEG) is the best, but needs ultra high vacuum. From the view point of 'cost performance', LaB 6 filament is recommended. As a damping factor to sin#(u), one more important function related to the granularity of the image recording medium should be introduced, which is called the modulation transfer function (MTF). 5 9 , 7 4 This will be discussed later in Section 34.3.3.1.iv. Table 2 Properties of Modern Electron Sources at 100 kV 2 5 ' 3 3 ' 5 6 Source

Radiance11 Energy width ( C s _ 1 c m _ 2 s t r - 1 ) A£(eV)

Effective source diameter

Lifetime (h)

Vacuum Emission Working required (Torr) current (/zA) temperature (K)

Thermionic W hairpin

5 x 105

2

30/mi

50

10" 5

100

2800

Thermionic W point

2 x 106

2

1-5 fim

10

10" 5

10

2800

Thermionic LaB 6

5 x 106

1

5-10 nm

500-1000

10" 6

50

1800

0.3

5-10 nm

500-1000

10" 9

50-100

1800

Thermal field emission W a

1 x 10

8

Electron flux per unit solid angle.

800

Microscopy

(Hi) Astigmatism of the objective lens In order to obtain high resolution electron micrographs with resolution better than 0.2 nm, the astigmatism of the objective lens must be compensated within about 10 nm, 79 because it introduces an extra difference in phase and/or amplitude into the diffracted electron beams according to their direction in the plane perpendicular to the optical axis of TEM. For low magnification/resolution microscopy, perforated films are used as specimens in correcting objective astigmatism. One can see the Fresnel fringe along the edge of the hole, 80 and this is not uniform if astigmatism exists. To obtain a uniform fringe on the viewing screen at a magnification of about 100000 adjustment of a stigmator is required. For high magnification/resolution work, astigmatism will be corrected by observing phase granularity of a thin amorphous specimen, like evaporated C, on the viewing screen at a higher magnification, say at least 400 OOO.5680 Stigmating, in this case, is done so as to give no anisotropic appearance of the phase granularity pattern. This method is more accurate than the previous one. However, the resolution and contrast of the image seen on the viewing screen of a higher voltage TEM is too poor to permit compensation with much accuracy. The method shown below is useful for accurate astigmatism correction. Astigmatism is most easily recognized from the optical diffraction pattern of a high resolution electron micrograph of a thin amorphous film.68 As a perfectly stigmated micrograph would give a diffraction pattern consisting of concentric circular rings due to sin2 x(w),70 departure from circu­ larity indicates the presence of astigmatism. 81 ' 82 The usual elliptic pattern of contrasting transfer zones and gaps is shown in Figure 13(a), which is an optical diffractogram from the micrograph of a thin C film taken with a certain amount of underfocusing before the astigmatism is corrected. The transfer gaps, namely dark rings, appear at spatial frequencies u which satisfy X(u)

=

nit (n integer)

(30)

Here the aberration function #(«) is given by equation (23). In a high voltage TEM with small Cs, only the second term in equation (23) is significant for spatial frequencies higher than 3 nm" 1 . When the first term dominates, the positions of the transfer gaps are given by ii

=

{n/\Af\Xy<2

(31)

The magnitude of defocus is estimated using the following equation |A/1 = L2n\2IM2r\X

(32)

where M, A, r„ and L are the electron optical magnification, the He-Ne gas laser wavelength (632.8 nm), the radius of the nth gap, and the camera length of the apparatus for optical trans­ formation, respectively. The defocus is measured for each principal astigmatism direction to determine the astigmatism difference ^/between the two principal values.68 The astigmatism is given

Figure 13 Optical diffractograms of images of a thin amorphous C film: (a) before and (b) after correction of astigmatism

801

Electron Microscopy in terms of rns, rnl and 6 which are observable (see Figure 13a), as Sf

=

(n\2L2/M2m/r2ns

-

l/r2nl)

(33)

When the x- and y-axis of the stigmator make an angle ofrc/4,the correction values of the stigmator currents are 82 AIX My

=

=

C'6f-sin(\0

C'8f-sm(\0

-

a


n/4\

TC/4) -

(34)

n/4)

Here a and C are calibration constants which are to be adjusted for individual TEMs. Figure 13(b) shows the result of an astigmatism correction by the procedure mentioned above. If the image intensity is recorded with methods other than photographic emulsions, the real-time stigmating can be achieved with a scheme similar to that mentioned in this section. 83 ' 84 (iv) The image-recording system In high resolution transmission electron microscopy, the best medium for image recording now available is photographic emulsion. Although various recording devices 85,86 such as an imaging plate 8 7 , 8 8 have been proposed for radiation sensitive specimens, the resolution of these devices is generally inferior to that of photographic emulsion. From the view point of cost performance, photographic films are recommended at present. Though various photographic films and plates are available, 8 9 - 9 9 we have used Mitsubishi (MEM) and FUJI (FG) electron microscopic films. Figure 14 shows the relationship between the exposure and the optical density D of both films for 100 keV and 200 keV (1 eV = 1.6 x 10" 1 9 J). 100 The developing conditions are in the figure caption. Both films show that there is quite good linearity of D against exposure, when the optical density is smaller than 1.0. Roughly speaking, MEM is about four times as sensitive as FG, but is more granular. Although some X-ray films are several times as sensitive as normal electron microscopic films such as MEM and FG, the resolution is much poorer. 56 As shown in Figure 14, the optical density, D, is practically proportional to the electron exposure, £, up to D = l.O. 8 9 , 9 0 , 9 9 High resolution electron micrographs should be taken at a certain exposure level to obtain the averaged optical density of about 0.5 through to 1.0. This density range is also desirable for photographic processes such as printing. The resolution limit of photographic emulsion is represented by the 'modulation transfer function (MTF)\ For an approximate MTF, the following function H(u) is proposed. 3 3 , 5 9 , 1 0 0 " 1 0 3 H(n)

2

=

1/{1

4

+

A(u/M)2}

6

(35)

8

10

Exposure [ x I0~" C c m 2 ]

Figure 14 Relationship between electron exposure and optical density of Mitsubishi MEM (a and b) and Fuji FG (c and d) films for 100 (a and c) and 200 keV (b and d) (1 eV = 1.6 x 10" 1 9 J), where MEM and FG were developed with Gekkol (Mitsubishi) in full strength and D-19 (Kodak) diluted 1:1, respectively, at 20 °C for 5 min

802

Microscopy

Here, A is a constant which may be dependent on some factors such as the kind of film, developing conditions, electron energy, exposure and so on. Also, in equation (35), u and M are the spatial frequency and electron optical magnification, respectively. When equation (35) is applicable as the MTF, the constant A is estimated from the highest spatial frequency that is recognizable in the optical diffractogram of the micrograph of an amorphous thin specimen which has been taken at a rather low magnification (~ 10000).59 As mentioned in Section 34.3.3.1.H, H(w) may be introduced in D F (M) as one of the damping factors to sinx(w). 59 ' 74

34.3.3.2

Resolution-limiting factors relating to the specimens

(i) Specimen thickness Equation (6) indicates that the specimen thickness should be smaller than i*max for the resolution of dmin, from the standpoint of the Fresnel diffraction effect. According to the two-beam dynamical theory, the extinction distance is given approximately by 104 t,

=

nVccosO/kFg

where Vc is the unit cell volume; 6 is the Bragg angle; and Fg is the structure factor corresponding to the diffracting direction g. When the reflection indexed as g is dominant, the scattering of electrons can be treated kinematically if the thickness of crystal is much smaller than <^/2. 105 If the specimen is rather thick, the dynamical scattering effect (multiple scattering, and so on) will be remarkable. Then TEM images do not directly reflect the crystal structure (namely, the projected potential distribution). 106-108 Using a multi-slice dynamical calculation,106 Kawaguchi 109 demonstrated that if the PE single crystal is too thick, the structure amplitudes of 110, 200, etc., greatly deviate from those for kinematical diffraction and forbidden reflections such as 010 and 100 increase in their intensity. (ii) Specimen orientation If individual chain stems in a polymer crystal are needed to be resolved separately in the micrographs, the electron beam must be introduced onto the crystal in the direction along its chain axis. The effect of specimen orientation is well demonstrated in Figure 25, where two kinds of high resolution micrographs of the a-form of a PPX single crystal are shown. 100 Incidence at <001> (namely, incidence along the molecular axis in the crystal) reveals the images of individual PPX chains in this crystal. Another example of the effect of orientation on high resolution images is demonstrated in Figure 31 for a solution-grown crystal of poly(p-phenylene sulfide) (PPS). 4 6 ' 1 1 0 Detailed discussion about these specimens will be given in Section 34.5.1.1 for PPX and Section 34.5.1.2 for PPS. It is possible to adjust the specimen orientation mechanically with a rotation/tilt or double tilt specimen holder for a side entry goniometer and with a double tilt holder for a top entry goniometer. The operation is, however, not easy for polymer specimens because of their electron irradiation damage during the operation of orientation adjustment. (Hi) Specimen drift We should avoid the mechanical stage drift after specimen movement. If the TEM mode is changed, for example from a diffraction mode to an imaging mode, electrical hysteresis of the intermediate lens may cause focus drift. Thus, focusing and subsequent photographing should be postponed for a few minutes after changing the TEM condition to avoid the above-mentioned drifts. We should also suppress the specimen drift due to thermal deformation and charge-up of the specimen and/or support film by applying electrons. Use of a C- and metal-coated microgrid (perforated film) is recommended.1 x x A very thin C-supporting film112 is deposited on the microgrid, as shown in Figure 15, for tiny specimens like polymer single crystals. Of course, a very wide specimen, like a stretched thin polymer film, can be deposited directly on the microgrid. 113 In such a case, but where the wide specimen has low electrical conductivity, it should be coated with a thin evaporated C layer to suppress specimen charge-up. If the energy from the incident beam is uniformly deposited throughout the irradiated cylindrical volume, and the front and back of the thin specimen are at the same temperature, then the heat flow is considered to be purely radial. According to Isaacson, 114 the temperature rise of the very thin Au

Electron Microscopy

803

Figure 15 The a-form (a) and /?-form (b) of PPX single crystals mounted on a C- and Au-coated microgrid on which a very thin C support film was deposited by indirect evaporation

support film in the center of the irradiated volume is estimated as a few degrees. Thus the temperature rise of the specimen and the radiation damage due to this temperature rise can be suppressed more or less by using an Au-coated microgrid. We are not willing to use a carbon support film on the microgrid, even if the film is very thin, because it gives extra noise on TEM images. However, it suppresses the electron charge-up and therefore the drift of the specimen. (iv) Radiation damage In general, polymer crystals such as PE, poly(oxymethylene) (POM) and so on are vulnerable to electron irradiation, and the molecular chains are crosslinked to become amorphous or are decomposed in a short time on applying electrons. Both a- and jS-forms of PPX crystals are, however, fairly strong, as compared with PE. Figure 16 shows the change in morphology and in the ED pattern of the 0-form of a PPX single crystal due to 80 ke V (1 e V = 10 " 1 9 J) irradiation. 115 This figure indicates that the radial stripes due to diffraction contrast disappear partially at first and then the observed area of no stripes spreads over the whole crystal, until entire stripes have disappeared. The crystalline reflections disappear from higher orders with increasing doses in the case of the a-form.115 However, in the case of the jS-form, the reflections of odd number indices such as (50.0), (41.0) and so on, disappear at first (see Figure 16c'), and the reflections having the indices of an integral multiple of four, such as (40.0), (44.0) and so on, remain (Figure 16d'). It seems from Figure 16(d') that molecular chains are packed in the crystal with hexagonal symmetry where only one chain segment is contained in a smaller unit cell at such an irradiation dose. Then, at last, all the crystalline reflections disappear. The disappearance of stripes due to diffraction contrast and/or of moire fringes, as well as the disappearance of crystalline reflections, denotes the 'death' of the crystals. The effects of electron irradiation on PE crystals were discussed by Kobayashi and Sakaoku. 116 ' 117 They illustrated that crosslinking between adjacent molecular chains in polymer crystals will take place under electron irradiation (Figure 17).116 Kawaguchi et al. demonstrated the effect of crosslinking in a single crystal of PE due to electron irradiation on lattice distortions by using optical transforms. 118 In the case of POM, decomposition follows crosslinking and the crystal disappears. 119 As shown in Figure 16, the external shape of single crystals of PPX has not changed, suggesting that crosslinking takes place in PPX crystals under electron irradiation without decomposition. A lucid explanation of the irradiation effects on polymer crystals can be expected in the future, if we carefully observe changes in electron micrographs as well as those in ED. Next, we will discuss quantitatively the effects of electron irradiation on polymer crystals. The changes of the lattice spacings by irradiation of 500 keV (1 eV = 1.6 x 10" 1 9 J) are plotted in

00

O

(a)

Figure 16 Changes in morphology and in the ED pattern of the /!-form of a PPX single crystal: (a')-(e') are the ED patterns corresponding to (a)-(e), respectively

Electron Microscopy

805

(a )

11

M

(b)

■4-

i i i

i I

1

p*

. 1 1 !

A

II

I !

-ft-

-*-

#

tf it— T

t*=

-fl tb= <*

in.,

Is-

*

F

a

Figure 17 Distorted crystal lattice of PE with a crosslink between molecular chains due to electron irradiation: 116 (a) side view along the b-axis; and (b) projection along the chain axis (c-axis) on the ab-plane (dashed lines represent the original (undistorted) lattice)

(a)

61-

(b)

6r-

40.0

Critical dose • Crystalline reflection ° Amorphous halo 0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Figure 18 Variation in lattice spacing d of PPX (1) crystals (n > 5000) with an increasing irradiation dose Q of 500 keV (1 eV = 1.6 x 10" 1 9 J): (a) changes of 020 and 110 spacings of the a-form single crystal; and (b) change of 400 spacing of the /?-form single crystal

Figure 18 for (a) the a-form and (b) the jS-form of single crystals of PPX. 14 These measurements were carried out with the single crystals mounted on an Al thin support film so as to give the diffraction rings of Al as reference. The electron beam current applied to the specimen was measured with a picoammeter connected to a Faraday cage inserted between the projector lens and the fluorescent screen. Even though such equipment is not now available, an exposure meter is installed in a present day TEM. Thus, with such a TEM, the electron beam current (i.e. screen current) can be measured approximately through reading the exposure meter which is connected to a viewing screen. 120,121 The lattice spacings corresponding to 020 and 110 reflections of the a-form get closer together, starting at a dose of about 0.3 C c m " 2 (this value may be defined as the 'critical dose'), and finally merge into each other. At a dose of about 0.5 C c m " 2 (the 'total end point dose', TEPD), amorphous halo rings start to replace crystalline reflections. In the case of the /?-form, the lattice spacing of the

806

Microscopy

40.0 reflection expands a little by irradiation, and halo rings appear at a dose of about 0.4 C c m " 2 (this value corresponds to the 'critical dose' and also the 'TEPD'). The polymer molecules which have benzene rings in their backbone chains seem to be somewhat more resistant against electron irradiation. As for PPX (1) crystals, the TEPD is about 20 times larger than that of PE crystals at a given energy of electrons. 118,121 The TEPD's, namely electron doses necessary for complete damage of various polymer crystals, are summarized in Table 3, where l C c m " 2 = 62420enm" 2 . The TEPD value of another accelerating voltage can be estimated from the dose-voltage relationship. The inelastic cross section or the absorption is proportional to (mA)2, that is 1/jS2,122"124 where m is the mass of an accelerated electron, k the electron wavelength, and /? the ratio of electron velocity to light velocity, respectively. Therefore the TEPD seems to be proportional to /?2. In the case of polymer specimens, however, it was also reported 125 that the TEPD is proportional to J?3 rather than f}2. In either case, the use of a higher accelerating voltage of electrons may be effective in reducing the radiation damage.

-(OW-Q-CH^(1)

Table 3 TEPD and Resolution Limit for Various Polymer Crystals at Room Temperature46 Polymer

TMPS N12 PE iPS PA PPS PPP PPX PPTA (SN)X

TEPD, N (enm - 2 ) 4x 5x 6x 2x 1x 1x 3x 3x 5x 6x

102 102 102 103 104 104 104 104 104 104

Electron energy (keV)

"ofcs

Resolution limit (nm) dP dLD

200 200 200 200 200 200 200 500 200 200

0.32 1.5 0.37 0.49 0.37 0.33 0.32 0.25 0.43 0.22

1.00 0.89 0.82 0.45 0.20 0.20 0.12 0.12 0.09 0.08

5.0 4.5 4.1 2.2 1.0 1.0 0.6 0.6 0.4 0.4

Cf- dLD = 1/0.1^0.25 N, dp = 5/0.1^0.25 N. Abbreviations: TMPS = poly(tetramethyl-p-silphenylene siloxane); PE = polyethylene; iPS = isotactic polystyrene; PS = polyacetylene; PPP = poly(pphenylene); PPS = poly(p-phenylene sulfide); N12 = nylon 12; PPX = poly(p-xylene); (SN)X = polysulfurnitride; PPTA = poly(p-phenylene terephthalamide).

The expected resolution of such radiation sensitive polymer crystals has been calculated with the modified Rose equation 1 2 6 1 2 7 d = y/CV/N

(36)

where C a n d / a r e the contrast and the net utilization factor, respectively. Empirically, C = 0.1 and / = 0.25 are used. In equation (36), N is the number of electrons passing through the unit area of the specimen during image recording. Here one may consider N as TEPD. The factor y is the signal-tonoise ratio in an area of d x d, and y = 5 was deduced by visual judgment for point resolution. 128 In Table 3, TEPD, the observed resolution limit dohs and the point resolution limit dP were calculated using equation (36) with y = 5, and are shown for various polymer crystals. Except for PPS and PPTA, dobs is rather smaller than dP. Here, dobs, which was estimated by optical diffraction of the electron micrograph, should not be considered as the point resolution but as the line resolution limit in the lattice image. Therefore in order to predict the ultimate limit in the lattice resolution of a certain polymer crystal with TEPD of AT, the value of y should be re-evaluated for this case, namely for lattice imaging. The computer simulation was thus carried out for this purpose, and visual judgment proved y = 1.5 ( ± 0.2).129 The result means that we were able to recognize and identified in the micrograph those lattice fringes for which the spacing has been predicted using equation (36) with y = 1.5. If the optical diffraction technique is adopted to judge the resolution limit, a smaller value of y can be

Electron Microscopy

807

expected and was actually found to be 0.85. 129 When y = 1 is assumed, the expected resolution limit dLD is calculated as shown in Table 3. Recently 0.49 nm lattice fringes were successfully obtained in a stretched isotactic PS thin film113 by a low dose technique with a minimum dose system (MDS) 271 (see Section 34.5.2.1.ii). This polymer does not have such a great TEPD value and then the expected point resolution limit dP is much larger (2.2 nm) than dobs. Nevertheless the expected line resolution limit dLD in Table 3 is in good agreement with dobs. For some polymers in Table 3, such as PPP, etc., dobs is much larger than dLD. This is mainly due to the resolving power of the microscope itself. Furthermore, in the case of the PE crystal, 0.37 nm (200) and 0.41 nm (110) fringes were resolved with a conventional TEM at room temperature. 1 3 0 - 1 3 2 These values greatly exceed the dLD value for PE. It should be deduced that this inconsistency is due to the choice of the values C and/or/ A study for the re-evaluation of C a n d / i s now in progress. For radiation sensitive specimens, MDS 2 7 1 or a low dose unit (LDU) 272 is frequently used to take high resolution images. It is noted, however, that this equipment uses an electron dose corre­ sponding to TEPD, namely N, only for recording images. From equation (33), higher resolution is expected if N increases for a given material. There are two ways to increase N; (i) to raise the accelerating voltage; and (ii) cryo protection. The former way is not so advantageous because the image contrast and the sensitivity of photo-emulsion decreases with increasing voltage, as pointed by Katayama. 133 As regards cryo protection, ifs effectiveness has been discussed in the literature. 1 3 4 ' 3 3 9 - 3 4 1 Recently we recognized the definite effect of cryo protection at 4.2 K by using a cryo electron microscope with a superconducting objective lens (JEOL JEM-2000SCM; 200 kV). 135 - 273 Table 4 shows the ratio N^2/N300, where N 4 2 and N300 are TEPD at 4.2 K and room temperature, respectively.46 A ratio of more than ten has been confirmed. Lattice images of a single PE crystal have been taken at an electron optical magnification of 90000 (160 kV, 4.2 K). One

Figure 19 The lattice image of a single PE crystal taken at a direct magnification of 90000 with a super-conducting cryo electron microscope (JEOL JEM-2000SCM) at 160 kV and 4.2 K. Inset is the correspondng optical diffractogram (OD) showing 110, 110 and 200 reflections

808

Microscopy Table 4

Temperature Dependence of

TEPD of Some Polymer Crystals 46 Polymer crystals

W4.2/W300

TMPS PE PBPP PPX PLA

60 15 140 9 20

Abbreviations: TMPS = poly(tetramethylp-silylphenylene siloxane); PE = poly­ ethylene; PPBP = poly(bisphenoxyphosphazene); PPX = poly(p-xylylene); PLA = poly(acetic acid).

of these is shown in Figure 19, with the optical diffraction pattern (OD) from the original negative.46 In this figure, the 200 and 110 lattice fringes are clearly seen. The 110 and/or 200 lattice fringes were also obtained from the stretched and annealed thin films of PE at M = 75 000 (160 kV, 4.2 K). 132 As mentioned above, although radiation damage is one of the most important factors to restrict the resolution limit in TEM of polymer solids, cryo protection will bring us higher resolution images which will give more information about the finer structures in polymer solids.

34.3.4

Some Aspects of Image Processing in High Resolution TEM

It should be possible to improve the resolution of a TEM up to the theoretical resolving limit 26 (Section 34.3.2) to enable the direct observation of molecular and atomic images. This expectation is difficult to fulfil because of aberrations (in particular, the spherical58 and chromatic aberrations) 136 of the objective lens in TEM and the photographic graininess 89 ' 90 in electron microscopic films (e.g. granularity of photographic emulsion, the quantum noise of electrons, etc.). The degradation of photographed images is mainly caused by this graininess. Though various processing techniques were proposed, 1 3 7 " 1 4 1 including holographic filtering based on Gabor's holography, 1 4 2 1 4 3 the degradation resulting from graininess should be eliminated prior to any correction of the effect of spherical aberration or defocusing, in order to obtain high resolution images. 144 Picture processing techniques have progressed to meet the requirements of space research, especially that of remote sensing. 20 ' 145 ' 146 In these techniques, pictures are converted to math­ ematical images (digitized), and picture processing techniques, such as geometric correction, noise removal, high frequency attenuation correction and so on, are applied. 147 These techniques have been applied to a posteriori image processing of electron micrographs and also to on-line processing when it is combined with a TV system directly connected to TEM. 8 3 ' 8 4 They are now indispensable for the high-resolving electron microscopy.55 Image processing methods for electron microscopy fall into two broad categories: (i) analog and (ii) digital processing. Although the apparatus for analog processing (usually a purely optical method) is simple and rapid, the process has poor reproducibility and is unsatisfactory for quantitative processing. On the other hand, digital processing shows good reproducibility and enables various kinds of processing with full accuracy, if the sampling method (especially, the sampling interval) is appropriate. 147 ' 148 This system, however, needs a large size computer for rapid handling of a great number of data.

34.3.4.1

The analog processing system (optical filtering)

The optical transform method, which was used for the first time by Bragg in 193915 and developed by Taylor and Lipson, 1 6 1 7 has been used for the anticipation and/or the interpretation of X-ray 1 4 9 " 1 5 2 or electron diffraction patterns, 1 0 9 ' 1 1 8 ' 1 5 3 " 1 5 6 and also for the analysis of electron micrographs. 6 8 1 5 7 " 1 6 4 Hosemann studied the paracrystalline structure in polymer crystals with this method. 165 In the field of high voltage and high resolution TEM, this simple method has been a sine qua non for accurate stigmating 81 ' 82 of the objective lens (see Section 34.3.3.1.hi) or for the performance test of EM. 5 9 , 7 4 On the basis of the optical transform principle, Klug et al. established

Electron Microscopy

809

the so-called optical filtering method for separating superposed images in a micrograph and applied this to the analysis of large biopolymer structures. 18 This method has progressed and has been applied in the wide field of electron microscopy. 5 2 , 1 6 6 " 1 7 8 From the processed images, reconstruc­ tion of three-dimensional structures has also been attempted with a digital computer. 1 7 9 " 1 8 9 A special specimen preparation method to give a two-dimensional periodical array like a twodimensional crystal has been proposed for image processing in biological electron microscopy. 190 Our apparatus was constructed so as to analyze electron micrographs by optical transforms and/or remove random noises in them by optical filtering.55 Figure 20 shows: (a) the general view, and (b) the scheme of our apparatus. This system is fixed on an iron girder (3 m long) with magnetic stands, so the system can be rearranged easily in accordance with experimental requirements. Similar systems are commercially available. 171-191

Figure 20 Apparatus for optical filtering: (a) a general view; and (b) a schematic arrangement, in which S is the light source (a He-Ne gas laser), L0 the condenser lens, Lc the collimator lens, Ld the diffraction lens, Lj the imaging lens, A the diaphragm, O the object plane, F the back focal plane of lens L d , and I the image plane

34.3.4.2

The digital processing system

An analog processing method offers little variety in the modes of image processing. On the contrary, digital processing has a wider application, and various methods have been p r o p o s e d . 2 0 , 1 3 9 - 1 4 1 ' 1 9 2 - 2 0 0 ' 2 6 8 Figure 21 shows: (a) a general view of our apparatus; and (b) a schematic flow of data. The facsimile receiver in this system is also used to display the simulated through-focal TEM images (see Figure 27 in Section 34.5.1.2.ii) and the results of the X-ray diffraction pattern simulation. 201

810

Microscopy

(MT ^

MT Recorder and controller

V

Microdensitometer

'' Digital computer

Graphic display

'1 (M

y

Figure 21

34.3.4.3

Facsimile receiver

'

Apparatus for digital image processing: (a) a general view, in which A is the microdensitometer, B the magnetic tape recorder and its controller, and C the facsimile receiver; and (b) a schematic flow of data

Theoretical treatment of image processing

(i) General background on spatial filtering An optical filtering system is shown in Figure 20. Suppose that an electron micrograph with amplitude transmittance g(x) is set in the object plane O in front of a lens Ld and illuminated with a collimated laser beam. Then, the amplitude distribution G(w) in the back focal plane F of lens Ld can be expressed in terms of a two-dimensional Fourier transform as G(«)

g(jr)exp(27ri«jr)djr

(37)

where the variables « = (^, v) and x = (x, y) are the spatial frequencies in Fourier space (plane F) and the position coordinates in the object plane O, respectively, and a constant phase factor is neglected. If a camera is set and the intensity | G ( H ) | 2 is recorded at this place (plane F), we can obtain the spatial frequency distribution (viz. an optical diffraction pattern) of the object g(x). After passing through the plane F the light waves form a real image on the plane I (i.e. the lens L; also produces the Fourier transform). If the coordinate axes taken in the image plane I are in the opposite direction to those in the plane O, as shown in Figure 20(b), and if an appropriate scale proportional to the magnification is defined, then the amplitude distribution ij/(X) in the plane I is given by
where X=(X,

|G(«)exp(-27riA'«)di/

(38)

Y). When a filter with amplitude transmittance T(«) is set in the plane F, the

Electron Microscopy

811

modified amplitude distribution \I/'(X) on the image plane I is given by *(X)

G(»)T(«)exp(-27ciAif)dii

=

g(*)*t(*)

(39)

where t(X) is the inverse Fourier transform of T(w) and the * denotes the convolution operation. The quantity \\j/'(X)\2 is the intensity distribution of a filtered image. This method is generally called 'spatial frequency filtering'.19'202 The correction of the spherical aberration will be possible with an appropriate filter T(w). 197 If random noises caused by the photographic graininess are superimposed on a periodic pattern, then G(w) consists not only of a set of discrete peaks due to periodicity, but also a continuous spectrum due to noise. If we insert a filter grating T(i#) in the plane F which can let through the sharp peaks but block the rest of the spectrum, then the periodic structure will be enhanced with respect to the noise. 1 4 4 ' 1 7 3 Another method to remove random noise is called linear integration', 1 6 9 ' 1 7 1 ' 2 0 3 - 2 0 5 i.e. the shifted superposition of a periodic picture. Since the noise is regarded as random, 89 ' 90 the yJN improve­ ment 20 in the S/N ratio will be attained by this procedure, where N is the number of repeated superpositions. These two methods are different in practice. In a special case, however, Hashimoto et al.115 and Aebi et al.173 have shown that the optical image contrast formed by spatial frequency filtering using a filter grating is equivalent to the picture contrast by linear integration. (ii) Image averaging So-called 'image averaging' using a filter grating made up of an array of pinholes was treated mathematically by Aebi et al.113 The effective averaging is determined by the spatial extent of the hole size in filter gratings. 144 Fraser and Millward discussed the effects of the size of the hole, and estimated the optimum filter hole size. 206 If both periodic and large scale irregular structures are contained in the original image to be processed, optical filtering should be carried out using a filter grating T(«) which has pinholes that are rather large in size. 55 ' 144 Such examples will be shown in Section 34.5.1.1.iii for lattice images containing edge dislocation. Next, a typical example of a filter grating for effective averaging will be described. The filter grating, which was used in the optical filtering of the micrograph of the jS-form of a PPX single crystal, is a hexagonal one (lattice constant 1 mm), having very small holes (100 jum in diameter).14 In the experiment, only the holes which corresponded to the sharp peaks in the diffractogram were used and the others were clogged. In this case, the hole size of the filter is much smaller than the lattice constant (the hole size is 0.1 of the lattice constant), and thus rather effective averaging was successfully obtained. Tanji et al. reported that for effective averaging, the hole size in the filter grating should be smaller than 0.075 of the lattice constant. 207 ' 208 Processed images were recorded on Minicopy film (copy film; Fuji Photo Film Co. Ltd.) to avoid quality degradation due to the granularity of photo-emulsion, and the film was developed at 20 °C for 6 min with Konidol Fine (Konishiroku Photo Ind. Co. Ltd.) to reduce too much high contrast of this film.144 A handy filter grating for optical filtering may be formed by making holes directly in the Polaroid-Land film on which the optical diffraction pattern of the micrograph is recorded. Optical filtering is very simple and useful, but several technical problems still remain. For example the multiple reflection of light between lenses causes an interference effect on the image. Lenses should be set at intervals long enough to suppress this effect.

34.4

SCANNING ELECTRON MICROSCOPY AND SCANNING TRANSMISSION ELECTRON MICROSCOPY

In the case of TEM, the specimen is illuminated rather widely with an electron beam for morphological observation. On the other hand, in the scanning electron microscope (SEM), a specimen is scanned with a focused fine beam. Using the signals from successive points in the specimen which rastered with the beam, the image is displayed on a TV monitor. In this case, the scanning raster in the TV is perfectly synchronized to the slow-scanning electron beam in the microscope; that is, the deflection coils of the cathode ray tube in the TV monitor are synchronized with the scanning coils of the incident illumination on the specimen in the microscope column. 21 ' 23 ' 25 The brightness at a certain point on the TV screen is modulated proportionally to the number of collected electrons which are emitted from the corresponding position of the specimen. There are two kinds of scanning electron

812

Microscopy

microscopes: (i) the so-called SEM for surface observation using some of the secondary electrons emitted from the specimen surface; and (ii) scanning TEM (STEM) using electrons transmitted through thin specimens, as is the case for TEM. For both, resolution depends on the size of the electron beam as a probe rastering the specimen. Thus the field emission gun (FEG) is recommended to get a reasonable current into a fine probe (see Table 2 in Section 34.3.3.l.ii).

34.4.1

Scanning Electron Microscopy (SEM)

For TEM, the specimen must be thin enough for electrons to pass through it (Section 34.3.3.2.i). Of course, the penetrating power of the electrons increases with increasing their energy (namely, accelerating voltage), but the maximum specimen thickness seems to be at most the order of jum.25 To observe the surface of bulk materials with TEM, the replication method is applicable (Section 34.2.2.2), but it is rather troublesome to make the replica. For these materials, SEM is easily employed. The contrast in SEM is formed by several mechanisms. Some are briefly introduced here. 2 0 9 ' 2 1 0 (i) Effect due to the angle between the incident beam direction and the specimen surface (surface tilt contrast); the surface normal to the incident beam direction is the darkest, (ii) Edge effect; protuberances on the specimen surface show bright contrast (diffusion contrast), (iii) Secondary emission rate; the image contrast depends on the amount of secondary electrons, namely, the difference of the kinds of constituent atoms in the specimens (material contrast), (iv) Effect of metal coating; to suppress the charging of insulating specimens and/or to increase secondary emission rate, heavy metals such as Au are used to coat the specimen surface, for example, using a sputter coater. In this case, rather large fluctuations in the thickness of evaporated metals induce an additional contrast as an artifact. An insulating specimen will be charged positively or negatively, depending on the total electron emission yield.209 Charging will introduce artifacts in the image contrast. Detailed discussion about charging and its effect on the image contrast have been presented by Reimer.209 As mentioned above, metal coating is frequently adopted to increase the electric conductivity of the specimen. Coating the specimen with a thin layer of evaporated metal brings the following additional benefits:25 (i) to decrease the radiation damage, and (ii) to increase the secondary emission rate. As a coating material, an Au-Pd (60:40) alloy is recommended, as it shows finer granularity than Au. 210 Some methods are proposed to increase the conductivity,25 including the use of a lower accelerating voltage. In the field of polymer science, SEM is widely used. For example, Tagawa et al. showed the lamellar structure in blown films of PE, using FEG as the electron source and with a coating of an Au-Pd alloy. 211 In order to observe internal morphology of PE solids with any inherent plastic deformation, Shimamura et al. proposed a method by fracturing, combined with treatment with fuming nitric acid. 2 1 2 - 2 1 4 SEM combined with the energy dispersive X-ray analysis (EDXA) has been applied to the study of lignin distribution in a wood, through the use of brominated wood. 215 To improve the spatial resolution, a thin section is recommended as a specimen. This thin specimen is mounted on a collodion film deposited on a single hole C grid and then this grid is set on a holder. The holder is also used as a Faraday cage. The single hole C grid is also applicable for TEM-EDXA experiments. 2 1 6 - 2 1 8

34.4.2

Scanning TEM (STEM)

The image contrast and resolution for STEM is, in principle, the same as in conventional TEM, according to the reciprocity theorem. 219 Thus, mass thickness contrast, diffraction contrast and phase contrast are expected with STEM, as in the case of conventional TEM. Of course, lattice imaging is also obtainable. 220 STEM has some advantages over conventional TEM as follows.23 (i) A rather thick specimen can be observed because there is almost no effect from chromatic aberration since there is no imaging lens following the specimen. (ii) Apparent radiation damage will be reduced, because the very fine probe falls on one point of the specimen or scans a certain tiny portion. Thus the rest of the specimen is still alive. This technique is similar to the low dose technique in conventional TEM, for example MDS (Section 34.3.3.2.iv). (iii) Microdiffraction is easily obtained. With this technique, a sequence of ED patterns from adjacent areas are observable, for example along the spherulite radius. 221

Electron Microscopy

813

(iv) A many beam annular dark field image is observed using an annular detector to collect one ring of the ED pattern from the specimen. (v) Contrast is electrically adjustable as is the case for SEM. If a computer image processing system is connected directly to STEM, on-line processing is applicable. 344 ' 345 Up to now, only a few works in polymer science have been reported with the use of STEM. 23 Further development is expected. 34.4.3

Scanning Tunneling Microscopy (STM)

Recently, STM has become a good tool to analyze the ultra fine structure in the surface of materials. 221 This technique is based on the tunnel effect in quantum mechanics. If a very thin and pointed probe (tip) approaches down to a certain distance from the specimen surface, electrons come out from the specimen by tunnelling through a potential barrier to the tip, i.e. forming a tunnel current. To control this tunnel current so that it is constant, the distance between the tip and the specimen surface is adjusted, and therefore this distance is monitored under synchronizaton of the scan of the probe along the surface. Another way, is to keep the height of the tip constant, and to monitor the tunnel current. With STM, atomic resolution is expected, but this is applicable mainly to conducting materials. Further developments are awaited. 34.5

THE APPLICATION OF ELECTRON MICROSCOPY TO THE STUDY OF POLYMER SOLIDS

Electron microscopy is widely used in the field of polymer science for morphological investi­ gations. 2 1 ' 2 2 ' 2 2 2 - 2 2 4 In particular, analytical SEM is now one of the indispensable tools used by companies to analyze the constituents and structure of newly developed materials. Thus most work reported in the literature used electron microscopes in a routine way with no special techniques. In this section, our results will be described as examples of structural investigations by electron microscopy. The new techniques, except those shown in previous sections, and some important results in the structural study of polymer solids are also described. 34.5.1

Solution-grown Crystals of Polymers

The morphologies of single crystals of various polymers are reviewed extensively by Geil 225 and Wunderlich. 223 In this section, structural studies of solution-grown crystals including so-called single crystals are described. Detailed discussions, however, are mainly focused on poly(p-xylylene) (PPX) and poly(p-phenylene sulfide), with some other examples introduced briefly at the end of this section. 34.5.1.1

Poly(p-xylylene)

(PPX)

The crystal structure of PPX was first reported in 1953 by Brown and Farthing 226 who discovered two crystalline modifications of a and /?, corresponding to the low and high temperature modifi­ cations, respectively. In 1966, Niegsch 227 found the presence of a new transition at 270 °C through differential thermal analysis. This transition appears uniquely in the polymer prepared from di-pxylylene. He also studied the morphology of both a and /? single crystals of PPX grown from a-chloronaphthalene solution. Kajiura et al228 have confirmed by X-ray measurements that these two single crystals correspond to the a- and /J-forms of the bulk materials observed by Brown and Farthing. Miles and Gleiter, 229 and Isoda et al230 studied the molecular mechanism of the a -»/? phase transition of single crystals of PPX by TEM using the heating specimen holder. Two entirely different types of single crystals (in fact, they are the so-called 'mosaic crystals') were developed from the solution (0.05%, 210°C), showing a rectangular habit (a-modification) and a hexagonal one (^-modification).227 The crystal thickness of the a-form was ~ 12 nm, and that of the /?-form was -8nm.14 (i) a-Modification of PPX In the case of the a-modification of single crystals of PPX, two types of diffraction patterns were obtained, corresponding to a single layer or multi-layer crystal.14 Figure 22 shows both kinds of

Microscopy

814

Figure 22

a-form of a PPX single crystal and the corresponding selected area ED patterns: the squares in (a) and (b) show the size and position of the selected area aperture

0=25° Figure 23 The change of an ED pattern of the a-form of a PPX single crystal due to specimen orientation. The specimen was tilted around the short axis of the rath crystal, using a rotation/tilt holder (0 = 25° corresponds to an <001 > incidence)

Electron Microscopy

815

selected area ED patterns and their double-exposed micrographs with a selected area aperture. Kubo and Wunderlich 231 reported the unit cell dimensions of the a-modification, and Iwamoto and Wunderlich 232 analyzed the crystal structure of this modification based on the result by Kubo and Wunderlich. As shown in Figure 22, a single layer crystal yields the ED pattern corresponding to an <102> incidence of electron beam. A multi-layer crystal yields the hkO reflections corresponding to an <001 > incidence of electrons as well as the diffraction pattern of an < 102> incidence. Accordingly it is concluded that the chain axis in the basal layer is not perpendicular to the crystal end surfaces (namely, not parallel to the direction of the incident electron beam). It also confirmed the change in the ED pattern when tilting the crystal around its fc-axis. As demonstrated in Figure 23, tilting the crystal to a certain direction by 25° gives strong hkO reflections and no 201 in the ED pattern. The chain axis in the layers except the basal one is, however, parallel to the incident beam direction. Figure 24 is the optical diffractogram (OD) of high resolution electron micrograph of the a-form of the single crystal.14 It resembles Figure 22(b'), and is apparently a micrograph of a double-layer crystal. Optical filtering (Section 34.3.4) was performed to separate superposed images into two. The results are shown in Figure 25(a) for a <001> incidence, and in Figure 25(b) for a <102> incidence. Encircled reflections in the OD at the upper right corner of each figure are those used for optical filtering. The inset in each figure shows the image simulated by computer (C s =1.06mm, X = 0.00142 nm, Af= 40 nm and resolution limit = 0.2 nm). Each dark ellipse in Figure 25(a) is to represent the projection of one PPX molecule viewed in the direction parallel to its molecular axis. The parallel fringes seen in the multi-layer parts in Figure 23 are moire image interference fringes. The radial stripes seen in the single basel layer are due to diffraction contrast, indicating that there exist six sectors, as shown by a tent-like structure, 231 prior to its deposition on the specimen support film. Moire fringes and radial stripes can also be observed in dark field images, as long as the crystal is living under electron irradiation. (ii) ^-Modification of PPX Most of the /?-form single crystals of PPX have nearly flat and regular hexagonal shapes, as shown in Figure 3 (Section 34.2.2.1) and Figure 16 (34.3.3.2.iv). The ED pattern of the /?-form single crystal

Figure 24

CPC—AA

Optical diffractogram of the high resolution image of a multi-layered single crystal of the a-form of PPX (this pattern is similar to the ED pattern shown in Figure 22b')

816

Microscopy

Figure 25 Optically filtered high resolution images of a multi-layered single crystal of the a-form of a PPX (a) <001) incidence; and (b) < 102> incidence. The inset at the upper right corner of each figure is the optical diffractogram in which the reflections used for optical filtering are encircled. The inset at the lower left corner of each figure is the computer-simulated image on the basis of the crystallographic data of the PPX a-form. Kinematical image simulation was performed with Cs = 1.06 mm, /. = 0.00142 nm, A/ = 40 nm and resolution limit = 0.2 nm. In (a), a' = asm [1 = 0.421 nm and b = 1.064 nm

shows no systematic absences of reflections, as reported by Niegisch,227 and has no symmetry planes (see Figure 3a or Figure 16a'). This pattern is characterized by merely six-fold rotational symmetry. 14 Spirally grown multi-layer crystals are frequently observed on the /?-form.115 The radial stripes which are seen in all the /?-form crystals are due to diffraction contrast as observed in aforms, and they indicate that there exist six (10.0) sectors in the /J-form single crystal. This is also recognized in the dark field image, as shown in Figure 3(b). All the sectors yield an identical diffraction pattern. The stripes disappear under strong electron irradiation (Figure 16). Niegisch has estimated the hexagonal unit cell dimension (a = b — 2.052 nm, c(fiber axis) = 0.685 nm) and con­ cluded that the molecules are all parallel to the c-axis, which is perpendicular to the single crystal end surface.227 The high resolution electron micrograph of the /?-form single crystal was obtained using 500 kV ultra high resolution TEM (JEM-500).14 In the case of the /?-form, the electron beam is incident on the platelet crystal in its < 001 > direction and parallel to the molecular axis. Therefore individual chains comprised in the crystal are expected to be resolved. Figure 26(b) is the optical diffractogram (OD) of the micrograph and resembles ED (Figure 26a). The similarity between ED and OD patterns shows that the micrograph has sufficient information about the crystal structure of the ftform. In order to extract structural information from the noisy micrograph, optical filtering was performed using the filter grating as described in Section 34.3.4.3.ii. The processed image is shown in Figure 26(c) with a structural model in Figure 26(d). In the case of the /Worm crystal, it is concluded from the density and lattice dimensions that a unit cell must contain 16 chain segments (the length of a chain segment is the fiber period), that is to say, 16 polymer chains ought to run through a unit cell. This has made the structure analysis of the /?form crystal complicated. Prior to the structure analysis of the jS-form of the PPX crystal, the polymer crystals belonging to the hexagonal or trigonal system were classified into three groups, as follows.233 Group 1 Each chain has a three- or six-fold axis or screw axis. The number of molecules in a unit cell is one or an integral multiple of three.

Electron Microscopy

817

Figure 26 The /?-form of a PPX single crystal: (a) the ED pattern taken at 500 kV, showing a net pattern with hkO reflections; (b) the optical diffractogram of the original negative taken with the ultra high resolution TEM JEM-500 operated at 500 kV. (c) the optically filtered high resolution image; and (d) the model structure analyzed by ED intensity

Group 2 Each chain has cylindrical or nearly cylindrical symmetry. In this case, a unit cell is made up of only one molecular segment and the symmetry is restricted to hexagonal or pseudohexagonal. Group 3 An integral multiple of three identical chain segments constitute a unit cell, though each molecular chain has no symmetry features of Group 1 or 2. The /?-form of the PPX crystal which does not suit any of the above-mentioned prerequisites is an unusual example, and the crystal structure was not previously analyzed. Each dark spot in Figure 26(c) represents the projection of one molecular chain on the ab-plane, as is the case of the a-form (Figure 25a). Some of the spots in this micrograph seem to be elliptical, showing the directions of the major axes of such ellipses. The significance of the image is its enhancement of the features of the molecular arrangement. Here the mutual positions of the molecular centers in the projection on the ab-plane are clearly observed, i.e. chains are arranged in a wave pattern of zigzag manner, for example in the 100 direction. 233 The feature of the arrangement of molecular centers seems to be represented in terms of the two-dimensional space group P6, which has no conditions limiting possible reflections. Indeed, the ED pattern of the /?-form of a PPX single crystal has neither systematic absences of reflections nor symmetry planes but only shows six-fold rotational symmetry, as described above. First, a two-dimensional structure model of the /J-form of the PPX crystal was assumed so as to satisfy the symmetry of P6, taking van der Waals' radii and the high resolution image (Figure 26c) into account. Here, the orientation of the molecule at the origin of a unit cell was assigned

Microscopy

818

statistically to one of three equivalent orientations to satisfy the symmetry of p6. The refinement of the structure analysis was attempted by the least squares method over the ED intensity data, which were obtained by optical densitometry of reflections which had appeared in ED patterns. A PPX 'single crystal' is a mosaic crystal which gives a spot pattern (so-called 'N-pattern') in its ED. Therefore l/dhk0 was used as the correction factor corresponding to the Lorentz factor in X-ray diffraction, where dkk0 is the (hkO) spacing of the crystal. 234 The molecular conformation of the /?-form of PPX was the same as that of the a-form.232 If the molecule at the origin of a unit cell is represented with a circle and others with ellipses, this result (Figure 26d) resembles the micrograph (Figure 26c) fairly well, and some of the corresponding ellipses and spots in these figures coincide in position and in orientation with each other. Moreover, an optical mask with the same structure as this model gives an OD pattern (Figure 8(a) in Section 34.2.2.2), which is almost identical to the ED pattern of the /?-form single crystal (Figures la, 16a' and 26a). Figure 27(a) schematically shows the result of crystal structure analysis of the /?-form of the PPX crystal by using X-ray diffraction.233 The crystal system and lattice constants are as follows: trigonal P3 ; a = b = 2.052 nm; c = 0.655 nm (molecular axis). The bold lines of the molecular backbone

\

Over focus

Cs = 1.06 mm; tfmin =1.4 &

0

-450 W jp.

■fP*-'

# # «* § *# * * ♦ 'f f**

r*

' I m | *i ♦ # ♦ * , ~*: ** $ 450 Scherzer focus

900

1350 Under focus

Figure 27 (a) the three-dimensional structure model of the /7-form of a PPX crystal, which is shown as the ab-plane projection: trigonal M , a = b = 2.052 nm, c = 0.655 nm, y = 120° 347 (the result of the final refinement should be cited from ref. 233). (b) the simulated through-focal images taken with a JEM-500, based on the structure model in (a): X = 0.00142 nm, C = 1.06 mm. resolution limit = 0.14 nm

Electron Microscopy

819

represent the upper part of a benzene ring in Figure 27(a). The molecule at the origin of the unit cell statistically takes one of three equivalent orientations shown in the figure. Here we have reached the stage where the consistency of the results of X-ray analysis and the highresolution electron micrograph should be examined. According to Kobayashi erroneous results may be obtained in the region of the focus of a microscope at its resolution limit. 235 The image intensity is greatly affected by the defocus and the spherical aberration through sin/(w) in phase contrast electron microscopy, as described in Section 34.3.2. Therefore it is necessary to compare the obtained electron micrograph with the simulated through-focal images, so as to confirm authenticity of the micrograph as well as the result of structure analysis. The computer simulation was performed according to the kinematical diffraction and using the following parameters: accelerating voltage = 500kV, spherical aberration coefficient C s =1.06mm, and resolving power = 0.14 nm). The result is shown in Figure 27(b), demonstrating the effect of defocusing. The simulated image at the Scherzer focus ( A / = 45 nm) is quite similar to the micrograph actually obtained. It is, however, not expected even with this ultra high resolution TEM to resolve individual C atoms of a PPX molecule in the afo-plane projection in which atoms are close together. (Hi) Direct observation of lattice defects in single crystals of PPX Diffraction experiments (X-rays, neutrons, electrons) give only statistical data which are averaged over the whole sample. On the other hand, EM is a powerful and unique tool with which defects in the periodic structure of a crystal can be studied visually. Polymer crystals are much more imperfect than crystals of ordinary low molecular weight materials, as shown by X-ray diffraction. Based on electron micrographs with moire image interference fringes22'24'223,236-24.0 ( u s u a u v explained in terms of double Bragg diffraction of the electron beam) or dislocation networks 2 2 3 , 2 4 0 - 2 4 3 (observed by virtue of the diffraction contrast) in bi-layered polymer single crystals, the im­ perfections in polymer crystals have been made considerably visible. Lattice defects in a PE single crystal due to electron irradiation were also investigated by the moire method. 244 It was reported that the image intensity of the moire fringe patterns in electron micrographs of two superimposed thin crystals is 'the square of the Patterson distribution', magnified by the factor l/2sin (e/2) (e is the relative rotation of the crystals).245 This type is called a 'rotation moire'. 223 Others are a moire fringe from crystals of slightly different lattice spacings 223 (parallel moire), and a tilt moire because of an effective misorientation from the Bragg condition. 246 These three types may be partly mixed. Therefore it is not easy to analyze the structure of dislocation on a molecular or atomic scale from moire fringes. The analysis of dislocation networks is much more difficult than that of simple moire fringes. In the case of inorganic or organic crystals which are very resistant to electron irradiation, high-resolution images of defects and dislocations can be obtained. 247 Polymer crystals, on the contrary, are so susceptible to electron irradiation that the lattice images including the defects are difficult to take. In Figure 28 are the first successfully obtained high resolution lattice images which resolve directly the edge dislocation in the a-form and jS-form of PPX single crystals. 248 Since the constituent atoms in a polymer crystal are linked together with covalent bonds to form molecules, the direction of the backbone chain is a unique direction in the crystal. The classification of the dislocations in a PE orthorhombic crystal was first carried out by Keith and Passaglia. 249 Seto 250 classified dislocations in polymej crystals into five types on the basis of the directional relationship among the Burgers vector^ A, the vector of the backbone chain direction in, and the vector of the dislocation line direction /. Figure 29 schematically show five models of dislocation which are predicted to exist in polymer crystals. Wada and Matsui 251 reclassified the dislocations in PE in terms of these five types. The characteristics of the dislocation types shown in Figure 29 are summarized as follows. Type (1): screw dislocation, which does not change the conformation of polymer chains. This can be first produced at the side faces of a thin polymer single crystal owing to thermal motion, and then proceeds into the crystal. 252 Type (2): edge dislocation, which was proposed in order to account for the slip bands in the plastic deformation of nylon 66. 253 This dislocation is considered to be much less likely because of the resistance to glide motion, especially in polymers where the chemical repeat distance is very long. 249 Type (3): edge dislocation, which is the most stable because this does not change the conformation of the polymer chains and passes through a lamellar crystal by the shortest course. This was observed through moire fringes in lamellar crystals (such as polyoxymethylene,238 PE 2 3 9 and so on) with TEM. Type (4): screw dislocation, which is energetically unstable. A concentration of dislocations of this type generates a twist boundary in a crystal. Hosemann et a\. considered, from the line profile analysis

820

Microscopy

Figure 28 High resolution images of the a-form (a) and ^-forrn (b) of PPX single crystals with lattice defects: (a) an edge type dislocation observed in 020 planes (0.53 nm in spacing), which is indicated by the arrow; (a') a schematic representation of (a), in which there is an extra half plane of 020, and no distortions observed in 201 planes; (b) each dark ellipse corresponds to the projection of one molecule along the chain direction, with extra half planes of the 400 type indicated by arrows; and (b') a schematic representation of (b), in which the filled circles represent the centers of individual molecules in (b) and the lines show 400 and 040 planes

Figure 29 Models of dislocations which are predicted to exist in polymer crystals: (1), (4) have a screw dislocation; and (2), (3) and (5) an edge dislocation 250 (a square prism represents a molecular chain, b a Burgers vector, 7 a dislocation line vector, and in a vector which shows the chain direction)

Electron Microscopy

821

of hkO X-ray reflections, that the polymer single crystals are mosaic, which they ascribed to this type of dislocation. 254 Type (5): edge dislocation, which is generated when the ends of chains stand in a line. A tilt boundary is caused by a concentration of dislocations of this type. 255 The screw dislocation of type (1) which has the Burgers vector parallel to the molecular axis, and the edge dislocation of type (3) whose Burgers vector is perpendicular to the molecular axis, should be very easily introduced in lamellar crystals. When the molecular axis in a thin lamellar crystal is perpendicular to the crystal's end surface, it appears to be difficult practically to observe the dislocations of types (1) and (2) because their Burgers vectors are parallel to the incident electrons. In the case of types (3), (4) and (5) dislocations can be observed using EM. The dislocation which has been observed in a PE single crystal corresponds to the partial dislocation of type (3). 240 ' 256 The edge dislocations in inorganic crystals have been observed on an atomic scale, 2 5 7 - 2 6 0 and the point defects have also been directly observed, 261 " 263 by high resolution electron microscopy. A high angle tilt grain boundary in a thin crystal of germanium was imaged with atomic resolution and was shown to consist of alternating columns of five- and seven-membered rings of germanium atoms. 264 The dislocations of various types are observed in the crystals of organic compounds such as hexadecachlorocopper phthalocyanine when the specimen is resistant to electron irradiation. 247 In order to obtain high resolution images of crystal defects with TEM, the defects should extend along the direction of the incident electrons, forming columns which produce proper contrast in an image. The edge dislocation image of the jS-form of a PPX single crystal in Figure 28(b) is the optically filtered image. Though the arrangement of molecules in the projection of the afc-plane is not very clear, the appearance of the dislocation is similar to Bragg and Nye's bubble model. 265 Two extra half planes of type 400 are designated by white arrows. The Burgers vector b of this partial dislocation is probably (1/4) [110] (see Figure 28b'). This should be type (3). Neither the mutual arrangement nor orientations of the molecular chains are defined in Figure 28(b) owing to a lack of higher resolution. Figure 28(a) is the high resolution lattice image with the lattice defect of the a-form of a PPX single crystal. Intense 020 lattice fringes (0.53 nm in spacing) and weak 201 ones (0.28 nm) are observed. The upper part of this figure contains one extra half plane of 020 (indicated by an arrow). As schematically shown in Figure 28(a'), there are no distortions observed in the 201 planes. Thus this dislocation is considered to be a partial one of type (3). The Burgers vector b is probably (1/2) [010] and a stacking fault should be associated with this. Details are not as yet known. Recently, a type (2) dislocation was found in an image, with moire fringes, of the bi-layered j6-form of a PPX single crystal. 266 Read and Young 267 reported a chain end dislocation dipole in a 010 lattice image of poly[l,6-di(iV-carbazoyl)-2,4-hexadiyne], which is one of the polydiacetylenes. Probably this corresponds to the type (5) dislocation in Figure 29, when viewed in the direction parallel to the vector 7.

34.5.1.2

Poly(v-phenylene sulfide) (PPS)

PPS is used in the electric and electronic field, mechanical field and so on, owing to its fairly high thermostability and small molding contraction. 274 Though the crystal structure of PPS was analyzed by Tabor et a/.275 and the electroconductive mechanism of doped PPS has been discussed by many workers, 276 ' 277 the morphologies of PPS itself and doped PPS have not been studied very well. Here the electron microscopical observation of a PPS solution-grown crystal will be shown. 1 1 0 ' 2 7 8 Figure 30(a) is a solution-grown fibrillar crystal of PPS and its ED pattern. The thickness and the width of the crystal were measured at 11.5 nm and at 100 to 300 nm, respectively. As deduced from the micrograph of the crystal shadowed with Pt-Pd (Figure 30b), a fibrillar crystal seems to consist of finer 'microfibrils'. The ED pattern (inset of Figure 30a) shows hkO reflections and some other reflections such as 111 and 211, as indicated by arrows in the figure. On the basis of Ewald construction, it was concluded that the fibrillar crystal grows in a direction parallel to the b-axis by changing its orientation around the b-axis. 278 Figure 31(a) is the same ED as the inset in Figure 30(a), showing that the angle between lines drawn from the origin to the centers of the 200 and 111 reflections is 49°. In principle, the ED pattern discussed above corresponds to <001> incidence of electron beams onto the crystal. Occasionally the ED pattern shown in Figure 31(b) was observed. It reveals hOO and hll reflections and the angle in question is 60°. In this case, the incident electron beam direction is parallel to <011> of the PPS crystal (<011> incidence is identical to <011> incidence). The total end point dose (TEPD) of PPS crystal is about 0.2 C c m " 2 at room temperature and

822

Figure 30

Microscopy

PPS solution-grown crystal (a) without and (b) with shadowing: the inset in (a) is a typical ED pattern of the crystal; in (b) Pt-Pd shadowing reveals that the crystal consists of several fibrillar crystals

200 kV. This means that PPS is fairly resistant to electron irradiation (see Table 3 in Section 34.3.3.2.iv). Two kinds of high resolution electron micrographs were obtained, as shown in Figures 31 (a') and (b'), which were the results of optical filtering. They are attributed to two different projections along the <001> and <011 > directions of the PPS crystal, respectively, judging from their optical diffractograms (OD). Figures 32(a) and (b) illustrate the projections of the crystal along <001 > and <011 >, respectively, based on the results of crystal structure analysis. 275 Comparison of Figure 31(a') with Figure 32(a) indicates that each dark ellipse in Figure 31(a') corresponds to a single molecular chain projected on the afc-plane along the chain direction. This is confirmed from

Electron Microscopy

823

Figure 31 Two kinds of ED patterns and corresponding high resolution images of a PPS solution-grown crystal: (a) the ED usually observed, consisting basically ofahkO reflection; (a') the high resolution image corresponding to < 001 > incidence (the inset at upper right corner is the simulated image: 1 = 0.00251 nm, Cs = 2.8 mm, A/°=90nm); (b) the ED occasionally observed, consisting of hOO and hi I reflections (<011 > or <011 > incidence); and (b') the high resolution image corresponding to the crystal orientation of (b) (the inset at upper right corner is the simulated image: A = 0.00251 nm, C, = 0.7 mm, A / = 48 nm). The insets at lower left corner in (a') and (b') are optical diflfractograms (OD) of the original negatives. In image simulation, the reflections up to 200 for (a') and those up to 211 for (b') were used

the_ simulated image which is inset at the upper right hand corner of Figure 31(a'). In the case of <011> incidence, the corresponding projection (Figure 32b) is denoted as follows. In A of Figure 32(b), C atoms of an 'edge-on' phenylene group come together and S atoms are close to the phenylene. On the other hand, C atoms of a nearly 'flat-on' phenylene as in B are not so condensed and S atoms are far from the phenylene. From above, each dark ellipse in Figure 3 l(b') is assigned to A and the region between ellipses to B. The simulated image (inset, upper right hand corner of Figure 31b') proves that the above consideration is reasonable. High resolution images of a crystal projected in two or more different crystallographic directions are very useful in determining its three-dimensional structure. In particular, they are important for the study of the three-dimensional distribution of the dopant relating to the position of the polymer chains in doped PPS. CPC—AA*

Microscopy

824

(a)

Figure 32 Projections of the crystal structure of PPS: (a) projection for the < 001 > incidence; and (b) projection for the < 011 > incidence (< 011 > incidence is identical to <011 > incidence) (in (a) and (b), S atoms are indicated by larger filled circles than C atoms, and H atoms are not shown)

34.5.1.3

Other polymers

Recently the morphology of solution-grown crystals of poly(aryl ether ether ketone) (PEEK) 279 was reported, and it is similar to that of PPS. The PEEK crystal is fairly resistant to electron irradiation. 280 We have obtained lattice images of the crystal and we will be reporting on this in the near future. 281 Lattice images of poly(ether ketone) (PEK) have been obtained. 282 These materials are fairly thermostable, as is pps. 2 8 2 * 2 8 3 Single crystals of poly(4-methyl-l-pentene) (P4M1P) are flat and square, as is well known. 284 It is not easy to take lattice images of P4M1P at room temperature because it is rather sensitive to electron bombardment. In this case, cryo protection is useful to obtain high resolution images, which show clear lattice fringes.285 In the case of the PE single crystal, it was reported that TEPD of a very tiny crystal is much greater than that of a crystal of normal or large size.286 Very recently, a tetragonal single crystal of poly(tetramethyl-p-silylphenylene siloxane) was used for high resolution observation, and the molecular arrangement in the crystal was clearly observed with a resolution of 0.32 nm. 1 3 2 ' 2 8 7 Preparation conditions of single crystals of various polymers were reviewed by Wunderlich 223 and Kawaguchi. 341 The procedure to make single crystals by film formation was also proposed. 342

34.5.2

Thin Films of Polymers

There has been much work reported on the morphological observations of polymer thin films, such as polyethylene terephthalate) (PET), 2 8 8 ' 2 8 9 PE, 2 2 2 polybutene-1 (PB-1),290 isotactic poly­ styrene (isotactic PS), 2 9 1 ' 3 5 0 poly(p-phenylene sulfide) (PPS), 278 poly(p-phenylene) (PPP), 292 poly-

Electron Microscopy

825

(aryl ether ether ketone) (PEEK) 280 and so on. In this section, some examples of electron microscopy in the study of polymer thin films will be described.

34.5.2.1

Isotactic polystyrene (isotactic PS)

The TEPD of isotactic PS is around 0.03 C c m - 2 ( ~ 2 0 0 0 e n m - 2 ) for 200 keV (1 eV = 1.6 x 10" 1 9 J) at room temperature and about three times that of PE (Table 3 in Section 34.3.3.2.iv). The lattice spacings of i-PS crystal^ in particular its hkO spacings, are invariant with increasing irradiation dose. 121 The largest spacing that appears in the ED pattern is 1.1 nm. It corresponds to the 110 lattice plane of isotactic PS crystal and is the most resistant to electron irradiation. 120 ' 121 Thus lattice imaging has already been reported for isotactic PS single crystals at 120 kV. 1 2 0 , 1 2 1 Lattice images of unstretched and stretched thin films of isotactic PS are also obtained. In particular, the lattice imaging from stretched films is expected to help in the elucidation of the crystallization mechanism at an early stage of stress-induced crystallization. (i) An unstretched thin film of isotactic p s 4 6 ' 1 1 3 A drop of hot solution (1-2 wt %) of p-xylene was spread on the surface of hot water to make a thin amorphous film of isotactic PS. The thickness of the film was around 100 nm as judged from its interference color. This is the same technique as that used to make thin films of PE and PP with a spherulitic structure. 222 The amorphous film of isotactic PS was mounted on electron microscope grids and annealed at 160-170 °C under a nitrogen atmosphere. Before annealing, unstretched films of isotactic PS were amorphous and did not give any crystalline reflections in the selected area ED pattern. Crystalline reflections, however, appeared in ED after annealing. This is the case of crystallization from the glassy state. 2 9 1 , 3 5 0 Specimens annealed for a short time, for example less than ten minutes, gave a sharp reflection corresponding to the 300 lattice plane, but no reflections attributed to the 110 and 220 lattice planes. By the method of defocus contrast (Section 34.2.3), a row structure, and a sheaf-like structure or immature spherulites are observable (Figure 9). Figure 33 shows the stacked lamellar structure in a isotactic PS thin film which was slightly stressed before and/or during depositing on EM grids. The change in contrast of the particle indicated by the white arrows demonstrates well the effect of defocusing. The ED pattern (Figure 33d) shows 'c-axis orientation' with a fairly strong 300 reflection. Dark striations in Figure 33(a) and bright ones in Figure 33(c) are attributed to crystalline lamellae, which is confirmed from the dark field image obtained by using the 300 reflection. Crystalline lamellae are set in the 'edge-on' position, and molecular chains of isotactic PS are set parallel to the specimen film surface. Thus it is deduced that a crystalline lamella grows in the direction normal to the 300 plane and its growing face is the 300 plane. Though the thickness of lamellae is measured as about 10 nm, for example in Figure 33(a), this value is not reliable because of a rather large amount of defocus. The distance between lamellae, namely the spacing between centers of them, however, should be constant with the change of defocus. Figure 34 shows a high resolution image from such a specimen, which was annealed and crystallized for seven minutes at 161 °C. Latttice fringes with a spacing of 0.63 nm, corresponding to the 300 lattice plane, are observed in narrow bands whose width is about 6 nm. The band is ascribed to a lamella; strictly speaking, to the crystalline core in the lamella. Thus the thickness of the crystalline core in a lamella is about 6 nm. This value is accurate and reliable because 0.63 nm lattice fringes are used as an internal standard for magnification calibration. The average value of the center-to-center distance between successive lamellae, namely the long period, was measured as about 12 nm from images by the defocus contrast method (Figure 33), from images using shadow casting (encircled region in Figure 5), from 300 dark field images and also from small angle ED (Section 34.5.2.2).46 If the system is assumed to be similar to a single crystal map, it may be considered that the period is equivalent to the average thickness of lamellae. Therefore it may be concluded that there exist surface layers on both sides of the lamella and their thickness is about 3 nm, half the difference between the lamellar thickness and the crystalline core thickness. The layers seem to have more or less a lack of regularity, but their detailed structure is not yet known. The specimen was annealed for a rather long time, for example more than one hour, and showed crystalline reflections assigned to 110 and 220 on the selected area ED pattern. When a small selected area aperture is used (1 //m in diameter or less on the specimen), a single-crystal-like diffraction pattern with hkO reflections is observed. Figure 35(a) is a defocused micrograph of a specimen which was annealed and crystallized for about one hour at 170 °C. In the figure, the regions

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Electron Microscopy

Figure 34

827

The high resolution image of an unstretched thin film of isotactic PS, crystallized at 161 °C for 7 min. Inset is the optical diffractogram (OD) of the image

indicated by arrows correspond to 'flat-on' lamellae because, for example, the ED pattern from the encircled area shows the single-crystal-like hkO N-pattern (inset in Figure 35a). This N-pattern is dominant in spite of the fact that there co-exists many edge-on lamellae within the circle. Figure 35(b) is a high resolution electron micrograph of such a specimen (annealed for about two hours at 170 °C). In the figure, 110 lattice fringes (1.1 nm) in three directions are recognized in the same area. These lattice lines intersect at an angle of 60° as is the case with a single crystal. 121 The 220 lattice fringes (0.55 nm) are also observed. The inset in Figure 35(b) is the optical diffractogram (OD) from the corresponding area in the negative. The diffractogram clearly demonstrates that there exists a single-crystal-like lamella in the 'flat-on' position.

Figure 35 An unstretched thin film of isotactic PS, crystallized at 170 °C for 1-2 h: (a) the defocused bright field image, the inset being the ED pattern from the encircled area; and (b) the high resolution image, being attributed to the area indicated by an arrow in (a), with the inset being the optical diffractogram (OD) of the image

Microscopy

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1L^«^J! Figure 36 A stretched thin film of high molecular weight isotactic PS (JW„ = 2.4 x 10°); (a) the ED pattern; (b) the high resolution image; and (c) the optical diffractogram (OD) of (b), showing 110, 220 and 211 reflections (the oblique dark band is a beam stop)

Electron Microscopy (ii) A stretched thin film of isotactic

829

ps46'113

Several drops of hot solution (0.3 wt %) were spread on a glass plate whose temperature was 180-190 °C. After evaporation of the solvent, the supercooled thin film of isotactic PS was vertically stretched upwards from the glass plate and then instantaneously quenched to room temperature. This procedure is essentially similar to that used by Petermann et al.295 for preparing oriented thin films of various polymers. The thickness of the stretched film was about 100 nm. Figure 36(a) is the ED of a stretched thin film of isotactic PS (not annealed), which reveals a typical fiber pattern with a weak amorphous halo. Figure 36(b) shows a high resolution image of the film and Figure 36(c) is the OD of the image. It clearly indicates in the image the existence of fringes with 1.1 and 0.55 nm spacings, which are attributed to the 110 and 220 lattice planes, respectively. The 0.49 nm fringe seems to be assigned to the 211 lattice plane. In Figure 36(b), a clear 1.1 nm fringe is running in the vertical direction, namely along the fiber axis. The size of the long, slender region along the fiber axis, in which the 1.1 nm fringe is observable, is about 15 nm in width and 200 nm in length. Though 1.1 nm lattice lines are slightly curved and partly disappear, most of them pass through the region, with no lattice defects recognizable for the 110 lattice plane. A region where lattice fringes appear should directly correspond to a crystallite. It is proposed that 'shish kebabs' appear in the process of crystallization from strained melts, 296 as is the case with flow-induced crystallization from solution. 297 Taking into account the procedure for specimen preparation, the regions mentioned above seem to be ascribed to the 'shish'. Molecular chains of isotactic PS seem to be fairly extended in such a shish crystal, judging from the defect-less feature of the 110 lattice fringe in Figure 36(b).

34.5.2.2

Polyethylene (PE)

For PE thin films, in which it is very difficult to take high resolution images at room temperature due to its radiation sensitivity, dark field and strongly defocused bright field modes, as well as the surface replication method, were useful for studying its structure. 222 ' 298 Figure 37 shows a thin film of a Marlex 6009 cast from a p-xylene solution, which was slightly stretched on a hot water surface, and subsequently deposited on EM grids. Defocus contrast method reveals that this film consists of lamellae whose fr-axes more or less orient, as deduced from the ED of the encircled area B. Stretching induces changes in the molecular orientation, as demonstrated with the ED pattern from area A. This ED pattern shows that PE molecules are aligned along the stretching direction. A PE fiber specimen was prepared by the rather strong stretching of a Sholex 6009 film case on a hot water surface and subsequently annealed at 126 °C. Figure 38(a) shows a selected area ED pattern, Figure 38(b) a dark field image taken with 110 and 200 reflections, and Figure 38(c) that taken with a 002 reflection. Figure 38(b) clearly shows that the fiber is made up of small crystallites (bright spots on a dark background) whose longitudinal thickness and lateral dimensions are about 20 nm. The bright spots align in a vertical direction, and thus the crystallites tend to align along the fiber axis, which suggests the existence of microfibrils with their lateral width of several tens of nm. Figure 39(a) is a defocused image and clearly shows a wavy stacking of lamellae as dark bands (about 20 nm thick) running in the horizontal direction (the stretching direction is vertical). Bright bands with a vertical thickness of about 10 nm correspond to the amorphous region between crystalline lamellae. The lateral dimension of these lamellae is of the order of jum and much larger than that of the crystallites shown as bright spots in Figure 38(b), whereas the thickness of the lamellae is of a magnitude similar to that of the crystallites. This fact suggests that a lamella is composed of many crystallites which do not have the same orientation, that is, the lamella has a mosaic texture. The optical transform (OD) (Figure 39b) of the image has broad but apparent intensity maxima which are indicated by arrows. It reveals the existence of a periodic texture consisting of stacked lamellae, corresponding to a low angle ED (LAED) pattern (Figure 39c). From Figures 39(b) and (c), the long period is estimated as about 30 nm. LAED patterns are observed without exciting the objective lens. 2 9 9 ' 3 0 0 ' 3 0 1 The specimen should be coated with evaporated C to suppress charge-up. 301 A structure model of the PE fiber is proposed based on the information from both dark field and defocus images. 298 Recently lattice images taken at room temperature with conventional 120 kV TEM were reported by Chanzy et a/.131 using ultradrawn gels of high molecular weight PE. In order to directly recognize the crystallite shape and/or the orientation of individual crystallites on the enlarged micrographs, however, cryo protection is indispensable. Such micrographs have already been obtained by the authors using a cryo TEM with super-conducting objective lens, 132 as mentioned in Section 34.3.3.2.iv.

830

Microscopy

*

2 fim Figure 37 A PE (Marlex 6009) thin film from a p-xylene solution, which was cast on a hot water surface and then moderately drawn there: (a) the ED from the encircled portion A in the deformed region, showing fiber orientation, and (b) the ED from the encircled portion B in the undeformed region

34.5.2.3

Other polymers

Stretched thin films of high molecular weight nylon 12 (t]v = 25) were prepared using the same method as for stretched isotactic PS films (Section 34.5.2.1 .ii), and then annealed at 170-175 °C after deposition on EM grids. The ED pattern of the film showed the fiber pattern with crystalline reflections which are indexed on the basis of the crystal structure of the ■y-form of nylon 12. 302 Sometimes ED patternsshowing special orientations were obtained. This pattern is characterized with a fairly strong 202 reflection, suggesting that the 200 plane, namely the plane on which hydrogen bonds are set, is oriented parallel to the film surface.303 From such specimens 020 lattice images (1.5 nm in spacing) were obtained. 303 The crystallite size in the direction parallel to the fiber axis (b-axis) is deduced as 8 to 15 nm because the number of lattice fringes recognized clearly within a coherent region in the micrograph is 5-10. Morphologies of thin films with a spherulitic texture have been studied extensively by TEM for various polymers such as PPS, PE, isotactic PS and so on. The strain-induced crystallization of isotactic PS from the glassy and rubbery state was examined by Yeh and Lamber 350 using TEM. Recently Geil discussed the presence of ordered domains in amorphous polymers. 304 Such materials were PE, P4M1P, poly(vinylidene fluoride), polypivalolactone, PP, PB and PET. Thin amorphous films of these polymers were prepared by an ultraquenching technique and examined by TEM. Roche and Thomas discussed the defocus microscopy of copolymers. 305 They introduced the phase contrast transfer function, sin %, to interpret the image contrast.

Electron Microscopy

831

Figure 38 A drawn PE film prepared by the hot drawing of a Sholex 6009 film from a p-xylene solution which was cast on a hot water surface and subsequently annealed at 126 °C: (a) the ED pattern; (b) the dark field image taken with 110 and 200 reflections; and (c) the 002 dark field image of the same specimen portion as (b)

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Figure 39 A drawn PE thin film which was prepared with the same material and by the same procedure as the film in Figure 38: (a) the defocused bright field image; (b) the optical diffraction (OD) pattern of (a); and (c) the low angle ED (LAED)

832

Microscopy

Kawaguchi et al. reported the preparation of oriented thin films of PPP and structural obser­ vations of them by TEM. 2 9 2 , 2 9 3 The paracrystalline nature of PPP was discussed by comparing its crystal structure with those of p-phenyls, in particular that of p-hexaphenyl. Here, p-phenyls such as p-hexaphenyl are oligomers of PPP. PPP and p-hexaphenyl are less radiation sensitive, and thus high resolution images were obtained for both materials. Stretched thin films of various polymers, such as PE, 3 0 6 isotactic p s , 3 0 6 - 3 0 8 PB-1 3 0 9 and some blends, were extensively studied using TEM by Petermann and his co-workers. 310,311 Recently, the epitaxial crystallization of PE onto uniaxially oriented PP was studied with TEM and is expected to be used for the adhesion of polymer laminates. 312 34.5.3

Fiber Structure

Stretched or oriented thin films of isotactic PS, PE, nylon 12 and PPP showing fiber patterns in their ED were mentioned in the previous Section (34.5.2). Some of these will also be discussed here. In this section, however, other examples which are not thin films but have a fiber structure will also be described. TEM, SEM and optical microscopy of fibers have been reviewed and should be referred to in ref. 314. 34.5.3.1

Poly(p-phenylene terephthalamide)

(PPTA)299

After annealing PPTA (Kevlar) at 400 °C, fibrillar fragments were obtained at room temperature by tearing. Figure 40(b) is a dark field image of PPTA taken with a 006 reflection. It shows a texture of alternating bright and dark bands with a period of about 500 nm. A similar texture is reported in longitudinal thin sections 314 and in fibrillar fragments.13 Careful inspection of the figure shows that there exist microfibrils running in the direction of the fiber axis and through these bands. Although Takahashi et al.315 have observed a line of bright spots in a bright band of the 006 dark field image, this is not recognizable in Figure 40(b). Figure 40(c) is a dark field image taken with 110 and 200 reflections of the same specimen portion that was used in Figure 40(b). This figure reveals that small crystallites (bright spots in the figure) are randomly dispersed throughout the fibrillar ribbon. Moreover, bright spots seem to be placed in a row in a certain region of the ribbon. A high resolution lattice image of the PPTA fiber is shown in Figure 41. Clear 110 lattice fringes can be seen. The area where lattice fringes appeared is of the order of 10 nm x 10 nm through to 20 nm x 20 nm, and is almost of the same order as the area of a bright spot in Figure 40(c). In the case of poly(p-phenylene benzobisthiazole) (PBT) fiber, such an area is slightly larger than that of PPTA and 20 nm wide by 40 nm long in the fiber axis. 316 This suggests

Figure 40

A PPTA fiber annealed at 400 °C: (a) the ED pattern; (b) the 006 dark field image; and (c) the 110 and 200 dark field image of the same specimen portion as (b)

Electron Microscopy

Figure 41

833

A high resolution image of a PPTA fiber. Inset is the optical diffractogram (OD) of the image

the reason why a PBT fiber has a greater modulus than a PPTA fiber. The direction of the 110 fringes in Figure 41, that is the c-axis of each crystallite, fluctuates slightly relative to the fiber axis in the plane of the figure. Even curved fringes can sometimes be seen. 13 ' 298 Examples of curved fringes are easily recognized by inspection of the region indicated by the arrow in Figure 41. Since PPTA is made of rigid macromolecules, it is not supposed to have the two-phase structure prevailing in flexible macromolecules such as PE, but has a microfibrillar texture which is similar to the model of bundling of parallel microfibrils proposed by Peterlin. 317 Recently a SAXS with long wavelength X-rays which showed equatorial discrete maxima was reported. 318 The curved 110 fringes in the lattice images and the results of dark field imaging with a 006 reflection or 110 and 200 reflections suggested that the microfibrils are distorted by bending and/or twisting. The 006 dark field image of PPTA (Figure 40b) reveals that individual microfibrils in a fibrillar ribbon have the texture of periodic bending, and as a consequence the ribbon possesses a pleated sheet texture. 314 The 110 and 200 dark field imaging, however, reveals the existence of twisting of microfibrils in the same ribbon (Figure 40c). Therefore, it should be concluded that a microfibril in a PPTA fiber is bent along its fiber axis with a rather large periodicity (about 500 nm), and it is also twisted randomly around the axis. The Ag2S insertion technique is also useful for morphological observations of the PPTA fiber.269 In the case of PBT, dark field images and lattice images showed that the crystallite size increases from several nm in width (equatorial direction) to 10-20 nm and in length (meridional direction) to 40 nm by annealing. 316 In lattice images, lattice fringes of 0.59 nm corresponding to the equatorial reflection were straight, but ones of 1.24 nm corresponding to the meridional reflection were wavy. It was deduced that this phenomenon is due to the paracrystalline nature of PBT. 319 In the diffraction pattern of PBT, many meridional and a few equatorial reflections are recognized, but the hkl ones are faint. 320,321 Thus crystal structure analysis of this polymer is difficult. Recently determination of the idealized crystal structure of PBT has been attempted based on its high resolution images. 322

834

Microscopy

Morphologies of polymers with rigid molecular chains including PPTA were reviewed by Takahashi. 321

34.5.3.2

Polymeric sulfur nitride

[(SN) X Y 23 > 324

(SN)^ is well known for its behaviour as a superconductor at low temperatures. 325 In the dark field image of a (SN)* fiber taken with 002 and 102 reflections and an image with a 020 reflection, fine striations are recognized along the chain direction (fr-axis) and these correspond to the microfibrils in which the 002 or 102 lattice plane is oriented to satisfy the Bragg condition. A coherent domain (microfibril) is very long in the direction of the chain axis, but very narrow in the lateral dimension. Therefore, a microfibril in a (SN)X fiber is untwisted and distinct from that in a PPTA fiber. Such a microfibrillar texture can be also deduced from the ED pattern, where each reflection is elongated to be a streak in the direction perpendicular to the fiber axis. The high resolution lattice images of (SN)X have been reported. 323 In the image of the (SN)X skin region of a fibrillar fragment, 002 lattice fringes (with a spacing of 0.359 nm) are observed. The lateral width of the domain where the fringes appeared is small, only about 2 nm. On the other hand, the core region gives a high resolution image of the single-crystal-like domain where the 002 and 010 fringes (with a spacing of 0.44 nm) are particularly well observed. The lateral dimension of the coherent domain is much larger than that in the skin region. This can be also deduced by comparison of the OD patterns of the images attributed to skin and core regions. To improve the electrical conductivity, (SN)X is intercalated with halogens. 326 ' 327 The character­ istics of the ED pattern from intercalated (SN)X are that the diffraction spots from (SN)X become more streaked perpendicularly to the fr-axis and that extra streaks appear between the layer lines of (SN) X . 323 From the high resolution micrograph of iodinated (SN)X and ODs of the micrograph at three regions which are 50 nm in diameter, it was concluded that iodine atoms invade preferentially in the skin regions of (SN)X which are disordered in the pristine state. 323 It has also been reported that such iodine atoms are structurized there. 324

34.5.3.3

PE fibers and others

For TEM, the specimen should be thin. Thus thin sections and/or thin films are prepared for TEM observation. Sometimes these specimens, however, do not represent the internal morphology of polymers in the bulk state because of plastic deformation during sectioning and the surface effect in thin films.319 In order to expose the internal morphology of polymer solids with less deformation and to observe it by SEM, a new fracture method combined with fumic nitric acid treatment is proposed 211 (see Section 34.4.1). Recently this technique was applied to high tenacity/high modulus PE fibers and it was found that disordered regions exist but are scattered uniformly throughout the specimen. 319 Very recently lattice images of ultradrawn gels of high molecular weight PE were reported. 131 In the near future, the structural requirements for obtaining high-performance polymers will be classified. Some of the natural polymers with fibrous morphologies, for example cellulose and chitin, should be discussed here, but these will be mentioned in the following Section (34.5.4).

34.5.4 Natural Polymers Cellulose crystals have been extensively studied by electron microscopy. The lateral crystallite size, namely the width or thickness of the microfibril of natural cellulose, is one of the important features of this polymer. Recently the effect of defocusing on the image contrast in TEM of negatively stained protofibrils of ramie cellulose was discussed on the basis of the defocus dependence of the phase contrast transfer function sin% (see Section 34.3) using the OD technique 328 and the digital correlation method. 329 Properly defocused images suggested the existence of a certain periodical structure (about 6 nm in periodicity) along the protofibril axis. Lattice imaging of cellulose crystal was achieved by Sugiyama et a/. 330 ' 331 whilst Revol 332 obtained imaging for Valonia cellulose, and very recently imaging for bacterial and ramie celluloses was obtained by Kuga et a/. 333,334 Lattice images appear to be useful in estimating the lateral crystallite size and discussing the existence of axial periodicity in cellulose. Morphologies of natural polymers other than cellulose have also been studied by electron

Electron Microscopy

835

microscopy. If biological specimens such as the tobacco mosaic virus (TMV), T4-phage, collagen, etc. are included in 'natural polymers', there are too many examples to be introduced here. There are, however, not so many examples of high resolution TEM of natural polymers. Apart from cellulose, lattice images of a few materials such as /?-chitin335 and poly(hydroxybutyrate) (PHB) 336 have been reported using a 120 kV TEM. Double stranded DNA molecules were directly visualized by high resolution TEM with MDS. 3 3 7

34.6 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20.

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