Quantitative analytical electron microscopy of metals and minerals

Ultramicroscopy 8 (1982) 121 - 132 North-Holland Publishing Company

121

QUANTITATIVE

ANALYTICAL

ELECTRON

MICROSCOPY

OF METALS

P. E. Champness I, G. Cliff 2 and G. W. IDepartment of Geology, 2joint U n i v e r s i t y / U M I S T

AND M I N E R A L S

Lorimer 2

The University, Manchester, M13 9PL, and Department of Metallurgy, Manchester MI 7HS,

U.K.

For a thin s p e c i m e n X-ray a b s o r p t i o n and f l u o r e s c e n c e can, to a first a p p r o x i m a t i o n , be ignored and o b s e r v e d c h a r a c t e r i s t i c X - r a y i n t e n s i t y ratios, IA/IB, can be c o n v e r t ed into w e i g h t fraction ratios, CA/C B b y m u l t i p l y i n g by a constant, kAB:

CA/C B

=

k~IA/I B

~B v a l u e s can be c a l c u l a t e d or d e t e r m i n e d e x p e r i m e n t a l l y . X-ray a b s o r p t i o n within the sample m u s t b e c o n s i d e r e d when there is a s i g n i f i c a n t d i f f e r e n c e in the e n e r g y o f the c h a r a c t e r i s t i c X-rays. Fluorescence effects due to c o n t i n u u m X-rays can be ignored in thin s p e c i m e n s and c h a r a c t e r i s t i c fluorescence is m u c h less than that o b s e r v e d in b u l k specimens. E x p r e s s i o n s are given for both the a b s o r p t i o n and fluor e s c e n c e corrections. Beam s p r e a d i n g has b e e n c a l c u l a t e d in a mineral at 100 k V u s i n g m o d e l s b a s e d on Rutherford-scattering, plural-scattering and M o n t e - C a r l o theory. The c a l c u l a t i o n s are c o m p a r e d with e x p e r i m e n t a l results. The a p p l i c a t i o n of AEM to m e t a l s is Mn and Cr in the p e a r l i t e reaction.

illustrated

by the

study of p a r t i t i o n i n g

of

Si,

Because m o s t m i n e r a l s are c o m p o s e d p r e d o m i n a n t l y of light elements, a b s o r p t i o n and f l u o r e s c e n c e can be ignored for a wide range of thicknesses. A p p l i c a t i o n s in m i n e r a l o g y are i l l u s t r a t e d by e x a m p l e s from p a r t i c l e a n a l y s i s (e.g., asbestos) and by the study of the p r e c i p i t a t i o n of a c e l l u l a r intergrowth of p y r o x e n e and spinel in olivine. I.

INTRODUCTION

Modern analytical electron-microscopes provide, in one instrument, morphological information with a r e s o l u t i o n of less than 2 A and crystallographic data and chemical analyses with a spatial resolution of less than 200 A from a single, thin specimen. The c h e m i c a l a n a l y s i s can be o b t a i n e d by a number of t e c h n i q u e s which include X - r a y spectrometry, e l e c t r o n e n e r g y - l o s s a n a l y s i s or A u g e r - e l e c t r o n s p e c t r o m e t r y . At the p r e s e n t time X - r a y s p e c t r o m e t r y has the d i s t i n c t a d v a n t a g e over these other t e c h n i q u e s in that q u a n t i t a t i v e a n a l y s e s can be c a r r i e d o u t for all e l e m e n t s Z > 11 w i t h an e n e r g y - d i s p e r s i v e X-ray (EDX) d e t e c t o r I (z > 3 with a crystal s p e c t r o m eter) by simple m o d i f i c a t i o n s of p r o c e d u r e s used in conventional microprobe analysis of bulk specimens. In a thin s p e c i m e n the spatial r e s o l u t i o n for chemical analysis is dramatically improved, compared to the bulk: the large, b e l l - s h a p e d region p r o d u c e d b y the d i f f u s i o n of the e l e c t r o n probe b e n e a t h the surface of the specimen, from which the m a j o r i t y of the X-rays are p r o d u c e d in a b u l k sample, Figure I, is a b s e n t in a thin foil. If the sample is s u f f i c i e n t l y thin to c a r r y out q u a n t i t a t i v e transmission electronmicroscopy at 100 k V the a c t i v a t e d v o l u m e is approximately a cylinder equal to the beam diameter. The m a i n d i s a d v a n t a g e of the use of thin s p e c i m e n s is that the a c t i v a t e d v o l u m e for

0304-3991/82/0000-0000/$02.75 © 1982 North-Holland

X-ray p r o d u c t i o n is small c o m p a r e d to a b u l k sample; X-ray c o u n t i n g rates are low and hence the potential accuracy is inferior to that generally accepted for b u l k specimens. This p r o b l e m can be p a r t i a l l y a m e l i o r a t e d by u s i n g v e r y short d e t e c t o r - t o - s p e c i m e n distances, as is p o s s i b l e with an e n e r g y - d i s p e r s i v e detector, and high c u r r e n t d e n s i t i e s in the a n a l y s i s probe, although these current densities can p r o d u c e severe damage p r o b l e m s in b e a m - s e n s i t i v e m a t e r i als.

Bulk

Thin Foil

f FluorescuKe~

n

ZAF

Figure 1. Schematic representation of the i n t e r a c t i o n of a h i g h - e n e r g y e l e c t r o n b e a m w i t h a b u l k a n d thin s p e c i m e n . To the first a p p r o x i m a t i o n a b s o r p t i o n and f l u o r e s c e n c e e f f e c t s can be i g n o r e d in the thin specimen.

P.E. Champltess et at / Electron microscop3, o f metals and rniJ~erals

122

2. QUANTITATIVE APPROXIMATION 2.1

Thin

X-RAY

ANALYSIS:

THIN

FILM

Film A p p r o x i m a t i o n

Characteristic X-ray fluorescence and X-ray absorption in thin s p e c i m e n s is less than in b u l k samples, Figure 1. To a first a p p r o x i m a tion X-ray a b s o r p t i o n and f l u o r e s c e n c e can be n e g l e c t e d and the ratio of two o b s e r v e d X - r a y intensities, IA/IB, can be related to the corresponding weight-fraction ratio C A / C B by the equation CA/C B = kAB IA/I B

Si -UBe pt Ax(QK~Ka)Si

Cx. kXS I - C-~i

lOOkV

_

....

(I)

where kAB is a constant at a given a c c e l e r a t i n g v o l t a g e and is independent of specimen t h i c k n e s s and composition. A normalisation procedure, e.g., ~C n = I, m u s t be used to convert the ratios of the weight fractions into weight percentages. In mineral specimens a s s u m p t i o n s m u s t also be m a d e c o n c e r n i n g o x i d a t i o n states: e.g., it is impossible to differentiate b e t w e e n Fe30 % and Fe203 if ratios are m e a s u r e d , and oxygen cannot be detected. Figure 2 shows a series of e x p e r i m e n t a l kXS i v a l u e s m e a s u r e d b y Cliff and Ix)rimer [I] at 100 k V from thin m i n e r al and alloy standards. These are c o m p a r e d with c a l c u l a t e d kXS i values (dotted line) which were obtained using the equation proposed by Goldstein et el. [2]:

kxsi =

lists e x p e r i m e n t a l and c a l c u l a t e d kA8 i v a l u e s at 120 k V r e c e n t l y p u b l i s h e d by Wood et el. [4]. Table Ib, taken from the w o r k of McGill and H u b b a r d [5], contains calculated and experimental kAS i v a l u e s for Na, Mg, AI, K and Ca at 100 kV. McGili and Hubbard d e t e r m i n e d their e x p e r i m e n t a l values using a d e f o c u s s e d probe a n d extrapolation to zero time, so as to m i n i m i s e errors due to e l e m e n t a l loss.

e X

(2)

Asi(QK~Ka) X e - U B e pt where A x and ASi are atomic weights, Q K the Green and C o s s l e t [3] v a l u e s of the K shell ionization cross sections, ~ K the f l u o r e s c e n c e yield, a the K ~ / ( K e + K 8) ratio (equal to one for Z < 19) and p ~ and U ~ the 'effective' mass-absorption coefficients of Si and the element X in the detector w i n d o w (the Be window, Si dead layer and Au contact film) of d e n s i t y p and thickness t. The ionization c r o s s - s e c t i o n was a s s u m e d to be c o n s t a n t along the electron trajectory. The a g r e e m e n t b e t w e e n the e x p e r i m e n t a l and c a l c u l a t e d kAB v a l u e s is s a t i s f a c t o r y for Z > Si, and for these elements it would appear to be sufficient to m e r e l y c a l c u l a t e kAB v a l u e s for a given d e t e c t o r and a c c e l e r a t i n g voltage. The origin of the divergence b e t w e e n experiment and t h e o r y at low Z is not known. However, the e x p e r i m e n t a l v a l u e s are very sensitive to the c l e a n l i n e s s of the Be w i n d o w (in some d e t e c t o r s a sealant c o n t a i n i n g silicon is applied to m a i n t a i n a h i g h vacuum) and it is recommended that for Z < Si the kAB v a l u e s for a given m a c h i n e are determined experimentally. C o n s i d e r a b l e experimental effort has b e e n expended to obtain a c c u r a t e kAB values, for, as discussed in section 2.5, the q u a l i t y of the analysis depends directly on kAB. Table la

Is~ Ix

Calculated

• Experimental

Nae

kxsi

•

. $i

.........

1

2

K"

3

Ti

4

Cr

5

+C u +- ~ -

+.+-

Fe

6

7

8

9

10

key

Figure 2. C o m p a r i s o n of calculated, [2] experimental, [1] kxs i values at 100 kV. Table Element Na Mg A1 Si P S K Ca Ti Cr Mn Fe Ni Ca Mo Ag

Z 11 12 13 14 15 16 19 20 22 24 25 26 28 29 42 47

and

la

I 3.57 1.49 1.12 1.00 0.99 1.08 1.12 1.15 1.12 1.46 1.34 1.30 1.67 1.59 4.95 12.4

II 1.83 1.31 1.14 1.00 1.04 1.07 1.05 1.04 1.17 1.24 1.32 1.36 1.48 1.65 4.68 7.08

Comparison of experimental, I, and calculated, II, k A S i data at 120 kV. Calculated values a s s u m e tBe = 7.5 ~m, tAu = 0.02 u m and tsi = 0.1 um [4]. Table Element Na Mg A1 Si K Ca I II III

Z 11

12 13 14 19 20

I 3.2 1.6 1.2 1.0 1.0 1.0

Ib II 2.85 1.67 1.15 1.00 1.10 1.08

Cliff and Lorimer (1975) McGill and F~bbard (1981) Calculated

III 2.02 1.39 1.16 1.00 1.08 1.11

123

t~E. Champness et al. / Electron microscop) o f metals and minerals

C o m p a r i s o n of e x p e r i m e n t a l and c a l c u l a t e d kAs i data at 100 kV. Calculated values (III) assume tBe = 8 ~m, tAu = 0.02 ~m, and tsi = 0.1 ~m [5]. 2.2.

Effects

of A b s o r p t i o n

in the

a b s o r p t i o n in the specimen on the sity ratios for o r t h o p y r o x e n e (a silicate) are shown in Figure 4.

X-ray intensingle-chain

Specimen 1"35

X-ray

absorption

follows

the

exponential

law 1-30

I = Io e -~px

(3) 1-25

where I is the transmitted X - r a y intensity, Io the initial X-ray intensity, ~ the m a s s absorption c o e f f i c i e n t of a m a t e r i a l of d e n s i t y p and path length x. When the ratio of characteristic X - r a y i n t e n s i t i e s is considered, the difference in X - r a y a b s o r p t i o n c o e f f i c i e n t s is the i m p o r t a n t parameter (if two c h a r a c t e r i s t i c X-rays have similar v a l u e s of D they will be absorbed e q u a l l y and their i n t e n s i t y ratio will be unaffected). If t is the sample t h i c k n e s s and ~ the angle between the line of the d e t e c t o r and the sample surface, the X-ray i n t e n s i t y ratio IA/I B r e c o r d e d by the detector will be m o d i f i e d by a b s o r p t i o n in the specimen from the ratio recorded for an infinitely thin specimen, IoA/IoB (no a b s o r p t i o n ) , as given in equation 4. The path length x is shown in Figure 3.

t

1.20 Fe/Si

(Ix/Isi) (Iox/'oSi) t. t5

1.10

1.0

0'95

0.90 MI/Si

0'85

-PA pt csc IA --= IB

IoA ~B

[I - e

]

0.80

(4) IoB ~A

-PB pt csc [I

-

e

] 0.75 ~ 0

where ~A and ~B are the m a s s a b s o r p t i o n coefficients of the c h a r a c t e r i s t i c r a d i a t i o n in the sample of density p. The effects of

X- ray detector

// ///(

0"1

0"2

0"3

0"4

0"5

0"8

0"7

0"8

i 0'9

1"0

thickness (microns)

Figure 4. The e f f e c t of a b s o r p t i o n on the o b s e r v e d ratio of X-ray i n t e n s i t i e s in a specim e n of o r t h o p y r o x e n e , MgFeSi206 , as a f u n c t i o n of t h i c k n e s s ( ~ = 45 ° ) . Carbon c o n t a m i n a t i o n can b u i l d up r a p i d l y on the top and b o t t o m s u r f a c e s of a thin s p e c i m e n when a probe a few tens or h u n d r e d s of A n g s t r o m s is used for analysis. This c a r b o n d e p o s i t will p r e f e r e n t i a l l y a b s o r b l o w - e n e r g y X-rays and can a f f e c t the r e s u l t i n g analysis. The e f f e c t s of carbon c o n t a m i n a t i o n are p a r t i c u l a r l y i m p o r t a n t when v e r y fine p r o b e s and long c o u n t i n g times are used. An example of the e f f e c t of the b u i l d - u p of carbon on the analysis of an orthopyroxene is shown in Figure 5.

t 2.3.

activated volume x :absorption path Figure 3. absorption absorption

G e o m e t r y used for the c a l c u l a t i o n of in the specimen where x is the path length, e q u a t i o n 3.

Effects

of

Fluorescence

in the

Specimen

F l u o r e s c e n c e due to the c o n t i n u u m can be ignored in thin foils and it is u s u a l l y safe to a s s u m e that c h a r a c t e r i s t i c fluorescence is also v e r y small. However, when strong characteristic f l u o r e s c e n c e is p r e d i c t e d in an e q u i v a l e n t b u l k specimen, it is n e c e s s a r y to account for it in the thin specimen as well. F l u o r e s c e n c e in thin specimens has b e e n discussed by Tixier [6] , Lorimer et al. [7] and N o c k o l d s et al. [8]. The model used by N o c k o l d s et al. for c a l c u l a t i n g the f l u o r e s c e n c e c o r r e c t i o n is shown in Figure 6. This predicts that in a thin, binary

P,E. Charnpness et al. / Electron microscopy o f metals and minerals

124

1.1of

A

J

t 14L o I

J

I

r -I A

A •

J

CA ~B alK

A

Fe/Si/

('x/'si)

1-02

r

(6)

A

U~ and ~B are the mass a b s o r p t i o n c o e f f i c i e n t s of X - r a d i a t i o n from element B in e l e m e n t A and the specimen, respectively. C A is the w e i g h t fractio~ of element A, ~KA is the fluorescence yield of element A and r A is the a b s o r p t i o n - e d g e jump-ratio. The ratio of c h a r a c t e r i s t i c X-ray intensities IA and IB can be calculated using the formula for K-shell ionisation crosssections p r o p o s e d by Green and C o s s l e t t [3] , a n d used to m o d i f y e x p r e s s i o n (6) to give the fluorescence enhancement ratio for A radiation IA/I A in a thin foil

1.00 0.98 0"96 0'94 0"92 0"90 O"88

A IF

0"1

0'2

0"3

0'4

0'5

0'6

07

0'8

0"9

rA-1 AA A = c ~o • ~ • - r" A--- " UB A B A B U ~nU B B • T ( 0.923_£n(UBT ) I UA£nU A 2

7

1:0

Thickness of carbon (microns)

The effect of carbon c o n t a m i n a t i o n on Figure 5. the o b s e r v e d ratio of X-ray i n t e n s i t i e s for the orthopyroxene in Figure 4. The d e n s i t y of carbon was a s s u m e d to be 2 gra cm -3.

ELECTRON BEAM

BINARY

S

Dz

----

B FLUORESCES A

d/,z

THICKNESS z T,pz

Model for the specimen [7].

fluorescence

specimen AB the intensity of d I ~ fluoresced in the annulus by f r o m point P is given by

A B

correction

radiation radiation

• tan ¢ ds dpz de

Beam

Spreading

(5)

Assuming s y m m e t r y about the centre of the foil, i n t e g r a t i o n over the mass thickness T gives the total i n t e n s i t y I~

Specimen

A simple a p p r o a c h to the p r o b l e m of b e a m spreading has been p r o p o s e d by Goldstein et al. [2] who a s s u m e d that a single, e l a s t i c s c a t t e r i n g event o c c u r s at the c e n t r e of the foil a n d d e f i n e d the X-ray source size as that v o l u m e in which 90% of the e l e c t r o n t r a j e c t o r i e s lie. The b e a m broadening, b, from a point p r o b e is g i v e n by:

6.2S

x

Z

Q

i0 s ~ ( ~ ) o

where Z is the ing v o l t a g e .

(-NB secCpz)

in the

Beam spreading in thin foils is c u r r e n t l y a lively topic of both e x p e r i m e n t a l i n v e s t i g a t i o n s and theoretical analysis, and the reader is referred to recently p u b l i s h e d a r t i c l e s [9,10, 11,12] which summarize the p r e s e n t state of the art.

b:

A IB A rA- 1 dIF = T-- C A PB ~ ~K exp A A

(7)

w h e r e U A and U B are the o v e r v o l t a g e ratios for e l e m e n t s A and B r e s p e c t i v e l y , and A A and A B are the r e l e v a n t atomic weights. (Note that if the sample is tilted t h r o u g h an angle ~ then expression (7) m u s t be m u l t i p l i e d by sec e to allow for the resultant increase in IB.) 2.4.

t

B

Figure 6. for a thin

0.923 - £n(~BT)

/

1.06~

A

Tt

IF = IB ~

1.08!

atomic

16 t3/2

number,

cm

ca)

E o the a c c e l e r a t -

In Figure 7 the p r e d i c t i o n s of e q u a t i o n 8 are compared with e x p e r i m e n t a l m e a s u r e m e n t s of b e a m spreading at 100 k V for an o r t h o p y r o x e n e . The results were o b t a i n e d at 100 k V with a probe of diameter (FW~M) of a p p r o x i m a t e l y 75 ~. The specimen was orientated, by diffraction, with a lamella of augite (Ca-rich pyroxene) parallel to the e l e c t r o n beam. Beam s p r e a d i n g was m o n i t o r e d

t~E. Champness et aL / Electron microscopy o f metals and minerals

-cok:uk3ted . . . . expefime~tol

1200

/

Goldsteinet oJ (2}

8O0 T ~

E

/

~

[imitSsc(dt~gi~lhe°rY

125

r a y counts are often at a p r e m i u m in thin specim e n s and it m a y be n e c e s s a r y to a c c e p t o n l y a few h u n d r e d counts for one element. If, for example, IA c o n t a i n e d only 900 counts a n d IB still e q u a l l e d 10,000 and the r e l a t i v e error in kAB was ±2%, then the relative error in IA would be ±6% and the total r e l a t i v e error in the C A / C B ratio would be &I0%! 2.6.

Thickness

Measurements

~00

~

MonteCorlo 1

2

3 ~. 5 Fo~IThickness ~urn

6

7

Figure 7. C o m p a r i s o n b e t w e e n e x p e r i m e n t a l and calculated beam broadening in an orthopyroxene, (Mg,Fe)Si206, at 100 kV. Experimental data o b t a i n e d with a Philips ~4 400T a n a l y t i c a l e l e c t r o n m i c r o s c o p e using a 75 ~ diameter probe. by d e t e r m i n i n g the Ca/Fe count ratio as a function of d i s t a n c e from the interface. The limits of b e a m s p r e a d i n g were d e f i n e d as the p o s i t i o n at which the Ca/Fe ratio fell to 10% of that in the a u g i t e lamella. Foil thickness was determ i n e d by m e a s u r i n g the p r o j e c t e d widths of the lamella/matrix interface when the specimen had b e e n tilted. Also included in Figure 7 are the v a l u e s of b e a m broadening predicted using Monte-Carlo and plural scattering t h e o r y [12]. The two limits of plural s c a t t e r i n g c o r r e s p o n d to single and a G a u s s i a n d i s t r i b u t i o n of s c a t t e r i n g events. The t h e o r e t i c a l values in Figure 7 are r e d u c e d b y a factor of I / ~ c o m p a r e d to those r e c e n t l y published [12]. This c o n v e r t s the t w o - d i m e n s i o n a l m o d e l s into the true t h r e e - d i m e n s i o n a l scattering process. An a d d i t i o n a l complication in experimentally determining beam broadening is that the a n a l y s i s p r o b e can have an e x t e n d e d n o n - G a u s s i a n 'tail' - the s h a d o w of the condenser a p e r t u r e - w h i c h can contain over 50% of the total number of incident e l e c t r o n s [13]. 2.5.

Statistics

of Analysis

This p r o b l e m has b e e n d i s c u s s e d by G o l d s t e i n and W i l l i a m s [9] and the f o l l o w i n g analysis is b a s e d on their a p p r o a c h . X - r a y c o u n t i n g statistics are u s u a l l y a s s u m e d to obey G a u s s i a n b e h a v i o u r and at the 20 c o n f i d e n c e level the r e l a t i v e error in the number of counts I is 2 {I. Using e q u a t i o n (I) a ratio of two counts is c o n v e r t e d into a w e i g h t - f r a c t i o n ratio via the constant, kAB. Thus it is n e c e s s a r y to add the total relative errors in IA, IB and kAB to and obtain the r e l a t i v e error in the w e i g h t - f r a c t i o n ratio C A / C B. If ~ 1 0 , 0 0 0 counts were obtained for both I A a n d IB, and kAB was known to an a c c u r a c y of ±2%, the total r e l a t i v e error in CA/C B w o u l d be 6%. Unfortunately, X-

In order to m a k e c o r r e c t i o n s for absorption, f l u o r e s c e n c e and beam s p r e a d i n g it is n e c e s s a r y to know the t h i c k n e s s of the sample. Various p a r a l l a x t e c h n i q u e s can be used [14], i n c l u d i n g the c o n t a m i n a t i o n spots formed on the top a n d b o t t o m of the foil during the a n a l y s i s . However, the m o s t a c c u r a t e technique is that of convergent-beam diffraction as described by Amelinckx [ 1 5 ] and Kelly et al. [16]. This enables specimen thicknesses to be d e t e r m i n e d with an a c c u r a c y of ±2%. Attempts have also been made to determine sample thickness by m e a s u r e m e n t s of absolute X - r a y [7] or t r a n s m i t t e d - e l e c t r o n [17] intensities. The a d v a n t a g e of the last two t e c h n i q u e s is that they can be a p p l i e d 'on-line', so that the c o r r e c t i o n s can be made at the time of the a n a l y s i s . 3.

PARTITIONING

IN P E A R L I T E

Analytical e l e c t r o n - m i c r o s c o p y has been used to study the partitioning of various alloying a d d i t i o n s d u r i n g the a u s t e n i t e - p e a r l i t e transformation in e u t e c t o i d steels, and the partit i o n i n g data o b t a i n e d to date has b e e n d i s c u s s e d in r e l a t i o n to p e a r l i t e growth k i n e t i c s [1821]. The following section is a s u m m a r y of some of this work. Pearlite is a lamellar t r a n s f o r m a t i o n product, consisting of ferrite (e) and cementite (Fe3C) , which forms when a u s t e n i t e (y) u n d e r g o e s eutectoidal decomposition. Pearlite n u c l e a t e s heterogeneously, primarily at a u s t e n i t e grain boundaries, and g r o w t h o c c u r s on a s p h e r i c a l front. In Fe-C a l l o y s p e a r l i t e growth p r o c e e d s r e l a t i v e l y rapidly. However, the g r o w t h rate can be m a r k e d l y retarded by the p r e s e n c e of relatively small c o n c e n t r a t i o n s (up to 4%) of alloying additions such as m a n g a n e s e , nickel, c h r o m i u m a n d m o l y b d e n u m , and this effect is of great c o m m e r c i a l s i g n i f i c a n c e in r e l a t i o n to the heat t r e a t m e n t of steels. The i n v e s t i g a t i o n s were c o n c e r n e d with e x a m i n i n g the ways in w h i c h the a l l o y i n g a d d i t i o n s p a r t i t i o n e d at the a u s t e n i t e / p e a r l i t e t r a n s f o r m a t i o n front, as a first step to u n d e r s t a n d i n g the m e c h a n i s m s w h e r e b y the a d d i t i o n s r e t a r d p e a r l i t e growth. 3.1.

Analysis

Technique

D u r i n g a n a l y s i s the i n t e n s i t i e s of the charact e r i s t i c X - r a y lines from Fe K~ and the partit i o n i n g e l e m e n t being i n v e s t i g a t e d were r e c o r d e d simultaneously. The ratios of the p a r t i t i o n i n g element and iron c h a r a c t e r i s t i c X - r a y intensities IX/IFe were c o n v e r t e d into w e i g h t concen-

126

R E. Champness et al. /Electron microscopy o f metals and minerals

trations of the p a r t i t i o n i n g e l e m e n t and iron, C x and CFe , r e s p e c t i v e l y , u s i n g the r e l a t i o n s h i p C

X

C

k

I

X

kFe

X

IFe

(9)

w h e r e k x and kFe were d e t e r m i n e d from alloy and m i n e r a l thin s t a n d a r d s [I]. The r e s u l t s of each a n a l y s i s were e x p r e s s e d as a p a r t i t i o n c o e f f i cient w h i c h was d e f i n e d as the ratio of the weight % of X in c e m e n t i t e , X(cem), to the w e i g h t % of X in ferrite, X(~)

Kcem(x)

X(cem) X(~)

(10)

The partition coefficients could be readily c o m p u t e d when m e a s u r e m e n t s were m a d e on the two p h a s e s c o n t a i n e d in a thin foil. However, for m e a s u r e m e n t s made on e x t r a c t e d c e m e n t i t e it was n e c e s s a r y to c a l c u l a t e the c o n c e n t r a t i o n of the a l l o y i n g element in f e r r i t e by using a m a s s balance procedure. F i g u r e 8 is a m i c r o g r a p h of a t h i n - f o i l s p e c i m e n of a e u t e c t o i d steel c o n t a i n i n g 2 wt% Mn w h i c h has b e e n i s o t h e r m a l l y t r a n s f o r m e d at 662°C for 240 m i n u t e s . The dark, minor p h a s e is c e m e n t i t e and the light phase is f e r r i t e . The c a r b o n contamination spots formed during individual a n a l y s e s can be seen on both p h a s e s . An e x a m p l e of the type of a n a l y t i c a l data o b t a i n e d d u r i n g investigations of partitioning is shown in Figure 9, which shows the v a r i a t i o n of the e x t e n t of p a r t i t i o n i n g of Mn to c e m e n t i t e as a f u n c t i o n of t r a n s f o r m a t i o n time at 642°C. In Figure 10 the p a r t i t i o n i n g data at the start of the r e a c t i o n (zero time in Figure 9) for the a l l o y is s u m m a r i s e d as a f u n c t i o n of t r a n s f o r m a tion t e m p e r a t u r e . Above a t e m p e r a t u r e of a b o u t 645°C p a r t i t i o n i n g of Mn o c c u r s at or a h e a d of the t r a n s f o r m a t i o n front, while at lower t e m p e r a t u r e s the r e a c t i o n p r o c e e d s w i t h o u t M~ partitioning.

Figure 8. Thin foil of a e u t e c t o i d steel containing 2 wt% Mn i s o t h e r m a l l y t r a n s f o r m e d at 662oc for 240 m i n u t e s . The c o n t a m i n a t i o n spots m a r k the p o s i t i o n s of the e l e c t r o n b e a m d u r i n g the a n a l y s i s .

5 3.2.

Effects of A b s o r p t i o n

If the p a r t i t i o n i n g e l e m e n t is of a low a t o m i c n u m b e r then it is n e c e s s a r y to c o r r e c t for the p r e f e r e n t i a l a b s o r p t i o n w i t h i n the s p e c i m e n of X-rays from this e l e m e n t . E f f e c t s due to preferential absorption of SiK X - r a y s have been o b s e r v e d d u r i n g an i n v e s t i g a t i o n of the partit i o n i n g of s i l i c o n [19]. Figure 11a shows the o b s e r v e d v a r i a t i o n in £n(Isi/IFe) as a f u n c t i o n of s p e c i m e n t h i c k n e s s for a 2 wt% Si e u t e c t o i d steel which had been quenched to p r o d u c e a m a r t e n s i t i c m i c r o s t r u c t u r e of u n i f o r m c o m p o s i tion. The line has a slope, as d e t e r m i n e d from a least s q u a r e s a n a l y s i s , equal to 2090 cm 2 gm -I . This is the a p p r o x i m a t e d i f f e r e n c e b e t w e e n the X-ray m a s s - a b s o r p t i o n c o e f f i c i e n t s of iron (2502 cm 2 gm -I ) and silicon (710 cm 2 gm -I ) X-rays in the specimen, a value that is in a g r e e m e n t with that p r e d i c t e d by e q u a t i o n 4.

cem 4 K(Mn) it

/

~42 °C

2% Mn

TIME

(HOURS)

Figure 9. P a r t i t i o n c o e f f i c i e n t of m a n g a n e s e b e t w e e n c e m e n t i t e and f e r r i t e v e r s u s r e a c t i o n time for a 2 wt% Mn e u t e c t o i d steel i s o t h e r m a l l y t r a n s f o r m e d at 642°C [18].

127

P.E. Charnpness et aL / Electron microscopy o f metals and minerals

z o

20

8

cem 4 K(Mn) (¥ start 3

0'

Z 3

-20 -4o

_z

~-~ ~

-80

N

I

- I00 0 600

i 610

I

I

620

I

I

630 640 650 T E M P E R A T U R E °C

I

L

I

660

670

680

Figure 10. P a r t i t i o n c o e f f i c i e n t of m a n g a n e s e b e t w e e n c e m e n t i t e a n d f e r r i t e at the a u s t e n i t e pearlite interface for a 2 wt% Mn e u t e c t o i d s t e e l , as a f u n c t i o n of t r a n s f o r m a t i o n temperat u r e [18].

L 0"6

L 0-8

~7

L I-0

0"9

II1

/'2

11.3

/-4

/'5

APPARENT SPECIMEN THICKNESS p m

F i g u r e 11b. E r r o r in the m e a s u r e d c o n c e n t r a t i o n of s i l i c o n as a f u n c t i o n of s p e c i m e n t h i c k n e s s for a m a r t e n s i t i c foil of a 2 wt% Si e u t e c t o i d steel. The a p p a r e n t i n c r e a s e in s i l i c o n c o n c e n t r a t i o n of the e d g e of a foil is due to the p r e s e n c e of a S i - r i c h s u r f a c e f i l m [21]. the s o l u t e - r i c h l a y e r can be r e m o v e d by e x p o s i n g the electropolished specimen to a 10 to 15 m i n u t e t r e a t m e n t in an ion b e a m t h i n n i n g a p p a r a t u s (4 kV, 20 to 25 ° i n c l i n a t i o n ) .

-3"4

o -3.6 -3"8 uI ,-4.0

3.4.

o

~~o

o

_¢~ -,I.2 _c -44

0

-4-6

0-8 SPECIMEN

1.0 THICKNESS

F i g u r e 11a. L o g a r i t h m of the t i e s of SiK to Fe K s r a d i a t i o n a 2 wt% Si s t e e l [21]. 3.3.

o

0

J 0"6

Surface

1.2

1.4

IN ~ m

ratio of intensivs. t h i c k n e s s for

Fluorescence

Effects

D u r i n g the i n v e s t i g a t i o n of p a r t i t i o n i n g in a I wt% Cr I wt% Mn eutectoid steel it was o b s e r v e d t h a t the h e i g h t of the Cr K~ p e a k w a s a l m o s t a l w a y s g r e a t e r t h a n t h a t of Mn K~. In addition, there was c l e a r l y an e f f e c t due to thickness; the t h i n n e r the s p e c i m e n the c l o s e r the ratio of the Mn K s to Cr K~ p e a k was to unity. Figure 12 s h o w s a s e r i e s of e n e r g y dispersive X-ray spectra from a martensitic s p e c i m e n of the C r - M n a l l o y . The a n a l y s e s w e r e obtained from progressively t h i c k e r r e g i o n s of the foil. The m o d e l of N o c k o l d s et al. [8] for calculating the f l u o r e s c e n c e c o r r e c t i o n s , e q u a t i o n 7, was u s e d to c o r r e c t the d a t a .

Films

The w o r k of M o r r i s et al. [22], a n d o t h e r s on aluminum alloys has clearly shown that during electropolishing solute-rich layers can be f o r m e d on the s u r f a c e of th~ s p e c i m e n , a n d t h a t these will produce a m a r k e d c h a n g e in the IX/IAI ratio near the edge of the specimen. Similar effects have been observed also on electropolished samples of eutectoid steels. F i g u r e 11b shows the e f f e c t in a thin, m a r t e n s i t i c s p e c i m e n of 2 wt% Si e u t e c t o i d s t e e l . The apparent silicon concentration is l e s s t h a n 2% in the t h i c k e r r e g i o n s of the foil, d u e to t h e p r e f e r e n t i a l a b s o r p t i o n of Si K r a d i a t i o n (disc u s s e d a b o v e ) , b u t n e a r the e d g e o f the sample the effect is reversed, i.e. the apparent s i l i c o n c o n t e n t is g r e a t e r than 2 wt%. In t h i s a n d o t h e r s t e e l s p e c i m e n s it h a s b e e n f o u n d t h a t

1

?

~

~

5

6

7

B

9

10 ~e~

FigtuCe 12. S e r i e s of X - r a y s p e c t r a f r o m m a r t e n s i t i c f o i l s of a I wt% Cr - I wt% Mn e u t e c t o i d steel showing the effect of progressively

P.E. Champness et al. / Electron microscopy o/metals and minerals

128

i n c r e a s i n g the s p e c i m e n t h i c k n e s s (top s p e c t r u m from the thinnest region) on the relative h e i g h t s of the Cr K s and Mn K s p e a k s [21]. 4.

APPLICATIONS

4.1.

in the

Environment

The thin-film approximation has also been exploited in the identification of mineral particles in the environment. The energydispersive detector is i d e a l for s u c h s t u d i e s because the chemical "finger-print" from a particle can be displayed and recorded in seconds and compared with spectra from standards. The six commercial varieties of asbestos are c h e m i c a l l y distinct (Figure 13). Thus if a p a r t i c l e is k n o w n or s u s p e c t e d to be a s b e s t o s , its t y p e can n o r m a l l y b e d e t e r m i n e d b y visual inspection of its energy-dispersive spectrum (Figure 14) [23]. Problems arise, however, for v e r y thin particles because the high current density and long analysis time r e q u i r e d can l e a d to a h e a v y b u i l d - u p of c a r b o n w h i c h a f f e c t s the r e c o r d e d r a t i o of X - r a y i n t e n sities (Figure 5). A 'clean' vacuum and a detector with a large solid-angle alleviate the problem. For 'thick' particles absorption in the s p e c i m e n m u s t a l s o be t a k e n i n t o a c c o u n t (cf. F i g u r e 4).

TO MINERALS

As most rock-forming minerals are composed p r e d o m i n a n t l y of l i g h t e l e m e n t s s u c h as s i l i c o n a n d o x y g e n the r e l e v a n t a b s o r p t i o n c o e f f i c i e n t s are s m a l l c o m p a r e d w i t h t h o s e for m e t a l s . The e f f e c t s of a b s o r p t i o n and f l u o r e s c e n c e , b o t h of which depend on the absorption coefficients (equations 4 a n d 7) are t h e r e f o r e also small (e.g., Figure 4) compared with errors that result from counting statistics. The t h i n - f i l m c r i t e r i o n ( e q u a t i o n I) is s a t i s f i e d as l o n g as the foil t h i c k n e s s is b e l o w a b o u t 0 . 1 5 m i c r o n s . Table 2 shows the a n a l y s e s of five minerals o b t a i n e d w i t h the a n a l y t i c a l e l e c t r o n m i c r o s c o p e E M M A - 4 at 100 kV. T h e y are c o m p a r e d w i t h w e t c h e m i c a l a n a l y s e s of the s a m p l e s a n d i l l u s t r a t e the q u a l i t y of a n a l y s e s t h a t m a y be o b t a i n e d u s i n g e q u a t i o n I.

Table

Mineral

Minerals

2

Na20

MgO

AI203

SiO 2

K20

CaO

MnO

FeO

Hornblende

EMMA GIVEN

3.0 2.8

13.4 13.4

17.1 15.7

42.2 43.2

0.7 0.6

10.1 10.4

0.2 0.2

13.4 13.6

Biotite

EMMA GIVEN

-

10.6 9.6

21.5 21.3

38.9 39.9

8.6 8.3

-

-

20.5 20.9

~MMA GIVEN

14.8 14.1

-

55.4 56.2

-

-

-

29.8 29.7

Tremolite

EMMA GIVEN

25.3 25.2

60.6 60.0

-

11.5 11.9

2.6 3.0

Actinolite

EMMA GIVEN

9.2 11.4

54.7 53.5

-

23.0 23.0

-

Cummingtonite

-

13.1 12.1

EMMA-4 analysis of mineral p a r t i c l e s at 100 k V u s i n g the e x p e r i m e n t a l k X S i v a l u e s f r o m F i g u r e 2 [23]. Each E M M A a n a l y s i s is the a v e r a g e of at l e a s t 10 sets of d a t a f r o m 10 i n d i v i d u a l f i b e r s . T h e s e s a m p l e s w e r e p r o v i d e d by P r o f e s s o r P. W. W e i b l e n of the D e p a r t m e n t of G e o l o g y , U n i v e r s i t y of M i n n e s o t a , a n d w e r e a n a l y s e d in h i s l a b o r a t o r y b y w e t chemistry.

PE. Champness et aL / Electron microseop>, o f metals and minerals

Although the identification of the type of a s b e s t o s m a y c o n f i d e n t l y be m a d e by A E M (with the c a v e a t s o u t l i n e d above), in the general case i d e n t i f i c a t i o n of c r y s t a l l i n e m i n e r a l p a r t i c l e s may require electron diffraction (possibly microdiffraction if the particle is v e r y small) to resolve a m b i g u i t i e s p r e s e n t e d by the chemical data. For instance, one of the p o s s i b l e contaminants of commercial talc, Mg3Si4OI0(OH)2, is a n t h o p h y l l i t e , a double-chain silicate that m a y be a s b e s t i f o r m (Figure 13). Its c h e m i s t r y is v e r y similar to talc (which can also exhibit fibrous m o r p h o l o g y ) . However, t a l c shows an hexagonal e l e c t r o n d i f f r a c t i o n p a t t e r n which is quite d i s t i n c t from that of a n t h o p h y l l i t e [24].

129

igneous intrusions and lunar rocks (Figure 15a). They were first r e c o g n i s e d in the last century, but their small size p r e c l u d e d their identification and full c h a r a c t e r i s a t i o n until the a d v e n t of t r a n s m i s s i o n electron-microscopy and AEM. The i n t e r g r o w t h s are thin (~ 0.2 ~m) platelets parallel to (I00) of olivine (Figure 15b).

/

i

i

S~R~ENT~E

AM~.mOLES

I

........

1

~z~4F~,~on~o.~ 2

Figure 13. asbestos.

I

~7si~02~ ~ 2

The

six

bl~~.b~¸ ~2r~ r~ s,,,~o~2

commercial

varieties

of

Si

Si Mg I , Chrysotile

Anthophyllite Mg

L~._.~Ca

0 1 2

3 4 5

FeK~ Fe 6 7keV ~1 2 3 4 5 6 7keV

Si

i•aA•

Amosite

Cr°cid°lite FeKw F~eK

A

FeK= l/

Mg

0 1 2 3 4 5 6 7keV 1 2 3 4 5 6 7keV Figure 14. EDX s p e c t r a v a r i e t i e s of a s b e s t o s . 4.3.

Cellular

from

Intergrowths

the

four

commonest

in Olivines

Olivines are silicates containing isolated SiO 4 t e t r a h e d r a . The o l i v i n e s of igneous and m e t a m o r p h i c rocks b e l o n g to the M g 2 S i O 4 - F e 2 S i O 4 solid-solution series w i t h o n l y m i n o r s u b s t i tution of other elements. Cellular intergrowths, c o n s i s t i n g of b r a n c h i n g rods of a dark brown, opaque phase s u r r o u n d e d by a t r a n s p a r e n t phase, occur in o l i v i n e s from a number of

Figure 15a. Optical m i c r o g r a p h (plane p o l a r i s e d light) of a (100) section of an olivine from the Bushveld intrusion, South Africa (composition 53% M g 2 S i O 4 ) . M o s e l e y (unpublished) i n v e s t i g a t e d a number of terrestrial samples by AEM. He found that the colonies contained spinel (the dark phase), which is fairly p u r e m a g n e t i t e , Fe30%, and a Carich pyroxene. Moseley proposes that the c o l o n i e s were formed by p r e c i p i t a t i o n of c a t i o n s that were i n c o r p o r a t e d into the o l i v i n e d u r i n g solidification, but which b e c o m e incompatible with the structure at lower temperatures. The r e a c t i o n can be written:

(M~+

Fe

2+ 3+ R2

I~] ) Si 4016

olivine 3+ 2+ 2+ = R 2 Fe 04 + 4M SiO 3 spinel

pyroxene

(11)

P.E. Champness et al. / Electron microscopy o f metals and minerals

130

where M = Mg, Ca, Fe2+; R = Fe3+, Cr3+; IZI = v a c a n c y and A1 is p r o b a b l y i n c o r p o r a t # d into the olivine by the s u b s t i t u t i o n Fe3+AI 3+ + M2+Si %+.

0.5urn

practical problems which must be overcome include limitations in spatial resolution a s s o c i a t e d with b e a m broadening, a b s o r p t i o n and fluorescence effects within the s p e c i m e n and, in m e t a l l i c specimens, the p r e s e n c e of s o l u t e - r i c h surface films. Once identified all of these problems can be overcome and quantitative a n a l y s i s data o b t a i n e d .

Long - range diffusion

t t t j~ [ d ! ~'1 u ju-

l

o.,v,.E *~ ~

Short - range d illusion Fe2" Mg,S,

Figure 16. Schematic d i a g r a m of the p r o p o s e d m e c h a n i s m of growth of a p y r o x e n e / s p i n e l c o l o n y in olivine. The colony is richer in Ca, AI, Fe 3+ and Cr 3+ and poorer in Mg (and, in most cases, Fe 2+ ) t h a n the m a t r i x olivine, so these e l e m e n t s m u s t u n d e r g o l o n g - r a n g e diffusion. ACKNOWLEDGEMENTS Figure 15b. Electron m i c r o g r a p h of colonies in an olivine (3% Mg2SiO 4) from the Skaergaard intrusion, Greenland. A pyroxene, B magnetite. The foil is p e r p e n d i c u l a r to (100). The m e c h a n i s m of p r e c i p i t a t i o n is similar to that involved in the pearlite reaction d e s c r i b e d in section 3, but there are i m p o r t a n t differences. Chemically, the difference is that, whereas the p e a r l i t e reaction requires o n l y s h o r t - r a n g e d i f f u s i o n across the a d v a n c i n g cellular interface, in the olivine + p y r o x e n e + spinel reaction, long-range d i f f u s i o n m u s t also occur (Figure 16). This is b e c a u s e the composition of the olivine on the l e f t - h a n d side of e q u a t i o n (11) is not that of the m a t r i x olivine. Thus, although Si and m o s t of the Mg a n d Fe 2+ need o n l y d i f f u s e across the interface of the colony with the olivine, and oxygen only requires local rearrangement, long-range d i f f u s i o n of Ca, AI, Fe 3+ is r e q u i r e d into the colony, while Mg and (usually) Fe 2+ diffuse into the matrix. 5.

Most of the e x p e r i m e n t a l work was c a r r i e d out on an AEZ EMMA-4 a n a l y t i c a l e l e c t r o n - m i c r o s c o p e and a Philips EM 400T which were p u r c h a s e d with grants from SRC and NERC. We are g r a t e f u l to Mr. D. M o s e l e y for a l l o w i n g us to quote from his u n p u b l i s h e d results. FOOTNOTE 1 "Window-less" EDX d e t e c t o r s are now a v a i l a b l e for scanning e l e c t r o n m i c r o s c o p e s , but are too bulky to be easily interfaced with current t r a n s m i s s i o n instruments. REFERENCES [I]

Cliff, G. and Lorimer, G. W., The quantitative a n a l y s i s of thin specimens, J. Microsc. 103 (1975) 203-207.

[2]

Goldstein, J. I., Costley, J. L., Lorimer, G. W. and Reed, S. J. B., Q u a n t i t a t i v e xray a n a l y s i s in the e l e c t r o n m i c r o s c o p e , SEM 1977, I Proc. W o r k s h o p on Analytical Electron Microscopy, O. Johari, (ed.) (IITRI, Chicago) 315-324.

[3]

Green, M. and Cosslett, of production of

SUMMARY

Analytical effective data with

electron m i c r o s c o p y is shown to be an technique for obtaining microprobe a spatial r e s o l u t i o n of <50 nm. The

V.

E., Efficiency characteristic

P E. Champness et al. / Electron microscopy o f metals and minerals

X-radiation in thick targets of elements, Proc. Phys. Soc. 78 (1961) 1214. [4]

[5]

pure 1206-

Wood, J., Williams, D. B. and Goldstein, J. I., Determination of Cliff-Lorimer k factors for Philips EM400T, in Lorimer, G. W. Jacobs, M. H. and Doig, P. (eds), Q u a n t i t a t i v e Analysis with High Spatial Resolution (Metals Society, London, 1981). McGill, R. J. and Hubbard, F. H., Thin film k - v a l u e calibration for low atomic number elements using silicate mineral standards, see ref. [4].

[6]

Tixier, R., Ph.D. Paris (1973).

[7]

Lorimer, G. W., A1-Salman, S. A. and Cliff, G., The q u a n t i t a t i v e a n a l y s i s of thin specimens: e f f e c t s of absorption, fluorescence and beam spreading, in Misell, D. C. (ed), Developments in Electron Microscopy and Analysis 1977 (Institute of Physics, London, 1977).

[8]

[9]

Thesis,

[16]

Kelly, P. M., Jostsons, A., Blake, R. G. and Napier, J. G., The d e t e r m i n a t i o n of foil thickness b y scanning transmission electron microscopy, Phys. Stat. Sol. (a), 31 (1975) 771-780.

[17]

Ilyin, N. P. and Pozsgai, I., Q u a n t i t a t i v e M i c r o a n a l y s i s of Thin Samples in the EMMA (Electron Microscope + Microanalyzer), Mikrochimica Acta (Wien), Suppl. 8 (1979) 213-228.

[18]

Razik, N. A., Lorimer, G. W. and Ridley, N., An investigation of manganese p a r t i t i o n i n g during the a u s t e n i t e - p e a r l i t e t r a n s f o r m a t i o n using analytical electron m i c r o s c o p y , Acta Met. 22 (1974) 1249-58.

[19]

AI-Salman, S. A., Lorimer, G. W. and Ridley, N., P a r t i t i o n i n g of silicon during p e a r l i t e growth in an e u t e c t o i d steel, Acta Met. 27 (1979) 1391-1400.

[20~

Ai-Salman, 8. A., Lorimer, G. W. and Ridley, N., Pearlite growth kinetics and p a r t i t i o n i n g in a Cr-Mn e u t e c t o i d steel, Met. Trans. 10A (1979) 1703-1709.

[21]

Ridley, N. and Lorimer, G. W., Analytical electron m i c r o s c o p y of p a r t i t i o n i n g in pearlite, see ref. [4].

[22]

Morris, P. L., Davies, N. C. and Treverton, J. A., Effects of a surface film upon thin foil m i c r o a n a l y s i s , see ref. [8].

[23]

Lorimer, G. W., Q u a n t i t a t i v e a n a l y t i c a l electron microscopy, Proc. 8th Intl. Conf. on X-ray Optics and Microanalysis (Pendell, Michigan) in press.

[24]

Champness, P. E., Cliff, G. and Lorimer, G. W., The i d e n t i f i c a t i o n of asbestos, J. Micros. 108 (1976) 231-249.

[25]

Champness, P. E., The electron m i c r o s c o p e and e n v i r o n m e n t a l problems, in Brederoo, P., and Boom, G., (eds), Proc. 7th Eur. Cong. Electron M i c r o s c o p y 3 (1980) 242249.

U n i v e r s i t e de

Nockolds, C., Nasir, M. J., Cliff, G. and Lorimer, G. W., X-ray fluorescence correction in thin foil analysis and direct methods for foil thickness measurement, in Mulvey, T. (ed), Developments in Electron M i c r o s c o p y and Analysis, 1979 (Institute of Physics, London, 1979). Goldstein, J. I. and Williams, D. B., Xray a n a l y s i s of thin specimens, see ref.

[4]. [10]

[11]

Doig, P., Lonsdale, D. and Flewitt, P. E. J., Electron i n t e n s i t y d i s t r i b u t i o n s in STEM-EDS X-ray microanalysis of thin foils, see ref. [4]. Stephenson, T. A., Loretto, M. H. and Jones, I. P., Beam s p r e a d i n g in thin foils, see ref. [4].

[12]

Cliff, G. and Lorimer, G. W., Influence of plural electron scattering on X-ray spatial resolution in TEM thin-foil m i c r o a n a l y s i s , see ref. [4].

[13]

Lorimer, G. W. and Cliff, G., X-ray analysis in the transmission electron microscope, to be published in Developments in Electron M i c r o s c o p y and Analysis 1981 (Institute of Physics, London, 1981).

[14]

Lorimer, G. W., P r e c i p i t a t i o n studies, in Belk, J. A. (ed), Electron M i c r o s c o p y and Analysis (Applied Science, London, 1979).

[15]

Amelinckx, S., The d i r e c t o b s e r v a t i o n of dislocations (Academic Press, New York, 1964).

131