Size, Shape, and Texture Analysis - ACS Symposium Series (ACS

Chapter 1

Size, Shape, and Texture Analysis J. K. Beddow

Downloaded by UNIV OF UTAH on November 28, 2014 | http://pubs.acs.org Publication Date: February 12, 1987 | doi: 10.1021/bk-1987-0332.ch001

Center for Particulate Material Processing Sciences, Department of Chemical and Materials Engineering, The University of Iowa, Iowa City, IA 52242

This paper is a brief review of original basic engineering research in morphological analysis applied to particle characterization which has been conducted during the last 20 years at the University of Iowa, Center for Particulate Material Processing Sciences. The topics discussed include definitions, theory, instrumental and experimental aspects of size, shape and texture measurements of particulate material. Morphological Analysis Morphological analysis is concerned with particle characterization in the case of particle size, particle shape and particle texture. Particle texture may deal with the particle surface characteristics and also with the particle microstructure. Particle size and shape influence physical and chemical properties of particulate materials. Morphological analysis is being developed in order to facilitate a more accurate description of the properties and behavior of particulate systems from a fundamental knowledge of the characteristics of the particles of the system [1,2]. Shape is defined as the pattern of relationships among a l l of the points of the surface or profile of the particle. The development of this operational definition has in turn led to the development of morphological analysis. Experimental An image of the particle is obtained, the profile of that image is converted to a set of x,y pairs, a process known as d i g i t i z i n g . The x,y set is then converted to polar coordinates, (R,6). The curve in the R,6 space is converted to a Fourier equation, the coefficients of which are extracted, and then mathematically transformed to morphic terms which themselves constitute the shape features of the particle. A sample usually consists of 100 particles, upwards of 150 profile points are extracted from each particle, giving a total of 15,000 x,y points per analysis. Once the morphic terms are obtained, the data analysis can be carried out in order to facilitate the 0097-6156/87/0332-0002$08.25/0 © 1987 American Chemical Society

In Particle Size Distribution; Provder, T.; ACS Symposium Series; American Chemical Society: Washington, DC, 1987.


1.

BEDDOW

3

Size, Shape, and Texture Analysis

s o l u t i o n of the problem a t hand. M o r p h o l o g i c a l a n a l y s i s i s c a r r i e d o u t u s i n g an i n s t r u m e n t known a s a Shape A n a l y z e r [ 3 ] , w h i c h c o n s i s t s e s s e n t i a l l y o f a h i g h q u a l i t y g r a p h i c s y s t e m and computer p l u s s o p h i s t i c a t e d s o f t w a r e and p e r i p h e r a l s [ 2 ] . The S h a p e A n a l y z e r i s a s c i e n t i f i c i n s t r u m e n t w h i c h i s u s e d t o a n a l y z e t h e s h a p e , s i z e , a n d t e x t u r e o f o b j e c t s . The i t e m f o r a n a l y s i s may be t h e o b j e c t i t s e l f , i t s p h o t o g r a p h , o p t i c a l o r e l e c t r o n m i c r o g r a p h , e t c . The s h a p e - s i z e a n a l y s i s i s a c h i e v e d b y c o n v e r t i n g t h e p r o f i l e t o a s e t o f shape and s i z e d e s c r i p t o r s w h i c h a r e c o m p l e t e , u n e q u i v o c a l and i n v a r i a n t . The t e x t u r e a n a l y s i s c o n v e r t s t h e f u l l image o f t h e o b j e c t i n t o a s e t o f t e x t u r a l d e s c r i p t o r s w h i c h a r e u n e q u i v o c a l , c o m p l e t e and i n v a r i a n t . These s h a p e , s i z e a n d t e x t u r e d e s c r i p t o r s c a n be u s e d i n r e s e a r c h , i n q u a l i t y c o n t r o l , i n p r o c e s s c o n t r o l and s p e c i f i c a t i o n s . A d d i t i o n a l d e t a i l s a r e g i v e n i n Table 1 and t h e A p p e n d i x . The m o r p h o l o g i c a l f e a t u r e s m e a s u r e d i n t h e S h a p e A n a l y z e r include the f o l l o w i n g :

1.

Table

Topic

Morphological Analysis

Application

Feature

Size

Equivalent radius Mean r a d i u s / d i a m e t e r

Hydraulic radius Sedimentation Correlations with other s i z e a n a l y s i s methods

particle

Shape

Not-roundness L2(2) L2(3) L2(4) Roughness Symmetry

Wear a n a l y s i s Dust e x p l o s i o n s Particle characterization Settling Bulk p r o p e r t i e s Slurry flow F l u i d i z e d beds

Texture

Mean t e x t u r e Standard d e v i a t i o n Symmetry

Microstructure analysis Cancer c e l l i d e n t i f i c a t i o n and differentiation

Mixtures

Cross-over

P a r t i c l e mixture

points

and b l e n d a n a l y s i s

Strategy The s h a p e a n d t e x t u r e f e a t u r e s a r e i n v a r i a n t , u n i q u e a n d unequivocal. They a r e a s s o c i a t e d w i t h i n d i c a t i o n s o f p h y s i c a l meaning. The u s e d f o r m o f t h e F o u r i e r e q u a t i o n i s

R(9)

= a

ο

+

f a s i n ηθ + b c o s η θ ) η η J


PARTICLE SIZE DISTRIBUTION

4

the raw F o u r i e r c o e f f i c i e n t s n o t u s e f u l t o d e s c r i b e t h e p r o f i l e because they change i n v a l u e as t h e p r o f i l e i s r o t a t e d * F o r t h i s r e a s o n t h e y a r e t r a n s f o r m e d i n t o i n v a r i a n t m o r p h o l o g i c a l s i z e and shape d e s c r i p t o r i n t h e f o l l o w i n g way: Theory o f M o r p h o l o g i c a l A n a l y s i s [4] S i z e a n d S h a p e D e s c r i p t o r s * The f o l l o w i n g s i z e a n d s h a p e t e r m s a r e defined* These a r e r o t a t i o n a l l y i n v a r i a n t and r e l a t e d t o t h e amplitudes, and b , as f o l l o w s * The s i z e t e r m i s d e f i n e d a s


n

/ a

2

o

I

+

2

(a

I

L

2

, ^ η n=l

+

b )

(1)

2

n'

i n w h i c h R i s termed " e q u i v a l e n t r a d i u s " and i s t h e r a d i u s o f a c i r c l e h a v i n g t h e same a r e a a s t h a t o f t h e p a r t i c l e p r o f i l e , a n d η i s the order of the c o e f f i c i e n t . The s h a p e t e r m s a r e d e f i n e d a s Q

a

L, =0 Ι,η

J

a

3,n

2 , n ~ ^ 2

r 2 (a a η 2n v

4R

J

(2) ο

for a l l η

1 L

/R

ο

0

(

1 a

( n

± +

b

(3) n)

b a + 2a b b J η η 2n η 2n 0

0

;

(4)

i s t h e mean r a d i u s . E q u a t i o n ( 2 ) d e f i n e s t h e v a l u e o f t h e s i z e n o r m a l i z e d mean radius of the p a r t i c l e . E q u a t i o n ( 3 ) d e f i n e s t h e s i z e n o r m a l i z e d sum of the squares of the F o u r i e r c o e f f i c i e n t s . Equation (4) defines the sum a n d d i f f e r e n c e s o f t h e m u l t i p l e s . I t h a s b e e n s h o w n t h a t t h e s e s i z e a n d s h a p e d e s c r i p t o r s c a n be u s e d t o r e g e n e r a t e t h e o r i g i n a l particle profile. This i n d i c a t e s that the d e s c r i p t o r s together c o n t a i n a l l o f t h e s i z e and shape i n f o r m a t i o n c o n t a i n e d i n t h e original profile. The m o r p h o l o g i c a l d e s c r i p t o r s d e s c r i b e d a b o v e w i l l be e x a m i n e d later f o rtheir physical interpretation. But f i r s t t h e i r very i n t e r e s t i n g relationship to the s t a t i s t i c a l properties of the p a r t i c l e p r o f i l e r a d i a l d i s t r i b u t i o n w i l l be c o n s i d e r e d * Q


1.


BEDDOW

Statistical

5

P r o p e r t i e s of Descriptors*

μ

• L R ο ο

Λ

U

(mean

radius)


ζ

w h e r e μ i s t h e r a d i a l s t a n d a r d d e v i a t i o n ( t h e NR a n d μ^ i s t h e r a d i a l s k e w n e s s ( S K E ) .

not-roundness)

2

Symmetry

[5]

Operations

I n c r y s t a l l o g r a p h y one i s a c c u s t o m e d t o t h e i d e a t h a t a s t r u c t u r e e i t h e r h a s a p a r t i c u l a r s y m m e t r y e l e m e n t o r i t d o e s n o t . The membership i s thus e i t h e r 1 o r z e r o . In morphological a n a l y s i s the s y m m e t r y h a s a v a l u e o f z e r o t h r o u g h 1 d e p e n d i n g u p o n how c l o s e l y t h e p r o f i l e a p p r o a c h e s t h e symmetry b e i n g c o n s i d e r e d * The d e f i n i t i o n s o f t h e s y m m e t r y o p e r a t i o n s a r e shown b e l o w : Rotation

C

m = ^ f c ô ô -

(-1.2.3.—Λ

(8)

Reflection

2 IL σ

(n)cos

(α -η3-2ηπ)

ι - —

(

9

)

if ZL (j-n) 2

u

j>i

ZL (n> 2

rj=m π Lj=2mJ


(10)

6

PARTICLE SIZE DISTRIBUTION Inversion ZL (2n) ?

I =

( 1 1

-ÎL7ÏÏ)

>

Rotation-Reflection ΣΧ (2n)


S

2 -5^(n7

ά

( 1 2 )

ί°1™ °0

=

Texture [6] T e x t u r e i s d e f i n e d as t h e p a t t e r n o f r e l a t i o n s h i p s between t h e g r a y l e v e l s o f t h e d e f i n e d i m a g e . The o b j e c t i v e o f t e x t u r e m o r p h o l o g y a n a l y s i s i s d e v e l o p a n a n a l y t i c a l m e t h o d w h e r e b y t h e i m a g e c a n be regenerated. I n o r d e r t o do t h i s t h e p o i n t s o f t h e i m a g e h a v e t o be incorporated i n t o the a n a l y s i s i n the form of i n v a r i a n t descriptors. The i n t e r p r e t a t i o n o f t h e t e x t u r a l m o r p h o l o g y f e a t u r e s depends upon t h e p h y s i c s o f t h e s i t u a t i o n ( f o r e x a m p l e , t h e g r a y l e v e l may be r e l a t e d t o a l t i t u d e o r i n a n o t h e r c a s e t o t h e c h e m i c a l a n a l y s i s from point t o p o i n t . The i n t e r p r e t a t i o n a l s o d e p e n d s u p o n the m a t h e m a t i c a l r e l a t i o n s h i p s between t h e v a r i o u s m o r p h o l o g i c a l d e s c r i p t o r s used. There a r e t h r e e major types o f m o r p h o l o g i c a l texture descriptors. These a r e : s t a t i s t i c a l t e r m s , symmetry o p e r a t i o n s , and i n v a r i a n t t e x t u r e m o r p h o l o g y d e s c r i p t o r s ( I T M D ' s ) .

_ G

L T

=

I

i Pi

(13)

i=l

4in

J i=l

(1 - G j

2

Pi

(14)

which: G

i s t h e mean g r a y l e v e l

T

o f t h e image

Τ σ

i s the standard L

Pi

deviation

o f t h e image g r a y

i s t h e maximum g r a y

level

level

i s the p r o b a b i l i t y d i s t r i b u t i o n at gray l e v e l i .

I f t h e i m a g e i s r o t a t e d b y 2π/η a n d t h e o r i g i n a l c o n f i g u r a t i o n i s r e p r o d u c e d , t h e i m a g e i s s a i d t o p o s s e s s a n η-fold r o t a t i o n a l symmetry. The t e x t u r a l s y m m e t r y i s


1. BEDDOW

Size, Shape, and Texture Analysis Cn

in

-

1 -

if[Gix. ) TGfx> y')] JJG(xy) dxdy (TDs) y

2

;

dxdy

which: G(xy) x'y'


7

i s the gray

are

level

at

(x,y)

locations corresponding

G(x.y)

The i n v a r i a n t ITMD's h a v e b e e n d e v e l o p e d u s i n g a c o m b i n e d F o u r i e r - B e s s e l e q u a t i o n i n which the F o u r i e r terms account f o r the r e p e t a t i v e n a t u r e o f t h e image d e s c r i b e d by a r a d i u s v e c t o r s w e e p i n g r o u n d on a c e n t r a l o r i g i n . The B e s s e l t e r m s d e a l w i t h t h e f e a t u r e s o f the image i n the d i r e c t i o n o u t w a r d s a l o n g t h e r a d i i f r o m the origin. The g e n e r a l f o r m o f t h e d e s c r i p t o r s w i l l be r e p o r t e d a t a l a t e r date. Indications

of

P h y s i c a l Meanings of

S h a p e and

Textural

Descriptors

Particle Size. The e q u i v a l e n t r a d i u s R may a l s o be r e p o r t e d o u t a s the e q u i v a l e n t p a r t i c l e d i a m e t e r 2R . The s i z e may be r e p o r t e d o u t a s mean a n d s t a n d a r d d e v i a t i o n a s s h o w n i n T a b l e I I o r a s a h i s t o g r a m as shown i n F i g u r e l a , b . The s i z e t e m p l a t e i n F i g u r e 2 i l l u s t r a t e s t h e p r i n c i p l e u n d e r l y i n g the R term. Q

Q

Q

Shape C l a s s i f i e r . I t h a s l o n g b e e n known t h a t d i f f e r e n t m e t h o d s o f p a r t i c l e p r o d u c t i o n w h i c h i n v o l v e d i f f e r e n t modes o f p a r t i c l e f o r m a t i o n w i l l produce p a r t i c l e s of d i f f e r e n t morphology. To d e m o n s t r a t e t h i s f a c t , t h r e e s a m p l e s o f a d i p i c a c i d p o w d e r w e r e made by t h r e e methods: a t o m i z a t i o n , c o m m i n u t i o n and c r y s t a l l i z a t i o n . The NR and SKE v a l u e s w e r e p l o t t e d a g a i n s t e a c h o t h e r f o r t h e t h r e e particulate materials. The d a t a s h o w n i n F i g u r e 3a,b c l e a r l y s h o w s t h a t i t i s p o s s i b l e t o c l a s s i f y t h e t h r e e p r o d u c t s on t h e b a s i s o f t h e i r morphology. The m e t h o d o f d a t a p l o t t i n g u s e d , s t r e t c h e s t h e p o i n t s o u t i n a d i a g o n a l f a s h i o n and t h i s p e r m i t s t h e c l a s s i f i c a t i o n l i n e s t o be d r a w n i n a s s h o w n . The ATM, RED and E L E C T d a t a c o r r e s p o n d to c o m m e r c i a l i r o n p o w d e r s made b y a t o m i z a t i o n , r e d u c t i o n and e l e c t r o l y t i c d e p o s i t i o n , r e s p e c t i v e l y . These c o m m e r c i a l m a t e r i a l d a t a do n o t c o r r e s p o n d t o t h e a d i p i c a c i d d a t a b e c a u s e t h e c o m m e r c i a l p r o c e s s e s a r e c o m p r i s e d o f many s t e p s i n c l u d i n g : c r u s h i n g and g r i n d i n g , s i n t e r i n g , hammer m i l l i n g , m i x i n g and b l e n d i n g . For e x a m p l e , c o n s i d e r t h e a t o m i z e d i r o n p o w d e r , e a c h one o f t h e t h e s e s t e p s i n f l u e n c e s t h e p a r t i c l e m o r p h o l o g y t o s u c h an e x t e n t t h a t t h e d a t a i s s h i f t e d i n t o the r e g i o n c o r r e s p o n d i n g t o the comminuted adipic acid. Not-Roundness. The s i z e n o r m a l i z e d r a d i a l s t a n d a r d d e v i a t i o n i s i l l u s t r a t e d i n t h e NR t e m p l a t e shown i n F i g u r e 4. T h u s , no m a t t e r how t h e p r o f i l e d e v i a t e s f r o m a c i r c l e t h e NR v a l u e w i l l o n l y i n d i c a t e the s t a t i s t i c a l p r o p e r t y of the r a d i a l d i s t r i b u t i o n . There i s no i n f o r m a t i o n i n t h i s t e r m c o n c e r n i n g t h e s e q u e n c e o f r a d i a l terms. L2(2) L2(2)

Indicator. The e f f e c t o f s h a p e c h a n g e on t e r m i s i l l u s t r a t e d i n F i g u r e 5.

the

size

of


the


8

T a b l e I I . S i z e R e p o r t e d a s Means and S t a n d a r d D e v i a t i o n s f o r S p h e r o i d a l Carbides i n F e r r i t e M a t r i x ( l e f t ) and f o r Atomized and Sponge I r o n Powders ( r i g h t ) .

R

R

ο

ο Mean


0.432

0.036

(CIF

40)

S t d . Dev.

Mean

S t d . Dev.

0.076

0.013

S p o n g e ( 1 0 ) 0.090

0.031

Atom (10)

25

20

1

15Ο

S J-l Pu ιοί

51

10 15 20 25 30 Diameter (microns)

35

40

F i g u r e l a . S i z e d i s t r i b u t i o n f o r Rey 511. Reproduced w i t h p e r m i s s i o n f r o m R e f . 8. C o p y r i g h t 1985 O x f o r d & IBH P u b l i s h i n g ,



1.

BEDDOW

22

-

20

-

1·

-

16

-

14

-

12

-

10

-

β

-

•

-

4

-

2

-

Size, Shape, and

Texture Analysis

9

Ο 3.3

3.7

3.»

4.1

4.3

4.5

4.7

3.1

3.3

Ro(/*m) κ

4.9

10*

3.5

3.7

5.9

4.1

4.3

F i g u r e l b . Histogram r e p r e s e n t a t i o n of a p a r t i c l e s i z e d i s t r i bution. R e p r o d u c e d w i t h p e r m i s s i o n f r o m R e f . 8. Copyright 1985 O x f o r d & IBH P u b l i s h i n g .



0

q

2

30

(Equivalent

Radius)

45

F i g u r e 2. Size template i l l u s t r a t i n g the p r i n c i p l e underlying R term. The a c t u a l s i z e d e p e n d s o n t h e m a g n i f i c a t i o n u s e d . a r e a o f t h e p r o f i l e i s IT R .

15

Size


the The

60

1.

BEDDOW

11


ADIPIC ACID ATOMIZED

COMMINUTED


CRYSTALLIZED

F i g u r e 3a. Morphologies of a d i p i c a c i d . f r o m R e f . 2. C o p y r i g h t 1984 CRC P r e s s .

10*

5

«

«

io*

e

7

\o

ι

ιο

ι β

ι

io RADIAL 5

Reproduced w i t h

1

1

1er 1er SKEWNESS 4

5

10**

permission

1-

10

F i g u r e 3b. M o r p h o l o g y p l o t f o r a d i p i c a c i d ; ATM - a t o m i z e d i r o n , RED - r e d u c e d i r o n , E L E C T - e l e c t r o l y t i c i r o n . Reproduced w i t h p e r m i s s i o n f r o m R e f . 2. C o p y r i g h t 1984 CRC P r e s s .


In Particle Size Distribution; Provder, T.; ACS Symposium Series; American Chemical Society: Washington, DC, 1987. 0.012

A

0.000

*

0.10

fl-t

f

Ο

0.026

California Sand

LU*)

Roundness

8

0.15

—I

Ο

0.063

Crushed Quartz

F i g u r e 4. NR t e m p l a t e i l l u s t r a t i n g t h e s i z e n o r m a l i z e d r a d i a l s t a n d a r d d e v i a t i o n . R e p r o d u c e d w i t h p e r m i s s i o n f r o m R e f . 8. C o p y r i g h t 1985 Oxford & IBH P u b l i s h i n g .

0.05

Arizona Sand

Sphere

Not


1 0.20

Ο

0.137

Phosphate Rock

1

Ο ^ 2 c Η

&

$


0

f>

F i g u r e 5.

Effect

0.05

H* 0.10

1

· the s i z e of

Limestone

o f s h a p e change on

Vitrain

L2(2)

the L2(2)

0.15

1

Titanium


term.

Fusain

0.20

·+

Coal

β

en α D

14 L2(3) L2(3)


Indicator. The e f f e c t o f s h a p e c h a n g e o n t h e v a l u e o f t h e t e r m s i n shown i n F i g u r e 6.


Roughness I n d i c a t o r . T h i s t e r m i s d e f i n e d a s t h e sum o f t h e h i g h e r o r d e r L2(n) terms. I t r e p r e s e n t s t h e m i n o r d e v i a t i o n s and i r r e g u l a r i t i e s i n t h e p a r t i c l e p r o f i l e and i s i l l u s t r a t e d i n t h e t e m p l a t e o f F i g u r e 7. Shape D i s t r i b u t i o n . One o f t e n h e a r s o f " n a r r o w s i z e d i s t r i b u t i o n " o r "broad s i z e d i s t r i b u t i o n " . I t i s also meaningful to consider a n a r r o w shape d i s t r i b u t i o n and a broad shape d i s t r i b u t i o n . Examples o f t h e s e a r e g i v e n i n F i g u r e 8. The n a r r o w s h a p e d i s t r i b u t i o n s h o w s a plot of not-roundness of c r y s t a l s of NaCl. After m i l l i n g , the broad shape d i s t r i b u t i o n r e s u l t s . Shape C o m p o s i t i o n . The NR i s c o m p o s e d o f t h e o t h e r above. Specifically:

NR = L 2 ( 2 )

+ L2(3)

+ L2(4)

terms

described

Φ L2(n)

An a c c o u n t i n g o f t h e p r o p o r t i o n o f NR f o r e a c h c o m p o n e n t t e r m s i s c a l l e d t h e Shape C o m p o s i t i o n . I t i s i l l u s t r a t e d i n Table 3 f o r the two s a m p l e s o f N a C l . The f i r s t c o l u m n c o r r e s p o n d s t o t h e r e c e i v e d c r y s t a l s , t h e second column c o r r e s p o n d s t o t h e m i l l e d s a l t m a t e r i a l . Residual Porosity. T h i s c a n be d e t e r m i n e d on a n a r e a b a s i s b y examination of s u i t a b l y prepared microstructures. F o r example, as shown i n T a b l e I V a , b , t h e r e a r e s u b s t a n t i a l d i f f e r e n c e s b e t w e e n t h e r e s i d u a l p o r o s i t y i n an a t o m i z e d s i n t e r e d i r o n compact and a s i m i l a r sponge i r o n compact. Shape Symmetry. The m e a n i n g o f t h e r o t a t i o n a l s y m m e t r y , f o r e x a m p l e , i s demonstrated i n F i g u r e 9. I n t h i s f i g u r e t h e v a l u e s o f C 2 , C3 a n d are compared between an e q u i l a t e r a l t r i a n g l e and an i s o s c o l e s triangle. The p r e c i s e d e f i n i t i o n s o f t h e s y m m e t r i e s a r e g i v e n b e l o w . F i g u r e 10 s h o w s a n i n t e r e s t i n g a p p l i c a t i o n o f p a r t i c l e s h a p e symmetry i n t h e case o f seven t y p e s o f i n s t a n t c o f f e e p r o d u c t s . I t w i l l be s e e n t h a t t h e s y m m e t r y a n a l y s i s shows t h a t c o f f e e #3 i s f u n d a m e n t a l l y d i f f e r e n t f r o m e a c h one o f t h e o t h e r c o f f e e p r o d u c t s . T e x t u r e a n a l y s i s i s i l l u s t r a t e d i n F i g u r e 11 w h i c h shows t h e g r a y l e v e l d i s t r i b u t i o n f o r a p o l i s h e d and e t c h e d sample o f t u n g s t e n carbide material. F r o m t h i s d i s t r i b u t i o n o n e c a n o b t a i n t h e mean a n d standard deviation of the texture. I n a d d i t i o n , t h e η* v a l u e i n d i c a t e s t h e sharpness o f t h e image. Some a p p l i c a t i o n s o f t h e mean g r a y l e v e l a r e s h o w n i n F i g u r e s 1 2 a , b and 1 3 . I n t h e m e a s u r e m e n t o f g r a i n s i z e i t i s n e c e s s a r y t o u t i l i z e t h e s e r v i c e s o f a s k i l l e d human o p e r a t o r i n o r d e r t o i n t e r p r e t t h e s i z e measurement. U s i n g t h e mean t e x t u r a l i n d i c a t o r t h e d e c i s i o n m i g h t be made b y t h e S h a p e A n a l y z e r . Thus, i n F i g u r e 12, a c o r r e l a t i o n i s d e p i c t e d showing that gray l e v e l can correspond t o g r a i n s i z e i n c a r e f u l l y prepared samples. F i g u r e 13 s h o w s f o u r s t a g e s d u r i n g t h e s i n t e r i n g o f F e - C compacts a t s u c c e s s i v e l y higher temperatures. A g a i n , t h e mean t e x t u r e v a l u e c a n be u s e d a s a n i n d i c a t o r o f t h e s i n t e r i n g temperature used i n t h e sample p r e p a r a t i o n .




5·

s

a s ex.

ϋ

δ*

I

α

m D

DO



16


1.

BEDDOW


material : sodium chloride two-step processing. BM 60


50


17


18

T a b l e I I I . Shape C o m p o s i t i o n Sodium C h l o r i d e


morphic descriptor

g

Changes f o r

a

BM^

L2(2)

49.80

65.94

L2(3)

6.92

14.08

L2(4)

31.53

8.16

Ruff

11.75

11.82

S indicates starting material. 'BM i n d i a t e s b a l l - m i l l i n g m a t e r i a l .

Table IVa.

Morphic

Features of Residual

P o r o s i t y i n I r o n Compacts

Elongation

Not- - R o u n d n e s s

Mean Atomized Sponge

Iron

Iron

Std.

Std.

Mean

Dev.

0.049

0.063

0.065

0.085

0.008

0.042

0.119

0.057

Table IVb. Morphic Properties of Speroidal Carbide P a r t i c l e s 40) i n a F e r r i t e M a t r i x

Elongation (ΙΟ- )

Not-Roundness (ΙΟ" )

2

Mean

3.3

Dev.

Std.

3.5

2

Dev.

Mean

4.1

Std.

Dev.

4.6


(n=

1.

BEDDOW

19


Includes r o t a t i o n , r e f l e c t i o n . Inversion 4 r o t a t i o n - r e f l e c t i o n

2^

^

(m •• I , 2, 3, · · · · · ·

)

£L (n) 2

0ί

c

2

Size, Shape, and Texture Analysis - ACS Symposium Series (ACS

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