Abstract
The size of grains and particles in metallic structures strongly influences many of the properties of the material. The kinetics of metallurgical processes, e.g. recrystallization, grain and particle growth, phase transformations, or sintering, are decisively determined by driving forces related to surface energy and, in turn, to the dispersion of the structural elements. Size and size distribution, therefore, rank as the most important parameters in describing the microstructure of materials.
Get full access to this article
View all access options for this article.
References
1.
"Quantitative Microscopy"
(edited by
DeHoff
R. .2
N
F.
. Rhines ). 1968 : New York and London (McGraw-Hill ).
2.
Exner
H. E.
, Metall , 1967 , 21 , 431 .
3.
Underwood
E. E.
, "Quantitative Stereology" . 1970 : Reading , Mass., and London (Addison-Wesley ).
4.
"Handbuch der Mikroskopie in der Technik"
(edited by
Freund
G.
), Vol. III . 1968 : Frankfurt (Umschau-Verlag ).
5.
Praktische Metallographie (Practical Metallography), Stuttgart (Riederer Verlag), and
Metallography (an International Journal) , New York (Elsevier ).
6.
Brandon
D. G.
, "Modern Techniques in Metallography" . 1966 : London (Butterworths).
7.
Paulus
M.
, Métaux-Corrosion-Ind ., 1963 , 38 , 14 .
8.
Exner
H. E.
, Praktische Metallographie , 1966 , 3 , 18 .
9.
Picklesimer
M. L.
, Ref. 1, Chap. 11, p. 326 .
10.
Mukherjee
T.
Stumpf
W. E.
Sellars
C M.
, J. Mat. Sci ., 1968 , 3 , 127 .
11.
Herdan
G.
L
M. L.
, "Small-Particle Statistics" . 1953 : New York and Amsterdam (Elsevier ); 1960 : London (Butterworths).
12.
Batel
W.
, "Korngrossenmesstechnik" . 1960 : Berlin (Springer).
13.
Orr
C.
M
J. M.
, "Fine-Particle Measurement" . 1959 : New York (Macmillan ).
14.
Hilliard
J. E.
, Trans. Met. Soc. AIME , 1962 , 224 , 906 .
15.
DeHoff
R. T.
, ibid ., 1965 , 233 , 25 .
16.
DeHoff
R. T.
, Ref. 1, Chap. 5, p. 128 .
17.
Saltykov
S. A.
, "Stereology" (edited by
Elias
H.
), 163 . 1967 : New York (Springer ).
18.
Nassenstein
H.
, Chem.-Ing.-Technik ., 1955 , 27 , 535 .
19.
Davis
C. N.
, Nature , 1962 , 195 , 768 .
20.
Kaye
B. H.
, Powder Technol ., 1968 –69, 2 , 97 .
21.
Walton
W. H.
, Nature , 1948 , 162 , 329 .
22.
Krumbein
W. C.
, J. Geology , 1935 , 43 , 482 .
23.
Fischmeister
H. F.
, Acta Polytech. Scand ., 1966 , (56) ,; Ref. 1, Chap. 12 , p. 336 .
24.
Wadell
H.
, J. Geology , 1935 , 43 , 250 .
25.
Heywood
H.
, Chem. and Ind ., 1937 , 56 , 149 .
26.
Stoeber
W.
, Lab. Invest ., 1965 , 14 , (154 ), 892 .
27.
Exner
H. E.
, Z. Metallkunde , 1966 , 57 , 755 .
28.
Underwood
E. E.
, Ref. 1, Chap. 6, p. 149 .
29.
Schükher
F.
, Acta Polytech. Scand ., 1966 , (54) ; Ref. 1, Chap. 7 , p. 201 .
30.
Berglund
T.
Hultgren
A.
Phragmén
G.
, Jernkontorets Ann ., 1937 , 121 , 579 .
31.
"Estimating the Average Grain Size of Metals", Standard E112-63.
Philadelphia, Pa. (Amer. Soc. Test. Mat. ).
32.
Hyam
E. D.
Nutting
J.
, J. Iron Steel Inst ., 1956 , 184 , 148 .
33.
Mönch
S.
E
H. E.
Metallkunde
Z.
, 1968 , 59 , 356 .
34.
Fischmeister
H. F.
, Praktische Metallographie , 1965 , 2 , 251 .
35.
Exner
H. E.
, ibid ., 1966 , 3 , 334 .
36.
Saltykov
S. A.
, "Sterometric Metallography" . 1958 : Moscow (Metallurgizdat) (available as English Rough Draft Trans-lation , ASTIA ).
37.
Paulus
M.
, Métaux-Corrosion-Ind ., 1962 , 37 , 447 .
38.
Roethlisberger
H.
, J. Geology , 1955 , 63 , 579 .
39.
Münzer
H.
Schneiderhöhn
P.
, Heidelberger Beitr. Mineral. Petrogr ., 1953 , 3 , 456 .
40.
Pelto
C. R.
, J. Geology , 1952 , 60 , 402 .
41.
Aboav
D. A.
G
T. G.
, Metallography , 1969 ,2 , 171 .
42.
Johne
R.
, Informationsdienst A.P.V. Mainz , 1966 , 12 , 29 .
43.
Chamot
E. M.
M
C. M.
, "Handbook of Chemical Microscopy. I. Principles and Use of Microscopes and ArePssories" . 1958 : New York and London (John Wiley ).
44.
"Tentative Recommended Practice for Particle-Size Distribu-tion of Particulate Substances of Subsieve Sizes"
, ASTM-Designation E 20-51 T.
45.
Brit
. Standard: "Determination of Particle Size of Powders: Microscope Method" .
46.
Fischmeister
H. F.
Blände
C.A.
Palmqvist
S.
, Powder Met ., 1961 , 7 , 82 .
47.
Gahm
J.
, Zeiss-Inform ., 1969 , 17 , 65 .
48.
Hörnsten
A.
, Bull. Geol. Inst. Univ. Uppsala , 1959 , 38 , 105 .
49.
Endter
F.
Gebauer
H.
, Optik , 1956 , 13 , 97 .
50.
Schluge
H.
, Zeiss-Werkzeitschrft , 1959 , 7 , 68 .
51.
Fisher
C. F.
, "Automatic Cleanness Assessment of Steel" (Publ. No. 112 ), p. 24 . 1968 : London (Iron Steel Inst. ).
52.
Fisher
C. F.
Cole
M.
, Microscope , 1968 , 16 , 81 .
53.
Exner
H. E.
, Leitz-Mitt. Wissensch. Techn ., 1967 , 4 , 97 .
54.
Dörfler
G.
, Praktische Metallographie , 1969 , 6 , 144 .
55.
Dörlier
G.
Plöckinger
E.
, Arch. Eisenhiittenwesen , 1965 , 36 , 649 .
56.
Roberts
F.
Z
J. Z.
, Proc. Inst. Elect. Eng ., 1952 , [A] , 99 , 69 .
57.
Young
J. Z.
Roberts
F.
, Nature , 1951 , 167 , 231 .
58.
Schafer
K.
, Praktische Metallographie , 1970 , Special Issue 1 , VI.
59.
Bockstiegel
G.
, ibid ., 1969 , 6 , 596 ; 1970 , 7, 577 .
Welboron
A. P.
Meijer
O.
, ibid. , 1972 , in the press.
60.
Hilliard
J. E.
, Trans. Met. Soc. AIME , 1968 , 242 , 1373 .
61.
Beadle
C.
, Praktische Metallographie , 1970 , 7 , 249 .
62.
Leschonski
K.
, Informationsdienst A.P.V. Mainz , 1966 , 12 , 1 .
63.
Rumpf
H.
, Staub , 1960 , 20 , 253 .
64.
Rumpf
H.
F
K. F.
, Chem.-Ing.-Technik , 1964 , 36 , 523 .
65.
Seemann
H. J.
Bentz
W.
, Z. Metallkunde , 1954 , 45 , 663 .
66.
Johne
R.
, Informationsdienst A.P.V. Mainz , 1966 , 12 , 12 .
67.
Aboav
D. A.
G
T. G.
, Metallography , 1969 , 1 , 333 .
68.
da
E. N.
Andrade
C.
Aboav
D. A.
, Proc. Roy. Soc ., 1966 , [A] , 291 , 18 .
69.
Feltham
P.
, Acta Met ., 1957 , 5 , 97 .
70.
Ashby
M. F.
Ebeling
R.
, Trans. Met. Soc. AIME , 1966 , 236 , 1396 .
71.
Stumpf
W. E.
M
C. M.
, Metallography , 1968 , 1 , 25 .
72.
Carl Schleicher u. Schüll, Einbeck, Germany, Papers 423 1/2 and
291/2 .
73.
Wagner
C.
Elektrochem.
Z.
, 1961 , 65 , 581 .
74.
Lifshits
I. M.
V
V. V.
, J. Physics Chem. Solids , 1961 , 19 , 35 .
75.
Exner
H. E.
Santa Marta
E.
Petzow
G.
, "Modern Developments in Powder Metallurgy" (edited by
Hausner
H. H.
), Vol. 4 , p. 315 . 1971 : New York (Plenum Press ).
76.
Markworth
A. J.
, Metallography , 1969 , 2 , 303 .
77.
Exner
H. E.
F
H. F.
, Z. Metallkunde , 1970 ,61 , 218 .
78.
Moreen
H. A.
, Metallography , 1969 , 1 , 349 .
79.
Wicksell
S. D.
, Biometrika , 1925 , 17 , 84 .
80.
Hagermann
T. H.
, Geol. Foren. Stockholm Forh ., 1925 , 46 , 325 .
81.
Scheil
E.
, Z. anorg. Chem ., 1931 , 201 , 259 .
82.
Scheil
E.
, Z. Metallkunde , 1935 , 27 , 199 .
83.
Huber
A.
, Z. Physik , 1935 , 93 , 227 .
84.
Schwartz
H. A.
, Metals and Alloys , 1934 , 5 , 139 .
85.
Lenz
F.
, Z. wiss. Mikroskopie , 1956 , 63 , 50 .
86.
Bach
G.
, ibid ., 1964 , 66 , 193 .
87.
Chayes
F.
, J. Geology , 58, 156 ; 1951 , 59 , 274 .
88.
Greenman
N. N.
, ibid ., 1951 , 59 , 268 , 447 .
89.
Lenz
F.
, Optik , 1954 , 11 , 524 .
90.
Elias
H.
, Z. wiss. Mikroskopie , 1954 , 62 , 32 .
91.
Reid
W. P.
, J. Math. Phys ., 1955 , 34 , 95 .
92.
Dietz°,
H. D.
Techn. Mitt. Krupp , 1955 , 13 , 51 .
93.
Hennig
A.
, Z. wiss. Mikroskopie , 1956 , 63 , 57 .
94.
Bach
G.
, ibid ., 1959 , 64 , 265 .
95.
Drapal
S.
Horalek
V.
, Acta Tech. Prague , 1959 , 6 ,474 .
96.
Papadakis
E. P.
, J. Acoust. Soc. Amer ., 1961 , 33 , 1616 .
97.
Bach
G.
, Z. wiss. Mikroskopie , 1963 ,65 , 285 .
98.
Papadakis
E. P.
, J. Appl. Physics , 1964 , 35 , 1586 .
99.
Bach
G.
, Metrika , 1965 , 9 , 228 .
100.
Oel
H. J.
, Ber. Deur. Keram. Ges ., 1966 , 43 , 624 .
101.
Goldsmith
P. L.
, Brit. J. AppL Phys ., 1967 , 18 , 813 .
102.
Bach
G.
, Ref. 17 , p. 174 .
103.
Bach
G.
, "Quantitative Methods in Morphology" (edited by
Weibel
E. .2
Elias
H.
), p. 23 . 1967 : Berlin , (Springer ).
104.
Hensler
H. J.
, J. Inst. Metals , 1968 , 96 , 190 .
105.
Crompton
J. M. G.
Waghorne
R. M.
Brook
G B.
, Brit. J. APPL. Phys ., 1966 , 17 , 1301 .
106.
Fryxell
E.
A
B. A.
, J. Amer. Ceram. Soc ., 1964 , 47 , 283 .
107.
Nicholson
N. L.
R
H. R.
, Ref. 17 , p. 191 .
108.
DeHoff
R. T.
, Trans. Met. Soc. AIME , 1962 , 224 , 474 .
109.
Krumbein
W. C.
J
F. J.
, "Manual of Sedimentary Petrography" . 1938 : New York (D. Appleton-Century Co. )
110.
Krumbein
W. C.
, J. Sedim. Petrol ., 1936 , 6 , 35 .
111.
Krumbein
W. C.
, J. Geology , 1950 , 58 , 160 .
112.
Rosenfeld
M. A.
Jacobsen
L.
Ferm
J C.
, ibid ., 1953 , 61 , 114 .
113.
Kendall
M. G.
A
P. A.
. Moran, "Geometrical Proba-bility" , p. 86 . 1963 : London (Griffin)
114.
Bockstiegel
G.
(Höganäs AB, Sweden), private communication , 1966 .
115.
Rostoker
W.
R
J. R.
, "Interpretation of Metallic Structures" , p. 206 . 1965 : New York and London (Aca-demic Press ).
116.
Johnson
A. W.
, Metal Progress , 1946 , 49 , 87 .
117.
Willis
T. F.
, Proc. Highway Research Board , 1949 , 29 , 184 .
118.
Spektor
A. G.
, Zavod. Lab ., 1950 , 16 , 173 .
119.
Lord
G. W.
F
T. F.
, ASTM Bull ., 1951 , ((177 ), 56 .
120.
Miinzer
H.
, Mitteilungsbl. mathem. Statistik , 1953 , [H] , 213 , 167 .
121.
Cahn
J. W.
L
R. L.
, Trans. Amer. Inst. Min. Met. Eng ., 1956 , 206 , 610 .
122.
Brophy
J. H.
J
M. J.
, Trans. Amer. Soc. Metals , 1961 , 54 , 65 .
123.
Bockstiegel
G.
, "Modern Developments in Powder Metal-lurgy" (edited by
Hausner
H. H.
), Vol. 1 , p. 155 . 1966 : New York (Plenum Press ).
124.
Bockstiegel
G.
, Ref. 17 , p. 193 .
125.
Bockstiegel
G.
, Z. Metallkunde , 1966 , 57 , 697 .
126.
Exner
H. E.
, Schweissen u. Schneiden , 1967 , 19 , 493 .
127.
Stjernberg
K. G.
, Metallography , 1969 , 2 , 161 .
128.
Exner
H. E.
, J. Inst. Metals , 1969 , 97 , 191 .
129.
Fullman
R. L.
, Trans. Amer. Inst. Min. Met. Eng ., 1953 , 197 , 447 .
130.
Cahn
J. W.
Nutting
J.
, Trans. Met. Soc. AIME , 1959 , 215 , 526 .
131.
Mack
C.
, Proc. Camb. Phil. Soc ., 50, 588 ; 1956 , 52,246 .
132.
James
P. F.
H
F. H.
, J. Nuclear Mat ., 1969 , 29 , 203 .
133.
Smith
A. F.
, Acta Met ., 1967 , 15 , 1967 .
134.
Bachmann
L.
M
B. M.
, "Proceedings of the European Regional Conference on Electron Microscopy" (edited by
Houwink
A. L.
Spit
B. J.
), p. 157 . 1960 : Delft (De Nederl. Veren. Electronenmikroscopie ).
135.
Siems
R.
Delavignette
P.
Amelinckx
S.
, Physica Status Solidi , 1962 , 2 , 421 .
136.
Exner
H. E.
F
H. F.
, Z. Metallkunde , 1966 , 57 , 187 .
137.
Bach
G.
, Z. angew. Math. Physik , 15, 205 ; 1965 , 16,224 .
138.
Hennig
H.
Elias
H.
, Z. wiss. Mikroskopie , 1963 , 65 , 133 .
139.
Fullman
R. L.
, Trans. Amer. Inst. Min. Met. Eng ., 1953 , 197 , 1267 .
140.
Hull
F. C.
J
W. J.
, ibid ., 1953 , 197 , 565 .
141.
DeHoff
R. T.
Bousquet
P.
, J. Microscopy , 1970 , 92 , 119 .
142.
Ardell
A. J.
B
R. B.
, Ada Met ., 1966 , 14 , 1295 .
143.
Okada
A.
, Rep. Chiba Inst. Technol ., 1968 , (11) , 14 ; Tetsu-to-Hagane , 1967 , 53 , 4 .
144.
Horikawa
E.
, Tetsu-to-Hagane , 1954 , 40 , 991 .
145.
Desch
C. H.
, J. Inst. Metals , 1919 , 2 , 241 .
146.
Williams
W. M.
S
C. S.
, Trans. Amer. Inst. Min. Met. Eng ., 1952 , 199 , 755 .
147.
Aaron
H. B.
Smith
R. D.
Underwood
E E.
, "Proceed-ings of the First International Congress on Stereology" paper No. 16 . 1963 : Vienna (Congressprint).
148.
Underwood,
E. E.
J. Microscopy , 1969 , 89 , (2 ), 161 .
149.
Scheil
E.
Wurst
H.
, Z. Metallkunde , 1936 , 28 , 340 .
150.
Exner
H. E.
Fischmeister
H.
, Arch. Eisenhiittenwesen , 1966 , 37 , 417 .
151.
Woodhead
J. J.
, Metallography , 1968 , 1 , 35 .
152.
Glagolev,
A. A.
Trans. Inst. Econ. Min., Moscow , 1933 , 59 , 1 .
153.
Hilliard
J. E.
W
J. W.
, Trans. Met. Soc AIME , 1961 , 221 , 334 .
154.
DeHoff
R. T.
, ibid ., 1961 , 221 , 975 .
155.
Smith
C. S.
Guttman
L.
, Trans. Amer. Inst. Min. Met. Eng ., 1953 , 197 , 81 .
156.
Bach
G.
, Z. Metallkunde , 1965 , 56 , 376 .
157.
Wicksell
S. D.
, Biometrzka , 1926 , 18 , 151 .
158.
Serra
J.
, "Introduction a la morphologie mathematique" . 1969 : Paris (Ecole Nat. Supérieure des Mines ).
159.
Bach
G.
, Z. wiss. Mikroskopie , 1963 , 65 , 285 .
160.
Hilliard
J. E.
, Ref. 17 , p. 195 .
161.
Guttman
I.
S
S. S.
, "Introductory Engineering Statistics" , p. 197 . 1965 : New York and London (John Wiley ).
162.
Exner
H. E.
L
H. L.
, Metallography , 1971 , 4 , 325 .
163.
Itoh
H.
, ibid ., 1970 , 3 , 407 .