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清水 順也
山﨑 政義
MITS 2011MIT
S 2
01
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2011年12月1日(木)
独立行政法人 物質・材料研究機構 材料情報ステーションNational Institute for Materials Science (NIMS) Materials Information Station
秋葉原コンベンションホールA東京都千代田区外神田1-18-13 秋葉原ダイビル2F
MITS 2011 Materials Information & Technology Solutions MITS 2011 Materials Information & Technology Solutions MITS 2011 Materials Information & Technology SolutionsMITS 2011 Materials Information & Technology Solutions MITS 2011 Materials Information & Technology Solutions MITS 2011 Materials Information & Technology Solutions
MITS 2011 Materials Information & Technology Solutions MITS 2011 Materials Information & Technology Solutions MITS 2011 Materials Information & Technology SolutionsMITS 2011 Materials Information & Technology Solutions MITS 2011 Materials Information & Technology Solutions MITS 2011 Materials Information & Technology Solutions
MITS 2011 Materials Information & Technology Solutions MITS 2011 Materials Information & Technology Solutions MITS 2011 Materials Information & Technology SolutionsMITS 2011 Materials Information & Technology Solutions MITS 2011 Materials Information & Technology Solutions MITS 2011 Materials Information & Technology Solutions
MITS 2011 Materials Information & Technology Solutions MITS 2011 Materials Information & Technology Solutions MITS 2011 Materials Information & Technology SolutionsMITS 2011 Materials Information & Technology Solutions MITS 2011 Materials Information & Technology Solutions MITS 2011 Materials Information & Technology Solutions
2011年12月
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1 Journal of Polymer Science 27452 Macromolecules 24553 Journal of Applied Polymer Science 22304 Polymer 18935 Makromolekulare Chemie 6206 Polymer Preprints (American Chemical Society, Division of Polymer Chemistry) 6097 Synthetic Metals 6028 European Polymer Journal 5419 Polymer Engineering and Science 42110 Annual Technical Conference - Society of Plastics Engineers 41811 Journal of Macromolecular Science 37012 Polymer Journal 32213 Journal of Chemical Physics 31914 Journal of Physical Chemistry 30915 Macromolecular Chemistry and Physics 29016 Langmuir 28117 Polymer International 27518 Journal of the American Chemical Society 26919 Journal of Applied Physics 25120 Proceedings of SPIE 251
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Historical Background, Attainment and Future Prospects of JSMS Databases on Fatigue Strength of Metallic Materials
II:Domestic Publication and Worldwide Prospects of Databooks and Databases on Fatigue Strength of Metallic Materials
by
Akira UENO , Tatsuo SAKAI , Atsushi SUGETA , Izuru NISHIKAWA
and Yoichi TAMIYA Key words: Material databook, Material database, Fatigue strength, Metallic materials, Worldwide prospects, JSMS
1 1) ICT
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Received * 525-8577 1-1-1, College of Science and Engineering, Ritsumeikan University,
1-1-1 Nojihigashi, Kusatsu, Shiga 525-8577 ** 525-8577 1-1-1, Research Organization of Science and Engineering,
Ritsumeikan University, 1-1-1 Nojihigashi, Kusatsu, Shiga 525-8577 *** 739-0046 1-4-1, Graduate School of Engineering, Hiroshima University,
1-4-1 Kagamiyama, Higashi-Hiroshima, Hiroshima 739-0046 **** 535-0002 5-16-1, Faculty of Engineering, Osaka Institute of Technology,
5-16-1, Ohmiya, Asahi-ku, Osaka 535-0002. ***** 661-8661 8-1-1, Mitsubishi Electric Corporation,
Advanced Technology R&D Center, 8-1-1, Tsukaguchi-Honmachi, Amagasaki, Hyogo 661-8661
JIS88
2317S-N
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CODATA [The Committee on Data for Science and Technology] VAMAS [Versailles Projects on Advanced Materials and Standards]
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1990 47760
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10
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:ISO[International Organization for Standardization]
SI
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”Databook on Fatigue Strength of Metallic Materials” Elsevier
Elsevier
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Royalty300
Elsevier
1996 Elsevier
”Databook on Fatigue Strength of Metallic Materials”6)
1992
Vol. 1 Vol. 2
Vol. 3 S-N
6),14)
Vol. 3
Chairman: K. Shiozawa (Toyama University) Vice-Chaiman: T. Sakai (Ritsumeikan University) Committee Members: T. Horikawa (Ryukoku University) T. Hoshide (Kyoto University) M. Jono (OsakaUniversity) M. Nakajima (Toyota College of Technology) I. Nishikawa (Osaka University) T. Ochiai (Mitsubishi Research Institute, Inc.) K. Okada (Takamatsu National College of Technology) A. Sugeta (Osaka University) H. Tokuno (Kobe University) T. Yoshida (Mitsui Engineering & Shipbuilding Co., Ltd.) S. Yoshioka (Mitsubishi Electric Corporation)
Vol. 3S-N
S-NS-N
S-NS-N
50
S-NS-N
JSMS-SD-6-02 7) 20022007 "Standard Evaluation Method of Fatigue Reliability for Metallic Materials Standard Regression Method of S-N Curves ", JSMS-SD-11-07 8)
S-N
1982
1992
1982 1992 SI
1996ITC
Floppy Disk (FD) 4mm DAT Cartridge 1/4inch Cartridge
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1) T. Sakai, A. Sugeta, I. Nishikawa, T. Shuto and A.
Ueno, “Historical Background, Attainment and Future Prospects of JSMS Databases on Fatigue Strength of Metallic Materials: Development and Diffusion of ICT Technology and Origin of Electronic Databases for Materials Property in Japan”, J. of Mat. Sci., Japan. (submitted)
2) T. Tanaka, et al., “Databook on Fatigue Strength of Metallic Materials”, Vol.1-Vol.3, (1982), JSMS.
3) T. Tanaka, et al., “Database on Fatigue Strength of Metallic Materials”, (1982), JSMS.
4) M. Jono, et al., “Databook on Fatigue Crack Growth Rates of Metallic Materials”, Vol.1&Vol.2, (1983), JSMS.
5) M. Jono, et al., “Database on Fatigue Crack Growth Rates of Metallic Materials”, (1983), JSMS
6) K. Shiozawa et al., “Databook on Fatigue Strength of Metallic Materials”, Vol.1-Vol.3, (1996), Elsevier and JSMS.
7) T. Sakai et al., “Standard Evaluation Method of Fatigue Reliability for Metallic Materials:Standard Regression Method of S-N Curves”, JSMS-SD-6-02, (2002), JSMS.
8) T. Sakai et al., “Standard Evaluation Method of Fatigue Reliability for Metallic Materials: Standard Regression Method of S-N Curves”, JSMS-SD-11-07, (2007), JSMS.
9) T. Tanaka and T. Sakai, "Data-Base on Fatigue Strength of Metallic Materials and Some Statistical Distribution Characteristics of Fatigue Life and Fatigue Strength", Structural Safety and Reliability, Vol.3, JSMS, pp.702-707, (1985).
10) T. Sakai, H. Yasui and T. Tanaka, “Statistical Fatigue Properties of Carbon Steels for Machine Structural Use Based on JSMS Database on Fatigue Strength of Metallic Materials”, J. of Mat. Sci., Japan, Vol.36, pp.915-921 (1987).
11) Edited by C. P. Sturrock and E. F. Begley, “Computerization and Networking of Materials Databases”, 4th Volume, STP 1257, ASTM, (1995).
12) M. Jono, et al., “Databook on Fatigue Strength of Metallic Materials”, Vol.4 & Vol.5, (1992), JSMS.
13) M. Jono, et al., “Database on Fatigue Strength of Metallic Materials”, (1992), JSMS.
14) T. Sakai, “Fatigue of Metallic Materials –Fundamentals and Mechanisms “, Shuwa System Co., Ltd., Tokyo, p.144-148, (2011)
15) http://www.w3.org/TR/html401/ 16) http://www.w3.org/XML/ 17) http://relaxng.org/ 18) http://www.matml.org/ 19)http://www.nims.go.jp/mat_info/AMM_DB/AMM-DB.htm
Eco-MCPS, a Web-database for Ecomaterials – For Analysing Environmental
Consciousness in Japan on Materials and Products
Web Eco-MCPS
Riko. Ozao Sony Institute of Higher Education, Atsugi, Kanagawa 243-8501, Japan
e-mail: [email protected]
ABSTRACTEco-MCPS database is a web-based database system that includes environment-friendly materials, components, products, and services. The access log of Eco-MCPS and the text data compiled in the Eco-MCPS were subjected to data mining. Word-frequency analysis and dependency parsing analysis were applied to the data to obtain the frequently used terms and their situations of use. The results showed that eco-products’ environmental performances are realized by the use of environment-friendly components or materials. The page views, which represent the visitors’ interest, were related with the frequently used term in the comments of Eco-MCPS to show the social consciousness on environment-friendly products. By further analyzing the access log, it was found that the word search rank followed the Zipf’s Law.
Key words: eco-material, eco-product, web database, data-mining, text-mining
KeywordSearch
Environmental Categories
ProductCategories
KeyCategories
Rankingof Most SearchedItems Search
Rankingof Most SearchedKeywordsSearch
1. INTRODCTION
"Eco-M C P S" database (simply Eco-MCPS) is
a web-based database system developed by the
database subcommittee of Ecomaterial Forum in
2006 [1], which includes fact data provided by the
manufacturers and environmental category
descriptions on ecological (environment-conscious)
items that fall in one of the groups of materials (M),
components (C), products (P), and services (S).
Data in Eco-MCPS were collected by the inquiry
survey to companies. New data for about 100 items
are added each year by the Information and
Publishing committee of the Ecomaterial Forum,
which searches and picks up data from news
sources such as newspapers, web magazines, and
the like. The data which appear in Eco-MCPS are
checked by the committee members to assure the
quality of the data.
Each data can be found with “Keyword Search”
and three different type of categories: product
categories, key categories, and environment
categories (Figure 1). Each category has a page
which includes a list of product items. Most items
appear in multiple categories (even in the same kind
of categories). Therefore, users can search each
item from a variety of performances. Eco-MCPS is
not only a simple compilation of facts, but also an
interactive site which changes according to the
access made by the Web site visitors. For example,
there are rankings of users’ action on the top page
as shown in Figure 1. Every visitor can see the
trend in the environmental interest items and
keywords from the top page.
It has been reported [2] that the general interest
to the environmental issues can be effectively
studied by analyzing the access log of Eco-MCPS
using a data mining technique. Since environmental
problems are not only a matter of technology but
are also related to human behavior or consciousness,
it is extremely important to involve such
methodologies of social science in analyzing the
general trends of eco-materials. Thus, by applying
text mining [3] to the text data compiled in
Eco-MCPS as product “profile (short sentence
describing the product)” and “comments (longer
description on the product)”, it was found that the
manufacturers and set-up companies use the term
“environment-friendly” to stress their product
superiority in energy saving or resource saving [4].
The present study aims to analyze the social
consciousness on environment-friendly products by
text-mining of the facts stored as data in the
Eco-MCPS. Word-frequency analysis and
dependency parsing analysis were applied to the
data to obtain the frequently used terms and their
situations of use.
2. METHOD
2.1. Eco-MCPS Web database
The database is freely accessible by the internet
at URL http://eco-mcpsdb.sntt.or.jp/index.php.
Referring to Fig.1, the products can be accessed
either from the product categories (shown with
Number 1 in Fig. 1), the key categories (Number 2),
or the environmental categories (Number 3) (from
the viewpoint of environmental impact reduction,
the environmental performance required for
resolving the problems, or from the life cycle stages
of interest). The environmental impacts considered
were: (A-1) climate change, (A-2) air pollution,
(A-3) hazardous substances, (A-4) wastes, and
(A-5) resource consumption. The environmental
performance was categorized by (B-1)
easy-to-recycle, (B-2) longer life, (B-3) resource
saving, (B-4) higher performance, (B-5) energy
saving, (B-6) environment cleaning, (B-7) use of
recycled materials. Concerning the life cycle of the
product, six stages as follows were set: (C-1)
extraction, (C-2) material and parts preparation,
(C-3) product design, (C-4) production, (C-5)
product use/maintenance/repair, and (C-6) waste.
In the Key categories, some products are related
to each other by providing “keys”; for instance, if
cell phone is categorized as OA/IT equipment, and
if the eco-material used for the casing is a
bio-polymer usable for other components such as
computers, this product is linked to “housing”.
Figure 2 shows the product page of the
Eco-MCPS. Each product item has two Japanese
text data: the profile and the comment (see Fig. 2).
The profile text is a short phrase to explain the
item’s feature. The comment text is a detailed
explanation of the item.
2.2. Analysis of item feature
Text Mining [3] was applied to the text data;
more specifically, the text data for the compiled up
to November, 2008, were imported in Text Mining
Studio (Mathematical Systems, Inc.), which is a
package program for text-mining, and were
subjected to word-frequency analysis. In the
analysis, the original text data were re-written
depending on the parse by leaving spaces among
the words, and the words were subjected to
dependency parsing. In this manner, frequently
used words were searched and checked to see at
which situation they were used.
2.3. Access log
The Eco-MCPS system logs every user access
under anonymity. The logged data are following:
(1) log id, (2) user id, (3) view page, (4) date, (5) IP,
(6) domain.
The access log data provides the information
how many times a particular page was viewed in a
certain period of time. That is, by keeping record of
the page views, the so-called access ranking can be
obtained.
3. RESULTS AND DISSCUTION
The following three results were obtained by
applying mining analyses to the data compiled in
Eco-MCPS and to access log data.
3.1. Frequency analysis and dependency parse
analysis of data items
Figure 3 shows the results of word frequency
analysis (left) and the dependency parse analysis
(right).
The results show that the rather abstract word
“consider or conscious” stands out in the profile
text data, and that the “object to be considered” is
energy-saving. This is in agreement with the
conclusion reported last year [4].
3.2. Word frequency vs page views
Figure 4 shows the page views between January
and September, 2008, which represents the visitors’
interest in this period, with the frequently used term
in the comments of Eco-MCPS. The dashed line
shows the approximate best fit of the plots for
categories (B-1) easy-to-recycle, (B-2) longer life,
(B-3) resource saving, (B-4) higher performance,
and (A-1) global warming and (A-3) toxic
chemicals.
It is natural that the page views increase with the
number of items stored in the database. However,
the figure reads that, unexpectedly, resource- and
energy- saving products are less viewed by the
database visitors. This may suggest that there is
some discrepancy concerning the environmental
interest between the users and the manufacturers;
i.e., companies and manufacturers focus on energy
and resource-saving products, whereas general
interest is more related to global warming and toxic
chemicals.
3.3. Zipf’s Law and searched words
Zipf's law [5] states that while only a few words
are used very often, many or most are used rarely.
Generally, the law is a power-law function
expressed by:
( ) -1 (1)
where frequency of occurrence of some event ( ),
as a function of the rank ( ) when the rank is
determined by the above frequency of occurrence.
As is shown in Fig.5, the searched words rank and
frequency plots nicely fit to this phenomenological
function (with the exponent being -0.998 -1).
Although there is no established explanation for this
phenomenon, this may suggest stable distribution of
searched words. The rank vs word frequency data
shown in Fig. 3 (top 7 ranked words and their
frequencies are given in Table 1 for reference) also
fits a power law function with an exponent of -1.4.
Hence, in the profile, the words seem to be
unevenly distributed.
(CANON INC) RoHS
(Toshiba Co.Ltd.)
4. CONCLUSION
By analyzing text data and access log of
Web-based database Eco-MCPS, it is suggested
that companies and manufacturers focus on energy
and resource-saving, whereas general interest is
more related to global warming and toxic
chemicals.
It is also suggested that Eco-MCPS is not only a
simple compilation of fact data, but it sensitively
reflects the social movement, i.e., with the
advancement in materials and technology, as well
as the general consciousness in environmental
issues.
w
ACKNOWLEDGMENTS
This work was partly supported by Shohoku
College Grant (2009).
The current members of Information and Publishing
committee of the Ecomaterial Forum are:
Dr. Hideki Kakisaawa(NIMS)
Dr. Xu Yibin(NIMS)
Dr. Taisuke Utsumi (Shohoku College)
Dr. Kazuyo Matsubae (Tohoku Univ.)
REFERENCES
[1] R. Ozao, M. Iji, T. Furuyama, K. Yamada, C.
Yoshida, Y. Nishimoto, Y. Shimura, K. Halada,
“Report on Ecomaterials for Sustainable Society
and Feasibility Study on the Development of
Eco-materials Database”, Report for The Watanabe
Memorial Foundation for the Advancement of
Technology (2006).
[2] R. Ozao, T. Sawaguchi, H. Ishida, M. Iji, T.
Furuyama, Y. Shinohara, K. Yamada, K. Halada:
Eco-MCPS: a Newly Developed Web-Based
Database for Eco-Materials in Japan,
, 48 (2007) pp.3043-49.
[3] R. Feldman and I Dogan: Knowledge Discovery
in Textural Datatbases (KDT), 1st
(KDD-95) (1995) pp.
112-117;
P. Cabena, P. Hadjinian, R. Stadler, J. Verhees, A.
Zanasi, “Discovering Data Mining, from Concept to
Implementation”, Prentice Hall, New Jersey (1997)
[4] H. Ishida, R. Ozao, T. Utsumi, Y. Shinohara,
K. Halada, Y. Nishimoto: Trends in Eco-materials
and Products as Observed through Studies on a
Web Database, Eco-MCPS,
, 34 (2009), pp.249-252.
[5] G. K. Zipf, Selected Studies of the Principle
of Relative Frequency in Language , Harvard
University Press (1932); T. Musha, “World of
Fluctuation”, Kodansha (1980) (in Japanese).
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0
500
1000
1500
2000
2500
ZEM
TAE
MAS
390
JPEQ
E6R
JIC
AQ
INO
MA
FR
MLY
AQJC
OM
AHJA
LCEU
CC
CTD
6A
RE
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JIM
EAP
TAIM
AFTM
SAAB
NIK
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ABN
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CODEN
Top 30 Journals (Constitution)
11
Tem
pera
ture
, °C
400
500
600
700
800
900
1000
1100
0 10 20 30 40 50 60 70 80 90 100
Ag CeAtomic Percent Cerium
Weight Percent Cerium1000 90 10 20 30 40 50 60 70 80
Ag
Ce3
Ag
Ce2
AgC
e
865°C 855°C
800°C
990°C
805°C
530°C
L
43Vog (wt.%)58Han (at.%)
14
Hansen
read (x,T) convert x draw
13
Tem
pera
ture
, °C
0 10 20 30 40 50 60 70 80 90 100
Eu Ga
1200
1000
800
600
400
200
0
Atomic Percent Gallium
Weight Percent Gallium1000 90 10 20 30 40 50 60 70 80
822°C
20495°C
607°C
660°C
790°C
1030°C 1015°C970°C
29.7741°C
L
(Eu)
EuG
a5
3
EuG
a
EuG
a2
3
/Eu
Ga 2
EuG
a2
5
EuG
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(Ga)
78Yat (at.%)90Mas (at.%)
16
Massalski handbookdigitize curve fit convert
15
Ag
Au
Cu
Au
AgCu
Ag-Au-Cu, Z. Metallkd., 18, 143-148 (1926)
wt.% at.%
18
convert trace
17
Fe-Zr, Scanned original
R. Vogel and W. Tonn, Arch. Eisenhuttenw., 5, 387-389 (1931/32)
wt.%
U-O system, J. Nucl. Mater., 137, 144-153 (1986)
0 2.0
O/U
0 66.7
at.% O
19
trace
Converted to at.%
at.%
0 10 20 30 40 50 60 70 80 90 100
Atomic Percent B
Tem
pera
ture
A B
A
BC
D
E
F
G
H IJ
K
L M
N
O
P
Q
R
ST
X
Y
Z
Liquid
1
2
24
0 10 20 30 40 50 60 70 80 90 100
Tem
pera
ture
, °C
Fe ZrAtomic Percent Zirconium
Weight Percent Zirconium
2000
1800
1600
1400
1200
1000
800
600
1000 90 10 20 30 40 50 60 70 80
Before adjustment
Pauling File - Multinaries Edition
number of chem.elements structure property constitution S / P / C biblioraphy
232
45678910
total
2'54516'33716'541 8'677 3'003 918 294
173237
48'725
2'1106'6595'0302'178
772264
4152
17'061
2'3365'095
-------
7'431
3'10618'76818'124
9'7123'4461'084
333177239
54'989
3'56320'93422'23613'458
4'8711'183
385185163
66'978
4572'1664'1123'7461'425
9953
8-
12'065
-
26
0 10 20 30 40 50 60 70 80 90 100
Atomic Percent B
Tem
pera
ture
A B
a
b
c
e
d
f
g
h
i
j
k
l
m
n
o
p q
r
s
t
G
L
1
2
AB
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1
2
3
4
25
1.
1958 M. Hansen and K. Anderko, “Constitution of Binary Alloys” McGraw-Hill,
New York. R.P. Elliott (1965), F.A. Shunk (1969) 1976 W.G. Moffat, “Handbook of Binary Phase Diagrams, General Electric Co.,
Schenectady, NY 1990 T.B. Massalski, H. Okamoto, P.R. Subramanian, and L. Kacprzak, Binary Alloy Phase
Diagrams, 2nd ed., ASM International, Materials Park, OH, 3,542 pp 1992 H. Baker and H. Okamoto, ASM Handbook, Vol. 3, Alloy Phase Diagrams, ASM
International, 500 pp 2001 365pp 2001 P. Villars, K. Cenzual, F. Hulliger, A. Prince, H. Okamoto, J. Daams, and K. Osaki,
Pauling File, Inorganic Materials Design System, Binary Edition, Crystal Impact, Germany
(CD) 2003 B. Predel, Phase Equilibria of Binary Alloys, Springer (CD) 2006 ASM Alloy Phase Diagrams Center, P. Villars, H. Okamoto and K. Cenzual;
http://www1.asminternational.org/AsmEnterprise/APD, ASM International (on-line) 2010 H. Okamoto, “Desk Handbook: Phase Diagrams for Binary Alloys, 2nd
Edition,” ASM International, 900pp 3 1995 P. Villars, A. Prince, and H. Okamoto, Handbook of
Ternary Alloy Phase Diagrams, ASM International, Materials Park, OH, 13,808 pp
6 8
2 1
MPDS (Materials Phases Data System) Dr. VillarsPauling File
1950 Journal
101978 ASM International American Society for Metals
National Institute of Standard and Technology (NIST, National Bureau of Standards) Data Program for Alloy Phase Diagrams (APD program)
400 NIST600 1000
APDIC (Alloy Phase Diagram International Commission)APD Program Bulletin of Alloy Phase
Diagrams 1986 T.B. Massalski, L. Bennet, H. Baker, Binary Alloy Phase Diagrams
1982 1990 Binary Alloy Phase
Diagrams Chemical Abstract2000 Desk Handbook: Phase Diagrams for Binary Alloys 2010
Pauling File Science Direct
Journal 11 Pauling File
2
Binary Alloy Phase Diagrams (Massalski ) 1915 Binary Alloy Phase Diagrams (Massalski 2 ) 2159 Desk Handbook: Phase Diagrams for Binary Alloys 2335 Desk Handbook: Phase Diagrams for Binary Alloys 2 2421
1 2
2 2
12
1
( 13,14) 2
NIST % ( 15,16)
33
( 17,18) 2 3. 3
3 %2 3
% 2
Mole% H2O 1/3
1 ( 19)
1/T, logX
20 23
4 H. Okamoto and T.B. Massalski, “Thermodynamically Improbable Phase Diagrams,” J.
Phase Equilibria, 12(2), 148-168 (1991) H. Okamoto, “Reevaluation of Thermodynamic Models for Phase Diagram Evaluation,”
J. Phase Equilibria, 12(6), 623-643 (1991) H. Okamoto and T.B. Massalski, “Guidelines for Binary Phase Diagram Assessment,” J.
Phase Equilibria, 14(3), 316-335 (1993) H. Okamoto and T.B. Massalski, “Binary Alloy Phase Diagrams Requiring Further
Study,” J. Phase Equilibria, 15(5), 500-521 (1994)
Desk Handbook: Phase Diagrams for Binary Alloys, 2nd Edition24 25
24 phase rule
A. The liquidus and solidus must meet at the melting point of the pure element. B. Two liquidus curves must meet at one composition at a eutectic temperature. C. A tie line must terminate at a phase boundary. D. Two solvus boundaries (or two liquidus or two solidus, or a solidus and a solvus) of
the same phase must intersect at one composition at an invariant temperature. E. A phase boundary must extrapolate into a two-phase field after crossing an
invariant point. F. A two-phase field cannot be extended to a pure element end. G. Two boundaries of must not be continuous at the invariant temperature. They
must cross one another. H. An invariant temperature line should involve equilibrium among three phases. I. There should be a two-phase field between two single-phase fields. J. When two phase boundaries touch at a point, they should touch at an extremity of
temperature. K. A touching liquidus and solidus (or any two touching boundaries) must have a
horizontal common tangent at the congruent point. In this case, the solidus at the melting point appears to be discontinuous.
L. A local minimum point in the lower part of a single-phase field cannot be drawn without an additional boundary in contact with it (minimum congruent point or monotectic reaction in this case).
M. A local maximum point in the lower part of a single-phase field cannot be drawn without a monotectic, monotectoid, syntectic, and syntectoid reaction occurring at a lower temperature. Alternatively, a solidus curve must be drawn to touch the liquidus at point M. (If the maximum is not local, as in a miscibility gap, this is not a phase rule violation.)
N. The temperature of an invariant reaction must be constant. (The reaction line must be horizontal.)
O. A phase boundary cannot terminate within a phase field (except the case when the boundary is unknown beyond this point).
P. The liquidus should not have a discontinuous sharp peak at the melting point of a compound. (See exceptions, below.)
Q. The compositions of all three phases at an invariant reaction must be different. R. Temperatures of liquidus and solidus (or any two boundaries) must either increase
or decrease together from one point on the pure element line as the content of a second element increases.
S. A four-phase equilibrium is not allowed in a binary system. T. Two separate phase boundaries that create a two-phase field between two phases in
equilibrium should not cross one another.
25 phase rule a) G + L two-phase field is too narrow. The opening angle of G + L at 0 at.% must be
much larger than that of L + because the heat of vaporization of an element is generally much greater than the heat of fusion.
b) Extrapolation of the liquidus should not cross the 0 at.% line. Otherwise, problem F of Fig. 1 occurs.
c) The liquidus of at point c is too flat in comparison with the liquidus of at pint e. Problems c, d, and e are related. Because entropy of fusion of elements and compounds cannot differ much (Charles’ law), curvatures of liquidus curves for compounds in a binary system must be similar. A phase with a shaper liquidus tends to decompose into two neighboring phases at low temperatures.
d) A compound with a flat liquidus is stable and will not decompose at low temperatures.
e) Liquidus at point e is too sharp in comparison with the liquidus at point c. f) Extrapolation of the liquidus of must have a peak at the composition of .
Otherwise problem P of Fig. 24 occurs. g) Change of liquidus slope associated with an allotropic transformation must be
small. h) Two compounds having similar compositions cannot be stable over a wide
temperature range. i) A phase field of a compound cannot extend over a neighboring phase. Problem T of
Fig. 24 occurs. j) The congruent melting point of AmBn compound is too far away from its
stoichiometric composition. k) The liquidus is too asymmetric. According to our rough criterion, a liquidus is
already too asymmetric if the liquidus width ratio to the left and right of a compound exceeds 2:3.
l) The transformation temperature of to 2 should be higher than the melting point of . Otherwise, the 2 phase is stable above point j.
m) Extrapolation of two boundaries of L + 2 should not cross. Problem T of Fig. 24. n) A two phase field must be narrower at higher temperatures o) The slope is too flat to have a maximum point at the composition of . p) The liquid miscibility gap is too close to the edge of a phase diagram. According to
our rough criterion, the peak composition of a liquid miscibility gap should fall in the range 25 to 75 at.%.
q) The liquidus slope is too steep. The initial slope of a liquidus is, as a rule, determined by the van’t Hoff relationship. If no solubility can be assumed for the solid phase, extrapolation of the initial liquidus should go through the horizontal axis at 0 K near approximately 110 at.%.
r) Extrapolation of two boundaries of L + 3 should cross at the 100 at.% line, not at some composition exceeding 100 at.%. Problem A of Fig. 24.
s) Two phase boundaries should have different initial slopes. The entropy of an allotropic transformation is not zero.
t) The slopes of two phase boundaries are too far apart. The entropy of an allotropic transformation is generally small.
5.
9 300
262 3 2500 Fe
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