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MATERIALS TRANSACTIONS
Vol. 47 (2006), No. 12

MATERIALS TRANSACTIONS Vol. 47 (2006), No. 12

Free Solidification of Undercooled Eutectics

Mingjun Li, Kazuhiko Kuribayashi

pp. 2889-2897

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Free Solidification of Undercooled Eutectics

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DOI:10.2320/matertrans.47.2889

Abstract

The traditional eutectic solidification theories always stress the role of eutectic growth and morphology selection. However, when a eutectic alloy solidifies freely from an undercooled state, the first step commences from nucleation and then follows eutectic growth. This paper reviews the free solidification behavior of various undercooled eutectic alloys from the viewpoints of nucleation and growth. It is realized that an independent eutectic colony should be the basic unit when discussing eutectic solidification rather than a bulk sample, which urges us to re-examine the previous discussions and conclusions that were based on bulk solidification in which the role of nucleation was frequently ignored. Regarding to the eutectic growth after nucleation, particular emphasis is devoted to shedding light upon the physical mechanisms of the anomalous eutectic formation when the eutectic is undercooled beyond a certain critical undercooling. The interface attachment kinetics of terminal phases in a eutectic reaction is of great importance in yielding decoupled growth between a mobile interface and a sluggish interface. Further growth behavior after decoupled growth occurs is investigated when the effect of crystallization heat on solidification is considered. Future work is briefly directed to improve current understanding on the free solidification from undercooled states.
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Dielectric Properties of Poly- and Single-Crystalline BaTi₂O₅

Rong Tu, Takashi Goto

pp. 2898-2903

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Dielectric Properties of Poly- and Single-Crystalline BaTi₂O₅

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DOI:10.2320/matertrans.47.2898

Abstract

Non-oriented and (010) oriented poly-crystalline BaTi₂O₅ (BT₂) was prepared by hot-pressing and arc-melting, respectively. The dielectric properties of poly-crystalline BT₂ were compared with those of single-crystalline BT₂ prepared by a floating zone method. The maximum permittivity of (010) oriented poly-crystalline BT₂ was 2000 at 720 K, whereas that of single-crystalline BT₂ was 6000 at the Curie temperature, T_c (750 K). The permittivity of non-oriented poly-crystalline BT₂ was 30 to 300, having a small peak at 720 K. The tanδ of all specimens was 0.01 to 0.2 below T_c and significantly increased with increasing temperature above T_c. The electrical conductivity of (010) oriented poly- and single-crystalline BT₂ had almost same values, which were one order higher than that of non-oriented poly-crystalline BT₂ and (001) oriented single-crystalline BT₂.
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Effects of Atomic Size for Voronoi Tessellation Technique on Binary and Ternary Systems of Metallic Glasses

Junyoung Park, Yoji Shibutani

pp. 2904-2909

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Effects of Atomic Size for Voronoi Tessellation Technique on Binary and Ternary Systems of Metallic Glasses

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DOI:10.2320/matertrans.47.2904

Abstract

A number of researchers are still employing the ordinary Voronoi tessellation technique to explore the atomic structures of metallic glasses. However, the ordinary Voronoi tessellation technique does not take into consideration the size of each atom, and this essentially leads to differences in the atomic volume and structure, such as the number of atoms with FCC or icosahedral structure. An alternative way, the radical plane technique, is applied to binary and ternary systems: such as Zr, ZrCu, ZrCuAl, ZrB, and ZrFeB. In the radical plane technique, the face is placed on the position in proportion to the atomic size. In this study, we found that the differences cannot be negligible. In some cases, the difference in the results between the two techniques is more than 50%.
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Liquidus Surfaces and Isothermal Section at 973 K of the BaO-ZnO-B₂O₃ Pseudo-Ternary System

Hiroshi Sato

pp. 2910-2917

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Liquidus Surfaces and Isothermal Section at 973 K of the BaO-ZnO-B₂O₃ Pseudo-Ternary System

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DOI:10.2320/matertrans.47.2910

Abstract

The liquidus surfaces and the isothermal section at 973 K of the pseudo-ternary BaO-ZnO-B₂O₃ system were determined using the thermal analysis and X-ray diffraction. The liquidus surface in equilibrium with ZnO spreads over a wide composition range and that in equilibrium with 5ZnO·2B₂O₃ extends long and narrow toward BaO·B₂O₃. The slope of the liquidus surface in equilibrium with ZnO is steep in the region of less than 20 mol%B₂O₃ but gentle when the B₂O₃ content exceeds 20 mol%. The liquidus surface in equilibrium with 3BaO·B₂O₃ widely extends and its slope is gentle in the region of less than 30 mol%B₂O₃ but steep when the B₂O₃ content exceeds 30 mol%. Pseudo-ternary BaO-ZnO-B₂O₃ compounds were not found in the composition range investigated. The ternary eutectic reactions are as follows: L→3BaO·B₂O₃+BaO·B₂O₃+ZnO, occurring at 1033 K at the composition 46.5 mol%BaO-14.5 mol%ZnO-39.0 mol%B₂O₃, L→BaO·B₂O₃+ZnO·B₂O₃+5ZnO·2B₂O₃, occurring at 1038 K at the composition 34 mol%BaO-21 mol%ZnO-45 mol%B₂O, L→BaO·2B₂O₃+BaO·4B₂O₃+ZnO·B₂O₃, occurring at 1008 K at the composition 19 mol%BaO-17 mol%ZnO-64 mol%B₂O₃.
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Mechanical Properties of High Strength Al-Mg-Si Alloy during Solidification

Hiromi Nagaumi, Pongsugitwat Suvanchai, Toshimitsu Okane, Takateru Umeda

pp. 2918-2924

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Mechanical Properties of High Strength Al-Mg-Si Alloy during Solidification

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DOI:10.2320/matertrans.47.2918

Abstract

Mechanical properties of high strength Al-Mg-Si alloy during solidification have been investigated. Tensile strength and ductility have been measured by using an electromagnetic induction heating tensile machine. The relation between solid fraction and temperature was calculated by the Gulliver-Scheil model applied with the thermodynamic data-base Thermo-Calc for multi-component system, and its validity was confirmed, comparing with the experiment. Zero Strength Temperature (ZST) and Zero Ductility Temperature (ZDT) were evaluated and correlated with the corresponding solid fraction. Furthermore, the capability of the high temperature tensile test to apply to the break-out of direct chill (DC) casting was examined, comparing the breaking section of the tensile test sample with that of DC billet. Main conclusions are as follows: (1) ZST and ZDT were 893 and 883 K at which the corresponding solid fraction were 0.69 and 0.77, respectively. (2) Breaking sections of the tensile testing sample and DC billet had a similar rupture structure where intergranular fracture was observed. Consequently, it was considered that breaking elongation and breaking strength that were obtained by the present tensile test can be used as one of the criteria of Direct-Chill casting crack formation.
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Precipitation Processes in a Cu–0.9 mass% Be Single Crystal

Ryoichi Monzen, Tsutomu Seo, Toshiro Sakai, Chihiro Watanabe

pp. 2925-2934

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Precipitation Processes in a Cu–0.9 mass% Be Single Crystal

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DOI:10.2320/matertrans.47.2925

Abstract

The precipitation processes in a Cu–0.9 mass%Be alloy single crystal containing only G.P. zones parallel to the matrix (001)_α plane have been studied by high-resolution transmission electron microscopy. The precipitation sequence found is: G.P. zones→γ″→γ′_I→γ_I+γ′→γ. The γ″ phase has a two-layer structure of Be atoms separated by a matrix layer parallel to (001)_α, and a body-centered tetragonal (bct) lattice. The γ′_I phase consisting of five to ten Be-layers is body-centered monoclinic. The γ_I phase continuously transforms from the G.P. zones via γ″ and γ′_I. The heterogeneous formation of γ′ occurs on the γ_I phase. The γ_I or γ′ phase is bct with a=b=0.254 nm and c=0.352 nm or a=0.254 nm and b=c=0.268 nm. The γ″, γ′_I or γ_I phase aligns with the matrix according to the Bain orientation relationship. The plate-shaped γ′ precipitates have the (1\\bar1\\bar2)_α habit plane and the orientation relationship, (1\\bar1\\bar2)_α||(0\\bar1\\bar2)_γ′; [110]_α||[100]_γ′ (OR I), or the (1\\bar13)_α habit plane and the orientation relationship, (1\\bar13)_α||(0\\bar13)_γ′; [110]_α||[100]_γ′ (OR II). The structure of γ′ successively changes into that of the γ phase with a=0.280 nm for OR I or 0.268 nm for OR II. The γ precipitates of OR I and OR II are elongated along approximately [1\\bar11]_α and [3\\bar3\\bar2]_α, which are in good agreement with the invariant-line directions.
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The Effect of Electrical Current on Tensile Properties and Vibration Characteristics of Sn-9Zn-1Cu Lead-Free Solder

Fei-Yi Hung, Truan-Sheng Lui, Li-Hui Chen, Ji-Ge You

pp. 2935-2941

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The Effect of Electrical Current on Tensile Properties and Vibration Characteristics of Sn-9Zn-1Cu Lead-Free Solder

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DOI:10.2320/matertrans.47.2935

Abstract

The effect of electrical current on the microstructure, the tensile properties and vibration deformation mechanisms of the Sn-9Zn-1Cu lead-free solder were examined in this study. Results showed that Zn-rich phase, Sn-Zn eutectic, Cu₅Zn₈ intermetallic compounds and proeutectic Sn-rich phase existed in the matrix of a Sn-9Zn-1Cu specimen. An electrical current flowing for a short duration was able to improve the tensile strength of the solder alloy. But prolonging the duration more than 7 hours led to a deterioration in the tensile mechanical properties and vibration resistance. Under both constant force and initial-deflection conditions, the electrical current caused the vibration life of the specimens to deteriorate. Lamellar-deformed structures (LDS) decreased and Cu₅Zn₈ fractured easily, which in turn decreased the crack propagation resistance.
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On the Hardening of Friction Stir Processed Mg-AZ31 Based Composites with 5–20% Nano-ZrO₂ and Nano-SiO₂ Particles

C. I. Chang, Y. N. Wang, H. R. Pei, C. J. Lee, J. C. Huang

pp. 2942-2949

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On the Hardening of Friction Stir Processed Mg-AZ31 Based Composites with 5–20% Nano-ZrO₂ and Nano-SiO₂ Particles

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DOI:10.2320/matertrans.47.2942

Abstract

Mg-AZ31 based composites with 10–20 vol% nano-sized ZrO₂ and 5–10 vol% nano-sized SiO₂ particles were fabricated by friction stir processing (FSP). The clusters of the nano-ZrO₂ and nano-SiO₂ particles, measuring 180–300 nm in average, were relatively uniformly dispersed. The average grain size of the Mg matrixes of the composites varied within 2–4 μm after four FSP passes. No evident interfacial product between the ZrO₂ particles and Mg matrix was found during the FSP mixing ZrO₂ into Mg-AZ31. However, significant chemical reactions occurred at the Mg/SiO₂ interface to form the Mg₂Si phase. The mechanical responses of the resulting nano-composites in terms of hardness and tensile properties of these Mg/nano-ZrO₂ and Mg/nano-SiO₂ composites were examined and compared. The grain refinements and the corresponding hardening mechanisms are also analyzed and discussed.
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Thermodynamic Analysis of the Undercooled Liquid and Glass Transition in the Cu-Mg-Y System

Mauro Palumbo, Marta Satta, Gabriele Cacciamani, Marcello Baricco

pp. 2950-2955

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Thermodynamic Analysis of the Undercooled Liquid and Glass Transition in the Cu-Mg-Y System

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DOI:10.2320/matertrans.47.2950

Abstract

A thermodynamic analysis of the undercooled liquid and glass transition in the ternary Cu-Mg-Y system has been carried out. To this purpose, a number of experimental data on the amorphous phase and on the undercooled liquid has been considered (glass transition temperatures, specific heat). A proper modelling of the glass transition has been applied, which has been proved suitable for the description of thermodynamic properties of the liquid-amorphous phase. Calculated and experimental quantities show a good agreement. An improved description of the behaviour of the specific heat of the liquid phase on undercooling has been obtained. The present thermodynamic assessment is suitable for estimating the Glass Forming Ability in this ternary system.
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Environmental Factors Affecting Hydrogen Entry into High Strength Steel due to Atmospheric Corrosion

Tomohiko Omura, Takeo Kudo, Shinji Fujimoto

pp. 2956-2962

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Environmental Factors Affecting Hydrogen Entry into High Strength Steel due to Atmospheric Corrosion

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DOI:10.2320/matertrans.47.2956

Abstract

Hydrogen entry into high strength steel has been investigated by hydrogen permeation measurements under wet-dry cyclic environments. Dominant environmental factors that control hydrogen entry were temperature, relative humidity, and the amount of sea salt on the steel surface. Corrosion rate increased with an increase in temperature, resulting in enhanced hydrogen permeation. Hydrogen entry was promoted at lower relative humidity (40–60%), by the hydrolysis of Fe³⁺ accelerated by condensed Cl⁻ ions in the water layer. A maximum hydrogen permeation coefficient was observed at the Cl⁻ amount of 0.03 kg/m² on the steel surface, corresponding to a maximum corrosion rate determined by an appropriate water layer thickness. Crack susceptibility of the steel has also been investigated by stress fracture tests under wet-dry cyclic environments. Steels with tensile strengths beyond 1400 MPa suffered from cracking at higher temperatures and the Cl⁻ of 0.03 kg/m². The fracture test results mean that crack susceptibility strongly depended upon the environmental severities which promoted hydrogen entry.
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Phase Relations, Activities and Minor Element Distribution in Cu-Fe-S and Cu-Fe-S-As Systems Saturated with Carbon at 1473 K

Leandro Voisin, Kimio Itagaki

pp. 2963-2971

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Phase Relations, Activities and Minor Element Distribution in Cu-Fe-S and Cu-Fe-S-As Systems Saturated with Carbon at 1473 K

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DOI:10.2320/matertrans.47.2963

Abstract

As a fundamental study to develop a new process for eliminating detrimental arsenic, recovering precious elements from the arsenic-rich matte produced from the copper concentrate, and treating the occasionally generated speiss in nonferrous smelting processes, the phase relations in the Cu-Fe-S and Cu-Fe-S-As systems saturated with carbon and the distribution of some minor elements between the phases in the miscibility gap, where three equilibrated phases of iron-rich alloy, copper-rich alloy and matte coexist, were investigated at 1473 K by using a quenching method.
The experimental results were discussed on the basis of activity coefficient of arsenic in the matte phase at different matte grades. By utilizing the obtained data, material balance calculations concerning to the treatment of arsenic-rich matte produced in copper smelting by adding the pig-iron was elaborated and also laboratory scale experiments using industrial matte were carried to corroborate the calculations. By using the phase separation, the recovery of valuable copper, silver and gold into the copper-rich alloy and matte phases as well as the elimination of iron and arsenic into the iron-rich alloy phase for discarding as a harmless and smaller deposit might be feasible.
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2. Mechanical Properties of High Strength Al-Mg-Si Alloy during Solidification MATERIALS TRANSACTIONS Vol.47(2006), No.12
3. Dielectric Properties of Poly- and Single-Crystalline BaTi₂O₅ MATERIALS TRANSACTIONS Vol.47(2006), No.12
Fabrication of In-Situ Intermetallic Compound Dispersed Aluminum Matrix Composites by Addition of Metal Powders

Mitsuaki Matsumuro, Tadashi Kitsudo

pp. 2972-2979

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Fabrication of In-Situ Intermetallic Compound Dispersed Aluminum Matrix Composites by Addition of Metal Powders

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DOI:10.2320/matertrans.47.2972

Abstract

A new process was proposed to fabricate intermetallic compound reinforced Al matrix composites by the reaction between metal powders and molten Al. The Ni powders were added gradually onto the surface of the molten pure Al by stirring. The Al₃Ni particles, which are smaller than the added Ni powder, were in situ formed and homogeneously dispersed in the Al. The processing temperature was lower and the stirring time was shorter than those of the conventional vortex method for fabricating non-metal (Al₂O₃, SiC etc) reinforced Al matrix composites. The effects of the processing variables, such as processing temperature, size of the Ni powder, and stirring time, on the formation and dispersion behavior of Al₃Ni were investigated. It was found that the size of the Al₃Ni decreased with the decreasing processing temperature and stirring time. The process was also applied to Ti, Zr, Cr, Mo, W and Fe powders. Al₃Ti, Al₃Zr, Al₇Cr and Al₁₂Mo were formed and homogeneously dispersed, but the others failed. The size of the intermetallic compounds significantly depended on the specific elemental metal powder. The dispersion of the intermetallic compounds was affected by the oxidation of the metal powders. This process was applicable to the JIS AC8A alloy for forming the AC8A-Al₃Ni composite.
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2. Environmental Factors Affecting Hydrogen Entry into High Strength Steel due to Atmospheric Corrosion MATERIALS TRANSACTIONS Vol.47(2006), No.12
3. Liquid Reaction during Synthesis of Ti₃SiC₂ through Pulse Discharge Sintering Ti/Si/TiC Mixed Powders MATERIALS TRANSACTIONS Vol.47(2006), No.12
The Formation and Characterization of Nanocrystalline Phases by Mechanical Milling of Biphasic Calcium Phosphate/Poly-L-Lactide Biocomposite

I. Nikcevic, D. Maravic, N. Ignjatovic, M. Mitric, D. Makovec, D. Uskokovic

pp. 2980-2986

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The Formation and Characterization of Nanocrystalline Phases by Mechanical Milling of Biphasic Calcium Phosphate/Poly-L-Lactide Biocomposite

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DOI:10.2320/matertrans.47.2980

Abstract

Biphasic calcium phosphate/poly-L-lactide granules of 150–200 μm sizes were subjected to high-energy mechanical milling in a planetary ball mill for up to 480 minutes. Characterization of the material obtained was carried out using X-ray diffraction (XRD), differential scanning calorimetry (DSC), environmentally scanning electronic microscopy (ESEM), transmission electron microscopy (TEM) and infrared spectroscopy (IR). These techniques confirmed that mechanical milling induced significant changes in the biocomposite structure and properties. The most significant changes are reduction of the HAp crystallites size from 99.8 to 26.7 nm and β-TCP from 97.3 to 29.6, as well as crystallinity of PLLA phases. Homogeneous phase distribution (arrangement) is obtained by extending the duration of mechanical milling.
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2. Environmental Factors Affecting Hydrogen Entry into High Strength Steel due to Atmospheric Corrosion MATERIALS TRANSACTIONS Vol.47(2006), No.12
3. Liquid Reaction during Synthesis of Ti₃SiC₂ through Pulse Discharge Sintering Ti/Si/TiC Mixed Powders MATERIALS TRANSACTIONS Vol.47(2006), No.12
Liquid Reaction during Synthesis of Ti₃SiC₂ through Pulse Discharge Sintering Ti/Si/TiC Mixed Powders

Yong Zou, Zheng Ming Sun, Shuji Tada, Hitoshi Hashimoto

pp. 2987-2990

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Liquid Reaction during Synthesis of Ti₃SiC₂ through Pulse Discharge Sintering Ti/Si/TiC Mixed Powders

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DOI:10.2320/matertrans.47.2987

Abstract

To understand the synthesis mechanism of Ti₃SiC₂ through pulse discharge sintering Ti/Si/TiC mixed powders, the shrinkage displacement curves were studied during sintering process. Liquid reaction above Ti-Ti₅Si₃ eutectic temperature was revealed. The Ti-Si liquid reaction was found not only to have assisted the Ti₃SiC₂ phase formation but also accelerated its densification. Ti₈C₅ was found to be the intermediate phase during this liquid reaction stage.
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Hydrogen Permeation of Ni-Nb-Zr Metallic Glasses in a Supercooled Liquid State

Shin-ichi Yamaura, Shuhei Nakata, Hisamichi Kimura, Akihisa Inoue

pp. 2991-2996

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Hydrogen Permeation of Ni-Nb-Zr Metallic Glasses in a Supercooled Liquid State

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DOI:10.2320/matertrans.47.2991

Abstract

In this study, the hydrogen permeation in the supercooled liquid state for Ni₆₅Nb₂₅Zr₁₀, Ni₆₀Nb₂₀Zr₂₀ and Ni₅₅Nb₁₅Zr₃₀ metallic glasses was investigated in conjunction with the discussion on the effect of hydrogen diffusion on hydrogen permeation. The hydrogen permeation of the Ni₆₅Nb₂₅Zr₁₀ and Ni₆₀Nb₂₀Zr₂₀ metallic glasses increases significantly by the transition from the glassy solid state to the supercooled liquid state. The temperature at which this significant increase in hydrogen permeation appears is much lower than T_g and is in correspondence with the onset temperature of the endothermic reaction relating to the glass transition. Moreover, it was found that the hydrogen permeation in the glassy phase was larger than that in the corresponding crystalline one. The contribution of hydrogen diffusion and solution to permeation is discussed in detail.
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Removal of Lead from Scrap Bronze

Atsushi Nakano, Naoki Kajiya, Kosaku Yamada, Syun-ichi Nakamura, Takehiko Matsuda, Hidekazu Sueyoshi

pp. 2997-3000

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Removal of Lead from Scrap Bronze

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DOI:10.2320/matertrans.47.2997

Abstract

Pb has been added to bronze to increase its machinability. However, due to the extreme toxicity of Pb that is harmful to the health, the public demand for the use of Pb-free bronze has increased. Therefore, scrap bronze containing Pb cannot be utilized as a recycling material and a large amount of scrap bronze will become industrial waste. So, it is necessary to remove Pb in the scrap bronze to promote recycling.
In the present study, the use of the compound-separation method is attempted for the removal of Pb from bronze containing 5.5 mass%Pb. The result shows that the percentage of Pb removal was effective up to 82% when NaF was added to molten bronze, followed by adding a Ca-Si alloy.
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3. The Formation and Characterization of Nanocrystalline Phases by Mechanical Milling of Biphasic Calcium Phosphate/Poly-L-Lactide Biocomposite MATERIALS TRANSACTIONS Vol.47(2006), No.12
A Quantitative Study of Precipitation of Metastable Phases in an Al-1.94 at%Cu Alloy during Isothermal Aging at 373 K

Sung-Kyu Son, Mahoto Takeda, Kyu-Seop Park, Masanori Mitome, Yoshio Bando, Ki-Woo Nam, Chang-Yong Kang

pp. 3001-3006

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A Quantitative Study of Precipitation of Metastable Phases in an Al-1.94 at%Cu Alloy during Isothermal Aging at 373 K

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DOI:10.2320/matertrans.47.3001

Abstract

Precipitation behavior of metastable phases in an Al-1.94 at%Cu alloy during isothermal aging at 373 K was investigated by means of Vickers microhardness tests, DSC measurements and TEM observations. The size distribution of the precipitates was quantitatively investigated based on the TEM, HRTEM and HAADF-STEM images, and statistical parameters that fit the precipitate size distribution were determined under a log-normal distribution approximation. We have successfully estimated the volume fraction of copper in precipitates, and found that the G.P.(II) formation results in increases of volume fraction of metastable particles, mean size and hardness.
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3. The Formation and Characterization of Nanocrystalline Phases by Mechanical Milling of Biphasic Calcium Phosphate/Poly-L-Lactide Biocomposite MATERIALS TRANSACTIONS Vol.47(2006), No.12
Carbothermic Reduction of Oxide Powder Prepared from Titanium Dioxide and Cobalt Nitrate

Gil-Geun Lee, Gook-Hyun Ha

pp. 3007-3011

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Carbothermic Reduction of Oxide Powder Prepared from Titanium Dioxide and Cobalt Nitrate

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DOI:10.2320/matertrans.47.3007

Abstract

The carbothermic reduction of a titanium-cobalt-oxygen-based oxide powder was analyzed to understand the carbothermal reduction step of the spray thermal conversion process for the synthesis of titanium carbide/cobalt composite powder. The starting powder was prepared by the combination of the spray drying and desalting methods using titanium dioxide powder and cobalt nitrate. The synthesized oxide powders were mixed with carbon black, and then these mixtures were heat treated under a flowing argon atmosphere. The changes in the phase structure and thermal gravity of the mixtures during heat treatment were analyzed using XRD and TG-DTA. The synthesized oxide powders have a mixed phase structure of anatase-TiO₂ and CoTiO₃ phases without regard to the cobalt content. These composite oxide powders were carbothermally reduced to the titanium carbide/cobalt composite powder through four steps with increasing temperature; reduction of CoTiO₃, reduction of anatase-TiO₂, formation of titanium oxycarbide and formation of TiC from titanium oxycarbide. The titanium carbide formability increased with the increasing relative amount of the complex oxide, CoTiO₃, in the titanium-cobalt-oxygen-based oxide powder.
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3. The Formation and Characterization of Nanocrystalline Phases by Mechanical Milling of Biphasic Calcium Phosphate/Poly-L-Lactide Biocomposite MATERIALS TRANSACTIONS Vol.47(2006), No.12

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MATERIALS TRANSACTIONS Vol. 47 (2006), No. 12

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