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A theory for steady state creep based on the motion of interstitial type jogs
Vol.
7, No. 9
ABSTRACTS
OF ARTICLES
in terms of three mechanisms, namely diffusion creep, grain boundary sliding and plastic deformation through dislocation glide. The efficiency of the grain boundaries as sources and sinks for vacancies is an important factor in such strain-relaxation. Numerical solutions of the applicable difference equations with appropriate boundary conditions, set up to describe strain-relaxation in thin films on substrates, are in fair agreement with available experimental data. These solutions also indicate that a planar elastic strain of about 2-3 X 10-3 and a dislocation density of the order of 109 cm/cm 3 or higher, may usually be expected in thin films even after annealing treatments. 12.
THERMOTRANSPORT STUDIES IN LIQUID ALKALI METAL ALLOYS S. P. Murarka*, T. Y. Kim, M. Y. Hsieh & R. A. Swalin Department of Chemical Engineering and Materials Science, University of Minnesota Minneapolis, Minnesota 55455 *Now: Bell Telephone Laboratories Murray Hill, New Jersey (Received June 14, 1973)
Thermotransport has been studied as a function of composition in the Na-K liquid alloy system. Thermotransport of trace concentration of Rb in K, Rb in Na and Na in Rb have also been investigated, A reversal in direction of specie migration occurred at an intermediate composition in the Na-K system. In K rich alloys Na for example migrated toward the hot end of the capillary whereas in Na rich alloys Na migrated to the cold end. At some intermediate composition (between 64.6 at % Na and 76.6 at % Na) a crossover occurred and consequently no thermotransport occurred at that composition. This study compares with electromigration studies by other investigators which indicate that a sign reversal in direction of electromigration occurs in both the Na-K and Na-Rb systems. Theoretical calculations of the heats of transport in the alloy systems studied yield quite good agreement with the observed sign of the heat of transport for most of the alloys investigated.
13.
TO APPEAR IN ACTA MET
xi
A MATHEMATICAL MODEL DESCRIBING THE EFFECTS OF MICRO VOIDS UPON THE DIFFUSION OF HYDROGEN IN IRON AND STEEL D. M. Allen-Booth & J. Hewitt* Dept. of Applied Physics Sheffield Polytechnic Pond St. Sheffield S1 IWB England *British
Steel Corporation
(Received June 28, 1973) A new model of hydrogen diffusion in iron and steel is proposed, based upon the assumption of an equilibrium between interstitial hydrogen and hydrogen present as a molecular gas in voids. The model accurately predicts the anomalous variation in the diffusion rate of hydrogen with temperature, together with an equilibrium gas pressure in the voids. The temperature dependence of this pressure is seen to correspond closely to the variation of embrittlement with temperature, as measured by Baldwin and Toh. 14.
A THEORY FOR STEADY STATE CREEP BASED ON THE MOTION OF INTERSTITIAL TYPE JOGS Mahendra Malu & John K. Tien Dept. of Metallurgy Henry Krumb School of Mines Columbia University, New York, New York 10027 (Received April i0, 1973: Revised July 30, 1973)
Another theory for steady state creep based on the thermally assisted motion of jogged screw dislocation is developed. This theory is based on the defendable premise that jogs on moving screw dislocation are mainly of interstitial emitting ~or vacancy absorbing) type, and that activation energy for creep depends on mesh size of dislocation networks. The theory predicts low activation energy, on the order of that for vacancy self-diffusion, for creep of pure metals and single phase alloys. More interestingly, the theory predicts high activation energy, on the order of that for interstitial self-diffusion,for creep of particle strengthened engineering systems. The theory provides a very sharp stress dependence for creep of systems with high activation energies, and a less sharp stress dependence for creep of systems with low activation energies. The theory is discussed with
xii
ABSTRACTS
OF ARTICLES
respect to existing experimental and found to be satisfactory. 15.
TO APPEAR IN ACTA MET
results
TEXTURES IN SUPERPLASTIC Zn-40wt%Al K. N. Melton, J. W. Edington J. S. Kallend & C. P. Cutler Department of Metallurgy and Materials Science University of Cambridge Cambridge, England (Received June 18, 1973; Revised July 30, 1973)
The activation volumes calculated from the data were 1.5 + 0.5cmJ/mol and 1.2 + 0.4 cm3/mol for liquid K and Rb r~spectively. *Now: Department of Physics Rensselaer Polytechnic Institute Troy, New York
DIFFUSION STUDIES IN LIQUID • POTASSIUM AND RUBIDIUM Martin Hsieh*& R. A. Swalin Department of Chemical Engineering and Materials Science University of Minnesota, Minneapolis, Minnesota 55455 (Received June 6, 1973: Revised July 23, 1973)
Self-diffusion coefficients were determined for liquid potassium and rubidium. The types of measurements made were self-diffusion of K and Rb as a function of temperature at one atmosphere pressure, the pressure dependence of self-diffusion coefficients of K and Rb, and the temperature dependence of selfdiffusivity at c o n s t a n t molar volume. The self-diffusion coefficients in liquid K and Rb at one atmosphere pressure could be represented by the following expressions. DK(345°K
- 868°K)
= -2.443 x 10 -5 + 5.344 x I0 -10
(TOK)2 cm2/sec
DR~337°K
- 856°K)
= -1.479 x 10 -5 + 3.824 x i0 -10
(TOK)2 cm2/sec
The empirical equation and Rb may be expressed as D / D m = 1.665
for both K
[(T/Tm) 2 - 0.399]
The linear dependence
of D versus T 2
7, No. 9
for both Rb and K, observed in the present investigation, tends to offer support to the predictions of the fluctuation theory proposed by Swalin. The experimental data also agree quite well with the dense gas-like model of Ascarelli and Paskin.
Quantitative texture measurements using the crystallite orientation distribution function have been made for both phases in a superplastic Zn-40wt%Al alloy as a function of strain rate. Although the overall level of the texture if reduced by superplastic deformation, certain components are retained. The results are interpreted in terms of grain boundary sliding combined with slip in both phases. 16.
Vol.
7, No. 9
ABSTRACTS
OF ARTICLES
in terms of three mechanisms, namely diffusion creep, grain boundary sliding and plastic deformation through dislocation glide. The efficiency of the grain boundaries as sources and sinks for vacancies is an important factor in such strain-relaxation. Numerical solutions of the applicable difference equations with appropriate boundary conditions, set up to describe strain-relaxation in thin films on substrates, are in fair agreement with available experimental data. These solutions also indicate that a planar elastic strain of about 2-3 X 10-3 and a dislocation density of the order of 109 cm/cm 3 or higher, may usually be expected in thin films even after annealing treatments. 12.
THERMOTRANSPORT STUDIES IN LIQUID ALKALI METAL ALLOYS S. P. Murarka*, T. Y. Kim, M. Y. Hsieh & R. A. Swalin Department of Chemical Engineering and Materials Science, University of Minnesota Minneapolis, Minnesota 55455 *Now: Bell Telephone Laboratories Murray Hill, New Jersey (Received June 14, 1973)
Thermotransport has been studied as a function of composition in the Na-K liquid alloy system. Thermotransport of trace concentration of Rb in K, Rb in Na and Na in Rb have also been investigated, A reversal in direction of specie migration occurred at an intermediate composition in the Na-K system. In K rich alloys Na for example migrated toward the hot end of the capillary whereas in Na rich alloys Na migrated to the cold end. At some intermediate composition (between 64.6 at % Na and 76.6 at % Na) a crossover occurred and consequently no thermotransport occurred at that composition. This study compares with electromigration studies by other investigators which indicate that a sign reversal in direction of electromigration occurs in both the Na-K and Na-Rb systems. Theoretical calculations of the heats of transport in the alloy systems studied yield quite good agreement with the observed sign of the heat of transport for most of the alloys investigated.
13.
TO APPEAR IN ACTA MET
xi
A MATHEMATICAL MODEL DESCRIBING THE EFFECTS OF MICRO VOIDS UPON THE DIFFUSION OF HYDROGEN IN IRON AND STEEL D. M. Allen-Booth & J. Hewitt* Dept. of Applied Physics Sheffield Polytechnic Pond St. Sheffield S1 IWB England *British
Steel Corporation
(Received June 28, 1973) A new model of hydrogen diffusion in iron and steel is proposed, based upon the assumption of an equilibrium between interstitial hydrogen and hydrogen present as a molecular gas in voids. The model accurately predicts the anomalous variation in the diffusion rate of hydrogen with temperature, together with an equilibrium gas pressure in the voids. The temperature dependence of this pressure is seen to correspond closely to the variation of embrittlement with temperature, as measured by Baldwin and Toh. 14.
A THEORY FOR STEADY STATE CREEP BASED ON THE MOTION OF INTERSTITIAL TYPE JOGS Mahendra Malu & John K. Tien Dept. of Metallurgy Henry Krumb School of Mines Columbia University, New York, New York 10027 (Received April i0, 1973: Revised July 30, 1973)
Another theory for steady state creep based on the thermally assisted motion of jogged screw dislocation is developed. This theory is based on the defendable premise that jogs on moving screw dislocation are mainly of interstitial emitting ~or vacancy absorbing) type, and that activation energy for creep depends on mesh size of dislocation networks. The theory predicts low activation energy, on the order of that for vacancy self-diffusion, for creep of pure metals and single phase alloys. More interestingly, the theory predicts high activation energy, on the order of that for interstitial self-diffusion,for creep of particle strengthened engineering systems. The theory provides a very sharp stress dependence for creep of systems with high activation energies, and a less sharp stress dependence for creep of systems with low activation energies. The theory is discussed with
xii
ABSTRACTS
OF ARTICLES
respect to existing experimental and found to be satisfactory. 15.
TO APPEAR IN ACTA MET
results
TEXTURES IN SUPERPLASTIC Zn-40wt%Al K. N. Melton, J. W. Edington J. S. Kallend & C. P. Cutler Department of Metallurgy and Materials Science University of Cambridge Cambridge, England (Received June 18, 1973; Revised July 30, 1973)
The activation volumes calculated from the data were 1.5 + 0.5cmJ/mol and 1.2 + 0.4 cm3/mol for liquid K and Rb r~spectively. *Now: Department of Physics Rensselaer Polytechnic Institute Troy, New York
DIFFUSION STUDIES IN LIQUID • POTASSIUM AND RUBIDIUM Martin Hsieh*& R. A. Swalin Department of Chemical Engineering and Materials Science University of Minnesota, Minneapolis, Minnesota 55455 (Received June 6, 1973: Revised July 23, 1973)
Self-diffusion coefficients were determined for liquid potassium and rubidium. The types of measurements made were self-diffusion of K and Rb as a function of temperature at one atmosphere pressure, the pressure dependence of self-diffusion coefficients of K and Rb, and the temperature dependence of selfdiffusivity at c o n s t a n t molar volume. The self-diffusion coefficients in liquid K and Rb at one atmosphere pressure could be represented by the following expressions. DK(345°K
- 868°K)
= -2.443 x 10 -5 + 5.344 x I0 -10
(TOK)2 cm2/sec
DR~337°K
- 856°K)
= -1.479 x 10 -5 + 3.824 x i0 -10
(TOK)2 cm2/sec
The empirical equation and Rb may be expressed as D / D m = 1.665
for both K
[(T/Tm) 2 - 0.399]
The linear dependence
of D versus T 2
7, No. 9
for both Rb and K, observed in the present investigation, tends to offer support to the predictions of the fluctuation theory proposed by Swalin. The experimental data also agree quite well with the dense gas-like model of Ascarelli and Paskin.
Quantitative texture measurements using the crystallite orientation distribution function have been made for both phases in a superplastic Zn-40wt%Al alloy as a function of strain rate. Although the overall level of the texture if reduced by superplastic deformation, certain components are retained. The results are interpreted in terms of grain boundary sliding combined with slip in both phases. 16.
Vol.