- Email: [email protected]
A thermal etching technique for revealing dislocations in silver
A THERMAL
ETCHING
TECHNIQUE
FOR
REVEALING
A. A. HENDRICKSONS
DISLOCATIONS
IN SILVER*t
and E. S. MACHLIN**
A thermal etching technique for revealing dislocations in silver has been developed. The technique reveals single dislocations in silver as evidenced by the close agreement between the experimentally measured area density of dislocations in bent single crystals and the area density calculated using the Cottrell formula for the excess density of dislocations as a function of the radius of curvature of the bent crystal. It has been found that the density of dislocations in recrystallized specimens and as solidified crystals is about 2X 10s per cm*, A new mode of subgrain formation has been found. The type of subgrain morphology obtained is shown to be dependent upon the orientation between the crystal and the tension direction. UNE TECHNIQUE
D’ATTAQUE THERMIQ~E PER~E~ANT LES DISLOCATIONS DANS L’ARGENT
DE Rl%‘BLER
On a developp6 une technique d’attaque thermique, qui permet de reveler des dislocations dans l’argent. Cette technique revele des dislocations individuelles dans l’argent, comme le prouve le bon accord obtenu entre la densite des dislocations mesuree exptirimentalement dans des monocristaux flechis et la densite calculee au moyen de la formule de Cottrell donnant la densite des dislocations en e&s, en fonction du rayon de courbure du cristal f&hi. On a constate que la densite des dislocations dans des 6chantillons recristallis& et dans des cristaux solidifies est d’environ 2X 106par cm*. Un nouveau mode de formation de sous-grains fut troud. On montre que le genre de morphologie des sous-grains, obtenu, depend de l’orientalion du cristal par rapport ii la direction de la tension. EINE THERMISCHE
ATZTECHNIK VERSETZUNGEN
ZUM SICHTBARMACHEN IN SILBER
VON
Es wurde eine thermische Atztechnik zum Sichtbarmachen von Versetzungen in Silber entwickelt. Die Technik zeigt einzelne Versetzungen auf. Dies kisst sich an der guten ~bereinstimmung zwixhen der experimentell bestimmten Flachendichte der Versetzungen in durch Biegung verformten Einkristallen und der nach Cottrell berechneten Flachendichte zeigen. Der Berechnung liegt Cottrells Formel fiir die zusiitzlithe Versetzungsdichte eines “gebogenen” Kristalls als Funktion des Kriimmungsradius zu Grunde. Es zeigte sich, dass die Versetzungsdichte in rekristallisierten und in aus der Schmelze gewachsenen Proben etwa 2X10& pro cm* betrug. Es wurde eine neue Art der Feinkornbildung gefunden. Es wird gezeigt, dass es von der relativen Orientierung des Kristalls zur Zugrichtung abbangt, welche Art von Feinkornmorphologie auftritt.
INTRODUCTION
this consideration alone, thermal etching promised to be a successful method for preferential etching of dislocation singular lines. The purpose of this research was to develop and verify a thermal etching technique for revealing dislocation lines in silver. A technique of this kind must be reproducible within the limits of laboratory control to draw any significant results. Hence it was required to show that there was an etching condition without a critical etching time to produce the same quantitative result. In addition, it had to be shown that correlations of the results of the technique with the amount of strain and geometry of deformation were consistent with the basic theory, Having established good evidence that the observed etch pits were dislocation intersections, other experiments were performed utilizing the thermal etching technique. Because of the limited application, these led to questions rather than answers in regard to the related topics of strain, recovery and recrystallization.
The concept of the dislocation has been used extensively and successfully to describe many phenomena in metals. However successful the theory has been in precisely describing the structure and properties of metals, it has lacked considerably for need of visual observation of a dislocation or of groups of single dislocations. Only recently have these observations been made in salt crystals’ and in lineage boundaries in Geraniums Since the strain energy of a dislocation line is small, a successful etching technique to delineate it must be able to differentiate small differences in energy. The work of Chalmers3 has indicated that a thermal etching of silver might well accomplish this purpose. Chalmers noted that thermal etching delineated grain boundaries at 300°C and at 600°C began to preferentially etch grooves along planes of high atomic population in order to minimize the very small surface energies involved. With * Received July 14, 1954. t This paper is based on a thesis submitted by A. A. Hendrickson in partial fulfillment of the requirements for the Master of Science degree at the School of Engineering, Columbia University. 1:Formerlv Graduate Student and Research Assistant. Columbia University; d now Physical Metallurgist, Ampco Mktal, Inc., Milwaukee, Wisconsin. ** Assocrate Professor of Metallurgy, Columbia University, New York, New York. ACTA METALLURGICA,
VOL. 3, JANUARY
19.55
SPECIMEN
PREPARATION
Single crystals were grown from 99.9 per cent silver utilizing a modified Bridgman technique. Slabs were cut from the crystals with a minimum amount of distortion by the use of a cut-off wheel 0.020 in. thick. Heating of the specimens during cutting was very low since a feed 64
PLATE I. FIG. l.-Appearance of a surface of a single crystal thermally etched for ten minutes at 600°C after it was bent to produce predominantly single glide and annealed at 800°C for 10 hours. 1700X. FIG. 2.-Thermally etched for 20 minutes at 600°C. 1700X. FIG. 3.-Thermally etched for 40 minutes at 600°C. 1700X. FIG. S.-Thermally etched surfaces of silver as a function of prior amounts of bending. 1000X. (a) No prior bending (as grown from melt). (b) Bent to 1 cm radius. Annealed 5 hours at 600°C.
65
6
13
12
PLATE II. FIG. &-Crystal bent about a 1 cm bend radius. Annealed for 5 hours at 600°C. 2800X. FIG. 7.---Cbserved number of etch pits after bending about a 0.25 cm radius. Annealed at 850°C for 10 hours. 1700X. FIG. 9.-Photomicrograph showing etch pit density in the strained (right) and recrystallized portions of a crystal bent around a 4 cm radius and annealed for 6 hours at 550°C. 420X, polarized light. FIG. Il.-Crystal bent around a 0.25 cm radius. Annealed at 800°C for 16 hours and at 850°C for 16 more hours. 1700X. FIG. 12.-Same as Fig. 11. 2800X. FIG. Id.-Bent to 4 cm radius. Annealed at 550°C for 6 hours, Thermally etched. Electropolished. Bent some more (to about 3 cm radius). Thermally etched. 1950x.
66
HENDRICKSON
AND
MACHLIN:
of only 0.010 in./min was used. Before bending, all specimens were electropolished in a 9 per cent KCN solution at as high a current density as would produce a smooth, stain-free surface. This current density was about 12.5 amps per sq. in. The specimen was agitated rapidly during this polishing operation. The specimen surfaces were then washed and dried thoroughly in cold water and alcohol followed by drying rapidly in a stream of argon. At least five minutes of washing in cold water is required to produce a stain-free surface on thermal etching. Microscopic examination at 600X insured a smooth, stain-free surface for etching. All thermal etching was carried out in a tube furnace controlled within sS“C with a Tag Select-Ray multiple point controller. The specimens were etched in a thoroughly cleaned, porcelain crucible inserted into a vicar tube. The etching medium was one part of oxygen
THERMAL
ETCHING
TECHNIQUE TABLE
Radius no
I.
Observed etch pit density, cm-2
of bend, cm
67
Calculated dislocation density. cm-2
2.5x 106 1.1x107 1.5XlO~ 2.9X lo7
bend : 1
6.9X lo8 1.2x107 3.5x 107 ____
minutes
after
it was bent
to produce
predominantly
single glide and annealed at 800°C for 10 hours. It had to be shown that the number of etch pits did not vary with etching time at this temperature. The same crystal with single glide predominating was thermally etched for 10, 20 and 40 minutes. Figures 1, 2 and 3 show that the observed number of dislocation intersections with surface did not increase with etching time but only growth of the etched areas proceeded. Thus, it was illustrated that a satisfactory temperature for thermally etching dislocation intersections existed and that the number of etch pits produced at this temperature was independent of etching time. EFFECT
OF BEND RADIUS
The excess density of edge dislocations of the same sign to produce a certain amount of strain in bending has been calculated by Cottrell :4 p = l,‘rb,
011 FIG.
4. Stereographic plot showing the axis of bend and tensile direction for specimens illustrated by Figs. 5a and Sb.
diluted in nine parts of argon. The gas ratio was controlled by a double connection to a water manometer. The total gas pressure of one inch of water provided satisfactory etching conditions. The X-ray patterns were obtained by the usual backreflection Laue techniques. Because of the small cross section of the specimens, the orientations found are accurate to only f5”. EFFECT
OF ETCHING
TEMPERATURE
AND TIME
Etching temperature was the first variable investigated. A high temperature, 850°C was first attempted. It was found that the growth of etched areas proceeded too rapidly for good control during etching. Consequently, a lower temperature, 600°C was investigated. This temperature provided satisfactory thermal etching conditions. Figure 1 illustrates the appearance of a surface of a single crystal thermally etched for ten
where p is the number of dislocations per unit area parallel to the bend axis, r is the bend radius at the neutral axis and b is the Burgers vector of the dislocation. In the case of silver, b is the interatomic distance in the (110) direction. In order to demonstrate that the observed density of etch pits was consistant with Cottrell’s relation, four single-crystal slabs were bent around an axis given in the stereographic plot of Fig. 4. The axis of the crystal parallel to the tension direction is also given in Fig. 4. These crystals were annealed for five hours at 600°C and then thermally etched. The observed and calculated density of dislocations are compared in Table I. Figures 5a and 5b illustrate the observed number of etch pits after no bending and a 1 cm bend radius respectively. In addition, a further comparison of calculated and observed densities of dislocations was made using Figs. 1, 6 and 7. In these specimens the bending geometry varied from specimen to specimen. Table II gives the comparison between the observed and calculated dislocation densities for varying crystal orientation-bend geometry. The correlation is sumTABLE Radius of bend, cm 4
1.3 0.25
II.
Observed etch pit density, cm-2
7.3X106 8.4X 10’ 1.8X108
Calculated dislocation density, cm-2
8.7x 106 2.7x107 1.4x 108
ACTA
METALLURGICA,
._
FIG. 8. Graphical correlation between predicted and observed densities of dislocations. marized in Fig. 8. It is apparent that the agreement between calculated and observed densities is extremely good. The observed discrepancies can be accounted for in a number of ways. The calculated value may be too small in the event that the Burgers vector should correspond to the (112) direction or that wrong sign edge dislocations have been generated during the bend but have not been annihilated during subsequent anneal or that screw dislocations have been generated and intersect the surface observed. The calculated value may be too high if the Burgers vector for the dislocations is oriented away from the tension direction. The fact that good agreement has been obtained may result from a cancellation of the above affects. It is interesting to note that the worst disagreement occurs foP the case where the Burgers vector (110) is parallel to the tension axis. In this case, the second factor would be negligible and the calculated value would be expected to be too low, as observed. Because the agreement is quantitative, it has been concluded that each pit corresponds to a single dislocation intersection with the surface. Another observation that has significance is the value of the dislocation density for the annealed state. The asgrown crystal of Fig. 5a has a density of 2.5X106/cm2. This value is in agreement with the value observed in a recrystallized grain. The density of the latter, calculated from Fig. 9, is about 2X 106/cm2. These observed values contrast with estimated values of 10*/cm2 for the annealed state.
VOL.
3, 1955
dominantly single glide and the appearance after annealing a specimen in this orientation after ten hours at 800°C is shown in Fig. 1. As shown, single glide (the existence of parallel dislocation singular lines) has led to the classical polygonized structure observed by Cahn6 in hexagonal crystals, that is, dislocations aligned in nearly plane boundaries normal to the slip direction. Multiple glide was involved in the specimens of group 2 and 3 orientations. Thus, the dislocations are not parallel in these specimens and as shown in Figs. 6 and 7, the dislocations tend to line up in curved walls. It is interesting to note that certain pits are darker than others. Although a number of explanations for this behavior may be given, it is preferred to abstain from speculation on this point. Perhaps, the most interesting observation made is shown in Figs. 11 and 12. These figures show the appearance of crystals of group 2 orientation after annealing for 16 hours at 800°C and 16 more hours at 850°C. The “dislocation-free” areas have been shown by means of Laue back-reflection diffraction patterns to be subgrains that are slightly disoriented from the deformed matrix. The rate of growth of these subgrains is extremely slow compared to the rate of migration of recrystallized-deformed crystal boundaries, such as shown in Fig. 9. It is believed that this fact implies two different mechanisms of boundary migration for the above two cases. This observation deserves further investigation. It is apparent that in order for the type of behavior illustrated in Figs. 11 and 12 to occur, it is necessary that no faster process leading to a decrease in dislocation density exist. Such processes are polygonization and recrystallization. By comparing the dislocation densities in the regions outside the subgrains shown in Figs. 11 and 12 with that determined from Fig. 7, it is found that no change in dislocation density
001
EFFECT OF BENDING GEOMETRY The effect of bending geometry was investigated superficially. The. orientations of the crystals are as shown in Fig. 10. Group 1 orientation showed pre-
011
FIG. 10. Stereographic plot of the bend axes and directions of the tensile stresses for predominently easy glide (l), complex glide (2), and greatest complexity (3).* * Smallest bend radius.
HENDRICKSON
AND
MACHLIN:
THERMAL
with annealing time has occurred in these regions. Hence, it can be concluded that these dislocations are stuck. The question arises as to whether recrystallization is absent in this set of specimens because of the immobility of the stuck dislocations or because no recrystallization nuclei are present. It was found that the specimens in group 3 tended to recrystallize at lower deformation and temperatures than the specimens in group 2 orientation. The question arises in this case as to whether the case of recrystallization of group 3 specimens is due to the presence of recrystallization nuclei absent in group 2, or whether the dislocations are stuck in group 2 but are not stuck in group 3. The answers to these questions must await further experimentation. The observations of Lucke and Lange7 on the strain hardenability of face-centered cubic crystals as a function of orientation of the tension axis are significant. They found that the resolved shear stress corresponding to a given resolved shear strain increases in the direction { 110) to { 111). The fact that we have found the ease of recrystallization to increase in this direction may imply a correlation between strain hardenability and ease of recrystallization. That further experimentation is required to establish this point is obvious. OBSERVATIONS
OF DISLOCATIONS SLIP BANDS
ALONG
The final survey made was to answer the question as to whether dislocations could be observed along slip bands using the thermal etching technique. A crystal was therefore subjected to the following treatment: Bent to 4 cm radius ; electropolished and annealed at 550°C for six hours followed by thermal etching; bent some more (larger than 3 cm radius) and thermally etched without prior electropolish. The resulting surface is shown in Fig. 13. The slip direction is at a slight angle to the plane of the figure. The following observations have been made. In the regions excluding the slip bands the dislocation density is about 9.5X lo6 dislocations/cm2 (compared to 8.7X106/cm2 calculated for the 4 cm radius). If the slip band region is included and a grand average density obtained the result is 1.3X107/cm2 (as compared to 1.2X 107/cm2 for a 3 cm radius of bend). It aooears therefore that new dislocations are introduced
ETCHING
TECHNIQUE
69
on new slip bands rather than on bands which already have dislocations. Before this deduction can be accepted, it is desireable to investigate this phenomenon further. It can be concluded, however, that dislocation distributions along slip bands can be made visual. The utility of this technique is obvious. CONCLUSIONS 1. Thermal etching of silver at 6OO’C in dilute solutions of oxygen produces microscopic etch pits; the number of these etch pits is independent of etching time. 2. The density of etch pits observed is proportional to the reciprocal radius of bend and correlates well with the calculated density of excess edge dislocations required for the bend radii. 3. The geometrical configuration of the etch pits varies with the complexity of deformation. Predominently single-glide results in the etch pits lining up into straight boundaries perpendicular to the slip direction. More complex glide results in boundary formation becoming more difficult and the boundaries formed are irregular in shape. 4. A high degree of complexity in deformation may immobilize the dislocations. Long annealing at high temperatures of immobilized dislocation configurations results in the formation and growth of subgrains which are relatively free of dislocations. These subgrains are slightly disoriented with respect to the deformed matrix. 5. The density of dislocations in recrystallized and as grown crystals is about 2X 106/cm2. 6. Dislocation distribution along slip bands can be revealed by thermal etching. REFERENCES 1. A. H. Cottrell, “Interactions 2. 3. 4.
5. 6. 7.
of Dislocations and Solute
Atoms,” Relation of Properties to Microstructure, American Society for Metals, 1954. W. T. Read, “What Makes Metals So Weak?” Metal Progress, February 1954. B. Chalmers and R. King, “Thermal Etching of Silver,” Proc. Rov. Sot. Tulv 21. 1948. A. ‘H. Co&eil. “dislocations and Plastic Flow in Crvstals.” * , Oxford at the Clarendon Press, 1953. R. D. Heidenreich and W. Shockley, “Report on the Strength of Solids,” London Physical Society, 1948. R. W. Cahn. “Conference on Strennth of Metals.” London, 1948; J. In& Metals, 1949. K. Lucke and H. Lanzze. 2. Metall.. 1952.
ETCHING
TECHNIQUE
FOR
REVEALING
A. A. HENDRICKSONS
DISLOCATIONS
IN SILVER*t
and E. S. MACHLIN**
A thermal etching technique for revealing dislocations in silver has been developed. The technique reveals single dislocations in silver as evidenced by the close agreement between the experimentally measured area density of dislocations in bent single crystals and the area density calculated using the Cottrell formula for the excess density of dislocations as a function of the radius of curvature of the bent crystal. It has been found that the density of dislocations in recrystallized specimens and as solidified crystals is about 2X 10s per cm*, A new mode of subgrain formation has been found. The type of subgrain morphology obtained is shown to be dependent upon the orientation between the crystal and the tension direction. UNE TECHNIQUE
D’ATTAQUE THERMIQ~E PER~E~ANT LES DISLOCATIONS DANS L’ARGENT
DE Rl%‘BLER
On a developp6 une technique d’attaque thermique, qui permet de reveler des dislocations dans l’argent. Cette technique revele des dislocations individuelles dans l’argent, comme le prouve le bon accord obtenu entre la densite des dislocations mesuree exptirimentalement dans des monocristaux flechis et la densite calculee au moyen de la formule de Cottrell donnant la densite des dislocations en e&s, en fonction du rayon de courbure du cristal f&hi. On a constate que la densite des dislocations dans des 6chantillons recristallis& et dans des cristaux solidifies est d’environ 2X 106par cm*. Un nouveau mode de formation de sous-grains fut troud. On montre que le genre de morphologie des sous-grains, obtenu, depend de l’orientalion du cristal par rapport ii la direction de la tension. EINE THERMISCHE
ATZTECHNIK VERSETZUNGEN
ZUM SICHTBARMACHEN IN SILBER
VON
Es wurde eine thermische Atztechnik zum Sichtbarmachen von Versetzungen in Silber entwickelt. Die Technik zeigt einzelne Versetzungen auf. Dies kisst sich an der guten ~bereinstimmung zwixhen der experimentell bestimmten Flachendichte der Versetzungen in durch Biegung verformten Einkristallen und der nach Cottrell berechneten Flachendichte zeigen. Der Berechnung liegt Cottrells Formel fiir die zusiitzlithe Versetzungsdichte eines “gebogenen” Kristalls als Funktion des Kriimmungsradius zu Grunde. Es zeigte sich, dass die Versetzungsdichte in rekristallisierten und in aus der Schmelze gewachsenen Proben etwa 2X10& pro cm* betrug. Es wurde eine neue Art der Feinkornbildung gefunden. Es wird gezeigt, dass es von der relativen Orientierung des Kristalls zur Zugrichtung abbangt, welche Art von Feinkornmorphologie auftritt.
INTRODUCTION
this consideration alone, thermal etching promised to be a successful method for preferential etching of dislocation singular lines. The purpose of this research was to develop and verify a thermal etching technique for revealing dislocation lines in silver. A technique of this kind must be reproducible within the limits of laboratory control to draw any significant results. Hence it was required to show that there was an etching condition without a critical etching time to produce the same quantitative result. In addition, it had to be shown that correlations of the results of the technique with the amount of strain and geometry of deformation were consistent with the basic theory, Having established good evidence that the observed etch pits were dislocation intersections, other experiments were performed utilizing the thermal etching technique. Because of the limited application, these led to questions rather than answers in regard to the related topics of strain, recovery and recrystallization.
The concept of the dislocation has been used extensively and successfully to describe many phenomena in metals. However successful the theory has been in precisely describing the structure and properties of metals, it has lacked considerably for need of visual observation of a dislocation or of groups of single dislocations. Only recently have these observations been made in salt crystals’ and in lineage boundaries in Geraniums Since the strain energy of a dislocation line is small, a successful etching technique to delineate it must be able to differentiate small differences in energy. The work of Chalmers3 has indicated that a thermal etching of silver might well accomplish this purpose. Chalmers noted that thermal etching delineated grain boundaries at 300°C and at 600°C began to preferentially etch grooves along planes of high atomic population in order to minimize the very small surface energies involved. With * Received July 14, 1954. t This paper is based on a thesis submitted by A. A. Hendrickson in partial fulfillment of the requirements for the Master of Science degree at the School of Engineering, Columbia University. 1:Formerlv Graduate Student and Research Assistant. Columbia University; d now Physical Metallurgist, Ampco Mktal, Inc., Milwaukee, Wisconsin. ** Assocrate Professor of Metallurgy, Columbia University, New York, New York. ACTA METALLURGICA,
VOL. 3, JANUARY
19.55
SPECIMEN
PREPARATION
Single crystals were grown from 99.9 per cent silver utilizing a modified Bridgman technique. Slabs were cut from the crystals with a minimum amount of distortion by the use of a cut-off wheel 0.020 in. thick. Heating of the specimens during cutting was very low since a feed 64
PLATE I. FIG. l.-Appearance of a surface of a single crystal thermally etched for ten minutes at 600°C after it was bent to produce predominantly single glide and annealed at 800°C for 10 hours. 1700X. FIG. 2.-Thermally etched for 20 minutes at 600°C. 1700X. FIG. 3.-Thermally etched for 40 minutes at 600°C. 1700X. FIG. S.-Thermally etched surfaces of silver as a function of prior amounts of bending. 1000X. (a) No prior bending (as grown from melt). (b) Bent to 1 cm radius. Annealed 5 hours at 600°C.
65
6
13
12
PLATE II. FIG. &-Crystal bent about a 1 cm bend radius. Annealed for 5 hours at 600°C. 2800X. FIG. 7.---Cbserved number of etch pits after bending about a 0.25 cm radius. Annealed at 850°C for 10 hours. 1700X. FIG. 9.-Photomicrograph showing etch pit density in the strained (right) and recrystallized portions of a crystal bent around a 4 cm radius and annealed for 6 hours at 550°C. 420X, polarized light. FIG. Il.-Crystal bent around a 0.25 cm radius. Annealed at 800°C for 16 hours and at 850°C for 16 more hours. 1700X. FIG. 12.-Same as Fig. 11. 2800X. FIG. Id.-Bent to 4 cm radius. Annealed at 550°C for 6 hours, Thermally etched. Electropolished. Bent some more (to about 3 cm radius). Thermally etched. 1950x.
66
HENDRICKSON
AND
MACHLIN:
of only 0.010 in./min was used. Before bending, all specimens were electropolished in a 9 per cent KCN solution at as high a current density as would produce a smooth, stain-free surface. This current density was about 12.5 amps per sq. in. The specimen was agitated rapidly during this polishing operation. The specimen surfaces were then washed and dried thoroughly in cold water and alcohol followed by drying rapidly in a stream of argon. At least five minutes of washing in cold water is required to produce a stain-free surface on thermal etching. Microscopic examination at 600X insured a smooth, stain-free surface for etching. All thermal etching was carried out in a tube furnace controlled within sS“C with a Tag Select-Ray multiple point controller. The specimens were etched in a thoroughly cleaned, porcelain crucible inserted into a vicar tube. The etching medium was one part of oxygen
THERMAL
ETCHING
TECHNIQUE TABLE
Radius no
I.
Observed etch pit density, cm-2
of bend, cm
67
Calculated dislocation density. cm-2
2.5x 106 1.1x107 1.5XlO~ 2.9X lo7
bend : 1
6.9X lo8 1.2x107 3.5x 107 ____
minutes
after
it was bent
to produce
predominantly
single glide and annealed at 800°C for 10 hours. It had to be shown that the number of etch pits did not vary with etching time at this temperature. The same crystal with single glide predominating was thermally etched for 10, 20 and 40 minutes. Figures 1, 2 and 3 show that the observed number of dislocation intersections with surface did not increase with etching time but only growth of the etched areas proceeded. Thus, it was illustrated that a satisfactory temperature for thermally etching dislocation intersections existed and that the number of etch pits produced at this temperature was independent of etching time. EFFECT
OF BEND RADIUS
The excess density of edge dislocations of the same sign to produce a certain amount of strain in bending has been calculated by Cottrell :4 p = l,‘rb,
011 FIG.
4. Stereographic plot showing the axis of bend and tensile direction for specimens illustrated by Figs. 5a and Sb.
diluted in nine parts of argon. The gas ratio was controlled by a double connection to a water manometer. The total gas pressure of one inch of water provided satisfactory etching conditions. The X-ray patterns were obtained by the usual backreflection Laue techniques. Because of the small cross section of the specimens, the orientations found are accurate to only f5”. EFFECT
OF ETCHING
TEMPERATURE
AND TIME
Etching temperature was the first variable investigated. A high temperature, 850°C was first attempted. It was found that the growth of etched areas proceeded too rapidly for good control during etching. Consequently, a lower temperature, 600°C was investigated. This temperature provided satisfactory thermal etching conditions. Figure 1 illustrates the appearance of a surface of a single crystal thermally etched for ten
where p is the number of dislocations per unit area parallel to the bend axis, r is the bend radius at the neutral axis and b is the Burgers vector of the dislocation. In the case of silver, b is the interatomic distance in the (110) direction. In order to demonstrate that the observed density of etch pits was consistant with Cottrell’s relation, four single-crystal slabs were bent around an axis given in the stereographic plot of Fig. 4. The axis of the crystal parallel to the tension direction is also given in Fig. 4. These crystals were annealed for five hours at 600°C and then thermally etched. The observed and calculated density of dislocations are compared in Table I. Figures 5a and 5b illustrate the observed number of etch pits after no bending and a 1 cm bend radius respectively. In addition, a further comparison of calculated and observed densities of dislocations was made using Figs. 1, 6 and 7. In these specimens the bending geometry varied from specimen to specimen. Table II gives the comparison between the observed and calculated dislocation densities for varying crystal orientation-bend geometry. The correlation is sumTABLE Radius of bend, cm 4
1.3 0.25
II.
Observed etch pit density, cm-2
7.3X106 8.4X 10’ 1.8X108
Calculated dislocation density, cm-2
8.7x 106 2.7x107 1.4x 108
ACTA
METALLURGICA,
._
FIG. 8. Graphical correlation between predicted and observed densities of dislocations. marized in Fig. 8. It is apparent that the agreement between calculated and observed densities is extremely good. The observed discrepancies can be accounted for in a number of ways. The calculated value may be too small in the event that the Burgers vector should correspond to the (112) direction or that wrong sign edge dislocations have been generated during the bend but have not been annihilated during subsequent anneal or that screw dislocations have been generated and intersect the surface observed. The calculated value may be too high if the Burgers vector for the dislocations is oriented away from the tension direction. The fact that good agreement has been obtained may result from a cancellation of the above affects. It is interesting to note that the worst disagreement occurs foP the case where the Burgers vector (110) is parallel to the tension axis. In this case, the second factor would be negligible and the calculated value would be expected to be too low, as observed. Because the agreement is quantitative, it has been concluded that each pit corresponds to a single dislocation intersection with the surface. Another observation that has significance is the value of the dislocation density for the annealed state. The asgrown crystal of Fig. 5a has a density of 2.5X106/cm2. This value is in agreement with the value observed in a recrystallized grain. The density of the latter, calculated from Fig. 9, is about 2X 106/cm2. These observed values contrast with estimated values of 10*/cm2 for the annealed state.
VOL.
3, 1955
dominantly single glide and the appearance after annealing a specimen in this orientation after ten hours at 800°C is shown in Fig. 1. As shown, single glide (the existence of parallel dislocation singular lines) has led to the classical polygonized structure observed by Cahn6 in hexagonal crystals, that is, dislocations aligned in nearly plane boundaries normal to the slip direction. Multiple glide was involved in the specimens of group 2 and 3 orientations. Thus, the dislocations are not parallel in these specimens and as shown in Figs. 6 and 7, the dislocations tend to line up in curved walls. It is interesting to note that certain pits are darker than others. Although a number of explanations for this behavior may be given, it is preferred to abstain from speculation on this point. Perhaps, the most interesting observation made is shown in Figs. 11 and 12. These figures show the appearance of crystals of group 2 orientation after annealing for 16 hours at 800°C and 16 more hours at 850°C. The “dislocation-free” areas have been shown by means of Laue back-reflection diffraction patterns to be subgrains that are slightly disoriented from the deformed matrix. The rate of growth of these subgrains is extremely slow compared to the rate of migration of recrystallized-deformed crystal boundaries, such as shown in Fig. 9. It is believed that this fact implies two different mechanisms of boundary migration for the above two cases. This observation deserves further investigation. It is apparent that in order for the type of behavior illustrated in Figs. 11 and 12 to occur, it is necessary that no faster process leading to a decrease in dislocation density exist. Such processes are polygonization and recrystallization. By comparing the dislocation densities in the regions outside the subgrains shown in Figs. 11 and 12 with that determined from Fig. 7, it is found that no change in dislocation density
001
EFFECT OF BENDING GEOMETRY The effect of bending geometry was investigated superficially. The. orientations of the crystals are as shown in Fig. 10. Group 1 orientation showed pre-
011
FIG. 10. Stereographic plot of the bend axes and directions of the tensile stresses for predominently easy glide (l), complex glide (2), and greatest complexity (3).* * Smallest bend radius.
HENDRICKSON
AND
MACHLIN:
THERMAL
with annealing time has occurred in these regions. Hence, it can be concluded that these dislocations are stuck. The question arises as to whether recrystallization is absent in this set of specimens because of the immobility of the stuck dislocations or because no recrystallization nuclei are present. It was found that the specimens in group 3 tended to recrystallize at lower deformation and temperatures than the specimens in group 2 orientation. The question arises in this case as to whether the case of recrystallization of group 3 specimens is due to the presence of recrystallization nuclei absent in group 2, or whether the dislocations are stuck in group 2 but are not stuck in group 3. The answers to these questions must await further experimentation. The observations of Lucke and Lange7 on the strain hardenability of face-centered cubic crystals as a function of orientation of the tension axis are significant. They found that the resolved shear stress corresponding to a given resolved shear strain increases in the direction { 110) to { 111). The fact that we have found the ease of recrystallization to increase in this direction may imply a correlation between strain hardenability and ease of recrystallization. That further experimentation is required to establish this point is obvious. OBSERVATIONS
OF DISLOCATIONS SLIP BANDS
ALONG
The final survey made was to answer the question as to whether dislocations could be observed along slip bands using the thermal etching technique. A crystal was therefore subjected to the following treatment: Bent to 4 cm radius ; electropolished and annealed at 550°C for six hours followed by thermal etching; bent some more (larger than 3 cm radius) and thermally etched without prior electropolish. The resulting surface is shown in Fig. 13. The slip direction is at a slight angle to the plane of the figure. The following observations have been made. In the regions excluding the slip bands the dislocation density is about 9.5X lo6 dislocations/cm2 (compared to 8.7X106/cm2 calculated for the 4 cm radius). If the slip band region is included and a grand average density obtained the result is 1.3X107/cm2 (as compared to 1.2X 107/cm2 for a 3 cm radius of bend). It aooears therefore that new dislocations are introduced
ETCHING
TECHNIQUE
69
on new slip bands rather than on bands which already have dislocations. Before this deduction can be accepted, it is desireable to investigate this phenomenon further. It can be concluded, however, that dislocation distributions along slip bands can be made visual. The utility of this technique is obvious. CONCLUSIONS 1. Thermal etching of silver at 6OO’C in dilute solutions of oxygen produces microscopic etch pits; the number of these etch pits is independent of etching time. 2. The density of etch pits observed is proportional to the reciprocal radius of bend and correlates well with the calculated density of excess edge dislocations required for the bend radii. 3. The geometrical configuration of the etch pits varies with the complexity of deformation. Predominently single-glide results in the etch pits lining up into straight boundaries perpendicular to the slip direction. More complex glide results in boundary formation becoming more difficult and the boundaries formed are irregular in shape. 4. A high degree of complexity in deformation may immobilize the dislocations. Long annealing at high temperatures of immobilized dislocation configurations results in the formation and growth of subgrains which are relatively free of dislocations. These subgrains are slightly disoriented with respect to the deformed matrix. 5. The density of dislocations in recrystallized and as grown crystals is about 2X 106/cm2. 6. Dislocation distribution along slip bands can be revealed by thermal etching. REFERENCES 1. A. H. Cottrell, “Interactions 2. 3. 4.
5. 6. 7.
of Dislocations and Solute
Atoms,” Relation of Properties to Microstructure, American Society for Metals, 1954. W. T. Read, “What Makes Metals So Weak?” Metal Progress, February 1954. B. Chalmers and R. King, “Thermal Etching of Silver,” Proc. Rov. Sot. Tulv 21. 1948. A. ‘H. Co&eil. “dislocations and Plastic Flow in Crvstals.” * , Oxford at the Clarendon Press, 1953. R. D. Heidenreich and W. Shockley, “Report on the Strength of Solids,” London Physical Society, 1948. R. W. Cahn. “Conference on Strennth of Metals.” London, 1948; J. In& Metals, 1949. K. Lucke and H. Lanzze. 2. Metall.. 1952.