Nomenclature

Aam Minimum detectable increase in austenite layer thickness A Mean areal intercept in stereology Ac3 Temperature at which a sample becomes fully austenitic during Ae3 Temperature separating the a + 7 and 7 phase fields for a specific Ar3 Temperature at which an austenitic sample begins to transform to ferrite during cooling Af Temperature at which the transformation to austenite is complete As Temperature at which the transformation to austenite begins As Mean free slip area in statistical...

152Notes Related to Table 151

Nucleation and growth reactions are of first order in the Ehrenfest classification in all such reactions, the parent and product phases can coexist, and are separated by well-defined interfaces. Martensitic transformations, although they can be rapid, still involve a nucleation and growth process. It is significant that all of the ferrite crystals which grow in the form of plates cause an invariant-plane shape deformation which is dominated by shear. The ferrite within pearlite does not have a...

377

Fig. 13.24 Charpy impact toughness data for Fe-0.43C-2Mn-3Si wt alloy transformed to a mixture of bainitic ferrite and carbon-enriched retained austenite. The data from the untempered microstructure are from Fig. 13.9. The other data were obtained after tempering the microstructure at 500 C for 1 h to induce the decomposition of the austenite into a mixture of ferrite and carbides. Ausforming is the deformation of austenite at temperatures well below Ae3, followed by transformation to...

Ab

Fig. 6.22 (a) Constant temperature free-energy curves showing the quantities G and Gn for the case where the interface compositions are as illustrated in (b). Note that the net free energy available for interfacial motion after allowing for strain energy and interface energy contributions is AG, which is the sum of the two dissipations Gdd and Gid. of solute ahead of the interface. The concentrations xa and Xj are not independent because the choice of either fixes the value of the other...

307

In fact, one of the tests for the susceptibility of bainitic microstructures to impurity-controlled embrittlement involves a comparison of the toughness of samples which are water quenched from a high tempering temperature (680 C) with those cooled slowly to promote impurity segregation (Bodnar et al., 1989). Studies of creep resistant bainitic steels show that phosphorus and tin, and to a lesser extent manganese and silicon, are all embrittling elements (Bodnar et al., 1989). Manganese is...

724 Comparison of Theory and Experimental Data

The general behaviour indicated by the calculations for plain carbon steels, is found to be that observed experimentally. Some interesting work by Oka and Okamoto (1986) proves that there is no upper bainite in plain carbon steels with more than 0.8 wt of carbon the only bainite observed in their experiments was classical lower bainite at all temperatures above the Ms temperature (Fig. 7.6a). Ohmori and Honeycombe (1971), in a study of plain carbon steels, showed that during isothermal...

240

Mole fraction of carbon in austenite Mole fraction of carbon in austenite Fig. 10.4 Data from experiments in which the austenite is transformed iso-thermally to acicular ferrite, showing that the reaction stops when the carbon concentration of the austenite reaches the TQ curve (Strangwood and Bhadeshia, 1987). that of bainite because it nucleates intragranularly in steels containing a greater number density of inclusions than austenite grain surface nucleation sites (Yang and Bhadeshia, 1986)....

336

It is believed that in ferritic steels, irradiation induces the formation of two kinds of dislocations, one of which is strongly biased whereas the other is neutral. This provides sinks for both interstitials and vacancies, resulting in a smaller excess of void-forming vacancies. There are differences in the void swelling resistance of creep-resistant ferritic steels because of variations in their microstructures. For a given vacancy concentration, a larger number density of vacancy traps leads...

71 The Matas and Hehemann Model

The transition between upper and lower bainite is believed to occur over a narrow range of temperatures. It is possible for both forms to occur simultaneously during isothermal transformation near the transition temperature (Pickering, 1967). Matas and Hehemann (1961) proposed that the difference between upper and lower bainite comes from a competition between the rate at which carbides can precipitate from ferrite and the speed with which carbon is partitioned from supersaturated ferrite into...

662 Growth Rate of Sheaves of Bainite

After nucleating at austenite grain surfaces, sheaves of bainite propagate by the repeated formation of sub-units, each of which grows to a limited size. New sub-units are favoured near the tips of existing platelets nucleation in adjacent positions occurs at a much lower rate. Therefore, the overall shape of the sheaf is also that of a plate in three dimensions with growth limited only by austenite grain or twin boundaries. Most direct observations have used optical microscopy and hence...

106

Fig. 4.12 (a) Solute concentration profile that develops during enrichment of cementite. c6a is the concentration in cementite which is in equilibrium with ferrite, (b) Size dependence of the cementite chemical composition, for particles extracted from a bainitic microstructure aged for 4 weeks at 565 C (Wilson, 1991). Detailed analysis shows that the scatter in the data is a consequence of the microanalysis technique. Fig. 4.12 (a) Solute concentration profile that develops during enrichment...

345

Fig. 13.2 The range of bainitic steels currently available on a commercial basis. TRIP stands for transformation-induced plasticity. Fig. 13.2 The range of bainitic steels currently available on a commercial basis. TRIP stands for transformation-induced plasticity. The tendency to soften depends on how far the original microstructure deviates from equilibrium (Table 13.3). Large deviations naturally lead to greater rates of softening because the driving force for tempering is the energy stored...

1286 Stress Corrosion Resistance

Cleavage fracture occurs when a critical stress is exceeded over a region ahead of the crack tip, such as to stimulate the growth of an existing microcrack. This critical stress can be reduced by environmental effects. Cleavage fracture then occurs at a critical stress intensity KISCC which is about a third of KIC. This means that stress corrosion can severely limit the effective use of high strength steels. The effect of corrosion manifests primarily via hydrogen embrittlement, the hydrogen...

261

10.6.1 Some Specific Effects of Allotriomorphic Ferrite We now proceed to consider a particular role of allotriomorphic ferrite formation in influencing the development of acicular ferrite in mixed microstructures. The effect is especially prominent in chromium- and molybdenum-containing steels. At relatively high concentrations of chromium (> 1.5 wt ) or molybdenum (> 0.5 wt ), the columnar austenite grains of steel weld deposits transform into bainite instead of acicular ferrite. The...

331 Partitioning and Distribution of Carbon

The carbon concentration of bainitic ferrite during transformation is of major importance in determining the kinetics of carbide precipitation. The transformation, however, occurs at high temperatures so excess carbon in the ferrite can be removed by precipitation or by partitioning into austenite. These two processes occur simultaneously, although one or the other may dominate depending on temperature. They can both be rapid because of the high mobility of carbon in iron. The partitioning of...

189

1968a), and in a Fe-4.08Cr-0.3C wt alloy which has a Bs temperature of 490 C. Ohmori and Honeycombe (1971) have shown that in a series of high purity Fe-0.16-0.81C wt alloys, lower bainite is not obtained when the carbon concentration is less than about 0.4 wt . Tsuzaki et al. (1991) found a similar result for Fe-Si-C alloys only upper bainite formed in a Fe-2Si-1Mn-0.34C wt steel, whereas both upper and lower bainite could be observed when a higher carbon variant (0.59 wt ) was examined. A...

142 The Weldability of Bainitic Steels

The region which is adjacent to the fusion zone of a weld is influenced by heat diffusion from the fusion zone. This region is the heat-affected zone (HAZ). Its boundaries need not be precisely defined because the definition depends on purpose. The heat dissipated into the HAZ can be detected as the temperature at any point rises to a maximum and then drops gently towards the far-field temperature. The severity of the heating or cooling cycles, and the peak temperature, depends on the location...

136 Steels with High Formability

The oil crisis of the seventies led to the development of the dual phase steels in an effort to reduce the weight of cars and make them fuel efficient. Fig. 13.10 (a) A light micrograph illustrating the effect of chemical segregation along the mid-thickness of heavy gauge plate. (b) Distribution of carbon concentration in the segregated zone for conventional control-rolled and rapidly cooled steel plates (Tamehiro et al., 1985c). Fig. 13.10 (a) A light micrograph illustrating the effect of...

118

Fig. 5.1 The chemical potentials ja and jb for components A and B respectively, in a solution containing a mole fraction x of B and 1 x of A. The potentials are given by the intercepts on the vertical axes of the tangent drawn at x to the curve representing the solution free energy. jA and jB are the molar Gibbs free energies of pure A and B respectively. Fig. 5.1 The chemical potentials ja and jb for components A and B respectively, in a solution containing a mole fraction x of B and 1 x of A....

239

Fig. 10.3 Nomarski interference contrast micrograph illustrating the displacements associated with the formation of acicular ferrite (Strangwood and Bhadeshia, 1987). Fig. 10.3 Nomarski interference contrast micrograph illustrating the displacements associated with the formation of acicular ferrite (Strangwood and Bhadeshia, 1987). et al.(1988) reported that the apparent plate thickness and length changed from about 1 to 2 m as the weld cooling rate was reduced.

247

Table 10.2 List of ceramics found to be chemically active in experiments designed to test for ferrite nucleation at ceramic steel bonds. Chemically Active Chemically Inactive Ti02 TiO, Ti203, TiC, TiB2, TiN in turn stimulates the nucleation of bainite. One such mineral is Ti02. Structural and behavioural analogues of Ti02 (Sn02, Mn02 and Pb02) are also found to stimulate bainite in the same manner. Ti02 and related minerals tend to form oxygen vacancy defects at elevated temperatures, thus...

35 Chemical Composition of Bainitic Carbides

It has long been established, using magnetic, chemical and X-ray methods on extracted carbides, that the cementite associated with upper bainite has a substitutional solute content which is close to, or slightly higher than that of Fig. 3.8 (a) The partition coefficient for chromium in cementite, when the cemen-tite is a part of bainite or pearlite, together with equilibrium data (Chance and Ridley, 1981). The partition coefficient is the ratio of the concentration in cementite to that in the...

109 Effect of Strain on the Acicular Ferrite Transformation

The distinguishing feature of acicular ferrite is that it must nucleate intragra-nularly on inclusions. The amount of acicular ferrite is reduced if the number density of grain boundary nucleation sites is increased relative to the number density of inclusions. The effect of deforming austenite prior to its transformation is to increase the nucleation potency and number density of the austenite grain boundaries. This is not helpful in promoting acicular ferrite. This is why the thermomechanical...

6113 Time TemperatureTransformation TTT Diagrams

Transformation curves on TTT diagrams tend to have a C shape because reaction rates are slow both at high and at low temperatures. The diffusion of atoms becomes difficult at low temperatures whereas the driving force for transformation is reduced as the temperature is raised. The phase diagram thus sets the thermodynamic limits to the decomposition of austenite (Fig. 6.31). Most TTT diagrams can be considered to consist essentially of two C curves, one for high temperatures representing...

357

C + Mn 6 + (Cr+Mo+V) 5 + (Ni+Cu) 15 wt Fig. 13.9 Relationship between the carbon equivalent and tensile strength for conventionally produced control-rolled steels and accelerated cooled steels the latter have a mixed microstructure of ferrite and bainite (Tamehiro et al., 1985a). Control-rolled steels are cast continuously so they contain pronounced chemical segregation along the mid-thickness of the plate. For example, the manganese concentration at the centre can reach twice the average...

134 Controlled Rolling of Bainitic Steels

The strengthening of iron via a reduction in grain size is an attractive option because a small grain size leads also to an improvement in toughness. This simple fact has led to the development of impressive thermomechanical processing technology capable of refining the austenite grain structure prior to its transformation to ferrite (Fig. 13.3). A fine austenite grain size leads to a correspondingly refined ferrite grain structure. The controlled-rolling process Fig. 13.3 Flow chart...

91

Fig. 4.1 The time scales associated with a variety of tempering phenomena for bainite. Fig. 4.1 The time scales associated with a variety of tempering phenomena for bainite. steels with a bainitic microstructure are slower than with martensite, because the coarser cementite particles take longer to dissolve (Woodhead and Quarell, 1965). Secondary hardening involves the replacement of metastable cementite with substitutional-solute-rich alloy carbides. When compared with martensite, bainite...

303

Theless be measured and if it is shown to be constant, then aF itself can be used as a measure of 'toughness' (Bowen et al., 1986), although it is not clear how possible variations in rc can be accounted for. A constant aF indicates that the critical step in the fracture process is the propagation of a microcrack. Bowen et al. used this approach, together with KIC studies to explain the toughness of tempered martensite and bainite in a low-alloy steel. In all cases, KIC values were found to...

6112 Precipitation in Secondary Hardening Steels

Whereas the analytical cases described above are revealing, it is unlikely in practice for the phases to be related in the way described. This is illustrated for secondary hardening bainitic and martensitic steels of the kind used commonly in the construction of power plant. The phases interfere with each other not only by reducing the volume available for transformation, but also by removing solute from the matrix and thereby changing its composition. This change in matrix composition affects...

11 The Discovery of Bainite

During the late 1920s, in the course of these pioneering studies on the isothermal transformation of austenite at temperatures above that at which martensite first forms, but below that at which fine pearlite is found, Davenport and Bain (1930) discovered a new microstructure consisting of an 'acicular, dark etching aggregate' which was quite unlike the pearlite or martensite observed in the same steel (Fig. 1.1). They originally called this microstructure 'martensite-troostite' since they...

257

Fig. 10.14 Calculations showing how the components of inclusions in welds change as the chemical composition is altered. Manganese and silicon oxides are progressively replaced by titanium oxide. When the oxygen has reacted completely with titanium, the latter begins to combine with nitrogen and helps to liberate boron. Fig. 10.14 Calculations showing how the components of inclusions in welds change as the chemical composition is altered. Manganese and silicon oxides are progressively replaced...

I2 14 16 18 20 22 24 Tempering parameter T20 logt

Fig. 4.7 Secondary hardening peak in a vanadium-containing bainitic steel (after Irvine and Pickering, 1957). The tempering parameter is defined with the absolute temperature T and the time t in hours. 1957). Whether or not peaks are observed in the tempering curves, the data are all consistent with secondary hardening because the tempering resistance is improved relative to plain carbon steels. It would be interesting to see whether it is possible to design a steel in which the bainite...

253 The Shape Change Further Considerations

In talking about the application of the phenomenological theory of martensite to bainite, the classical view (Hull, 1954 Bilby and Christian, 1956 Christian, 1962) that the experimentally observed invariant-plane strain shape deformation implies a coordinated movement of at least the iron and substitutional atoms was implicitly accepted. Given that there has been some confusion in the literature about the interpretation of this shape change, it is worth presenting an assessment of the...

316

For a high strength steel transformed isothermally to a mixed microstructure of bainite, martensite and retained austenite, Ritchie (1977a) found that the deformation-induced transformation of retained austenite to martensite reduced the reversibility of plastic strain during cyclic deformation, causing the cyclic yield strength to exceed the ordinary yield strength and consequently leading to a reduction in AK0 (Fig. 12.17). Later work on metastable austenitic stainless steel...

663 Growth Rate of Sub Units of Bainite

The growth rate of martensite can be so fast as to be limited only by the speed of sound in the metal. Although bainite grows rapidly, the lengthening rate is much smaller than that for martensite. The interface moves relatively slowly even though it is glissile. This is probably because of the plastic work that is done as the bainite grows. A good analogy is to compare brittle failure in a glass where cracks propagate rapidly, with cleavage failure in metals which is not as rapid because of...

194

(b) upper & lower bainite (c) no upper bainite (b) upper & lower bainite (c) no upper bainite 200 300 400 500 600 700 Temperature C 200 300 400 500 600 700 Temperature C 200 300 400 500 600 700 Temperature C 200 300 400 500 600 700 Temperature C 200 300 400 500 600 700 Temperature C 200 300 400 500 600 700 Temperature C Fig. 7.4 Illustration of how differences in the relative variation of the decarbur-isation time td and the precipitation time te can lead to (a) a steel which is incapable...

238

Fig. 10.2 Scanning transmission electron micrograph of a nonmetallic inclusion in a steel weld metal. The inclusion surface is very irregular, and it features many phases (after Barritte, 1982). Fig. 10.2 Scanning transmission electron micrograph of a nonmetallic inclusion in a steel weld metal. The inclusion surface is very irregular, and it features many phases (after Barritte, 1982). resulting dislocations are inherited by the acicular ferrite as it grows, giving a dislocation density which...

9 From Bainite to Austenite

Many commercial processes cause the steel to revert into the austenitic condition. The transformation of low-temperature ferrite into high-temperature austenite differs from the case where the latter transforms during cooling. Transformation during cooling follows a C curve kinetics in which the overall transformation rate goes through a maximum as a function of the undercooling below the equilibrium temperature. This is because diffusion coefficients decrease but the driving force increases as...

366

The drawing reduction is determined by the ability of the thinner, work-hardened section which leaves the die, to sustain the drawing force without further deformation. An alternative process achieves the reduction in section using inductive heating. The region of the rod which passes through the hot zone softens and is extended by the drawing force. It stops deforming on leaving the hot zone. The process avoids all the difficulties associated with die erosion and requires a smaller drawing...

123 Ratio of Proof Stress to Ultimate Tensile Strength

If a material does not exhibit a sharp yield point, then it is necessary to define a proof stress which is the stress needed to produce a specified amount of plastic strain (usually 0.2 ). The strain rate of the test should also be defined but this is usually neglected because for steels there is only a 10 increase in the flow stress with an order of magnitude change in strain rate (Knott, 1981). Sharp yield points are not observed in stress-strain curves of bainite so it is usual to specify...

681 Stability

In Fig. 6.20, xm represents the maximum concentration of carbon that can be tolerated in ferrite which precipitates from austenite of composition x. A higher concentration cannot be sustained because there would be an increase in free energy on transformation. Growth with partial supersaturation, such as the case where the interface compositions are given by x xm and x7 x is expected to be unstable to perturbations since the concentration field must tend to adjust towards lower free energy...

611 Transformation Start Temperature

Widmanstatten Ferrite

It is a common observation that the Widmanstatten ferrite-start (Wg) and bainite-start (Bs) temperatures are more sensitive to the steel composition than is the Ae3 temperature. This indicates that the influence of solutes on the nucleation of Widmanstatten ferrite and bainite is more than just thermodynamic (Fig. 6.3a). Some clues to this behaviour come from studies of time-temperature-transformation diagrams, which consist essentially of two C-curves. The lower C-curve has a characteristic...

62 Possible Mechanisms of Nucleation

Widmanstatten Ferrite

Phase fluctuations occur as random events due to the thermal vibration of atoms. An individual fluctuation may or may not be associated with a reduction in free energy, but it can only survive and grow if there is a reduction. There is a cost associated with the creation of a new phase, the interface energy, Fig. 6.6 (a) Free energy curves for the nucleation of Widmanstatten ferrite and bainite in a low alloy steel for which the AGm and GN curves exhibit a double intersection, (b) Calculated...

8

Civil Term With Diagram

Assumed that bainite growth is diffusionless, any carbon supersaturation in bainitic ferrite being relieved subsequent to growth, by partitioning into the residual austenite. The atomic mechanism of bainite growth was not discussed in detail, but he believed that unlike martensite, there is no strain energy associated with the growth of bainite. Thus bainite should form at a temperature just below T0, where the austenite and ferrite of the same composition have identical free energies (Fig....

321 Precipitation within Lower Bainitic Ferrite

There are many observations that reveal the precipitation of carbides from supersaturated lower bainite in a process identical to the tempering of martensite. In situ hot-stage transmission electron microscopy has shown that the lower bainitic ferrite remains supersaturated with carbon some time after the completion of the ferrite growth (Kang etal., 1990). Unlike the microstructure of tempered martensite, the carbides tend to adopt a single crystallographic variant in a given plate of lower...

255 The Structure of the Interface

It has already been pointed out that any atomic height steps in the bainitic austenite interface are transformation dislocations, with strain fields whose character can be specified by assigning a Burgers vector to each such dislocation. The motion of these steps (or coherency dislocations) which are in forced coherency, leads to phase change there is continuity of planes and vectors across the steps so that regions of the parent lattice are homogeneously deformed into that of the product as...

139 High Strength Bainitic Steels without Carbides

We have seen in Chapters 2 and 3 that an interesting microstructure results when a silicon or aluminium-alloyed steel is transformed into upper bainite. The carbon that is partitioned into the residual austenite does not precipitate as cementite, but remains there to make the austenite stable at ambient temperature. The microstructure obtained consists of fine plates of bainitic ferrite separated by carbon-enriched regions of austenite (Fig. 13.21). The potential advantages of this mixed...

449

Carbide enrichment 107-8 concentration 9 distribution 71-2 equivalent 388, 398-9 partitioning 71-2, 150-2 redistribution 8 cast irons 388-96 CCT see continuous cooling transformation bainitic ferrite heating 234-5 coarsening 98-100 composition 101-8 cooperative growth 161-2 habit planes 77 orientation relationship 76-7 precipitation kinetics 191-4 Charpy test 298-300 chemical composition alloying elements 29-35 carbides 85-8 chemical driving forces 202-4 chemical potential 118-22 chemical...

682 The Interface Response Functions

6.8.2.1 The Interface Mobility (Martensitic Interface) The interfacial mobility is formulated using the theory for thermally activated motion of dislocations (Olson et al., 1989, 1990). This is justified because a glissile interface consists of an array of appropriate dislocations. The interfacial velocity Vi is then given by where G* is an activation free energy and the pre-exponential factor V0 can be taken to be 30 ms-1 based on experimental data from single-interface martensitic...

612 Evolution of the Nucleus

Widmanstatten Ferrite

The nucleus is identical for Widmanstatten ferrite and for bainite it must therefore be growth which distinguishes them. But what determines whether the nucleus evolves into bainite or Widmansstatten ferrite Fig. 6.4 The free energy change necessary in order to obtain a detectable degree of transformation. Each point represents a different steel and there is no distinction made between Widmanstatten ferrite or bainite. (a) Calculated assuming the partitioning of carbon during nucleation. (b)...

5

Fig. 1.2 An example of the results obtained by Greninger and Troiano (1940), showing the irrational habit of bainite, which changed as a function of the transformation temperature. Notice also that the habit plane of bainite is different from that of martensite in the same steel. Fig. 1.2 An example of the results obtained by Greninger and Troiano (1940), showing the irrational habit of bainite, which changed as a function of the transformation temperature. Notice also that the habit plane of...

810 Stress Affected Carbide Precipitation

The idea that cementite at low temperatures precipitates by a displacive mechanism with only the partitioning of carbon is not unnatural - this mechanism has been demonstrated for the precipitation of vanadium hydride (Bowles et al, 1977). The evidence for cementite has been discussed in Chapter 3. Although the shape deformation associated with precipitation has yet to be measured, it is believed to be an invariant-plane strain with a shear of 0.211 parallel to the habit plane and a...

315

Significance because many cracked components spend a good proportion of their fatigue life in that region. The threshold value of AK i.e. AK0 correlates directly with the cyclic yield strength Fig. 12.16 which is in general less than the yield strength as measured in a uniaxial tensile test Ritchie, 1979 . The sensitivity of AK0 to strength decreases as the mean stress amplitude increases. This correlation is expected because the plastic zone at the fatigue crack tip is subject to alternating...

291

Fig. 12.4 Variation in the tensile strength of structural steels as a function of the temperature at which the rate of transformation is greatest during continuous cooling heat treatment Irvine et al., 1957 . Fig. 12.4 Variation in the tensile strength of structural steels as a function of the temperature at which the rate of transformation is greatest during continuous cooling heat treatment Irvine et al., 1957 . Bauschinger effect. A simple explanation is that deformation creates reversible...

433

International Metals Reviews 4 1979 205-230. Ritchie, R. O., Knott, J. F. and Rice, J. R. J. Mech. Phys. Sol. 21 1973 395-400. Ritchie, R. O., Moss, C. M. and Suresh, S. J. Engng. Materials Technology Trans. ASME, H 102 1980 293. Ritchie, R. O., Parker, E. R., Spencer, P. N. and Todd, J. A. J. Materials for Energy Systems 6 1984 151-162. Roberts, C. S., Averbach, B. L. and Cohen, M. Trans. ASM 45 1957 576. Roberts, M. J. Metall. Trans. 1 1970 3287-3294. Robertson, J. M. Journal...

45 Secondary Hardening and the Precipitation of Alloy Carbides

Secondary hardening is usually identified with the tempering of martensite in steels containing strong carbide forming elements like Cr, V, Mo and Nb. The formation of these alloy carbides necessitates the long-range diffusion of sub-stitutional atoms and their precipitation is consequently sluggish. Carbides like cementite therefore have a kinetic advantage even though they may be meta-stable. Tempering at first causes a decrease in hardness as cementite precipitates at the expense of carbon...

Nishiyama Wasserman Orientation Relationship

Bain Orientation Relationship

Little misorientation between the plates within any given sheaf. Where they touch, adjacent plates are separated by low-misorientation grain boundaries. The relative orientations of the bainitic ferrite and its parent austenite are always close to the classic KS Kurdjumov-Sachs, 1930 and NW Nishiyama-Wasserman, 1934 relationships Fig. 2.16 , although as will become evident later, they can never be exactly KS or NW. These two rational relations differ only by a relative rotation of 5.26 about...