Volume 09 - Metallography and Microstructures Part 16 ppt

As mentioned earlier, this is because a clearly defined subgrain structure can be observed in a thin-foil specimen parallel to the rolling plane only when the thickness of the subgrains

Fig 8 Annealed at 400 °C (750 °F) for

1280 min Reduced dislocation density and random arrays of dislocations are evident

Fig 10 Annealed at 800 °C (1470 °F)

for 5 min Increased average diameter

of the subgrains is due to subgrain growth

Fig 7 High density of dislocations

and no well-defined cell structure is

revealed in the as-rolled condition

Fig 9 Annealed at 600 °C (1110 °F) for

1280 min Well-defined subgrains resulting

from polygonization are shown

Effect of annealing time and temperature on the microstructure of an Fe-3Si single crystal, cold rolled 80% in the (001)[110] orientation Thin-foil TEM specimens prepared parallel to the rolling plane All at 17,2000×

When the microstructure of a heavily rolled crystal is revealed using thin-foil specimens parallel to the cross sections of the strip, the thin, ribbon-like deformation cells are readily observed Figure 11 shows the dislocation substructure of an as-deformed iron crystal cold rolled in the (111)[110] orientation to 70% reduction (see also Fig 4 for a much finer microstructure in a heavily rolled polycrystalline stainless steel) During recovery, the thickness of the ribbon-like subgrains increases, as shown in Fig 12 Subgrain growth at these early stages cannot be clearly observed when thin-foil specimens parallel to the rolling plane are used for transmission electron microscopy examination As mentioned earlier, this is because a clearly defined subgrain structure can be observed in a thin-foil specimen parallel to the rolling plane only when the thickness of the subgrains exceeds that of the foil

Fig 11 Fig 12

Electrolytic iron single crystal, cold rolled 70% in the (111)[ 110] orientation Fig 11: thin, ribbon-like cells stacked up in the thickness dimension of the as-rolled crystal Fig 12: annealed at 550 °C (1020 °F) for 20 min Increased cell thickness resulting from subgrain growth Thin-foil TEM specimens prepared parallel to the transverse cross section Both at 11,000× (Ref 4)

References cited in this section

2 R.R Eggleston, J Appl Phys., Vol 23, 1952, p 1400

3 J.T Michalak and H.W Paxton, Trans AIME, Vol 221, 1961, p 850

4 B.B Rath and H Hu, in Proceedings of the 31st Annual Meeting of the Electron Microscopy Society of America, San Francisco Press, 1973, p 160

Recrystallization

Following recovery, recrystallization (or primary recrystallization) occurs by the nucleation and growth of new grains, which are essentially strain-free, at the expense of the polygonized matrix During incubation, stable nuclei are formed by the coalescence of subgrains that leads to the formation of high-angle boundaries From that time on, subsequent growth

of new grains can proceed rapidly, because of the high mobility of the high-angle boundaries The rate of recrystallization later decreases toward completion as concurrent recovery of the matrix occurs and more of the new grains impinge upon each other Accordingly, isothermal recrystallization curves are typically sigmoidal (see Fig 24 and 30) Because recrystallization is accomplished by high-angle boundary migration, a large change in the texture occurs

Sufficient deformation and a sufficiently high temperature of annealing are required to initiate recrystallization following recovery With a low degree of deformation and a low annealing temperature, the specimen may recover only without the

occurrence of recrystallization In situ recrystallization, or complete softening without the nucleation and growth of new

grains at the expense of the polygonized matrix, is a process of recovery, not recrystallization, because it does not involve

high-angle boundary migration Consequently, there is no essential change in texture following in situ recrystallization

Nucleation Sites. Because of the highly nonhomogeneous microstructure of a plastically cold-worked metal, recrystallization nuclei are formed at preferred sites Examples of preferred nucleation sites include the original grain boundaries; the boundaries between deformation bands within a crystal or grain; the intersections of mechanical twins, such as Neumann bands in body-centered cubic crystals; the distorted twin-band boundaries; and the regions of shear bands Limited recrystallization may also occur by the growth of grains nucleated at large and hard inclusion particles

In general, preferred nucleation sites are regions of relatively small volume where the lattice is highly distorted (having high lattice curvature) In such regions, the dimension of the substructure is fine, and the orientation gradient is high Therefore, the critical size for a stable nucleus to form in these regions is relatively small and so can be attained more readily Furthermore, the nucleus needs only to grow through a relatively short distance to form a high-angle boundary with the matrix

Figure 13 shows recrystallized grains formed in the boundary region between two main deformation bands in a crystal of Fe3Si that was cold rolled 80% in the (001)[100] orientation, then annealed at 600 °C (1110 °F) for 25 min What appears

as a thin-line boundary between main deformation bands in an optical micrograph (Fig 13) actually contains a group of narrow, elongated, microband segments, among which nucleation occurs by the coalescence of the segments into a recrystallized grain (Fig 14) Nucleation in such microband regions is also termed transition band nucleation, because the large orientation difference between the main deformation bands is accommodated in small steps by the microband segments In heavily deformed polycrystalline specimens, such transition regions must exist between different deformation texture components, but they may not be as clearly defined and readily identified as in the similarly deformed specific single-crystal specimens

Fig 13 Fe-3Si single crystal, cold rolled 80% in the (001)[100] orientation and annealed at 600 °C (1110 °F)

for 25 min Optical micrograph shows recrystallized grains formed at boundaries (microband region or transition bands) between the main deformation bands See also Fig 16 5% nital 400×

Fig 14 Fe-3Si single crystal, cold rolled 80% in the(001)[100] orientation and annealed at 600 °C (1110 °F)

for 125 min Transmission electron micrograph showing a recrystallized grain grown from the microband region (transition bands) Thin-foil specimen prepared parallel to the rolling plane Compare with Fig 15 14,740×

Figures 15 and 16 show the nucleation of recrystallized grains in heavily rolled polycrystalline copper by the coalescence

of subgrains in the microband regions These micrographs, which were obtained from thin-foil specimens prepared parallel to the cross section of the sheet, show the evolution of the microstructure in nucleation When thin-foil specimens prepared parallel to the rolling plane of the heavily rolled sheet are used for nucleation studies, the characteristics of the nucleation site cannot be defined with certainty (Fig 17 and 18)

Fig 15 Fig 16

Electrolytic copper, cold rolled 99.5% Fig 15: annealed at 100 °C (212 °F) for 625 min Recrystallization nuclei formed among microbands are shown 17,100× Fig 16: annealed at 100 °C (212 °F) for 25 min Recrystallization nuclei formed among microbands by subgrain coalescence are shown 34,200× Both thin-foil TEM specimens prepared parallel to the transverse section

Fig 17 Low-carbon steel, cold rolled 70% and annealed at 450 °C (840 °F) for 260 h and 42 min

Well-developed recrystallized grains and recrystallization nuclei during their formation by subgrain coalescence in the recovered matrix still exhibit a "messy" substructure Thin-foil TEM specimen prepared parallel to the rolling plane 7,020×

Fig 18 Type 304L stainless steel, cold rolled 90% at 25 °C (75 °F) and annealed at 600 °C (1110 °F) for 1 h

Early recrystallized grains with annealing twins in a highly "messy" matrix Thin-foil TEM specimen prepared parallel to the rolling plane 21,600× (Ref 5)

In moderately deformed samples with relatively coarse initial grains, the microstructure near the grain boundaries and the evolution of the microstructure during nucleation can be studied in considerable detail, even when thin-foil specimens parallel to the rolling plane are used for transmission electron microscopy examinations Figure 19 shows the grain-boundary bands observed adjacent to an initial grain boundary in commercial-purity aluminum that was cold rolled 50% The cumulative misorientations across the bands (16.5°), as shown in the inset, indicate similarity in feature between these grain-boundary bands and the transition bands described earlier These grain-boundary bands obviously would not form at every grain boundary, but would depend on the relative orientations of the two adjacent grains

Fig 19 Fine-grained commercial-purity aluminum, cold rolled 50% A 9-μm wide grain boundary band

consisting of elongated subgrains that was developed along an initial grain boundary marked by arrows The inset shows the misorientations regarding the grain interior as a function of the distance from the grain boundary Thin-foil TEM specimen prepared parallel to the rolling plane 7,300× (Ref 6)

Grain-boundary nucleation by the "bulging out" of a section of an initial boundary from the region of a low dislocation content into a region of high dislocation content is frequently observed in large-grained materials deformed at low and medium strains This bulging mechanism of nucleation for recrystallization is a consequence of the strain-induced boundary migration Figure 20 shows a recrystallization nucleus that has formed by straddling a grain boundary in a coarse-grained aluminum that was cold rolled 30% and annealed at 320 °C (610 °F) for 30 min Such grain-boundary nucleation was observed to have three types of structural detail As shown in Fig 21, the nucleus may be formed by subgrain growth to the right of the original grain boundary (Fig 21a), by grain-boundary migration to the right and subgrain growth to the left forming a new high-angle boundary (Fig 21b), and by grain-boundary migration to the right and subgrain growth to the left but without forming a new high-angle boundary (Fig 21c)

Fig 20 Coarse-grained commercial-purity aluminum cold rolled 30% and annealed at 320 °C (610 °F) for 30

min A recrystallization nucleus (denoted A) developed near arrow-marked FeAl3 particles, and is shown straddling an initial grain boundary (marked by dotted line) Thin-foil TEM specimen prepared parallel to the

rolling plane 3,650× (Ref 6)

Fig 21 Schematic showing three types of grain-boundary nucleation and the growth of the nucleus (N) at the

expense of the polygonized subgrains See text for detailed explanation (Ref 6)

When a polycrystalline specimen is deformed to a very small strain less than 2 or 3%, for example then annealed at a sufficiently high temperature, recrystallization occurs by strain-induced boundary migration of only a few grains These few grains grow very large at the expense of the small matrix grains The maximum level of strain below which such coarsening occurs is commonly termed critical strain This behavior has been used to grow single crystals in the solid state by the so-called "strain-anneal" technique

Figure 22 shows recrystallized grains nucleated and grown at a large and hard FeAl3 inclusion particle in 90% cold-rolled aluminum after annealing in the high-voltage electron microscope at 264 °C (507 °F) for 480 s Unless the volume fraction of the inclusion particles is substantially large, the contribution of particle-nucleated grains constitutes only a small fraction of the total recrystallization volume From the above discussions on nucleation sites, it is easy to understand that the size of the recrystallized grains, as recrystallization is complete, decreases with increasing deformation, because the number of nuclei increases with increasing deformation

Fig 22 Fine-grained commercial-purity aluminum, cold rolled 90% and heated in a high-voltage electron

microscope at 264 °C (507 °F) for 480 s Recrystallized grains (denoted by letters) nucleated at a large FeAl 3 particle and grown into the polygonized matrix Thin-foil TEM specimen prepared parallel to the rolling plane 2,810× (Ref 6)

Growth of Nucleated Grains. The growth of the newly formed strain-free grains at the expense of the polygonized matrix is accomplished by the migration of high-angle boundaries Migration proceeds away from the center of boundary curvature The driving force for recrystallization is the remaining strain energy in the matrix following recovery This strain energy exists as dislocations mainly in the subgrain boundaries Therefore, the various factors that influence the mobility of the high-angle boundary or the driving force for its migration will influence the kinetics of recrystallization For example, impurities, solutes, or fine second-phase particles will inhibit boundary migration; therefore, their presence will retard recrystallization Figure 23 shows the pinning of a mobile low-angle boundary by a fine alumina (Al2O3) particle in an aluminum-alumina specimen during recovery In connection with the driving force for recrystallization, a fine-subgrained matrix has a higher strain-energy content than does a coarse-subgrained matrix Accordingly, recrystallization occurs faster in a fine-subgrained matrix than in a coarse-subgrained matrix During recrystallization, continued recovery may occur in the matrix by subgrain growth, resulting in a reduction of the driving energy for recrystallization and therefore a decrease in the recrystallization rate From driving energy considerations, it is understandable that the tendency for recrystallization is stronger in heavily deformed than in moderately or lightly deformed specimens For a given deformation, the finer the original grain size the stronger the tendency for recrystallization Figure 24 shows such effects in low-carbon steel

Fig 23 Aluminum-aluminum oxide specimen, cold rolled and annealed Shown is the pinning of a mobile

low-angle boundary by a small Al2O3 particle during a recovery anneal Thin-foil TEM specimen 47,000× (Ref 7)

Fig 24 Effect of penultimate grain size on the recrystallization kinetics of a low-carbon steel, cold rolled 60%

and annealed at 540 °C (1005 °F) Note the incubation time is shortened as the penultimate grain size before cold rolling is decreased (Ref 8)

References cited in this section

5 S.R Goodman and H Hu, Trans Met Soc AIME, Vol 233, 1965, p 103; Vol 236, 1966, p 710

6 B Bay and N Hansen, Met Trans A, Vol 10, 1979, p 279; Vol 15A, 1984, p 287

7 A.R Jones and N Hansen, in Recrystallization and Grain Growth of Multiphase and Particle Containing Materials, N Hansen, A.R Jones, and T Leffers, Ed., Riso National Laboratory, Denmark, 1980, P 19

8 D.A Witmer and G Krauss, Trans ASM, Vol 62, 1969, p 447

Normal or continuous grain growth occurs in pure metals and single-phase alloys During isothermal growth, the increase in the average grain diameter obeys the empirical growth law, which can be expressed as D = Kt n where D ¨is

the average grain diameter, t is the annealing time, and K and n are parameters that depend on material and temperature

Therefore, when D and t are plotted on a logarithmic scale, a straight line should be obtained, with K as the intercept and

n the slope The value of n, the time exponent in isothermal grain growth, is usually less than, or at most equal to, 0.5 A

typical example for isothermal grain growth in zone-refined iron is shown in Fig 25 The deviation from a straight-line relationship for very short annealing times at low temperatures is due to recrystallization, and that for long annealing times at high temperatures is due to the limiting effect of the sheet specimen thickness

Fig 25 Normal grain growth in zone-refined iron during isothermal anneals Closed circles represent specimens

for which statistical analysis of grain-size and grain-shape distributions was conducted

One of the structural characteristics during normal grain growth is that the grain size and grain-shape distributions are essentially invariant; that is, during normal grain growth, the average grain size increases, but the size and shape distributions of the grains remain essentially the same before and after the growth, differing only by a scale factor Figures

26 and 27 show, respectively, the size and shape distributions of the grains in zone-refined iron after normal grain growth

at 650 °C (923 K) for various lengths of time The data points fit the same distribution curves Therefore, to a first approximation, normal grain growth is equivalent to photographic enlargement

Fig 26 Grain-size distribution in zone-refined iron during isothermal grain growth at 650 °C (923 K), using a

scalar-adjusted grain diameter for each specimen The plot indicates that the grain-size distribution remains essentially unchanged during normal grain growth

Fig 27 Grain-shape distribution in zone-refined iron during isothermal grain growth at 650 °C (923 K), using

the number of sides of individual grains The plot indicates that the grain-shape distribution remains essentially unchanged during normal grain growth

During the normal grain growth, the change in texture is small and gradual Assuming the initial grains are nearly random-oriented, after extensive normal grain growth some weak preferred orientations may be developed among the final grains, depending on such factors as the energies of the free surfaces of the grains If the initial grains are strongly textured, normal grain growth may be inhibited as a consequence of low mobility of the matrix-grain boundaries (see the next section of this article) Figure 28 shows the grain aggregate of a zone-refined iron specimen after normal grain growth at 800 °C (1470 °F) for 12 min The size and shape distributions of these grains are essentially the same as those

of the much finer grains before growth

Fig 28 Zone-refined iron, cold rolled to a moderate reduction and annealed for recrystallization for several

cycles to refine the penultimate grain size without introducing preferred orientation Micrograph shows grain structure after normal grain growth at 800 °C (1470 °F) for 12 min 2% nital 45×

Abnormal grain growth, or secondary recrystallization, occurs when normal growth of the matrix grains is inhibited and when the temperature is high enough to allow a few special grains to overcome the inhibiting force and to grow disproportionately The commonly known conditions for inhibiting grain growth are a fine dispersion of second-phase particles, a strong single-orientation texture, and a stabilized two-dimensional grain structure imposed by sheet thickness These conditions for inhibiting grain growth are readily understandable, because the fine particles exert a pinning force on the boundary motion, the matrix grain boundaries are predominantly low-angle boundaries, and therefore both low mobilities and the boundary grooving at the sheet, surfaces retard boundary motion

Figure 29 shows abnormal grain growth or secondary recrystallization in the cube-textured matrix of a type 304 stainless steel The cube-textured matrix is characterized by the small grains; the twin traces within the cube grains are oriented at 45° to the rolling direction This particular example of abnormal grain growth or secondary recrystallization in cube-textured type 304 stainless steel probably represents the combined effect of particle-inhibition and texture-inhibition on secondary recrystallization

Fig 29 Type 304 stainless steel, rolled 90% at 800 °C (1470 °F) to produce a copper-type rolling texture,

recrystallized to cube texture by annealing at 1000 °C (1830 °F) for 30 min, then annealed at 1000 °C (1830

°F) for 96 h to cause secondary recrystallization Large secondary grains are shown in a cube-textured primary matrix Rolling direction: left to right Electrolytic etch 20× (Ref 5)

Like primary recrystallization, secondary recrystallization consists of nucleation and growth Stable nuclei of the secondary grains are formed during incubation In the case of high-permeability, grain-oriented silicon steel, secondary recrystallization nuclei have been reported to form by the coalescence of the (110) oriented grains Subsequent growth of the newly formed secondary grains is by the migration of high-angle boundaries Consequently, a large change in texture results Therefore, the characteristic features of primary and secondary recrystallizations are similar However, the driving energy for secondary recrystallization, in contrast to the strain energy for primary recrystallization, is the grain-boundary energy of the primary grains, which is much smaller than the strain energy after recovery Figure 30 shows the kinetics of secondary recrystallization in Fe-3Si for the formation of a cube-textured sheet by isothermal annealing at 1050 °C (1920

°F) Being similar to the kinetics of primary recrystallization, the curve is sigmoidal

Fig 30 Kinetics of secondary recrystallization for cube texture formation in Fe-3Si during isothermal annealing

at 1050 °C (1920 °F) The characteristics of this curve for secondary recrystallization are quite similar to those for primary recrystallization (Ref 9)

References cited in this section

5 S.R Goodman and H Hu, Trans Met Soc AIME, Vol 233, 1965, p 103; Vol 236, 1966, p 710

9 F Assmus, K Detert, and G Ibe, Z Metallkd, Vol 48, 1957, p 344

Typical microstructures of 4-79 Moly Permalloy (4Mo-79Ni-17Fe) Fig 1: Cold working has produced elongated grains and a textured structure Fig 2: Although annealing after working has produced

equiaxed grains, this structure is also textured Electrolytic etchant: H3PO4 saturated with Cr2O3 85×

In general, crystals are anisotropic with respect to properties; thus, control of texture is important, because it provides a means for optimizing desired properties in given directions in a polycrystalline metal For example, a single crystal of iron is magnetized easily in the cube direction; that is, the [001] direction is parallel to the rolling direction This phenomenon is important in the manufacture of iron-silicon transformer sheet

Grain-oriented transformer sheet, in which the cube directions of the grains are closely aligned in the rolling direction (the direction of magnetization), exhibits magnetic properties that are superior to those of sheet with randomly oriented grains However, the texture developed in transformer sheet is undesirable for drawing When grain-oriented transformer sheet is drawn into the shape of a cup, unwanted "ears" are produced These ears, which must be trimmed, form because the sheet

is anisotropic with regard to mechanical as well as magnetic properties Thus, the sheet is weaker or softer in given directions; when stressed in these directions greater metal flow occurs, causing the ears to form Micrographs of grain-oriented silicon steels can be found in the article "Magnetic and Electrical Materials" in this Volume

As shown in Table 1, several physical and mechanical properties are influenced by crystal direction Consequently, in polycrystalline metals, the same properties are similarly affected by texture

Table 1 Dependence of mechanical and physical properties on crystal direction

Property (a) Metal Crystal direction Value of property

<111> 193,000 MPa (28 × 106 psi) Young's modulus Copper

Magnetic-flux density Cobalt c-axis 1.8 T (8, 000 G)(b)

coefficient of friction, magnetic-flux density (below saturation), magnetic permeability, magnetostriction The following properties are isotropic for cubic crystals: coefficient of thermal expansion, thermal conductivity, electrical resistivity, dielectric constant Thomson coefficient, Peltier coefficient, index of refraction

(b) At a magnetic field strength of 1.6 × 10 A/m (2016 Oe)

Origins of Texture

Texture may develop in a metal during such processing operations as metal-film deposition, casting, plastic deformation, and annealing Films prepared by sputtering, electrodeposition, or chemical vapor deposition frequently exhibit texture The mechanisms of texture formation in metal films are complex and not well understood In castings, the long grains of the columnar zone are usually textured, and the equiaxed grains in the central zone exhibit a more random orientation A discussion of the origins of orientation in cast structures can be found in the article "Solidification Structures of Steel" in this Volume

During plastic deformation of a cast ingot or a deformed and annealed metal specimen, the crystalline lattice rotates toward one or more stable (preferred) orientations, thus establishing a deformation texture Lattice rotation occurs by slip

or twinning (Fig 3) The final deformation texture for a given specimen depends primarily on the initial grain orientation, the change in shape imposed on the specimen, and the temperature at which the specimen is deformed

Fig 3 Schematic of lattice rotation during compression Slip planes in specimen (a) are tilted toward

compression plane (b and c)

When a deformed metal is annealed, recovery or recrystallization occurs, depending on the annealing temperature In general, annealing at low temperatures results in recovery, with little change in texture At higher annealing temperatures, primary recrystallization occurs The texture of the recrystallized structure is generally different from, but related to, the deformation texture

At still higher annealing temperatures, some grains exhibit significant grain growth, thus consuming surrounding grains This process, known as secondary recrystallization, reduces the grain-boundary surface area and therefore the energy of the workpiece This results in the formation of still different textures

Types of Texture

Fiber texture exhibits rotational symmetry around an axis Ideally, a single crystallographic direction in each grain is aligned parallel to a specimen direction called the fiber axis The grains are randomly aligned in the plane normal to the fiber axis The fiber axis may be the growth direction of columnar grains in a casting, the axial direction of a drawn wire,

or the axis normal to the surface of a compressed (rolled) sheet Figure 4(a) illustrates a <100> fiber texture in wire

Fig 4 Schematic of (a) <100> fiber texture in wire and (b) {110} <112> sheet texture Positions of unit cells

in the wire and the sheet represent orientations of several grains

Generally, there is considerable scatter around the ideal orientation Also, two or more directional components may appear; some grains may be aligned in a given direction parallel to the fiber axis, while others are aligned in a different direction

Sheet texture exhibits three mutually perpendicular mirror planes of symmetry Although commonly observed in rolled sheet, sheet texture is not restricted to sheet Extruded tubing and flattened wire also exhibit sheet textures

Two parameters are generally used to describe a sheet texture: a plane in the specimen that coincides with one of the symmetry planes and a symmetry direction in that plane In rolled sheet, the rolling plane and the rolling direction have been adopted as reference parameters Thus, the designation {110} <112> for a rolled sheet texture signifies that the grains have a {110} plane parallel to the rolling plane and a <112> direction parallel to the rolling direction This texture

is illustrated in Fig 4(b) In this specimen, all variants of a texture (110)[ 112] and (110)[11 2] are represented

Texture Control

The desirability of a specific texture depends on the desired properties, the directions in which these properties are optimum, and the direction of intended use for any given engineered material or alloy Selection of a manufacturing process usually depends on several variables Brittle materials cannot be deformed, and therefore the desired textures must be developed by casting, powder metallurgy techniques, or electrodeposition Techniques of directional solidification can be used to enhance casting texture by favoring columnar grain growth

Alnico permanent magnets are examples of alloys in which the desired texture is achieved by casting In these alloys, the direction of intended use coincides with the optimum direction for the property involved To ensure optimum matching of direction, it may be necessary to alter the direction of heat flow during solidification, to change the direction of growth by adding another element, or to employ seeding techniques using a properly oriented seed crystal

Powder metallurgy techniques that incorporate conventional compaction and sintering usually do not produce textures However, if some or all of the metal powders are magnetic, application of a magnetic field prior to and during compaction will orient the magnetic powder particles and cause a texture to develop This magnetizing technique is applied commercially in the production of ferrite and Co5Sm permanent magnets The application of a uniaxial stress during compaction may also orient the particles mechanically to ensure texture

Combining several types of deformation processing offers a means of developing various deformation textures A narrow strip, for example, may be produced by conventional rolling followed by slitting or by wiredrawing followed by flattening The textures developed by these two processing sequences usually are different Intermediate annealing operations, normally performed to soften a workpiece for further deformation, can also be used for additional texture control similar to that obtained through recovery or recrystallization

Random orientation in a casting can be obtained by chill casting or by ultrasonic vibration or mechanical stirring during solidification Appreciable deformation textures in wrought products do not develop at strains of less than 50% and thus can be suppressed by appropriate cycles of straining and annealing at moderate temperatures

Characterization of Textures

Because physical and mechanical properties such as Young's modulus and magnetic-flux density are affected by crystal direction (see Table 1), texture can be investigated by measuring these properties However, although the dependence of a property on direction often can be calculated if the texture is known, the reverse is generally not true Furthermore, factors other than texture may be the cause of the observed dependence on direction For example, properties that involve plastic deformation, such as tensile yield strength and elongation, are affected by alignment of second-phase particles (mechanical fibering) as well as by crystallographic texture

Texture can be investigated directly by x-ray, electron, or neutron diffraction Electron diffraction is generally limited to thin-film samples less than 100 nm (1000 Ao ) thick Because of the much lower absorption coefficient for neutrons compared to x-rays, neutron diffraction can be used to study thick specimens (several millimeters) without a large absorption correction

Nevertheless, x-ray diffraction is usually preferred because of the general availability of equipment Also, specimens of convenient size can be examined in the laboratory X-ray diffraction can be applied to thin samples in the transmission mode and thick samples in the reflection mode The latter, however, samples only the surface grains

The Laue x-ray technique of orienting single crystals is widely used, and the diffraction camera and other equipment used are readily available in x-ray diffraction laboratoratory The Laue technique can be used to determine the orientation

of individual grains in polycrystalline specimens by transmission (thin specimens) or by reflection (thick specimens) Generally, it is limited to relatively coarse grains (average dimension ≥1 mm, or 0.04 in.) In the Laue camera, the size of the collimated beam required for smaller grains necessitates excessively long exposure times This technique may be used for specimens deformed at small to moderate strains, but the Laue spots become diffuse after large strains

Pinhole photography uses the same apparatus as the Laue technique Instead of impinging white radiation on a single grain, as in the Laue technique, a pinhole photograph is obtained by impinging characteristic (monochromatic) radiation

on a large number of grains Again, both transmission and reflection modes are possible

Figure 5 schematically illustrates transmission through a thin wire The various crystallographic planes diffract to form concentric rings, called Debye rings, on the film A uniform intensity of the Debye rings is indicative of random orientation, except when the x-ray beam coincides with the direction of the fiber axis in a specimen having a fiber texture

To ensure that random orientation is the cause of uniformly intense Debye rings, two or more pinhole photographs should

be taken, each with the specimen tilted at a slightly different angle (10° variation, for example)

Fig 5 Schematic of pinhole photography The diameter, U, of each Debye ring equals 2D tan 2θ, where D is the

distance from the specimen to the film and 2θ is the diffracted angle

A nonuniform intensity of the Debye rings is an almost certain indication of texture, which can be analyzed quantitatively

by examining the positions of the intensity maximums Transmission pinhole photographs of iron-nickel alloy wires, made using zirconium-filtered Moκα radiation, are shown in Fig 6 and 7

Figure 8 shows the intensities obtained from specimens of randomly oriented and textured material Diffraction-line intensities determined by the diffractometer technique refer to crystal planes parallel to one plane of the specimen only (the surface of a sheet, for example) However, the most thorough investigation of texture requires pole-figure techniques

Fig 8 Diffractometer traces of two compacted-powder specimens of permanent magnet alloy

Co 3.45 Fe 0.25 Cu 1.35 Sm The Miller indices of the basal planes are marked on the graph Note the high line intensity of the basal planes in the specimen oriented in a magnetic field during compacting

diffraction-Pole-Figure Techniques. A pole figure is a stereographic projection that shows the distribution of poles, or plane normals, of a specific crystalline plane, using specimen axes as reference axes These techniques are widely used for examining sheet textures For example, in examining a sheet specimen, all directions in the plane of the sheet (rolling plane) are projected as points on the circumference of the pole-figure circle (Fig 9)

Fig 9 Schematic of pole-figure representation of crystal orientation In (a) a crystal unit cell is aligned as

shown (b) and (c) are pole figures showing positions of poles in (a), represented by arrows emanating from the center of the unit cell RD, rolling direction; TD, transverse direction; ND, normal direction

The rolling direction is usually located at the top, and the transverse direction is usually designated at the right of the pole figure The center of the circle corresponds to the direction normal to the plane of the sheet (normal direction) Directions lying at angles between the normal direction and the rolling plane project as points inside the circle

As a simple illustration, consider a unit cell of a single grain oriented in the sheet so that the (100) plane is parallel to the plane of the sheet and so that the two cube directions in the (100) plane [010] and [001] are aligned in the transverse and rolling directions, respectively This is illustrated by the position of the unit cell in Fig 9(a) The poles of the cube planes, which can be projected in the pole figure, are marked by arrows 1 to 5

A {100} pole figure, showing the positions of these poles, is illustrated in Fig 9(b) The {111} poles of the same crystal are marked by arrows 6 to 9 The {111} pole figure then appears as shown in Fig 9(c) Both pole figures indicate the same orientation of the unit cell; they appear different only because poles of different planes are used A pole figure is always specified by the Miller indices of the poles

Pole-figure construction by point plotting, as illustrated in Fig 9, is useful for coarse-grained specimens, in which the orientation of each grain can be determined by Laue photography For fine-grained material, the intensity data usually are presented as contours of equal value Generally, the intensity value of each contour is expressed as the ratio of the value measured for a textured specimen to the value for a randomly oriented specimen

Data are conveniently gathered with commercially available automatic pole-figure goniometers With the diffraction angle fixed at the desired pole position, the pole-figure goniometer rotates the specimen to bring all specimen orientations

to the diffracting position Data are obtained by determining the diffraction-line intensity of poles as a function of specimen orientation The measured intensities can then be plotted as contour lines

An example of {200} and {111} pole figures of a cube-textured sheet of annealed copper is shown in Fig 10 From the positions of the intensity maximums, so-called ideal textures are often derived These are summarized in Table 2 for textures developed in metals by various processing operations

Table 2 Summary of metal textures developed by various processing operations (a)

Casting (fiber axis of columnar grains)

Recrystallization after uniaxial compression or forging

Ag, Yb, Ni-15Mo, Ni-50Co, Co-10Fe, 18-8

stainless steel, Cu alloys(d)

Al, Au, Cu, Cu-Ni, Fe-Cu-Ni, Ni, Ni-Fe, Th {100}<001>

Ag, Ag-30Au, Ag-1Zn, Cu-(5-39Zn), Cu-(1-5Sn),

Cu-0.5 Be, Cu-0.5Cd, Cu-0.05P, Co-10Fe

{113}<21 1 >

Fe, Fe-Si, V {111}< 2 11>, and {001} + {112} with < 1 10> 15° from RD(e)

Fe-Si {110}<001> after two-step rolling and annealing (Goss method); also

{110}<001>, {100}<001> after high-temperature anneal (>1100 °C, or 2012 °F)

are listed separately Alloy composition is in wt% For more detailed information on individual metals and processing conditions, consult the Selected References at the end of this article

sheet textures, both the lattice plane parallel to the rolling plane and the lattice direction parallel to the fiber axis are listed Some textures comprise two superimposed components, forming a duplex texture

(c) Approximate percentage of <100> component: Al, Pb, 10Fe, Cu-8Al (< 10%); Au (15%); Ni, 4Mo-79Ni-17Fe, Cu, Cu-2Al, Cu-4Al, 35Ni(25-35%); Co-40Ni (50%); Ag (>90%)

Fig 10 Actual {111} and {200} pole figures for electrolytic tough pitch copper that was rolled to 96%

reduction in thickness and then annealed for 5 min at 200 °C (390 °F) Intensity values are given in arbitrary units Positions of intensity maxima indicate cube texture plus twins of cube orientation, denoted by , (100)[001], and by , (122)[21 2 ], respectively

The technique described above for constructing pole figures using monochromatic beams from a characteristic radiation is generally referred to as angle-dispersive diffractometry In recent years, pole figures have also been constructed using the technique of energy-dispersive diffractometry, in which a polychromatic beam is used and several Bragg reflections are recorded simultaneously as a function of the photon energy of the scattered x-rays

The principle of energy-dispersive diffractometry is shown in Fig 11 Usually, the continuous, or white, radiation of an ray tube is used The entire spectrum of x-ray energy irradiates the sample The diffracted intensity is measured with a semiconductor detector and registered in a multichannel analyzer Figure 12 shows an example of the energy-dispersive diffraction patterns for iron The data can then be analyzed to yield an inverse pole figure showing the distribution of pole densities along a specimen direction (Fig 13) Normal pole figures such as those in Fig 10 can also be generated The principal advantage of the energy-dispersive method is that, with the specimen fixed at a given geometry and with rapid data acquisition, it is relatively easy to examine texture changes under dynamic conditions, such as those encountered in recrystallization studies or tensile testing

x-Fig 11 Schematic illustrating the principles of the x-ray energy-dispersive method

Fig 12 Energy-dispersive x-ray diffraction pattern of iron 2θ0 = 50° (a) Random specimen (powder) (b) Rolled sheet, rolling direction parallel to scattering vector (c) Rolled sheet, surface normal parallel to scattering vector (Ref 1)

Fig 13 Inverse pole figure of iron sheet showing the distribution of pole densities along the rolling direction

(Ref 1)

The orientation distribution function is a more quantitative description of texture beyond the idealized orientation

of pole figures This technique expresses the probability of a crystallite having an orientation described by the Euler angles that relate the specimen axes with the crystal axes (Fig 14) This function can be expressed by a series expansion

in generalized spherical harmonics The coefficients of this series can be obtained from the pole distribution obtained from the pole figure, which is similarly expanded in a series of spherical harmonics Greater precision is obtained using data from several pole figures

Fig 14 Euler angles ψ, θ, φ , relating the specimen axes, RD (rolling direction), TD (transverse direction), ND

(normal direction), with the crystal axes, x, y, z (Ref 2)

The orientation distribution function can be plotted in two-dimensional sections using two of the Euler angles, as shown

in Fig 15 However, its usefulness lies in the quantitative comparison with the anisotropic properties of a textured specimen, such as Young's modulus, yield strength, and magnetocrystalline anisotropy energy In these cases, the orientation dependence of a given property in a polycrystalline sample is often expressed in terms of the coefficients of the series development of the crystallite orientation distribution Additional information on orientation distribution functions can be found in Ref 3 and 4

Fig 15 The crystallite orientation distribution function for cold-rolled Cu-30Zn after 90% reduction Numbers

indicate the orientation points per unit volume (Ref 2)

References cited in this section

1 L Gerward, S Lehn, and G Christiansen, Texture, Vol 2, 1976, p 95

2 J.S Kelland and G.J Davies, Texture, Vol 1, 1972, p 51

3 K Lücke et al., On the Problem of the Production of the True Orientation Distribution from Pole Figures, Acta Metall., Vol 29, 1981, p 167-185

4 D.J Willis, A Complete Description of Preferred Orientations, Metals Forum, Vol 1 (No 2), June 1978, p

which is similar to the W cI2 type illustrated in Fig 1 Substitutional atoms are those located at atom positions normally

occupied by the close pairs and clusters of point defects, such as divacancies, trivacancies, and interstitial-vacancy pairs

Line Defects. Dislocations are line defects that exist in nearly all real crystals An edge dislocation, which is the edge of

an incomplete plane of atoms within a crystal, is represented in cross section in Fig 4 In this illustration, the incomplete plane extends partway through the crystal from the top down, and the edge dislocation (indicated by the standard symbol

⊥) is its lower edge

If forces, as indicated by the arrows in Fig 5, are applied to a crystal, such as the perfect crystal shown in Fig 5(a), one part of the crystal will slip The edge of the slipped region, shown as a dashed line in Fig 5(b), is a dislocation The portion of this line at the left near the front of the crystal and perpendicular to the arrows, in Fig 5(b), is an edge dislocation, because the displacement involved is perpendicular to the dislocation

The slip deformation in Fig 5(b) has also formed another type of dislocation The part of the slipped region near the right side, where the displacement is parallel to the dislocation, is termed a screw dislocation In this part, the crystal no longer

is made of parallel planes of atoms, but instead consists of a single plane in the form of a helical ramp (screw)

As the slipped region spread across the slip plane, the edge-type portion of the dislocation moved out of the crystal, leaving the screw-type portion still embedded, as shown in Fig 5(c) When all of the dislocation finally emerged from the crystal, the crystal was again perfect but with the upper part displaced one unit from the lower part, as shown in Fig 5(d) Therefore, Fig 5 illustrates the mechanism of plastic flow by the slip process, which is actually produced by dislocation movement

The displacement that occurs when a dislocation passes a point is described by a vector, known as the Burgers vector The fundamental characteristics of a dislocation are the direction of the vector with respect to the dislocation line, and the length of the vector with respect to the identity distance in the direction of the vector The perfection of a crystal lattice is restored after the passage of a dislocation, as indicated in Fig 5(d), provided that no additional defects are generated in the process

Each dislocation in a crystal is the source of local stresses The nature of these microstresses is indicated by the arrows in Fig 6, which represent (qualitatively) the stresses acting on small volumes at different positions around the dislocation at the lower edge of the incomplete plane of atoms Interstitial atoms usually cluster in regions where tensile strains and stresses make more room for them, as in the lower central part of Fig 6

In addition to the large-angle boundaries that separate crystal grains, which have different lattice orientations, the individual grains are separated by small-angle boundaries (subboundaries) into subgrains that differ very little in orientation These subboundaries may be considered as arrays of dislocations; tilt boundaries are arrays of edge

dislocations, and twist boundaries are arrays of screw dislocations A tilt boundary is represented in Fig 7 by the series of edge dislocations in a vertical row Compared with large-angle boundaries, small-angle boundaries are less severe defects, obstruct plastic flow less, and are less effective as regions for chemical attack and segregation of alloying constituents In general, mixed types of grain-boundary defects are common All grain boundaries are sinks into which vacancies and dislocations can disappear and may also serve as sources of these defects; they are important factors in creep deformation

Stacking faults are two-dimensional defects that are planes where there is an error in the normal sequence of stacking

of atom layers Stacking faults may be formed during the growth of a crystal They may also result from motion of partial dislocations Unlike a full dislocation, which produces a displacement of a full distance between the lattice points, a partial dislocation produces a movement that is less than a full distance

Twins are portions of a crystal that have certain specific orientations with respect to each other The twin relationship may be such that the lattice of one part is the mirror image of that of the other, or one part may be related to the other by a rotation about a specific crystallographic axis Growth twins may occur frequently during crystallization from the liquid

or the vapor state by growth during annealing (by recrystallization or by grain-growth processes) or by the movement between different solid phases, such as during phase transformation Plastic deformation by shear may produce deformation (mechanical) twins Twin boundaries generally are very flat, appearing as straight lines in micrographs, and are two-dimensional defects of lower energy than large-angle grain boundaries Twin boundaries, therefore, are less effective as sources, and sinks, of other defects and are less active in deformation and corrosion than are ordinary grain boundaries Textbooks and reference books, such as Ref 6, 7, and 8 list the indices of twinning planes (shear planes) and the directions of shear that occur when deformation twins are formed

References cited in this section

6 C.S Barrett and T.B Massalski, Structure of Metals, 3rd ed., Pergamon Press, 1980

7 A.G Guy, Elements of Physical Metallurgy, Addison-Wesley, 1959

8 L.H Van Vlack, Elements of Materials Science, Addison-Wesley, 1964

Crystal Structure of Metals

C.S Barrett, Professor of Metallurgy, University of Denver

Crystallographic Terms and Concepts

The terms and concepts defined and explained in this section are basic to an understanding of the descriptions and illustrations of crystal structures presented in the next section of this article

Crystal structure is the arrangement of atoms in the interior of a crystal A fundamental unit of the arrangement repeats itself at regular intervals in three dimensions throughout the interior of the crystal

A unit cell is a parallelepiped whose edges form the axes of a crystal A unit cell is the smallest pattern of atomic arrangement A crystal consists of unit cells stacked tightly together, each identical in size, shape, and orientation with all

others The choice of the boundaries of a unit cell is somewhat arbitrary, being conditioned by symmetry considerations and by convenience

Crystal Systems. Crystallography uses seven different systems of axes, each with a specified equality or inequality to others of axial lengths and interaxial angles These are the basis of the following crystal systems triclinic (anorthic), monoclinic, orthorhombic, tetragonal, hexagonal, rhombohedral (trigonal), and cubic employed in the classification of crystals

The edge lengths a, b, and c (along the corresponding crystal axes) of unit cells are expressed in angstroms (1 Ao = 0.1 nm,

or 10-10 m) Faces of unit cells are identified by the capital letter A, B, or C, when the faces contain axes b and c, c and a,

Table 1 Relationships of edge lengths and of interaxial angles for the seven crystal systems

Crystal system Edge lengths Interaxial angles Examples

Trichnic (anorthic) a ≠b ≠c α≠β≠γ≠90° HgK

Monoclinic a ≠b ≠c α= γ= 90° ≠β β-S; CoSb 2

Orthorhombic a ≠b ≠c α= β= γ= 90° α-S; Ga; Fe 3 C (cementite)

Tetragonal a = b ≠c α= β= γ= 90° β-Sn (white); TiO 2

Hexagonal a = b ≠c α= β= 90°; γ= 120° Zn; Cd; NiAs

Rhombohedral(a) a = b = c α= β= γ≠90° As; Sb; Bi; calcite

Cubic a = b = c α= β= γ= 90° Cu; Ag; Au; Fe; NaCl

(rhombohedral-hexagonal)

A lattice (space lattice or Bravais lattice) is a regular, periodic array of points (lattice points) in space, at each of which

is located the same kind of atom or a group of atoms of identical composition, arrangement, and orientation in a perfect crystal (at least, on a time-average basis)

There are five (actually, four plus rhombohedral) basic arrangements for lattice points within a unit cell, and each is identified by a Hermann-Mauguin letter symbol in a space-lattice notation These letter symbols and the arrangements

they identify are P, for primitive (simple), with lattice points only at cell corners; C, for base-face centered centered), with lattice points centered on the C faces or ends of the crystal; F, for all-face centered, with lattice points centered on all faces; and I, for innercentered, with lattice points at the center of volume of the unit cell (body-centered) The rhombohedral cell, also primitive, has R as its symbol

(end-The face having the base-face centered lattice point may be designated the C face, because the choice of axes is arbitrary

and does not alter the atom positions in the space lattice Rhombohedral crystals can be considered as having either a rhombohedral cell or a primitive hexagonal cell

The above letter symbols and definitions apply only to basic arrangement of atoms and do not limit the number of atoms

in a unit cell Atoms may be found at each corner of a base-centered, face-centered, or inner-centered cell and in some crystals also at other positions on the cell faces or within the cell

There are 14 kinds of space lattices, derived from all the combinations of equality and inequality of lengths of axes and interaxial angles They are listed in Table 2, along with Hermann-Mauguin and Pearson symbols The Pearson symbols

(Ref 1) consist of Hermann-Mauguin space-lattice letters preceded by a, m, o, t, h, and c to denote, respectively, six

crystal systems: triclinic (anorthic), monoclinic, orthorhombic, tetragonal, hexagonal, and cubic

Table 2 The 14 space (Bravais) lattices and their Hermann-Mauguin and Pearson symbols

System Space lattice Hermann-

Mauguin symbol

Pearson symbol

Triclinic (anorthic) Primitive P aP

(a) The face that has a lattice point at its center may be chosen as the c face (the xy plane), denoted by the symbol C, or as the a or b face, denoted

by A or B, because the choice of axes is arbitrary and does not alter the actual translations of the lattice

Structure symbols are arbitrary symbols that designate the type of crystal structure The Strukturbericht symbols (Ref

2) were widely used in the past and are still used today, but this system of naming structure types has been overwhelmed

by the number and complexity of types that are now recognized Furthermore, the final publication of Strukturbericht was

in 1939

Today, the accepted system of naming the types of crystal structures that metals and alloys adopt is to select arbitrarily the formula of a phase with the structure type (that is, a prototype), followed by the Pearson symbol for the Bravais lattice of the structure, then the number of atoms in the conventionally chosen unit cell Therefore, the nickel-arsenide structure is

referred to as the NiAs hP4 type (meaning hexagonal, primitive, 4 atoms per unit cell) and rock salt as the NaCl cF8 type

The arbitrariness in the system does not appear to be a problem, because norms become established by common usage

Therefore, the ordered AuCu structure should properly be described as AuCu tP2, according to the smallest primitive cell, but due to association of the structure with ordering from a face-centered cubic solid solution (cF4), it is typically referred

to as AuCu cF4

The advantage of this way of naming structure types is that it is open ended, that is, not limited in use by future discoveries of new crystal-structure types Secondly, compared to using only a formula name, it is crystallographically informative due to the addition of the Pearson symbol and thus amenable to classification Therefore, upon discovering a new intermetallic phase and establishing for it preliminary crystallographic information (the space lattice and the number

of atoms in the unit cell), a table of known structure types, classified by Pearson symbols can be consulted to determine what already characterized types may resemble the newly discovered phase For convenience, Table 3 lists Strukturbericht structure symbols, prototype names, and the corresponding Pearson symbols

Table 3 Conversion of Strukturbericht to Pearson symbol

Strukturbericht

designation

Structure prototype

Structure Prototype. To assist in classification and identification, each structure type has been given the name of a representative substance (an element or phase) having that structure Unit cells with the same structure type generally do not have dimensions identical to the prototype or to each other, because different materials with the same type of atomic

arrangement have atoms that differ in size, causing the lengths of the a, b, and c edges to differ Similarly, the position coordinates x, y, and z vary among different materials

atom-Atom Positions. The position of an atom, or the lattice point, in a unit cell is expressed by three coordinates (Ref

5) the three distances parallel to 5) the a, b, and c axes, respectively, from 5) the origin at one corner of 5) the cell to 5) the atom in question These distances are expressed in fractions of the edge lengths a, b, and c, respectively, rather than in angstroms

2 is at the center of the

volume of the unit cell The letters x, y, and z are used for the coordinates that are not convenient fractions or that differ in

the corners and at the center of all six faces The lattice points are at 0,0,0; 0, 1

Point Groups. A structure described by a specific space lattice (for example, cP) may not have any atoms lying at the

(space) lattice points; instead, groups of atoms with specific so-called point symmetries may be clustered identically about

each of the space-lattice points Nevertheless, the same space-lattice symmetry (cP) still pertains to the crystal structure Thus, for example in the close-packed-hexagonal structure Mg hP2, the primitive space-lattice points are vacant, and the

two magnesium atoms are located within the unit cell at 1

4 The structure type hP1, where

only the primitive hexagonal space-lattice points are occupied, does not exist

Alternatively, the space-lattice points may be occupied by atoms, and, in addition, there may be groups of other atoms with various point-group symmetries surrounding the atoms on the space-lattice points, as in the CaF2 cF12 structure,

where calcium occupies the face-centered cubic space-lattice sites; the fluorine atoms surround these sites

Equivalent Positions. In each unit cell, there are positions that are equivalent because of crystal symmetry This is often true of atoms at special positions (such as 1

2,0,0) and also of atoms at x, y, and z, where the coordinates may have

specific values At each point of a set of equivalent positions in a unit cell, the same kind of atom will be found (if the crystal if perfect), and all of the cells will be identical The coordinates listed for each kind of atom in the descriptions of crystal structure in Table 4 are thus coordinates of sets of equivalent positions

Table 4 Crystal structures of the elements