Surface Characterization

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CHAPTER 1

THE SURFACES OF A SOLID are the free bounding faces forming interfaces with the surrounding environment. The bulk of the material constitutes the bulk phase, while the free bounding face is known as the surface phase. The formation of a solid surface from liquid is accompanied by heat extraction at the freezing temperature. The latent heat of fusion is the quantity of heat to be extracted for liquid to transform to solid. The surface of the solid, or the surface phase, retains sufficient free energy in order to remain in equilibrium with its surroundings. The microstructural features on the solidified surface depend on composition and rate of cooling. The subsequent forming and thermal processes alter the surface morphology. Finally, the roughness of the surface or surface texture is dependent on the forming and finishing processes. The tendency for surface free energy of solids to decrease leads to an adsorption of molecules from the interfacing environment at the surface. The adsorbed layer is probably not more than a single molecule in thickness due to the rapid fall in intermolecular forces with distance. The nature of bonding may be physical or chemical and, accordingly, is termed van der Waal adsorption or chemisorption. The adsorbed product on the surface may be quite stable (e.g., the self-replenishing layer of chromium oxide in stainless steels) or unstable (e.g., loose oxide scale on mild steel), thus affording protection to the surface or leading to loss in material from the surface. The loss in material due to interaction with the environment has been termed wear. The surface properties can be altered suitably in order to reduce surface wear. The energy, morphology, and composition of the surface phase play a significant role in surface wear. Surface hardness has been widely used as a rough indicator of resistance to wear. While the intrinsic properties of the material mainly control the behavior of the bulk phase, the surface characteristics of the material to a large extent determine wear of the surface phase. chap01.qxd 6/1/01 5:52 PM Page 2

Surface Energy

An important quality of a material is its surface free energy at different conditions and temperatures. The amount of free energy at the surface of a material depends on various factors such as crystal structure, alloy con- tent, temperature, and interfacing phases. The surface of liquid or solid has excess free energy, a result of which causes a tendency for free energy to decrease in order to attain the stable state. In the case of liquid, the state of strain on the surface is known as surface tension. The surface free energy of solid, depending on the interfacing environment, can be that γ γ between solid-vapor ( sv) or solid-liquid ( sl). The grain boundary, stacking fault, and twin boundary represent solid-solid interfaces. The free energy at these interfaces is the surface energy value expressed for grain γ γ γ boundaries ( gb), stacking faults ( sf), and twin boundaries ( tb). Beyond free energy, residual stresses develop at the surface during deformation, thermal shrinkage, and transformation processes. The effect of residual stress on wear depends on the type and magnitude of the stress.

Free Energy at the Surface

The free energy at the surface of a solid depends on the solid itself and the interfacing material. The interfacing phase may be liquid, vapor, or solid. Accordingly, the interfacial energy is expressed as the free energy of γ γ γ solid-liquid ( sl), solid-vapor ( sv), and solid-solid ( ss) interfaces, respectively. γ Free Energy at Solid-Liquid Interface ( sl). The total free energy change (∆F) in creating a new solid surface from the liquid is the sum of the decrease in volume free energy and increase in surface free energy (Ref 1):

4 ¢F πr3¢F 4πr2g (Eq 1.1) 3 v sl

where 4⁄3 πr3 is the volume of a spherical embryo of volume free energy ∆ π 2 γ Fv,4 r is the surface area of the sphere, and sl is the surface free energy. When the embryo reaches the critical size of r = r*, the stable nucleus is in equilibrium with the liquid, and the change in free energy with respect to nucleus size is zero, or otherwise (Ref 1):

4 d πr3¢F 4πr2g d ¢F a3 v slb 1 2 0 dr dr π 2¢ π 4 r* Fv 8 r*gsl 0 (Eq 1.2) ¢ Fvr* g sl 2 chap01.qxd 6/1/01 5:52 PM Page 3

γ γ sv sv Ω Vapors Vapor

Grain A Grain B

Solid Solid

γ gb

γ γ Ω Fig. 1.1 Free energy at surface ( sv) and grain boundary interface ( gb). s, dehedral angle ∆ ∆ The volume free energy, Fv, is related to latent heat of fusion, H,the ∆ freezing temperature, Tm, and the degree of undercooling, T, as follows:

¢F ¢H ¢T T (Eq 1.3) v > m ∆ Substituting Fv from Eq 1.2 in Eq 1.3:

g ¢H ¢T T 2r* sl > m The surface free energy at solid-liquid interface increases with increasing degree of undercooling and latent heat of fusion. Some typical values are given in Table 1.1. Solid-Solid and Solid-Vapor Interfacial Free Energy. The solid-vapor γ surface energy sv at the free surface is the summation of energy vectors γ due to vapor/solid interface and that of solid-solid at grain boundary ( gb), γ γ stacking fault ( sf), and twin boundary ( tb) (Fig. 1.1).

Measurement of Free Surface Energy

Some of the important techniques for measurement of free surface energy of solid materials are described here. The zero-creep method consists of determining free energy of the surface from the stress that just fails to produce creep in a wire loaded at ele- vated temperature. Simultaneously, the grain boundary free energy can be found from the dihedral angle measurement of thermally etched grain boundary grooves of the same specimen (Ref 2). γ Principle (Ref 2, 3). The equation correlating surface free energy sv, γ the grain boundary free energy gb, and the load for zero creep W0 is as follows:

n W πr g g r 0 c sv gb a l bd (Eq 1.4)

πrg W πr2g n l sv 0 gb1 > 2 chap01.qxd 6/1/01 5:52 PM Page 4

where r is the radius of the wire, and n/l the average number of grains per unit length. At zero creep, the free energy on any section of the surface of the wire is equal to energy due to grain boundaries plus the load at zero creep. According to Smith (Ref 3), after prolonged annealing (i.e., at equi- Ω librium), the dihedral angle ( s) is a function of the surface and grain boundaries involved. At the equilibrium configuration (Fig. 1.1) the dihedral angle is related to surface and grain boundary energies by the follow- ing equation:

g 2 g cos 2 (Eq 1.5) gb sv 1 s> 2 γ Substituting gb from Eq 1.4 by Eq 1.5:

W g 0 sv πr 1 2 n l rcos 2 (Eq 1.6) 3 1 > 2 1 s> 24 The load at zero creep, average number of grains (n) present in the section, Ω and the dihedral angle ( s) between the grains are required to be deter- γ mined (Eq 1.6) in order to find the free energy at the surface ( sv). Method (Ref 2). In a thin wire (0.127 mm or 0.005 in., diameter) test specimen, several knots are made at 50 mm (2.0 in.) intervals. Each knot serves as a gage marker, and the weight of the knot acts as applied load. A large knot of the same wire serves the purpose of the rest of the load (Fig. 1.2). The total load to be applied is estimated from the surface tension of the liquid metal. The assembly is preannealed at or near test temperature, after which the initial gage measurement is carried out. The whole assembly is heated in a controlled-atmosphere furnace. During the creep anneal, the added weight has a tendency to allow the wire to elongate, while the surface free energy tends to shorten the wire. At the zero-creep stage, the tensile loads balanc- ing the opposing surface forces lead to neither elongation nor contraction of the wire. The gage length measurements are made on each segment before and after creep by a vertical measurement microscope, which is capable of measuring ±0.00127 mm (50 µin.). The number of grains per unit length is counted and the average value of (n/l) found. The strain for each segment and effective load are measured at midpoints of the segments (Fig. 1.2). The balance load for zero creep, W0, is found graphically from the least-square line of the plot of load versus strain as shown in Fig. 1.3. Results. Hondros (Ref 4) determined the surface free energy of 12 binary alloys as a function of composition using the zero-creep technique. The γ measured slopes of the sv versus concentration at infinite dilution; that is, γ (d sv/dx) at x = 0 of some of the binary systems, are indicated as follows:

System Fe-O Fe-Si Cu-Au

γ 7 d sv/dx (x = 0) 10 70 1 chap01.qxd 6/1/01 5:52 PM Page 5

Sketch of wire specimen showing how the effective loads, W, and Fig. 1.2 ε ε strains, , were determined. = (L – L0)/L0, where L is specimen length and L0 is original specimen length. Source: Ref 2

0 Strain

w5 w4 w3 w2 w1 Load

Fig. 1.3 Diagram of strain vs. load showing zero creep load. Source: Ref 2

The results indicate that the tendency toward grain boundary embrittlement in the binary systems is directly related to surface adsorption. The high energy at grain boundaries tends to cause precipitation of new phases at these locations, often resulting in grain boundary embrittlement. chap01.qxd 6/1/01 5:52 PM Page 6

The temperature coefficient of surface free energy for Fe+3%Si alloys has been reported as –0.36 ergs/cm2 °C, which compares favorably with the commonly accepted value of –0.50 ergs/cm2 °C (Ref 4). The surface energy of zinc has been found to be 0.83 J/m2. Annealing of Gas-Free Void. The rate of shrinkage of small voids is measured in quenched thin foils of copper and aluminum using transmission electron microscopy (TEM) (Ref 4). The driving force for void shrinkage is surface tension. The surface energy values of copper and aluminum have been found to be 1.74 and 0.97 J/m2, respectively. Inert Gas Bubble Shape. From a solid/vapor interface, the surface energy of the solid has been derived from the measurements of inert gas bubble shapes and aspect ratios at increasing temperatures (Ref 4). The bubble shapes and aspect ratios for zinc implanted with argon are measured at different temperatures. At 130 °C (320 °F), basal, prismatic, and pyramidal planes are present. At 300 °C (570 °F), a rounding of prismatic and pyramidal faces has occurred. The surface energy of a basal plane at 300 °C (570 °F) is approximately 0.60 J/m2. Dihedral Angle Measurement. According to Smith’s equation (Eq γ γ 1.5), the ratio of sl/ gb is a function of the dihedral angle at the liquid/grain boundary junction of an alloy at a particular temperature. From the measurements of the dihedral angles at liquid/grain boundary γ γ junctions in alloys held at different temperatures, sl/ gb ratios were cal- culated as a function of compositions (Ref 4). Linear relationships have γ γ been found in sl/ gb versus composition plots for Al:Sn and Zn:Sn sys- γ γ tems, which on extrapolation to 0% tin gave the ratio of sl/ gb as ~0.45 for pure Al and Zn. γ Fracture Experiments. The solid-solid surface energy ss has been cal- culated from the measurement of fracture stress σ at various temperatures using the Griffith equation of fracture (Ref 4). Griffith’s equation on stress required (σ) to form a crack of a length 2a is as follows:

2g E 1 2 s ss > (Eq 1.7) a πa b

γ where ss is surface tension and E is Young’s modulus. A sharp crack is introduced into <100> single crystal of silicon-iron. The stress (σ) required for the growth of the crack causing fracture and the crack γ length (2a) are measured. The surface energy ( ss) is determined by using the Griffith equation. At a testing temperature of 4.2 K, the computed value γ 2 of ss has been found to be 2.20 N/m (Ref 4). According to Griffith’s equation, the fracture stress (σ) should vary inversely with the square root of crack length; however, the slope of the line varies with the crack initiation temperature and testing temperature. It has been shown that the larger the initial crack is, the lower is the computed value of the surface energy. The γ 2 accepted value of ss is 2.50 N/m (Ref 4) obtained from specimens tested at chap01.qxd 6/1/01 5:52 PM Page 7

77 K. The fracture experiments suffer from the uncertainty of determining the energy required for fracture and that for deformation. The zero-creep method is considered the most accurate and satisfactory means of determining absolute values of surface free energy but is found unacceptable in metals with a high affinity for oxygen, such as aluminum. In such cases, annealing out of gas-free voids provided a possible alterna- tive method. The free energy values of the surface interfacing with different media are shown in Table 1.1.

Surface Defects and Free Energy

The defects in crystalline materials, such as grain boundaries, stacking faults, and twinning, contribute to the total free energy of the surface. The interfacial free energies of some metals at surface, grain boundary, stacking fault, and twinning are tabulated in Table 1.1. Grain Boundary. In a polycrystalline structure, the grains are joined together at grain boundaries. The grain boundary is the narrow transition region between two crystals of different atomic arrangements. The grain boundary is only a few atoms thick. The grain boundary energy of copper has been found to be 0.55 N/m2 (559 ergs/cm2) (Ref 6). The latent heat of melting for copper is 10–13 ergs/ atom. Since the disorder at the boundary is comparable to that of a liquid, the energy of an atom at the boundary is similar to that in liquid. Assuming thickness as d cm, the number of atoms in 1 cm2 of grain boundaries is 1023d, and the energy is 10–13 × 1023d = 550, indicating d value as about two atoms thick. A grain boundary has surface tension since its atoms have higher free energy than those within the grains (Ref 7). The surface tension, T,is equal to γ, the surface (free) energy per unit area. The surface tensions (Fig. 1.4) TA, TB, and TC at the common meeting point with angles A, B, and C should form a triangle of forces so that

TA/sin A = TB sin B = TC sin C (Eq 1.8)

Table 1.1 Surface free energy of selected metals Type of interfacial Free energy, J/m2 free energy Cu Al Fe Zn Pt (γ Solid-vapor sv) 1.74 0.97 ... 0.83 ... γ Solid-liquid ( sl) 0.177 ... 0.204 ...... γ Stacking fault ( sf) 0.075 0.20 ...... 0.095 γ Grain boundary ( gb) 0.645 0.625 0.78 ... 1.00 γ Twin boundary ( tb) 0.045 0.12 0.19 ... 0.195 Source: Ref 1–5 chap01.qxd 6/1/01 5:52 PM Page 8

T B

TA A

T C

Fig. 1.4 Relation between grain boundary surface tension (T) and angle

The energy of large angle grain boundary is not much influenced by the orientation of the grain boundary, and in such a case TA = TB = TC, so that A = B = C = 120°. Any departure from equilibrium conditions (i.e., angle ≠ 120° or number of sides ≠ 6) may cause grain boundaries to move in order to restore the equilibrium conditions when sufficient energy is available during processes such as annealing or creep. The high energy at grain boundaries can cause nucleation of new phases and etching at the boundary regions. The boundary diffusion rates are very high compared with lattice diffusion, resulting in faster enrichment of diffused elements adjacent to grain boundaries than within the grains. Twin Boundaries. The crystals with two parts symmetrically related to each other are known as twinned crystals, and the interface areas between the two are known as a twin boundary. There are two main types of twinning, depending on whether the symmetry operation is a 180° rotation about an axis, called the twin axis, or a reflection across a plane, called the twin plane (Ref 8). Two types of twinning can occur through annealing and deformation. The twinnings are known by their formation processes. Annealing twins normally occur in face-centered cubic (fcc) metals and alloys (e.g., Cu, Ni, α-brass, Al) after annealing of cold-worked alloy. Annealing twins in fcc metals can be rotation as well as reflection twins. Two parts are either related by a 180° rotation about a twin axis of the form [111] or related by reflection across the (111) plane normal to the twin axis. The fcc annealing twins are formed by a change in the normal grain growth process. Consider a grain boundary is roughly parallel to the (111) plane. Growth advances normal to the boundary (i.e., [111] by adding layers of atoms). These layers are piled up in the sequence A B C A B C... in an fcc chap01.qxd 6/1/01 5:52 PM Page 9

crystal. If, however, a mistake occurs in the sequence resulting in a change to C B A C B A..., the crystal so formed would still be fcc but a twin of the former sequence. The twin band can be indicated as follows:

ABCAB CBACBA CABCABC S 4 d † † parent crystal twin band parent crystal

Deformation twins are formed during the deformation of hexagonal close-packed (hcp) metals (e.g., Zn, Mg, Be) and body-centered cubic (bcc) metals (e.g., α-iron, W). In the bcc structures, the twin plane is (112) and twinning shear is in the [111 ] direction. A common example of twins of this type is α-iron deformed by impact, where they occur as extremely narrow twin bands called Neumann bands. In hcp metals, twin plane is –– normally (1012 ) and twinning shear in the direction of [211] for metals with c/a ratio 6 23 (Be,Ti,Mg) and on the reverse direction [211 ] for metals with c/a ratio 7 23 (Zn,Cd). There can be more than one type of twins in a grain (e.g., in cold-worked and annealed copper). The twin boundary energy values of copper and aluminum constitute 7.0% and 19.2% of their respective grain boundary energies (Table 1.1). The twin boundary impedes the movement of dislocations and thus the deformation process in the same way but less effectively than grain boundaries. The strength of the material increases with the increasing number of twins in the structure. Stacking Fault. The fault in the stacking sequence of fcc crystals (i.e., from a perfect A B C A B C A B C to imperfect A B C A B A B C A B C) results in a stacking fault in the A B A B region, where the stacking sequence corresponds to an hcp lattice. In terms of dislocation theory, when imperfect or partial dislocations with Burgers vector less than a unit lattice vector are formed by dissociation of a unit dislocation, the region between the partial dislocations is a stacking fault in an fcc crystal. The stacking fault region consists of four layers of hcp metal. The energy required to form such an unstable high-energy region is the stacking fault energy (SFE) and is defined as the energy required to produce a unit area of hcp material four atom layers in thickness. A higher stacking fault energy indicates a stable fcc phase, while low values lead to the transformation to hcp through dissociation of dislocations. The dissociation and association of dislocations are dependent on SFE; therefore, SFE controls several properties of the material, including the work-hardening rate, creep rate, recovery and recrystallization mode, type of martensite formation, stress corrosion, and precipitation (Ref 9). The hardest and highly wear-resistant martensite phase in steel is formed during rapid cooling from high-temperature austenitic region by a shear transformation process. The body-centered tetragonal (bct) crystalline form of martensite is formed due to fcc austenite with low SFE chap01.qxd 6/1/01 5:52 PM Page 10

getting faulted twice (i.e., first to hcp and then to bct during the transformation process). Similar to twinning, the stacking fault interferes with the slip process of deformation by making cross slip difficult. An element such as manganese reduces the SFE of the austenitic matrix and increases the work- hardening rate. The high rate of work hardening makes the surface of tough high-manganese steels (Hadfield steel) hard and wear resistant because of rapid work hardening in the initial stage of usage in repetitive impact applications such as railway frogs. The steady state creep rate in crystalline solids is a direct function of SFE. High creep strengths can be obtained by adding solutes (e.g., Co in Ni-alloys), lowering SFE. Among the various methods for determining SFE are measuring node radii from thin foils in TEM (transmission electron microscopy) and determining the annealing twin frequency as a function of grain growth. Both methods have limitations (Ref 8). The twin frequency method allows a wider range of SFE (0.001–0.100 J/m2) to be determined. However, it is applicable only at temperatures where grain growth occurs. The radii of nodes in the thin foil surface (R) are related to SFE (γ) as follows (Ref 10):

Gb2 g (Eq 1.9) 4πR ln R b 1 > 2 where G is the shear modulus and b, the Burgers vector. The measurement of the node radii is only suitable for materials with an SFE between 0.001 and 0.030 J/m2 and ideal for specimens at room temperature.

Strain Energy at the Surface

The residual stress on the surface can be generated as a result of cold working, welding, carburizing, nitriding, and so on. The residual stress on the surface of a shot-peened or carburized surface is schematically shown in Fig. 1.5 and 1.6. The hardened surface layer of the shaft (A,A in Fig. 1.5), shows the presence of high compressive residual stress (AY, AY in Fig. 1.6). The softer core region of the shaft will develop high tensile residual stress. While the tensile residual stress at the surface can add to fatigue damage, the onset of surface damage by fatigue is delayed by the presence of compressive stress. Additionally, the compressive stress retards the development and propagation of surface cracks (Ref 11). Residual compressive or tensile stress also can develop on the surface during wear (Ref 12). ASM International is the society for materials engineers and scientists, a worldwide network dedicated to advancing industry, technology, and applications of metals and materials.

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