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7.9 Solid-Solution Strengthening  •  231

                                    Small-angle grain boundaries (Section 4.6) are not effective in interfering with the
                                 slip process because of the slight crystallographic misalignment across the boundary.
                                 However, twin boundaries (Section 4.6) effectively block slip and increase the strength
                                 of the material. Boundaries between two different phases are also impediments to move-
                                 ments of dislocations; this is important in the strengthening of more complex alloys. The
                                 sizes and shapes of the constituent phases significantly affect the mechanical properties
                                 of multiphase alloys; these are the topics of discussion in Sections 10.7, 10.8, and 16.1.


              7.9  SOLID-SOLUTION STRENGTHENING
                                 Another technique to strengthen and harden metals is alloying with impurity atoms
                                 that go into either substitutional or interstitial solid solution. Accordingly, this is called
              solid-solution     solid-solution strengthening.  High-purity metals are almost always softer and weaker
               strengthening     than alloys composed of the same base metal. Increasing the concentration of the
                                 impurity results in an attendant increase in tensile and yield strengths, as indicated in
                                 Figures 7.16a and 7.16b, respectively, for nickel in copper; the dependence of ductility
                                 on nickel concentration is presented in Figure 7.16c.
                                    Alloys are stronger than pure metals because impurity atoms that go into solid solu-
                          : VMSE  tion typically impose lattice strains on the surrounding host atoms. Lattice strain field



                                                                 180
                                                                                                    25
                                                    60           160
                 400                                             140                                20
               Tensile strength (MPa)  300          50   Tensile strength (ksi)  Yield strength (MPa)  120  15  Yield strength (ksi)





                                                                 100
                                                    40
                                                                 80
                                                                                                    10
                                                    30
                 200                                             60
                   0     10     20    30    40     50              0     10    20     30    40     50
                             Nickel content (wt%)                            Nickel content (wt%)
                                   (a)                                            (b)

                 60


               Elongation (% in 2 in.)  50


                 40


                 30


                 20
                   0     10     20    30    40     50     Figure 7.16  Variation with nickel content of (a) tensile
                             Nickel content (wt%)         strength, (b) yield strength, and (c) ductility (%EL) for
                                   (c)                    copper–nickel alloys, showing strengthening.
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