Errata for SOLIDIFICATION (First Edition, 2009)

Transcription

1 Errata for SOLIDIFICATION (First Edition, 29) J. A. Dantzig and M. Rappaz March 2, 217 Chapter 1: Overview Page 2, first line: the definition of r should have a square root. i.e., r = (ξ 2 + y 2 + z 2 ) 1/2 Chapter 2: Thermodynamics Page 35, Fig. 2.4: The length of the thermal arrests at the boiling point T v and at the melting point T f should be L v /ḣ and Lf/ḣ, respectively. In the figure caption, the units of c p should be J g 1 K 1, and the latent heat of vaporization should be L v rather than L V. Page 38, 2 lines after Eq. (2.28): the reference should be to Eq. (2.26) instead of Eq. (2.27) Page 56, after Eq. (2.64): θ should be defined as the angle between the local normal vector and a reference direction in the crystal, not necessarily corresponding to the direction of maximum surface energy. Chapter 3: Phase Diagrams Page 85, Fig. 3.12(b): There should be a second common tangent line to indicate the equilibrium between solid phases α 1 and α 2 at 83 K. Page 85, 2 lines before the end of page: Both systems are simple binary eutectic systems, rather than one eutectic and one peritectic system. Page 89, 3 lines after Table 3.4: delete CALPHAD 1

2 Page 95, Figure 3.21: The second sentence of the caption should read as follows: Isotherms on the liquidus surface are shown as dashed curves, and isotherms on the solidus are shown as solid curves inside the ternary triangle. Page 11, Table 3.5: The significance of Point a should be Maximum solubility point for phase β Chapter 4: Balance Equations Page 113, 2 lines after Eq. (4.31): The reference should be to Leibniz rule, rather than Gauss rule. The derivation is otherwise correct. Page 144, Eq. (4.16): The dimensionless time τ should be defined as: τ = v ct L Chapter 5: Analytical Solutions Page 153, Eq. (5.3): the second column should read x. Page 155, Eq. (5.26): the second term in the opening curly braces should have a + sign, rather than a - sign. The corrected equation reads as follows: φ exp ( φ 2) + c ps(t T f ) exp ([1 α s /α l ] φ 2 ) L f π erfc (φ k ) l ρ l c pl α s /α k s ρ s c ps l { } k s ρ s c ps erf (φ) + = c ps(t f T ) = Ste k m ρ m c pm L f π π Page 156, Example 5.1: The error in the previous item continues in this example. The equation under the table should read: { φ exp ( φ 2) +.41 exp } (.968φ2 ) {erf (φ) } = f(φ) = 1.79 erfc (1.43φ) The correct value of φ is.636, and T ms = 453 C. The corrected form of the four 2

3 equations at the top of Page 171: x (t) = t T m = erf (96.7 t x ) T s = erf (6.2 t x ) T l = erfc (84.17 t x ) Finally, the graphs shown at the end of the example change slightly as well: f(φ) - Ste / π 1/ Temperature [ o C] Graphite mold Solid Liquid φ Distance from mold-solid interface [m] Page 174, Figure 5.9 and several lines below: All references to λ should be α T. Page 18: Eq. (5.151) should read: Ste = Iv 2D (Pe) or Ste = Iv 3D (Pe) Page 186, Figure 5.15: The label on the ordinate should be: θ s,l = (T s,l T f )/(T f T ) Chapter 6: Numerical Methods Page 195: Eq. (6.19) should read: k T n I+1 T n I 1 2 x = h T (T n I T ) + O( x 2 ) Page 241, Exercise 6.1: The symbol r is the grid Fourier number, and hence should be Fo g 3

4 Part II: Microstructure Page 247, Line 3: following chapters should be preceding chapters Chapter 7: Nucleation No corrections at this time. Chapter 8: Dendritic Growth Page 34, Eq. (8.4): There should be only one = sign before the final term Page 31, just before Eq. (8.71):... neglect the last term in Eq. (8.67) instead of Eq. (8.68) Page 311, Line 4:... one can solve Eq. (8.67) numerically instead of Eq. (8.68) Page 32, Figure 8.19 and the text three lines above it: 1.5 K should be 1. K 1 8 DT =.5 K DT = 1. K R tip = 2.34 C.25 /DT DT =.5 K DT = 1. K v * = DT 2.5 /C 1.5 R tip [mm] 6 4 v * [mm/s] C [Wt% Cu] C [Wt% Cu] (a) Tip radius, R tip (b) Tip velocity, v * Fig Values of R tip and v, computed with Eqs. (8.83) and (8.86), for Al-Cu alloys at two undercoolings. The dashed lines represent the approximate forms considering only the solute, given in Eqs. (91) and (92), valid at low undercooling for compositions that are not too small. Page 324, Eqs. (8.97) and (8.98): there should be no minus sign inside the parentheses. 4

5 Page 322, Fig. 8.21: The filled squares in the legend indicating Pe ln(1 + 1/Pe) should be open circles. Page 324, Eq. (8.97): the numerator (T ) 2 should be ( T ) 2 Page 324, line after Eq. (8.97): equality should read T T Page 335, Eq. (8.12) should read as follows: d = β 1 W λ ; c p L f µ k = β 1τ W λ ( 1 β 2 λ W ) 2 ατ Page 337, Fig. 8.29(a): The ordinate should be labeled.5,.1,.15 ascending Page 337, Fig. 8.29(b): The abscissa should be labeled a 1 instead of a 1 Chapter 9: Eutectics and Peritectics Page 35, Figure 9.6: The CBr 4 C 2 Cl 6 should be labeled (c) instead of (d) Page 351, second paragraph, line 5 should read as follows: The figure also shows Al 11 and Zn 112 pole figure... Same correction in Figure 9.7: The Al pole figures should be labeled 11. The corrected figure is: <112> Zn <112> Zn (1) Zn (1) Zn (111) Al (111) Al <11> Al 2 mm <11> Al Fig. 9.7 Two grains of the lamellar Al-Zn regular eutectic with the corresponding pole figures for the fcc Al and hcp Zn phases, transverse cross section. (After Rhême et al. [33].) Page 374, line 7: the comma should be before follow rather than after. 5

6 Page 392, Exercise 9.6: There is a minus sign missing from the first term on the right hand side of the second equation. It should read as follows: [ ( ) vβ = dx β 1 = ( ) dc β l λ2 dt Cβ l dt 2 C x β l β D ] C α β β x C β β l x α Chapter 1: Microsegregation Page 4: In the caption for Figure 1.3, and in the 9th line of the text, DTA should be replaced by DSC Page 49, Eq. (1.4): There is a minus sign missing from the first term on the right hand side. The equation should read as follows: ( ) dx ( ) C l β Cl β = dc l λ2 dt dt 2 C β x β(t) D β x Chapter 11: Macro-micro Modeling Page 431, Figure 11.2(a): Globulitic is misspelled in the subfigure caption. Page 437, Eq. (11.17): The final = sign should be omitted, so that the Eq. (11.17) reads: q b 4πRg 2 = d ρh 4π dt 3 R3 g = ρc p 4π 3 R3 gt 4πR 2 v g ρl f Page 473, Reference [22]: dendrite is misspelled. x β Chapter 12: Porosity Page 49, Section head 12.4: First word should be Thermodynamics. Page 493, just before Eq. Raoult s Law (12.3): This should be Henry s Law, rather than Page 51, Eq. (12.48): The symbol R p in the denominator should be R p. Chapter 13: Mechanical Behavior and Hot Tearing Figure 13.5(b): The lower portion of the ingot is in compression, whereas the upper part is in tension. Please see the color version of this figure on solidification.org for improved clarity. 6

7 Chapter 14: Macrosegregation No corrections at this time. Index Page 613: The entry for Gauss rule should be deleted. (see Leibniz rule below) Page 614: An entry should be added for Henry s Law on p Page 615: The entry for Leibniz rule should refer to pages 113 and 114. Page 618: The entry for Raoult s should be deleted. (see Henry s Law above) 7