Fundamentals of Materials Science and Engineering: An Integrated Approach, 3e

GTBL042-11 GTBL042-Callister-v3 October 4, 2007 11:59

2nd Revised Pages

454 • Chapter 11 / Phase Transformations

are either bulky or polar. Molecular weight and degree of branching also affectTm

andTg.

IMPORTANT TERMS AND CONCEPTS

Alloy steel

Artificial aging

Athermal transformation

Bainite

Coarse pearlite

Continuous cooling

transformation diagram

Fine pearlite

Free energy

Glass transition temperature

Growth (phase particle)

Isothermal transformation

diagram

Kinetics

Martensite

Melting temperature

(polymers)

Natural aging

Nucleation

Overaging

Phase transformation

Plain carbon steel

Precipitation hardening

Precipitation heat treatment

Solution heat treatment

Spheroidite

Supercooling

Superheating

Tempered martensite

Thermally activated

transformation

Transformation rate

REFERENCES

Atkins, M.,Atlas of Continuous Cooling Transfor-

mation Diagrams for Engineering Steels, British

Steel Corporation, Sheffield, England, 1980.

Atlas of Isothermal Transformation and Cooling

Transformation Diagrams, ASM International,

Materials Park, OH, 1977.

Billmeyer, F. W., Jr.,Textbook of Polymer Science,

3rd edition, Wiley-Interscience, New York,

1984. Chapter 10.
      Brooks, C. R.,Principles of the Heat Treatment of
      Plain Carbon and Low Alloy Steels, ASM In-
      ternational, Materials Park, OH, 1996.
      Porter, D. A. and K. E. Easterling,Phase Trans-
      formations in Metals and Alloys, Chapman and
      Hall, New York, 1992.

Shewmon, P. G., Transformations in Metals,

McGraw-Hill, New York, 1969. Reprinted by

Williams Book Company, Tulsa, OK.

Vander Voort, G. (Editor), Atlas of Time–

Temperature Diagrams for Irons and Steels,

ASM International, Materials Park, OH,

1991.

Vander Voort, G. (Editor), Atlas of Time–

Temperature Diagrams for Nonferrous Al-

loys, ASM International, Materials Park, OH,

1991.

Young, R. J. and P. Lovell,Introduction to Poly-

mers, 2nd edition, CRC Press, Boca Raton, FL,

1991.

QUESTIONS AND PROBLEMS

Additional problems and questions for this chapter may be found on both Student and

Instructor Companion Sites atwww.wiley.com/college/callister.

The Kinetics of Phase Transformations

11.1 (a)Rewrite the expression for the total free

energy change for nucleation (Equation

11.1) for the case of a cubic nucleus of

edge lengtha(instead of a sphere of

radiusr). Now differentiate this expres-

sion with respect toa(per Equation 11.2)

and solve for both the critical cube edge

length,a∗, and alsoG∗.

(b)IsG∗greater for a cube or a sphere?

Why?

11.2 (a)For the solidification of nickel, calculate

the critical radiusr∗and the activation

free energyG∗if nucleation is homo-

geneous. Values for the latent heat of fu-

sion and surface free energy are –2.53×

109 J/m^3 and 0.255 J/m^2 , respectively.

Use the supercooling value found in Ta-

ble 11.1.

(b)Now calculate the number of atoms

found in a nucleus of critical size. Assume

a lattice parameter of 0.360 nm for solid

nickel at its melting temperature.