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References

1

J.R. MacDonald and W.B. Johnson, "Fundamentals of Impedance Spectroscopy," pp. 12-26 in Impedance Spectroscopy: Emphasizing Solid Materials and Systems. Edited by J. R. MacDonald. Wiley, New York, 1987.

2

C.A. Scuderi, T.O. Mason, and H.M. Jennings, "Impedance Measurements on Cement Paste," J. Mat. Sci. Lett., 7, 1056-1057 (1988).

3

B.J. Christensen, T.O. Mason, and H.M. Jennings, "Influence of Silica Fume on the Early Hydration of Portland Cements Using Impedance Spectroscopy," J. Am. Ceram. Soc. 75 (4), 939-45 (1992).

4

Z. Xu, P. Gu, P. Xie, and J.J. Beaudoin, "Application of A.C. Impedance Techniques in Studies of Porous Cementitious Materials, (II). Relationship Between ACIS Behavior and the Porous Microstructure," Cem. Conc. Res., in press.

5

P. Gu, P. Xie, J.J. Beaudoin, and R. Brouseau, "A.C. Impedance Spectroscopy: I. A New Equivalent Circuit Model for Hydrated Portland Cement Paste," Cem. Concr. Res., 22, 833- 40 (1992).

6

P. Xie, P. Gu, Z. Xu, and J.J. Beaudoin, "A Rationalized A.C. Impedance Model for Microstructural Characterization of Hydrating Cement Systems," Cem. Concr. Res., 23, 359-67 (1993).

7

H.F.W. Taylor, Cement Chemistry (Academic Press, London, 1990).

8

E.J. Garboczi and D.P. Bentz, "Computer Simulation of the Diffusivity of Cement- Based Materials," J. Mat. Sci. 27, 2083-2092 (1992).

9

E.J. Garboczi and D.P.Bentz, "Digital Simulation of the Aggregate-Cement Paste Interfacial Zone in Concrete," J. Mat. Res. 6, 196-201 (1991).

10

L.M. Schwartz, F. Auzerais, J. Dunsmuir, N. Martys, D.P. Bentz, and S. Torquato, "Transport and Diffusion in Three-Dimensional Composite Media," to be published in Physica A: Proceedings of the 3rd International Meeting on Electrical Transport and Optical Properties of Inhomogeneous Materials (ETOPIM3), Guanajuato, Mexico, August 9-13, 1993.

11

E.J. Garboczi and D.P.Bentz, "Fundamental Computer Simulation Models for Cement-Based Materials," in Materials Science of Concrete, Vol. 2, ed. J. Skalny (American Ceramic Society, Westerville, Ohio, 1991).

12

E.J. Garboczi and D.P. Bentz, "Computational Materials Science of Cement-Based Materials," Mater. Res. Soc. Bulletin 18, 50-54 (1993).

13

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14

R.T. Coverdale, E.J. Garboczi, B.J. Christensen, T.O. Mason, and H.M. Jennings, "Computer Simulation of Impedance Spectroscopy in Two Dimensions: Application to Cement Paste," J. Am. Ceram. Soc., 76 (6), 1153-60 (1993).

15

D.J. Frank and C.J. Lobb, "Highly efficient algorithm for percolative transport studies in two dimensions," Phys. Rev. B37, 302-307 (1988).

16

D.B. Gingold and C.J. Lobb, "Percolative Conduction in Three Dimensions," Phys. Rev. B 42, 8220-8223 (1990).

17

D.P. Bentz, E.J. Garboczi, D.B. Gingold, C.J. Lobb, and H.M. Jennings, "Diffusion Studies in a Digital-Image-Based Cement Paste Microstructural Model," Ceram. Trans. 16, 227- 236 (1990).

18

S. Kirkpatrick, "Percolation and Conduction," Rev. Mod. Phys. 45, 574-588 (1973).

19

J.R. Reitz and F.J. Milford, Foundations of Electromagnetic Theory, 2nd Edition (Addison-Wesley, Reading MA, 1967).

20

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21

W.H. Press, B.P. Flannery, S.A. Teukolsky, and W.T. Vetterling, Numerical Recipes: The Art of Scientific Computing (FORTRAN Version) (Cambridge University Press, Cambridge, 1989).

22

E.J. Garboczi, Finite element and finite difference programs for computing the linear electrical and elastic operties of digital images of random materials , NISTIR 6269 (1998).

23

Ref. 1, small c₂ limit of eq. (14), p. 198.

24

A.S. Sangani and A. Acrivos, "The effective conductivity of a periodic array of spheres," Proc. R. Soc. Lond. A 386, 263 (1982).

25

N. Bonanos and E. Lilley, "Conductivity Relaxations in Single Crystals of Sodium Chloride Containing Suzuki Phase Precipitates," J. Phys. Chem. Solids 42, pp. 943-952 (1981).

26

H. Fricke, "The Maxwell-Wagner Dispersion in a Suspension of Ellipsoids," J. Phys. Chem. 57, 934-937 (1953).

27

D.R. Clarke, "Interpenetrating Phase Composites," J. Amer. Ceram. Soc. 75, 739- 759 (1992).

28

D.S. McLachlan, M.B. Blaszkiewicz, and R.E. Newnham, "Electrical Resistivity of Composites," J. Am. Ceram. Soc., 73 (8), 2187-2203 (1990).

29

D. Stauffer, Introduction to Percolation Theory (Taylor and Francis, London, 1985).

30

D.P. Bentz and E.J. Garboczi, "Percolation of Phases in a Three-Dimensional Cement Paste Microstructural Model," Cem. Conc. Res. 21, 325-344 (1991).

31

R. Landauer, "Electrical Conductivity in Inhomogeneous Media," pp. 2-45 in AIP Conf. Proc. No. 40, Electrical Transport and Optical Properties of Inhomogeneous Media. Edited by J.C. Garland and D.B. Tanner (American Institute of Physics, New York, 1978).

32

E.J. Garboczi, M.F. Thorpe, M. DeVries, and A.R. Day, "Universal Conductivity Curve for a Plane Containing Random Holes," Phys. Rev. A43, 6473-6482 (1991).

33

R.T. Coverdale, B.J. Christensen, H.M. Jennings, T.O. Mason, D.P. Bentz, and E.J. Garboczi, "Interpretation of Impedance Spectroscopy of Cement Paste via Computer Modelling Part I: Bulk Conductivity and Offset Resistance," J. Mater. Sci. 30, 712-719 (1995).

34

R.T. Coverdale, B.J. Christensen, T.O. Mason, H.M. Jennings, and E.J. Garboczi, "Interpretation of Impedance Spectroscopy of Cement Paste via Computer Modelling Part II: Dielectric Response," J. Mater. Sci. 29, 4984-4992 (1994).