Abstract

From analysis of a series of vibrational spectra of ir energy absorption and laser Raman, an attempt is made to interpret solid solution hardening from an atomistic point of view for the system CaF2/SrF2. It is shown to be caused by the combined action of three atomic characteristics, i.e., their changes as a function of composition. They are deformation of the atomic coordination polyhedrons, overlap of the outer electron shells of the atom pairs, and the ratio of the ionic to covalent share of binding. A striking nonlinear behavior of the three characteristics, as a function of composition, gives maximum atomic bond strength to the 55/45 position of the system CaF2/SrF2, in agreement with the measured data of the solid solution hardening. The curve for atomic bond Strength, derived from the three characteristics, is almost identical to the curve for measured microhardness data This result suggests that the atomistic interpretation, put forward in this paper, is correct.

© 1971 Optical Society of America

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References

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  1. J. N. Plendl, P. J. Gielisse, L. C. Mansur, S. S. Mitra, A. Smakula, P. C. Tarte, Appl. Opt. 10, 1129 (1971).
    [CrossRef] [PubMed]
  2. For pertinent literature, see Ref. 1.
  3. For definition, see Refs. 1 and 2.
  4. R. K. Chang, Brad Lacina, P. S. Pershan, Phys. Rev. Lett. 17, 755 (1966).
    [CrossRef]
  5. J. N. Plendl, “Damping of Lattice Vibrations in Solids,” Appl. Opt. 10, 87 (1971); also in AFCRL Rept. No. 69-0429 (1969).
    [CrossRef] [PubMed]
  6. For example, Ψ(I)=12=1:2 says that the covalent share of binding is twice the ionic share, i.e., the latter is one third of the total binding.
  7. To be eliminated for determining both damping and anharmonic factor.
  8. J. N. Plendl, Appl. Opt. 9, 2768 (1970); AFCRL Rep. 69-03531969; Characteristic Energy Absorption Spectra of Dielectric Solids (Plenum, New York, 1970).
    [PubMed]

1971 (2)

1970 (1)

1966 (1)

R. K. Chang, Brad Lacina, P. S. Pershan, Phys. Rev. Lett. 17, 755 (1966).
[CrossRef]

Appl. Opt. (3)

Phys. Rev. Lett. (1)

R. K. Chang, Brad Lacina, P. S. Pershan, Phys. Rev. Lett. 17, 755 (1966).
[CrossRef]

Other (4)

For example, Ψ(I)=12=1:2 says that the covalent share of binding is twice the ionic share, i.e., the latter is one third of the total binding.

To be eliminated for determining both damping and anharmonic factor.

For pertinent literature, see Ref. 1.

For definition, see Refs. 1 and 2.

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Figures (4)

Fig. 1
Fig. 1

Characteristic energy absorption spectra for five different compositions of the solid solution system CaF2/SrF2.1

Fig. 2
Fig. 2

Damping parameters (Δν/ν0)ir derived from infrared data (Fig. 1) and (Δν/ν0)LR derived from laser Raman spectra8 as a function of composition of the system CaF2/SrF2.

Fig. 3
Fig. 3

Overlap characteristic ψ(A)−2, deformation characteristic ψ(D), and ionic to covalent binding characteristic ψ(I) vs composition for the system CaF2/SrF2; also the resulting characteristic ψ(B) = ψ(I) × ψ(D) × ψ(A)−2 as a function of composition.

Fig. 4
Fig. 4

Characteristic for atomic bond strength [1 + ψ(B)] and measured microhardness MH vs composition for the system CaF2/SrF2. Note the two scales for the atomic bond strength.

Tables (1)

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Table I Data Used in the Analysis of the System CaF2/SrF2

Equations (3)

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Ψ ( I ) = [ ( ν 0 / Δ ν ) ionic / ( ν 0 / Δ ν ) covalent ] 1 2 .
Ψ ( D ) = 1 + ν H - ν T O ν T O ,
Ψ ( B ) = Ψ ( I ) × Ψ ( A ) - 2 × Ψ ( D ) .

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