Interpretation of Solid Solution Hardening with Vibrational Spectra

J. N. Plendl; P. J. Gielisse; L. C. Mansur; S. S. Mitra; A. Smakula; P. C. Tarte

doi:10.1364/AO.10.001129

Applied Optics
Vol. 10,
Issue 5,
pp. 1129-1133
(1971)
•https://doi.org/10.1364/AO.10.001129

Interpretation of Solid Solution Hardening with Vibrational Spectra

J. N. Plendl, P. J. Gielisse, L. C. Mansur, S. S. Mitra, A. Smakula, and P. C. Tarte

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J. N. Plendl, P. J. Gielisse, L. C. Mansur, S. S. Mitra, A. Smakula, and P. C. Tarte, "Interpretation of Solid Solution Hardening with Vibrational Spectra," Appl. Opt. 10, 1129-1133 (1971)

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Abstract

Solid solution hardening has been reviewed with respect to existing experimental data. It is shown with the aid of new experimental data on two inorganic systems (NiO–CoO and CaF₂–SrF₂) that the large increase in hardness of intermediate compositions correlates qualitatively and can also be quantitatively justified by the use of selected values of the parameters in a previously developed atomistic hardness formula. The key parameters are the variations in the unit cell dimensions, the eigenfrequency, and anharmonic factor of the structure.

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Solid	r₀, 10⁻⁸ cm	V, cm³	ν_T_0,(110) cm⁻¹	Ψ(A)	Δν/ν₀	Exptl. H₍₁₁₀₎, kg mm⁻²	Calc. H₍₁₁₀₎, kcal cm⁻³	Calc. MH₍₁₀₀₎, kg mm⁻²	[ν₀/Ψ(A)]², cm⁻² × 10⁴
NiO	2.09	11.0	450	0.88	0.18	575	110	605	26.2
CoO	2.13	11.65	390	0.82	0.39	315	93	515	28.2
NiO/CoO	2.11	11.3	413	0.78	0.26	605	119	655	22.6
CaF₂/SrF₂
100:0	2.36	—	291	0.87	0.12	166	28.0	170	112
75:25	2.39	—	290	0.825	0.23	199	32.0	195	122
50:50	2.43	—	281	0.82	0.18	208	31.8	195	118
25:75	2.46	—	268	0.85	0.23	180	27.8	170	100
0:100	2.50	—	252	0.84	0.20	137	25.6	155	88

Solid	Structure	U, kcal mole⁻¹	V, cm³	U/V, kcal cm⁻³	U/V, kbar	MH, kg mm⁻²	K, kbar
BaF₂	Fluorite	550	35.8	15.5	650	80	570
SrF₂	Fluorite	590	29.3	20	830	135	650
CaF₂	Fluorite	630	24.5	25.5	1070	163	900
CaCO₃	Calcite	710	36.9	19.5	810	135	700
ZnS	Zinc blende	795	24.1	33	1370	205	800
SiO₂	Quartz	3150	22.7	138	5800	750	2000
Ge	Diamond	3500	2 × 13.6	129	5400	700	—
Si	Diamond	4400	2 × 12.1	182	7500	1000	—

Solid	r₀, 10⁻⁸ cm	V, cm³	ν_T_0,(110) cm⁻¹	Ψ(A)	Δν/ν₀	Exptl. H₍₁₁₀₎, kg mm⁻²	Calc. H₍₁₁₀₎, kcal cm⁻³	Calc. MH₍₁₀₀₎, kg mm⁻²	[ν₀/Ψ(A)]², cm⁻² × 10⁴
NiO	2.09	11.0	450	0.88	0.18	575	110	605	26.2
CoO	2.13	11.65	390	0.82	0.39	315	93	515	28.2
NiO/CoO	2.11	11.3	413	0.78	0.26	605	119	655	22.6
CaF₂/SrF₂
100:0	2.36	—	291	0.87	0.12	166	28.0	170	112
75:25	2.39	—	290	0.825	0.23	199	32.0	195	122
50:50	2.43	—	281	0.82	0.18	208	31.8	195	118
25:75	2.46	—	268	0.85	0.23	180	27.8	170	100
0:100	2.50	—	252	0.84	0.20	137	25.6	155	88

Solid	Structure	U, kcal mole⁻¹	V, cm³	U/V, kcal cm⁻³	U/V, kbar	MH, kg mm⁻²	K, kbar
BaF₂	Fluorite	550	35.8	15.5	650	80	570
SrF₂	Fluorite	590	29.3	20	830	135	650
CaF₂	Fluorite	630	24.5	25.5	1070	163	900
CaCO₃	Calcite	710	36.9	19.5	810	135	700
ZnS	Zinc blende	795	24.1	33	1370	205	800
SiO₂	Quartz	3150	22.7	138	5800	750	2000
Ge	Diamond	3500	2 × 13.6	129	5400	700	—
Si	Diamond	4400	2 × 12.1	182	7500	1000	—

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Applied Optics