Characteristic Spectra of Energy Absorption for Dielectric Solids

J. N. Plendl

doi:10.1364/AO.9.002768

Applied Optics
Vol. 9,
Issue 12,
pp. 2768-2786
(1970)
•https://doi.org/10.1364/AO.9.002768

Characteristic Spectra of Energy Absorption for Dielectric Solids

J. N. Plendl

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J. N. Plendl, "Characteristic Spectra of Energy Absorption for Dielectric Solids," Appl. Opt. 9, 2768-2786 (1970)

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Abstract

A method has been developed of deriving the fundamental absorption spectra of solids directly from experimental infrared data without having to resort to computational evaluation. These characteristic lattice absorption spectra represent the true energy absorption spectra of solids. As opposed to the traditional absorption coefficient (k) vs frequency curve, which is regarded as the absorption spectrum for solids in the region of anomalous dispersion, the spectra, as derived by the proposed method, clearly resolve the transverse and longitudinal modes of vibration. They also exhibit the characteristics of anharmonicity and damping. The method uses the combined reflection and transmission data on single-crystal and thin-film specimens. Its validity has been verified on a wide variety of solids. The most recent data obtained from emission, laser-Raman, or cold neutron scattering techniques, is in complete agreement with the derived values. A method of calculating the various modes of vibration of solids, directly from elastic constants, is also advanced. It is simultaneously used to render further support for the developed characteristic energy absorption spectra. The importance of these spectra is discussed with regard to some problems in solid state physics.

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No.	Solid	Structure	ρ g cm⁻³	r₀ 10⁻⁸ cm	C₁₁	C₁₂	C₄₄	ν_TO(110) cm⁻¹	ν_TO(100) cm⁻¹	ν_LO(100) cm⁻¹	ν_LO(100) cm⁻¹	ν_LO(111) cm⁻¹	ν_ctr cm⁻¹
No.	Solid	Structure	ρ g cm⁻³	r₀ 10⁻⁸ cm	—10¹¹ dyn cm⁻²—			ν_TO(110) cm⁻¹	ν_TO(100) cm⁻¹	ν_LO(100) cm⁻¹	ν_LO(100) cm⁻¹	ν_LO(111) cm⁻¹	ν_ctr cm⁻¹
1	MgO	[NaCl]	3.59	2.10	28.9	8.80	15.5	420	522	715	765	796	520
								422^b	515^b	725^b	750^b		513^b
2	LiF	[NaCl]	2.64	2.01	11.77	4.33	6.28	310	405	555	612	632	421
								303	396^b	525^b		640^a	415^b
								307^a				655^b
								306b
3	NaF	[NaCl]	2.80	2.31	9.70	2.50	2.80	257	229	425	406	402	302
								250^a,^b		425^a,^b	400^b	400^b	290^b
								249^b
4	NaCl	[NaCl]	2.16	2.815	4.68	1.23	1.19	167	139	276	258	253	196
								169^a,^b	139^b	290^b	248^b	248^b	190^b
								166.5^b
5	NaBr	[NaCl]	3.20	2.98	4.96	1.24	1.29	135	112	220	211	222	156
								136.5^b	115^b				156^b
6	NaI	[NaCl]	3.67	3.23	3.80	0.70	0.70	112	75	175	155	147	119
								122^a,^b		170^a,^b	155^a,^b		120^b
								118^b
7	KCl	[NaCl]	1.99	3.14	3.69	0.81	0.79	143	106	228	208	200	161
								145^b	114^b	245^b	208^b	208^b	162^b
8	KBr	[NaCl]	2.75	3.295	3.49	0.58	0.51	117	69	181	155	144	120
								121	60–70^b	180^b	164^a,^b		119^b
								1185			160^b
9	KI	[NaCl]	3.13	3.525	3.32	0.58	0.62	99	52	154	121	129	103
								100.5^b	50^b	160^b	125^b	130^b	102^b
10	RbCl	[NaCl]	2.80	3.27	3.65	0.61	0.48	121	66.5	184	156	145	123
								120.5^b	<75^b	>160^b	160^b		126^b
11	RbBr	[NaCl]	3.35	3.425	3.10	0.49	0.38	96	52	148	124	115	98
								92.5^b	<60^b	145^b	125^b	115^b	96^b
12	RbI	[NaCl]	3.55	3.665	2.54	0.41	0.28	78.5	40	121	101	94	81
								77.5^b	40^b	120^b	100^b	95^b	83^b
13	CsBr	[CsCl]	4.40	3.715	3.07	0.80	0.72	71.5	58	118	110	107	83.5
								74.5^b	<60^b	125^b	105^b	105^b	84.5^b
14	CsI	[CsCl]	4.50	3.95	2.46	0.65	0.63	60	50	99	93	110	70
								64.2^b	<50^b	100^b	91^b		69^b
15	TlBr	[CsCl]	7.55	3.45	3.73	1.50	0.75	58	48	107	85	55	84
								535	53^b	112^b	85^b	53^b	85.5^b

No.	Substance	Structure	CN	r₀ 10⁻⁸ cm	d 10⁻⁴ cm	d/r₀ Number of atomic layers	F[A_C(ν)]	F[A_C(ν)] × (d/r₀) Depth of absorption	F[A_C(ν)] d/r₀ Atomic layer absorption × 10⁻⁴
1	NaCl	NaCl	6:6	2.815	0.17	600	2.4	1450	40
2	NaCl	NaCl	6:6	2.815	1.35	4800	2.8	13500	5.9
3	NaCl	NaCl	6:6	2.815	2.3	8200	2.7	22200	3.3
4	NaCl	NaCl	6:6	2.815	3.6	12800	1.85	23400	1.45
5	LiF	NaCl	6:6	2.01	0.3	1500	2.5	3750	16.7
6	KCl	NaCl	6:6	3.14	0.56	1800	3.2	5700	17.6
7	KI	NaCl	6:6	3.52	2.20	6200	2.5	15500	4.0
8	RbCl	NaCl	6:6	3.27	2.52	7700	2.5	19500	3.3
9	RbBr	NaCl	6:6	3.42	2.03	5900	2.8	16500	4.7
10	RbI	NaCl	6:6	3.66	1.50	4100	2.2	9000	5.3
11	RbI	NaCl	6:6	3.66	3.54	9700	2.3	22500	2.4
12	CsCl	CsCl	8:8	3.56	0.97	2720	1.4	3800	5.2
13	CsBr	CsCl	8:8	3.72	0.35	940	1.4	1300	15.0
14	CsBr	CsCl	8:8	3.72	1.02	2750	1.7	4600	6.1
15	CsI	CsCl	8:8	3.95	2.06	5200	1.8	9400	3.4
16	CsI	CsCl	8:8	3.95	5.0	12600	2.3	2900	1.8
17	TlBr	CsCl	8:8	3.41	0.92	2700	1.5	4000	5.5
18	TlI	CsCl	8:8	3.62	0.98	2700	1.9	5100	7.0

No.	Solid	Structure	ρ g cm⁻³	r₀ 10⁻⁸ cm	C₁₁	C₁₂	C₄₄	ν_TO(110) cm⁻¹	ν_TO(100) cm⁻¹	ν_LO(100) cm⁻¹	ν_LO(100) cm⁻¹	ν_LO(111) cm⁻¹	ν_ctr cm⁻¹
No.	Solid	Structure	ρ g cm⁻³	r₀ 10⁻⁸ cm	—10¹¹ dyn cm⁻²—			ν_TO(110) cm⁻¹	ν_TO(100) cm⁻¹	ν_LO(100) cm⁻¹	ν_LO(100) cm⁻¹	ν_LO(111) cm⁻¹	ν_ctr cm⁻¹
1	MgO	[NaCl]	3.59	2.10	28.9	8.80	15.5	420	522	715	765	796	520
								422^b	515^b	725^b	750^b		513^b
2	LiF	[NaCl]	2.64	2.01	11.77	4.33	6.28	310	405	555	612	632	421
								303	396^b	525^b		640^a	415^b
								307^a				655^b
								306b
3	NaF	[NaCl]	2.80	2.31	9.70	2.50	2.80	257	229	425	406	402	302
								250^a,^b		425^a,^b	400^b	400^b	290^b
								249^b
4	NaCl	[NaCl]	2.16	2.815	4.68	1.23	1.19	167	139	276	258	253	196
								169^a,^b	139^b	290^b	248^b	248^b	190^b
								166.5^b
5	NaBr	[NaCl]	3.20	2.98	4.96	1.24	1.29	135	112	220	211	222	156
								136.5^b	115^b				156^b
6	NaI	[NaCl]	3.67	3.23	3.80	0.70	0.70	112	75	175	155	147	119
								122^a,^b		170^a,^b	155^a,^b		120^b
								118^b
7	KCl	[NaCl]	1.99	3.14	3.69	0.81	0.79	143	106	228	208	200	161
								145^b	114^b	245^b	208^b	208^b	162^b
8	KBr	[NaCl]	2.75	3.295	3.49	0.58	0.51	117	69	181	155	144	120
								121	60–70^b	180^b	164^a,^b		119^b
								1185			160^b
9	KI	[NaCl]	3.13	3.525	3.32	0.58	0.62	99	52	154	121	129	103
								100.5^b	50^b	160^b	125^b	130^b	102^b
10	RbCl	[NaCl]	2.80	3.27	3.65	0.61	0.48	121	66.5	184	156	145	123
								120.5^b	<75^b	>160^b	160^b		126^b
11	RbBr	[NaCl]	3.35	3.425	3.10	0.49	0.38	96	52	148	124	115	98
								92.5^b	<60^b	145^b	125^b	115^b	96^b
12	RbI	[NaCl]	3.55	3.665	2.54	0.41	0.28	78.5	40	121	101	94	81
								77.5^b	40^b	120^b	100^b	95^b	83^b
13	CsBr	[CsCl]	4.40	3.715	3.07	0.80	0.72	71.5	58	118	110	107	83.5
								74.5^b	<60^b	125^b	105^b	105^b	84.5^b
14	CsI	[CsCl]	4.50	3.95	2.46	0.65	0.63	60	50	99	93	110	70
								64.2^b	<50^b	100^b	91^b		69^b
15	TlBr	[CsCl]	7.55	3.45	3.73	1.50	0.75	58	48	107	85	55	84
								535	53^b	112^b	85^b	53^b	85.5^b

No.	Substance	Structure	CN	r₀ 10⁻⁸ cm	d 10⁻⁴ cm	d/r₀ Number of atomic layers	F[A_C(ν)]	F[A_C(ν)] × (d/r₀) Depth of absorption	F[A_C(ν)] d/r₀ Atomic layer absorption × 10⁻⁴
1	NaCl	NaCl	6:6	2.815	0.17	600	2.4	1450	40
2	NaCl	NaCl	6:6	2.815	1.35	4800	2.8	13500	5.9
3	NaCl	NaCl	6:6	2.815	2.3	8200	2.7	22200	3.3
4	NaCl	NaCl	6:6	2.815	3.6	12800	1.85	23400	1.45
5	LiF	NaCl	6:6	2.01	0.3	1500	2.5	3750	16.7
6	KCl	NaCl	6:6	3.14	0.56	1800	3.2	5700	17.6
7	KI	NaCl	6:6	3.52	2.20	6200	2.5	15500	4.0
8	RbCl	NaCl	6:6	3.27	2.52	7700	2.5	19500	3.3
9	RbBr	NaCl	6:6	3.42	2.03	5900	2.8	16500	4.7
10	RbI	NaCl	6:6	3.66	1.50	4100	2.2	9000	5.3
11	RbI	NaCl	6:6	3.66	3.54	9700	2.3	22500	2.4
12	CsCl	CsCl	8:8	3.56	0.97	2720	1.4	3800	5.2
13	CsBr	CsCl	8:8	3.72	0.35	940	1.4	1300	15.0
14	CsBr	CsCl	8:8	3.72	1.02	2750	1.7	4600	6.1
15	CsI	CsCl	8:8	3.95	2.06	5200	1.8	9400	3.4
16	CsI	CsCl	8:8	3.95	5.0	12600	2.3	2900	1.8
17	TlBr	CsCl	8:8	3.41	0.92	2700	1.5	4000	5.5
18	TlI	CsCl	8:8	3.62	0.98	2700	1.9	5100	7.0

Abstract

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Equations (14)

Applied Optics