Determining absolute thermal expansion of titania–silica glasses: a refined ultrasonic method

H. E. Hagy; W. D. Shirkey

doi:10.1364/AO.14.002099

Applied Optics
Vol. 14,
Issue 9,
pp. 2099-2103
(1975)
•https://doi.org/10.1364/AO.14.002099

Determining absolute thermal expansion of titania–silica glasses: a refined ultrasonic method

H. E. Hagy and W. D. Shirkey

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H. E. Hagy and W. D. Shirkey, "Determining absolute thermal expansion of titania–silica glasses: a refined ultrasonic method," Appl. Opt. 14, 2099-2103 (1975)

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Abstract

Specific test conditions for determining ultrasonic velocities in titania-silica glasses are shown to improve the experimentally established linear correlation between velocity and thermal expansion. Finer surface finish, normalized thermal history (annealing), and controlled temperature for the test specimen improve the relationship. A statistical analysis shows that 5–35°C average expansion coefficients can be accurately predicted from ultrasonic velocities with a standard deviation of 1 ppb/°C. Excellent agreement is established between the ultrasonic predicted expansion and test results supplied by the University of Arizona Optical Sciences Center.

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	A	B	σ, ppb/°C

			All data	Under 4 in. thick
Before anneal
Intervalometer	64,920	0.226434	7.95	8.02
Pulse overlap	66,300	0.226437	7.81	7.57
After anneal
Intervalometer	59,840	0.226123	7.81	7.16
Pulse overlap	60,310	0.226153	7.64	7.26

Glass	d	S_i	S_p	k	V_i	V_P	α_d	α_i	α_p	α_i – α_d	α_p – α_d	α_i – α_p
1A. Glass thicker than 4 in.
327–134	6.14258	54.575	—	0.243	0.226113	—	−28	−17	—	+11	—	—
347–130	6.04379	53.688	—	0.244	0.226173	—	−20	−14	—	+6	—	—
347–129	6.00829	53.372	—	0.245	0.226186	—	−13	−13	—	0	—	—
337–124	5.69469	50.620	50.3590	0.250	0.226114	0.226164	−29	−17	−14	+12	+15	−3
317–123	5.64349	50.145	49.9087	0.251	0.226219	0.226153	−15	−11	−15	+4	0	+4
347−133	5.57504	49.567	49.3097	0.252	0.226099	0.226124	−2	−18	−17	−16	−15	−1
337–125	5.18328	46.091	45.8218	0.257	0.226176	0.226236	−11	−14	−10	−3	+1	−4
317–121	5.18287	46.075	45.8152	0.257	0.226237	0.226251	0	−10	−9	−10	−9	−1
347–135	5.03383	44.777	44.5281	0.258	0.226143	0.226097	−14	−16	−18	−2	−4	+2
347–134	4.92159	43.778	43.5165	0.259	0.226181	0.226194	−10	−13	−13	−3	−3	0
317–122	4.80809	42.788	42.5224	0.259	0.226109	0.226144	−6	−18	−16	−12	−10	−2
357−102	4.55220	40.540	40.2795	0.261	0.226033	0.226031	−15	−22	−22	−7	−7	0
347–132	4.22544	37.628	37.3665	0.262	0.226165	0.226162	−9	−14	−14	−5	−5	0
357–111	4.21093	37.500	37.2328	0.262	0.226163	0.226195	−14	−14	−13	0	+1	−1
317–124	4.20837	37.476	37.2079	0.262	0.226171	0.226208	−2	−14	−12	−12	−10	−2

1B. Glass Thinner than 4 in.										σ_A = 8.69	σ_B = 8.70	↓

337–102	3.83800	34.241	33.9665	0.263	0.225911	0.225987	−16	−29	−25	−13	−9	−4
347–113	3.79616	33.849	33.5816	0.264	0.226063	0.226086	−24	−20	−19	+4	+5	−1
357–109	3.78762	33.796	33.5354	0.264	0.225911	0.225888	−40	−29	−31	+11	+9	+2
337–110	3.77002	33.600	33.3317	0.264	0.226183	0.226212	−24	−13	−12	+11	+12	−1
357–103	3.76158	33.545	33.2775	0.264	0.226050	0.226074	−27	−21	−20	+6	+7	−1
357–113	3.75647	33.522	33.2628	0.264	0.225899	0.225866	−29	−30	−32	−1	−3	+2
337–123	3.75410	33.343	33.0750	0.264	0.226978	0.227000	+29	+34	+35	+5	+6	−1
357–110	3.72071	33.182	32.9292	0.264	0.226059	0.225982	−28	−21	−25	+7	+3	+4
437–101	3.60339	32.144	31.8771	0.265	0.226067	0.226080	−11	−20	−19	−9	−8	−1
347–116	3.46704	30.964	30.6975	0.266	0.225881	0.225884	−32	−31	−31	+1	+1	0
347–107	3.46293	30.924	30.6494	0.266	0.225907	0.225970	−32	−30	−26	+2	+6	−4
437−105	3.46291	30.907	30.6306	0.266	0.226031	0.226108	−21	−22	−18	−1	+3	−4
347–115	3.22347	28.822	28.5472	0.268	0.225781	0.225834	−37	−37	−34	0	+3	−3
347−101	3.15490	28.201	27.9375	0.269	0.225899	0.225854	−29	−30	−33	−1	−4	+3
337–106	2.92153	26.161	25.8796	0.270	0.225679	0.225779	−50	−43	−37	+7	+13	−6
337–107	2.91650	26.098	25.8244	0.270	0.225840	0.225872	−34	−34	−32	0	+2	−2
										σ_C = 6.71	σ_D = 7.03	σ_E = 2.66

Temperature, °C	Expansivity, ppb/°C

	OSC measured	OSC calculated	α_i	α_p
137.3	+71	+70.7
112.3	+69	+70.3
86.8	+62	+59.1
60.8	+40	+43.0
35.5	+20	+17.6
20.0	—	−5.4 ± 1.3^a	−6.4 ± 0.5^a	−5.8 ± 0.9^a
12.7	−21	−18.6
−10.8	−69	−70.5
−35.9	−140	−140.9
−60.9	−227	−225.0
−86.8	−335	−336.1
−112.7	−508	−507.8

	A	B	σ, ppb/°C

			All data	Under 4 in. thick
Before anneal
Intervalometer	64,920	0.226434	7.95	8.02
Pulse overlap	66,300	0.226437	7.81	7.57
After anneal
Intervalometer	59,840	0.226123	7.81	7.16
Pulse overlap	60,310	0.226153	7.64	7.26

Glass	d	S_i	S_p	k	V_i	V_P	α_d	α_i	α_p	α_i – α_d	α_p – α_d	α_i – α_p
1A. Glass thicker than 4 in.
327–134	6.14258	54.575	—	0.243	0.226113	—	−28	−17	—	+11	—	—
347–130	6.04379	53.688	—	0.244	0.226173	—	−20	−14	—	+6	—	—
347–129	6.00829	53.372	—	0.245	0.226186	—	−13	−13	—	0	—	—
337–124	5.69469	50.620	50.3590	0.250	0.226114	0.226164	−29	−17	−14	+12	+15	−3
317–123	5.64349	50.145	49.9087	0.251	0.226219	0.226153	−15	−11	−15	+4	0	+4
347−133	5.57504	49.567	49.3097	0.252	0.226099	0.226124	−2	−18	−17	−16	−15	−1
337–125	5.18328	46.091	45.8218	0.257	0.226176	0.226236	−11	−14	−10	−3	+1	−4
317–121	5.18287	46.075	45.8152	0.257	0.226237	0.226251	0	−10	−9	−10	−9	−1
347–135	5.03383	44.777	44.5281	0.258	0.226143	0.226097	−14	−16	−18	−2	−4	+2
347–134	4.92159	43.778	43.5165	0.259	0.226181	0.226194	−10	−13	−13	−3	−3	0
317–122	4.80809	42.788	42.5224	0.259	0.226109	0.226144	−6	−18	−16	−12	−10	−2
357−102	4.55220	40.540	40.2795	0.261	0.226033	0.226031	−15	−22	−22	−7	−7	0
347–132	4.22544	37.628	37.3665	0.262	0.226165	0.226162	−9	−14	−14	−5	−5	0
357–111	4.21093	37.500	37.2328	0.262	0.226163	0.226195	−14	−14	−13	0	+1	−1
317–124	4.20837	37.476	37.2079	0.262	0.226171	0.226208	−2	−14	−12	−12	−10	−2

1B. Glass Thinner than 4 in.										σ_A = 8.69	σ_B = 8.70	↓

337–102	3.83800	34.241	33.9665	0.263	0.225911	0.225987	−16	−29	−25	−13	−9	−4
347–113	3.79616	33.849	33.5816	0.264	0.226063	0.226086	−24	−20	−19	+4	+5	−1
357–109	3.78762	33.796	33.5354	0.264	0.225911	0.225888	−40	−29	−31	+11	+9	+2
337–110	3.77002	33.600	33.3317	0.264	0.226183	0.226212	−24	−13	−12	+11	+12	−1
357–103	3.76158	33.545	33.2775	0.264	0.226050	0.226074	−27	−21	−20	+6	+7	−1
357–113	3.75647	33.522	33.2628	0.264	0.225899	0.225866	−29	−30	−32	−1	−3	+2
337–123	3.75410	33.343	33.0750	0.264	0.226978	0.227000	+29	+34	+35	+5	+6	−1
357–110	3.72071	33.182	32.9292	0.264	0.226059	0.225982	−28	−21	−25	+7	+3	+4
437–101	3.60339	32.144	31.8771	0.265	0.226067	0.226080	−11	−20	−19	−9	−8	−1
347–116	3.46704	30.964	30.6975	0.266	0.225881	0.225884	−32	−31	−31	+1	+1	0
347–107	3.46293	30.924	30.6494	0.266	0.225907	0.225970	−32	−30	−26	+2	+6	−4
437−105	3.46291	30.907	30.6306	0.266	0.226031	0.226108	−21	−22	−18	−1	+3	−4
347–115	3.22347	28.822	28.5472	0.268	0.225781	0.225834	−37	−37	−34	0	+3	−3
347−101	3.15490	28.201	27.9375	0.269	0.225899	0.225854	−29	−30	−33	−1	−4	+3
337–106	2.92153	26.161	25.8796	0.270	0.225679	0.225779	−50	−43	−37	+7	+13	−6
337–107	2.91650	26.098	25.8244	0.270	0.225840	0.225872	−34	−34	−32	0	+2	−2
										σ_C = 6.71	σ_D = 7.03	σ_E = 2.66

Abstract

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Applied Optics