Reflectance of Compacted Powder Mixtures

Elihu A. Schatz

doi:10.1364/JOSA.57.000941

Journal of the Optical Society of America
Vol. 57,
Issue 7,
pp. 941-950
(1967)
•https://doi.org/10.1364/JOSA.57.000941

Reflectance of Compacted Powder Mixtures

Elihu A. Schatz

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Elihu A. Schatz, "Reflectance of Compacted Powder Mixtures," J. Opt. Soc. Am. 57, 941-950 (1967)

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Abstract

The spectral reflectance of compacted powder mixtures in the 0.23 to 2.65 μ range was calculated from the reflectances of the components. Accurate control was maintained over particle size and compaction pressure. Mixtures could be classified into three categories according to the opacities of the powder particles: opaque–opaque, opaque–transparent, and transparent–transparent. The reflectances of opaque–opaque mixtures were always intermediate to those of the components. However, mixtures of opaque–transparent powders could have reflectances either intermediate or considerably lower than those of the components. On the other hand, transparent–transparent mixtures had reflectances intermediate to those of the components, or at most three percent above or below. Equations were developed for calculation of the reflectances of mixtures for the three cases. The equations involved parameters such as the spectral reflectances of the components, their percent surface areas in the mixture, the relative transparencies of the powders, and the single-particle reflectances. Good agreement was obtained in most cases between calculated and experimental data.

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Equations (14)

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Mixture	Wt.%	Surface area%	Reflectance at
			280 mμ		650 mμ		2150 mμ
			Calc.	Meas.	Calc.	Meas.	Calc.	Meas.
Ni–TiB₂	100 Ni	100Ni	⋯	0.122	⋯	0.26	⋯	0.48
(−230+270 mesh powders)	75–25	60–40	0.113	0.115	0.216	0.215	0.400	0.395
	50–50	33–67	0.107	0.115	0.186	0.185	0.346	0.335
	25–75	14–86	0.103	0.110	0.165	0.155	0.31	0.33
	100TiB₂	100TiB₂	⋯	0.100	⋯	0.15	⋯	0.28
Ni–B₄C	100Ni	100Ni	⋯	0.125	⋯	0.265	⋯	0.48
(−230+270 mesh powders)	90–10	72–28	0.12	0.115	0.213	0.21	0.37	0.37
	75–25	46–54	0.116	0.125	0.18	0.17	0.27	0.27
	50–50	22–78	0.112	0.115	0.12	0.105	0.176	0.15
	25–75	8.6–91.4	0.110	0.108	0.096	0.085	0.124	0.11
	100B₄C	100B₄C	⋯	0.108	⋯	0.08	⋯	0.09
Al–TiB₂	100Al	100Al	⋯	0.657	⋯	0.665	⋯	0.885
[−400 +500 mesh TiB₂ (∼34 μ) mixed with −150 +170 mesh Al(∼97 μ)]	75–25	64–36	0.46	0.533	0.48	0.515	0.67	0.694
	50–50	37–63	0.306	0.315	0.344	0.36	0.50	0.52
	25–75	16–84	0.19	0.247	0.234	0.28	0.38	0.417
	100TiB₂	100TiB₂	⋯	0.10	⋯	0.152	⋯	0.28
TiB₂–ZrSi₂	100TiB₂	100TiB₂	⋯	0.11	⋯	0.16	⋯	0.282
(−400 +500 mesh powders)	75–25	76.4–23.6	0.133	0.16	0.164	0.17	0.269	0.274
	50–50	52–48	0.157	0.18	0.168	0.16	0.257	0.245
	25–75	26.5–73.5	0.182	0.20	0.173	0.165	0.244	0.235
	100ZrSi₂	100ZrSi₂	⋯	0.208	⋯	0.178	⋯	0.23
TiB₂–ZrSi₂	100TiB₂	100TiB₂	⋯	0.14	⋯	0.165	⋯	0.27
(−230 +270 mesh powders)	75–25	76.4–23.6	0.161	0.15	0.168	0.165	0.26	0.24
	50–50	52–48	0.183	0.19	0.172	0.17	0.25	0.23
	25–75	26.5–73.5	0.206	0.21	0.176	0.17	0.24	0.23
	100ZrSi₂	100ZrSi₂	⋯	0.23	⋯	0.18	⋯	0.23
Al–Ni	100Al	100Al	⋯	0.65	⋯	0.655	⋯	0.884
(−230 +270 mesh powders)	90–10	96.7–3.3	0.63	0.57	0.65	0.60	0.87	0.82
	75–25	90.8–9.2	0.60	0.524	0.63	0.55	0.847	0.77
	50–50	77–23	0.53	0.425	0.57	0.50	0.79	0.73
	25–75	52–48	0.40	0.363	0.47	0.445	0.69	0.655
	10–90	27–73	0.266	0.196	0.37	0.32	0.59	0.54
	100Ni	100Ni	⋯	0.124	⋯	0.262	⋯	0.478
Al–Ti	100Al	100Al	⋯	0.623	⋯	0.65	⋯	0.822
(−230 +270 mesh powders)	75–25	83.3–16.7	0.536	0.53	0.588	0.594	0.748	0.743
	50–50	62.5–37.5	0.428	0.367	0.511	0.482	0.656	0.64
	25–75	35.7–64.3	0.289	0.243	0.41	0.38	0.538	0.516
	100Ti	100Ti	⋯	0.103	⋯	0.278	⋯	0.38

Mixture	Wt.%	Surface area%	Reflectance at
			280 mμ		650 mμ		2150 mμ
			Calc.	Meas.	Calc.	Meas.	Calc.	Meas.
SiO₂–Al	100SiO₂	100SiO₂	⋯	0.74	⋯	0.87	⋯	0.953
	90–19	91–9	0.675	0.71	0.783	0.79	0.87	0.876
R_A^S = 0.34	75–25	78–22	0.60	0.68	0.68	0.66	0.78	0.78
(−23 +270 mesh powders)	50–50	54–46	0.525	0.582	0.568	0.55	0.69	0.66
	25–75	28–72	0.535	0.577	0.554	0.555	0.72	0.75
	10–90	11.5–88.5	0.59	0.606	0.60	0.60	0.80	0.78
	100Al	100Al	⋯	0.654	⋯	0.665	⋯	0.881
ZrO₂–Al	100ZrO₂	100ZrO₂	a	0.12	⋯	0.76	⋯	0.88
	99–1	98–2	0.13	0.13	0.75	0.70	0.865	0.835
R_A^S = 0.14	90–10	81–19	0.22	0.19	0.65	0.54	0.76	0.69
(−230 +270 mesh powders)	75–25	59–41	0,34	0.275	0.57	0.51	0.68	0.675
	50–50	33–67	0.48	0.46	0.56	0.56	0.68	0.73
	25–75	14–86	0.58	0.57	0.61	0.63	0.75	0.785
	10–90	5–95	0.62	0.61	0.65	0.655	0.80	0.82
	1–99	0.599.5	0.647	0.62	0.668	0.655	0.826	0.82
	100Al	100Al	a	0.65	⋯	0.67	⋯	0.83
ZrO₂–Al	100ZtO₂	100ZrO₂	a	0.15	⋯	0.725	⋯	0.765
	99–1	99.1–0.9	0.154	0.15	0.718	0.71	0.76	0.73
R_A^S = 0.14	90–10	91.2–8.8	0.184	0.15	0.665	0.682	0.718	0.72
(−170 Al with −400 mesh ZrO₂)	75–25	77.5–22.5	0.237	0.17	0.59	0.647	0.664	0.715
	50–50	53.5–16.5	0.329	0.235	0.512	0.58	0.626	0.72
	25–75	27.7–72.3	0.428	0.37	0.503	0.54	0.665	0.73
	10–90	11.3–88.7	0.492	0.46	0.538	0.57	0.733	0.77
	1–99	1.1–98.9	0.531	0.555	0.575	0.59	0.793	0.80
	100Al	100Al	a	0.535	⋯	0.58	⋯	0.80
ZrO₂–Al	100ZrO₂	100ZrO₂	a	0.11	⋯	0.734	⋯	0.895
	99–1	95.2–4.8	0.133	0.115	0.702	0.67	0.856	0.827
R_A^S = 0.14	90–10	64.5–35.4	0.282	0.17	0.56	0.51	0.689	0.69
(−170 mesh ZrO₂ with −400 mesh Al)	75–25	37.8–62.2	0.412	0.315	0.527	0.477	0.658	0.683
	50–50	16.8–83.2	0.514	0.465	0.561	0.545	0.711	0.74
	25–75	6.3–93.7	0.655	0.54	0.598	0.59	0.762	0.79
	10–90	2.2–97.8	0.585	0.56	0.616	0.608	0.786	0.80
	1–99	0.2–99.8	0.595	0.57	0.625	0.611	0.799	0.80
	100Al	100Al	a	0.596	⋯	0.626	⋯	0.80
MoO₃–B₄C	100MoO₃	100MoO₃	a	0.13	a	0.58	⋯	0.71
	99–1	98.2–1.8	0.129	0.13	0.571	0.575	0.693	0.685
R_A^S = 0.4	90–10	83–17	0.123	0.13	0.495	0.50	0.561	0.52
(−230 +270 mesh powders)	75–25	62.5–37.5	0.115	0.12	0.392	0.40	0.405	0.39
	50–50	36–64	0.104	0.12	0.26	0.25	0.242	0.25
	25–75	16–84	0.096	0.105	0.16	0.13	0.148	0.135
	10–90	6–94	0.092	0.09	0.11	0.09	0.115	0.10
	100B₄C	100B₄C	a	0.09	a	0.08	⋯	0.09
MoO₃–Ni	100MoO₃	100MoO₃	a	0.125	a	0.58	⋯	0.735
	99–1	99.5–0.5	0.12	0.12	0.579	0.58	0.733	0.735
R_A^S = 0.5	90–10	95.4–5.5	0.12	0.12	0.563	0.55	0.709	0.69
(−230 +270 mesh powders)	75–25	85–15	0.12	0.12	0.535	0.545	0.668	0.67
	50–50	65.5–34.5	0.12	0.12	0.476	0.515	0.596	0.61
	25–75	39–61	0.12	0.12	0.395	0.44	0.527	0.57
	10–90	17–83	0.12	0.12	0.329	0.34	0.494	0.52
	1–99	1.9–98.1	0.12	0.12	0.283	0.29	0.485	0.50
	100Ni	100Ni	a	0.115	a	0.277	⋯	0.485

Mixture	Wt.%	Surface area%	Reflectance at
			280 mμ		650 mμ		2150 mμ
			Calc.	Meas.	Calc.	Meas.	Calc.	Meas.
TiO₂–Ti	100TiO₂	100TiO₃	⋯	0.11	⋯	0.69	⋯	0.537
	99–1	99–1	0.110	0.11	0.69	0.69	0.536	0.537
−230 +270 mesh powders	90–10	90.5–9.5	0.112	0.11	0.66	0.67	0.529	0.515
	75–25	76–24	0.116	0.115	0.61	0.64	0.517	0.49
	50–50	51.5–48.5	0.122	0.115	0.53	0.59	0.497	0.49
	25–75	26–74	0.129	0.115	0.45	0.48	0.476	0.47
	10–90	10.5–89.5	0.132	0.12	0.395	0.405	0.464	0.45
	1–99	1–99	0.135	0.13	0.36	0.36	0.456	0.455
	100Ti	100Ti	⋯	0.135	⋯	0.36	⋯	0.455
TiO₂–ZrSi₂	100TiO₂	100TiO₂	⋯	0.12	⋯	0.685	⋯	0.50
	99–1	99.1–0.9	0.12	0.12	0.68	0.66	0.498	0.48
−230 +270 mesh powders	90–10	91–9	0.13	0.12	0.64	0.64	0.478	0.48
	75–25	77.5–22.5	0.14	0.12	0.574	0.58	0.446	0.47
	50–50	53.5–46.5	0.17	0.14	0.455	0.475	0.388	0.405
	25–75	28–72	0.20	0.17	0.33	0.34	0.327	0.335
	10–90	11–89	0.218	0.20	0.245	0.26	0.286	0.295
	1–99	1.1–98.9	0.229	0.22	0.195	0.195	0.263	0.26
	100ZrSi₂	100ZrSi₂	⋯	0.23	⋯	0.19	⋯	0.26

Mixture	Wt.%	Surface area%	Reflectance at
			280 mμ		650 mμ		2150 mμ
			Calc.	Meas.	Calc.	Meas.	Calc.	Meas.
TiO₂–Al	100TiO₂	100TiO₂	^a	0.11	⋯	0.64	⋯	0.504
(compacted at 16 200 newtons/sq. cm.) (−230 +270 mesh powders) (R_A^S = 0.20 at 650 mμ)(R_A^S = 0.17 at 2150 mμ)	75–25	65.5–34.5	0.297	0.195	0.55	0.628	0.558	0.583
	50–50	39–61	0.441	0.243	0.55	0.608	0.654	0.658
	25–75	17.4–82.6	0.558	0.376	0.59	0.58	0.767	0.70
	10–90	6.7–93.4	0.617	0.47	0.63	0.59	0.835	0.74
	1–99	0.6–99.4	0.650	0.54	0.65	0.56	0.876	0.77
	100Al	100Al	^a	0.653	⋯	0.665	⋯	0.88
TiO₂–Al	100TiO₂	100TiO₂	^a	0.116	⋯	0.645	⋯	0.50
(compacted at 48 600 newtons/sq. cm.) (−230 +270 mesh powders) (R_A^S = 0.20 at 650 mμ) (R_A^S = 0.17 at 2150 mμ)	75–25	65.5–34.5	0.335	0.173	0.591	0.532	0.553	0.44
	50–50	39–61	0.503	0.235	0.622	0.508	0.647	0.53
	25–75	17.4–82.6	0.641	0.42	0.693	0.567	0.758	0.645
	10–90	6.7–93.4	0.709	0.467	0.744	0.61	0.825	0.716
	1–99	0.6–99.4	0.747	0.56	0.777	0.615	0.866	0.76
	100Al	100Al	^a	0.751	⋯	0.78	⋯	0.87
SiO₂–Ni	100SiO₂	100SiO₂	^a	0.696	⋯	0.866	⋯	0.97
(−230 +270 mesh powders) R_A^S= 0.034	75–25	92–8	0.648	0.658	0.753	0.725	0.857	0.686
	50–50	80–20	0.577	0.605	0.604	0.62	0.710	0.604
	25–75	56.5–43.5	0.437	0.40	0.381	0.415	0.499	0.48
	10–90	30–70	0.279	0.32	0.239	0.365	0.386	0.455
	100Ni	100Ni	^a	0.10	⋯	0.22	⋯	0.417
SiO₂–TiB₂	100SiO₂	100SiO₂	^a	0.695	^a	0.87	⋯	0.93
(−230 +270 mesh powders) (R_A^S = 0.034)	99–1	99.5–0.5	0.692	0.695	0.867	0.855	0.922	0.885
	90–10	95–5	0.666	0.69	0.834	0.82	0.855	0.737
	75–25	86–14	0.613	0.66	0.770	0.73	0.731	0.61
	50–50	67–33	0.502	0.59	0.634	0.61	0.517	0.505
	25–75	40–60	0.344	0.42	0.441	0.41	0.325	0.38
	10–90	18–82	0.215	0.22	0.284	0.24	0.265	0.31
	1–99	2–98	0.122	0.12	0.169	0.157	0.279	0.28
	100TiB₂	100TiB₂	^a	0.11	^a	0.155	⋯	0.28
SiO₂–TiB₂	100SiO₂	100SiO₂	^a	0.665	^a	0.833	⋯	0.87
(−170 mesh SiO₂ with −400) mesh TiB₂) (R_A^S = 0.034)	99–1	98.8–1.2	0.658	0.665	0.825	0.815	0.853	0.82
	90–10	88–12	0.599	0.636	0.753	0.69	0.713	0.576
	75–25	71–29	0.506	0.59	0.641	0.585	0.532	0.445
	50–50	45–55	0.363	0.48	0.468	0.467	0.348	0.36
	25–75	21.5–78.5	0.233	0.33	0.313	0.323	0.279	0.325
	10–90	8.4–91.6	0.161	0.218	0.226	0.24	0.281	0.312
	1–99	0.8–99.2	0.119	0.13	0.175	0.178	0.295	0.305
	100TiB₂	100TiB₂	^a	0.115	^a	0.17	⋯	0.297
SiO₂–TiB₂	100SiO₂	100SiO₂	^a	0.705	^a	0.845	⋯	0.93
(−170 mesh TiB₂ with −400 mesh SiO₂) (R_A^S = 0.034)	99–1	99.8–0.2	0.704	0.695	0.844	0.845	0.927	0.90
	90–10	97.7–2.3	0.692	0.66	0.829	0.778	0.895	0.704
	75–25	93.3–6.7	0.666	0.66	0.799	0.686	0.831	0.56
	50–50	82.3–17.7	0.60	0.66	0.724	0.658	0.686	0.50
	25–75	61–39	0.477	0.42	0.578	0.412	0.466	0.378
	10–90	34–66	0.319	0.33	0.393	0.324	0.304	0.332
	1–99	4.5–95.5	0.146	0.135	0.191	0.175	0.277	0.295
	100TiB₂	100TiB₂	^a	0.12	^a	0.16	⋯	0.286

Mixture	Wt.%	Surface area%	Reflectance at
			280 mμ		650 mμ		2150 mμ
			Calc.	Meas.	Calc.	Meas.	Calc.	Meas.
Al₂O₃–SiO₂	100Al₂O₃	100Al₂O₃	^a	0.43	⋯	0.785	⋯	0.768
R^S(SiO₂) = 0.034	75–25	64–36	0.542	0.592	0.816	0.817	0.831	0.83
R^S(Al₂O₃) = 0.078	50–50	37–63	0.625	0.67	0.840	0.817	0.880	0.83
(−230 +270 mesh powders)	25–75	16–84	0.690	0.713	0.858	0.85	0.919	0.903
	100SiO₂	100SiO₂	^a	0.74	⋯	0.873	⋯	0.95
ZrO₂–Al₂O₃	100ZrO₂	100ZrO₂	^a	0.113	⋯	0.75	⋯	0.88
R^S(ZrO₂) = 0.14	99–1	98.6–1.4	0.117	0.113	0.751	0.75	0.878	0.88
R^S(Al₂O₃) = 0.078	90–10	86.5–13.5	0.154	0.132	0.757	0.75	0.864	0.86
(−230 +270 mesh powders)	75–25	68–32	0.210	0.175	0.767	0.76	0.841	0.845
	50–50	42–58	0.288	0.24	0.781	0.778	0.808	0.805
	25–75	19–81	0.358	0.312	0.794	0.794	0.777	0.79
	10–90	7.4–92.6	0.393	0.367	0.801	0.81	0.762	0.79
	1–99	0.7–99.3	0.413	0.385	0.805	0.794	0.753	0.752
	100Al₂O₃	100Al₂O₃	^a	0.415	⋯	0.805	⋯	0.752
MoO₃–SiO₂	100MoO₃	100MoO₃	^b	0.12	⋯	0.57	⋯	0.69
R^S(MoO₃) = 0.4	90–10	81.5–18.5	0.126	0.15	0.595	0.57	0.718	0.69
R^S(SiO₂) = 0.034	75–25	59.5–40.5	0.245	0.19	0.642	0.585	0.753	0.695
(−230 +270 mesh powders)	50–50	33–67	0.346	0.31	0.724	0.672	0.816	0.75
	25–75	14–86	0.514	0.43	0.800	0.70	0.873	0.78
	10–90	5–95	0.609	0.55	0.840	0.795	0.903	0.875
	1–99	0.5–99.5	0.660	0.58	0.862	0.81	0.919	0.882
	100SiO₂	100SiO₂	^b	0.666	⋯	0.864	⋯	0.92
MoO₃–SiO₂	100MoO₃	100MoO₃	^b	0.123	⋯	0.58	⋯	0.745
R^S(MoO₃) = 0.4	99–1	98.8–1.2	0.122	0.13	0.582	0.585	0.747	0.75
R^S(SiO₂) = 0.034	90–10	88.1–11.9	0.122	0.16	0.596	0.61	0.759	0.765
	75–25	71.3–28.7	0.151	0.208	0.626	0.629	0.783	0.775
(−170 mesh SiO₂ −270 mesh MoO₃)	50–50	45.2–54.8	0.274	0.31	0.696	0.695	0.834	0.836
	25–75	21.6–78.4	0.464	0.466	0.781	0.77	0.892	0.878
	10–90	8.4–91.6	0.592	0.57	0.839	0.805	0.929	0.895
	1–99	0.8–99.2	0.689	0.68	0.875	0.86	0.952	0.93
	100SiO₂	100SiO₂	^b	0.70	⋯	0.879	⋯	0.955
ZrO₂–TiO₂	100ZrO₂	100ZrO₂	^a	0.114	^b	0.72	^b	0.876
R^S(ZrO₂) = 0.14	99–1	98.7–1.3	0.11	0.125	0.712	0.718	0.862	0.78
(−230 +270 mesh powders)	95–5	93.6–6.4	0.11	0.112	0.680	0.664	0.808	0.672
	90–10	87.4–12.6	0.11	0.109	0.646	0.645	0.748	0.616
	75–25	70–30	0.11	0.095	0.574	0.625	0.609	0.573
	50–50	43.5–56.5	0.11	0.095	0.532	0.64	0.484	0.559
	25–75	20–80	0.11	0.095	0.563	0.655	0.459	0.555
	100TiO₂	100TiO₂	^a	0.11	^b	0.64	^b	0.502
MnO–TiO₂	100MnO	100MnO	^a	0.11	^a	0.167	^b	0.805
R^S(MnO) = 0.17	99–1	98.8–1.2	0.11	0.11	0.173	0.185	0.794	0.74
(−230 +270 mesh powders)	90–10	88–12	0.112	0.12	0.227	0.26	0.699	0.515
	75–25	71.4–28.6	0.116	0.12	0.309	0.36	0.582	0.462
	50–50	45.5–54.5	0.121	0.12	0.438	0.50	0.470	0.462
	25–75	22–78	0.126	0.13	0.555	0.577	0.443	0.45
	10–90	8.5–91.5	0.128	0.13	0.623	0.635	0.458	0.47
	1–99	0.8–99.2	0.13	0.13	0.661	0.66	0.478	0.475
	100TiO₂	100TiO₂	^a	0.13	^a	0.665	^b	0.48

Abstract

Cited By

Figures (9)

Tables (5)

Equations (14)

Journal of the Optical Society of America