Clarke number

This article is about the geochemistry term. For modern data, see Abundance of elements in Earth's crust. For the geodesy term, see Earth ellipsoid § Historical Earth ellipsoids.

Clarke number or clarke is the relative abundance of a chemical element, typically in Earth's crust. The technical definition of "Earth's crust" varies among authors, and the actual numbers also vary significantly.

History

In the 1930s, USSR geochemist Alexander Fersman defined the relative abundance of chemical elements in geological objects, denoted in percents, as Russian: кларки, lit. 'the clarkes'.^{[F 1]: 141} This was in honor to the American geochemist Frank Wigglesworth Clarke, who pioneered in estimating the chemical composition of Earth's crust, based on Clarke and colleague's extensive chemical analysis of numerous rock samples, throughout 1889 to 1924(^{[C 1][C 2][C 3][C 4][C 5][C 6][C 7][C 8][C 9]}).

Examples based on Fersman's definition:

• Russian: весовой кларк, lit. 'weight clarke': When the whole mass of a planet X is ${\displaystyle Mx}$ [kg], and the mass of oxygen there is ${\displaystyle Mo}$ [kg], then the weight clarke of oxygen in planet X is ${\displaystyle Km={\frac {Mo}{Mx}}}$ (dimensionless)
• Russian: кларк числа атомов, lit. 'clarke of atom count': When the whole count of atoms in a rock Y is ${\displaystyle Ay}$ [mol], and the atom count of silicon there is ${\displaystyle As}$ [mol], then silicon's clarke of atom count in rock Y is ${\displaystyle Ka={\frac {As}{Ay}}}$ (dimensionless)
• Fersman's "clarke of Earth's crust" is the Earth's surface including 16 km-thick lithosphere, hydrosphere and atmosphere.^{[F 1]: 141}

In Russian

Russian: кларки is synonymous to "the relative abundance of elements" in any object, either in weight ratio or in atomic (number of atoms) ratio, regardless of how "Earth's crust" is defined, and denotation is not restricted to percents.^{[x 1]}

In English

In the English speaking world, the term "clarke" was not even used in Wells(1937)^{[U 1]: 4} which introduced Fersman's proposal, nor in later USGS articles such as Fleischer(1953).^{[U 2]} They used the term "relative abundance of the elements". Brian Mason also mentioned the term "clarke" in Mason(1952)^{[M 1]: 42}(mistakenly attributing it to Vladimir Vernadsky, later corrected to Fersman in Mason(1958)^{[M 2]: 47}), but the definition slightly differed from Fersman's, limiting it only to the average percentage in Earth's crust, but allowed to exclude hydrosphere and atmosphere. Besides for explaining the term, Mason himself did not use the term "clarke".^{[M 2]}

A variant term "clarke value" is occasionally used (examples:^{[x 2][x 3]: 778}). However, "clarke value" can have a different meaning, the clarke of concentration (example:^{[x 4]: 412}).

Terms "clarke number" and "Clarke number" are found in articles written by Japanese authors (example:^{[x 5]: 55}).

Usage in Japan

In Japan, "clarke" is translated as kurākusū (クラーク数, clarke number). The word sū (数, number) is always added, which happens to make the term appear similar in form with scientific constants such as abogadorosū (アボガドロ数, the Avogadro constant). The term may have a narrower sense than Fersman's. Several of the following constraints may apply:

• Only of Earth's crust^{[I 1]}
• Lithosphere approximated as a 10 mile-deep layer from sea level^{[I 1]}
• Must include all of three layers: lithosphere (93.06%), hydrosphere (0.91%) and atmosphere (0.03%)^{[I 1]}
• Only mass ratio^{[I 1]})
• Denote in percents^{[I 1]}) (not in ppm or ppb)
• (What the quoter believes to be) data from Clarke and Washington(1924)

Another peculiarity in Japan is the existence of a popular version of data, which was tabulated in reference books such as the annual "Chronological Scientific Tables" (RCST1939(1938)^{[R 1]: E46}), the "Dictionary of Physics and Chemistry" (IDPC(1939)^{[I 1]: app.VI}) and other prominent books on geochemistry and chemistry.^{[H 1]: (62)} This version Kimura(1938)^{[K 1]} was devised by chemist Kenjiro Kimura [ja].^{[K 2]: 5} It was often quoted as The "Clarke numbers" (unsourced examples:^{[x 6]: 443},^{[H 2]: 429 t2}). The numbers differed from any versions by Clarke / Clarke&Washington (1889–1924^{[C 1][C 2][C 3][C 4][C 5][C 6][C 7][C 8][C 9]}), or anything listed in foreign (non-Japanese) articles such as the USGS compilation ^{[U 2]: 4 t2}, thus unknown outside of Japan. Yet the numbers were sometimes quoted in English articles without citation (example:^{[x 5]: 55}).

As geological definition of "Earth's crust" evolved, the "10 mile-deep" approximation were deemed out-of-date, and some people considered the term "clarke number" obsolete too.^{[H 2]} Yet other people may have meant broader senses, not limiting to Earth's crust, leading to confusion.^{[I 2]: 355} RCST1961(1961) switched their "clarke number" table from Kimura(1938) to Mason(1958) based^{[R 2][R 3]}, and the label "clarke number" on table was removed in RCST1963(1962)^{[R 4]}. IDPC(1971)^{[I 3]} removed the "clarke number" table which was a Kimura(1938)'s variant^{[I 4][D 1]}. IDPC(1981) said the term is mostly abandoned,^{[I 2]} and the dictionary entry for "clarke number" itself was removed from IDPC(1998).^{[H 2]: 431} So "clarke numbers" became associated almost solely with Kimura(1938)'s data, but Kimura's name forgotten. Incidentally, in major reference books, there was no data table titled "clarke numbers" which showed Clarke's original tables.

Despite being removed from major reference books, data from Kimura(1938) and phrases such as "the Clarke number of iron is 4.70", unsourced, continue to circulate, even in the 2010s (example:^{[x 7]: 799}).

Example data

This section lists only historical data. For recent data, see Abundance of elements in Earth's crust.

Technical definition of "clarke", "Earth's crust" and "lithosphere" differ among authors, and the actual numbers vary accordingly, sometimes by several times. Even the same author presents multiple versions, with various estimation parameters or knowledge refinements. Yet they are often quoted without source, rendering the data unverifiable. Clarke & Washington^{[C 7]: 114 [C 8]: 34 t17} presented estimations of the average composition of the outer part of Earth with four variants:

1. 10-mile crust, hydrosphere and atmosphere.
2. 20-mile crust, hydrosphere and atmosphere.
3. 10-mile crust, only igneous rocks and sedimentary rocks. (i.e. exclude hydrosphere and atmosphere)
4. 10-mile crust, only igneous rocks. (i.e. exclude hydrosphere and atmosphere)

"The earth's crust" in Clarke and Washington works can mean two different things: (a) The whole outer part of Earth, i.e. lithosphere, hydrosphere and atmosphere; (b) Only the lithosphere, which in their works just meant "the rocky crust of the earth". "Crust" here means (b).

• Following tables do not cover all elements. Some elements not on the table may have larger abundance. Some minor elements are listed here to aid identifying the origin of unsourced documents.
• Some entries contain data for the disputed element 43 masurium.
• Precision (number of digits) may be adjusted to improve legibility.

Of the mass of 10 mile-thick lithosphere plus hydrosphere and atmosphere

Tables of historical data for some elements of their relative abundance in Earth's crust.

cited as		Clarke (1889)	Clarke (1891)	Clarke (1908)	Clarke (1911)	Clarke (1916)	Clarke (1920)	Clarke & Washington (1922)	Clarke & Washington (1924)	Clarke (1924)	Berg (1929)	Berg (1932)	Fersman (1923)	Fersman (1934)	RCST1937 (1936)	RCST1939 (1938)	Kimura (1939)
cited in		[C 1]: 138 c.3	[C 2]: 39 c.3	[C 3]: 32 c.3	[C 4]: 34-35 c.3	[C 5]: 34 c.3	[C 6]: 35 c.3	[C 7]: 114 c.1	[C 8]: 34 t.17 c.1	[C 9]: 36 c.3	[B 1]: 11	[B 2]: 113 t.15	[F 2]: 18 t.VI c.5	[F 1]: 148 t.XV c.X  [F 3]: 174 t.15 c.X	[R 5]: 316	[R 1]: E46	[K 2]: 5 t.4
	titled "clarke"?	-	-	-	-	-	-	-	-	-			-	Yes	Yes	Yes	Yes
	elements	19	19	20	20	20	20	31	27	20			28	87	89	89	89
lithosphere		93%	93%	93%	93%	93%	93%	93%	93%	93%	13.5/14.5		Yes	Yes	Yes	Yes	Yes
	definition	10 miles	10 miles	10 miles	10 miles	10 miles	10 miles	10 miles	10 miles	10 miles	16 km	16 km		16 km	16 km	16 km	10 miles
	rock types	All	All	All	All	All	All	All	All	All	All		All	All	All	All	All
hydrosphere		ocean 7%	ocean 7%	ocean 7%	ocean 7%	ocean 7%	ocean 7%	7%	7%	7%	1/14.5		Yes	Yes	Yes	Yes	Yes
atmosphere		N 0.02%	N 0.02%	N 0.02%	N 0.02%	N 0.02%	N 0.02%	0.03%	0.03%	Yes			Yes	Yes	Yes	Yes	Yes
remarks		often mentioned							often cited. >100%			>100%	>100%			popular in Japan
Z	element	(mass%)	(mass%)	(mass%)	(mass%)	(mass%)	(mass%)	(mass%)	(mass%)	(mass%)	(mass%)	(mass%)	(mass%)	(mass%)	(mass%)	(weight%)	(weight%)
8 O	oxygen	49.98	49.98	49.78	49.85	50.02	50.02	49.190	49.520	49.20	49.5000	49.500	49.70	49.130	49.500	49.500	49.500
14 Si	silicon	25.30	25.30	26.08	26.03	25.80	25.80	25.710	25.750	25.67	25.7000	25.300	26.00	26.000	25.300	25.800	25.800
13 Al	aluminium	7.26	7.26	7.34	7.28	7.30	7.30	7.500	7.510	7.50	7.5000	7.500	7.45	7.450	7.500	7.560	7.560
26 Fe	iron	5.08	5.08	4.11	4.12	4.18	4.18	4.680	4.700	4.71	4.7000	5.080	4.20	4.200	5.040	4.700	4.700
20 Ca	calcium	3.51	3.51	3.19	3.18	3.22	3.22	3.370	3.390	3.39	3.3900	3.390	3.25	3.250	3.390	3.390	3.390
11 Na	sodium	2.28	2.28	2.33	2.33	2.36	2.36	2.610	2.640	2.63	2.6300	2.630	2.40	2.400	2.630	2.630	2.630
19 K	potassium	2.23	2.23	2.28	2.33	2.28	2.28	2.380	2.400	2.40	2.4000	2.400	2.35	2.350	2.400	2.400	2.400
12 Mg	magnesium	2.50	2.50	2.24	2.11	2.08	2.08	1.940	1.940	1.93	1.9300	1.930	2.35	2.350	1.930	1.930	1.930
1 H	hydrogen	0.94	0.94	0.95	0.97	0.95	0.95	0.872	0.880	0.87	0.8700	0.870	1.00	1.000	0.870	0.870	0.870
22 Ti	titanium	0.30	0.30	0.37	0.41	0.43	0.43	0.648	0.580	0.58	0.5800	0.630	0.50	0.610	0.630	0.460	0.460
17 Cl	chlorine	0.15 (Cl+Br)	0.15 (Cl+Br)	0.21	0.20	0.20	0.20	0.228	0.188	0.19	0.1900	0.190	0.20	0.200	0.190	0.190	0.190
25 Mn	manganese	0.07	0.07	0.07	0.08	0.08	0.08	0.108	0.080	0.09	0.0900	0.090	0.09	0.100	0.090	0.090	0.090
15 P	phosphorus	0.09	0.09	0.11	0.10	0.11	0.11	0.142	0.120	0.11	0.1200	0.120	0.10	0.120	0.120	0.080	0.080
6 C	carbon	0.21	0.21	0.19	0.19	0.18	0.18	0.139	0.087	0.08	0.0800	0.080	0.35	0.350	0.080	0.080	0.080
16 S	sulfur	0.04	0.04	0.11	0.10	0.11	0.11	0.093	0.048	0.06	0.0600	0.060	0.10	0.100	0.060	0.060	0.060
7 N	nitrogen	0.02	0.02	0.02	0.03	0.03	0.03	0.030	0.030	0.03	0.0300	0.030	0.04	0.040	0.030	0.030	0.030
9 F	fluorine	-	-	0.02	0.10	0.10	0.10	0.030	0.027	0.03	0.0270	0.026	0.08	0.080	0.026	0.030	0.030
37 Rb	rubidium	-	-	-	-	-	-	-	-	-	0.0033	3.50E-03	-	0.008	3.50E-03	0.030	0.030
56 Ba	barium	0.03	0.03	0.09	0.09	0.08	0.08	0.075	0.047	0.04	0.0400	0.040	0.04	0.050	0.040	0.023	0.023
40 Zr	zirconium	-	-	-	-	-	-	0.048	0.023	-	0.0230	0.023	-	0.025	0.023	0.020	0.020
24 Cr	chromium	0.01	0.01	-	-	-	-	0.062	0.033	-	0.0330	0.038	0.02	0.030	0.033	0.020	0.020
38 Sr	strontium	-	-	0.03	0.03	0.02	0.02	0.032	0.017	0.02	0.0200	0.020	0.02	0.040	0.020	0.020	0.020
23 V	vanadium	-	-	-	-	-	-	0.038	0.016	-	0.0160	0.018	0.02	0.020	0.013	0.015	0.015
28 Ni	nickel	-	-	-	-	-	-	0.030	0.018	-	0.0180	0.018	0.02	0.020	0.018	0.010	0.010
29 Cu	copper	-	-	-	-	-	-	0.010	0.010	-	0.0100	0.010	0.02	0.010	0.010	0.010	0.010
58 Ce	cerium	-	-	-	-	-	-	0.019 (Ce+Y)	0.014 (Ce+Y)	-	0.0022	2.00E-03	-	2.90E-03	2.00E-03	4.50E-03	4.50E-03
30 Zn	zinc	-	-	-	-	-	-	0.004	-	-	0.0045	0.017	-	0.020	0.017	4.00E-03	4.00E-03
32 Ge	germanium	-	-	-	-	-	-	-	-	-	2.00E-08	1.00E-04	-	4.00E-04	1.00E-04	6.50E-04	6.50E-04
43 Ma	masurium	-	-	-	-	-	-	-	-	-	-	-	-	1.00E-07	1.00E-07	1.00E-07	1.00E-07
others		0.00	0.00	0.48	0.47	0.47	0.47	0.00	0.032	0.47

Other variants

Some authors call these "clarkes" too, some do not.

cited as		Clarke (1889)	Clarke & Washington (1924)	Clarke & Washington (1924)	Clarke & Washington (1924)	Clarke (1924)	Goldschmidt (1937)	Goldschmidt (1937)	Mason (1952)	Mason (1958)	RCST1961 (1961)	Mason (1966)	Mason & Moore (1982)
cited in		[C 1]: 138 c.1	[C 8]: 34 t.17 c.2	[C 8]: 34 t.17 c.3	[C 8]: 20 t.11 c.1	[C 9]: 36 c.1	[G 1]: 99–100	[U 2]: 4 t.2	[M 1]: 41 t.8	[M 2]: 44 t.9	[R 2]	[M 3]: 45 t.3.3	[M 4]: 46 t.3.5
	titled "clarke"?	-	-	-	-	-		-	-	-	Yes	-	-
	elements	19	27	27	35	20			80	80	85	78	78
lithosphere		100%	Yes	100%	100%	100%	100%	100%	100%	100%	100%	100%	100%
	definition	10 miles	20miles	10 miles	10 miles	10 miles			10 miles	10 miles	10 miles
	rock types	All	All	igneous + sedimentary	igneous	All	igneous	igneous	All	All	All	All	All
hydrosphere		(no)	Yes	(no)	(no)	(no)	(no)	(no)	(no)	(no)	Yes	(no)	(no)
atmosphere		(no)	Yes	(no)	(no)	(no)	(no)	(no)	(no)	(no)	Yes	(no)	(no)
remarks											wrong composition
Z	element	(mass%)	(mass%)	(mass%)	(mass%)	(mass%)	(mass ppm)	(weight%)	(mass ppm)	(mass ppm)	(weight%)	(mass ppm)	(mass ppm)
8 O	oxygen	47.29	48.080	46.710	46.590	46.46		46.600	466,000	466,000	46.600	466,000	466,000
14 Si	silicon	27.21	26.720	27.690	27.720	27.61	277,200	27.720	277,200	277,200	27.720	277,200	277,200
15 Al	aluminium	7.81	7.790	8.070	8.130	8.07	81,300	8.130	81,300	81,300	8.130	81,300	81,300
26 Fe	iron	5.46	4.870	5.050	5.010	5.06	50,000	5.000	50,000	50,000	5.000	50,000	50,000
20 Ca	calcium	3.77	3.520	3.650	3.630	3.64	36,300	3.630	36,300	36,300	3.630	36,300	36,300
11 Na	sodium	2.36	2.690	2.750	2.850	2.75	28,300	2.830	28,300	28,300	2.830	28,300	28,300
19 K	potassium	2.40	2.490	2.580	2.600	2.58	25,900	2.590	25,900	25,900	2.590	25,900	25,900
12 Mg	magnesium	2.68	2.010	2.080	2.090	2.07	20,900	2.090	20,900	20,900	2.090	20,900	20,900
1 H	hydrogen	0.21	0.510	0.140	0.130	0.14	nicht ber.	-	1,400	1,400	0.140	1,400	1,400
22 Ti	titanium	0.33	0.600	0.620	0.630	0.62	4,400	0.440	4,400	4,400	0.440	4,400	4,400
17 Cl	chlorine	0.01	0.101	0.045	0.048	0.05	480	0.048	314	200	0.020	130	130
25 Mn	manganese	0.08	0.090	0.090	0.100	0.09	1,000	0.100	1,000	1,000	0.100	950	950
15 P	phosphorus	0.10	0.130	0.130	0.130	0.12	800	0.118	1,180	1,180	0.118	1,050	1,050
6 C	carbon	0.22	0.091	0.094	0.032	0.09		0.032	320	320	0.032	200	200
16 S	sulfur	0.03	0.050	0.052	0.052	0.06	520	0.052	520	520	0.052	260	260
7 N	nitrogen	-	0.016	-	-	-		-	46	46	0.0046	20	20
9 F	fluorine	-	0.028	0.029	0.030	0.03		0.030	300	700	0.070	625	625
37 Rb	rubidium	-	-	-	-	-	310	0.031	310	120	0.012	90	90
56 Ba	barium	0.03	0.048	0.050	0.050	0.04	250	0.025	250	400	0.040	425	425
40 Zr	zirconium	-	0.024	0.025	0.026	-	220	0.022	220	160	0.016	165	165
24 Cr	chromium	0.01	0.034	0.035	0.037	-	200	0.020	200	200	0.020	100	100
38 Sr	strontium	-	0.017	0.018	0.019	0.02	150	0.015	300	450	0.045	375	375
23 V	vanadium	-	0.016	0.016	0.017	-	150	0.015	150	110	0.011	135	135
28 Ni	nickel	-	0.018	0.019	0.020	-	100	0.010	80	80	0.008	75	75
29 Cu	copper	-	0.010	0.010	0.010	-	100	0.010	70	45	0.0045	55	55
58 Ce	cerium	-	0.014 (Ce+Y)	0.014 (Ce+Y)	0.015 (Ce+Y)	-	46.1	0.0046	46	46	0.0046	60	60
30 Zn	zinc	-	-	-	0.004	-	40	0.004	132	65	0.0065	70	70
32 Ge	germanium	-	-	-	n*E-11	-	7	0.0007	7	2	2.00E-04	1.5	1.5
43 Ma	masurium	-	-	-	-	-	-	-	-	-	-	-	-
others			0.033	0.033		0.500

Clarke of concentration

A related term "clarke of concentration" or "concentration clarke", synonym: "concentration factor (mineralogy)", is a measure to see how rich a particular ore is. That is, the ratio between the concentrations of a chemical element in the ore, and its concentration in the whole Earth's crust (i.e. "clarke") ^{[M 1]: 42 [x 8]: 43}.

If the concentration of a commodity in an ore X is ${\displaystyle Kx}$ [ppm], and the "clarke" of that commodity is ${\displaystyle Ke}$ [ppm], then "the clarke of concentration" of that commodity X is ${\displaystyle Kk={\frac {Kx}{Ke}}}$ (dimensionless).

The value represents the degree to which the commodity is concentrated from crustal abundances to the ore by natural geochemical processes; a clue for whether the commodity could be mined economically.^[1]