Clarke number

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. 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().

Examples based on Fersman's definition:
* russian: весовой кларк, lit=weight clarke: When the whole mass of a planet X is $Mx$ , and the mass of oxygen there is $Mo$ , then the weight clarke of oxygen in planet X is $Km=\frac$ (dimensionless)
* russian: кларк числа атомов, lit=clarke of atom count: When the whole count of atoms in a rock Y is $Ay$ , and the atom count of silicon there is $As$ , then silicon's clarke of atom count in rock Y is $Ka=\frac$ (dimensionless)
* Fersman's "clarke of Earth's crust" is the Earth's surface including 16km-thick lithosphere, hydrosphere and atmosphere.

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.

In German

In English

In the English speaking world, the term "clarke" was not even used in Wells(1937) which introduced Fersman's proposal, nor in later USGS articles such as Fleischer(1953). They used the term "relative abundance of the elements". Brian Mason also mentioned the term "clarke" in Mason(1952)(mistakenly attributing it to Vladimir Vernadsky, later corrected to Fersman in Mason(1958)), 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 didn't use the term "clarke".

A variant term "clarke value" is occasionally used (examples:). However, "clarke value" can have a different meaning, the clarke of concentration (example:).

Terms "clarke number" and "Clarke number" are found in articles written by Japanese authors (example:).

Usage in Japan

In Japan, "clarke" is translated as . The word is always added, which happens to make the term appear similar in form with scientific constants such as . The term may have a narrower sense than Fersman's. Several of the following constraints may apply:
* Only of Earth's crust
* Lithosphere approximated as a 10 mile-deep layer from sea level
* Must include all of three layers: lithosphere(93.06%), hydrosphere(0.91%) and atmosphere(0.03%)
* Only mass ratio)
* Denote in percents) (not in ppm or ppb)
* (What the quoter believes to be) data from Clarke&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)), the "Dictionary of Physics and Chemistry" (IDPC(1939)) and other prominent books on geochemistry and chemistry. This version Kimura(1938) was devised by chemist . It was often quoted as ''The'' "Clarke numbers" (unsourced examples:,). The numbers differed from any versions by Clarke / Clarke&Washington (1889–1924), or anything listed in foreign (non-Japanese) articles such as the USGS compilation , thus unknown outside of Japan. Yet the numbers were sometimes quoted in English articles without citation (example:).

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. Yet other people may have meant broader senses, not limiting to Earth's crust, leading to confusion. RCST1961(1961) switched their "clarke number" table from Kimura(1938) to Mason(1958) based, and the label "clarke number" on table was removed in RCST1963(1962). IDPC(1971) removed the "clarke number" table which was a Kimura(1938)'s variant. IDPC(1981) said the term is mostly abandoned, and the dictionary entry for "clarke number" itself was removed from IDPC(1998). 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:).

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 presented estimations of the average composition of outer part of Earth with 4 variants:
# 10-mile crust, hydrosphere and atmosphere.
# 20-mile crust, hydrosphere and atmosphere.
# 10-mile crust, only igneous rocks and sedimentary rocks. (i.e. exclude hydrosphere and atmosphere)
# 10-mile crust, only igneous rocks. (i.e. exclude hydrosphere and atmosphere)
"The earth's crust" in Clarke & Washington works can mean two different things: (a) The whole outer part of Earth, ie. 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.

Other variants

Some authors call these "clarkes" too, some don't.

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") .

Example:
If the concentration of iron in an ore X is $Kx$ , and the "clarke of iron" is $Ke$ ,
then "the clarke of concentration of iron in ore X''" is $Kk=\frac$ (dimensionless)

References

Footnotes

Cited works

* C: Frank Wigglesworth Clarke of USGS and Henry Stephens Washington


* Based on 880 igneous rock samples.
* Chlorine and bromine data are summed.


* Numbers identical to .





* Numbers identical to


* Based on 5159 igneous rock samples.
* Table contains data for 31 elements, most comprehensive among Clarke's publications. Amount of cerium and yttrium are summed.


* Often cited. Beware there is another article in the same year reporting different results.
* Based on 5159 igneous rock samples.
* p17 mentions that the 10miles crust consist of lithosphere:93.06%; hydrosphere:6.91%; atmosphere:0.03%, but p34 explains that table 17 is calculated using approximations ie. lithosphere:93%; hydrosphere:7%; atmosphere:0.03%. No mention of the exact calculation process.
* Table 17 contains data for 27 elements. Amount of cerium and yttrium are summed.


* p.27 mentions , numbers differ. Data for only 20 elements, lesser than previous works such as .
* Based on 5159 igneous rock samples.
* Amount of cerium and yttrium are summed.


* U: United States Geological Survey (USGS)


(a review)


* B:




* F: Alexander Fersman



* p141: definitions of "clarke".
* p146 table 15 column 1 quotes in ) but actual data is on p138, and the numbers on Fersman's are different from anything in .
* p161 fig.18 "clarkes of meteorites": An example of applying the term "clarke" to objects other than geospheres.

(Posthumous revision. Data in p174 table 15 seems identical to )

* G: Victor Goldschmidt

* M: Brian Mason


* Attributing the term "clarke" to Vladimir Vernadsky. The numbers he gave as examples ("the clarke of oxygene is 46.60, of silicon, 27.72") was his own data (based on Clarke&Washington(1924) and Goldschmidt) for rocky crust excluding hydrosphere and atmoshpere.

p.42
Attributing the term "clarke of concentration" to Vladimir Vernadsky, but without specifying location in source. Mason himself used the term "concentration clarke" instead.


* p.47 Corrected the term "clarke" originator to Fersman. He maintained "Clarke of concentration" come from Vernadsky.
* p.45 Table 9 "The Average Amount of Elements in the Earth's Crust": Mason claims data for major elements are taken from Clarke and Washington but they are not. Most data for major elements are identical to , which were only about igneous rocks. Mason argues that the average of igneous rocks can reasonably represent the whole crust.


(other format )
* pp.46-47 Table 3.5 "The Average Amounts of the Elements in Crustal Rocks in Grams per Ton or Parts per Million"


* K:

Kimura(1938) =
(p.5 table 4 is the clarke number table. Identical to )


* H: Research on the history of chemistry


* An essay.
* p429: translation of quote: "today our knowledge have sub-ppb level accuracy. Clarke numbers, which are defined as percent-based, became inconvenient."
* table 2 "clarke numbers": Lack citation. Values identical to .
* table 1 "average composition of igneous rocks": mis-cited as Clarke&Washington's are not. They are actually Mason's heavily modified version .


* An essay.
* p.(62) denotes "Unfortunately, Rikanenpyō edition 34() and edition 35()'s usage of clarke numbers are erratic", but doesn't mention how.

Examples of usage

* R: ( :ja:理科年表) : An (mostly) annual reference book published in Japan since 1925CE. Note that the actual published year is typically 1 year earlier than the nominal (book title) year.


* Edition 1937 was the first edition to use the term "". Same data on edition 1937–1938.


* Edition 1939 was the first edition to adopt . Same data on edition 1939–1961.


* Switched from to based. Table's column title is "clarke number" on edition 1961–1962. Lists 85 elements, which is more than Mason(1958). Same data on edition 1961–1966.


* based. Table's column title is "clarke number", which conflicts with the definition on the same page (see quote). Lists 85 elements which is more than Mason(1958). Same data on edition 1961–1966.


* based. Table's column title changed to "weight percent ratio". Lists 85 elements which is more than Mason(1958). Same data on edition 1961–1966.


* I: : Revised roughly by each decade. First edition 1935CE.


* First revision of IDPC where term "clarke number" and data table appeared. Unsourced. Data identical to .
* Translation of quote from dictionary entry "clarke number": "F.W. Clarke assumed that rocks downto 10 miles (approx 16 km) below sea level should be quite similar to rocks on the surface of Earth. He determined a portion consisting of this, the hydrosphere and atmosphere as the outer part of the earth which is directly accessible to our observation, that is in weight percentage ratio of 93.06% lithosphere, 0.91% hydrosphere and 0.03% atmosphere. This portion is about 0.3% of the whole Earth. He calculated the weight percentage of elements in this portion. Thus, in accordance to A.Fersmann ics proposal, the abundance of elements in this range, denoted in weight percentage, are called ''clarke number''s." This differs from 's "clarke", is rather similar to his "clarke of Earth's crust", but further binding to just one of Clarke's variants through a vague phrase "''in this range''".


* p365 dictionary entry "clarke number": Author of this entry is not mentioned. Text identical with except spelling "A.Fersmann"(sic) changed to "A.Fersman".
* p1379 Appendix XI clarke number data table: Unsourced. Data almost identical to , except masurium been removed, and footnotes added: "Recently, following updates are reported: Zn:8x10-3, Cu:7x10-3, Nb:2.4x10-3, Co:2.3x10-3, Tl:3x10-4, Ta:2.1x10-4, Cd:1.5x10-5 ... 93 Np: 1x10-18 (abundance rank 89 90), 94 Pu: 1x10-18 (abundance rank 89 90)". Data in these footnotes are not incorporated into the main table. Identical table is in "Kyoritsu Great Dictionary of Chemistry" (Concise edition ).
* From 2nd edition, "Iwanami" was added to the title of the book.


* Have no data table titled "clarke number". The table titled "abundance of elements" was credited "based mostly on Taylor(1964) and Mason(1966)".


* Have no data table titled "clarke number".


*D: Kyoritsu Great Dictionary of Chemistry


* Publication date of 1st non-concise edition is 1960
* Entry's author is Ken Sugawara. Cited source is . Table content identical to , with the same footnotes.
* Extra quotes: "In addition to the typical mass/mass% table, Miyake recently proposed a novel table re-written in mol/kg (Miyake,1954)"


*X: Other usage examples


* Example data given (A.P.Vinogradov(1962), K.H.Wedepohl(1967)) are of igneous rocks in Earth's crust, excluding both hydrosphere and atmosphere.
* Mistaken :de:Karl Hans Wedepohl's first name with "Clarke".

(translation of several Russian academic papers to English)

occurrence of "clarke value"

(reprint fro
ACTA GEOLOGICA SINICA 1965, v.45 no.1 p.82-91. (PRC)

* "Clarke values" in introduction. Chinese abstract zh, c=克拉克值, l=clarke value


* p43 says the originator of term "clarke of concentration" is Fersman(1933) but reference in p774 actually refers to


* Presenting only the ratio of Clarke numbers between strontium and calcium as 0.0059, without showing individual numbers nor source. "Clarke" is capitalized.


* quote table with numbers identical to without mentioning source

{{Cite magazine
, last1=Takada
, first1=Jun
, last2=Nakanishi
, first2=Makoto
, year=2017
, title=Development of Novel Reddish Iron Oxide Based on Traditional Pigment "Bengala"
, script-title=ja:伝統の"ベンガラ"から新規な赤色酸化鉄への研究展開 ―備中吹屋ベンガラの復元から微生物由来酸化鉄ベンガラへの飛躍―
, language=ja
, journal=Journal of the Society of Materials Science, Japan
, script-journal=ja:材料
, volume=66
, issue=11
, pages=799–803
, publisher=The Society of Materials Science, Japan
, doi=10.2472/jsms.66.799
, url=https://www.jstage.jst.go.jp/article/jsms/66/11/66_799/_article/-char/ja
, format=PDF
, quote=the clarke number of iron is 4.70

* Using clarke numbers without citation

See also

* Abundance of elements in Earth's crust, modern data

Structure of the Earth
Geochemistry
Earth sciences