A Remark on Correlation Between Relaxation Parameter and Covalence of Cr³⁺—O Bonds in Some Mineral Structures
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Інститут геохімії, мінералогії та рудоутворення ім. М.П. Семененка НАН України
2011
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| Cite this: | A Remark on Correlation Between Relaxation Parameter and Covalence of Cr³⁺—O Bonds in Some Mineral Structures / A.N. Platonov, V.S. Urusov, K. Langer // Мінералогічний журнал. — 2011. — Т. 33, № 4. — С. 49-52. — Бібліогр.: 26 назв. — англ. |
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| citation_txt | A Remark on Correlation Between Relaxation Parameter and Covalence of Cr³⁺—O Bonds in Some Mineral Structures / A.N. Platonov, V.S. Urusov, K. Langer // Мінералогічний журнал. — 2011. — Т. 33, № 4. — С. 49-52. — Бібліогр.: 26 назв. — англ. |
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49ISSN 0204-3548. Мінерал. журн. 2011. 33, № 4
© A.N. PLATONOV, V.S. URUSOV, K. LANGER, 2011
UDC 549.02 : 548.32
A.N. Platonov 1, V.S. Urusov 2, K. Langer 3
1 M.P. Semenenko Institute of Geochemistry, Mineralogy
and Ore Formation of the NAS of Ukraine, Kyiv
34, Palladina Prospect, 03680, Kyiv-142, Ukraine
E-mail: platonov@i.com.ua
2 Lomonosov Moscow State University, Russia
1, Vorobievy Gory, GSP-1, 119991, Moscow, Russia
3 Institute für Angew. Geowissenschaften, Techn. Univ., Berlin, Deuschland
Ernst-Reuter-Platz, 1, D-10623, Berlin, Germany
А REMARK ON CORRELATION BETWEEN RELAXATION
PARAMETER AND COVALENCE OF Cr3+—O BONDS
IN SOME MINERAL STRUCTURES
The local interatomic distances R loc
<Cr—O>
and the local lattice relaxation coefficient ε for low-chromium members of solid
solution series corundum — escolaite, spinel — magnesiochromite, YAlO
3
— YCrO
3
(perovskites), pyrope — knorringite,
grossular — uvarovite, jadeite — kosmochlore, spodumene — LiAlSi
2
O
6
were calculated. The correlation between rela-
xation coefficient ε and Racah parameter B
35
of Cr3+, which reflects the covalent character of the respective (Cr3+—O)-
bonds was firstly revealed. The observed dependence could be preliminary explained by the so-called "rule of mutual in-
fluence of different bonds in the crystal structure".
МІНЕРАЛОГІЧНИЙ ЖУРНАЛ
MINERALOGICAL JOURNAL
(UKRAINE)
As it was demonstrated by Urusov [22] in his
model of binary solid solutions the local lattice
relaxation coefficient, ε, reflects the response of
the mineral structures on the incorporation of
substituting foreign ions different in sizes compa-
ring with the substituted host ions.
It has been shown that local mean (O—M3dN)-
distances, R loc
<M—O>
, can be determined from elec-
tronic absorption spectra of M3dN-ions-bearing mi-
neral solid solutions [9]. The presupposition is that
R loc
<M—O>
and the crystal field parameter 10Dq for
the end members are known as reference va lues.
A local relaxation parameter, ε, can also be cal cu-
lated from the data obtained from electronic ab-
sorption spectra using the following equations [9]:
(R loc
<M—O>
)
xi
= (R
<M—O>
)
х =1
· [(10Dq)
х =1
/(10Dq)
xi
]1/5,
and
ε = (R loc
<M—O>
xi
– R
<M—O> х = 0
)/
(R
<M—O> х = 1
– R
<M—O>х = 0
).
Here we show that the local relaxation, ε,
around the substituting VICr3+ depends on the
Racah parameter B
35
of Cr3+, which reflects the
covalent character of the respective (Cr3+—O)-
bonds.
The data to check for such possible effects are,
except of the B
35
-values, mostly taken from the
literature (Table). Columns 1, 2, 6 and 7 of Table
give the reference values, needed to calculate the
data in columns 3 and 4.
In Figure the results of our calculations of the
local relaxation coefficient, ε, for some Cr3+-
bearing minerals noted in Table are shown as a
fun ction of the Racah parameter values, B
35
, of
Cr3+ in the respective structural matrix. This Fi-
gu re demonstrates a strong dependence of the lo-
cal lattice relaxation coefficient, ε, on the charac-
ter of the Cr—O bond in the oxide structures of
type (1), (2), and (3). This strong dependence
becomes weak in the case of the chain silicate
structures (6), (7), which exhibit high relaxation
coefficients. Data for orthosilicates, e. g. garnets,
(4) and (5), plot in an intermediate range.
50 ISSN 0204-3548. Mineral. Journ. (Ukraine). 2011. 33, No 4
Fig. 8. The dependence of the lattice relaxation parameter
ε on the Racah parameter of interionic interaction B
35
In the chain silicate structures the substitution
of Cr3+ in M1-sites obviously approaches the "hard
sphere" concept. The values of R loc
<Cr—O>
in these
minerals are very close to the sum of ionic radii
[6]Cr3+ and O2_
[18]: the ratio R loc
<Cr—O>
/ ∑(r Cr3++
+ r O2_
) ≥ 0.99, and the corresponding relaxation
parameter is equal in average 0.95.
The observed correlation could be prelimi-
nary explained by the so-called "rule of mutual
influ ence of different bonds in the crystal
structure" [21]. According to this rule, the ioni-
city of the given bond, in our instance Al—O or
Cr—O, turns to be higher when the neighboring
bonds become to be more covalent. In the
discussed set of the mineral structures, they form
the following range in order of Cr—O bond ioni-
city increase (co va lency decrease): perovski te —
spi nel — co run dum — garnets — pyroxenes. Be-
sides that, in this range of structures the O coor-
dination number n and especially a number of
the nearest Al(Cr) neigh bors are remarkably dec-
rea sing: 4Y + 2Al (n = 6) in perovskite, 4Al (n =
= 4) in corundum, 3Al + 1Mg (n = 4) in spinel,
1Al + 2Mg + Si (n = 4) in garnets, 2Al + Na +
+ Si (O1), 1Al + 2Na + Si(O2), 2Na + 2Si (O3)
Experimental data (columns 1, 2, 6 and 7) used this note for calculating the mean local distances, R loc
<Cr—O>
,
and lattice relaxation coefficient, ε, around substituting chromium in some [6]Cr3+-bearing minerals (columns 3 and 4)
R
<Al—O>
, Å 10Dq, cm–1 R loc
<Cr—O>
, Å ε B
35
, cm–1 R
<Cr—O>
, Å 10Dq, cm–1
1 2 3 4 5 6 7
(1) Corundum, Al
2
O
3
, (x
Cr
= 0.09) Eskolaite, Cr
2
O
3
1.9141 18060 1.954 0.47 622 1.9862 166503
(2) Spinel, MgAl
2
O
4
, (х
Cr
= 0.01) Magnesiochromite, MgCr
2
O
3
1.926 185204 1.968 0.58 612 1.9845 171506,7
(3) Perovskite-type, YAlO
3
, (х
Cr
= 0.02)8 YCrO
3
, (х
Cr
= 1)8
1.911 17870 1.950 0.54 609 1.984 16400
(4) Pyrope, Mg
3
Al
2
Si
3
O
12
, (х
Cr
= 0.02) Knorringite, Mg
3
Cr
2
Si
3
O
12
1.8869 1800010 1.944 0.77 653 1.9611 1729012
(5) Grossular, Ca
3
Al
2
Si
3
O
12
, (х
Cr
= 0.005) Uvarovite, Ca
3
Cr
2
Si
3
O
12
1.9269 1659013 1.978 0.77 655 1.99414 1593014
(6) Jadeite, NaAlSi
2
O
6
, (х
Cr
= 0.02) Kosmochlor, NaCrSi
2
O
6
1.92815 1574016 1.996
0.94
0.95
712
1.99815
2.00017
1557018
1600019
(7) Spodumene, LiAlSi
2
O
6
, (х
Cr
= 0.004) LiCrSi
2
O
6
1.91915 1610020 1.988 0.98 817 1.99221 1595518
N o t e. 1Finger & Hazen (1978), 2Finger & Hazen (1980), 3McClure (1963), 4Wood et al. (1968), 5O’Neill & Dollase
(1994), 6Reinen (1969), 7Cervelle et al. (1984), 8Cruciani (2009), 9Geiger (2004), 10Geiger et al. (2000), 11Novak & Gibbs
(1971), 12Taran et al. (2004), 13Langer et al. (2004), 14Wildner & Andrut (2002), 15Clark et al. (1969), 16Khomenko &
Platonov (1987), 17Origlieri et al. (2003), 18Taran et al. (2010), 19White et al. (1971), 20Platonov et al. (1984), 21Ohashi &
Sato (2003).
A.N. PLATONOV, V.S. URUSOV, K. LANGER
51ISSN 0204-3548. Мінерал. журн. 2011. 33, № 4
(n
av
= 3.5) in jadeite and 2Al + Li + Si (O1),
1Al + Li + Si (O2), Li + 2Si (O3) (n
av
= 3.2) in
spodu mene. In average, only 1Al is the nearest
neig hbor of O atoms in the pyroxene structure.
Re member that the relaxation of a crys tal structure
is mostly dependent on the shift of non-substitu-
ted structural unit from its regular po sition [22,
23]; in all the cases under consi de ration these
are O atoms. The mentioned crystal chemical
features are needed in further refinement and
discussion.
1. Cervelle B., Coutures J.-P., Malezieux J.-M., Priou B.
Crystallochimie des chromites : etude sur des produits
de synthese du systeme Mg(Al, Cr)
2
O
4
// Bull. Mi-
ner. — 1984. — 107. — P. 627—634.
2. Clark J.R., Appelman D.E., Papike J.J. Crystal chemical
characterization of clinopyroxenes based on eight new
structure refinements // Miner. Soc. Amer. Spec.
Pap. — 1969. — No 2. — P. 31—50.
3. Cruciani G., Ardit M., Dondi M. et al. Structure rela-
xation around Cr3+ in YAlO
3
—YCrO
3
perovskites from
electron absorption spectra // J. Phys. Chem. —
2009. — 113. — P. 13772—13778.
4. Finger L.W., Hazen R.M. Crystal structure and comp-
ression of ruby to 46 kbars // J. Appl. Phys. — 1978. —
49. — P. 5823—5826.
5. Finger L.W., Hazen R.M. Crystal structure and iso-
ther mal compression of Fe
2
O
3
, Cr
2
O
3
, and V
2
O
3
to 50
kbars // Ibid. — 1980. — 51. — P. 5362—5367.
6. Geiger C.A. Spectroscopic investigation related to the
structural, crystal-chemical and lattice-dynamic pro-
per ties (Fe2+, Mn2+, Mg, Ca)
3
Al
2
Si
3
O
12
garnets. A
review and analysis // EMU Notes in Mineralogy. —
2004. — 6. — P. 589—645.
7. Geiger C.A., Stahl A., Rossman G.R. Single-crystal IR-
and UV/VIS-spectroscopic measurements on transi-
tion-metal-bearing pyrope : the incorporation of hyd-
ro xide in garnets // Eur. J. Mineral. — 2000. — 12. —
P. 259—271.
8. Khomenko V.M., Platonov A.N. The rock-forming py-
ro xenes : optical spectra, the colour and pleochro-
ism. — Kiev : Nauk. dumka, 1987. — 214 p. (in
Russian).
9. Langer K. A note on mean distances, R[M O
6
], in
substituted polyhedra [(M
1—x
M
x
)O
6
] in the crystal
structures of oxygen-based solid solutions : local versus
crystal averaging methods // Z. Kristallogr. — 2001. —
216. — P. 87—91.
10. Langer K., Platonov A.N., Matsyuk S.S. Local mean
chromium-oxygen distances in Cr3+-centered
octahedra in natural grossular-uvarovite garnet solid
solutions from electronic absorption spectra // Ibid. —
2004. — 219. — Р. 272—277.
11. McClure D.S. Comparison of the crystal fields and op-
tical spectra of Cr
2
O
3
and ruby // J. Chem. Phys. —
1963. — 38. — P. 2289—2294.
12. Novak G.A., Gibbs G.V. The crystal chemistry of the
silicate garnets // Amer. Miner. — 1971. — 56. —
P. 791—825.
13. O’Neill H.St.C., Dollase W.A. Crystal structures and
cation distribution in simple spinels from powder XRD
structure refinements : MgCr
2
O
4
, ZnCr
2
O
4
, Fe
3
O
4
and
the temperature dependence of the cation distribution
in ZnAl
2
O
4
// Phys. and Chem. Minerals. — 1994. —
20. — P. 541—555.
14. Ohashi H., Sato A. Studies on P21/c LiMSi
2
O
6
pyro-
xenes // X-ray study of Si—O bonding / Ed. H. Oha-
shi. — Tokyo : Maruzen Publ. Serv. Center, 2003. —
P. 229—243.
15. Origlieri M.J., Downs R.T., Thompson R.M. et al. High-
pressure crystal structure of kosmochlor, NaCrSi
2
O
6
,
and systematics of anisotropic compression in pyro-
xenes // Amer. Miner. — 2003. — 88. — P. 1025—
1032.
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colour of gemstones. — Moscow : Nedra, 1984. —
196 p. (in Russian).
17. Reinen D. Ligand-field spectroscopy and chemical
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gite garnets, [8]Mg
3
[6](Al
1—x
Cr3+
x
)
2
[4]Si
3
O
12
, from elec-
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High-pressure electronic absorption spectroscopy of
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Received 5.09.2011
А REMARK ON CORRELATION BETWEEN RELAXATION PARAMETER AND COVALENCE
52 ISSN 0204-3548. Mineral. Journ. (Ukraine). 2011. 33, No 4
А.Н. Платонов, В.С. Урусов, К .Лангер
ЗАМЕТКА О КОРРЕЛЯЦИИ
МЕЖДУ ПАРАМЕТРОМ РЕЛАКСАЦИИ
И КОВАЛЕНТНОСТЬЮ СВЯЗЕЙ Cr3+—O
В СТРУКТУРАХ НЕКОТОРЫХ МИНЕРАЛОВ
Приведены расчеты локальных межатомных расстоя-
ний Rloc
<Cr—O>
и локального коэффициента решеточ-
ной релаксации ε для минералов изоморфных ря-
дов корунд — эсколаит, шпинель — магнезиохромит,
YAlO
3
— YCrO
3
(структура перовскита), пироп —
кнор рингит, гроссуляр — уваровит, жадеит — космо-
хлор, сподумен — LiAlSi
2
O
6.
Впервые установлена кор-
реляция между коэффициентом релаксации ε и пара-
метром Ракá B
35
, отражающим степень ковалентности
связей Cr3+—O. Выявленную зависимость можно объ-
яснить в первом приближении эффектом взаимного
влияния различных связей катион—лиганды в кри-
сталлической структуре, содержащей примесные ионы.
О.М. Платонов, В.С. Урусов, К. Лангер
ЗАМІТКА ПРО КОРЕЛЯЦІЮ
МІЖ ПАРАМЕТРОМ РЕЛАКСАЦІЇ
Й КОВАЛЕНТНІСТЮ ЗВ’ЯЗКІВ Cr3+—O
У СТРУКТУРАХ ДЕЯКИХ МІНЕРАЛІВ
Наведено розрахунки локальних міжатомних від ста-
ней Rloc
<Cr—O>
і локального коефіцієнта ґраткової ре-
лак сації ε для мінералів ізоморфних рядів корунд —
есколаїт, шпінель — магнезіохроміт, YAlO
3
— YCrO
3
(структура перовскіту), піроп — кнорингіт, гросу-
ляр — уваровіт, жадеїт — космохлор, сподумен —
LiAlSi
2
O
6.
Вперше встановлено кореляцію між коефі-
цієнтом релаксації ε і параметром Ракá B
35
, що від-
биває ступінь ковалентності зв’язків Cr3+—O. Ви -
яв лену залежність можна пояснити в першому на б-
лиженні ефектом взаємного впливу різних зв’язків
катіон—ліганди у кристалічній структурі, що містить
домішкові іони.
A.N. PLATONOV, V.S. URUSOV, K. LANGER
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/NLD (Gebruik deze instellingen om Adobe PDF-documenten te maken die zijn geoptimaliseerd voor prepress-afdrukken van hoge kwaliteit. De gemaakte PDF-documenten kunnen worden geopend met Acrobat en Adobe Reader 5.0 en hoger.)
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| id | nasplib_isofts_kiev_ua-123456789-64106 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 0204-3548 |
| language | English |
| last_indexed | 2025-11-30T15:52:54Z |
| publishDate | 2011 |
| publisher | Інститут геохімії, мінералогії та рудоутворення ім. М.П. Семененка НАН України |
| record_format | dspace |
| spelling | Platonov, A.N. Urusov, V.S Langer, K. 2014-06-11T12:55:19Z 2014-06-11T12:55:19Z 2011 A Remark on Correlation Between Relaxation Parameter and Covalence of Cr³⁺—O Bonds in Some Mineral Structures / A.N. Platonov, V.S. Urusov, K. Langer // Мінералогічний журнал. — 2011. — Т. 33, № 4. — С. 49-52. — Бібліогр.: 26 назв. — англ. 0204-3548 https://nasplib.isofts.kiev.ua/handle/123456789/64106 549.02 : 548.32 en Інститут геохімії, мінералогії та рудоутворення ім. М.П. Семененка НАН України Мінералогічний журнал Мінералогiя A Remark on Correlation Between Relaxation Parameter and Covalence of Cr³⁺—O Bonds in Some Mineral Structures Замітка про кореляцію між параметром релаксації й ковалентністю зв’язків Cr³⁺—O у структурах деяких мінералів Заметка о корреляции между параметром релаксации и ковалентностью связей Cr³⁺—O в структурах некоторых минералов Article published earlier |
| spellingShingle | A Remark on Correlation Between Relaxation Parameter and Covalence of Cr³⁺—O Bonds in Some Mineral Structures Platonov, A.N. Urusov, V.S Langer, K. Мінералогiя |
| title | A Remark on Correlation Between Relaxation Parameter and Covalence of Cr³⁺—O Bonds in Some Mineral Structures |
| title_alt | Замітка про кореляцію між параметром релаксації й ковалентністю зв’язків Cr³⁺—O у структурах деяких мінералів Заметка о корреляции между параметром релаксации и ковалентностью связей Cr³⁺—O в структурах некоторых минералов |
| title_full | A Remark on Correlation Between Relaxation Parameter and Covalence of Cr³⁺—O Bonds in Some Mineral Structures |
| title_fullStr | A Remark on Correlation Between Relaxation Parameter and Covalence of Cr³⁺—O Bonds in Some Mineral Structures |
| title_full_unstemmed | A Remark on Correlation Between Relaxation Parameter and Covalence of Cr³⁺—O Bonds in Some Mineral Structures |
| title_short | A Remark on Correlation Between Relaxation Parameter and Covalence of Cr³⁺—O Bonds in Some Mineral Structures |
| title_sort | remark on correlation between relaxation parameter and covalence of cr³⁺—o bonds in some mineral structures |
| topic | Мінералогiя |
| topic_facet | Мінералогiя |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/64106 |
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