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8Journal of Siberian Federal University. Engineering & Technologies 2 (2010 3) 147-153
УДК 550.382.3
Time Deviations of Physical Properties of Natural Minerals
Viktor V. Onufrienok*
Siberian Federal University, 79 Svobodny, Krasnoyarsk, 660041 Russia 1
Received 7.05.2010, received in revised form 28.05.2010, accepted 8.06.2010
The opportunity of inversion the spin is shown at the several of configuration of defects in the second coordination of sphere. The principle of calculation of energy of cationic vacancies is offered. The condition of splitting of single levels of cationic vacancies in the power zone is certain. It is proved, that inversion the spin - result of transition of vacancy on an extrinsic level.
Keywords: cationic vacancies, inversion of the spin, configuration of defects, extrinsic level.
Introduction
Physical properties at natural minerals sometimes can change in due course, and the sample thus can not be exposed to what - that to external influence and to be in rather stable thermodynamic conditions. If the mineral was in contact to an atmosphere this effect usually speaks influence of an atmosphere, however not all these changes can be explained by atmospheric influence? Such changes can take place even when atmospheric influence can be excluded (in vacuum or in depth dense layers of breed). The reason of this phenomenon - in influence on physical properties of a mineral of dot defects (for example, cationic vacancies).
Magnetic properties of minerals are in direct dependence on a direction of spin on units of magnetic under-lattices. The direction a back depends on size of a local magnetic field. Presence in crystal structure of dot defects can influence essentially size of a local magnetic field, so and on a direction a back. As spontaneous redistribution of dot defects, hence, probably and change of magnetic properties in due course is possible in due course [1-3].
The purpose of work: to give an explanation change of physical properties of minerals in due course
Inversion of the spin at a various configuration of defects in the second coordination sphere
Let's show it by the example of structure such as NiAs (Fig. 1 b) with various distributions of cationic vacancies in structure. Let in this system ferromagnetic spin ordering in basic planes and antiferromagnetic between planes is carried out. Magnetic properties of system can be described Heisenberg Hamiltonian
* Corresponding author E-mail address: [email protected]
1 © Siberian Federal University. All rights reserved
H 1 fmSfSm?
jm
where f, m - units of a crystal lattice; Ifm - exchange parameters; Sf - the operator of the spin on unit f.
Though generally exchange inte raction can be long-range and oscillatory (mechanism RKKI), we shall be limited to consideration of a case when Ifm are distinct from zero only for the nearest neighbours. In the elementary case exchange parameters accept only two values: I22 between basic planes and Iu - inside a plane.
If to be limited to a case of consideration Ising patts H amiltonian
>
(where d f = 2SJ), own values partial own functions
l«U4=[n|t)BnM
Therefore own values energy Wn po^sit)le; to write down as:
l^ /, ^ € i, \ 1
^ = -T£J> f- I*-, = -4SI> ¿T*If.
fo i m
From a condition of a minimum of energy Ws=min(^'„) it; is received
^ = -4 2»s
f
f,
where
0 _ ^T S
S f ~ 2-,1 fm" ).
m
it is local field on unit f.
Thus, a necessary condition of minimum WO is cr.s. > S, from which follows, that the direction for the apin is unequivocally connected with is familiar a local field
For example, if e=0, spin in unit f h «paramagnetic» and can have any orientation. Inclusion of a small magnetic field along an axis of quantization removes this deaeneration and spin accepts value -0 = 1.
Within the fsamework of considered model there is a final number of types of the local fields described by various type of distribution of vacancies around of the given unit f. For crystal structure such as NiAs the basic condition the back on unit f, not containing vacancy in the nearest environment, looks like
e° =6 Ilh -2Ii2 <0.
If in a basic plane in which there is a consiieied unit f, there are vacancies the basic condition wi(l depe6d on their sumber, however the sign on a local field thus will not vary :
£js = eiu- iii2 < o,
£m0 = -2/i2 < o.
22
fj^
t^ 5 %
>
ion S
• AAAt # AA/V •
1 f IO
• aw # jyw m
IO 1
AAA/
AAA/
ioriFe
W
W* AA/V
A/W
•^AA/V O A/W
Jn - Jji
A/W
O AA/V «
AAA/^ P
**7WV 0 A/W ffi
Fig. 1. Crystal structure type ofNiAs with the various maintenance (contents) of vacancies of cations
I.e. sf consistently accepts values for 1, 2, ...., 6 vacancies in the nearest environment. For definiteness, the magnetic structure submitted on Fig. 1 with is considered. An axis of quantization - X.
If vacancies are in the next basic planes the local field on unit f can accept both positive and negative value. Even if to accept, that i.e. presence of one vacancy does not result in change of a sign at a local field 6In<Iee on unit f e°f (Fig. 1c) two vacancies located in planes a, inevitably should cause reorientation a back (Fig. 1b) [4-7]. The basic condition for the first case will look like
¿6= 6/n- /ef<f,
and for the second -
e i=6/n
If the unit f is surrounded with vacancies and in a plane a, and in a plane p spins will be in this case in a «paramagnetic» condition.
Concept and principle of calculation of energy of cationic vacancies
For celculation of energy of dot defects of any kind it is necessary to write down Hamiltonian which should take into account all peocesses in which these defects participate. Own values of it Hamiltonian afso will be sef of the resolved power levels which can borrow dot defects.
That the role of defects was enough appreciable, their concentration in structure should be concerning big. It is the best way to lead the mathematical analy sis by the example of any stoichiometric connectioe, for example, a pyrrhotite in which structure there are cationic vacancies [5-7].
Hamiltonian conditions of vacancies in stoichiometric connections of type can be presented a pyrrhotite as:
h = Z
efafaf
+ HBfina}af + TVfi™nfn™ + f + <Pad
f f,n f™ fi
Where af {af) the operator of a birth (destruction) of vacancy in f unit of a crystal lattice, nf = a +faf - the operator of number of vacancies in f an ohm unit, Bfm, - integral of carry of vacancies between units f and m, Vf m - potential of interaction of vacancies, races put in units f and m, 9 -amplitude of probability formation in crystal structure of defect on Frenkel.
The physical se nse of the first sum in H amiltonian can be understood from the following reasons. Hamiltonian magnetic interaction for stoichiometric connection it is possible to write down kind:
H =_ TiIjmSfSm
jm
If in crystal structure there are vacancies of mrgnetic cations, Hamiltonian magnetic interaction signs the follow ing kind:
H =" UfinPfifPrne
)e
pf = 1 it there is no vacancy id unit f, pf = r if there is a vacancy in unit f, Ifm integral of exchange interaction, Sf -the operator of the spin in f u nit of a crystal lattice.
From the formulas submitted above follows, that at change of concentration of vacancies in a firm body his magnetic energy will change. If )n a crystal the re are no vacancies energy of magnetic interaction of some ion of the iron located in unit f, will tie equal:
IjeffN r p.
je
If in this unit f vacancy eneray of magnetic interaction will change on size was formed (the axis X coincides with a direction a spin in crystal structure.) It is necessary to note, that the size ef generally should depend on unit 1". since in the nearest environment new vacancy in turn can be formed. It will be shown below, that at the account of interaction between vacancies the size ef practically will not depend on numtier of unit. Thus, ef own values of ihe openator of potential energy of the vacancies, numerically equal energy necessary for destruction of magnetic interaction in f unit of crystal structure.
The second sum in Hamiltonian describes processes of moving of vacancies in the structure. It is obvious, that formed in some unit of a crystallographic plane vacancy can change the position as a result of processes next cation jump in the given vacant position.
Now we shall find out physical sense of the third sum to the very first formula Hamiltonian. The crystal structure of any stoichiometric connection is steady up to the certain number of vacancies in individual volume. We shall designate Nr - limiting number of vacancies in some volume Vr of substance. At Nn> Nr this volume of substance is reconstructed in new structure, i.e. there is a single transition. It is natural to assume, that b connection there cannot be a local phase transition if the chosen volume Vr is small enough (for example if have chosen one elementary cell). From here follows, that energy of transition of some volume Vr in new structure should surpass energy of pushing out of superfluous vacancy, if in the neighbor it volume Vn number of vacancies less critical. Thus, if as a result of fluctuation in the next volume Vn of substance N <Nr, and in the given volume N> Nr, vacancies diffuse in the next volume Vf.
The fact, that vacancies «feel» presence of other vacancies in elementary volume, Vr at N> Nr allows to enter interaction between vacancies, having simulated definitely potential of this interaction. It is obvious, that this potential gets out of structural features of concrete not stoichiometric connection.
Fourth (last) sum in Hamiltonian (H) describes processes of formation (destructions) of the vacancies caused by transition of cations from planes in interstitial space (or back), i.e. usual defects on Frenkel which probability of formation grows with increase in temperature of a crystal. At downturn of temperature of a firm body the ions located in interstice, with the greater probability take again vacant positions, than pass in interstice from units of lattice new cations. In case of constant thermodynamic parametets procesnes of formation and destruction of vacancies occur equiprobably.
Condition or splitting of single levels of cat ionic vacancies in a powe r zone
It is possible to show, that the account of moving of vacancies in structure results in splitting initial levels of energy ef in some pow er zone.
Let's write down Hamiltonian H only as two sums:
sfauaf + E rrma +far' r {r,B
ar =<iyNf *'¥
e J a
k
After transformation Fourier
a.=(V, ,
ir k
Hamiltonian Ht signs the following kind:
f { f ifm) J
Let's make replacementef average value a s follow si:
1 ^ N
E=-k S f =St —— = EtV
N J f N 0
Where v - concyntration of vacancies in a planei N-number of units in a plane, NB - number of vacancies in a plane. Similar averaging of energy ef means the assumption of an equiprobable arrangement of vacancies in all units' f crystal structure.
For transformation of the second expression to parentheses in the formula we shall take advantage of the following designations: m=f+h
b (h)=fn+h
f
Finally Hamiltonian Ht it is possible to presen( as:
Ht + B(f)} afaf
f
From last formula follows, that the single power level ef is split at the account of movement of vacancies in some zone, which width B (k).
Inversion a back - result of transition of vacancy on extrinsic a level
It is obvious, that vacancies are distributed on the resolved power levels within the limits of a zone, however vacancies, induced process revolution a spin appear below power zone, i.e. on foreign a level near to a bottom of a zone.
____Q_______________
Fig. 2. Power levels of cationic vacancies
Really, the spin after inversion, passes, apparently from Fig. 1 in a condition with smaller energy since his orientation coincides with an axis of quantization. However this condition is possible only at presence in the nearest environment of the cationic vacancy responsible for this inversion. Leaving of vacancy from the given position would be accompanied by increase in energy of cation; therefore she is stabilized in this condition. This condition energetically lowers, than a similar condition of vacancy close cation with no inverting spin. Thus inverting the back on unit near to vacancy translates her on foreign a level with formation of pair «Vacancy - cation».
Generally parity between exchange integrals can be others, and the configuration of cationic vacancies in the second coordination sphere, the surrounding given unit of crystal structure, can be other. Vacancies can be in even and odd basic planes and accordingly the total magnetic moment of under-lattices (and in a result and the magnetic moment of a mineral) can or grow or decrease, depending on a concrete case.
In the conclusion it is possible to draw conclusions:
1. The opportunity of inverting spin, induced is proved to dot defects;
2. The opportunity of formation in structure of steady pairs «vacancy - cation», minerals influencing magnetic properties is shown.
3. The opportunity is proved at enough high concentration of defects (the stoichiometric connections possessing the distant magnetic order) magnetic properties of minerals can change eventually without thermodynamic, chemical, radiating, atmospheric or other external influence.
References
1. Rumpel A.A. Effect atomic - vacancy orderings in stoichiometric carbide. Successes of physical sciences, 1996, v.166, № 1, p. 33-62.
2. Gucev A.A .Transformation the order - disorder and phase balance in strongly stoichiometric connections. Successes of physical sciences, 2000, v.170, №1, p. 3-40.
3. A.L.Ivanovsky, N.I.Medvedeva, S.V.Okatov. Influence of vacancies on an electronic structure and intern clear interaction in nitride of zirconium. Inorganic material. 2001 v.37, № 5, p. 552-559.
4. D.B.Chesnokov, M.I.Kamchatka Modeling of processes lattice damage and properties chalcogenide led. Inorganic material. 2001, v.37, № 2, p. 157-164.
- 152 -
5. Belov N.V. Description on structural mineralogy. М., Bowels, 1976, p.3126.
6. Ward J.C. The structure and properties of some iron sulphides. Rev.Pure.Appl.Chem.1970, v. 20, p.175.
7. Mashukov A., Onufrienok V.V., Mashukova A. The influence of the cation vacancies on the minerals formation processes. J.Geochimica ET Cosmochimica Acta., v.72, № 12S, 2008.
Временные девиации физических свойств природных минералов
В.В. Онуфриенок
Сибирский федеральный университет, 660041 Россия, Красноярск, пр. Свободный, 79
Показана возможность инверсии спина при различной конфигурации дефектов во второй координационной сфере. Предложен принцип расчета энергии катионных вакансий. Определено условие расщепления одиночных уровней катионных вакансий в энергетическую зону. Доказано, что инверсия спина - результат перехода вакансии на примесный уровень.
Ключевые слова: инверсия спина, конфигурации дефектов, энергетическая зона, примесный уровень.
