Electric Field Gradients at 57Fe Nuclei in the Sr3Fe2Ge4O14 Trigonal Germanate

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Electric Field Gradients at 57Fe Nuclei in the Sr3Fe2Ge4O14 Trigonal Germanate

D. Barb, S. Constantinescu, D. Tarina

To cite this version:

D. Barb, S. Constantinescu, D. Tarina. Electric Field Gradients at 57Fe Nuclei in the

Sr3Fe2Ge4O14 Trigonal Germanate. Journal de Physique I, EDP Sciences, 1997, 7 (12), pp.1701-

1708. �10.1051/jp1:1997164�. �jpa-00247481�

Electric Field Gradients _at ~~Fe _{Nuclei in the} Sr3Fe2Ge4014 llkigonal Germanate

D.

Barb, S. Constantinescu (*)

^{and D.}

^Tarina

Institute of Atomic

Physics,

INFM, PO Box Mg-07, Bucharest, Romania

(Received

16

May

1997, revised 7

July

1997, accepted 24

July 1997)

PACS.76.80.+y

M6ssbauer

effect;

other i~ray spectroscopy

Abstract. A computation of the lattice electric field

gradient

tensor at the octahedral and tetrahedral

Fe~+

_{sites in the} Sr3Fe2Ge4014

trigonal

germanate ^is

performed, taking

into account the fractional ionic

charges provided by

the valence summation

procedure.

The correlation of the calculated M6ssbauer

quadrupole splittings

with those found experimentally shows the role of the local environment distortion in the

quadrupole

interaction of iron nuclei in this structure.

1. Introduction

The strontium iron

germanate Sr3Fe2Ge4014,

characterized

by

the _space group

P321, belongs

to _a class of acentric

crystals,

_very

interesting

for their

special

nonlinear

properties iii.

The

structure consists of successive

layers

of

large

_oxygen

polyhedra

A

(Thompson cubes)

with

8-coordinated cation sites

(position

3e with

symmetry 2) occupied by ^Sr~+

and octahedra Oh

(position

la with

symmetry 32) alternating

at

z/c

rw 0.5 with

layers

of two

types

^of

tetrahedra,

one Tl at the two fold axis

(position 3f), surrounding

octahedra to the

triple

axis

law,

the other _ones T2 at the

triple

axis

(position 2d) _[2].

In

previous

M6ssbauer

spectroscopy

studies [3] it ^was shown that

high spin Fe~+

ions _are

statistically

distributed

together

with

Ge~+

_{ions over} the octahedral Oh and also _over the tetrahedral Tl

sites,

while _no iron was found to enter in the tetrahedra

T2,

these

being occupied only by ^Ge~+

ions. The _room temperature ^M6ssbauer

spectrum

of the studied

sample,

resolved in two

Fe~+ quadrupole doublets,

is shown in

Figure

I. The

corresponding spectral

parameters

(isomer

shift _&,

quadrupole splitting AE(~~

^{and the line width}

r) characterizing

the

crystal chemistry

and the

symmetry

of iron in the structure, as well _as the iron occupancy x of the Oh and Tl sites _are listed in Table I. The _x values _were calculated from the

corresponding spectral

area ratios A

by

the

assumption

of identical recoil-free fractions in the

respective

cation sites.

According

to the

AE(~~

^{values in Table}

^I,

^{both octahedral and} tetrahedral sites

occupied by

iron _{are very} distorted. The _very

large

r values found for the tetrahedral iron

species

show

the _presence of _more

crystallographically inequivalent

Tl sites with different

distortions,

the

listed

AE(~~

^values

^being

a mean value of the

corresponding quadrupole splittings.

In this paper a

computation

of the electric field

gradient

tensor at the octahedral and tetra~

hedral iron sites has been

performed.

The correlation of the calculated M6ssbauer

quadrupole

(*)

Author for

correspondence (e~mail: [email protected])

@

Les

#ditions

_de

_Physique

₁₉₉₇

1702 JOURNAL DE

PHYSIQUE

I N°12

57Fe.Tl

@@

T7

0998

w0996 E

$0994

(

0992

~ ~ ^x E~~~(v)

~«~4

bkgnd(v)=0 99929+0 00003189*v+0 00001896*v2

7 6 5 4 3 2 0 2 3 4 5 6

v[mm/s]

Fig. ^1. The experimental M6ssbauer spectrum of Sr3Fe2Ge4014 sample at room temperature fitted

by

the

spectral

_parameters given in Table I.

Table 1. M0ssbauer

spectral parameters

and iron occupancy

of

octahedral and tetrahedral sites. The

figures

in

parenthesis give

^{the standard} deviations.

Site

Oh T1

Parameters

*&[mm/s] 0.404(5) 0.270(5) AE(~~[mm/s] ^{0.94(1) 1.73(1)}

r[mm/s]

0.34

(1) 0.51(2)

A

0.36(4) 0.64(4)

x

* Isomer shift is referred to metallic iron.

splittings

with the

experimentally

found

AE(~~

^{shows the role of the local} environment dis- tortion in the lattice

quadrupole

interaction of

~~Fe

nuclei in this structure.

2. Electric Field Gradient

Computation

The electric field

gradient (EFG)

and the M6ssbauer

quadrupole splittings (AE(~~~)

^{at the}

iron sites

ro(xo,

_yo,

zo)

in the

Sr3Fe2Ge4014

structure have been calculated

by

the

computer

program

QSCOMP

described _{in [4] and}

fully published

in

[5], starting

^{from the}

expression

of the second rank tensor

Vnp:

Vno

=

((j))

,

lxn,

_xo

= x, v,

z) Ii)

n

~~~~~

vj~)= /

~~~~

~dr

^~~~

4~Eo

~

jr

_ro

is the Coulomb

potential

of the

charge

distribution

p(r)

around the iron

nucleus,

_{xn, xp,} the

rectangular

coordinates and _Eo the _vacuum electric

permittivity.

The electric

charge density

arises from both _a lattice contribution and _a valence electrons _one:

N ~ ~k

~~~~~~~

~

_{~~~~~ ~~~~ ~~~~~~}

_[~~~~21~i ^~~L, (~ks(r)(~ (3)

~ ~

~j

e~kBT

s,=i

where _r~ and _q~

ii

=

1, 2, N)

_are the

position

and

respectively

the ionic net

charge

of the ith ion from the N considered

ions, n(e

is the iron electronic

charge corresponding

to the ksth atomic orbital

(AO),

described

by

the _wave function

ilks(r) (here

k

designates

the quantum numbers nl of the shell and _s is the

magnetic one) weighted

at the

temperature

^{T and} for the

crystalline splitting parameters A) (given

relative to the iron ion

ground level).

Taking

into account both the electric

charge

contributions the EFG tensorial components

Vnp

are

given by

the relation:

Vnp

=

ii i~u)Vj)~

+

(l R)V]j (4)

where'fm

and R _are the Sterheimer's

antishielding

and

shielding

factors

[6j.

The distortion parameter _a, ^{defined and derived} as in

[lsj

for the

ferrigehlenites A2Fe2X07 (A

=

Ba, Sr;

X

=

Ge, Si);

and strontium-iron

germanates Sr3-yLn~Fe2+yGe4-yO14 (Ln

₌

La, Nd;

_y

=

0-1),

_[3] showed the essential role of the lattice

distortion,

the location of the

high spin

ferric ion in octahedral and tetrahedral sites and also

suggested

that the contribution of

V]j

was low. As _a result the authors considered the lattice contribution to the EFG tensor components as a

good approximation.

<it 1 ^~

~~

~~~~ ^31xn _{zoo)ixo~ zoo)}

r~

ro~&aP'

^i~~

where _&mp is the Kroneker

symbol.

The

positions

_r~ of the

crystallographic

sites _are

given by

the subroutine LATTICE

according

to the relation:

r~ =

(z)

₊

la)I

+

(y)

₊

mb)j

₊

(z)

+

nc)k, _(I,

_{m, n}

=

0, +1, +2, (6)

where

r) (z), y), z)) designates

the

positions

of the

N/ charges

_q~ in the

rectangular

unit cell with the lattice constants a, b, c,

(I

₌

1, 2,

N and N

=

(2

(l(

+1)(2 _(m( +1)(2

_{(n( +}

I)N/.

The coordinates

z), y), z/

^{and the} lattice constants a, b, c for the studied structure are obtained

by X~ray

diffraction measurements

[7].

The actual values for the

charges

_q~ can be obtained

by

the valence summation

procedure

_[8],

using

the

empirical law,

described in Section 3 _or

by

the net ionic

charge computing procedure using

a quantum

chemistry

method

[13].

The first

procedure

has been

applied successfully

in

crystalline

structure of minerals

[14j

^{and the} second one to ionic molecular _groups. It would

appear that the summation

procedure

is both _more realistic and faster than the second _one

for the studied

crystalline

structure.

With the above mentioned

quantities known,

the matrix of the EFG tensor is

provided by

the subroutine GRADIENT. The

principal components V~, _{k~~, (z}

and the

corresponding eigen

vectors are obtained

by

the

diagonalization

subroutine EIGEN.

Using

^the calculated

eigen vectors,

the program

gives

also the

angles (qJ,0,

_ifi) between the

principal

axes of the EFG _tensor and the

crystallographic

_axes.

1704 JOURNAL DE

PHYSIQUE

I N°12

The M6ssbauer

quadrupole splitting

for

~~Fe isotope

_can be calculated

according

to the well known relation [9]:

AE(~~~

=

~^~

)~ ii?)

where

~ =

~~~j ^~~~ 18)

is the

asymmetry

parameter

(0

< ~ ^<

l)

and

eQ

is the nuclear

quadrupole

moment of

5~Fe.

Table II. The estimated

Lm~x (Iii for cation~ozygen

^bonds in

Sr3Fe2Ge4014 using

the ef~

fectme

ionic radii

given

in

ill j.

Nc

cc 8 6 4

ion

O~~

_{1.42 1.40 1.38}

Sr~+

_{1.92 3.34}

Fe~+

_{1.08 2.48 2.46}

Ge~+

_{0.90 2.30 2.28}

Table III. Bond

lengths

L

(upper

value in ~$)

f12j

and estimated bond valence _v

(lower

value in v,u.

)

in

Sr3Fe2Ge4014 compound.

~

A(3e) Oh(la) Tl(3f) T2(2d)

~~~~~

Sr~~ Fe~~2Ge(~s Fe(~8Ge(~2 ^Ge~~ ~~

_~

~

?2.638(4)+ _1.698(12)

~ ~~~

0.256 l.071

~

2.600(9)+ 1.859(9)+ 1.747(8)?

~ 0.271 0.817 0.978

,

2.883(8)+

-2.232

°2

~ ~~~

~

2.496(10)+ 1.924(3)* 1.766(8)+

~ 0.317 0.547 0.973

~'~~~

L 2.654

1.942(3) 1.812(9) 1.735(9)

LQ(f~~~~

3.340 2.43 2.36 2.28

p 3.869 3.802 3.307 3.183

v)~~~~~~~ ^{0.25 0.547 0.893 1.}

£~v

2.02 3.280 3.579 4.005

+ two bonds _per cations; i7

(left)

three bonds _per anion; i7

(right)

three bonds _per cation;

* six bonds per cation.

Table IV. The ions

positions

around the octahedral

Fe~+

_site

m the lattice

of Sr3Fe2Ge4014 crystal (The origin of

coordinates _{is m}

3f (Tl )).

N Ions

viii

_z

Riii _q~iv.ui

0 S-II 5.46 2.52 0.00 3.280

1

03:6g

5.27 3.95 3.70 1.92 -1.836

2 3.73 4.84 1.34 1.92 -1.836

3 3.73 6.09 3.70 1.92 -1.836

4 6.34 6.35 3.70 1.92 -1.836

5 6.34 4.57 1.34 1.92 -1.836

6 5.27 6.98 1.34 1.93 -1.836

7

Fe((~Ge((~:3f

4,14 3.77 0.00 3,19 3.579

8 4.14 3.77 5.04 3,19 3.579

9 7.07 5.47 0.00 3,19 3.579

10 7.07 5.47 5.04 3.19 3.579

II 4.14 7.16 0.00 3.20 3.579

12 4.14 7.16 5.04 3.20 3.579

13 Sr:3e 6.86 2.44 2.52 3.49 2.02

14 1.61 5.46 2.52 3.50 2.02

IS 6.86 8.49 2.52 3.51 2.02

3. Valence Summation Procedure for

Sr3Fe2Ge4014

In th18 Section the valence Summation for

Sr3Fe2Ge4014

18

performed

in order to obtain the actual values for the ionic

charges

_q~ in the

respective

structure. The

procedure

is based _on

an

empirical

_curve

_[10] expressing

formal bond valence _v in terms of bond

length

L for any coordination

polyhedron

in _a

given crystal:

t

^P

u=u~ for L<L

(9)

L

and

u =

u~~~~

^~ _for

I

_{< L <}

Lm~x (10)

Lmax

L with

p =

~

(II)

Lm~x

L

where _u~ is the ratio of formal cation valence to coordination number

(Nc),

L is the _mean value of the observed cation-anion distances in the

given polyhedron, Lm~x

is the _sum of the

"maximum radii" for cation and anion

(when Nc

~

cc).

As it _was mentioned

above,

there _are four kinds of coordination

polyhedra

in

Sr3Fe2Ge4014 compound: Thompson

cubes

occupied by Sr~+ ions,

tetrahedra T2

occupied by Ge~+,

octahedra Oh and tetrahedra Tl both with random

occupation

^{of the}

type Fe((~Ge((~

and

Fe([~Ge((~, respectively.

The bond

lengths

L and

£

_{for all} these

polyhedra

_are taken from

X~ray

diffraction data [7]. ^The

Lm~x

values for

cation~oxygen

bonds in

Sr3Fe2Ge4014

lattice _were estimated

by using

the effective ionic radii

given

in Table II.

1706 JOURNAL DE

PHYSIQUE

I N°12

Due to the statistical distribution of

Fe~+

_and

Ge~+

ions _over the Oh and Tl

sites,

^the

corresponding weighted Lm~x

and _u~ have been calculated for the above sites

using

the relations:

Llltf~~~~ioh)

=

Zion)Litxife~+)

₊

ii Zion))LitxiGe~+), i12)

Lzjjhted(Tij

=

z(TijLjj~(Fe3+)

₊

₍₃ z(TijjLjj(Ge4+); (13j vi~'~~~~~ (Oh)

=

Zion)vi~ife~+)

₊

ii xioh))vi~iGe~+); _i14) li~>~h~~d(Tij

=

x(Ti)vji _(Fe3+)

₊

_{(3 x(Ti} ))vii _{(Ge4+ j. (isj}

The bond valence _u calculated

by equations (9-15)

and the valence summation _over both anions

£~

u and cations

£~

_u of the

Sr3Fe2Ge4014

structure _are

presented

in Table III.

4. Electric Field Gradients of the Octahedral and Tetrahedral Iron Sites in the

Sr3Fe2Ge4014

Germanate

A

computation

of the lattice EFG tensor at the octahedral and tetrahedral

Fe~+

sites in the

Sr3Fe2Ge4014 compound

has been

performed according

to the

procedure

described in Sec- tions 2 and 3. The lattice of

rectangular

unit cell

(a

=

8.271,

_b

= 2acos30°

=

14.3241,

c = 5.04

1),

_built

_by

_{the subroutine} LATTICE with

origin

of coordinates in the

crystallo- graphical position

^3f

(Tl)

is illustrated in Table IV for the first IS

neighbors

of the octahedral

Fe~+

_ion.

Table V. The EFG data and

AE(~~~

^values

of

octahedral _iron

for

_some relevant coordination

spheres (The

standard deviation

for _AE(~~~

value is about 0. 05

mm/s).

~

~l ~~$~l

ll~~l ^~~$~l

^~

~~

~~~~~~~~~~~~

6 1.93 0.32 0.33 -0.65 0.02 0.65 0.85

12 3.20 -0.59 -0.62 1.21 0.02 1.21 0.79

IS 3.51 -0.37 -0.39 0.76 0.03 0.76 0.53

353 10.08 -0.17 -0.21 0.38 0.09 0.38 1.65

915 14.52 -0.20 -0.25 0.45 0.ll 0.46 1.41

1875 20.20 -0.19 -0.22 0.41 0.07 0.42 1.53

Table VI. The EFG data and

AE(~~~

^values

of

tetrahedral _iron

for

_some relevant coordina~

tion

spheres (The

standard deviation

for _AE(~~~

value is about o. off

mm/s).

4 1.86 0.48 0.55 -1.03 0.06 1.03 1.37

12 3.39 -0.08 -1.37 1.45 0.89 1.62 0.22

24 3.95 0.36 0.97 -1.33 0.46 1.37 0.71

40 5.04 0.17 0.89 -1.06 0.68 1.13 1.18

280 9.58 0.17 0.93 -1.10 0.70 1.19 1.06

1707 20.0 0.19 0.82 -1.01 0.62 1.08 1.27

Sr~Ga~Ge~O~_~

-h- AE caic(Qh

a

f

a

E

~

~j

_{_~}

i~

^~

_2~~/4%//~

^{~ ~'~~}

f~

^~ ( ~

02

00 25 50 75 loo 12.5 150 175 200

RjAj

Fig.

2. The calculated

quadrupole splitting AE]~~~(R)

^{values for}

Fe~~.Oh.

Sr~Fe~Ge~O~~

i ^-h- AE~Ca'C(Ti)

~

i

~

°a

~i

00 25 50 75 loo 125 150 175 200 225

R[Ai

Fig.

3. The calculated quadrupole splitting

AE]~~~(R)

^{values for Fe~~.T1.}

In Tables V and

VI,

we

present

the main

components

^{of the EFG} tensor for the Oh and

respectively

Tl iron

sites,

as well as the

corresponding _AE(~~~ values,

obtained

with'fm

" -10

and

Q

=

0.21x10~~~ m~,

and their

departure

from

AE(~~ ^{(with respect}

^{to the half}

line-widths).

They

_were

provided by

the subroutine

GRADIENT, taking

into account the LATTICE

output

data for N ₁ 2000 ions

(involved

into a coordination

sphere

with the radius R1 20

1).

The convergence of the

AE(~~~ values,

^{as a function of the radius R is}

given

in

Figures

2 and

3,

both for the octahedral and the tetrahedral iron. In both _{cases one can see}

rapid

convergence,

practically

obtained for _a coordination

sphere

with the radius R of

only

5

1.

However, comparing

^{the limit}

_AEj~~~

values to those

AE)~

found

experimentally

for the studied

compound (Tabs. I, V, VI),

_a less

satisfactory correspondence

_can be observed.

1708 JOURNAL DE

PHYSIQUE

I N°12

The actual lattice distortion felt

by

the

respective

iron nuclei _{seems to} be almost two times

stronger

than that

predicted by

the calculated effect of the whole lattice. On the other hand the

departure

ratio shows _a lower value for the first cation environments. It _seems that iron nuclei in the

respective

sites feel _more the

strong

^{distortion effect of the first} environment than that much diminished _one of the whole lattice.

Indeed,

from the convergence curves of

AEj~~~(R)

^{to the}

AE(~~

^values

^{(see Figs. 2, 3),}

one can

clearly

_see that the well known value i~u = -10

given

_{in [6]}

corresponds

to IS and 12 ionic

neighbors

of octahedral and tetrahedral iron

respectively.

The above results confirm _some

previous findings

discussed in

[12]

^and proves the essential role of the first local environment _on the behavior of the M6ssbauer

probes.

As it is

known,

the

studied

compound belongs

to the class of disordered

crystalline

media [3] ^{due to the random} distribution of _more than _a

single

sort of ions _over the first environment of the cationic sites and in this _case the local environment disorder is needed to reveal the

dispersion

of local lattice

electric field

properties (as potential, intensity

and

gradient

tensor

components

of the electric

field)

and their calculations _are of

special importance.

References

[Ii

Kaminskii

A.A.,

Proc, lst Int. School _on Excited States of Transition

Elements,

Ksiaz

Castle, 1988,

^B.

Jezowska-Trzebiatowska,

J.

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and W.

Strek,

Eds.

(World

Scientific

Singapore, 1989)

_p. ^649.

[2] Belokoneva

E.L.,

Simionov N.A., Butashin

A.V.,

Mill B.V. and Belov

N.V.,

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Nauk USSR 255

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Barb

D.,

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S.,

Tarina D. and

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in press.

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Calogero S., QSCOMP: "Program

of the

5~Fe

_M6ssbauer

quadrupole splitting

parameters

evaluation", QCMP

172,

QCPE

Bulletin vol.

17,

_no. I

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[8]

Donnay

G. and Allmann

R.,

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Cryst.

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[9]

Wertheim _K.G.,

_M6ssbauer

effect, principles

and

applications (Academic Press,

New

York, 1964).

[10]

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Donnay

_y, Acta

Cryst.

B 27

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1871.

[iii

Shannon R-D- and Prewitt

C.T.,

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[13]

^Howell

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