Refinemenf of the Garnet structure by neutron diffraction

(1)

HAL Id: jpa-00205800

https://hal.archives-ouvertes.fr/jpa-00205800

Submitted on 1 Jan 1964

HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Refinemenf of the Garnet structure by neutron diffraction

Wolfram Prandl

To cite this version:

Wolfram Prandl. Refinemenf of the Garnet structure by neutron diffraction. Journal de Physique,

1964, 25 (5), pp.440-441. �10.1051/jphys:01964002505044000�. �jpa-00205800�

(2)

440. REFINEMENF OF THE GARNET STRUCTURE BY NEUTRON DIFFRACTION

By ^WOLFRAM PRANDL,

Universitätsinstitut für Kristallographie, ^München.

Résumé. 2014 Des données de diffraction neutronique ônt été obtenues à partir d’un monocristal de grossulaire [1], grenat naturel de composition îdéale Al2Ca3(SiO4) 3. On a déterminé les paramètres thermiques pour Al, Ca, Si, Ô êt ^les paramètres ^de position ^d’O âu moyen d’un raffinement par moindre-carrés utilisant la matrice complète. ^La comparaison âvec ^les paramètres ôbtenus âux

rayons ^{X et} publiés par Abrahams ^et Geller [2] et par Geller [3] ^s’accorde ^seulement ^avec les para- mètres de position.

Abstract.

²⁰¹⁴

Neutron diffraction data have been collected from a single crystal ^of grossularite [1],

a natural garnet ^with îdeal composition Al2Ca3(SiO4)3. By ^means ôf â full matrix least _squares refinement thermal parameters ^for Al, Ca, Si, ⁰ ând positional parameters for oxygen have been obtained. Comparison ^with X-ray parameters published by Âbrahams ând ^Geller ^[2] and Geller [3]

gives agreement only ^{with the} positional parameters.

LE JOURNAL DE PHYSIQUE ^TOME 25, ^MAI 1964,

For an exact determination of the oxygen para- meters in the presence of ^the heavier atoms Abrahams and Geller [2] ^selected X-ray reflections to which Al gives ^no contribution, while Ca and Si contribute only with the difference t6a fl, fla

and /[1 being the atomic scattering factor multi-

plied by ^the Debye-Waller factor. The data were

treated by ^the Sayre diagonal matrix program, and the resulting ^thermal parameters ^seemed ^to ^be

reasonable. Later Geller [3] ^showed by applying

the Busing-Levy full_ matrix program ^{that there} is a strong interaction between the Ca- and Si- thermal parameters resulting ^{from the} special

choice of reflections.

On account of the large scattering length ^{of the}

oxygen (compared ^with ^that ôf ^the ôther ions) ân investigation by ^neutron diffraction was thought

to be an effective method for the parameter ^deter-

mination. Moreover, ^neutrons ^are scattered iso-

tropically ^so ^{that the} computed thermal para- meters are free from assumptions ^on ^the ^electron

distribution in the X-ray ^case.

Two cylindrical samples ôf â natural grossu- larite from Xalostoc (Mexico) ^were used, ône ^with

the [111]

^-

^direction âs axis, ^the ôther ône

with [110]. ^Data ^were ^collected ^{f rom the} ^zero ^and

first layer ^line ^{of the} [111]

^-

^zone ^and ^{from the}

zero layer line of the [110]

^-

^zone up ^to sin 0/À

⁼

^{0 . 73.} ^As ^a ^{whole 154} ^non-zero ^reflec-

tions with an intensity ratio 1 : 103 were observed.

Some reflections were measured with two different

wavelengths, ^{but there} ^was ^no indication of extinc- tion. As the absorption ^cross sections of the atoms involved are small, ^no correction was applied.

The main difficulty ^arose from the fact that with ^a

wavelength X

⁼

^1.08 Â ând â ^lattice ^constant

a

⁼

11.874 ~ [2] ^the reciprocal lattice has an

abundance of reflections and overlap ^occurs ^at higher Bragg angles. ^The angular resolution could

be much improved by increasing ^the Bragg angle

of the monochromator [4]. ^In figure ¹ ^{the full}

line width A(20) ^is plotted against ^the ^mean Bragg angle ^for ^two different monochromator angles.

For both curves the wavelength ^was ^{1. 08} ^A.

FIG. 1.

^-

Full line width of reflections vs. mean Bragg angle, measured with two different monochromator

angles.

The data were treated by ^the Busing-Levy ^least

squares program for the IBM 7090 computer.

After several preliminary stages all reflections were

given ^unit weight in the last run. In this run

parameter ^shifts ^were practically ^zero ^{after the}

third cycle. ^Table 1 shows the neutron results

compared ^{with the} X-ray ^results. ^The ^{errors are} computed standard deviations.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:01964002505044000

(3)

441 TABLE 1

the complete results will be published ^{in the} Zeitschrift für Kristallographie.

I would like to thank Dr Dachs for his permanent

interest and for helpfull discussions. I am obliged

to Pr Maier-Leibnitz for having provided the oppor-

tunity ^to ^use the facilities at the Forschungs-

reaktor Munchen, ^and ^to ^the Deutsches-Rechnen- zentrum and the computer department ^of ^the

Institut für Plasmaphysik, ^Munchen.

Discussion

Dr ABRAHAMS. - 11 est int6ressant et d’ailleurs

pr6visible que les coordonn6es des positions ^dans

1’etude pr6sente ^aux ^neutrons ^ne soient pas sensi- blement différentes de ^nos r6sultats de 1958 aux

rayons X. La large variation des param6tres ^ther- miques, cependant, ^reflete les diff erentes erreurs

systematiques ^{des deux} techniques de diffraction.

A combien pr6s estimez-vous approcher ^les ^vrais

facteurs de Debye ?

M. PRANDL. - Les erreurs systematiques a ^con-

sid6rer peuvent 6tre divisées ^en deux _{groupes :} celles dues a la ^mesure et celles dues au mod6le

physique d’interpr6tation ^de ^ces ^mesures. ^Je ^ne

voudrais pas comparer ici les techniques ^instru-

mentales des rayons X ^et des neutrons. Les donn6es

aux rayons X ^sont interprétées ^avec ^les hypotheses

suivantes :

(1) Le nuage 6leetronique ^{a une} ^extension ^limit6e

et sa charge ^totale ^est ^connue.

(2) ^Le type de liaison est purement ionique, ^de

sorte que le nuage 6lectronique ^est sph6rique.

Comme ces deux hypotheses ^sont ^absentes ^en

diffraction de neutrons, ^les vrais facteurs de Debye

sont probablement ^mieux approch6s par les valeurs

aux neutrons.

Dr IBERS.

^-

Cela ne me parait pas ^correct. Les facteurs de forme atomique ^sont ^bien ^{connus en}

rayons X ^aux angles ^6lev6s ^ou les eff ets thermiques

sont importants. Donc, ^des ^erreurs ^de ^facteur ^de

forme ne devraient _pas affecter la determination des param6tres thermiques.

REFERENCES [1] ^MENZER (G.), ^Die Kristallstruktur der Granate. Z. Kris-

tall., 1929, 69, ^300.

[2] ^ABRAHAMS (S. C.) and GELLER (S.), Refinement of the structure of a grossularite garnet. ^Acta Cryst., 1958, 11, ^437.

[3] ^GELLER (S.), Parameter interaction in least _squares structure refinement. Acta Cryst., 1961, 14, ^1026.

[4] ^STEHR (H.), ^Das Reflexionsvermögen ^von ^Mosaikkri-

stallen im Hinblick auf ihre Verwendung ^als ^Mono-

chromatoren in Neutronenbeugungsspektrometern.

Z. Kristall., 1963, 118, ^263.

Refinemenf of the Garnet structure by neutron diffraction

HAL Id: jpa-00205800

https://hal.archives-ouvertes.fr/jpa-00205800

Submitted on 1 Jan 1964

HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Refinemenf of the Garnet structure by neutron diffraction

Wolfram Prandl

To cite this version:

Wolfram Prandl. Refinemenf of the Garnet structure by neutron diffraction. Journal de Physique,

1964, 25 (5), pp.440-441. �10.1051/jphys:01964002505044000�. �jpa-00205800�

440.

REFINEMENF OF THE GARNET STRUCTURE BY NEUTRON DIFFRACTION

By WOLFRAM PRANDL,

Universitätsinstitut für Kristallographie, München.

rayons X et publiés par Abrahams et Geller [2] et par Geller [3] s’accorde seulement avec les para- mètres de position.

Abstract.

Neutron diffraction data have been collected from a single crystal of grossularite [1],

a natural garnet with ideal composition Al2Ca3(SiO4)3. By means of a full matrix least squares refinement thermal parameters for Al, Ca, Si, 0 and positional parameters for oxygen have been obtained. Comparison with X-ray parameters published by Abrahams and Geller [2] and Geller [3]

gives agreement only with the positional parameters.

LE JOURNAL DE PHYSIQUE TOME 25, MAI 1964,

For an exact determination of the oxygen para- meters in the presence of the heavier atoms Abrahams and Geller [2] selected X-ray reflections to which Al gives no contribution, while Ca and Si contribute only with the difference t6a fl, fla

and /[1 being the atomic scattering factor multi-

plied by the Debye-Waller factor. The data were

treated by the Sayre diagonal matrix program, and the resulting thermal parameters seemed to be

reasonable. Later Geller [3] showed by applying

the Busing-Levy full_ matrix program that there is a strong interaction between the Ca- and Si- thermal parameters resulting from the special

choice of reflections.

On account of the large scattering length of the

oxygen (compared with that of the other ions) an investigation by neutron diffraction was thought

to be an effective method for the parameter deter-

mination. Moreover, neutrons are scattered iso-

tropically so that the computed thermal para- meters are free from assumptions on the electron

distribution in the X-ray case.

Two cylindrical samples of a natural grossu- larite from Xalostoc (Mexico) were used, one with

the [111]

direction as axis, the other one

with [110]. Data were collected f rom the zero and

first layer line of the [111]

zone and from the

zero layer line of the [110]

zone up to sin 0/À

0 . 73. As a whole 154 non-zero reflec-

tions with an intensity ratio 1 : 103 were observed.

Some reflections were measured with two different

wavelengths, but there was no indication of extinc- tion. As the absorption cross sections of the atoms involved are small, no correction was applied.

The main difficulty arose from the fact that with a

wavelength X

1.08 A and a lattice constant

a

11.874 ~ [2] the reciprocal lattice has an

abundance of reflections and overlap occurs at higher Bragg angles. The angular resolution could

be much improved by increasing the Bragg angle

of the monochromator [4]. In figure 1 the full

line width A(20) is plotted against the mean Bragg angle for two different monochromator angles.

For both curves the wavelength was 1. 08 A.

FIG. 1.

Full line width of reflections vs. mean Bragg angle, measured with two different monochromator

angles.

The data were treated by the Busing-Levy least

squares program for the IBM 7090 computer.

After several preliminary stages all reflections were

given unit weight in the last run. In this run

parameter shifts were practically zero after the

third cycle. Table 1 shows the neutron results

compared with the X-ray results. The errors are computed standard deviations.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:01964002505044000

441 TABLE 1

the complete results will be published in the Zeitschrift für Kristallographie.

I would like to thank Dr Dachs for his permanent

interest and for helpfull discussions. I am obliged

to Pr Maier-Leibnitz for having provided the oppor-

tunity to use the facilities at the Forschungs-

reaktor Munchen, and to the Deutsches-Rechnen- zentrum and the computer department of the

Institut für Plasmaphysik, Munchen.

Discussion

Dr ABRAHAMS. - 11 est int6ressant et d’ailleurs

pr6visible que les coordonn6es des positions dans

1’etude pr6sente aux neutrons ne soient pas sensi- blement différentes de nos r6sultats de 1958 aux

rayons X. La large variation des param6tres ther- miques, cependant, reflete les diff erentes erreurs

By ^WOLFRAM PRANDL,

Universitätsinstitut für Kristallographie, ^München.

rayons ^{X et} publiés par Abrahams ^et Geller [2] et par Geller [3] ^s’accorde ^seulement ^avec les para- mètres de position.

Neutron diffraction data have been collected from a single crystal ^of grossularite [1],

a natural garnet ^with îdeal composition Al2Ca3(SiO4)3. By ^means ôf â full matrix least _squares refinement thermal parameters ^for Al, Ca, Si, ⁰ ând positional parameters for oxygen have been obtained. Comparison ^with X-ray parameters published by Âbrahams ând ^Geller ^[2] and Geller [3]

gives agreement only ^{with the} positional parameters.

LE JOURNAL DE PHYSIQUE ^TOME 25, ^MAI 1964,

For an exact determination of the oxygen para- meters in the presence of ^the heavier atoms Abrahams and Geller [2] ^selected X-ray reflections to which Al gives ^no contribution, while Ca and Si contribute only with the difference t6a fl, fla

plied by ^the Debye-Waller factor. The data were

treated by ^the Sayre diagonal matrix program, and the resulting ^thermal parameters ^seemed ^to ^be

reasonable. Later Geller [3] ^showed by applying

the Busing-Levy full_ matrix program ^{that there} is a strong interaction between the Ca- and Si- thermal parameters resulting ^{from the} special

On account of the large scattering length ^{of the}

oxygen (compared ^with ^that ôf ^the ôther ions) ân investigation by ^neutron diffraction was thought

to be an effective method for the parameter ^deter-

mination. Moreover, ^neutrons ^are scattered iso-

tropically ^so ^{that the} computed thermal para- meters are free from assumptions ^on ^the ^electron

distribution in the X-ray ^case.

Two cylindrical samples ôf â natural grossu- larite from Xalostoc (Mexico) ^were used, ône ^with

^direction âs axis, ^the ôther ône

with [110]. ^Data ^were ^collected ^{f rom the} ^zero ^and

first layer ^line ^{of the} [111]

^zone ^and ^{from the}

^zone up ^to sin 0/À

^{0 . 73.} ^As ^a ^{whole 154} ^non-zero ^reflec-

wavelengths, ^{but there} ^was ^no indication of extinc- tion. As the absorption ^cross sections of the atoms involved are small, ^no correction was applied.

The main difficulty ^arose from the fact that with ^a

^1.08 Â ând â ^lattice ^constant

11.874 ~ [2] ^the reciprocal lattice has an

abundance of reflections and overlap ^occurs ^at higher Bragg angles. ^The angular resolution could

be much improved by increasing ^the Bragg angle

of the monochromator [4]. ^In figure ¹ ^{the full}

line width A(20) ^is plotted against ^the ^mean Bragg angle ^for ^two different monochromator angles.

For both curves the wavelength ^was ^{1. 08} ^A.

The data were treated by ^the Busing-Levy ^least

given ^unit weight in the last run. In this run

parameter ^shifts ^were practically ^zero ^{after the}

third cycle. ^Table 1 shows the neutron results

compared ^{with the} X-ray ^results. ^The ^{errors are} computed standard deviations.

the complete results will be published ^{in the} Zeitschrift für Kristallographie.

tunity ^to ^use the facilities at the Forschungs-

reaktor Munchen, ^and ^to ^the Deutsches-Rechnen- zentrum and the computer department ^of ^the

Institut für Plasmaphysik, ^Munchen.

pr6visible que les coordonn6es des positions ^dans

1’etude pr6sente ^aux ^neutrons ^ne soient pas sensi- blement différentes de ^nos r6sultats de 1958 aux

rayons X. La large variation des param6tres ^ther- miques, cependant, ^reflete les diff erentes erreurs

systematiques ^{des deux} techniques de diffraction.

A combien pr6s estimez-vous approcher ^les ^vrais

M. PRANDL. - Les erreurs systematiques a ^con-

sid6rer peuvent 6tre divisées ^en deux _{groupes :} celles dues a la ^mesure et celles dues au mod6le

physique d’interpr6tation ^de ^ces ^mesures. ^Je ^ne

voudrais pas comparer ici les techniques ^instru-

mentales des rayons X ^et des neutrons. Les donn6es

aux rayons X ^sont interprétées ^avec ^les hypotheses

(1) Le nuage 6leetronique ^{a une} ^extension ^limit6e

et sa charge ^totale ^est ^connue.

(2) ^Le type de liaison est purement ionique, ^de

sorte que le nuage 6lectronique ^est sph6rique.

Comme ces deux hypotheses ^sont ^absentes ^en

diffraction de neutrons, ^les vrais facteurs de Debye

sont probablement ^mieux approch6s par les valeurs

Cela ne me parait pas ^correct. Les facteurs de forme atomique ^sont ^bien ^{connus en}

rayons X ^aux angles ^6lev6s ^ou les eff ets thermiques

sont importants. Donc, ^des ^erreurs ^de ^facteur ^de

forme ne devraient _pas affecter la determination des param6tres thermiques.

REFERENCES [1] ^MENZER (G.), ^Die Kristallstruktur der Granate. Z. Kris-

tall., 1929, 69, ^300.

[2] ^ABRAHAMS (S. C.) and GELLER (S.), Refinement of the structure of a grossularite garnet. ^Acta Cryst., 1958, 11, ^437.

[3] ^GELLER (S.), Parameter interaction in least _squares structure refinement. Acta Cryst., 1961, 14, ^1026.

[4] ^STEHR (H.), ^Das Reflexionsvermögen ^von ^Mosaikkri-

stallen im Hinblick auf ihre Verwendung ^als ^Mono-

Z. Kristall., 1963, 118, ^263.