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The electron charge distribution in V3Si
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Solid State Communications, Vol. 26, pp. 461—468. ®Pergamon Press Ltd. 1978. Printed in Great Britain
THE ELECTRON CHARGE DISTRIBUTION IN V
3S1*
J.—L. Staudenmann Department of Physics University of Missouri at Columbia Columbia, Missouri 65201
(Received on 8 November 1977, in revised form 21 February 1978, by E.F. Bertaut) The electrot~ charge distribution in a martensitically transforming single— crystal of V Si in the superconducting state has been obtained from accurate X—ray diffra~tionmeasurements. The most significant differences between the electron density maps at room temperature and below the superconducting transition are the disappearance of the bond between the Si atom and the V—V bond on a chain at the lower temperature and the appearance of two anisotropic rings around each V—V bond at 13.5 K. By comparing our results with various physical properties, we conclude that, on cooling, V Si begins to anticipate a martensitic transformation at about 130 K even though t~istransformation does not actually occur before ~2l K.
INTRODUCTION V Si is a prototype of the large family of biJry compounds exhibiting the A15—type structure. It has many physical properties which seen to be linked with the existe~~ of linear chains of V atoms, in particular with superconductivity CT 16.85 K for the stoi— chiometric compositiSn). In order to build physical models, it is important to know the real electron distribution within the crystal. A knowledge of the temperature dependence of the electron distribution is highly desirable for A15 alloys such as V Si, which have many strong temperature depeJent physical pro— perties. It is possible, with carefully measured X—ray diffraction intensities, to obtain directly the electron charge distribution. We have prç~~ji~ys1y applied this technique at 300 K to V Si’ ‘ and t~3t~non—superconducting MS ~ompound Cr Si We describe here the most 1jnport~ntresults of a study on v3si at 13.5K, below both the superconducting and martensitic transition temperatures, It is of interest to correlate our X—ray measurements on V Si with other physical pro— perties such as temper~u~y dependence of the electrical resistivity ‘ , the sound 8’9~ and the
at the same time and received the sane heat treatment (see table 2). The influence of the conical Al fiber on the intensity of the V Si reflections is very small and represents a~prox— imately 1% of the measured background. The spherical single—crystal measured here exhibits a martensitic transformation, so the composition is stoichiometric. Step scan data were col— lected in a Be dewq with Pd filtered Ag K~ra— diation (A = 0.559 A) on a Picker automated 4— circle diffractometer. 1289 reflections at 13.5 K referred to the cubic sp~c~ group Pm3n were measured (sin /A 1.59 A ). The
max temperature was measured on the copper block of the cryostat and the stabilization was better than 2 K at 13.5 K. REFINEMENTS Good agreement between our measurements of lattice parameters below the martensitic transformation and thti~luee published by (13) Batterman and Barrett and those of Hess was obtained (see table 1). From our lattice parameters at 13.5 K, the low temperature structure of V Si can be more complicated than tetragonal, pJhaps orthorhombic or even mono— clinic. Symoetrically equivalent reflections were averaged after correction for Lorents leading to anfactors internal consistency factor and polarizhtion and also for absorption analogous to the conventional R factor between symmetry equivalen~ 2yeflections of 2.7% (1.7% for the 300 K data ). The 300 K data was corrected for thermal diffuse scatte~f~5 effects (TDS) according to Helmholdt and Vos . Using the sou1~)velocitYconstants of Testardi and Bateman a very sma~J~ TDS contributi~)was found even for the (12 2 2) reflection Thus, such a correction was not made for the 13.5 K data. The extinction corrections used here are the same employed in ref. 2.
magnetic susceptibility . The X—ray measure— velocity~~~, the specif~0~eat~ ments can also be helpful in explaining the rea— son for the sign reversal of the first deriva— pressure dependence of the shear EXPERIMENTAL A V Si spherical single—crystal of 0.115 ~s radius glued on a thin conical aluminum fiber in order to have a good thermal contact. This single—crystal is not thc same as the one used for the 300 K measurement but it was groufld
*ThIs work was presented at the A.C.A. meeting at East Lansing in August, 1977 (A.C.A. abstracts 5, 82 (l~77).
461
462
THE ELECTRON CHARGE DISTRIBUTION IN V
3SI
Table 1:
Lattice
Vol. 26, No. 8
constants of V3Si as a function of the temperature.
Table 1 Temperature (K)
Radiation
Reflection(s) used in the measurement
Number of measurements and lea3t squares fit
Lattice constants (mean values of the least squares results) 0
300
Ag
xa
6 forms of 800 24 forms of 840
1
a
5
a ~ 4.7180 ± .0011 A spherical single— crystal of 0.023 cm diameter
=
4.7240 ±0005 A spherical single— crystal of 0.008 cm diameter 0
78
Ag Na
15
Cu
1 2 6 6 4
form of 800 forms of 844 forecas of 880 forms of 884 forms of 12 00
0
xa
600
a
=
4.7147 A
400
c
=
4.7250 A
C
/
a
432
a
=
4.7144 ± .0003 A
4~2
c
=
4.7271 ± .0005
C
/
a
0
14.2
Cu
xu
1.0024 Batterman & ~-.rrett 0 0
A
1.0027 Bess 1975 0
13.5
Ag K~
1 2 6 5 4
form of 800 forms of 844 forms of 880 forms of 844 forms of 12 00
After measuring some reflections in Nb Sn at 33 K and the (3 0 0) reflection as a fuJ— tion of the temperature below the martensitic trau!~tiontemperature (45 K), Shirane and Axe concluded that the space group for the low temperature phase of Nb Sn is P4 /manc. From the literature there are Jme indications that the low temperature phase cf V Si is the same as that of Nb Sn. We consideJd various models in attempti~g to determine the true structure of V Si below the martensitic trans— formation, i.e? the following tetragonal space groups P4 /mmc, P42mc, P42/m, P~+2,and the two orthorhoJic space groups Pnmun and Pmin2. Our results permit us to establish that the low temperature structure of V Si is probably not described by P42/mnc. In ~very case listed above, it was impossible to refine the thermal parameter of the Si atom in the anisotropic form even when the chosen space group provides this possibility. The allowed general positions for the V atoms also ±ntroducemany difficulties into the refinements and very seldom was a significant displacement from the corresponding cubic position. For instance the maximum dis— placement found in analyzed tetragonal space
3
a 4.7135 ± .0024 A b 4.7268 ± .0019 c 4.7163 ±.0017 A cos~ 0.0010 ± .0007 2b / (a+c) 1.0025 spherical si’igle— crystal of 0.023 cn~ diameter
A A
groups is J0.00042 ±0.000141 on the coordinate 0.25 of one of the V atoms. The corresponding maximum displacement for the two orthorhombic space groups is 0.00035 ±0.000141 on the same coordinate 0.25 for a V atom. We know that the agreement factors have to be better for a tetragonal space group than for the cubic approximation because of the cell dimensions (see table 1). Though we did not find that for the following reason. We began the refme— ments with the anomalous dispersion corrections for the No radiation (mist~~3) instead of those for the Ag radiation and the agree— ment factors were in favor of the tetragonal space groups in the tetragonal average. The neat step with the good corrections gave ex— actly the opposite conclusions, i.e. the cubic approximation provided a better refinement In the tetragonal average. Therefore the key—point of the problem mmPli~2yot only a study in a single domain sample , but also an experi— mental determination of the anomalous dispersion corrections as a fu-iction of the temperature. It should be noted th.~st it is probably the first tine that the temperature dependence of
THE ELECTRON CHARGE DISTRIBUTION IN V
Vol. 26, No. 8
3S1
Table 2
463
Crystallographic single—crystal data for V3Si at 300 K for one single—crystal, and at 13.5 K for a second single-crystal
in the cubic space group Pm3n.
The
standard deviations are given between parentheses.
Table 2 X-ray data temperature (°K) Heat treatment (hours/temp., °C/Arpressure, atm.) Sphere radius
R (cm)
X-ray radiation wavelength A
Ka1
(A)
linear absorption coef. 1i(cm’~) li* R
cubic lattice constant a (A) Scale factor VANADIUM
SILICON
300
2k/lttOO/l~
U22
=
U33
U12
=
U13
U23
2a position occupancy 02 temperature factor U,. (A )
Extinction parameter ~ 10~~ Becker E Cop”,ens (ref. 24) Type I, Lorentzian profile
24/1400/4
o.oii
0.0115
n~1~ 0.71069
Ag Ica 0.55941
137.78 1.521
4.7240 21.88(.15)
Sc positic~r. O~CU~~flCY 02 temperaturt~factors (A ) U11
13.5
63,56 0.731
3.719 (.002) k.1722(.0057)
(1/4,0,1/2) 1.0
(1/k~O,1/2) 1.0
0.00452 (.00010
0.001574 (.000038)
0.00571 (.00009)
0.001815 (.000024)
0.0
0.0
(0,0,0) 1.0 0.00570 (.00011)
0.513(.028)
(0,0,0) 1.0 0.002164 (.000063)
0.0733(.0051)
Number of independent reflections used in the least squares refinements (sinO/ Agreement factors
A in 11)
166 (1.3)
155 (1.6)
R(F)
0.011
0.0091
WR(F)
0.026
0.0078
the anomalous dispersion corrections is sug— gested even though there is no theory which predicts it. For all these reasons, the only way to have an idea on the electron distribu— tion is to use the cubic approximation (see table 2 for the results of the refinements). We have attempted to determine the number of vacancies in,~g4erto check the assertion of Varma et al.’ ‘ who claim a vacancy con— centration of about 1% in V S±. The smallest number of vacancics (0.5%) introduced in the least squares refincne’it produced an increase
of the R factors. More recently, ~~yrate density measurements of Cox et al. on V3Si at room temperature show that the vacancy co~16 centration is less than 0.25%. Varina et al. also proposed that the vacancies could be or— dered. If this is the case, and there are any significant number of ordered vacancies, then the cubic space group Pm3n would not be valid for V~Si. DENSITY MAPS AND ERRORS 4 The total observed-electron density p(r) in real space is obtained by Fourier trans—
464
THE ELECTRON CHARGE DISTRIBUTION IN V
3Si
forming the observed structure fa*tors Fob ~ at each reciprocal lattice point G. The o~— -I.
calculated structure F is (G). The with total the ob— served structure factor compared served electron densitycalc is mo~senaitjve enough to give bonding information so this density is replaced by the valence density which is $he Fourie~ transform of t1~edifference p b (G)— F 8r (C), calculated~ffhthe where F (G) is form the ~g~ors struc~u!e for
Vol. 26, No. 8 V
Si
13.5 K
_____________
Si
vaI.njn~....___~~I
-
/2 0 0)
~
~.06
the core electrons of the atoms. fi~
V
in anThe equal population average on thedomain atomicapproximation displacements
(1/2.1/4.0)
is so small that it will have insignificant effect on the electron distribution maps even
descrip~iou in the true space ~s also group. used b~-~.Therefore w the m~r~ens(.tic the aubic
-~®
(001) ~1ane of V Si ~t 13.5 K is presented in tranØtion Fig. 1. To (21 alloa K). a T1~evalence direct comPa~s~y, density the In ~1~o
valence density of V Si Fig. at 300 KFigure ‘ in shows the same plane is given one and a half units ~n of the 2. face of the 2 cubic cell of the Al5 structure in order to illustrate
a~”9 (~/2
)
~
~
)/2 1/2 0)
the shape of the electron density around the V atom chain, while Fig. 1 only shows one half of the face. The c~ystallogrnphIcpoints are added for the recognition of the equivalent points in both figures. Calculation of the
deviat~o~ erroreA distribution mapshows of h~gher V an Si average at for 13.5the standard K bond of between 0.06 two , in butthe somewhat 0c~nsecutiveV atoms on a chain about 0.1 eA , ~~row 1) and at the central nuclear position It is evident from Fig. 1 and Fig. 2 that the major difference between the two maps is that the bond from the Si atom toward the V—V bond does not exi~.at 13.5 K (arrow 2). Above and below the martensitic transition, the inter— chain d—d interaction (arrow 3) is negligible and the intrachain bond (arrow 1) rema~nsthe most important interaction at all temperatures. The valence density map (Fig. 1) of V3Si at 13.5 K exhibits two significant deformations (arrow 4) and two other insignificant deforma— tions (arrow 5) around the V—V intrachain (arrow 1) and of course around the V atoms on the same chain. The valence density map (not shown here) on a plane perpendicular to the chain and passing throu~hthe areas indicated by the arrows 4 and 5 (the areas “5” are per— pendicular to the areas “4”) clearly shows the shape of a ring even though the deformations located by the arrows 5 are not significantly separated from the V—V bond (arrow 1). These deformations surround the intrachain bond (arrow 1) as two rings and they do not exist at 300 K (Fig. 2). Their origin is unknown but they could be related to the disappearance of the bond between the Si atom and the V—V bond on a chain (arrow 2). The fact that the rings are paired around an intrachain could also be indicative of the presence of super— conducting electrons. The valence electron density of a ring changes continuous1~’~e— tween the valence de~is~ties on 0.32 eA (arrow 4) and 0.20 eA (arrow 5). In view of their particular shape, combined with the disappearance of the bond between the Si atom and th~eV—V interaction on a chain at 13.5 K,
(i/2,3/4.o V
~I:\o
.00~
Si
(01,0)
•.cfrons/A’
,I,0)
Fig. 1: Valence ectectron density of V3Si at 13.5K in the (001) plane, below the superconduc— 3 ting and the martensitio phase transition tempe a~ures. Con~o~rs at 0.1 ea— 3below i.o e~ and 0.5 ea above 1.0 e~ Negative areasoh?tched. Reflections up to sinO/2’~O.65K’ are included in the Fourier transform. See Fig. 2. for the arrows catalogue.
these rings also imply very small displace— ments of the V atoms on a chain. CHARGE—TRANSFER According to the valence density maps (Fig. 1 and 2), ~ ~toms donate electrons to V atoms at 300 K ‘ as well as at 13.5 K. Fig. 1 of ref. 2 exhibits two plateaux: the first one indicating a charge—transfer of 1.8 electrons from a Si to three V, the second 2.4 electrons (with a typical standard deviation of 0,3 electrons for both plateaux). By con—
Vol. 26, No. 8
THE ELECTRON CHARGE DISTRIBUTION IN V
3S1
465
V3 Si Si
(0,0,0)
(1/2.
~
(0 1/2 0)
Suoio
‘,,,
~
I
Si (1,0.0)
/
,,,.
(11/20)
~
,~,,.
(0.1/2.0)
or”°
~cc~
*
r
*
°r’. s”.
.
i
(
~
°~‘
SlillO)
~*
~,\ ~\\
.
(1/2.1~O)..._..Ø
3,
a
4.724
~
.
(1.1/2.0)
A
= ~b.~I~O..(L) 5= 0.05 eA Fig. 2: Valence electron density of V 3Si at 301 in the (001) plane. Contours at 0.1 eA 0—3 0—3 0—3 below l.OeA and 0.2 eA above 1.0 eA 0—1 Reflections up to sino/A = 0.6 eA are included in the Rourier transform.
Arrow 1:
V—V bond, Arrow 2: bond from Si toward V—V bond, Arrow 3: area between two different perpendicular
chains, Arrow 4: maximum
density of the ring, Arrow 5: minimum density of the ring.
paring carefully every electron density plane in an eight of a V3Si unit cell at both tern— ~peratures,we arrive at the conclusion that the
mean value of the charge—transfer at 13.5 K would be shifted to approximately the second plateau. The fact that the b2 bends have pro—
THE ELECTRON CHARGE DISTRIBUTION IN V
466
3Si
bably been transformed in rings around bl V—V bonds implies a slightly more pronounced charge transfer at 13.5 K than at 300 K. But taking into account the standard deviation (=‘0.3 electrons), it is clear that the charge— transfers at 300 K and at 13.5 K should not be significantly different. Therefore the charge— transfer at 13.5 K has not be.en calculated ax— plicitely and is su~p~yed to be the sane at 13.5 K as at 300 K ‘ . RELATION TO OTHER PHYSICAL PROPERTIES a) extension of our work We have also done a measurement at 78 K but unfortunately the agreement factors are not good enough to present density maps. How— ever by studying the behavior of the ratio of the structure at two different temperatures parameters exp(c(U F IF 2thermal as a function of the ratio of the iso— t~pi~ 2—U 1))—where U is the isotropic mean square d~spl~cement a temperature t—, it is possible to confirm the main result presented here: i.e. the b2 bond(~~aPPears at the rnartensitic transi— tion . As a matter of fact, it is found out that the thermal influence of the Si atoms become smaller and smaller when the temperature is cooling down to 78 K. This can happen only if the strei~~b of the b2 bond diminishes with temperature because the effect of the ther— mal expansion on the positional parameters in the relation of the structure factor is negli— gible. b) connection with other ph~Mal properties Clogston and Jaccarino explained the correlation between nuclear magnetic resonance, the sup~nrconducting transition temperature T and the behavior of the susceptibility as a c function of the temperature for V X alloys with a model of a sharp peak in the de~sityof states curve at 0 K. They speculated that “such a peak in the density of states could be associated with the particular crystal structure of the V X corn— pounds whic~15~ndsto isolate the X—site prom each other” . But i-lie only way to isolate the X sites from each other Is to have no in— teraction between the Si atoms and the V atom chains (arrow ~ has performed resistivity Marchenko measurements on V Si samples between 17.1 and 1100 K. The resi~tivitybegins to saturate at 125 K and deviates considerably fron the Bloch—Grtlneisen relation. The relation be— tween our work and resistivity work is as follows: The onset of saturation on heating at 125 K may be associated with the beginning of the transition from nearly independently linear V chains (belo~ 125 K) to V chains coupled with the body centered ‘ell of Si (above 125 K). The martensitic transition probably occurs when the bond between the Si atoms and the V—V intra—
chain interaction has completely disaPPeared(5) Taub and Williamson and Milewits et al. also measured resistivity on V3Si single—crystals between 17 and 77 K. The difficulty in finding unique coefficients for temperature dependent terms of form Tm may be expained by the temper— ature dependence we have found in the electron density maps. Thus the bond breaking could also be related to the sign reversal of the first de— rivativ~11f1~e pressure dependence of the shear modulus and to the curvature measured a— bove the nartensi~fc8t~nsition temperature in the specific heat The comparison between the work of Schweiss at ~ on inelastic neutron scattering and ours implies the introduction of an important ionic force between the V and Si atoms. This ionic force seems to be almost constant below 300 K. This position is supported by the l~g~)charge—transfer we have found in V Si
CONCLUSION
In conclusion, we have found that the interaction between the Si atoms and the V chains (arrow 2) Is temperature dependent, and that the V chains have an independent linear character below the martensitic tran9ition. This could ~ success of simple models ‘ . We also remark that the “bonding transition” in V Si begins at about 125 K and ends at the mart~nsItic transition (21 K). The marten— sitic transformation is probably due to the disappearance of thu bond between the Si atoms and the V—V bord (arrow 2) and the appearance of two an’aotropic rings could (arrows 4 and 5) around each V—V bond which be related to the existence of superconducting electrons at 13.5 K. Acknowledgements: I would like to especially thank Dr. A. Manuel gave me Prof. the single—crystal used inwho this work, S. A. Werner of for V3Si his support and many helpful discussions, Prof. 3. Muller icr his constant support, Prof. E. F. Bertaut and Prof. E. Parth~ for their interest; Dr. R. 14. Waterst:at, Prof. H. Taub, Dr. E. P. Skelton, L. suggestions, R. Testardi, Dr. andD.Prof. B. DeFacio for theirDr. many Pautler and Dr. E. Stevens for technical assistance. The Swiss National Fund (request No. 820.360.75) which enabled me to spend one year in the laboratory of Prof. P. Coppens at the State University of New York at Buffalo and U.S. National Science Foundation support through Grant No. THY 76 08960 at the University of Missouri at Columbia are gratefully acknow— ledged.
REFERENCES 1.
Junod,
A., Staudenmann J.—L., Muller 3., and Spitzli P., J.
Low Temp. Phys. 5, 25 2.
Staudenmann J.-L.,
(1971).
Coppens P., and Muller 3., Solid State
Comm. 19, 29 (1976).
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Vol. 26, No. 8
THE ELECTRON CHARGE DISTRIBUTION IN V
3SI
3.
467
Staudenmann J.—L., “Densiti~s~lectroniques des alliages de structure A15 V3Si et Cr3Si et leur relation avec l.a supra— conductivitg.”
4.
Thesis 0~o. 1735, University of Geneva, 1976.
Staudenmann .7.—L., Solid State Comm. 23, 121 (1977).
5a. Taub H. and Williamson S. 3., Solid State Comm. 15, 181
(1974).
Sb. Milewits M., Williamson S.J. and Taub 11., Phys. Rev. 1313, 5199 (1976). 6.
Marchenko V. A., Soy. Phys. Solid State 15, 1261 (1973).
7.
Testardi L. R. and Bateman T. B., Phys. Rev. 154, 402 (1967).
8.
Surikov V. 3., Shtolz A. K., and Zagriavskii
V. L., Doklady
ARad. NAUK SSSR 215, 833 (1974). 9a. Knapp C. S., Bader S. 13., Culbert H~. N., Fradin F. Y., and IClippert 3. E., Phys. Rev. 1311, 4331 (1)75). 9b. Knapp G. B
,
Bader S. D., and Fisk Z., Phys. Rev. 1313, 3783
(1976). 10.
Clogston A. M., and Jaccarino, V., Phys. Rev. 121, 1357 (1961).
11.
Garcia P. F., Barsch C. R., and Testardi L. R., Phys. Rev. Lett.
27, 944 (1971).
12.
Batterman B. W., and Barrett C. S., Phys. Rev. 145, 296 (1966).
13.
Hess E., Z. fttr Xristallographie
14.
Helmholdt R. B. and Von A., Acta Crysta. A33, 38 (1977).
15.
Shirane G., and Axe J. D., Phys. Rev. B4, 2957 (1971).
16.
Varma C. M.~ Phillips 3. C., and Chui S. T., Phys. Rev. Lett.
142, ~35 (1975).
33, 1223 (1974). 17.
Cox D. (1977) private communication.
18.
Testardi L. R., Rev. Mod. Physics 47, 637 (1975).
19.
Schweiss B. P., Renker B., Scluieider E. and Reichardt W., In Superconductivity in d— and f—Band Metals, 2nd Rochester Conference, Editor D. M. Douglass, Plenum Press, N. Y. 1976.
20.
Mattheiss L. F., Phys. Rev. 1312, 2161 (1975).
21.
Weger M., and Goldberg 1.13., in Solid State Physics edited by
22.
H. Ebrenreich,
F. Seit~ and 13. Turnbull (Academic, New York.
1973), vol.
—
Labb~ 3.,
28
Goldberg L. B., 3. Phys. C. 8, 1159 (1975).
and Friddel
303 (1966).
3., 3. de Physique 27, 153 (1966); 27,
468
THE ELECTRON CHARGE DISTRIBUTION IN V
3Si
23.
Cohen R.
‘.,
Cody C. 13., Halloran 3.3., Phys. Rev. Lett. 19,
840 (1967). 24.
Becker P.3. a~~d Coppens P., Acta Cryst. A30, 129 (1974).
25.
International
Tables for X—ray Crystallography,
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Kynoch Press, Birmingham 1975. 26.
Pukamachi T., Technical report of the Institute for Solid State
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The University of Tokyci
ntai 1971. 27.
J.—L.
Staudenmann, to be published.
-
Series B No. 12,
Vol. 26, No. 8
Solid State Communications, Vol. 26, pp. 461—468. ®Pergamon Press Ltd. 1978. Printed in Great Britain
THE ELECTRON CHARGE DISTRIBUTION IN V
3S1*
J.—L. Staudenmann Department of Physics University of Missouri at Columbia Columbia, Missouri 65201
(Received on 8 November 1977, in revised form 21 February 1978, by E.F. Bertaut) The electrot~ charge distribution in a martensitically transforming single— crystal of V Si in the superconducting state has been obtained from accurate X—ray diffra~tionmeasurements. The most significant differences between the electron density maps at room temperature and below the superconducting transition are the disappearance of the bond between the Si atom and the V—V bond on a chain at the lower temperature and the appearance of two anisotropic rings around each V—V bond at 13.5 K. By comparing our results with various physical properties, we conclude that, on cooling, V Si begins to anticipate a martensitic transformation at about 130 K even though t~istransformation does not actually occur before ~2l K.
INTRODUCTION V Si is a prototype of the large family of biJry compounds exhibiting the A15—type structure. It has many physical properties which seen to be linked with the existe~~ of linear chains of V atoms, in particular with superconductivity CT 16.85 K for the stoi— chiometric compositiSn). In order to build physical models, it is important to know the real electron distribution within the crystal. A knowledge of the temperature dependence of the electron distribution is highly desirable for A15 alloys such as V Si, which have many strong temperature depeJent physical pro— perties. It is possible, with carefully measured X—ray diffraction intensities, to obtain directly the electron charge distribution. We have prç~~ji~ys1y applied this technique at 300 K to V Si’ ‘ and t~3t~non—superconducting MS ~ompound Cr Si We describe here the most 1jnport~ntresults of a study on v3si at 13.5K, below both the superconducting and martensitic transition temperatures, It is of interest to correlate our X—ray measurements on V Si with other physical pro— perties such as temper~u~y dependence of the electrical resistivity ‘ , the sound 8’9~ and the
at the same time and received the sane heat treatment (see table 2). The influence of the conical Al fiber on the intensity of the V Si reflections is very small and represents a~prox— imately 1% of the measured background. The spherical single—crystal measured here exhibits a martensitic transformation, so the composition is stoichiometric. Step scan data were col— lected in a Be dewq with Pd filtered Ag K~ra— diation (A = 0.559 A) on a Picker automated 4— circle diffractometer. 1289 reflections at 13.5 K referred to the cubic sp~c~ group Pm3n were measured (sin /A 1.59 A ). The
max temperature was measured on the copper block of the cryostat and the stabilization was better than 2 K at 13.5 K. REFINEMENTS Good agreement between our measurements of lattice parameters below the martensitic transformation and thti~luee published by (13) Batterman and Barrett and those of Hess was obtained (see table 1). From our lattice parameters at 13.5 K, the low temperature structure of V Si can be more complicated than tetragonal, pJhaps orthorhombic or even mono— clinic. Symoetrically equivalent reflections were averaged after correction for Lorents leading to anfactors internal consistency factor and polarizhtion and also for absorption analogous to the conventional R factor between symmetry equivalen~ 2yeflections of 2.7% (1.7% for the 300 K data ). The 300 K data was corrected for thermal diffuse scatte~f~5 effects (TDS) according to Helmholdt and Vos . Using the sou1~)velocitYconstants of Testardi and Bateman a very sma~J~ TDS contributi~)was found even for the (12 2 2) reflection Thus, such a correction was not made for the 13.5 K data. The extinction corrections used here are the same employed in ref. 2.
magnetic susceptibility . The X—ray measure— velocity~~~, the specif~0~eat~ ments can also be helpful in explaining the rea— son for the sign reversal of the first deriva— pressure dependence of the shear EXPERIMENTAL A V Si spherical single—crystal of 0.115 ~s radius glued on a thin conical aluminum fiber in order to have a good thermal contact. This single—crystal is not thc same as the one used for the 300 K measurement but it was groufld
*ThIs work was presented at the A.C.A. meeting at East Lansing in August, 1977 (A.C.A. abstracts 5, 82 (l~77).
461
462
THE ELECTRON CHARGE DISTRIBUTION IN V
3SI
Table 1:
Lattice
Vol. 26, No. 8
constants of V3Si as a function of the temperature.
Table 1 Temperature (K)
Radiation
Reflection(s) used in the measurement
Number of measurements and lea3t squares fit
Lattice constants (mean values of the least squares results) 0
300
Ag
xa
6 forms of 800 24 forms of 840
1
a
5
a ~ 4.7180 ± .0011 A spherical single— crystal of 0.023 cm diameter
=
4.7240 ±0005 A spherical single— crystal of 0.008 cm diameter 0
78
Ag Na
15
Cu
1 2 6 6 4
form of 800 forms of 844 forecas of 880 forms of 884 forms of 12 00
0
xa
600
a
=
4.7147 A
400
c
=
4.7250 A
C
/
a
432
a
=
4.7144 ± .0003 A
4~2
c
=
4.7271 ± .0005
C
/
a
0
14.2
Cu
xu
1.0024 Batterman & ~-.rrett 0 0
A
1.0027 Bess 1975 0
13.5
Ag K~
1 2 6 5 4
form of 800 forms of 844 forms of 880 forms of 844 forms of 12 00
After measuring some reflections in Nb Sn at 33 K and the (3 0 0) reflection as a fuJ— tion of the temperature below the martensitic trau!~tiontemperature (45 K), Shirane and Axe concluded that the space group for the low temperature phase of Nb Sn is P4 /manc. From the literature there are Jme indications that the low temperature phase cf V Si is the same as that of Nb Sn. We consideJd various models in attempti~g to determine the true structure of V Si below the martensitic trans— formation, i.e? the following tetragonal space groups P4 /mmc, P42mc, P42/m, P~+2,and the two orthorhoJic space groups Pnmun and Pmin2. Our results permit us to establish that the low temperature structure of V Si is probably not described by P42/mnc. In ~very case listed above, it was impossible to refine the thermal parameter of the Si atom in the anisotropic form even when the chosen space group provides this possibility. The allowed general positions for the V atoms also ±ntroducemany difficulties into the refinements and very seldom was a significant displacement from the corresponding cubic position. For instance the maximum dis— placement found in analyzed tetragonal space
3
a 4.7135 ± .0024 A b 4.7268 ± .0019 c 4.7163 ±.0017 A cos~ 0.0010 ± .0007 2b / (a+c) 1.0025 spherical si’igle— crystal of 0.023 cn~ diameter
A A
groups is J0.00042 ±0.000141 on the coordinate 0.25 of one of the V atoms. The corresponding maximum displacement for the two orthorhombic space groups is 0.00035 ±0.000141 on the same coordinate 0.25 for a V atom. We know that the agreement factors have to be better for a tetragonal space group than for the cubic approximation because of the cell dimensions (see table 1). Though we did not find that for the following reason. We began the refme— ments with the anomalous dispersion corrections for the No radiation (mist~~3) instead of those for the Ag radiation and the agree— ment factors were in favor of the tetragonal space groups in the tetragonal average. The neat step with the good corrections gave ex— actly the opposite conclusions, i.e. the cubic approximation provided a better refinement In the tetragonal average. Therefore the key—point of the problem mmPli~2yot only a study in a single domain sample , but also an experi— mental determination of the anomalous dispersion corrections as a fu-iction of the temperature. It should be noted th.~st it is probably the first tine that the temperature dependence of
THE ELECTRON CHARGE DISTRIBUTION IN V
Vol. 26, No. 8
3S1
Table 2
463
Crystallographic single—crystal data for V3Si at 300 K for one single—crystal, and at 13.5 K for a second single-crystal
in the cubic space group Pm3n.
The
standard deviations are given between parentheses.
Table 2 X-ray data temperature (°K) Heat treatment (hours/temp., °C/Arpressure, atm.) Sphere radius
R (cm)
X-ray radiation wavelength A
Ka1
(A)
linear absorption coef. 1i(cm’~) li* R
cubic lattice constant a (A) Scale factor VANADIUM
SILICON
300
2k/lttOO/l~
U22
=
U33
U12
=
U13
U23
2a position occupancy 02 temperature factor U,. (A )
Extinction parameter ~ 10~~ Becker E Cop”,ens (ref. 24) Type I, Lorentzian profile
24/1400/4
o.oii
0.0115
n~1~ 0.71069
Ag Ica 0.55941
137.78 1.521
4.7240 21.88(.15)
Sc positic~r. O~CU~~flCY 02 temperaturt~factors (A ) U11
13.5
63,56 0.731
3.719 (.002) k.1722(.0057)
(1/4,0,1/2) 1.0
(1/k~O,1/2) 1.0
0.00452 (.00010
0.001574 (.000038)
0.00571 (.00009)
0.001815 (.000024)
0.0
0.0
(0,0,0) 1.0 0.00570 (.00011)
0.513(.028)
(0,0,0) 1.0 0.002164 (.000063)
0.0733(.0051)
Number of independent reflections used in the least squares refinements (sinO/ Agreement factors
A in 11)
166 (1.3)
155 (1.6)
R(F)
0.011
0.0091
WR(F)
0.026
0.0078
the anomalous dispersion corrections is sug— gested even though there is no theory which predicts it. For all these reasons, the only way to have an idea on the electron distribu— tion is to use the cubic approximation (see table 2 for the results of the refinements). We have attempted to determine the number of vacancies in,~g4erto check the assertion of Varma et al.’ ‘ who claim a vacancy con— centration of about 1% in V S±. The smallest number of vacancics (0.5%) introduced in the least squares refincne’it produced an increase
of the R factors. More recently, ~~yrate density measurements of Cox et al. on V3Si at room temperature show that the vacancy co~16 centration is less than 0.25%. Varina et al. also proposed that the vacancies could be or— dered. If this is the case, and there are any significant number of ordered vacancies, then the cubic space group Pm3n would not be valid for V~Si. DENSITY MAPS AND ERRORS 4 The total observed-electron density p(r) in real space is obtained by Fourier trans—
464
THE ELECTRON CHARGE DISTRIBUTION IN V
3Si
forming the observed structure fa*tors Fob ~ at each reciprocal lattice point G. The o~— -I.
calculated structure F is (G). The with total the ob— served structure factor compared served electron densitycalc is mo~senaitjve enough to give bonding information so this density is replaced by the valence density which is $he Fourie~ transform of t1~edifference p b (G)— F 8r (C), calculated~ffhthe where F (G) is form the ~g~ors struc~u!e for
Vol. 26, No. 8 V
Si
13.5 K
_____________
Si
vaI.njn~....___~~I
-
/2 0 0)
~
~.06
the core electrons of the atoms. fi~
V
in anThe equal population average on thedomain atomicapproximation displacements
(1/2.1/4.0)
is so small that it will have insignificant effect on the electron distribution maps even
descrip~iou in the true space ~s also group. used b~-~.Therefore w the m~r~ens(.tic the aubic
-~®
(001) ~1ane of V Si ~t 13.5 K is presented in tranØtion Fig. 1. To (21 alloa K). a T1~evalence direct comPa~s~y, density the In ~1~o
valence density of V Si Fig. at 300 KFigure ‘ in shows the same plane is given one and a half units ~n of the 2. face of the 2 cubic cell of the Al5 structure in order to illustrate
a~”9 (~/2
)
~
~
)/2 1/2 0)
the shape of the electron density around the V atom chain, while Fig. 1 only shows one half of the face. The c~ystallogrnphIcpoints are added for the recognition of the equivalent points in both figures. Calculation of the
deviat~o~ erroreA distribution mapshows of h~gher V an Si average at for 13.5the standard K bond of between 0.06 two , in butthe somewhat 0c~nsecutiveV atoms on a chain about 0.1 eA , ~~row 1) and at the central nuclear position It is evident from Fig. 1 and Fig. 2 that the major difference between the two maps is that the bond from the Si atom toward the V—V bond does not exi~.at 13.5 K (arrow 2). Above and below the martensitic transition, the inter— chain d—d interaction (arrow 3) is negligible and the intrachain bond (arrow 1) rema~nsthe most important interaction at all temperatures. The valence density map (Fig. 1) of V3Si at 13.5 K exhibits two significant deformations (arrow 4) and two other insignificant deforma— tions (arrow 5) around the V—V intrachain (arrow 1) and of course around the V atoms on the same chain. The valence density map (not shown here) on a plane perpendicular to the chain and passing throu~hthe areas indicated by the arrows 4 and 5 (the areas “5” are per— pendicular to the areas “4”) clearly shows the shape of a ring even though the deformations located by the arrows 5 are not significantly separated from the V—V bond (arrow 1). These deformations surround the intrachain bond (arrow 1) as two rings and they do not exist at 300 K (Fig. 2). Their origin is unknown but they could be related to the disappearance of the bond between the Si atom and the V—V bond on a chain (arrow 2). The fact that the rings are paired around an intrachain could also be indicative of the presence of super— conducting electrons. The valence electron density of a ring changes continuous1~’~e— tween the valence de~is~ties on 0.32 eA (arrow 4) and 0.20 eA (arrow 5). In view of their particular shape, combined with the disappearance of the bond between the Si atom and th~eV—V interaction on a chain at 13.5 K,
(i/2,3/4.o V
~I:\o
.00~
Si
(01,0)
•.cfrons/A’
,I,0)
Fig. 1: Valence ectectron density of V3Si at 13.5K in the (001) plane, below the superconduc— 3 ting and the martensitio phase transition tempe a~ures. Con~o~rs at 0.1 ea— 3below i.o e~ and 0.5 ea above 1.0 e~ Negative areasoh?tched. Reflections up to sinO/2’~O.65K’ are included in the Fourier transform. See Fig. 2. for the arrows catalogue.
these rings also imply very small displace— ments of the V atoms on a chain. CHARGE—TRANSFER According to the valence density maps (Fig. 1 and 2), ~ ~toms donate electrons to V atoms at 300 K ‘ as well as at 13.5 K. Fig. 1 of ref. 2 exhibits two plateaux: the first one indicating a charge—transfer of 1.8 electrons from a Si to three V, the second 2.4 electrons (with a typical standard deviation of 0,3 electrons for both plateaux). By con—
Vol. 26, No. 8
THE ELECTRON CHARGE DISTRIBUTION IN V
3S1
465
V3 Si Si
(0,0,0)
(1/2.
~
(0 1/2 0)
Suoio
‘,,,
~
I
Si (1,0.0)
/
,,,.
(11/20)
~
,~,,.
(0.1/2.0)
or”°
~cc~
*
r
*
°r’. s”.
.
i
(
~
°~‘
SlillO)
~*
~,\ ~\\
.
(1/2.1~O)..._..Ø
3,
a
4.724
~
.
(1.1/2.0)
A
= ~b.~I~O..(L) 5= 0.05 eA Fig. 2: Valence electron density of V 3Si at 301 in the (001) plane. Contours at 0.1 eA 0—3 0—3 0—3 below l.OeA and 0.2 eA above 1.0 eA 0—1 Reflections up to sino/A = 0.6 eA are included in the Rourier transform.
Arrow 1:
V—V bond, Arrow 2: bond from Si toward V—V bond, Arrow 3: area between two different perpendicular
chains, Arrow 4: maximum
density of the ring, Arrow 5: minimum density of the ring.
paring carefully every electron density plane in an eight of a V3Si unit cell at both tern— ~peratures,we arrive at the conclusion that the
mean value of the charge—transfer at 13.5 K would be shifted to approximately the second plateau. The fact that the b2 bends have pro—
THE ELECTRON CHARGE DISTRIBUTION IN V
466
3Si
bably been transformed in rings around bl V—V bonds implies a slightly more pronounced charge transfer at 13.5 K than at 300 K. But taking into account the standard deviation (=‘0.3 electrons), it is clear that the charge— transfers at 300 K and at 13.5 K should not be significantly different. Therefore the charge— transfer at 13.5 K has not be.en calculated ax— plicitely and is su~p~yed to be the sane at 13.5 K as at 300 K ‘ . RELATION TO OTHER PHYSICAL PROPERTIES a) extension of our work We have also done a measurement at 78 K but unfortunately the agreement factors are not good enough to present density maps. How— ever by studying the behavior of the ratio of the structure at two different temperatures parameters exp(c(U F IF 2thermal as a function of the ratio of the iso— t~pi~ 2—U 1))—where U is the isotropic mean square d~spl~cement a temperature t—, it is possible to confirm the main result presented here: i.e. the b2 bond(~~aPPears at the rnartensitic transi— tion . As a matter of fact, it is found out that the thermal influence of the Si atoms become smaller and smaller when the temperature is cooling down to 78 K. This can happen only if the strei~~b of the b2 bond diminishes with temperature because the effect of the ther— mal expansion on the positional parameters in the relation of the structure factor is negli— gible. b) connection with other ph~Mal properties Clogston and Jaccarino explained the correlation between nuclear magnetic resonance, the sup~nrconducting transition temperature T and the behavior of the susceptibility as a c function of the temperature for V X alloys with a model of a sharp peak in the de~sityof states curve at 0 K. They speculated that “such a peak in the density of states could be associated with the particular crystal structure of the V X corn— pounds whic~15~ndsto isolate the X—site prom each other” . But i-lie only way to isolate the X sites from each other Is to have no in— teraction between the Si atoms and the V atom chains (arrow ~ has performed resistivity Marchenko measurements on V Si samples between 17.1 and 1100 K. The resi~tivitybegins to saturate at 125 K and deviates considerably fron the Bloch—Grtlneisen relation. The relation be— tween our work and resistivity work is as follows: The onset of saturation on heating at 125 K may be associated with the beginning of the transition from nearly independently linear V chains (belo~ 125 K) to V chains coupled with the body centered ‘ell of Si (above 125 K). The martensitic transition probably occurs when the bond between the Si atoms and the V—V intra—
chain interaction has completely disaPPeared(5) Taub and Williamson and Milewits et al. also measured resistivity on V3Si single—crystals between 17 and 77 K. The difficulty in finding unique coefficients for temperature dependent terms of form Tm may be expained by the temper— ature dependence we have found in the electron density maps. Thus the bond breaking could also be related to the sign reversal of the first de— rivativ~11f1~e pressure dependence of the shear modulus and to the curvature measured a— bove the nartensi~fc8t~nsition temperature in the specific heat The comparison between the work of Schweiss at ~ on inelastic neutron scattering and ours implies the introduction of an important ionic force between the V and Si atoms. This ionic force seems to be almost constant below 300 K. This position is supported by the l~g~)charge—transfer we have found in V Si
CONCLUSION
In conclusion, we have found that the interaction between the Si atoms and the V chains (arrow 2) Is temperature dependent, and that the V chains have an independent linear character below the martensitic tran9ition. This could ~ success of simple models ‘ . We also remark that the “bonding transition” in V Si begins at about 125 K and ends at the mart~nsItic transition (21 K). The marten— sitic transformation is probably due to the disappearance of thu bond between the Si atoms and the V—V bord (arrow 2) and the appearance of two an’aotropic rings could (arrows 4 and 5) around each V—V bond which be related to the existence of superconducting electrons at 13.5 K. Acknowledgements: I would like to especially thank Dr. A. Manuel gave me Prof. the single—crystal used inwho this work, S. A. Werner of for V3Si his support and many helpful discussions, Prof. 3. Muller icr his constant support, Prof. E. F. Bertaut and Prof. E. Parth~ for their interest; Dr. R. 14. Waterst:at, Prof. H. Taub, Dr. E. P. Skelton, L. suggestions, R. Testardi, Dr. andD.Prof. B. DeFacio for theirDr. many Pautler and Dr. E. Stevens for technical assistance. The Swiss National Fund (request No. 820.360.75) which enabled me to spend one year in the laboratory of Prof. P. Coppens at the State University of New York at Buffalo and U.S. National Science Foundation support through Grant No. THY 76 08960 at the University of Missouri at Columbia are gratefully acknow— ledged.
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THE ELECTRON CHARGE DISTRIBUTION IN V
3SI
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THE ELECTRON CHARGE DISTRIBUTION IN V
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Vol. 26, No. 8