Physical properties of α and γ arsenic

J. Phys.

Chew

Solids

Pergamon Press 1965. Vol. 26, pp. 69-74.

PHYSICAL

PROPERTIES

Printed in Great Britain.

OF o( AND y ARSENIC

J. B. TAYLOR Division of Applied Chemistry,

National Research Council of Canada, Ottawa and and R. D. HEYDING

S. L. BENNETT Department

of Chemistry, (Received

Queen’s University,

Kingston

27 July 1964)

Abstract-The unit cell dimensions and the electrical and magnetic properties of crystalline (LX) arsenic have been measured as a function of temperature. The resistivities at 293°K parallel and perpendicular to the major (trigonal) crystallographic axis are: p,, = 35.6+1.8.10-s

a-cm;

pI = 25~5+0~5~10-6

a-cm,

and the temperature coefficients are 4.5 -10-s and 4.0.10-s deg-l, respectively. susceptibilities of a single crystal specimen at 292°K were found to be: al xy = -21.4+0.7.10-6emu/gat. Xe = +44.4*0.8.10-semu/gat.;

The

magnetic

The signs and magnitudes of these values were confirmed by the determination of the magnetic anisotropy of three single crystals in a homogeneous field. The susceptibilities of several polycrystalline specimens are recorded and discussed. The hexagonal unit cell dimensions at 295.6”K are: a = 3.7598kO.0003

A;

c = 10.547 kO.002 A.

Between 295’ and 673°K there is little or no change in the unit cell parallel to the basal plane. The coefficient of expansion along the c axis is 47.2 -10-s deg-1. No evidence was found for a second order transformation in G(As at ca. 500°K as suggested by Klemm. Amorphous (y) arsenic is diamagnetic, the susceptibility at 298°K being - 22.6 kO.3 -10-s emu/g atom. The susceptibility is only slightly temperature dependent from 80” to 450°K.

tropy(x ,,-xl), which implies that the susceptibility with the field perpendicular to the major (trigonal) axis of the crystal is more positive than the susceptibility parallel to the major axis. The crystal was found to be essentially isotropic in the basal plane. In addition to their studies on resistivity and susceptibility, KLEMM et aZ.(334) measured the variation in heat capacity and lattice dimensions of polycrystalline a As with temperature. The important point at the moment is that small discontinuities were observed in all of these properties at ca. 500”K, indicative of a second order transformation in the crystal. To examine this transformation independently, we obtained X-ray diffraction patterns of a polycrystalline specimen at various temperatures, and prepared single crystals for electrical and magnetic studies. In the preparation of crystalline specimens,

1. INTRODUCTION

THE PUCKEREDdouble-layer structure of metallic CCAs is well known. The electrical resistivity of polycrystalline specimens of this modification have been reported by LITTLE(~) and the dependence on temperature by MCLENNAN et aZ.@) and by KLEMM. (334) Studies on the resistivity anisotropy of single crystals have been made by BRIDGMAN(~)and by HATTON.@) Polycrystalline specimens of a As have been found to be paramagnetic at low temperatures (ca. 90°K) but diamagnetic above room temperature.(3**97) The supposition can be made that the crystal is paramagnetic along at least one magnetic axis. No susceptibilities for single crystals have been reported, but in studying the de Haas-van Alphen effect in arsenic, BERLINCOURT@) observed a negative steady state aniso69

70

J.

B.

TAYLOR,

S. L.

BENNETT

amorphous y As was obtained as an intermediate. Magnetic susceptibilities of this modification were determined as a matter of course. 2. SPECIMEN PREPARATION All specimens were prepared from Cominco ‘69’ Research Grade Arsenic, containing the impurities Ca, Cu, Pb, Mg and S, each less than O-1 p.p.m., and Si, less than O-2 p.p.m.Thispolycrystalline material was heated in wucuoat 623°K to remove the oxide impurity formed during handling, then sublimed in the same tube at 650-700°K to reduce the carbon content.* Although the gradient along the tubes was varied over appreciable limits, the amorphous p and y forms did not condense in distinct regions as ST&-IR had described.(T) At the cold end of the tube (- 373°K) rods characteristic of the y modification were well defined. These rods were progressively less well developed towards the warmer regions of the tube. In some instances rods were still apparent in the warmest region, and in others diffraction patterns showed evidence of crystallization. For the preparation of single crystals the form of the deposit was of no consequence. For susceptibility studies, samples were selected from the deposit in the coolest region, i.e. where the deposit was amorphous to X-rays and obviously the y modification by Stohr’s definition. BRIDGMAB(@ firstdemonstrated the feasibility of growing arsenic crystals by directional freezing of a melt contained in heavy walled fused quartz tubing. Recent reports of arsenic crystal growth using the same technique have indicated the value of the method for purification.(s-1s) The growth tube was clear fused quartz tubing (i.d. 0.6 or 0.8 cm, o.d. I.2 cm, length 20 cm) having the lower end drawn to a fine capiiliary and sealed. Prior to use, the tube was treated for 20 min with 48 y0 hydrofluoric acid at room temperature, rinsed thoroughly with water and heated strongly to the softening point with a flame to ensure that the inner walls were smooth so that polynucleation, during crystal growth was minimized. After loading the arsenic into this tube, any oxide contaminant resulting from the handling operation was sublimed off at 570’K under vacuum and the tube finally sealed off at a pressure less than 10-5 torr. The tube was supported in a vertical resistance heated furnace maintained at 1173’K and held at this temperature for * We estimate the carbon content in the arsenic as received and handled to be less than 10 p.p.m.

and R. D. HEYDING

16 hr. After this period, the furnace temperature was maintained at 1173OK while the tube was lowered from the furnace at 0.1 in. per hour. This rate is considerably less than that used by Bridgman (30 cm/hr) but higher rates were found to give polycrystals. Modifications to the shape of the tapered end of the tube appeared to have no effects on the ease of obtaining large mono-crystals.

Crystals were cut on a tungsten wire saw (O*OlO in. wire) using alumina abrasive (600 mesh) in glycerine. Thin sections perpendicular to the hexagonal c axis were obtained by cleaving. Orientation was determined by reference to the strong basal cleavage plane and checked by back reflection Laue photographs. Contrary to previously published information(5), the normal growth direction was not observed in the 001 plane but at an angle to 20” 40’ i_ 1” (mean of determinations on five separate crystals) to this piane. It may be fortuitous that this is very close to tan-r a/c (19” 38’). The monocrystal usually obtained was 4.0 cm long after removal of the ‘tail’ and 1-O cm ‘top’. Along this length, change in orientation was barely detectable with the equipment available. Spectrographic analysis of the centre portions of the crystals indicated a significant increase in silicon content of up to 20 p.p.m. 3. CRYSTALLOGRAPHIC

EXAMINATION

Patterns of GCAs above room temperature were obtained in a 19 cm Unican camera, calibrated with respect to specimen temperature by CALVERT.@~) Camera temperatures were recorded continuously during exposure. Ni filtered Cu radiation (K,, = 1*54050 A) was used throughout. The sample was ground from polycrystalline material as received, and mounted in a 0.5 mm silica capillary which was evacuated at 600°K and sealed, leaving negligible void volume. The specimen was sealed in turn in an evacuated vycor tube containing a small quantity of arsenic to equalize the pressure on the capillary walls, annealed for some weeks at lOOO’K, and slowly cooled to room temperature. The arsenic diffraction pattern contains no high order hk*O or 00*1 reflections, consequently Nelson-Riley plots cannot be made directly. Precise values of a and c (hexagonal cell) were obtained by successive cyclic approximations using selected reflections for the NelsonRiley plots.

The results are recorded in Table 1. Between 300” and 700°K the coefficient of linear expansion in the basal plane of the crystal is essentially zero.

PHYSICAL

Table

1.

Hexagonal

PROPERTIES

OF

a AND

and rhombohedral unit cell dimensions of cc arsenic function of temperature (A7, Did, R3m) Hexagonal cell (A)

Order of experiment 1,9 3 6 8 4 7 5 2

Temp. OK(l)

a* ( * 0.0003)

295.6 kO.5 382+1 482+2 501 k2 523k2 543k2 570*3 677k2

3.7598 3.7599 3.7599 3.7601 3.7598 3.7599 3.7599 3.7595

cn ( f 0.002) 10.547 10.587 10,635 10.647 10.658 10.669 10.682 10.738

(1) Error limits combine uncertainty in camera temperature temperature during exposure.

The coefficient of expansion along the major axis, i.e. perpendicular to the double layers of arsenic atoms, is 47*2.10-s deg-1. The coefficient of volume expansion is, of course, also 47*2*10-s deg-1. 4. ELECTRICAL

RESISTMTY

measurement were approximately 5 mm x 6 mm x 1 mm and were cut in two orientations having the longest axis either parallel or perpendicular to the crystallographic c-axis. In the case of samples cut parallel to the c-axis it was not practicable to use slices less than 1 mm thickness because of the strong 001 cleavage. Crystals

71

y ARSENIC

for

Cross-sectional areas were obtained by one micrometer measurement and one weighing. A four contact measurement technique was used with the two current carriers in the form of 1 mm thick silver plates cemented to the ends of the sample with Waldman No. 3012 Conductive Silver-Epoxy cement. Satisfactory bonding of these electrodes was only achieved after preparing the crystals by thermal etching 600°K for 30 min under vacuum, then applying the electrode with a thin cement coating and curing at 550°K for one hour in a purified argon gas stream. This cement was not capable of withstanding temperatures in excess of 500°K indefinitely. The crystal holder was made from a flat ceramic disc of one inch diameter into which were fastened the potential electrodes of electrolytically pointed inconel wire. The self-spring action of these wires also served to hold the arsenic crystal against the ceramic base. Chromel-alumel and copper-constantan thermocouples were located on the base close to the crystal and the whole assembly was suspended on fine wires in a sealed glass tube under 10 cm of argon pressure. Correction for mis-

Rhombohedral ar ( * 0*0004) 4.1318 4.1432 4.1568 4.1603 4.1633 4.1665 4.1702 4.1860

as a

cell (A) a( * 30”) 54” 8’ 53O 58’ 53O 47’ 53O 44’ 53” 40’ 53O 38’ 53” 36’ 53O 22’

calibration curves and variation in

alignment of the potential vector relative to the current vector were made after the measurement by observing the slight depressions left by the potential probes on the surface of the crystal. Normal potential probe separation was between 2 and 2.25 mm. Electrical measurements were made using a Keithley Model 503 milliohmeter which is a combined 40 c/s square wave generator and synchronous a.c. voltmeter. The output from the detector stage was fed to a Leeds Northrup 8687 potentiometer. Modification to the equipment enabled continuous plotting to be achieved. The furnace temperature was controlled by a BarberColeman WUP7 Universal Programmer and the output from the milliohmeter was applied to the Y-axis of a Mosley 2D2 series X-Y recorder. The X-axis of the recorder was fed from the sample thermocouple.

The room temperature resistivities recorded in Table 2 were computed from measurements on three crystal sections parallel to the major axis, and four crystal sections perpendicular to the major axis. All seven sections were obtained from the same single crystal. Following the determination, spectroscopic analysis was obtained on that part of one of the crystal sections lying between the two potential probes. The results in p.p.m. were as follows: Mg, 0.3; Si, 7; Fe, 2; Bi, 2; Cu, 7; Ag, 0.2; Ca, 0.2. Seven sections cut parallel to the major axis and one perpendicular to the major axis from three different crystals were examined in the range 293-553°K with increasing temperature in ten resistances of five of these degree increments; samples were also measured as the temperature was decreased. One sample of each orientation was

72

J.

B.

TAYLOR,

S. L. BENNETT

examined by the continuous plotting procedure overthe same temperature interval at a linear rate of increase of 60°/hr. The temperature coefficients are given in Table 2. The recorded continuous plots were linear and exhibited no discontinuities in the temperature range studied. 5. MAGNETIC

and R. D. HEYDING

+ 0.7 * 10-s emu at 292”K, respectively. Although the absolute values of the term (x ,,-xl) are of the same order of magnitude as those observed by BERLINCOURT@) (cf. Table 3), the sign is positive rather than negative. To confirm the sign of the term, the magnetic anisotropy of three crystal sections from two parent crystals were determined in homogeneous

SUSCEPTIBILITY

Experimental method Susceptibilities of several polycrystalline samples and one single crystal specimen were measured by the Curie method. The magnet and its calibration have been described previously.(l4) 5.1

Apparent changes in weight were determined in a closed system under nitrogen at 380 torr with an Ainsworth semimicro vacuum balance, modified to operate as a manually controlled null-point instrument. Specimen temperatures were controlled to within I” in the range SO”-550°K. Measurements were made at five field gradients (8Hz/&) from 30.2 to 48.8 kG2 cm-l Powdered specimens were held in a quartz bucket of one gram capacity. The crystal was supported by a quartz fibre cradle.

5.2 Amorphous y As Amorphous y As is diamagnetic (Fig. l), with an atomic susceptibility of -22.6 + 0.3 - 10-s emu at 298°K. The data are in good agreement with the values reported by STOHR.(~) 5.3 Single crystal cc As The single crystal was 8 mm dia. and 4 mm long. Spectroscopic analysis of the parent crystal close to this section indicated these impurities in p.p.m. : Si, 20; Cu, 2; Fe, 10. Susceptibilities at infinite field strength parallel and perpendicular to the major axis are shown in Fig. 1. The crystal is paramagnetic along the trigonal axis and diamagnetic in the basal plane, with atomic susceptibilities of + 44.4 k 0.8 - 10-s emu, and - 21.4

IC)-

el-

6

a

,” 4 ; al 2 c 2 ‘*” 0 -2

F

-4

I 100

I

200

1

300

TEMPERATURE

400 (OK)

FIG. 1. Variation in mass susceptibility of amorphous y As and of single crystal and polycrystalline ccAs with temperature. A Single crystal, field parallel to trigonal axis B Polycrystalline, annealed at 1100°K C Curve: Calculated polycrystalline susceptibility Points: Polycrystalline, as received Crosses: KLEMM, SPITZER and NIERMANN@) D Amorphous y As annealed at IOOO’K E Crushed single crystal annealed at IOOO’K F Single crystal, field perpendicular to trigonal axis G Amorphous y As

Table 2. Resistivity of u As

Crystal orientation

Resistivity (Q-cm) (293’K)

Temp.

coefficient (deg-1) (293-373’K)

Parallel to major axis

35~6+l~8.10-6(1~

45 + 6. IO-4(3)

Perpendicular

25.5 kO.5

40

to major axis

(1) Mean of three crystal sections (2) Mean of four crystal sections

I

500

- lo-s(s)

. IO-4(4)

(3) Mean of seven crystal sections t4) One crystal section only

PHYSICAL

PROPERTIES

Table 3. Magnetic

-

TW) 77 300

OF

anisotropy

a AND

of u As (x1, -xl)*

BERLINCOURT@) Crystal 2 Crystal 1

73

y ARSENIC

106, emu/g

Curie method

-1.2

-0.8

+1.32

-0.82

-0.54

$0.86

Torsion method

+0.84*0.03 __-

=_.

fields by the static torsion method. All three crystals aligned themselves in the field with the trigonal axis parallel to the field. The crystal for which the data is given in Table 3 was a thin oval section cleaved from the parent crystal, 1.5 mm thick along the trigonal axis, and with major and minor axes of 8 mm and 6 mm in the basal plane. The other two crystals, considerably larger and therefore subject to greater shape factor errors, exhibited values of (x,, -xl) some 10 per cent greater than the small specimen. 5.4 Polycrystalline CLAs The susceptibility of a powdered polycrystalline sample of As, randomly oriented in the field, is given by(ls)

(1) Aside from the effect of impurities, the apparent susceptibility of polycrystalline specimens will be subject to two additional uncertainties. The small particles may assume preferred orientation in the specimen holder as a result of their shape, defined largely by cleavage planes; or the crystals may be badly damaged by grinding.* The former effect may result in susceptibilities either greater or less than the true susceptibility. The latter effect will lead only to lower values, i.e. to susceptibilities approaching the diamagnetic susceptibility of amorphous arsenic. The mass susceptibilities of the single crystal and of several polycrystalline samples are compared in Fig. 1. Curves A and F represent the principal susceptibilities, and curve C the susceptibility of polycrystalline As, calculated via Equation * Several authors have reported damage to crystals of arsenic on grinding. We have observed repeatedly that powder diffraction patterns are ill defined, particularly from planes parallel or nearly parallel to the basal plane, unless the powders are annealed in situ.

(1). The experimental points were obtained for a specimen consisting of small polycrystals selected from the arsenic as received, with no further grinding or annealing. By virtue of minimal handling, this was the purest and least damaged specimen examined. Agreement with the calculated curve is good. Agreement with the data of Klemm et al.@) is also good, although the history and purity of their specimens were not reported. A sample of polycrystalline As, crushed and annealed for a number of weeks at llOO”K, exhibited susceptibilities greater than the calculated values (curve B), while a single crystal, crushed and annealed at 1000°K for 3 days, gave values less than those calculated (curve E). Amorphous y As (represented by curve G), converted to c( As by annealing for 36 hr at lOOO”K, also exhibited susceptibilities below the calculated values (curve D). It is evident that a powdered polycrystalline specimen of arsenic may exhibit any mass susceptibility between the magnetic anisotropic limits, depending on its history and the manner in which it is handled. It may also be that the rate of transformation of y As to u As is much less than had been assumed, and that samples annealed sufficiently to produce satisfactory diffraction patterns may still contain appreciable amounts of the amorphous modifications. 6. THE

TRANSFORMATION

IN u, AS

No evidence was found for a second order transformation at 500°K in tc As. Experimental points in the 470-550°C range for magnetic susceptibilities of the single crystal and for unit cell dimensions were obtained in random order and are sufficiently numerous to define a smooth and continuous variation with temperature. None of the resistivity curves for eight specimens prepared from four separate single crystals showed

74

J.

B.

TAYLOR,

S. L. BENNETT

any evidence of a transformation from room temperature to 550”K, and for two of these the data were recorded continuously. We do not believe that the Knicken in the various curves observed by Klemm et al. can be attributed to a transformation in CC As, but we have no satisfactory alternative explanation to offer. The magnitude of the disturbances in heat capacity and in electrical and magnetic properties is not much greater than the experimental uncertainty as represented by the size of the points on the diagrams. Nevertheless a disturbance in four distinct properties was observed at essentially the same temperature, and it is unlikely that all can be dismissed as fortuitous. It may be significant that the rate of transformation of t63 and y As to crystalline arsenic becomes appreciable at about 520”K.(7) Acknowledgements-We are indebted to Mr. G. J. G. DESPAULT for valuable practical assistance, and Drs. L. D. CALVERT and C. M. PLEATSfor assistance with diffraction patterns and susceptibilities respectively. The work at Queen’s was supported by Research Grants from The Consolidated Mining and Smelting Co. Ltd., and from the National Research Council, for which we are most grateful.

and R. D. HEYDING

REFERENCES 1. LITTLE N. C., Phys. Rev. 28, 418 (1926). 2. MCLENNAN J. C., NI~EN C. D. and WILHELM J. D., Phil. Mug. 6, 666 (1928). 3. KLEMM W., SPITZER H. and NIERMANNH., Angew. Chen. 72, 985 (1960). 4. KLEMM W. and. NIERMANN H., Angew. Ckem. (International Edition) 2. 523 (1963). 5. BR~GMAN P. W., Proc: Amer. ‘Acad. Sci. 68, 39 (1932/33). 6. HATTON J., Phys. Rev., 100, 681 (1955). 7. ST~~HRH., Z. anorg. Chem. 242, 138 (1939). 8. BERLINCOURTT. G., Phys. Rev. 99, 1716 (1955). 9. WEISBERGL. R., ROSI F. D. and HERKART P. G., Properties of Elemental and Compound Semiconductors (Editor: Gates H. C.), Interscience N.Y. (1960). 10. R.C.A. Rep. PB 161541 (1959). 11. BLUM S. E., Compound Semiconductors (Editors: Willardson R. K. and Goering H. L.) Vol. I, Reinhold, N.Y. (1962). 12. WEISBERGL. R. and CELMER P. R., J. Electrochem. Sot. 110, 56 (1963). 13. CALVERT L. D., Division of Applied Chemistry, National Research Council of Canada. Unpublished data. 14. HEYDINC R. D., TAYLOR J. B. and HAIR M. L., Rev. Sci. Instrum. 32, 161 (1961). 15. WOOSTER W. A., Experimental Crystal Physics, Oxford (1957). 16. BATESL. F., Modern Magnetism, Cambridge (1961).