7
Phase Dtagrmn Evaluations: Section H The Bi-Se (Bismuth-Selenium) System H. Okamoto Asahi University Equilibrinm Diagram The definition of a "phase" in the Bi-Se system is somewhat vague. Bi2Se 3 is the most dominant phase in this system in the ordinary sense. On the Se-Rich side, Bi2Se 3 forms a simple en- tectic with (Se) (Fig. 1). On the other hand, many compounds have been reported on the Bi-rich side of Bi2Se 3. There is no doubt that these are stable compounds prepared at certain com- positions, but it has not been clearly demonstrated whether or not these compounds are phases. For example, Bi6Se 5 and BisSe 7 (see Fig. 1) are experimentally observed "phases." However, it has not been clarified ifa specimen with a compo- sition between these two "phases" would develop into a two- phase state, i.e., Bi6Se 5 + BisSe q, in the equilibrium condition. It is possible that a new, more complex compound is formed after very long annealing. It is also possible that the specimen becomes "single phase," possibly with short-range fluctua- tions in composition. At any rate, there has been no report on the existence of a two-phase field between the two "phases." As discussed below, a compound with any concentration can be configured in the composition range 0 to 60 at.% Se by stacking layers ofBi 2 and Bi2Se 3. Some compounds with spe- cific configurations of layers appear to form more readily than others. To constitute a compact unit cell, the Bi2-to-Bi2Se3 ra- tio must be simple (see "Crystal Structure" section). However, it appears that there is no driving force to separate a Bi-Se alloy (0 to 60 at.% Se) into two phases when the ratio is not simple. Because these stable compounds do not constitute phases in the ordinary sense, i.e., the phase boundaries are not well defined, they are called stacking variants in this evalu- ation. Liquidus. The Bi-Se liquidus data reported by [13Par], [19Tom], [60Abr], [66Oha], [75Gat], [76Bro], and [86She] are shown in Fig. 1. The data points of [60Abr], [75Gat], and [86She] were read from very small diagrams and may not be accurate. The liquidus boundaries for 0 to 60 at.% Se may rep- resent many peritectic reactions. For accurate determination of the liquidus, the configuration of stacking variants must be clarified. (Bi) Terminal Solid Solution. The melting point of Bi is 271.442 ~ [Melt]. No solubility of Se in (Bi) was detected by lattice parameter measurements [30Par]. However, some (not well defined) solubility was indicated by electrical resistivity (-1 at.%) [36Tho], magnetic susceptibility [34Goe], and Hall coefficient (<1 at.%) [55Iva] data. Bi-Rieh Euteetie Reaction. The Bi-dch eutectic composition is essentially 0 at.% Se [04Pel, 13Par, 19Tom]. Therefore, the eutectic temperature must be close to the melting point of Bi. Table 1 Bi-Se Crystal Structure Data Composition, Pearson Space Strukturbericht Phase at.% Se symbol group designation Prototype Reference (txBi) ............................................ 0 BiTSe3 ........................................... 30 Bi2Se............................................ 33.3 BisSe3(a)...................................... 37.5 Bi3Se2 ........................................... 40 Bi,tSe3 ........................................... 42.9 BitSe5 ........................................... 45.5 BisSe7 ........................................... 46.7 BiSe .............................................. 50 BisSe9 ........................................... 52.9 BitSe7 ........................................... 53.8 Bi,Ses........................................... 55.6 Bi3Se,4 ........................................... 57.1 Bi2Se3 ........................................... 60 (Se)............................................... IO0 Metastable phases BiSe(b) ........................................ 59 Bi2Se3HIa ..................................... 60 High pressurephases Bi2Se3H (c) ................................... 60 Bi2Se3HI ....................................... 60 BiSe2............................................ 66.7 (a) Laitakarite. (b) Thinfilm. (c) Bismuthite. hR2 /~_-m A7 if.As [Kingl] hR20 R...3m . . . . . . [70lma] hP9 P3ml . . . . . . [60Abr] hP48 P3ml . . . . . . [59Vor] hP30 P3m1 . . . . . . [86She] hR7 R_3m . . . . . . [65Sta] hP33 P3ml . . . . . . [67Sta3] hP45 P3ra 1 . . . . . . [67Sta3] hPl 2 P3_m 1 . . . . . . [67Sta3] hRl7 R_3m . . . . . . [67Sta3] hP39 P3_ml . . . . . . [86She] hP27 P3_ml . . . . . . [701ma] hP42 P3ml . . . . . . [54Semi hR5 R3m 6"33 Bi2Te 3 [51Don] hP3 P3121 A8 ~Se [Kingl] cF8 Fm'3ra B1 NaCI [54Sem] c** . . . . . . . . . [73Atal] oP20 Pnma D58 Sb2S 3 [64Ver] tP40 P42/na~ 1959 Zn3P 2 [73Atal] . . . . . . . . . . . . [65Sil] Journal of Phase Equilibria Vol. 15 No. 2 1994 195

The Bi-Se (Bismuth-Selenium) System

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hR2 /~_-m A7 if.As [Kingl] oP20 Pnma D58 Sb2S3 [64Ver] P42/na~ 1959 Zn3P2 [73Atal] . . . . . . . . . . . . [65Sil] H. Okamoto Asahi University R_3m ...... hR20 R...3m ...... Journal of Phase Equilibria Vol. 15 No. 2 1994 195 cF8 Fm'3ra Phase Dtagrmn Evaluations: Section H tP40

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Page 1: The Bi-Se (Bismuth-Selenium) System

P h a s e D t a g r m n E v a l u a t i o n s : S e c t i o n H

The Bi-Se (Bismuth-Selenium) System H. Okamoto

Asah i Universi ty

Equilibrinm Diagram

The definition of a "phase" in the Bi-Se system is somewhat vague. Bi2Se 3 is the most dominant phase in this system in the ordinary sense. On the Se-Rich side, Bi2Se 3 forms a simple en- tectic with (Se) (Fig. 1). On the other hand, many compounds have been reported on the Bi-rich side of Bi2Se 3. There is no doubt that these are stable compounds prepared at certain com- positions, but it has not been clearly demonstrated whether or not these compounds are phases. For example, Bi6Se 5 and BisSe 7 (see Fig. 1) are experimentally observed "phases." However, it has not been clarified i fa specimen with a compo- sition between these two "phases" would develop into a two- phase state, i.e., Bi6Se 5 + BisSe q, in the equilibrium condition. It is possible that a new, more complex compound is formed after very long annealing. It is also possible that the specimen becomes "single phase," possibly with short-range fluctua- tions in composition. At any rate, there has been no report on the existence of a two-phase field between the two "phases." As discussed below, a compound with any concentration can be configured in the composition range 0 to 60 at.% Se by stacking layers ofBi 2 and Bi2Se 3. Some compounds with spe- cific configurations of layers appear to form more readily than others. To constitute a compact unit cell, the Bi2-to-Bi2Se 3 ra- tio must be simple (see "Crystal Structure" section). However,

it appears that there is no driving force to separate a Bi-Se alloy (0 to 60 at.% Se) into two phases when the ratio is not simple. Because these stable compounds do not constitute phases in the ordinary sense, i.e., the phase boundaries are not well defined, they are called stacking variants in this evalu- ation.

Liquidus. The Bi-Se liquidus data reported by [13Par], [19Tom], [60Abr], [66Oha], [75Gat], [76Bro], and [86She] are shown in Fig. 1. The data points of [60Abr], [75Gat], and [86She] were read from very small diagrams and may not be accurate. The liquidus boundaries for 0 to 60 at.% Se may rep- resent many peritectic reactions. For accurate determination of the liquidus, the configuration of stacking variants must be clarified.

(Bi) Terminal Solid Solution. The melting point o f Bi is 271.442 ~ [Melt]. No solubility of Se in (Bi) was detected by lattice parameter measurements [30Par]. However, some (not well defined) solubility was indicated by electrical resistivity (-1 at.%) [36Tho], magnetic susceptibility [34Goe], and Hall coefficient (<1 at.%) [55Iva] data.

Bi-Rieh Euteetie Reaction. The Bi-dch eutectic composition is essentially 0 at.% Se [04Pel, 13Par, 19Tom]. Therefore, the eutectic temperature must be close to the melting point o f Bi.

Table 1 Bi-Se Crystal Structure Data

Composition, Pearson Space Strukturbericht Phase at.% Se symbol g r o u p d e s i g n a t i o n P r o t o t y p e Reference

(txBi) ............................................ 0 BiTSe3 ........................................... 30 Bi2Se ............................................ 33.3 BisSe3 (a) ...................................... 37.5 Bi3Se2 ........................................... 40 Bi,tSe3 ........................................... 42.9 BitSe5 ........................................... 45.5 BisSe7 ........................................... 46.7 BiSe .............................................. 50 BisSe9 ........................................... 52.9 BitSe7 ........................................... 53.8 Bi,Ses ........................................... 55.6 Bi3Se,4 ........................................... 57.1 Bi2Se3 ........................................... 60 (Se) ............................................... IO0

Metastable phases

BiSe(b) ........................................ 59 Bi2Se3HIa ..................................... 60

High pressure phases

Bi2Se3H (c) ................................... 60 Bi2Se3HI ....................................... 60 BiSe2 ............................................ 66.7

(a) Laitakarite. (b) Thin film. (c) Bismuthite.

hR2 /~_-m A7 if.As [Kingl] h R 2 0 R . . . 3 m . . . . . . [70lma] hP9 P3ml . . . . . . [60Abr] hP48 P3ml . . . . . . [59Vor] hP30 P3m 1 . . . . . . [86She] hR7 R _ 3 m . . . . . . [65Sta] hP33 P3ml . . . . . . [67Sta3] hP45 P3ra 1 . . . . . . [67Sta3] hPl 2 P3_m 1 . . . . . . [67Sta3] hRl7 R_3m . . . . . . [67Sta3] hP39 P 3 _ m l . . . . . . [86She] hP27 P 3 _ m l . . . . . . [701ma] hP42 P 3 m l . . . . . . [54Semi hR5 R3m 6"33 Bi2Te 3 [51Don] hP3 P3121 A8 ~Se [Kingl]

c F 8 Fm'3ra B 1 NaCI [54Sem] c** . . . . . . . . . [73Atal]

oP20 Pnma D58 Sb2S 3 [64Ver] t P 4 0 P42/na~ 1959 Zn3P 2 [73Atal ]

. . . . . . . . . . . . [65Sil]

Journal of Phase Equilibria Vol. 15 No. 2 1994 195

Page 2: The Bi-Se (Bismuth-Selenium) System

S e c t i o n 111: P h a s e D i a g r a m E v a l u a t i o n s

L)

c~

i

800 -

700 d

600-

500

400

300.

200

t00-+,-,- o

B1

�9 ~3 P a r x 19 T o m

a 60 Abr o 6 6 Oha o 75 G a t + 76 B r o v 8 6 S h e

Weight Percent Selen*um 20 30 40

,r,

7 *C a

t II

i i I1~1

50 60

i i i i

~o 20 30 40 50 60 70 go

A t o m i c P e r c e n t S e l e n i u m

70 60

X •

• X

gO

gO I00

i

\Lz L t

i

100

S e

Fig. 1

800 -

700

500-

o

500-

~ 4 0 0 2

&, E--

3oo- 2 r r c _ I ~

zoo I ', ,~

100 . . . . . . . . , . : . . . . .

0 I0

B1

Atomle Percent Selemum 50 60 70 BO 10 20 30 40 90

~ . J . . . . l , t . , . i . . . . . I . . . . . . . I . [ . . . . . ) " 'E . . . . . . ' r , [ . . . . . . . r l ~ . . . . . . i . . . . . . . L ' ' l . . . . . . .

/

7os*c L1 /

r /

~221~

, L 2

i

I00

I

i

20 30

~21"C

(Se)~ . i . i . . . . . . . . i . ~ q . . . . .

40 50 60 7~ ~- 8~0 90 ]00

Weight P e r c e n t Selenlum Se

Assessed Bi-Se phase diagram.

BizSe3. [ 1859Lit] probably found the correct molecular for- mula, according to the weight percent configuration given in the literature ("BiSe3" in [1859Lit] seems to be a misprint of Bi2Se3). The melting point of Bi2Se 3 was reported to be 710 + 5 [62Yar], 706 [94Pel], 704 [66Oha], 700 + 5 [63Kul], 700

[63Kuz], or 688 ~ [19Tom]. It is shown at 705 ~ in Fig. 1 based on the f'trst five reports. The composition at the congru- em melting point is 59.98 + 0.02 at% Se [59Off], which is within experimental uncertainty of the ideal 60 at.%. Interlay- ering of pure Bi with Bi2Se 3 can give rise to a variety of stack-

196 Journal of Phase Equilibria Vol. 15 No. 2 1994

Page 3: The Bi-Se (Bismuth-Selenium) System

P h a s e D i a g r a m E v a l u a t i o n s : S e c t i o n H

Table 2 Bi-Se Lattice Parameter Data

Composition, Lattice parameters, nm Phase at.% Se a b c Comment Reference

c ~ B i . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0

Bi7Se3 ........................................... 30 Bi2Se ............................................. 33.3 Bi5Se3 ........................................... 37.5 Bi3Se2 ........................................... 40 Bi,Se3 ........................................... 42.9

Bi6Se5 ........................................... 45.5

BiaSe7 ........................................... 46.7 BiSe .............................................. 50

BiaSe9 ........................................... 52.9

Bi6Se7 ........................................... 53.8 Bi3Se4 ........................................... 57.1 Bi2Se3 ........................................... 60

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 0 0

Metastable phases

BiSe .............................................. 50

Bi2Se3IVa ...................................... 60

High-pre~sure phases

Bi2Se3lll ........................................ 60

Bi2Se3IV ....................................... 60

0.47460 ... (t = 57.23 ~ [Kingl] 0 .4 43 . . . i i . 6 4 c ~ m d [7OIm~l

. . . . . . . . . [60Abr] 0.423 ... 3.99 Sul~ll? [59Vot] 0.4256 ... 5.872 ... [86She] 0.427 ... 3.99 ... [65Sta] 0.427 ... 4.00 ... [68Sta] 0.422 ... 6.26 ... [67Stz3] 0.4246 ... 6.32 ... [86She] 0.422 ... 8.565 ... [67Sta2] 0.418 ... 2.28 ... [64Sta] 0.418 ... 2.29 ... [65Sta] 0.4236 ... 2.306 ... [86She] 0.416 ... 9.71 ... [67Sta3] 0.4222 ... 9.71 ... [86She] 0.4189 ... 7.43 [86She] 0.423 ... 4.96 Half'~li? [54Sem] 0.415 ... 2.863 ... [53Sch] 0.4148 ... 2.896 ... [54Sr 0.415 ... 2.90 ... [55Sem] 0.4138 ... 2.864 ... [60Wie] 0.415 ... 2.88 ... [62God] 0.4134 ... 2.860 ... [62Yar] 0.4140 ... 2.861 ... [63Kuz] 0.4135 ... 2.864 ... [63Lan] 0.4143 ... 2.8636 ... [63Nak] 0.415 ... 2.855 ... [64(3ol3] 0.413 ... 2.87 ... [65Sta] 0.414 ... 2.86 ... [67Sta3] 0.418 ... 2.28 Misprint? [67Stal ] 0.4115 ... 2.853 ... [68Bon] 0.4151 ... 2.825 ... 175Bcel 0.4161 ... 2.863 ... [86She] 0.43655 ... 0.49576 ... [Kingl]

0.599 . . . . . . . . . [54Sem] 0.587 . . . . . . . . . [72Dhel 1 . 2 9 8 . . . . . . . . . [73Atal ]

1.163 1.176 0.406 ... [64Ver] 1.162 1.183 0.409 ... [73Ata2] 0.923 ... 1.27 ... [73Atal]

ing variants, as d i scussed below. On ly Bi2Se 3 fo rms w h e n a layer o f Bi is depos i t ed on Se substrate [61Efe], w h i c h indi- cates that Bi2Se 3 is the only s table fo rm w h e n enou g h Se ex- ists.

S t a c k i n g V a r i a n t s . Because o f the c lose similari ty in structure

and size (see "Crystal Structure" sect ion) , any n u m b e r o f lay-

ers o f Bi 2 and Bi2Se 3 can stack in the c d i rec t ion o f a hexagona l

cell in any order, and some configurations are energetically more

favorable. Approximately ten ordered stacking variants wi th

s imple Bi2-to-Bi2Se 3 ratios have b e e n observed (Fig. 1). They

are s h o w n wi th solid l ines in Fig. 1 (upper tempera ture l imits

are u n k n o w n for mos t o f the variants) . More o f these stable

variants wi th relatively simple structures might be found if

enough t ime is al lowed for equilibration, especially at low tern-

peratures. D as h ed l ines in Fig. 1 show the poss ib le pos i t ions o f

such s tacking variants.

Reports on identifications and solubility ranges o f various

"phases" were confusing. Based on thermal analysis 4zta, [60Abr] p ro p o s ed a sol id solut ion range for BiSe f r o m 41.3 to

55.5 at .% Se. [62God] p r o p o s e d an even wider con t inuous

range f r o m 33.3 to 60 a t % Se based on X- ray data (a na r rower

range f r o m 38.9 to 60 at .% Se was g iven in [65God]). Lat t ice

parameter data indica ted the Bi-r ich l imit o f the Bi2Se 3 sol id

solut ion to lie at some compos i t i on b e t w e e n 40 and 45 at .% Se

[63Lan]. [75Gat] and [86She] p roposed a d i ag ram wi th the

BiSe sol id solut ion p h a s e ranging f r o m - 4 6 to 56 at .% Se and

f rom 42.5 to 54.5 at .% Se, respect ively. The per i tect ic mel t ing

point o f this cont inuous phase was found to be 607 ~ at 55.5

at.% Se [61Abr], 609 ~ at 56 at.% Se [75Gat] ( f rom graph), or

Journal o f Phase Equil ibria Vol. 15 No. 2 1994 197

Page 4: The Bi-Se (Bismuth-Selenium) System

S e c t i o n H: P h a s e D i a g r a m E v a l u a t i o n s

Table 3 Ordered Stacking Variants in the Bi-Se System

No. ofstacks No. of layers Total "5" "2"' Total Bi Se

Lattice, Composition, parameter

Formula at.% Se c, nm (a) Observed

3 ...................... 3 0 15 6 9 2 1 12 6 6 1 2 9 6 3 0 3 6 6 0

6 ...................... 5 1 27 12 15 3 3 21 12 9 1 5 15 12 3

9 ...................... 8 1 42 18 24 7 2 39 18 21 5 4 33 18 15 4 5 30 18 12 2 7 24 18 6 1 8 21 18 3

12 ..................... 11 1 57 24 33 9 3 51 24 27 7 5 45 24 21 5 7 39 24 15 3 9 33 24 9 1 11 27 24 3

15 ..................... 12 3 66 30 36 9 6 57 30 27 6 9 48 30 18 3 12 39 30 9

21 ..................... 9 12 69 42 27 6 15 60 42 18 3 18 51 42 9

Note: "5" ~- Se-Bi-Se-Bi-Se; "2" -= Bi-Bi. (a) Calculated value assuming 0.19 nm/layer.

Bi2Se 3 60 2.85 Yes BiSe 50 2.28 Yes Bi2Se 33.3 1.71 Yes

Bi 0 1.14 Yes Bi4Se 5 55.6 5.13 Yes Bi4Se 3 42.9 3.99 Yes Bi4Se 20 2.85 No

Bi3Se 4 57.1 7.98 Yes Bi6Se 7 53.8 7.41 Yes Bi6Se 5 45.5 6.27 Yes Bi3Se 2 40 5.7 Yes Bi3Se 25 4.56 No Bi6Se 14.3 3.99 No

BisSell 57.9 10.83 No BisSe 9 52.9 9.69 Yes BigSe 7 46.7 8.55 Yes BisSe 5 38.5 7.41 No BisSe 3 27.3 6.27 No BisSe 11.1 5.13 No BisSe 6 54.5 12.54 No Bil0Se 9 47.4 10.83 No BisSe 3 37.5 9.12 Yes Bil0Se3 27.3 7.41 No Bi14Se9 39.1 13.11 No BiTSe 3 30 11.4 Yes Bi14Se 3 17.6 9.69 No

606 ~ at 54.5 at.% Se [86She]. This point is shown in Fig. 1 as the peritectic melting ofBi4Se 5 (55.6 at.% Se), which is one of the simplest variants in this composition range. A series of stacking variants may have caused the appearance of continu- ous solution in these reports.

In this composition range, the existence of a BiSe line compound was reported by [02Pel], [04Pel], [09Pel], [13Par], and [19Tom]. The peritectic formation temperature of BiSe was found to be 605 [13Par] or 599 to 605 ~ [19Tom]. Similarity in the temperature suggests that the peritectic formation of Bi4Se 5 was probably detected by [13Par] and [19Tom] at 50 at.% Se. Alternatively, the peritectic formation temperature of BiSe is only slightly lower than that of BiaSe 5. Further clarifi- cation is needed.

Similar peritectic temperatures were reported also for Bi2Se (468 ~ [60Abr] and Bi3Se 2 (470 ~ [75Gat, 86She]. Be- cause the Se concentration is the only important difference be- tween Bi2Se and Bi3Se a, BiaSe (richer in Bi) would have a lower melting point. Therefore, it is more likely that the peritectic temperature belongs to Bi3Se a (or even to Be4Se 3, which is probably even more stable because of its simple Bi 2- to-Bi2Se 3 ratio).

[19Tom] observed thermal effects in cooling curves at 404 to 435 ~ (Fig. 1, probably considerably lower than actual tem- peratures as are other data in [19Tom]), and attributed them to a polymorphic transition in BiSe. Because no polymorphism is

know in BiSe at 1 bar pressure, the thermal effects may be due to peritectic formation of some other stacking variants.

L 1 --> Bi2Se 3 + L 2 Monotectic Reaction. The monotectic temperature is 618 [13Par], 614 [66Oha], or 605 ~ [19Tom]. The liquidus compositions at the monotectic temperature are 73 and 98 at.% Se [13Par] or 73 and 96 at.% Se [19Tom]. The Bi-rich side of the liquid miscibility gap is based on the vapor pressure data of [66Oha]. Alloys formed by vapor quenching in the monotectic composition range contain more than one amorphous phase, which corresponds to the monotectic phase relationship [68Sch].

Se-Rich Eutectic Reaction. The Se-rich eutectic composition is nearly 100 at.% Se [19Tom]. Therefore, the eutectic tem- perature must be nearly identical to the melting point of Se. The temperature observed by [19Tom] (150 to 170 ~ is too low, probably due to supercooling.

(Se) Terminal Solid Solution. The melting point of Se is 221 ~ [Melt]. The solubility of Bi in (Se) must be very small be- cause the Se-rich eutectic composition is nearly 100 at.% Se.

M e t a s t a b l e P h a s e s

[54Sem] and [72Dhe] observed NaCl-type BiSe in a vapor de- posited film. Annealing of high-pressure Bi2Se311I (see "Pres- sure" section) at 50 ~ and 1 bar for 1 h resulted in a transition to a new metastable phase, Bi2Se3IIIa [73Atal].

198 Journal of Phase Equilibria Vol. 15 No. 2 1994

Page 5: The Bi-Se (Bismuth-Selenium) System

Phase Diagrum Evaluations: Sec t ion II

Table 4 Partial Molar Enthalpy at Infinite Dilution of Se in (Bi)

Temperature, AHsr ~ kJ Imol Reference

463 .............................. -28.7 [72Mae] 390 .............................. -27 .4 [67Cha] 350 .............................. -24 .9 [64Howl 300 .............................. -25 .4 [67Cha] 287 .............................. -23 .9 [76Bro]

P r e s s u r e

Bi2Se 3. [64Ver] found an irreversible phase transition of Bi2Se 3 t o S b 2 S 3 (bismuthite)-type Bi2Se3II at high pressures and temperatures (120 kbar at 750 ~ and 65 kbar at 800 ~ [73Ata2] confirmed the existence of Bi2SeaII and determined the atomic coordinates. [73Atal] proposed a nonequilibrium pressure-temperature diagram of Bi2Se 3 for pressures up to 110 kbar, in which the Sb2S3-type phase is named Bi2Se3I[I. Bi2Se3II and Bi2Se3IV exist between Bi2Se3 and Bi2Se3III and at higher pressures than Bi2Se3IlI in the pressure-temperature diagram, respectively. Bi2Se3II was shown to exist above -300 ~ at 1 bar, although no other reports indicated allotropic transformation at 1 bar. [74Yak] also proposed apressure-tem- perature diagram up to 27 kbar, in which the Bi2SeaII of [73Atal] was not reported. Because of insufficient informa- tion on Bi2Se3II in [73Atal], the Bi2Se31lI and Bi2Se3IV in [73Atal] are designated Bi2Se31I and Bi2Se3III, respectively, in this evaluation. Bi2Se 3 becomes metallic at pressures above - 100 kbar at room temperature [64Its].

BiSe2. [65Sil] synthesized a new compound, BiSe 2, at 45 kbar and 1280 ~ No further information is available.

C r y s t a l S t r u c t u r e s a n d L a t t i c e P a r a m e t e r s

Crystal structure and lattice parameter data of the Bi-Se phases are / summarized in Tables 1 and 2, respectively. The data of [30Par] are not included because of significant disagreement with other research.

According to the expression used by [70Ima], the unit cell of BiSe is "552," which consists of two Bi2Se 3 stacks represented by "5" and one Bi 2 stack represented by "2." The Bi2Se 3 stack consists of five layers of atoms in the order of Se-Bi-Se-Bi-Se in the c axis direction of a hexagonal structure, and the Bi 2 stack is two layers of pure Bi in the same direction. Bi2Se 3 con- sists of "5" only and expressed as "555," where the total num- ber of unit stacks in a hexagonal unit cell must be a multiple of three because of crystal symmetry requirements. For example, Bi4Se3, Bi6SeT, and BisSe 9 are expressed as 525252, 555525552, and 555255525552 (more detail in Table 3). The bonding between "5" and "5" (or Se and Se) is weak van der Waals type associated with layered compounds. The "5" to "2" bonding is more stable than bonding between "5" and "5" or "T' and "2." The repulsive force between "2"'s appears to be considerably long-range, judging from the existence of such variants as Bi4Se 5 (555552).

Table 3 lists a few simple stacking variants (columns 1 to 3) from which the number of layers in a unit cell (columns 4 to 6) is derived. The formula of a compound comes from columns 5 and 6. Because the c axis length is -0.19 nm/layer (see below), the c value can be estimated by multiplying the total number of layers by 0.19. This approximate value (column 9) agrees quite well with the experimental results (Table 2). For stacking variants with more than 15 total stacks, only a few combina- tion are listed in Table 3. The criteria for rejection from this ta- ble are (1) long stacking sequence (small entropy or high Gibbs energy) and (2) high Bi concentration (low melting point). According to these criteria, stacks with a total number of 18 do not appear in the table. Compounds marked "No" in the last column in Table 3 have not been reported in literature, but they are possible configurations found in stable states.

Both "5" and "2" stacks have a rhombohedral symmetry (Ta- ble 1). The equivalent hexagonal stmcture consists of close- packed layers, which are normal to the c axis. Because each fundamental cph cell is made of three layers, the average inter- layer distance for "5" is approximately 0.19 nm (dividing an average c value of Bi2Se 3 in Table 2 by 3 x 5). The interlayer distance for "2" is slightly larger (1.1862/3/2 = 0.1977). Be- cause most stacking variants are found on the Bi2Se 3 side, 0.19 nrn/layer was used to calculate the c parameters of stacking variants (column 9 of Table 3).

T h e r m o d y n a m i c s

Thermodynamic Data. The enthalpy of formation of Bi2Se 3 at 25 ~ is approximately -28 kJ/g-atom [55Gat, 65And, 68Bon, 68Mal, 68Vas].

The heat of fusion of BiESe 3 is approximately 17 kJ/g-atom [76Bro]. The heat of sublimation is 42 k J/g-atom at 547 ~ [67Kre].

The enthalpy of mixing of the liquid state was measured by [72Bae] at 725 ~ and by [76Bro] at 615 ~ and a very strong tendency of Bi2Se 3 associate formation was shown. The en- thalpy of mixing minimum (-22.4 k J/g-atom at 725 ~ is at 60 at.% Se [72Mae]. The partial molar enthalpies of solution at in- finite dilution of Se in (Bi) are given in Table 4. Activity data also showed BiESe 3 cluster formation in the liquid state [75Pre].

Thermodynamic Modeling. [84Gla] claimed that the ther- modynamic parameters of the Bi-Se liquid calculated from the curvature of the liquidus at the melting point of Bi2Se 3 agreed well with the data of [72Mae]. According to [75Kuz], the cal- culated liquidus of Bi2Se 3 based on a regular-solution model agreed perfectly with the data of [ 13Par]. Because the interac- tion parameter was not given, the model cannot be corrobo- rated. At any rate, the enthalpy of mixing data of [72Mae] and [76Bro] and the activity data of [75Pre] disagree with the regu- lar-solution model.

Cited References

1 8 5 9 L i t : G. Li t t le , " O n S o m e M e t a l Se l en ides , " Ann. Chem., 112, 211- 214 (1859) in German. (Equi Diagram; Experimental)

Journal of Phase Equilibria Vol. 15 No. 2 1994 199

Page 6: The Bi-Se (Bismuth-Selenium) System

S e c t i o n H: Phs.Ae D i a g r a m E v a l u a t i o n s

02Pel: H. Pelabon, "Action of Hydrogen on Sulfur and Selenium," Ann. Chint Phys., 25, 362-432 (1902) in French. (Equi Diagram; Experi- mental)

04Peh H. Pelabon, J. Chim. Phys., 2, 328-330 (1904); quoted in [Han- sen]. (Equi Diagram; Experimental)

09Pei: H. Pelabon, "Fusibifity of Mixtures of Sulphur, Selenium, and Tellurium with Certain Metals," An~ Chin~ Phys., 17, 526-566 (1909) in French. (Equi Diagram; Experimental)

*13Par: N. Parravano, 'q3ae System: Bismuth-Selenium," Gaz~ Chin~ ltd., 43(1), 201-209 (1913) in Italian. (Equi Diagram, Thermo; Ex- perimental; #)

*lgTom" N. Tomoshige, "Metallographic Investigation of the System Bismuth-Selenium," Men~ Coll. Sci. Kyoto Imp. Univ., 4, 55-60 (1919). (Equi Diagram; Experimental; #)

30Par: N. Parravano and V. Caglioti, "Investigation of the System: Bis- muth-Selenium," Gaz~ Chim. Ital., 60, 923-933 (1930) in Italian. (EquiDiagram, Crys Structure; Experirnental)

34Goe: A. Goetz and A.B. Focke, 'q'he Crystaldiamagnetism of Bis- muth Crystals," Phys. Rev., 45, 170-199 (1934). (Equi Diagram; Ex- perimental)

36Tho: N. Thompson, 'q'he Electrical Resistance of Bismuth Alloys," Proc. R. Soc. (London)A, 155, 111-123 (1936). (Equi Diagram; Ex- perimental)

51Don: E. Donges, "On the Chalcogen Halogenides of Trivalent Anti- mony and Bismuth. 13I. On Tellurium Halogenides of Trivalent Anti- mony and Bismuth and on Antimony- and Bismuth(III)-Telluride and Bismuth(m)-Selenide," Z Anorg. Chen~, 265(1-3), 56-61 (1951) in German. (Crys Structure; Experimental)

*53Sch: K. Schubert, K. Anderko, M. Kluge, H. Beeskow, M. llschner, E. Dorre, and P. Esslinger, "Structure of Alloy Phases Cu2Te, CuTe, Cu3Sb, InTe, Bi2Se 3, PdsSb 3, and PdsBi3," Naturwissenschaften, 40, 269 (1953 ) in German. (Crys Structure; Experimental)

*54Sem: S.A. Semiletov, '~Electrographic Investigation of the Slructure of Sublimed Films of the Composition BiSe and BiTe," Tr. Inst. Krist. Akad. Nauk SSSI~ 10, 76-83 (1954) in Russian (1956). (Meta Phases, Crys Structure; Experimental)

55Gat: G. Gattow and A. Schneider,'q'he Heat of Formation of Bismuth Chalcogenides," Angew. Chem., 67, 306-307 (1955) in German. (Thermo; Experimental)

55Ira: G.A. Ivanov and A.R. Regel, "Electrig Properties of Bismuth Al- loys. I. Solubility of Admixtures and Their Effect on Electric Proper- ties of Bismuth" Zh~ Tekh. Fit, 25, 39-48 (1955). (Equi Diagram; Experimental)

55Sere: S.A. Semiletov and Z.G. t~insker, "Electronographic Investiga- tion of the Bismuth-Selenium System," Dokl. Akad. Nauk SSSR, 100, 1079-1082 (1955) in Russian. (Q-ys Structure; Experimental)

59Off: G. Offergeld and J. Van Cakenberghe, "Stoichiometry of Bis- muth Telluride and Related Compounds," Nature, 184(4), 185-186 (1959). (Equi Diagram; Experimental)

59Vor: A. Vorma, 'q_aitakarite, a New Bismuth-Selenium Mineral from Orijarvi (Southern Finland)," Geologi, 11, 11 (1959). (Crys Structure; Experimental)

*60Abr: N.Kh. Abrikosov, V.E Bankina, and K.E Kharitonovich, "Phase Diagram of the Bi-Se System," Zh. Neorg. Khim., 5(9), 2011- 2016 (1960) in Russian; TRz Russ. J. Inorganic Chem., 5(9), 978-982 (1960). (Equi Diagram, Crys Slructure; Experimental; #)

60Wie: J.R. Wiese and L. Muldawer, "Lattice Constants of Bi2The 3- Bi2Se 3 Solid Solution Alloys," Phys. Chem. Solids, 15(112), 13-16 (1960). (Crys Structure; Experimental)

61Ere: G.A. Efendiev and R.B. Shafizade, "An Electron Diffraction Study of Phase Formation in Bi-Se Binary Layers," Fiz Tverd. Tela, 3(9), 2564-2566 (1961) in Russian; TR: Sov. Phys. Solid State, 3(9), 18 64-1866 (1962). (Equi Diagram; Experimental)

62God: A.A. Godovikov, "X-Ray Diffraction Investigation of Individ- ual Representatives of the Bi-Se System," Zh. Strukt. Khint, 3(3), 44-

50 (1962) in Russian;TR: J. Struct. ChertL USSR, 3(3),38-43(1962). (Equi Diagram, Crys Structure; Experimental)

62Yar: E.I. Yarembash and E.S. Vigileva, "Reaction Between Arsenic Selenide andBismuth Selenide," Zh. Neorg. Khint, 7(12), 2752-2755 (1962) in Russian; TR: Russ. J. Inorganic Chem., 7(12), 1435-1437 (1962). (Equi Diagram, Crys Structure; Experimental)

63Kul: B.M. Kulwicki, '~l]ae Phase Equilibrium of Some Compound Semiconductors by DTA (Differential Thermal Analysis) Cal- orimetry," dissertation, Univ. Michigan, Ann Arbor, 188 p (1963). (Equi Diagram; Experimental )

63Kuz:V.G. Kuznetsov and K.K. Palkina, "Equilibrium Diagram and Structures of Alloys in the Bi2Se 3- Sb2The 3 and B i2The3-Sb2Se3," Zh. Neorg. Khim., 8, 1204-1218 (1963)in Russian; TR: Russ. J. Inorganic Chem., 8, 624-632 (1963). (Equi Diagram, Crys Structure; Experi- mental)

63Lan: S.A. Langston and B. Lewis, "Compounds with the C33 Tetradymite-Type Slructure," J. Phys. Chem. Solids, 24, 1387-1389 (1963). (Equi Diagram, CS"ys Structure; Experimental)

63Nak: S. Nakajima, 'qhe Crystal Structure ofBieTe3_x-Sex," J. Phys. Chem. Solids, 24(3), 479-485 (1963). (CYys Slructure; Experimental)

64Gob: H. Gobrecht, K.E. Boeters, and G. Pantzer, "Crystal Structure and Electrical Properties of Bismuth Selenides Bi2Se 2 and BizSe3," Z Phys., 177, 68-83 (1964) in German. (Crys Structure; Experimental; #)

64How: B.W. Howlett, S. Misra, and M.B. Bever, "On the Thermody- namic Properties of the Compounds Sb2Se3, Bi2Se3, Sb2Te3, and Bi2The3," Metall. Trans. AIME, 230(10), 1367-1372 (1964). (Thermo; Experimental)

64Its: E.S. Itskevich, E.Ya. Atabaeba, and S.V. Popova, "Effect of Pres- sure on the Electrical Resistivity of Bismuth Selenide," Fi~ Tverd. Tela, 6(6), 1765-1768 (1964) in Russian; TR: Sov. Phys. Solid State, 6(6), 1385 - 1387 (1964). (Pressure; Experimental)

*64Sta: M.M Stasova, "X-Ray Investigation of Some Bismuth and An- timony Chalcogenides," Zh. Strukt. Khin~, 5(5), 793-794 (1964) in Russian; TR: J. Struct. Chem. USSR, 5(5), 731-732 (1964). (Crys Structure; Experimental)

64Ver: L.E Vereshchagin, E.S. Itskevich, E.Ya. Atabaeva, and S.V. Pop- ova, "A New Modification of Bi2Se3," Fit Tverd. Tela, 6(7), 2223- 2225 (1964) in Russian; TR: Sov. Phys. Solid State, 6(7), 1763-1764 (1965). (Pressure, Crys Structure; Experimental)

65And: L.L. Andreeva and A.A. Kudryavtsev, "Heat of Formation of Bismuth Triselenide (Bi2Se3)," Tr. Mosk. Khim. TechnoL Inst., 49, 25- 27 (1965) in Russian. (Thermo; Experimental)

65God: A.A. Godovikov, NA. Ilyasheva, V.A. Klyakhin, G.N. Kuznet- sov, V.S. Pavlyuchenko, N.N. Popova, and Zh.N. Fedorova, "Physi- cochemical Investigation of the Bi-Se System," Tr. Inst. Geol. Geofi~ Akad. Nauk SSSR, Sib. Otd, 31, 18-49 (1965) in Russian. (Equi Dia- gram; Experimental)

65Si1: M.S. Silverman,"High Pressure Synthesis of New Compounds--- Bismuth Diselenide and Bismuth Monosulfide Monoselenide," Inor- ganic Chen~, 4(4), 587-588 (1965). (Pressure, Crys Structure; Experimental)

*65Sta: M.M. Stasova, "X-Ray Study of the Region of Homogeneity in Bismuth-Selenium System," Izv. Akad. Nauk SSSR, Neorg. Mater.. 1(12), 2134-2137 (1965) in Russian; TR: Inorganic Mater. USSR, 1 (12), 1930-1932 (1965). (Crys Structure; Experimental)

*66Oha: T. Ohashi, Z. Kozuka, and J. Moriyama, "Vapor Pressure Measurements on Bismuth-Selenium Alloys," Nippon Kinzoku Gak- kai-sh~ 30(8), 785-788 (1966) in Japanese. (Equi Diagram; Experi- mental; #)

67Cha: E Chaudhari and M.B. Bever, "A Calorimetric Investigation of the Bismuth-Rich Region of the System Bismuth-Selenium," Metall. Trans. AIME, 239(4), 501-504 (1967). (Thermo; Experimental)

67Kre: A.N. Krestovnikov and S.I. Gorbov,"Vapor PressureofBismuth Selenide," Zh. F~ Khim., 41(3), 726-728 (1967) in Russian; TR:

200 Journal of Phase Equilibria Vol. 15 No. 2 1994

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P h a s e D l a g r a n l E v a l u a t i o n s : S e c t i o n 11

Russ. J. Phys. Chem., 41(3), 376-378 (1967). (Crys Structure; Experi- mental)

67Stal: M.M. Stasova, "Crystal Structure of Bismuth Selenides and Bismuth and Antimony Tellurides," Zh. Strukt. Khim., 8(4), 584-589 (1967). (Crys Structure; Experimental)

67Sla2: M.M. Stasova, thesis, Moscow Univ. (1967); quoted in [70Ima]. (Crys Structure; Experimental)

67Sta3: M.M. Stasova and O.G. Karpinskii, "Layer Structures of Bis- muth Tellurides and Selenides and Antimony Tellurides," Zh. Strukt. Khim., 8(1), 85-88 (1967)in Russian;TR: "J.Struct. CherrL, 8(1), 69- 72 (1967). (Crys Structure; Experimental)

68Bon: Z. Boncheva-Mladenova, A.S. Pashinkin, and A.V. No- voselova, "Determination of the Saturated Vapor Pressure of Solid Bismuth Selenide," lzv. Akad. Nauk SSSR, Neorg. Mater, 4(7), 1027- 1031 (1968) in Russian; TR: Inorganic Mater USSlZ 4(7), 904-907 (1968). (Crys Structure, Thermo; Experimental)

68Mal: B.T. Malekh and S.A. Semenkovich, 'q'hermodynarnic Proper- ties of Bi(l~) Telluride and Selenide," Izv. Akad Nauk SSSIL Neorg. Mater, 4(8), 1346-1348 (1968) in Russian; TR: Inorganic Mater USSR, 4(8), 1180-1182 (1968). (Thermo; Experimental)

68Seh: J.C. Schottmiller, D.L. Bowman, and C. Wood, "New Vitreous Semiconductors," J. Appl. Phys., 39(3), 1663-1669 (1968). (Equi Diagram; Experimental)

68Sta: M.M. Stasova, "Crystal Structure of the Bismuth Selenide Bi4Se3," lz~. Akad. Nauk SSSR, Neorg. Mater, 4(1), 28-31 (1968) in Russian; TR: Inorganic Mater USSR, 4(1), 21-23 (1968). (Crys Structure; Experimental)

68Vas: V.P. Vasil'ev, A_P. Somov, A.V. Nikol'skaya, and Ya.I. Gerasi- mov, "Thermodynamic Properties of Bismuth Selenide Investigated by the ean.f. Method," Zh. Fiz, KhirrL, 42(3), 675-677 (1968) in Rus- sian; TR: Russ. J. Phys. Chem., 42(3), 355-356 (1968). (Thermo; Ex- perimental)

*701ram: EM. Irnarnov and S.A. Semiletov, 'q'he Crystal Structure of the Phases in the Systems Bi-Se, Bi-Te, and Sb-Te," Kristallografiya, 15(5), 972-978 (1970) in Russian; TR: Sov. Phys. Crystallogr, 15(5), 845-850 (1971 ). (Crys Structure; Theory)

72Dhe: N.G. Dhere and A. Goswami, "Vapor Phase Deposits of Bis- muth Selenide," J. Vac. Sci. Technol., 9(1), 523-527 (1972). (Meta Phases, Crys Structure; Experimental)

72Mae: T. Maekawa, Yokokawa, and K. Niwa,"Enthalpies of Mixing in the Liquid State. IV. Bi + Se and Sb + Se," J. CherrL Thermodyn., 4, 873- 878 (1972). (Thermo; Experimental)

*73Atal: E.Ya. Atabaeva, N.A. Bendeliani, and S.V. Popova, "Poly- morphism ofBi2Se 3 at High Pressures and Temperatures," Fiz. Tverd. Tela, 15(12), 3508 -3512 (1973) in Russian; TR: Soy. Phys. SolidState, 15(I 2), 2346-2348 (1974). (Meta Phases, Pressure, Crys Structure; Experimental;#)

73Ata2: E.Ya. Atabaeva, S.A. Mashkov, and S.V. Popova, "Crystal Structure of a New Modification, Bi2Se3II, ' ' Kristallografiya, 18(1), 173-174 (1973) in Russian; TR: Sov. Phys. Crystallogr, 18(1), 104- 105 (1973). (Crys Structure; Experimental)

74Yak: V.G. Yakushev and V.A. Kirkinskii, "Phase Diagram ofBi2Se 3 at High Pressures," lzv. Akad Nauk SSSR, Neorg. Mater, 10(7), 1195- 1199 (1974) in Russian; TR: Inorganic Mater USSR, 10(7), 1025- 1028 (1974). (Pressure; Experimental; #)

75Boe: V.E Boechko and V.I. Isarev, "Crystallization Conditions and Properties of Single Crystals of p-Type Bi2Se3," lzv. Akad. Nauk SSSR, Neorg. Mater, It(8), 1510-1511 (1975) in Russian; TR: Inor- ganic Mater USSR, 11(8), 1288-1290 (1975). (Crys Structure; Ex- perimental)

*75Gat: B. Gather and R. Blachnik, '~rernary Systems Containing Chal- cogenides. II. The Gold-Bismuth-Selenium System," Z Metallkd., 66(6), 356-359 (1975 ) in German. (Equi Diagram; Experimental; #)

75Kuz: G.M. Kuznetsov, M.P. Leonov, A.S. Luk'yanov, V.A. Kovaleva, and M.P. Shapovalov, "Describing the Liquidus Curves of AmBn Chemical Compounds," DokL Akad Nauk SSSR, 223(1), 124-126 (1975) in Russian; TR: DoM. Phys. Chem., 223, 667-678 (1975). (l'hermo; Theory;#)

75Pre: B. Predel, J. Piehl, and M J. Peo 1, 'q'hermodynamic Properties of LiquidThallium-Selenium, Bismuth-Selenium, and Antimony-Sele- nium Alloys," Z. Metallkd., 66(7), 388-395 (1975) in German. (Thermo; Experimental)

76Bro: H. Bros, R. Castanet, and H.V. Kehiaian, "Calorimetric Study of the Bi-Se System,"High Temp.--HighPress., 8(3), 271-278 (1976) in French. (Equi Diagram, Thermo; Experimental; #)

79Pre: B. Predel, E Gerdes, and U. Gerling, "Effect of the Vapor Phase Association on the Activity of Liquid Selenium-Thallium, Selenium- Bismuth, and Selenium-Antimony Alloys," Z. Metallkd., 70(2), 109- 112 (1979) in German. (Thermo; Experimental)

84Gla: V.M. Glazov, LNI. Pavlova, and D.S. Gaev, 'q'he Thermal Sta- bifity of the Selenides of the Elements of Groups IV and V of the Peri- odic System, from the Data on the Curvature of the Liquidus at the Melting Point," Zh. Neorg. Khim., 29(4), 1079-1085 (1984) in Rus- sian; TR: Russ. J. Inorganic Chem., 29(4 ), 620-624 (1984). (Thermo; Theory; #)

*86She: A.A. Sher, I.E Odin, and A.V. Novoselova,"Investigation of the Phases in the Bi-Se System," Zh. Neorg. Khim., 31(3), 764-767 (1986) in Russian; TR: Russ. J. Inorganic ChenL, 31(3), 435-437 (1986). (Equi Diagram, Crys Structure; Experimental; #)

*Indicates key paper. /ndicatespresence ofaphase diagram.

Bi-~Se evaluation contributed by H. Okamoto, Asahi University, Hosumi-cho, Motosu-gun, Gifu-ken, Japan. This work was supported by ASM International. Lit- erature searched through 1987. Dr. Okamoto is the Alloy Phase Diagram Program Category Editor for miscellaneous binary alloys.

Journal of Phase Equilibria Vol. 15 No. 2 1994 201