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Yttrium aluminum garnet crystal growth in vacuum with account for melt evaporation
Journal of Crystal GTowth 52 (1981) 530—533 © North-Holland Publishing Company
YTTRIUM ALUMINIUM GARNET CRYSTAL GROWf H IN VACUUM WITH ACCOUNT FOR MELT EVAPORATION L.A. OGANESYAN Institute for Physical Research, Academy of Sciences of the Armenian SSR Ash tarak, USSR
and V.Ya. KHAIMOV-MAL’KOVt Institute of Crystallography, Academy of Sciences of the USSR, Leninskii Prospekt 59. 177333 Moscow, USSR
Evaporation of the YAG melt during uniaxial crystallization in vacuum results in a distortion of the stoichiometry. Consequently, the melt is not transformed completely into the single crystal. Accounting for evaporation of the melt enabled the authors to propose analytical expressions for relating the length of the single crystal to growth parameters in the case of Bridgman—Stockbarger and boat growth techniques. Satisfactory agreement with experimental data is reported.
rate, melt surface temperature, evaporation rates of system components, melt geometry), and to make a comparison with experimental data obtained during growth from the melt by Bridgman—Stockbarger and boat techniques.
1. Introduction Single crystals of yttrium aluminium garnet (YAG) doped with rare-earths are considered as one of the basic solid-state materials for optical quantum generators. A necessity appeared recently for growing large single crystals. Since considerable time periods are required for growing such crystals and the equilibrium vapour pressures of the components (A1203 and Y203)
2. Theoretical considerations Let us consider a two-component system. We can assume that at the moment of time amount of melt in this system is
over the melt differ, the stoichiometry of the melt becomes gradually distorted because of unequal evaporation of the components [1]. When YAG crystals are grown from the melt in vacuum in Bridgman—Stockbarger or boat techniques, the interface passes across the entire sample, the end portion of the melt of length 1o—X (1~is the melt length and X is the maximum length of the single crystal) solidifies in the form of a two-phase mixture: garnet Y3A15012 and perovskite YAIO3. The aim of this study was to find an analytical relationship between the length of the single crystal, X, and the growth parameters (growth
t
=
0 the
M(0) = M1(0) + M2(0) (where M1(O) and M2(O) are the quantities of the first and second components, respectively) and the stoichiometric ratio of I and 11 components is: M1(0)/M2(0) = a/(1
—
When no chemical interaction of the melt with crucible material and chamber atmosphere takes place, the only cause of the gradual distortion of melt stoichiometry is the evaporation of the melt. Now let us find the evaporation conditions
t Deceased, 530
L.A. Oganesyan, V. Ya. Khaimov-Mal’kov / YAG growth in vacuum
which ensure the constant stoichiometry of the system. Let 71 and 72 be the evaporation rates of the components I and II, respectively (note that y’ and 72 are functions of temperature [2]). If temperature and pressure of the melt are constant, the amounts of I and II components at time t are equal to M1(t) and M2(t); at the moment of time t+z~t (where i~t is a time increment): ,M’1(t +
M’1(t)
—
yiS ~t,
(la)
M2(t + z~t)= M2(t)
—
72S
(ib)
~t)
=
531
melt which crystallizes at a rate V. the stoichiometry of the growing crystal being M1/M2 = a/(1
—
a).
Then we can write: ~M1
—ap~t,~V— y1S~t,
(4a)
z~M2=—(1—a)p,~V—y2Si~t,
(4b)
=
where S is the melt surface area. If we assume the amount of evaporation to be negligibly small, i.e. 71S L~t~ M1(t) and -y2S L~t~ M2(t), then, as a first approximation, the change of the ratio of the components during the time period Lu is:
where P. is the specific gravity of the crystal and z~V is the increment of its volume. These equations show the loss of components I and II, respectively, from the melt during a period of time ~t due to crystal growth and due to evaporation. The crystal growth will continue until the ratio between the amounts of the cornponents I and II in the remaining melt reaches a certain critical value C:
~ A1~12 M1(t+z~t) M1(t) )%4’2(t + i.~t) M’2(t)
.M’1(t1)/M’2(t2) = C.
—
=
~t,
—
—
S ( M2(t)
Y’
—
~~Q) \ M2(t)
72)
2’ .
‘
It follows that z~M1,2 0 (i.e. the ratio of the components does not change from the moment t) if: Vt
=
=
0.
(3a)
or 7/72
=
M1(t)/M7(t);
(3b)
whereas stoichiometry will be maintained at the moment t = 0 if: Vt
=
72 =
0,
(3a’)
or 71/72 =
M1(0)/M2(0) = a/(1
—
a).
(3b’)
Let us now consider the case of an evaporating
(5)
The following assumptions were made in solving the system (4) jointly with condition (5): (a) The portion of the melt that has evaporated is substantially smaller than the initial melt bulk. It is important to note that a minor deviation from stoichiometry in the system can result in the formation of a chemically stable compound of another composition that corresponds to a similar stoichiometry. In our case, if the stoichiometry shifts towards a decrease of aluminium oxide, the resulting phase is perovskite. (b) The second phase formed in the melt is not incorporated by the crystal. If we take into account these assumptions and replace time increment with coordinate increment (i.e. pass into the coordinate system related to the interface so that X = vt, where v is the growth rate), we can transform the system of equations (4) into: z~M1= —ap, z~ V— y1S i~X/v,
(6a)
i~M2= —(1
(6b)
—
a)ps z~ V
—
y2S AX/v,
532
L.A. Oganesyan, V.Ya. Khaimov-Mal’kov / YAG growth in vacuum
and condition (5) into: M1(X)/M2(x)
=
and boat techniques it is necessary, first of all, to estimate the physical and technological
C.
(7)
If we take the point of crystal growth start as a coordinate origin and consider, as usually accepted, that the densities of the melt and crystal are equal (p,,, Ps), we can solve (6) and (7) for various crystallization techniques. The results below relate the length X of the single crystal grown to the above-mentioned parameters. Accounting for evaporation, we can subdivide the melt growing techniques into three groups [3]: with constant evaporation surface area (Bridgman—Stockbarger, Czochralski, zone melting and Verneuil); with variable evaporation surface area (bc~attechnique and Kyropoulos), and techniques in which evaporation is negligible for one reason or another. Consider the techniques of growth by Bridgman—Stockbarger and in a boat which fit the assumptions made above, For the case of Bridgman—Stockbarger:
—
‘8’ “ ~
10
—
1
+
(y1— C’y2)/i3pv’
where 1~is the length of melt (height in Bridgman’s vertical method), and f3 = a C(1 a) is a constant. It follows from (8), if the conditions (3) are fulfilled, that X = 10. For the case of crystal growth in a boat: —
j3pdv 112 /\7~ /3pdv I C X—lo+ Y’— Cy~+iio+i —
—
\2]1/2 i i
72j
j
—
9~t
/ ,
.~
~
where 1~is the length of the melt (boat), d is the melt thickness, and /3 = a c(1 a) is a constant. If the conditions (3) are fulfilled, it can be shown easily that X = 1~. —
—
3. Experimental results In order to compare the expressions (8) and (9) with experimental data on the growth of YAG crystals from the melt by Bridgman—Stockbarger
parameters of the growth process, i.e. to find the values of y~,72 and C, and determine a reasonable range of growth rates v for obtaining single crystals of satisfactory quality. The growth was conducted from a melt with a stoichiometry corresponding exactly to garnet composition, i.e. at the beginning of growth (X = 0) the ratio between the amounts of aluminium and yttrium oxides was equal to a/(l a), where a = 0.429. The evaporation rates for aluminium and yttrium oxides ~ and 72) were accepted according to ref. [4] where the rates of A1203 and Y203 evaporation from garnet melt were found as a function of temperature. The constant C was determined from experimental results as follows. Quantitative X-ray analysis was used for determining the phase composition of the non-single-crystalline end portion (1~ X) of the sample which is a mixture of garnet (Y3A5012) and yttrium aluminate (YAIO3) and the value of C found from the ratio between the amounts of A1203 and Y203. Measurements have shown that C depends on the growth rate; in the case of Bridgman— Stockbarger techniques C = 0.48 at v = 1.55 mm/h, and C = 0.53 at v = 4.5 mm/h. In the boat growth techniques C = 0.587 at v = 8 mm/h. The conditions of growth by Bridgman— Stockbarger technique were as follows: average temperature of melt surface Tav = 2320 K, pressure P = (4_5)x 10 ‘Torr, v = 1.55 mm/h; sample length varied from one run to another within 4 to 10 cm. The conditions for growing in a boat were: Tav = 2270 K, P = (3—4) x i0~Torr, v = 8mm/h in two runs. In one of them the length of the melt was varied within 5 to 16 cm, melt thickness being constant (d = 0.9 cm), in the other the length was kept constant (1~= 10 cm) and the thickness varied within 0.4 to 1 cm. The boundary between the single crystalline and end portions of the samples was not distinct, whichever growth technique was used. With Bridgman—Stockbarger technique, the crystalline —
—
L.A. Oganesyan, V.Ya. Khaimov-Mal’kov / YAG growth in vacuum
533
foX, CI?!
0
2
4
6
8 ~flt
Fig. I. Length of non-single-crystalline portion of sample versus melt length (YAG grown by Bridgman—Stockbarger technique).
U
W
d.,cm
Fig. 3. Length of non-single-crystalline portion of sample versus melt thickness (YAG grown in a boat).
cm the transition zone where the single crystal is
~/// 0 5 10 15 ~, cm Fig. 2. Length of non-single-crystalline portion of sample versus melt (boat) length (YAG grown in a boat),
phase of the new composition is first forced out to the side surface, but gradually it fills the entire volume of the crystal. The total length of crystal 10 was found, then the crystal was cleaned of the second phase mechanically, and weighed. The length of the single-crystalline portion X was calculated as X = m/rrr2p, where m is the mass of garnet single crystal, p is its density and r is the radius of the cylindrical sample. In the case of the samples grown in a boat the length of the single-crystalline portion was taken as the distance from the point X = 0 up to the middle of
The experimental results are shown by circles in fig. I (Bridgman—Stockbarger), and figs. 2 and 3 (boat technique). The solid line in fig. I corresponds replaced gradually to the curve by the calculated two-phasefrom mixture. formula (8), and in figs. 2 and 3 from formula (9). The agreement between the theoretical and experimental data is satisfactory. The results of this study can be used to predict the growth process under certain growth conditions, and to calculate the compensatory additions to the charge for obtaining single crystals that consist of one phase throughout the entire volume of crucible.
References Fl] G.V. Maksimova, V V Osiko, A.A. Sobol and MI. Timoshechkin, Izv. Akad. Nauk SSSR, Neorg. Mater. 9 (1973) 1763. [2] J.P. Hirth and G.M. Pound, Evaporation and Condensation, in: Progress in Materials Science, Vol. 11(1963)p. 1. [3] V.Ya. Khaimov-Mal’kov, J. Crystal Growth 35 (1976) 302.
[41L.A.
Oganesyan and V.Ya. Khaimov-Mal’kov, Kristallografiya 25 (1980) 886.
YTTRIUM ALUMINIUM GARNET CRYSTAL GROWf H IN VACUUM WITH ACCOUNT FOR MELT EVAPORATION L.A. OGANESYAN Institute for Physical Research, Academy of Sciences of the Armenian SSR Ash tarak, USSR
and V.Ya. KHAIMOV-MAL’KOVt Institute of Crystallography, Academy of Sciences of the USSR, Leninskii Prospekt 59. 177333 Moscow, USSR
Evaporation of the YAG melt during uniaxial crystallization in vacuum results in a distortion of the stoichiometry. Consequently, the melt is not transformed completely into the single crystal. Accounting for evaporation of the melt enabled the authors to propose analytical expressions for relating the length of the single crystal to growth parameters in the case of Bridgman—Stockbarger and boat growth techniques. Satisfactory agreement with experimental data is reported.
rate, melt surface temperature, evaporation rates of system components, melt geometry), and to make a comparison with experimental data obtained during growth from the melt by Bridgman—Stockbarger and boat techniques.
1. Introduction Single crystals of yttrium aluminium garnet (YAG) doped with rare-earths are considered as one of the basic solid-state materials for optical quantum generators. A necessity appeared recently for growing large single crystals. Since considerable time periods are required for growing such crystals and the equilibrium vapour pressures of the components (A1203 and Y203)
2. Theoretical considerations Let us consider a two-component system. We can assume that at the moment of time amount of melt in this system is
over the melt differ, the stoichiometry of the melt becomes gradually distorted because of unequal evaporation of the components [1]. When YAG crystals are grown from the melt in vacuum in Bridgman—Stockbarger or boat techniques, the interface passes across the entire sample, the end portion of the melt of length 1o—X (1~is the melt length and X is the maximum length of the single crystal) solidifies in the form of a two-phase mixture: garnet Y3A15012 and perovskite YAIO3. The aim of this study was to find an analytical relationship between the length of the single crystal, X, and the growth parameters (growth
t
=
0 the
M(0) = M1(0) + M2(0) (where M1(O) and M2(O) are the quantities of the first and second components, respectively) and the stoichiometric ratio of I and 11 components is: M1(0)/M2(0) = a/(1
—
When no chemical interaction of the melt with crucible material and chamber atmosphere takes place, the only cause of the gradual distortion of melt stoichiometry is the evaporation of the melt. Now let us find the evaporation conditions
t Deceased, 530
L.A. Oganesyan, V. Ya. Khaimov-Mal’kov / YAG growth in vacuum
which ensure the constant stoichiometry of the system. Let 71 and 72 be the evaporation rates of the components I and II, respectively (note that y’ and 72 are functions of temperature [2]). If temperature and pressure of the melt are constant, the amounts of I and II components at time t are equal to M1(t) and M2(t); at the moment of time t+z~t (where i~t is a time increment): ,M’1(t +
M’1(t)
—
yiS ~t,
(la)
M2(t + z~t)= M2(t)
—
72S
(ib)
~t)
=
531
melt which crystallizes at a rate V. the stoichiometry of the growing crystal being M1/M2 = a/(1
—
a).
Then we can write: ~M1
—ap~t,~V— y1S~t,
(4a)
z~M2=—(1—a)p,~V—y2Si~t,
(4b)
=
where S is the melt surface area. If we assume the amount of evaporation to be negligibly small, i.e. 71S L~t~ M1(t) and -y2S L~t~ M2(t), then, as a first approximation, the change of the ratio of the components during the time period Lu is:
where P. is the specific gravity of the crystal and z~V is the increment of its volume. These equations show the loss of components I and II, respectively, from the melt during a period of time ~t due to crystal growth and due to evaporation. The crystal growth will continue until the ratio between the amounts of the cornponents I and II in the remaining melt reaches a certain critical value C:
~ A1~12 M1(t+z~t) M1(t) )%4’2(t + i.~t) M’2(t)
.M’1(t1)/M’2(t2) = C.
—
=
~t,
—
—
S ( M2(t)
Y’
—
~~Q) \ M2(t)
72)
2’ .
‘
It follows that z~M1,2 0 (i.e. the ratio of the components does not change from the moment t) if: Vt
=
=
0.
(3a)
or 7/72
=
M1(t)/M7(t);
(3b)
whereas stoichiometry will be maintained at the moment t = 0 if: Vt
=
72 =
0,
(3a’)
or 71/72 =
M1(0)/M2(0) = a/(1
—
a).
(3b’)
Let us now consider the case of an evaporating
(5)
The following assumptions were made in solving the system (4) jointly with condition (5): (a) The portion of the melt that has evaporated is substantially smaller than the initial melt bulk. It is important to note that a minor deviation from stoichiometry in the system can result in the formation of a chemically stable compound of another composition that corresponds to a similar stoichiometry. In our case, if the stoichiometry shifts towards a decrease of aluminium oxide, the resulting phase is perovskite. (b) The second phase formed in the melt is not incorporated by the crystal. If we take into account these assumptions and replace time increment with coordinate increment (i.e. pass into the coordinate system related to the interface so that X = vt, where v is the growth rate), we can transform the system of equations (4) into: z~M1= —ap, z~ V— y1S i~X/v,
(6a)
i~M2= —(1
(6b)
—
a)ps z~ V
—
y2S AX/v,
532
L.A. Oganesyan, V.Ya. Khaimov-Mal’kov / YAG growth in vacuum
and condition (5) into: M1(X)/M2(x)
=
and boat techniques it is necessary, first of all, to estimate the physical and technological
C.
(7)
If we take the point of crystal growth start as a coordinate origin and consider, as usually accepted, that the densities of the melt and crystal are equal (p,,, Ps), we can solve (6) and (7) for various crystallization techniques. The results below relate the length X of the single crystal grown to the above-mentioned parameters. Accounting for evaporation, we can subdivide the melt growing techniques into three groups [3]: with constant evaporation surface area (Bridgman—Stockbarger, Czochralski, zone melting and Verneuil); with variable evaporation surface area (bc~attechnique and Kyropoulos), and techniques in which evaporation is negligible for one reason or another. Consider the techniques of growth by Bridgman—Stockbarger and in a boat which fit the assumptions made above, For the case of Bridgman—Stockbarger:
—
‘8’ “ ~
10
—
1
+
(y1— C’y2)/i3pv’
where 1~is the length of melt (height in Bridgman’s vertical method), and f3 = a C(1 a) is a constant. It follows from (8), if the conditions (3) are fulfilled, that X = 10. For the case of crystal growth in a boat: —
j3pdv 112 /\7~ /3pdv I C X—lo+ Y’— Cy~+iio+i —
—
\2]1/2 i i
72j
j
—
9~t
/ ,
.~
~
where 1~is the length of the melt (boat), d is the melt thickness, and /3 = a c(1 a) is a constant. If the conditions (3) are fulfilled, it can be shown easily that X = 1~. —
—
3. Experimental results In order to compare the expressions (8) and (9) with experimental data on the growth of YAG crystals from the melt by Bridgman—Stockbarger
parameters of the growth process, i.e. to find the values of y~,72 and C, and determine a reasonable range of growth rates v for obtaining single crystals of satisfactory quality. The growth was conducted from a melt with a stoichiometry corresponding exactly to garnet composition, i.e. at the beginning of growth (X = 0) the ratio between the amounts of aluminium and yttrium oxides was equal to a/(l a), where a = 0.429. The evaporation rates for aluminium and yttrium oxides ~ and 72) were accepted according to ref. [4] where the rates of A1203 and Y203 evaporation from garnet melt were found as a function of temperature. The constant C was determined from experimental results as follows. Quantitative X-ray analysis was used for determining the phase composition of the non-single-crystalline end portion (1~ X) of the sample which is a mixture of garnet (Y3A5012) and yttrium aluminate (YAIO3) and the value of C found from the ratio between the amounts of A1203 and Y203. Measurements have shown that C depends on the growth rate; in the case of Bridgman— Stockbarger techniques C = 0.48 at v = 1.55 mm/h, and C = 0.53 at v = 4.5 mm/h. In the boat growth techniques C = 0.587 at v = 8 mm/h. The conditions of growth by Bridgman— Stockbarger technique were as follows: average temperature of melt surface Tav = 2320 K, pressure P = (4_5)x 10 ‘Torr, v = 1.55 mm/h; sample length varied from one run to another within 4 to 10 cm. The conditions for growing in a boat were: Tav = 2270 K, P = (3—4) x i0~Torr, v = 8mm/h in two runs. In one of them the length of the melt was varied within 5 to 16 cm, melt thickness being constant (d = 0.9 cm), in the other the length was kept constant (1~= 10 cm) and the thickness varied within 0.4 to 1 cm. The boundary between the single crystalline and end portions of the samples was not distinct, whichever growth technique was used. With Bridgman—Stockbarger technique, the crystalline —
—
L.A. Oganesyan, V.Ya. Khaimov-Mal’kov / YAG growth in vacuum
533
foX, CI?!
0
2
4
6
8 ~flt
Fig. I. Length of non-single-crystalline portion of sample versus melt length (YAG grown by Bridgman—Stockbarger technique).
U
W
d.,cm
Fig. 3. Length of non-single-crystalline portion of sample versus melt thickness (YAG grown in a boat).
cm the transition zone where the single crystal is
~/// 0 5 10 15 ~, cm Fig. 2. Length of non-single-crystalline portion of sample versus melt (boat) length (YAG grown in a boat),
phase of the new composition is first forced out to the side surface, but gradually it fills the entire volume of the crystal. The total length of crystal 10 was found, then the crystal was cleaned of the second phase mechanically, and weighed. The length of the single-crystalline portion X was calculated as X = m/rrr2p, where m is the mass of garnet single crystal, p is its density and r is the radius of the cylindrical sample. In the case of the samples grown in a boat the length of the single-crystalline portion was taken as the distance from the point X = 0 up to the middle of
The experimental results are shown by circles in fig. I (Bridgman—Stockbarger), and figs. 2 and 3 (boat technique). The solid line in fig. I corresponds replaced gradually to the curve by the calculated two-phasefrom mixture. formula (8), and in figs. 2 and 3 from formula (9). The agreement between the theoretical and experimental data is satisfactory. The results of this study can be used to predict the growth process under certain growth conditions, and to calculate the compensatory additions to the charge for obtaining single crystals that consist of one phase throughout the entire volume of crucible.
References Fl] G.V. Maksimova, V V Osiko, A.A. Sobol and MI. Timoshechkin, Izv. Akad. Nauk SSSR, Neorg. Mater. 9 (1973) 1763. [2] J.P. Hirth and G.M. Pound, Evaporation and Condensation, in: Progress in Materials Science, Vol. 11(1963)p. 1. [3] V.Ya. Khaimov-Mal’kov, J. Crystal Growth 35 (1976) 302.
[41L.A.
Oganesyan and V.Ya. Khaimov-Mal’kov, Kristallografiya 25 (1980) 886.