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Crystal growth and temperature variation of the lattice parameters in LaF3, CeF3, PrF3 and NdF3
Journal of Crystal Growth 61 (1983) 601—605 North-Holland Publishing Company
601
CRYSTAL GROWTH AND TEMPERATURE VARIATION OF THE LATTICE PARAMETERS IN LaF3, CeF3, PrF3 AND NdF3 Wies~awaKORCZAK and Pawel MIKOLAJCZAK Experimental Physics Department, Institute of Physics, M. Curie - Sklodowska University, Lublin, Poland
Received 10 May 1982; manuscript received in final form 14 October 1982
The growth of REF3 (RE = La, Ce, Pr, Nd) single crystals by the Bridgman—Stockbarger method is described. The temperature dependence of the lattice parameters a and c and the thermal expansion coefficients a of these materials in the range of 87—291 K are reported.
I. Introduction In order to study electron paramagnetic resonance (EPR), high quality single crystals of LaF3, 3~have been CeF3, PrF3 and NdF3 doped with Gd grown in a dynamic helium atmosphere in a modified Bridgman—Stockbarger type furnace. Single crystals of REF 3 (RE La, Ce, Pr, Nd) have received considerable attention over the past few decades. The rare earth fluorides are successful hostinmaterials. There has been considerablelaser interest the EPR and optical spectra of rare earth ions in rare earth fluoride single crystals. By doping a series of the rare earth fluorides with Gd3~ions, the surroundings of the ionic impurity may be varied while preserving the local point symmetry of the substituted rare earth host ions. This family of crystals has therefore been recognized as useful for investigating the crystal field model. =
The importance of the thermal expansion in laser, optical and EPR experiments has emphasized the need for additional thermal data concerning the rare earth trifluorides. In this paper we report the successful application of the simple Bridgman—Stockbarger technique to the single crystal growth of the rare earth trifluorides. The temperature dependence of the lattice parameters and thermal expansion coefficient in the range of 87—291 K for these materials is also reported.
Single crystals of REF3 have been obtained by two growth methods: the Bridgman—Stockbarger [1—3]and the Czochralski [4,5] method. In those methods anhydrous fluoride (HF) was used to convert the hydrogen oxyfluorides or hydroxyfluorides to the fluoride. The method employed in our experiments is simpler. It has the advantage of not using an HF atmosphere. In our experiments the crystals were grown in a dynamic helium atmosphere. Optically 3~ clear singlegrown crystals of REF3 dopedusing withthe Gd have been in our laboratory apparatus described below.
2. Experimental procedure 2.1. Crystal growth
Anhydrous REF 3 materials were obtained from Alfa-Ventron (USA). All REF3 materials were of 99.9% purity. Generally all starting materials were prepurified (the moisture content can cause hydrolysis when heated) by carefully heating to elevated temperatures, about 5 h at 90°Cand I h at 500—550°C,in a helium atmosphere. The crystal growing furnace is shown in fig. 1. A 20 mm diameter quartz tube about 35 cm long was clamped between two stainless-steel end plates with rubber rings. Helium gas (99.995% purity)
0022-0248/83/0000—0000/$0300 © 1983 North-Holland
602
W. Korczak, P. Mikolajczak
/
Growth and temperature variation of lattice parameters
Often the liquid—solid interface of the growing crystal is concave towards the solid. The higher the
2
temperature gradient, the more planar is the liquid—solid interface, and usually better crystals can be produced. In our experiments we used a
15 14
150°C/cm temperature gradient in the furnace, and a growth rate of 0.5 mm/h which was found to be optimum. For crystal growth, the polycrystalline starting material (REF3 + 0.01% GdF3) was loaded into the
11 1
10kw 460 kHz
0
a
crucible (see fig. 1). After flushing the system with He for After 2 h the was slowly raised to 90°C. 2 htemperature the temperature was raised to
10
/
550°Cand after another 2 h the temperature raised to 50°Cabove the melting point. The crucible was held at this temperature for 3 h and then lowered at a rate of 0.5 mm/h. Single crystals were prepared in a two-day growth cycle. Using the above technique transparent single 3~(5 mm in diamcrystals dopedhave withbeen Gd grown. All of the eter and of20REF3 mm long) crystals discussed are quite easy to grow by this
9
6
He 2
5 VrO.5 .~.4mm/h
Fig. I. Crystal growing furnace: (I) radio-frequency generator (460 kHz, 10 kW); (2) temperature controller; (3) flowmeter; (4) variable speed motor and puller; (5) helium cylinder; (6) stainless steel bottom disk; (7) rubber 0 ring; (8) quartz tube; (9) stainless steel pull rod; (10) radio-frequency coil; (11) graphite crucible; (12) graphite lid; (13) graphite susceptor; (14) control thermocouple (Pt/Pt—l0%Rh); (IS) air cooled
method. The following important points should be stressed for growing good rare earth trifluoride crystals: (1) Fluorides must be oxide and water free. Small amount of RE203 and/or REOF make REFS~ crystals cloudy and opaque in appearance. This problem arises from impure starting materials: REF3
+
H20
2 REOF
+
—s
H2O
REOF -s
+
2 HF,
RE203 +2 HF.
stainless steel end plate.
The reactions proceed rapidly above about 600°C flowed through stainless-steel tubing at 1 1/mm and the radio-frequency power, at 460 kHz, was coupled to a graphite susceptor. The temperature was sensed by a Pt/Pt—l0%Rh thermocouple in the susceptor and controlled so that the temperature variation at the control point was ±1°C. Graphite was the best crucible material; the corrosive nature of the melt did not affect it. The fluorides do not wet graphite, making removal of the product quite easy. Crucibles were made from graphite manufactured by Alfa-Ventron. One of the most important factors in growing crystals from the melt is the temperature gradient.
[41.
(2) High temperature gradient and slow growth rates must be used if large crystals with low dislocation densities are to be produced. 2.2. Lattice parameters and thermal expansion of LaFq, CeF?, PrF3 and NdF~
X-ray studies of REF3 at room temperature have been carried out by a number of authors [6,7]. The values for the lattice parameters determined in these investigations were generally in good agreement. The temperature variation of the unit cell parameters has been previously reported
W. Korczak, P. Mikolajczak
/
603
Growth and temperature variation of lattice parameters
only by Klein and Croft [7] solely for LaF3. These data agree reasonably well with the present results. No temperature variation of the unit cell parameter data were found for CeF3, PrF3 and NdF3. The thermal expansion coefficient versus temperature relation can be used to calculate the Gruneisen parameter y as a function of temperature. This in turn can be related to the phonon dispersion curves. In laser, optical and EPR experiments we also need the thermal expansion coefficient. Only two references (refs. [6,7]) for the thermal expansion of REF3 were found; for LaF3 (at 111, 209 and 299 K) and for CeF3 (from 293 to 613 K).
Table I Observed lattice parameters of REF3s (RE = La, Ce, Pr or Nd); experimental errors are ~a = ~c = ±0.001 A Crystal
T (K)
a (A)
c (A)
LaF3
288 237 187 137 87 291 233 183 97 291 233 183 133 97 291 183 133 97
7.186 7.181 7.176 7.174 7.173 7.131 7.127 7.123 7.120 7.078 7.072 7.068 7.065 7.064 7.032 7.022 7.019 7.018
7.352 7.349 7.345 7.343 7.341 7.288 7.282 7.277 7.273 7.240 7.234 7.231 7.228 7.226 7.200 7.191 7.188 7.187
CeF,
PrF3
2.2.1. Lattice parameter measurements
The single crystals of REF3 were pulverized and used in determining the lattice parameters. The unit cell dimensions for REF3 were derived from powder diffractometer patterns using Cr K,,, (A 2.2909 A) radiation with a V filter. Si was used as an internal standard. Low temperature diffractometry data were taken for REF3 from 87 to 291 K. The temperatures were measured to within ±1 K by a constantan—copper thermocouple. In order to determine the lattice parameters a and c the extrapolation function f(9) was used: 2O cos29 \ cos sine + ~ (1)
NdF,
=
2.2.2. Thermal expansion of REF3s
The linear thermal expansion coefficient a of a solid is usually measured in terms of the change in length 1 with respect to the length 10 at some fixed temperature T0. To a very good approximation a is given by a (l//~) dl/dT. (4) Many authors in the literature give temperature=
The experimental errors for a and c were L~a L~c ±0.001 A. The lattice parameters of all the fluorides studied are listed in table 1. The room temperature lattice parameters (see table 1) are in generally excellent agreement when compared with those reported in ref. [6], within experimental error. The unit cell parameters for LaF 3, CeF3, PrF3 and NdF3 are plotted and displayed in fig. 2. In our work, the unit cell parameters between room temperature and liquid nitrogen temperature were fitted using the least-squares method to the polynomials: 2, (2) =
=
a(T)
=
c(T)
=
a0 + a1T+ a2T 2 2 c0 + c1T+ c T
(3)
The computed parameters of our polynomials for LaF 3, CeF3, PrF, and NdF3 are listed in table 2.
averaged values of the thermal expansion coefficient: ~
=
(l/l~— 1 )/( T — 1~).
(5)
In general there is a difference between the macroscopic length change with ~ 1) measured mechanically andtemperature the lattice parameter —
change (a/a0 1) measured by X-rays. In this paper all values of the coefficient are defined by eq. (4). In cubic crystals a is scalar. In REF3 crystals which symmetry, the principal values of ahave are hexagonal those parallel and perpendicular to the c axis, i.e. a~ tively. The directionally averaged1and lineara1expansion respeccoefficient d is given by —
,
=
~(a~1+ 2aj.
(6)
W. I(orczak, 1-’. Mikotajczak / Growth and temperature variation oJ lattice parameters
604
7.4C
Table 3 • La F
3
o Pr F3
xCeF3
S NdF3
Linear thermal expansion of REF, along a and c axes Crystal
T(K)
a1
(x •~___—•-—~• 288
17.0
10.7
14.9
237 187
13.0 9.1
9.1 7.5
11.7 8.6
137
5.2
6.1
5.5
87 291 233 183
1.4 12.9 10.0 7.6
4.5 16.5 13.1 10.1
2.4 14.1 12.2 8.4
PrF,
291 233 183 133 97
16.4 12.8 9.6 6.5 4.2
14.0 11.4 9.3 7.1 5.5
15.6 12.3 9.5 6.7 4.6
NdF,
291
17.4
14.7
16.5
183
9.5
8.8
9.3
133
5.9
6.1
6.0
97
3.2
4.1
3.5
7 2 0
~
-
a
7.10
106
K’)
CeF,
_______
(x
106
K’)
-
c
(x
K’) LaF,
7.30
a; 106
The anisotropy A in a is given by
a
(7)
A=a1/a11—l.
In our experiment the thermal expansion coefficient a1 was computed from (2) and (4): a1
and a11 was computed from (3) and (4):
-
7.00~
2111
a11
3~J
T EK] Fig. 2. The temperature dependence of the lattice parameters a and c in REF,.
=
0+c1T+c2T a~
7)
a 1 (><10’)
LaF, CeF, PrF, NdF 3
7.174 7.119 7.063
—3.884 — 1.002 — 1.348
a,(X10 2.792 1.748 2.228
7.018
—2.685
2.559
(9)
(1/c300) (c1 + 2c2T),
where a300 and c300 are the computed values of the lattice parameters at 300 K. The a~1and a1 values are given in table 3. At room temperature, A has
Table 2 Values of parameters c(T)=c 2 if (from temperature 87 to 291 variations K) of REF1s are fitted by a function of the type a(T) Crystal
(8)
(1/a300) (a1 + 2a2T),
=
2 and =
a0 + a1T + a2T
c
7) 0
c1 (X10’)
c2(Xl0
7.339 7.271 7.224
1.391 —0.506 0.930
1.117 2.151 1.573
7.186
—0.902
1.976
W. Korczak, P. Mikolajczak
18
•-LaF 3 - Ce F3 Pr F3
14
Nd F3
/
3. Conclusions 3~-dopedLaF Gd 3, CeF3, PrF3 and NdF3 single crytals of excellent quality have been grown in graphite crucibles by the Bridgman—Stockbarger technique. In order to obtain rare earth trifluoride crystals of optical quality, the starting materials must be oxide and water free and a high temperature gradient and slow growth rates must be used. The unit cell parameters (a and c) between room temperature and liquid nitrogen temperature may be described by the cpolynomials: a(T) a0 + a~T 2 and c(T) 2.
x
•
-
~ 10
4
•
60
I I
100
=
=
+ a2T I
I
200
605
Growth and temperature variation of lattice parameters
0 + c~T+c2T
I
300
T[K] Fig. 3. The directionally averaged linear expansion coefficient 4 (eq. (6)) of REF 3 versus temperature.
Acknowledgement We are thankful to Dr. R. Frak from UMCS Central Laboratory for help in X-ray measurements. References
the approximate value of 0.59 for LaF3, —0.22 for CeF3, 0.17 for PrF3 and 0.18 for NdF3. The values of a (eq. (6)) for REF3 (table 3) are shown in fig. 3. The value of a1 for LaF3 at room temperature found in ref. [7] is 10% higher and that of a11 is 9% lower. The value of a1 for LaF3 at 300 K found in ref. [6] is 12% lower and that of a11 is exactly the same. The value of a1 for CeF3 at room temperature found in ref. [6] is 9% lower and that of a11 is 21% higher.
(I] [2] [3] [4] [5] [6] [7]
D.A. Jones and WA. Shand, J. Crystal Growth 2 (1968) 361. H. Guggenheim, J. AppI. Phys. 34 (1963) 2482. M. Robinson and D.M. Cripe, J. Appi. Phys. 37 (1966) 2072. P.F. Weller and J.A. Kucza, J. Appl. Phys. 35 (1964) 1945. SI. Warshaw and R.E. Jackson, Rev. Sci. Instr. 36 (1965) 1774. Gmelin Handbuch der Anorganischen Chemie, No. 39, C3 (1976) ~ 55, 161, 171. PH. Klein and W.J. Croft, J. AppI. Phys. 38 (1967) 1603.
601
CRYSTAL GROWTH AND TEMPERATURE VARIATION OF THE LATTICE PARAMETERS IN LaF3, CeF3, PrF3 AND NdF3 Wies~awaKORCZAK and Pawel MIKOLAJCZAK Experimental Physics Department, Institute of Physics, M. Curie - Sklodowska University, Lublin, Poland
Received 10 May 1982; manuscript received in final form 14 October 1982
The growth of REF3 (RE = La, Ce, Pr, Nd) single crystals by the Bridgman—Stockbarger method is described. The temperature dependence of the lattice parameters a and c and the thermal expansion coefficients a of these materials in the range of 87—291 K are reported.
I. Introduction In order to study electron paramagnetic resonance (EPR), high quality single crystals of LaF3, 3~have been CeF3, PrF3 and NdF3 doped with Gd grown in a dynamic helium atmosphere in a modified Bridgman—Stockbarger type furnace. Single crystals of REF 3 (RE La, Ce, Pr, Nd) have received considerable attention over the past few decades. The rare earth fluorides are successful hostinmaterials. There has been considerablelaser interest the EPR and optical spectra of rare earth ions in rare earth fluoride single crystals. By doping a series of the rare earth fluorides with Gd3~ions, the surroundings of the ionic impurity may be varied while preserving the local point symmetry of the substituted rare earth host ions. This family of crystals has therefore been recognized as useful for investigating the crystal field model. =
The importance of the thermal expansion in laser, optical and EPR experiments has emphasized the need for additional thermal data concerning the rare earth trifluorides. In this paper we report the successful application of the simple Bridgman—Stockbarger technique to the single crystal growth of the rare earth trifluorides. The temperature dependence of the lattice parameters and thermal expansion coefficient in the range of 87—291 K for these materials is also reported.
Single crystals of REF3 have been obtained by two growth methods: the Bridgman—Stockbarger [1—3]and the Czochralski [4,5] method. In those methods anhydrous fluoride (HF) was used to convert the hydrogen oxyfluorides or hydroxyfluorides to the fluoride. The method employed in our experiments is simpler. It has the advantage of not using an HF atmosphere. In our experiments the crystals were grown in a dynamic helium atmosphere. Optically 3~ clear singlegrown crystals of REF3 dopedusing withthe Gd have been in our laboratory apparatus described below.
2. Experimental procedure 2.1. Crystal growth
Anhydrous REF 3 materials were obtained from Alfa-Ventron (USA). All REF3 materials were of 99.9% purity. Generally all starting materials were prepurified (the moisture content can cause hydrolysis when heated) by carefully heating to elevated temperatures, about 5 h at 90°Cand I h at 500—550°C,in a helium atmosphere. The crystal growing furnace is shown in fig. 1. A 20 mm diameter quartz tube about 35 cm long was clamped between two stainless-steel end plates with rubber rings. Helium gas (99.995% purity)
0022-0248/83/0000—0000/$0300 © 1983 North-Holland
602
W. Korczak, P. Mikolajczak
/
Growth and temperature variation of lattice parameters
Often the liquid—solid interface of the growing crystal is concave towards the solid. The higher the
2
temperature gradient, the more planar is the liquid—solid interface, and usually better crystals can be produced. In our experiments we used a
15 14
150°C/cm temperature gradient in the furnace, and a growth rate of 0.5 mm/h which was found to be optimum. For crystal growth, the polycrystalline starting material (REF3 + 0.01% GdF3) was loaded into the
11 1
10kw 460 kHz
0
a
crucible (see fig. 1). After flushing the system with He for After 2 h the was slowly raised to 90°C. 2 htemperature the temperature was raised to
10
/
550°Cand after another 2 h the temperature raised to 50°Cabove the melting point. The crucible was held at this temperature for 3 h and then lowered at a rate of 0.5 mm/h. Single crystals were prepared in a two-day growth cycle. Using the above technique transparent single 3~(5 mm in diamcrystals dopedhave withbeen Gd grown. All of the eter and of20REF3 mm long) crystals discussed are quite easy to grow by this
9
6
He 2
5 VrO.5 .~.4mm/h
Fig. I. Crystal growing furnace: (I) radio-frequency generator (460 kHz, 10 kW); (2) temperature controller; (3) flowmeter; (4) variable speed motor and puller; (5) helium cylinder; (6) stainless steel bottom disk; (7) rubber 0 ring; (8) quartz tube; (9) stainless steel pull rod; (10) radio-frequency coil; (11) graphite crucible; (12) graphite lid; (13) graphite susceptor; (14) control thermocouple (Pt/Pt—l0%Rh); (IS) air cooled
method. The following important points should be stressed for growing good rare earth trifluoride crystals: (1) Fluorides must be oxide and water free. Small amount of RE203 and/or REOF make REFS~ crystals cloudy and opaque in appearance. This problem arises from impure starting materials: REF3
+
H20
2 REOF
+
—s
H2O
REOF -s
+
2 HF,
RE203 +2 HF.
stainless steel end plate.
The reactions proceed rapidly above about 600°C flowed through stainless-steel tubing at 1 1/mm and the radio-frequency power, at 460 kHz, was coupled to a graphite susceptor. The temperature was sensed by a Pt/Pt—l0%Rh thermocouple in the susceptor and controlled so that the temperature variation at the control point was ±1°C. Graphite was the best crucible material; the corrosive nature of the melt did not affect it. The fluorides do not wet graphite, making removal of the product quite easy. Crucibles were made from graphite manufactured by Alfa-Ventron. One of the most important factors in growing crystals from the melt is the temperature gradient.
[41.
(2) High temperature gradient and slow growth rates must be used if large crystals with low dislocation densities are to be produced. 2.2. Lattice parameters and thermal expansion of LaFq, CeF?, PrF3 and NdF~
X-ray studies of REF3 at room temperature have been carried out by a number of authors [6,7]. The values for the lattice parameters determined in these investigations were generally in good agreement. The temperature variation of the unit cell parameters has been previously reported
W. Korczak, P. Mikolajczak
/
603
Growth and temperature variation of lattice parameters
only by Klein and Croft [7] solely for LaF3. These data agree reasonably well with the present results. No temperature variation of the unit cell parameter data were found for CeF3, PrF3 and NdF3. The thermal expansion coefficient versus temperature relation can be used to calculate the Gruneisen parameter y as a function of temperature. This in turn can be related to the phonon dispersion curves. In laser, optical and EPR experiments we also need the thermal expansion coefficient. Only two references (refs. [6,7]) for the thermal expansion of REF3 were found; for LaF3 (at 111, 209 and 299 K) and for CeF3 (from 293 to 613 K).
Table I Observed lattice parameters of REF3s (RE = La, Ce, Pr or Nd); experimental errors are ~a = ~c = ±0.001 A Crystal
T (K)
a (A)
c (A)
LaF3
288 237 187 137 87 291 233 183 97 291 233 183 133 97 291 183 133 97
7.186 7.181 7.176 7.174 7.173 7.131 7.127 7.123 7.120 7.078 7.072 7.068 7.065 7.064 7.032 7.022 7.019 7.018
7.352 7.349 7.345 7.343 7.341 7.288 7.282 7.277 7.273 7.240 7.234 7.231 7.228 7.226 7.200 7.191 7.188 7.187
CeF,
PrF3
2.2.1. Lattice parameter measurements
The single crystals of REF3 were pulverized and used in determining the lattice parameters. The unit cell dimensions for REF3 were derived from powder diffractometer patterns using Cr K,,, (A 2.2909 A) radiation with a V filter. Si was used as an internal standard. Low temperature diffractometry data were taken for REF3 from 87 to 291 K. The temperatures were measured to within ±1 K by a constantan—copper thermocouple. In order to determine the lattice parameters a and c the extrapolation function f(9) was used: 2O cos29 \ cos sine + ~ (1)
NdF,
=
2.2.2. Thermal expansion of REF3s
The linear thermal expansion coefficient a of a solid is usually measured in terms of the change in length 1 with respect to the length 10 at some fixed temperature T0. To a very good approximation a is given by a (l//~) dl/dT. (4) Many authors in the literature give temperature=
The experimental errors for a and c were L~a L~c ±0.001 A. The lattice parameters of all the fluorides studied are listed in table 1. The room temperature lattice parameters (see table 1) are in generally excellent agreement when compared with those reported in ref. [6], within experimental error. The unit cell parameters for LaF 3, CeF3, PrF3 and NdF3 are plotted and displayed in fig. 2. In our work, the unit cell parameters between room temperature and liquid nitrogen temperature were fitted using the least-squares method to the polynomials: 2, (2) =
=
a(T)
=
c(T)
=
a0 + a1T+ a2T 2 2 c0 + c1T+ c T
(3)
The computed parameters of our polynomials for LaF 3, CeF3, PrF, and NdF3 are listed in table 2.
averaged values of the thermal expansion coefficient: ~
=
(l/l~— 1 )/( T — 1~).
(5)
In general there is a difference between the macroscopic length change with ~ 1) measured mechanically andtemperature the lattice parameter —
change (a/a0 1) measured by X-rays. In this paper all values of the coefficient are defined by eq. (4). In cubic crystals a is scalar. In REF3 crystals which symmetry, the principal values of ahave are hexagonal those parallel and perpendicular to the c axis, i.e. a~ tively. The directionally averaged1and lineara1expansion respeccoefficient d is given by —
,
=
~(a~1+ 2aj.
(6)
W. I(orczak, 1-’. Mikotajczak / Growth and temperature variation oJ lattice parameters
604
7.4C
Table 3 • La F
3
o Pr F3
xCeF3
S NdF3
Linear thermal expansion of REF, along a and c axes Crystal
T(K)
a1
(x •~___—•-—~• 288
17.0
10.7
14.9
237 187
13.0 9.1
9.1 7.5
11.7 8.6
137
5.2
6.1
5.5
87 291 233 183
1.4 12.9 10.0 7.6
4.5 16.5 13.1 10.1
2.4 14.1 12.2 8.4
PrF,
291 233 183 133 97
16.4 12.8 9.6 6.5 4.2
14.0 11.4 9.3 7.1 5.5
15.6 12.3 9.5 6.7 4.6
NdF,
291
17.4
14.7
16.5
183
9.5
8.8
9.3
133
5.9
6.1
6.0
97
3.2
4.1
3.5
7 2 0
~
-
a
7.10
106
K’)
CeF,
_______
(x
106
K’)
-
c
(x
K’) LaF,
7.30
a; 106
The anisotropy A in a is given by
a
(7)
A=a1/a11—l.
In our experiment the thermal expansion coefficient a1 was computed from (2) and (4): a1
and a11 was computed from (3) and (4):
-
7.00~
2111
a11
3~J
T EK] Fig. 2. The temperature dependence of the lattice parameters a and c in REF,.
=
0+c1T+c2T a~
7)
a 1 (><10’)
LaF, CeF, PrF, NdF 3
7.174 7.119 7.063
—3.884 — 1.002 — 1.348
a,(X10 2.792 1.748 2.228
7.018
—2.685
2.559
(9)
(1/c300) (c1 + 2c2T),
where a300 and c300 are the computed values of the lattice parameters at 300 K. The a~1and a1 values are given in table 3. At room temperature, A has
Table 2 Values of parameters c(T)=c 2 if (from temperature 87 to 291 variations K) of REF1s are fitted by a function of the type a(T) Crystal
(8)
(1/a300) (a1 + 2a2T),
=
2 and =
a0 + a1T + a2T
c
7) 0
c1 (X10’)
c2(Xl0
7.339 7.271 7.224
1.391 —0.506 0.930
1.117 2.151 1.573
7.186
—0.902
1.976
W. Korczak, P. Mikolajczak
18
•-LaF 3 - Ce F3 Pr F3
14
Nd F3
/
3. Conclusions 3~-dopedLaF Gd 3, CeF3, PrF3 and NdF3 single crytals of excellent quality have been grown in graphite crucibles by the Bridgman—Stockbarger technique. In order to obtain rare earth trifluoride crystals of optical quality, the starting materials must be oxide and water free and a high temperature gradient and slow growth rates must be used. The unit cell parameters (a and c) between room temperature and liquid nitrogen temperature may be described by the cpolynomials: a(T) a0 + a~T 2 and c(T) 2.
x
•
-
~ 10
4
•
60
I I
100
=
=
+ a2T I
I
200
605
Growth and temperature variation of lattice parameters
0 + c~T+c2T
I
300
T[K] Fig. 3. The directionally averaged linear expansion coefficient 4 (eq. (6)) of REF 3 versus temperature.
Acknowledgement We are thankful to Dr. R. Frak from UMCS Central Laboratory for help in X-ray measurements. References
the approximate value of 0.59 for LaF3, —0.22 for CeF3, 0.17 for PrF3 and 0.18 for NdF3. The values of a (eq. (6)) for REF3 (table 3) are shown in fig. 3. The value of a1 for LaF3 at room temperature found in ref. [7] is 10% higher and that of a11 is 9% lower. The value of a1 for LaF3 at 300 K found in ref. [6] is 12% lower and that of a11 is exactly the same. The value of a1 for CeF3 at room temperature found in ref. [6] is 9% lower and that of a11 is 21% higher.
(I] [2] [3] [4] [5] [6] [7]
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