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The low-temperature thermal expansion of polycrystalline V3Ge
QA 5
Physica I08B (1981) 1011.1012 North-Holland Publishing Company
THE LOW-TEMPERATURE
THERMAL EXPANSION OF POLYCRYSTALLINE
T. R. Finlayson,
V3Ge
E. E. Gibbs and T. F. Smith
Department of Physics, Monash University, Clayton, Victoria 3168, Australia
The expansion coefficient for polycrystalline V3Ge has been measured in three mutually perpendicular directions through the sample using capacitance dilatometry ~. Anisotropy is found at temperatures below 40 K. This behaviour is discussed in terms of the related physical properties for V3Ge and can be explained in terms of a coupling between the elastic compliance constants and an internal stress in the sample.
INTRODUCTION
EXPERIMENTAL
The existence of anomalous physical properties in association with superconductivity in the AI5 compounds has been the stimulus for extensive studies of these materials. In single-crystal V3Si the shear modulus c' = ½(Cll - c12) decreases dramatically with decreasing temperatures, towards a temperature T , a few degrees above the superconducting transition temperature, T c (i). At Tm, which for V3Si is about 21 K, X-ray diffraction measurements provide evidence of a cubic to tetragonal transformation for some crystals (2). Thermal expansion measurements in both single-crystal and polycrystalline V3Si display an anisotropy in the linear expansion coefficient which persists to temperatures as high as 90 K (3,4). This can be interpreted as evidence for tetragonality within this material at temperatures well above that previously recognized as T m
The sample is one of a series of vanadium-based AI5 materials which were prepared in polycrystalllne form by argon-arc casting. Preliminary expansion data taken by measuring length changes for an approximately 3 cm sample cut directly from the roughly cylindrical casting have been published previously (9). Our measurements are made'in a three-terminal capacitance dilatometer identical in design to that described by White and Collins (i0).
(5).
The related compound, V3Ge, does not generally display physical properties whose temperature dependencies are as highly anomalous as those for V3Si. Whilst the shear modulus c' does soften by about 5% from room temperature to 75 K, on reduction of temperature below this value it stiffens and at 4.2 K is about 8% larger than the room temperature value (6). However c' is strongly pressure dependent, with the application of hydrostatic pressure below i00 K resulting in a softening of this shear modulus (7). To date however no static distortion of V3Ge away from cubic symmetry has been reported. Thermal expansion studies on a single-crystal of V3Ge, while producing only two points of data for temperatures below 40 K, indicate that the low-temperature expansion coefficient is negative (8). This is qualitatively consistent with the observed pressure derivatives for the elastic constants. We report here complete low-temperature thermal expansion measurements for a polycrystalline sample of V3Ge.
0378.4363/81/0000-0000/$02~50
© North-HollandPublishingCompany
DETAILS
In the present experiment, conducted several years after our initial measurements, the original sample was again re-measured and the data found to agree with that referred to above. The ingot was then spark-machined, spark-planed and lapped to form rectangular prisms. These enabled the expansion coefficient to be measured along three mutually perpendicular axes within the original specimen. Naturally one of these is the same as the original direction i.e., parallel to the hearth of the casting furnace. The other two were parallel and perpendicular to the furnace hearth respectively. RESULTS The results for temperatures below 50 K are shown in Figure i. The main source of error during these measurements on stacked prisms is capacitance stability which is temperature dependent. At 20 K for example the experimental error in is 5% which is of the order of the point size on the figure. At about 35 K the error is 15%. For all three directions the expansion coefficient becomes negative below about 38 K and exhibits a minimum value near 25 K. There is a sharp increase in e at the superconducting transition temperature (6.1 K) below which remains positive to the lowest temperature reached and decreases steadily towards zero.
1011
1012
The resulting contribution to the thermal strain is of the form I
I
5O
[
I
I
I
I
3s s = ~o
i
I
V30e (inear expansion
coeffl[ient
where s is the elastic compliance component appropriate to the stress o, and AT is an increment of temperature. Calculation of the magnitude of the internal stress required to produce the observed anisotropy, using the published elastic data (6), yields a value of 5 MPa which is well within the stress levels which can be found in cast metals
8
Ilax~s
]o
o ± axtsllhearth o J_ axis g hearfh
20
0
/.
O
W
0 0
11 -10
-20 o3(
•J•°•Oao
0
(ll)
8
ACKNOWLEDGEMENTS
o a
One of us (EEG) has been in receipt of a Monash Graduate Scholarship and the financial support of the Australian Research Grants Committee is gratefully acknowledged.
°o~
° ° ° ° °~°°
o o a ~a 6
I 10
20
AT
o
T[K]
30
50 REFERENCES
Figure 1 :
Expansion data for V3Ge
The expansion coefficients for the two directions parallel to the furnace hearth are similar whilst that for the perpendicular direction is less negative for temperatures between T c and about 35 K. This anisotropy in a cubic polycrystalline material is most surprising. The anisotropic thermal strain which would have developed in the sample on cooling it to I0 K would have been 1.5 x 10 -6. DISCUSSION A possible explanation for this anisotropy is the existence of a low-temperature structural transformation. Such strains away from cubic symmetry would be too small to be detected in a conventional diffraction experiment. It is worthwhile noting that during the discussion which followed one of our previous papers on this subject Barsch made the suggestion of a departure from cubic symmetry to explain anisotropy in the thermal expansion of some AI5 materials at low temperature (9). While the only measurement of for single-crystal V3Ge yielded a negative expansion coefficient at 30 K (8), the data are inadequate to prove or disprove that the lowtemperature expansion for that crystal was anisotropic. Thus a further investigation of the expansion coefficient for single-crystal V3Ge would be of considerable interest. Alternatively, anlsotropy in a polycrystalline, cubic sample may arise from an anisotropic internal stress field acting through the temperature dependence of the elastic compliance constants to contribute a second order effect to the thermal expansion. Such a stress field might originate from the casting and subsequent cooling of the sample or be associated with defects in the sample. Such a situation has been discussed recently with reference to the anisotropic thermal expansion observed in polycrystalline V3Si (4).
[i] Testardi, L.R., Bateman, T.B., Reed, W.A. and Chirba, V.G., Phys.Rev.Letters 15 (1965) 250-252. [2] Batterman, B.W. and Barrett, C.S., Phys.Rev. 145 (1966) 296-301. [3] Fukasi, T., Kobayashi, T., Isino, M., Toyota, N. and Muto, Y., J. de Physique C6 (1978) 406-407. [4] Gibbs, E.E., Finlayson, T.R. and Smith, T.F., Solid State Con~n. 37 (1981) 33-35. [5] Milewits, M. and Williamson, S.J., J. de Physique C6 (1978) 408-409, [6] Rosen, M., Klimker, H. and Weger, M., Phys.Rev. 194 (1969) 466-471. [7] Carcia, P.F. and Barsch, G.R., Phys. Rev. B 8 (1973) 2505-2515. [8] Testardi, L.R., Phys.Rev. B 5 (1972) 43424349. [9] Smith, T.F. and Finlayson, T.R., in HighPressure and Low-Temperature Physics, Chu, C.W. and Woollam, J.A. (eds.), (Plenum, 1978) 315-335. [i0] White, G.K. and Collins, J.G., J.Low-Temp. Phys. 7 (1972) 43-75. [ii] Angus, H.T., Cast Iron: Physical and Engineering Properties, Ch.6 (Butterworths, 1976) 392-412.
Physica I08B (1981) 1011.1012 North-Holland Publishing Company
THE LOW-TEMPERATURE
THERMAL EXPANSION OF POLYCRYSTALLINE
T. R. Finlayson,
V3Ge
E. E. Gibbs and T. F. Smith
Department of Physics, Monash University, Clayton, Victoria 3168, Australia
The expansion coefficient for polycrystalline V3Ge has been measured in three mutually perpendicular directions through the sample using capacitance dilatometry ~. Anisotropy is found at temperatures below 40 K. This behaviour is discussed in terms of the related physical properties for V3Ge and can be explained in terms of a coupling between the elastic compliance constants and an internal stress in the sample.
INTRODUCTION
EXPERIMENTAL
The existence of anomalous physical properties in association with superconductivity in the AI5 compounds has been the stimulus for extensive studies of these materials. In single-crystal V3Si the shear modulus c' = ½(Cll - c12) decreases dramatically with decreasing temperatures, towards a temperature T , a few degrees above the superconducting transition temperature, T c (i). At Tm, which for V3Si is about 21 K, X-ray diffraction measurements provide evidence of a cubic to tetragonal transformation for some crystals (2). Thermal expansion measurements in both single-crystal and polycrystalline V3Si display an anisotropy in the linear expansion coefficient which persists to temperatures as high as 90 K (3,4). This can be interpreted as evidence for tetragonality within this material at temperatures well above that previously recognized as T m
The sample is one of a series of vanadium-based AI5 materials which were prepared in polycrystalllne form by argon-arc casting. Preliminary expansion data taken by measuring length changes for an approximately 3 cm sample cut directly from the roughly cylindrical casting have been published previously (9). Our measurements are made'in a three-terminal capacitance dilatometer identical in design to that described by White and Collins (i0).
(5).
The related compound, V3Ge, does not generally display physical properties whose temperature dependencies are as highly anomalous as those for V3Si. Whilst the shear modulus c' does soften by about 5% from room temperature to 75 K, on reduction of temperature below this value it stiffens and at 4.2 K is about 8% larger than the room temperature value (6). However c' is strongly pressure dependent, with the application of hydrostatic pressure below i00 K resulting in a softening of this shear modulus (7). To date however no static distortion of V3Ge away from cubic symmetry has been reported. Thermal expansion studies on a single-crystal of V3Ge, while producing only two points of data for temperatures below 40 K, indicate that the low-temperature expansion coefficient is negative (8). This is qualitatively consistent with the observed pressure derivatives for the elastic constants. We report here complete low-temperature thermal expansion measurements for a polycrystalline sample of V3Ge.
0378.4363/81/0000-0000/$02~50
© North-HollandPublishingCompany
DETAILS
In the present experiment, conducted several years after our initial measurements, the original sample was again re-measured and the data found to agree with that referred to above. The ingot was then spark-machined, spark-planed and lapped to form rectangular prisms. These enabled the expansion coefficient to be measured along three mutually perpendicular axes within the original specimen. Naturally one of these is the same as the original direction i.e., parallel to the hearth of the casting furnace. The other two were parallel and perpendicular to the furnace hearth respectively. RESULTS The results for temperatures below 50 K are shown in Figure i. The main source of error during these measurements on stacked prisms is capacitance stability which is temperature dependent. At 20 K for example the experimental error in is 5% which is of the order of the point size on the figure. At about 35 K the error is 15%. For all three directions the expansion coefficient becomes negative below about 38 K and exhibits a minimum value near 25 K. There is a sharp increase in e at the superconducting transition temperature (6.1 K) below which remains positive to the lowest temperature reached and decreases steadily towards zero.
1011
1012
The resulting contribution to the thermal strain is of the form I
I
5O
[
I
I
I
I
3s s = ~o
i
I
V30e (inear expansion
coeffl[ient
where s is the elastic compliance component appropriate to the stress o, and AT is an increment of temperature. Calculation of the magnitude of the internal stress required to produce the observed anisotropy, using the published elastic data (6), yields a value of 5 MPa which is well within the stress levels which can be found in cast metals
8
Ilax~s
]o
o ± axtsllhearth o J_ axis g hearfh
20
0
/.
O
W
0 0
11 -10
-20 o3(
•J•°•Oao
0
(ll)
8
ACKNOWLEDGEMENTS
o a
One of us (EEG) has been in receipt of a Monash Graduate Scholarship and the financial support of the Australian Research Grants Committee is gratefully acknowledged.
°o~
° ° ° ° °~°°
o o a ~a 6
I 10
20
AT
o
T[K]
30
50 REFERENCES
Figure 1 :
Expansion data for V3Ge
The expansion coefficients for the two directions parallel to the furnace hearth are similar whilst that for the perpendicular direction is less negative for temperatures between T c and about 35 K. This anisotropy in a cubic polycrystalline material is most surprising. The anisotropic thermal strain which would have developed in the sample on cooling it to I0 K would have been 1.5 x 10 -6. DISCUSSION A possible explanation for this anisotropy is the existence of a low-temperature structural transformation. Such strains away from cubic symmetry would be too small to be detected in a conventional diffraction experiment. It is worthwhile noting that during the discussion which followed one of our previous papers on this subject Barsch made the suggestion of a departure from cubic symmetry to explain anisotropy in the thermal expansion of some AI5 materials at low temperature (9). While the only measurement of for single-crystal V3Ge yielded a negative expansion coefficient at 30 K (8), the data are inadequate to prove or disprove that the lowtemperature expansion for that crystal was anisotropic. Thus a further investigation of the expansion coefficient for single-crystal V3Ge would be of considerable interest. Alternatively, anlsotropy in a polycrystalline, cubic sample may arise from an anisotropic internal stress field acting through the temperature dependence of the elastic compliance constants to contribute a second order effect to the thermal expansion. Such a stress field might originate from the casting and subsequent cooling of the sample or be associated with defects in the sample. Such a situation has been discussed recently with reference to the anisotropic thermal expansion observed in polycrystalline V3Si (4).
[i] Testardi, L.R., Bateman, T.B., Reed, W.A. and Chirba, V.G., Phys.Rev.Letters 15 (1965) 250-252. [2] Batterman, B.W. and Barrett, C.S., Phys.Rev. 145 (1966) 296-301. [3] Fukasi, T., Kobayashi, T., Isino, M., Toyota, N. and Muto, Y., J. de Physique C6 (1978) 406-407. [4] Gibbs, E.E., Finlayson, T.R. and Smith, T.F., Solid State Con~n. 37 (1981) 33-35. [5] Milewits, M. and Williamson, S.J., J. de Physique C6 (1978) 408-409, [6] Rosen, M., Klimker, H. and Weger, M., Phys.Rev. 194 (1969) 466-471. [7] Carcia, P.F. and Barsch, G.R., Phys. Rev. B 8 (1973) 2505-2515. [8] Testardi, L.R., Phys.Rev. B 5 (1972) 43424349. [9] Smith, T.F. and Finlayson, T.R., in HighPressure and Low-Temperature Physics, Chu, C.W. and Woollam, J.A. (eds.), (Plenum, 1978) 315-335. [i0] White, G.K. and Collins, J.G., J.Low-Temp. Phys. 7 (1972) 43-75. [ii] Angus, H.T., Cast Iron: Physical and Engineering Properties, Ch.6 (Butterworths, 1976) 392-412.