Elasticity Tensor for La:21; [La-Cu-O] Measurement Method: Resonant ultrasonic method
"The mechanical resonant response of a solid depends on its shape, density, elastic moduli and dissipation. We describe here instrumentation and computational methods for acquiring and analyzing the resonant ultrasound spectrum of very small (0.001 cm³ samples a function of temperature... one unique feature of resonant ultrasound spectroscopy (RUS) is that all moduli are determined simultaneously to very high accuracy. ... RUS is also sensitive to fundamental symmetry of the object under test so that certain symmetry breaking effects are uniquely observable, and because transducers require neither couplant nor a flat surface, broken fragments of a material can be quickly screened for phase transitions and other temperature-dependent responses. ... Our system uses commercial 30 MHz compressional mode LiNbO₃ discs 1.5 mm in diameter and approximately 0.1 mm thick. ...a diamond cylinder 1.5 mm in diameter and 1.0 mm long has a lowest mode of 4.47 MHz. Thus if we bond the diamond to the transducer, the assembly has a lowest mode near 4 MHz. ... We also use a Ag-coated polyimide film 25 µm thick with 1 µm of the evaporated Ag as the ground plane, and a strip of this material 1.5 mm wide as a low inductance, low mechanical Q electrical contact by inserting the strip between diamond and LiNbO₃. ... All joints are made with a nonconducting epoxy; because at these frequencies no direct electrical contact with the transducer is required, capacitive coupling is sufficient. ...we mount the transducers in a Mg machined 'tone arm' assembly... The tone arm is suspended on 1 mm wide strips of Ag-coated polyimide film, the same used in the transducer. ...we observe less than 20 ppm frequency shifts for changes in loading from 2 g to 0.5 g. ... To access temperatures from 20 K to 400 K, our measurement cell is inserted into a vacuum-insulated cylinder. ... The cold boil-off gas passes through the transfer line into the insulated cylinder and around the measurement cell. A... 50 Ω heater, constructed of 10 Ω/m cotton-insulated resistance wire... is inserted in the gas flow path at the flow cryostat/transfer tube joint and is controlled using any commercial cryogenic temperature controller. Temperature sensing is via silicon diode thermometer mounted inside the RUS cell within a few millimeters of the sample. This arrangement ...is capable of 20 mK temperature control. The weak signals produced by our transducers and low contact force require the best possible signal/noise ratio (s/n) for the receiver electronics to ensure detection of as many modes as possible. ...we use an accurately unity gain preamp at the end of a triaxial cable connecting preamp to transducer. ... The preamp is followed by a simple but quiet RF amplifier with a bandwidth of about 20 MHz... Following the preamp is a mixer/filter... After the mixer is a state-variable analog filter... The absolute value of the 320 readings is averaged with software to generate the resonance amplitude at the frequency step chosen."

Cautions: Evaluated Data
"The errors are about 1.3% for c , i = 1, 3; 0.05% for c , i = 4, 6; and 3.1% for the off-diagonal moduli for La₂CuO₄."

Material Specification for La:21; [La(Sr)-Cu-O] Process: Floating Zone
Notes: The authors cite S.W. Cheong et al., Physica C, Vol. 158, 109 (1989) and I. Tanaka et al., Nature, Vol. 337, 21 (1989), and summarize the procedures as follows. Measurements were made for "an untwinned, orthorhombic crystal of La₂CuO₄ (1.735 mm x 1.536 mm x 1.108 mm, 7.026 g/cm³) and also for a tetragonal crystal of La_1.86Sr_0.14CuO₄ (2.470 mm x 2.267 mm x 2.192 mm, 6.946 g/cm³)... The La₂CuO₄ crystal was grown... from a flux. The Sr doped crystal was produced by... a travelling solvent/floating zone system."
Formula: La_1.86Sr_0.14CuO₄
Informal Name: La:21
Chemical Family: La(Sr)-Cu-O
Chemical Class: Oxide
Structure Type: Single Crystal
Manufacturer: In House
Commercial Name: In House
Production Date:
Lot Number:
Production Form:

Elasticity Tensor for La:21; [La(Sr)-Cu-O] Measurement Method: Resonant ultrasonic method
"The mechanical resonant response of a solid depends on its shape, density, elastic moduli and dissipation. We describe here instrumentation and computational methods for acquiring and analyzing the resonant ultrasound spectrum of very small (0.001 cm³ samples a function of temperature... one unique feature of resonant ultrasound spectroscopy (RUS) is that all moduli are determined simultaneously to very high accuracy. ... RUS is also sensitive to fundamental symmetry of the object under test so that certain symmetry breaking effects are uniquely observable, and because transducers require neither couplant nor a flat surface, broken fragments of a material can be quickly screened for phase transitions and other temperature-dependent responses. ... Our system uses commercial 30 MHz compressional mode LiNbO₃ discs 1.5 mm in diameter and approximately 0.1 mm thick. ...a diamond cylinder 1.5 mm in diameter and 1.0 mm long has a lowest mode of 4.47 MHz. Thus if we bond the diamond to the transducer, the assembly has a lowest mode near 4 MHz. ... We also use a Ag-coated polyimide film 25 µm thick with 1 µm of the evaporated Ag as the ground plane, and a strip of this material 1.5 mm wide as a low inductance, low mechanical Q electrical contact by inserting the strip between diamond and LiNbO₃. ... All joints are made with a nonconducting epoxy; because at these frequencies no direct electrical contact with the transducer is required, capacitive coupling is sufficient. ...we mount the transducers in a Mg machined 'tone arm' assembly... The tone arm is suspended on 1 mm wide strips of Ag-coated polyimide film, the same used in the transducer. ...we observe less than 20 ppm frequency shifts for changes in loading from 2 g to 0.5 g. ... To access temperatures from 20 K to 400 K, our measurement cell is inserted into a vacuum-insulated cylinder. ... The cold boil-off gas passes through the transfer line into the insulated cylinder and around the measurement cell. A... 50 Ω heater, constructed of 10 Ω/m cotton-insulated resistance wire... is inserted in the gas flow path at the flow cryostat/transfer tube joint and is controlled using any commercial cryogenic temperature controller. Temperature sensing is via silicon diode thermometer mounted inside the RUS cell within a few millimeters of the sample. This arrangement ...is capable of 20 mK temperature control. The weak signals produced by our transducers and low contact force require the best possible signal/noise ratio (s/n) for the receiver electronics to ensure detection of as many modes as possible. ...we use an accurately unity gain preamp at the end of a triaxial cable connecting preamp to transducer. ... The preamp is followed by a simple but quiet RF amplifier with a bandwidth of about 20 MHz... Following the preamp is a mixer/filter... After the mixer is a state-variable analog filter... The absolute value of the 320 readings is averaged with software to generate the resonance amplitude at the frequency step chosen."

Cautions: Evaluated Data
The authors indicate that the errors are about 0.25% for c, i = 1, 3, 0.01% for c, i = 4, 6, and 1.0% for the off-diagonal moduli for La_1.86Sr<0.14>CuO₄.