Ultrasonic studies on sodium-doped LaMnO₃ perovskite material

Figures & data

Figure 1. XRD spectrum of the LNMO samples.

Figure 2. EDX pattern of the LNMO samples.

Figure 3. SEM pattern of the LNMO samples.

Table 1. Physical and ultrasonic parameters of the LNMO samples at 300 K

Parameters	LNMO10	LNMO15	LNMO20
Crystal size (XRD) nm	42.635	35.973	29.848
Particle size (SEM) nm	193.3	155.5	143.3
Density kgm^−3	5,213	5,329	5,467
Longitudinal velocity (UL) m s^−1	5,935	5,739	5,525
Shear velocity (US) m s^−1	2,982	2,921	2,863
Long. attenuation (αL) dBcm^−1	1.3395	1.3922	1.4706
Shear attenuation (αS) dBcm^−1	7.4977	7.8616	8.1426
Longitudinal modulus (L) GPa	183.6239	175.5166	166.8836
Shear modulus (G) GPa	46.3557	45.4683	44.8117
Bulk modulus (K) GPa	121.8318	114.9073	107.1495
Young’s modulus (E) GPa	123.4127	120.508	117.9851

Figure 4. Variation of longitudinal velocity (U_L) with temperature in the LNMO samples.

Figure 5. Variation of shear velocity (U_S) with temperature in the LNMO samples.

Figure 6. Variation of longitudinal attenuation (α_L) with temperature in the LNMO samples.

Figure 7. Variation of shear attenuation (α_S) with temperature in the LNMO samples.

Figure 8. Variation of Young’s modulus (E) with temperature in the LNMO samples.

Table 2. Anomalous region, area of anomalous region, transition width and first derivative of ultrasonic parameters of the LNMO samples

Ultrasonic parameters		LNMO10	LNMO15	LNMO20
Anomalous region	Start K	314	320	328
	Anomaly K	320	328	334
	End K	326	334	342
Area of anomalous region	UL m/s	2,466.10	2,237.805	1,518.563
	US m/s	1,415.28	1,269.819	993.360
	E GPa	114.73	111.866	87.812
Transition width	UL m s^−1	212	166	111
	US m s^−1	121.5	94.5	72
	αL dB cm^−1	0.0682	0.05715	0.04155
	αS dB cm^−1	0.79055	0.6501	0.5182
	E GPa	15.9603	11.4593	8.7216
First derivative	ΔUL/ΔT m s^−1 K^−1	202.85	117.36	65.0
	ΔUS/ΔT m s^−1 K^−1	117.9476	66.5457	41.1855
	ΔαL/ΔT dBcm^−1 K^−1	0.0664	0.0416	0.02491
	ΔαS/ΔT dBcm^−1 K^−1	0.7876	0.4673	0.2981

Figure 9. Variation of the first derivative of longitudinal velocity (U_L) with temperature in the LNMO samples.