H. L. Alberts

The elastic constants and distance dependence of the magnetic interactions of Cr2O3

Abstract The six single crystal elastic stiffness constants of Cr 2 O 3 have been determined at 20°C by a pulse-echo-overlap technique. The results are: c 11 = 3.74, c 12 = 1.48, c 13 = 1.75, c 33 = 3.62, c 44 = 1.59 and c 14 = 0.19 all in units of 10 12 dyne/cm 2 . The magnetic anomalies in lattice parameters at 0 K were also determined. These results were used to approximately calculate the interatomic distance dependence of the magnetic interactions in Cr 2 O 3 .

Ultrasonic and neutron diffraction studies of dilute Cr-Re and Cr-Ru alloy single crystals

Measurements are reported on the temperature dependence of the elastic constants of dilute Cr-Ru and Cr-Re alloy single crystals, containing respectively 0.3 at.% Ru, 0.5 at.% Ru, 0.3 at.% Re and 0.5 at.% Re. Neutron diffraction experiments were also performed on the two Cr-Ru crystals. Well defined anomalies were observed in all the elastic constants as well as in the integrated neutron intensities at the magnetic phase transitions of the alloys. The commensurate (C) spin density wave (SDW) to paramagnetic (P) and incommensurate (I). SDW to P transitions are second-order phase transitions, while the ISDW-CSDW and CSDW-ISDW transitions are of first order. A thermodynamic model describes the temperature dependence of the magnetic contributions ( Delta B) to the bulk modulus (B) reasonably well, but fails to give the observed relationship between Delta B and the magnetization.

Magnetoelasticity of dilute Cr-Si alloy single crystals

Measurements are reported of the temperature dependence of the elastic constants and thermal expansion of dilute Cr-Si alloy single crystals containing 0.5, 1.2, 1.6 and 3.0 at.% Si. Well defined anomalies in all elastic constants, and in the thermal expansion, were observed at the Neel points (TN) and at the commensurate-incommensurate spin density wave transition temperatures (TIC) of the alloys. Elastic anomalies were also observed at the longitudinal-transverse incommensurate spin density wave transition temperature of the Cr+0.5 at.% Si crystal, but not in the thermal expansion thereof. The transition at the Neel point of the Cr+0.5 at.% Si crystal is continuous, that of the Cr+1.2 at.% Si and Cr+1.6 at.% Si crystals of first order, while the order of the transition in the Cr+3.0 at.% Si crystal could not be determined unambiguously. For the Cr+1.2 at.% Si and Cr+1.6 at.% Si crystals the discontinuous transitions at TN show hysteresis behaviour. In the 1.2 at.% Si crystal it is also accompanied by structure effects that were absent for 1.6 at.% Si. Hysteresis, accompanied by structure effects, was also observed at TIC for Cr+1.2 at.% Si. The structure effects are ascribed to the possibility of mixed incommensurate-commensurate spin density wave states in the dilute Cr-Si magnetic phase diagram. The magnetovolume and magnetic contributions to the bulk modulus have been found to fit the equation a+bT2+cT4, predicted by theory, rather well up to temperatures (T) close to the Neel points of Cr+0.5 at.% Si and Cr+1.6 at.% Si.

A magnetoelastic study of Cr-Fe alloys

Measurements are reported of the temperature variation of the sound velocity and thermal expansion of 18 polycrystalline Cr-Fe alloys in the concentration range from 0.5 to 30 at.% Fe which covers the antiferromagnetic, spin-glass, re-entrant spin-glass, and ferromagnetic phases. In the antiferromagnetic phase, well defined anomalies in both the longitudinal velocity of sound and the thermal expansion coefficient were observed at the transition temperatures. The magnetic contributions to the volume strain ( Delta omega ) and bulk modulus ( Delta B) have been found to fit the equations Delta B= Sigma n=02AnT2n and Delta omega = Sigma n=02BnT2n rather well up to temperatures close to the Neel temperature. In the spin-glass phase, anomalies in the velocity of sound were observed between 4 and 150 K. These anomalies could not be attributed solely to spin-glass transitions as antiferromagnetism may still exist in these Cr-Fe alloys. In the ferromagnetic region no anomalies in either the velocity of sound or thermal expansion were observed at the Curie temperatures.

Magnetic effects in dilute Cr-Si alloys

Measurements have been made of the thermal expansion and elastic constants of seven Cr-Si alloys in the concentration range from 0 to 3.42 at.% Si. The results point to the absence of a re-entrant feature in the vicinity of the triple point where the paramagnetic (P), commensurate (C) spin density wave and incommensurate (I) spin density wave states coexist, favouring the sequence of phase changes from P to C to I. The first-order C-P transitions are marked by discontinuities in the thermal expansion and by large ultrasonic attenuation near TN. Calculated latent heats associated with the first-order transitions compare well with direct measurements. Application of existing itinerant electron theories to the magnetoelastic data does not give the correct concentration dependence of the magnetic moment and Neel temperature.

Elastic constants and thermal expansion of dilute Cr-Ge alloys

Abstract The temperature dependence of the elastic moduli and thermal expansion coefficient of ten Cr-Ge alloys in the concentration range 0 B . Alloys which either remain in this state or in the incommensurate SDW state at all T below the Neel temperature have been found to satisfy the relation ( ∂T N ∂ϱ ) CSDW ≈(2.4 ± 0.4)( ∂T N ∂ϱ ) ISDW . The magnetic phase diagram has been determined from the magnetoelastic data. The concentration dependence of the incommensurate-commensurate and commensurate-paramagnetic boundary lines agrees well with theory.

Magnetovolume and magnetoelastic effects in dilute Cr-Ga alloys

The thermal expansion and elastic constants of a series of dilute Cr-Ga alloys are reported between 77 and 500K. In addition to magnetic anomalies at the Neel temperature, TN, well defined anomalies in both properties have been observed for the first time at the incommensurate-commensurate transition temperatures of this system which has a triple point near 0.5 at.% Ga and 280K where the paramagnetic, incommensurate (I) and commensurate (C) spin density wave (SDW) states coexist. The temperature dependence of the magnetovolume, Delta omega , of alloys showing I-C transitions is analysed to yield the ratio (m2(0))CSDW/(m2(0))ISDW=1.5+or-0.2, where (m2(0)) is the mean squared value of the effective local moment at 0K. Using this result the magnetic contribution to the bulk modulus at 0K in a Cr+1.00 at.% Ga alloy is found to be mod Delta B(0) mod CSDW=(0.20+0.05)*1011 N m-2. Also for this alloy, for example, delta ln TN/ delta omega ISDW=20+or-4, in good agreement with independent measurements. For some alloys the calculated pressure dependence of the Neel temperatures agrees fairly well with direct measurements. Above TN the magnetovolume due to antiferromagnetic spin fluctuations decays roughly exponentially with temperature.

The effect of the incommensurate-commensurate SDW transition on the magnetoelasticity of dilute Cr―Ru alloys

Measurements of the temperature dependence of the elastic moduli and the thermal expansion of two Cr-Ru alloys containing 0.3 and 0.5 at.% Ru are reported. In addition to anomalies at the transition from the incommensurate (I) to the commensurate (C) phase and from C to the paramagnetic phase in both the thermal expansion coefficient and the bulk modulus a new anomaly in the shear modulus has been observed at TIC. Existing itinerant electron theories have been applied to analyse the data. In particular (1/TN)d2TN/d gamma 2, where gamma is the shear strain and TN the Neel temperature has been found to be (13+or-3) and (11+or-3) for the 0.3 and 0.5 at.% Ru alloys respectively.

Magnetic behaviour of dilute Cr-Al alloys from sound velocity measurements

Abstract Measurements of the longitudinal ultrasonic wave velocity in a series of dilute Cr-Al alloys as a function of temperature have shed new light on the magnetic behaviour of compositions in the range 2 ≲ c ≲ 4 at% al.

Composition–temperature and pressure–temperature magnetic phase diagrams of the Cr–Ir alloy system

Abstract The concentration–temperature, ( x – T ), and pressure–temperature, ( p – T ), magnetic phase diagrams of the dilute Cr–Ir alloy system were obtained from ultrasonic wave velocity measurements on a series of Cr–Ir alloy single crystals. A similarity is found between the ( x – T ) and ( p – T ) phase diagrams by using linear transformations between p and x .