Low Wavenumber Region Research Articles

The dislocation theory: a consistent way for including the gravity effect in (visco)elastic plane-earth models

SUMMARY A homogeneous or stratified viscoelastic half-space has often been used as a simple earth model to calculate the deformation induced by an earthquake or a regional deglaciation. Recent publications have shown that, when taking into account the coupling between the earth’s gravity and the dilatational motion, the response of the model exhibits singularities for wavenumbers below a critical value (k g). It is shown here that the boundary-value problems based on such earth models have no solution at all for this low-wavenumber region (k ≤ k g). In fact, previous authors tried unintentionally to solve an unsolvable system by analytical or numerical extrapolation from the valid wavenumber range (k > k g )t othe invalid range (k ≤ k g). Therefore, non-physical singularities appear in their numerical results. In particular, the previous elasticgravitational dislocation theory includes an incorrect treatment of these singularities, which may lead to significant errors in the deformation models. This paper analyses the mathematical and physical causes for the unsolvability and proposes a consistent way to solve the difficulty. In particular, numerical tests show that an elastic-gravitational deformation model would become even less reliable than the corresponding elastic model, if the coupling between gravity and deformation were considered in the incorrect way published previously.

Raman scattering study of La-, Nd- and Sm-substituted Bi4Ti3O12

Raman modes of bismuth-layered perovskite Bi4-xLaxTi3O12 ceramic samples were studied as a function of La content from x=0.00 to 0.75. In the low-wavenumber region (35∼150 cm-1), the rigid mode was found to be insensitive to La substitution, while the compositional change caused a frequency upshift of one of the soft modes. In the high-wavenumber region, the results indicated that a structure transition from orthorhombic to tetragonal may occur above x=0.75, since the B2g and B3g modes showed evidence of coalescence into Eg modes with increasing La content. Raman spectra of Bi3.25Nd0.75Ti3O12 and Bi3.25Sm0.75Ti3O12 are presented and compared with Bi4-xLaxTi3O12.

Raman spectroscopy of the mineral rhodonite

The mineral rhodonite an orthosilicate has been characterised by Raman spectroscopy. The Raman spectra of three rhodonites from Broken Hill, Pachapaqui and Franklin were compared and found to be similar. The spectra are characterised by an intense band at around 1000 cm −1 assigned to the ν 1 symmetric stretching mode and three bands at 989, 974 and 936 cm −1 assigned to the ν 3 antisymmetric stretching modes of the SiO 4 units. An intense band at around 667 cm −1 was assigned to the ν 4 bending mode and showed additional bands exhibiting loss of degeneracy of the SiO 4 units. The low wave number region of rhodonite is complex. A strong band at 421.9 cm −1 is attributed to the ν 2 bending mode. The spectra of the three rhodonite mineral samples are similar but subtle differences are observed. It is proposed that these differences depend upon the cationic substitution of Mn by Ca and/or Fe 2+ and Mg.

Raman scattering ofL-valine crystals

Single crystals of L-valine, C5H11O2N, have been studied by Raman spectroscopy at temperatures from 17 to 300 K over the spectral range 20–3300 cm−1. A tentative assignment of the bands is given. Careful analysis of the Raman spectra suggests that a series of changes in the low-wavenumber region may be associated with a phase transition undergone by the material, and this possibility is discussed. Copyright © 2005 John Wiley & Sons, Ltd.

Investigation of europium(III) and gadolinium(III) complexes with naphthoyltrifluoroacetone and bidentate heterocyclic amines

Lewis base adducts of the type Ln(NTA) 3·phen and the binuclear complexes [Ln(NTA) 3] 2·bpym [NTA=1-(2-naphthoyl)-3,3,3-trifluoroacetone, phen=1,10-phenanthroline, bpym=2,2′-bipyrimidine; Ln=Eu, Gd] have been prepared by replacement of the coordinated water molecules in the complexes Ln(NTA) 3·2H 2O. The compounds were characterised by elemental analysis, 1H NMR, X-ray diffraction (XRD), thermogravimetric analysis, FTIR and FT Raman spectroscopy, and photoluminescence (PL) spectroscopy. For both, new bands were observed in the Raman spectra in the low-wavenumber region (100–600 cm −1), assigned to Ln–N stretching vibrations (in agreement with ab initio calculations). The crystal structures of the Eu III complexes were determined by single crystal XRD. In both complexes the coordination polyhedra can be regarded as square antiprisms, distorted towards a bicapped trigonal prism for the mononuclear complex and towards a dodecahedron for the binuclear complex. A Eu–Eu distance of 6.856 Å was found for the latter. Powder XRD indicates that the corresponding gadolinium(III) compound has a similar structure. The room temperature PL spectra of the europium complexes in the solid state present a series of sharp lines assigned to 5D 0→ 7F 0–4 transitions. No emission from the organic part of the compounds is observed, indicating that energy transfer from the ligands to the Eu 3+ ion is quite efficient. A number of parameters were determined from the PL spectra, including estimates for the overall crystal field strengths, and 5D 0 lifetimes and quantum efficiencies. The PL spectra for ethanol solutions of the Eu complexes confirm that the NTA and N-ligands remain attached. Slight changes in the PL data upon solubilisation are attributed to an interaction of solvent molecules with the metal centres.

Raman spectroscopic study of the uranyl tricarbonate mineral liebigite

Raman spectroscopy at 298 and 77 K has been employed to study the structure of the uranyl tricarbonates liebigite {Ca 2[UO 2(CO 3) 3]11H 2O}. The spectra of the samples are sample dependent and significant differences in the Raman spectra are obtained upon cooling to 77 K. It is proposed that the mineral undergoes a phase change upon cooling. Significant changes in the Raman spectra are observed in the hydroxyl stretching region and in the low wavenumber region. Two Raman bands are observed at 3468 and 3528 cm −1 showing the non-equivalence of the water units in the structure. Obtaining spectra at 77 K enables well resolved bands at 3530, 3501, 3482, 3463, 3443, 3405 and 3364 cm −1. Two well resolved bands at 1087 and 1073 cm −1 in the 298 K spectra become bands at 1093, 1076 and 1008 cm −1 in the 77 K spectrum proving the non-equivalence of the carbonate units. This non-equivalence is reflected in the observation of multiple bands in the carbonate bending regions. The (UO 2) 2+ units are characterised by the antisymmetric stretching vibrations at 902, 885 and 873 cm −1 and by the ν 2 bending modes at 248 cm −1. Two bands near 820 cm −1 may be assigned to the ν 1 (UO 2) 2+ symmetric stretching vibrations, however, a coincidence of these vibrations with the ν 2 (CO 3) 2− out-of plane bending vibrations cannot be excluded. The use of Raman spectroscopy enables a better definition of the vibrational modes of liebigite and shows changes in the molecular structure upon reaching 77 K.

Spectroscopic characterization of chromite from the Moa-Baracoa Ophiolitic Massif, Cuba

The Cuban chromites with a spinel structure, FeCr 2O 4 have been studied using optical absorption and EPR spectroscopy. The spectral features in the electronic spectra are used to map the octahedral and tetrahedral co-ordinated cations. Bands due Cr 3+ and Fe 3+ ions could be distinguished from UV–vis spectrum. Chromite spectrum shows two spin allowed bands at 17390 and 23810 cm −1 due to Cr 3+ in octahedral field and they are assigned to 4A 2g(F) → 4T 2g(F) and 4A 2g(F) → 4T 1g(F) transitions. This is in conformity with the broad resonance of Cr 3+ observed from EPR spectrum at g = 1.903 and a weak signal at g = 3.861 confirms Fe 3+ impurity in the mineral. Bands of Fe 3+ ion in the optical spectrum at 13700, 18870 and 28570 cm −1 are attributed to 6A 1g(S) → 4T 1g(G), 6A 1g(S) → 4T 2g(G) and 6A 1g(S) → 4T 2g(P) transitions, respectively. Near-IR reflectance spectroscopy has been used effectively to show intense absorption bands caused by electronic spin allowed d -d transitions of Fe 2+ in tetrahedral symmetry, in the region 5000–4000 cm −1. The high frequency region (7500–6500 cm −1) is attributed to the overtones of hydroxyl stretching modes. Correlation between Raman spectral features and mineral chemistry are used to interpret the Raman data. The Raman spectrum of chromite shows three bands in the CrO stretching region at 730, 560 and 445 cm −1. The most intense peak at 730 cm −1 is identified as symmetric stretching vibrational mode, A 1g(ν 1) and the other two minor peaks at 560 and 445 cm −1 are assigned to F 2g(ν 4) and E g(ν 2) modes, respectively. Cation substitution in chromite results various changes both in Raman and IR spectra. In the low-wavenumber region of Raman spectrum a significant band at 250 cm −1 with a component at 218 cm −1 is attributed F 2g(ν 3) mode. The minor peaks at 195, 175, 160 cm −1 might be due to E g and F 2g symmetries. Broadening of the peak of A 1g mode and shifting of the peak to higher wavenumber observed as a result of increasing the proportion of Al 3+O 6. The presence of water in the mineral shows bands in the IR spectrum at 3550, 3425, 3295, 1630 and 1455 cm −1. The vibrational spectrum of chromite gives raise to four frequencies at 985, 770, 710 and 650 cm −1. The first two frequencies ν 1 and ν 2 are related to the lattice vibrations of octahedral groups. Due to the influence of tetrahedral bivalent cation, vibrational interactions occur between ν 3 and ν 4 and hence the low frequency bands, ν 3 and ν 4 correspond to complex vibrations involving both octahedral and tetrahedral cations simultaneously. Cr 3+ in Cuban natural chromites has highest CFSE (20,868 cm −1) when compared to other oxide minerals.

Raman spectroscopy of phosphates of the variscite mineral group

AbstractRaman spectra of phosphates of the variscite mineral group, namely strengite, variscite, metavariscite and phosphosiderite, were obtained at 298 and 77 K using a thermal stage and complemented with selected infrared data using a diamond attenuated total reflection cell. Multiple phosphate stretching bands are observed. Bands for strengite at 1006, 1012 and 1026 cm−1 at 298 K and at 997, 1006, 1014 and 1027 cm−1 at 77 K are observed. Variscite is characterized by PO stretching vibrations at 1023, 1005 and 938 cm−1 and phosphosiderite by bands at 1009 and 993 cm−1. These minerals are readily identified by their Raman spectrum both in the PO stretching region and in the low‐wavenumber region. Multiple bands attributed to the bending modes of PO4 are identified for each of the minerals. A model is proposed involving non‐hydrogen‐bonded PO4 and strongly hydrogen‐bonded PO4 units together with [Al or Fe(OH)2]+ ·(H2PO4)2−‐type species. Raman spectroscopy shows that at the molecular level multiple species of phosphate anions exist for the variscite phosphate minerals. Copyright © 2004 John Wiley & Sons, Ltd.

Raman and infrared spectroscopy of selected vanadates

Raman and infrared spectroscopy has been used to study the structure of selected vanadates including pascoite, huemulite, barnesite, hewettite, metahewettite, hummerite. Pascoite, rauvite and huemulite are examples of simple salts involving the decavanadates anion (V 10O 28) 6−. Decavanadate consists of four distinct VO 6 units which are reflected in Raman bands at the higher wavenumbers. The Raman spectra of these minerals are characterised by two intense bands at 991 and 965 cm −1. Four pascoite Raman bands are observed at 991, 965, 958 and 905 cm −1 and originate from four distinct VO 6 sites. The other minerals namely barnesite, hewettite, metahewettite and hummerite have similar layered structures to the decavanadates but are based upon (V 5O 14) 3− units. Barnesite is characterised by a single Raman band at 1010 cm −1, whilst hummerite has Raman bands at 999 and 962 cm −1. The absence of four distinct bands indicates the overlap of the vibrational modes from two of the VO 6 sites. Metarossite is characterised by a strong band at 953 cm −1. These bands are assigned to ν 1 symmetric stretching modes of (V 6O 16) 2− units and terminal VO 3 units. In the infrared spectra of these minerals, bands are observed in the 837–860 cm −1 and in the 803–833 cm −1 region. In some of the Raman spectra bands are observed for pascoite, hummerite and metahewettite in similar positions. These bands are assigned to ν 3 antisymmetric stretching of (V 10O 28) 6− units or (V 5O 14) 3− units. Because of the complexity of the spectra in the low wavenumber region assignment of bands is difficult. Bands are observed in the 404–458 cm −1 region and are assigned to the ν 2 bending modes of (V 10O 28) 6− units or (V 5O 14) 3− units. Raman bands are observed in the 530–620 cm −1 region and are assigned to the ν 4 bending modes of (V 10O 28) 6− units or (V 5O 14) 3− units. The Raman spectra of the vanadates in the low wavenumber region are complex with multiple overlapping bands which are probably due to VO subunits and MO bonds.

Tropone?Containing Conjugated Polymer, Part V

p–Phenylenevinylene type (P1), p–phenylene type (P2), and p–phenyleneethynylene type (P3) conjugated polymers containing tropone in the main chain were obtained by Heck reaction, Suzuki coupling, and Sonogashira coupling, respectively. The carbonyl stretching vibration peaks in the IR spectra were always detected at the lower wavenumber region compared with that of tropone. P1 and P2 in chloroform had the absorption peak maximum at 515 nm and 400 nm, respectively. The fluorescence from these polymer solutions was almost quenched, in contrast to previously reported P4 bearing benzotropone unit (λem = 566 nm). The acid–doping to P1 did not bring about any spectral change in the UV spectra. From the powder XRD pattern, P1 was found to have the π-stacked structure in the solid state.

Peisleyite an unusual mixed anion mineral—a vibrational spectroscopic study

The mineral peisleyite has been studied using a combination of electron microscopy and vibrational spectroscopy. Scanning electron microscope (SEM) photomicrographs reveal that the peisleyite morphology consists of an array of small needle-like crystals of around 1 μm in length with a thickness of less than 0.1 μm. Raman spectroscopy in the hydroxyl stretching region shows an intense band at 3506 cm −1 assigned to the symmetric stretching mode of the OH units. Four bands are observed at 3564, 3404, 3250 and 3135 cm −1 in the infrared spectrum. These wavenumbers enable an estimation of the hydrogen bond distances 3.052(5), 2.801(0), 2.705(6) and 2.683(6) Å. Two intense Raman bands are observed at 1023 and 989 cm −1 and are assigned to the SO 4 and PO 4 symmetric stretching modes. Other bands are observed at 1356, 1252, 1235, 1152, 1128, 1098 and 1067 cm −1. The bands at 1067 cm −1 is attributed to AlOH deformation vibrations. Bands in the low wavenumber region are assigned to the ν 4 and ν 2 out of plane bending modes of the SO 4 and PO 4 units. Raman spectroscopy is a useful tool in determining the vibrational spectroscopy of mixed hydrated multianion minerals such as peisleyite. Information on such a mineral would be difficult to obtain by other means.

Anti-symmetric waves in pre-stressed imperfectly bonded incompressible elastic layered composites

The effect of an imperfect interface on the dispersive behavior of in-plane time-harmonic symmetric waves in a pre-stressed incompressible symmetric layered composite, was analyzed recently by Leungvichcharoen and Wijeyewickrema (2003). In the present paper the corresponding case for time harmonic anti-symmetric waves is considered. The bi-material composite consists of incompressible isotropic elastic materials. The imperfect interface is simulated by a shear-spring type resistance model, which can also accommodate the extreme cases of perfectly bonded and fully slipping interfaces. The dispersion relation is obtained by formulating the incremental boundary-value problem and using the propagator matrix technique. The dispersion relations for anti-symmetric and symmetric waves differ from each other only through the elements of the propagator matrix associated with the inner layer. The behavior of the dispersion curves for anti-symmetric waves is for the most part similar to that of symmetric waves at the low and high wavenumber limits. At the low wavenumber limit, depending on the pre-stress for perfectly bonded and imperfect interface cases, a finite phase speed may exist only for the fundamental mode while other higher modes have an infinite phase speed. However, for a fully slipping interface in the low wavenumber region it may be possible for both the fundamental mode and the next lowest mode to have finite phase speeds. For the higher modes which have infinite phase speeds in the low wavenumber region an expression to determine the cut-off frequencies is obtained. At the high wavenumber limit, the phase speeds of the fundamental mode and the higher modes tend to the phase speeds of the surface wave or the interfacial wave or the limiting phase speed of the composite. The bifurcation equation obtained from the dispersion relation yields neutral curves that separate the stable and unstable regions associated with the fundamental mode or the next lowest mode. Numerical examples of dispersion curves are presented, where when the material has to be prescribed either Mooney–Rivlin material or Varga material is assumed. The effect of imperfect interfaces on anti-symmetric waves is clearly evident in the numerical results.

Raman investigation of the structural changes in anatase LixTiO2 upon electrochemical lithium insertion

AbstractMicro‐Raman spectrometry and x‐ray diffraction (XRD) experiments were performed on the anatase LixTiO2 system (0 ≤ x ≤ 0.6) produced from the electrochemical discharge of a TiO2 composite cathode in propylene carbonate LiClO4 solution at room temperature. Raman spectrum modifications indicate local structural and chemical changes as lithium enters the anatase host lattice. The existence of a tetragonal to orthorhombic phase transition is clearly demonstrated by the Raman and XRD measurements. Moreover, lithium extraction is only partially quantitative for Li uptake ≤0.5, as shown both from structural and electrochemical data in the 3–1.5 V potential range. For the first time, the Raman fingerprint of the lithium titanate (LT) Li0.5TiO2 orthorhombic phase is clearly evidenced. A theoretical analysis of the lattice dynamics suggested a complete interpretation of the experimental Raman spectra in the LixTiO2 system, which provided valuable information on the Li atom positions and coordination in LT. Taking into account the possibility of rather short LiO distances, the complex band structure in the high‐wavenumber region is assigned to the LiO vibrations. Furthermore, spectra simulation offers an explanation for the new shape of the TiO2 lattice modes observed in the low‐wavenumber region. Copyright © 2004 John Wiley & Sons, Ltd.

A theoretical investigation of the far-infrared RAIRS experiment applied to a buried metal layer substrate

In this paper we report a theoretical investigation of the reflection absorption infrared spectroscopy (RAIRS) experiment applied to non-metallic substrates incorporating a buried metal layer (BML). In particular we concentrate on the low wavenumber region (280–480 cm−1) typically studied using synchrotron based RAIRS experiments. To illustrate this study, an example system consisting of a hypothetical isotropic layer adsorbed on thin-films of tin(IV) oxide on tungsten has been used. Using a four-layer model, systematic wavenumber-dependent Greenler type calculations of ΔR/R (often taken as a measure of the sensitivity of the experiment) have been performed. The calculated spectra show the absorption band associated with the adsorbate but also reproduce an “inverse absorption” feature, which has been observed experimentally. The results show that the factors which influence the intensity of these adsorbate-induced inverse absorption bands are different from those that influence adsorbate bands and may therefore be used to discriminate between these two types of feature. A partial first order approximation of the full Greenler-type formula has then been used to rationalise the calculated dependences of the intensities of both absorption and inverse absorption bands and system parameters like layer thicknesses, incidence angles and optical characteristics of the adsorbate.

A theoretical investigation of the far-infrared RAIRS experiment applied to a buried metal layer substrate

In this paper we report a theoretical investigation of the reflection absorption infrared spectroscopy (RAIRS) experiment applied to non-metallic substrates incorporating a buried metal layer (BML). In particular we concentrate on the low wavenumber region (280–480 cm −1 ) typically studied using synchrotron based RAIRS experiments. To illustrate this study, an example system consisting of a hypothetical isotropic layer adsorbed on thin-films of tin(IV) oxide on tungsten has been used. Using a four-layer model, systematic wavenumber-dependent Greenler type calculations of Δ R / R (often taken as a measure of the sensitivity of the experiment) have been performed. The calculated spectra show the absorption band associated with the adsorbate but also reproduce an “inverse absorption” feature, which has been observed experimentally. The results show that the factors which influence the intensity of these adsorbate-induced inverse absorption bands are different from those that influence adsorbate bands and may therefore be used to discriminate between these two types of feature. A partial first order approximation of the full Greenler-type formula has then been used to rationalise the calculated dependences of the intensities of both absorption and inverse absorption bands and system parameters like layer thicknesses, incidence angles and optical characteristics of the adsorbate.

Spectroscopic behavior of copper complexes of nonsteroidal anti-inflammatory drugs.

The proposed curative properties of Cu-based nonsteroidal anti-inflammatory drugs (NSAIDs) have led to the development of numerous Cu(II) complexes of NSAIDs with enhanced anti-inflammatory activity. Crystalline complexes, Cu(II)-NSAID (ibuprofen, naproxen, tolmetin, and diclofenac), with a carboxylic function have been studied by means of infrared and Raman spectroscopy. All NSAIDs bind the metal through the carboxylate group. On the basis of the comparison between the wavenumber of the COO(-) group vibrations and Delta nu (nu(asimm)COO(-) - nu(simm)COO(-)) between Na salts and Cu(II) complexes, conclusions on the probable structure of the complexes have been drawn. The spectroscopic data support the formation of dimeric [Cu(2)L(4)(H(2)O)(2)] complexes in which the COO(-) group behaves as a bridging bidentate ligand. The low wavenumber region of the Raman spectrum provided information on Cu-O and Cu-Cu bonds in the complexes. Thermogravimetric results gave further support to the vibrational data.

Raman spectroscopy of some basic chloride containing minerals of lead and copper

Raman spectroscopy has been used to characterise several lead and mixed cationic-lead minerals including mendipite, perite, laurionite, diaboléite, boléite, pseudoboléite, chloroxiphite, and cumengéite. Raman spectroscopy enables their vibrational spectra to be compared. The low wavenumber region is characterised by the bands assigned to cation-chloride stretching and bending modes. Phosgenite is a mixed chloride–carbonate mineral and a comparison is made with the molecular structure of the aforementioned minerals. Each mineral shows different hydroxyl stretching vibrational patterns, but some similarity exists in the Raman spectra of the hydroxyl deformation modes. Raman spectroscopy lends itself to the study of these types of minerals in complex mineral systems involving secondary mineral formation.

Raman spectra of L‐histidine hydrochloride monohydrate crystal

AbstractSingle‐crystal samples of L‐histidine hydrochloride monohydrate (LHICL), C6H9N3O2·HCl·H2O, were studied by Raman spectroscopy at temperatures ranging from 295 to 40 K over the spectral range 20–3400 cm−1. A tentative assignment of the bands is given. The effect of temperature change on the vibrational spectrum is discussed. The behavior of the Raman spectra, in particular the emergence of new modes in the low‐wavenumber region, indicates that LHICL undergoes a structural phase transition between 140 and 110 K. There are further indications that, possibly, a second change of structure occurs for temperatures between 80 and 60 K. Copyright © 2004 John Wiley & Sons, Ltd.

Decaying quasi-two-dimensional turbulence in a rectangular container: laboratory experiments

Results from a new series of experiments on quasi-two-dimensional turbulence decaying in a rectangular container are presented. The flows are generated electromagnetically in a thin layer of conducting fluid when different configurations of permanent magnets are used to specify the initial characteristics of the flow. The particle image velocimetry method is used to determine the velocity and vorticity fields. These fields are further used to determine the global characteristics of the flow such as the energy, enstrophy and the net angular momentum with respect to the center of the container. The experimental results demonstrate that variations of net angular momentum occur due to the interactions of coherent vortex dipoles/jets with the walls of the container. The variation of the angular momentum of the system, which occurs due to the action of stresses at the solid boundary, can be obtained quantitatively if the initial linear impulse exerted by the magnets on the fluid is known. An analysis of external forces and torques allows one to predict that during the intermediate state of the flow evolution the pattern of the flow will be a rotating quadrupole. The energy spectra of the flow demonstrates upscale energy transfer and corresponding growth of the energy-weighted mean scale. Power law exponents are obtained for both the low and high wave number regions of the spectra. Growth of the Reynolds number of the flow was observed during the intermediate phase of the flow evolution.

Dispersion effects of extensional waves in pre-stressed imperfectly bonded incompressible elastic layered composites

The effect of an imperfect interface, on time-harmonic extensional wave propagation in a pre-stressed symmetric layered composite is considered. The bimaterial composite consists of incompressible isotropic elastic materials. The shear spring type resistance model employed to simulate the imperfect interface can accommodate the extreme cases of perfect bonding and a fully slipping interface. The dispersion relation obtained by formulating the incremental boundary-value problem and the use of the propagator matrix technique, is analyzed at the low and high wavenumber limits. For the perfectly bonded and imperfect interface cases in the low wavenumber region, only the fundamental mode has a finite phase speed, while other higher modes have an infinite phase speed when the dimensionless wavenumber approaches zero. However, for the fully slipping interface in the low wavenumber region, both the fundamental mode and the next lowest mode have finite phase speeds. In the high wavenumber region, when the dimensionless wavenumber tends to infinity, the phase speeds of the fundamental mode and the higher modes depend on the phase speeds of the surface and interfacial waves and on the limiting phase speed of the composite. An expression to determine the cut-off frequencies is obtained from the dispersion relation. Numerical examples of dispersion curves are presented, where when the material has to be prescribed either Mooney–Rivlin material or Varga material is assumed. The effect of the imperfect interface is clearly evident in the numerical results.