Introduction

Micro-Raman spectroscopy provides facts on the structure and chemistry of numerous mineral groups (e.g. Beran and Libowitzky 2004; Smith and Dent 2005; Dubessy et al. 2012) and facilitates an exact, conspicuous determination of major minerals (e.g., silicates; Wang et al. 1999; Dubessy et al. 2012), accessory minerals (e.g., phosphates, oxides and sulfides; Kharbish 2012; White 2009; Kharbish et al. 2014), and secondary minerals (e.g., sulfates, carbonates, sulfosalts and phyllosilicate clay minerals; Wang et al. 2002a; White 2009; Kharbish and Andráš 2014; Kharbish and Jeleň 2016; Kharbish 2016, 2017). It can also identify the hydroxyl group and the bound and unbound types of water (Libowitzky 1999; Wang et al. 2001; Dubessy et al. 2012).

Spinel group minerals belong to a large group of oxides (in a closer sense and in contrast to sulfide spinels) with the general chemical formula A2+B3+ 2O4 (A = Mg, Fe2 +, etc., B = Cr, Al, Fe3 +, etc.). They crystallize in the cubic space group Fd3m, with an almost cubic close packing of oxygen anions, and with A and B cations at interstitial tetrahedral (T) and octahedral (M) sites (D’lppolito et al. 2015). In general, A2 + and B3 + cations can occupy on both T and M sites, thus resulting in a variable degree of disorder, which is expressed by the inversion parameter i (defined as the fraction of the B3 + cations at the T sites; Sickafus et al. 1999). In the spinel minerals, two ordered configurations occur at low and ambient temperatures, i.e. the normal spinel structure TAMB2X4 with i = 0 and the completely inverse spinel structure TBM(AB)X4 with i = 1 (D’lppolito et al. 2015).

Chromium bearing spinels (Cr-spinel) are the most important ore minerals of the metal chromium and are common raw materials for refractory industry. Among them, Mg-rich Cr-spinel (magnesiochromite, MgCr2O4) is very sensitive to conditions during rock formation; therefore, it stores information concerning the tectonic settings in which its host rocks crystallized. Thus Mg-rich Cr-spinel is vastly considered a significant petrogenetic indicator (e.g. Barnes 2000; Kharbish 2013). Fe2+- Fe3+-rich Cr-spinel (ferrian chromite; (Fe2+,Mg)(Cr,Fe3+)2O4; informally referred to as ferritchromite) is considered as an alteration product of Cr-spinel (e.g. Barnes 2000).

Most previous Raman investigations have focused on the Raman-active mode assignments and the spectral features of natural and synthetic spinels with different compositions (e.g. Malézieux et al. 1983; Malézieux 1985; Wang et al. 2002b; Yong et al. 2012; Lenaz and Lughi 2013; D’lppolito et al. 2015). Only a few articles dealt with the change in the Raman spectra within a solid solution series (Reddy and Frost 2005; Lenaz and Lughi 2013, 2017; Lenaz and Skogby 2013; Wang et al. 2002b; Yong et al. 2012).

Except for the Raman studies of synthetic series MgCr2O4 – MgFe2O4 by Lenaz and Lughi (2013) and natural Al-rich Cr-spinel (Lenaz and Lughi 2017), no Raman spectroscopic studies to the best of the author’s knowledge, have characterized naturally occurring Al3+- Fe3+- poor magnesiochromite and Fe2+- Fe3+- rich ferrian chromite solid solutions. Considering the importance of these solid solutions as petrographic indicators for the host rock genesis and alteration conditions, the present article aims, therefore, at a systematic analysis of the characteristic Raman spectroscopic features of the naturally occurring magnesiochromite and ferrian chromite solid solutions and to specify the chemical substitution effects on their Raman spectra.

Samples and experiments

Samples used in the present work are from different localities in the central Eastern Desert of Egypt (e.g. Gabal Al-Degheimi, Kab Amiri district and Gabal El-Rubshi). These localities belong to the Arabian–Nubian Shield (ANS) that covers huge areas of NE Africa and the Arabian Peninsula and are covered by a dismembered ophiolite of Precambrian age, where their ultramafic section is well-developed, being dominated by serpentinites (Kharbish 2010, 2013). Stratigraphically, the Neoproterozoic ANS comprises four units; volcanosedimentary successions, dismembered ophiolite complexes, gabbro–diorite-tonalite complexes and unmetamorphosed volcanic and pyroclastic sequences that are intruded by granodiorite–granite complexes (Kharbish 2010, 2013). Spinels are hosted in serpentinites and occur interstitially as isotropic irregular zoned fractured grains of gray color and red internal reflection (visual appearance of polished sections under a reflected light microscope). The core of the grain that is identified as magnesiochromite, is darker than the outer rim (identified as ferrian chromite) which is lighter gray in color due to higher reflectance.

A Cameca electron probe microanalyzer (EPMA; Cameca SX 100, 15 kV accelerating voltage, 20 nA beam current, 1 μm beam diameter) was used to determine their chemical compositions. The peak and background counting times were 10 and 5 s, respectively. The investigated minerals were analyzed using the K α line for Si, Al, Cr, Fe, Mg, Mn, Ca and Ti. Data were calibrated by natural and synthetic reference materials (adularia for Si, Al; chromite for Cr, Fe; periclase for Mg; rhodonite for Mn; wollastonite for Ca and rutile for Ti) and were corrected by the ZAF software.

The charge balance equation of Droop (1987) was used to calculate Fe3 + from EPMA data. In general, the number of Fe3 + ions per X oxygens in the mineral formula, F, is given by; F = 2 × (1 - T/S), where T is the ideal number of cations per formula unit, and S is the observed cation total per X (= 32) oxygens calculated assuming all iron to be Fe2 +.

The non-polarized micro-Raman spectra were acquired on a Horiba JobinYvon LabRAM-HR, in the spectral range from 50 to 1200 cm− 1. 632.8 nm excitation from a He-Ne laser with a polarization extinction exceeding 500: 1 was focused with a 100×/0.80 objective on the sample surface. To avoid heating influence on samples, the incident laser was attenuated to < 1 mW energy (measured behind the objective). The spectra were collected in quasi-backscatter geometry and analyzed with a 1200 lines/mm grating monochromator. The spectral resolution and wavenumber accuracy were 0.8 cm− 1 in the red range and ± 2 cm− 1, respectively. Data acquisition, instrument control, baseline correction and background subtraction were performed with LabSpec 5 software (Horiba Jobin–Yvon). Based on the signal intensity, eight acquisitions with 60–90 s per ‘spectral window’ were adopted. Accurate band centers were determined by band fitting assuming combined Gaussian–Lorentzian (Voigt) band shapes, using the PeakFit 4.12 software (Jandel Scientific).

Results and discussion

Mineral chemistry

The investigated magnesiochromites (Fig. 1) are Al-Fe3+-poor Cr-spinels having a high Cr# [= Cr/(Cr + Al + Fe3+); 0.63–0.75], a low Fe3 +# [= Fe3+/ (Fe3 ++Cr + Al); < 0.10] and Al2O3 content (9.84–18.06 wt%) (Table 1). They are chemically characterized by an intermediate Mg# [=Mg/(Mg + Fe2 +); 0.43–0.57] (Table 1). The studied magnesiochromites show the following approximate compositions: (Mg0.43−0.57,Fe2 + 0.42−0.57)(Al0.38−0.68,Cr1.26−1.50,Fe3 + 0.02−0.16)O4.

Fig. 1
figure 1

Plot of Fe3 +# against Fe2 +# (i.e. the fraction of Fe3+ in three-valent cations against the fraction of Fe2 + in two-valent cations; in apfu; data from Table 1), visualizing the chemical compositions of the spinels investigated. Sizes of symbols exceed the analytical errors

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Table 1 Representative results of EPMA chemical analyses and calculated mineral formulae for magnesiochromite and ferrian chromite
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The composition of ferrian chromite (Fig. 1) is characterized by very small amounts of Al2O3 (< 1 wt%), similar Cr2O3 (~ 20–39 wt%) and FeO contents (~ 25–30 wt%) and higher Fe2O3 contents (~ 27–48 wt%). Therefore, they are characterized by a high Fe3 +# (0.46–0.70), a high Fe2 +# [Fe2+/(Mg + Fe2+); 0.80–0.94] and thus Mg # (0.06–0.20) (Table 1). The studied ferrian chromites show the approximate compositions (Mg0.06−0.19,Fe2 + 0.78−0.94)(Al0.00−0.04,Cr0.61−1.16,Fe3 + 0.78−1.36)O4.

Raman spectroscopy

Factor group analysis and band assignment

Magnesiochromite and ferrian chromite Raman spectra are depicted in Fig. 2, a band summary is given in Table 2. In the cubic spinel structure (space group Fd3m, No. 227; O h point symmetry, Z = 8) the O anionic array is described by the Wyckoff position 32(e) [3m (C 3v ) site symmetry]. The A2 + and B+ 3 atoms occupy only 1/8 of all potential T sites [8(a) Wyckoff position, −43m (T d )] and 1/2 of all potential M sites [16(d), −3m (D 3d )]. The number of Raman- and infrared- (IR) active phonons is evaluated for a definite crystal structure via group theory in the form of classical factor group analysis (FGA) using the O h spectroscopic symmetry. The F-centered unit cell of the investigated minerals contains 56 atoms (i.e. 8 A2 +, 16 B3 +, 32 O), however, the primitive (Bravais) unit cell contains 14 atoms leading to 42° of freedom (39 vibrations corresponding to optical modes and three modes to acoustic vibrations) as predicted by FGA. In terms of irreducible representations (Γ), these 42 normal vibrational modes at the Brillouin zone center can be decomposed as:

Fig. 2
figure 2

Raman spectra of magnesiochromite and ferrian chromite solid solutions. Raman-shift values of the main bands (obtained by band fitting; goodness of fit r 2 > 0.997) are quoted

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Table 2 Spectral positions and assignment for Raman bands of magnesiochromite and ferrian chromite, in comparison with literature data
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$$\Gamma ={A_{1g}}\left( R \right)+2{A_{2u}}+{E_g}\left( R \right)+2{E_u}+{F_{1g}}+5{F_{1u}}\left( {IR} \right)+3{F_{2g}}\left( R \right)+2{F_{2u}},$$

The (R) and (IR) identify Raman- and IR-active modes, respectively, whereas the rest of the species are silent or acoustic modes. The E and F modes are doubly and triply degenerate, respectively and the three acoustic modes belong to one F 1u species. Thus, FGA predicts five and four active optical modes in Raman- (i.e. A 1g  + E g  + 3F 2g ) and IR- (viz. 4F 1u ) spectroscopy, respectively.

Band assignments for the investigated minerals are based on the sequence of band energies given in the literature (e.g. Chopelas and Hofmeister 1991; Wang et al. 2002b, 2004; Reddy and Frost 2005; Laguna-Bercero et al. 2007; Errandonea 2014; D’lppolito et al. 2015): ν 1(A 1g ) > ν 3(F 2g ) > ν 4(F 2g ) > ν 2(E g ) > F 2g (trans) [trans = translatory lattice mode]. In the present work, the internal vibration of the MBO6 octahedron is considered to be the major contributor to the main Raman bands of the investigated minerals based on the following reasons.

The covalency degrees of B3+- O bonds (41–49%) in spinels are high relative to those of A2+ - O bonds (31% and 29%) (Wang et al. 2001). The degree of covalency of a chemical bond in a crystal structure is generally applied to predict the major ionic group contributing to Raman spectral features (Chopelas and Hofmeister 1991; Wang et al. 2001). The MB – O central interatomic force constant dominates over the TA – O one for the Raman- and IR-active vibrations (Gupta et al. 1989). Moreover, Laguna-Bercero et al. (2007) mentioned that the higher-energy vibrations in spinels depend more strongly on the nature of the octahedral cation.

The high-Raman-shift bands located between 690 and 710 cm− 1 in magnesiochromite and between 670 and 700 cm− 1 in ferrian chromite (Table 2 and Fig. 2) are viewed as the v 1(A 1g ) symmetric stretching vibration of the MBO6 groups (B=Cr, Al, Fe3 +). The medium to weak intensity bands in the intermediate Raman-shift region in magnesiochromite (597–615 cm− 1, Table 2 and Fig. 2) and ferrian chromite (615–629 cm− 1, Table 2 and Fig. 2), are attributed to the v 3(F 2g ) modes in agreement with previous studies (e.g. Lenaz and Lughi 2013, 2017; D’lppolito et al. 2015). This mode has been also assigned to the MBO6 groups symmetric stretching vibration (Reddy and Frost 2005; Marinković Stanojević et al. 2007).

The assignments of the E g and v 4(F 2g ) species are quite controversial. While Wang et al. (2002b) and Zhang and Gan (2011) assigned the bands around 500 cm− 1 to E g symmetry and those around 450 cm− 1 to v 4(F 2g ) symmetry, others, did it in the opposite way (e.g. Sinha 1999; Lenaz and Lughi 2013; D’lppolito et al. 2015). Based on the commonly accepted sequence of modes (see above) and theoretical calculations by Sinha (1999) to predict the zone center phonon frequencies for spinels, the bands at 545–561 cm− 1 (magnesiochromite, Table 2 and Fig. 2) and at 472 to 504 cm− 1 (ferrian chromite, Table 2 and Fig. 2) correspond to the v 4(F 2g ) bending vibrations (Marinković Stanojević et al. 2007). The E g symmetric MB–O stretching vibrations (Reddy and Frost 2005; Marinković Stanojević et al. 2007) occur from 476 to 500 cm− 1 (magnesiochromite, Table 2 and Fig. 2) and from 438 to 463 cm− 1 (ferrian chromite, Table 2 and Fig. 2).

The lowest and weakest Raman shift F 2g (trans) band was considered as a translatory lattice mode (Marinković Stanojević et al. 2007; Errandonea 2014; D’lppolito et al. 2015). In the present study the F 2g (trans) lattice vibrations appear around 195 cm− 1 in both magnesiochromite and ferrian chromite (Table 2 and Fig. 2).

In addition to the above described modes, two weak bands and shoulders occur from 650 to 670 and from 569 to 583 cm− 1 (Table 2 and Fig. 2) in magnesiochromite and one weak band appears from 333 to 350 cm− 1 (Table 2 and Fig. 2) in ferrian chromite. Similar unexpected modes were recorded by many other authors (e.g. Wang et al. 2002a, b, 2004; Marinković Stanojević et al. 2007; D’lppolito et al. 2015), while their origin remained unclear.

Band positions and numbers

Figure 2 reveals that all Raman bands of magnesiochromite and ferrian chromite increase in Raman shift (blue shift) and additionally change in band shape and amplitude with increasing Fe3 + #. In addition, the Raman spectra of the studied minerals show more bands (7 in magnesiochromite and 6 in ferrian chromite) than predicted by FGA (Fig. 2).

Except for the A 1g mode, the blue shifts of other Raman bands (i.e. to higher Raman-shift values) with increasing Fe3 + # are inconsistent with what has been published so far (e.g. Wang et al. 2002a, 2004; Lenaz and Lughi 2013, 2017; D’lppolito et al. 2015). In fact, higher Raman shifts that are observed for all bands with increasing content of the heavier Fe3 + ions and elongated/weakened bonds (relative to Cr), are an unexpected feature. This observation is in stark contrast to the general physics of vibrational spectroscopy and to previously published literature (e.g. D’lppolito et al. 2015; Lenaz and Lughi 2013, 2017).

The band position can be calculated by Hooke’s law: v = 1/2π√f/u derived by the model of the harmonic oscillator, in which f is the force constant which characterizes bond stiffness, and u is the reduced mass (defined by u = mA. mB / mA + mB). The mass difference between Fe and Cr ions is very small and consequently they have a very close reduced mass (u Fe−O = 20.65 × 10− 27 kg; u Cr−O = 20.31 × 10− 27 kg). Therefore their reduced masses have little or no effect on the vibration spectra. Preudhomme and Tarte (1971) mentioned that in spinels, the band positions depend mainly on the bonding force between the trivalent cation and the oxygen anion, with no significant relationship with the mass of the trivalent cations. Furthermore, Shannon’s ionic radii (Shannon 1976) of B3 + are Fe > Cr > Al, therefore the B3 + - O bond distances are Fe > Cr > Al. Thus, the blue shifts of all Raman bands with increasing Fe3 + # cannot be attributed directly to the stronger bonds (i.e. higher force constant).

A possible explanation of this unexpected behavior is the inversion of the spinel structure. A temperature dependence study on cation inversion of magnesium ferrite (MgFe2O4) shows slight decrease in lattice parameter with increasing degree of inversion and is generally to be expected for 2–3 spinels, with cations of sizes similar to Mg2 + and Fe3 + (O’Neill et al. 1992). The cation inversion between the octahedral and tetrahedral sites forces the incorporated Fe3 + to occupy the tetrahedral site and thus the divalent cation occupies the octahedral sites (for more details see Sickafus et al. 1999). The inversion starts with initial substitution of iron, which is supported by theoretical calculations and experimental data. Park and Kim (1992) calculated the cation distribution of NiFexCr2−xO4 solid solution, and showed that at an iron content of 0 ≤ x ≤ 1, nearly all the Ni2 + had been displaced from the tetrahedral sites. The same conclusion was reached by Allen et al. (1988) in their characterization for numerous Ni- Cr- Fe spinels. An increase in the inversion parameter as the Fe3 + content increases results in a decrease in the lattice parameter that could be attributed to the tetrahedrally coordinated Fe3 + having a smaller ionic radius than Mg2 + (Shannon 1976). The high-pressure studies on various spinels (e.g. Wang et al. 2002a, b) indicate an increase in Raman shift of the Raman-active modes with a decrease in unit cell volume of the spinels. From this contraction, affecting also the coordination octahedra at the M sites, it should be expected that the Raman-shift values of the samples investigated will increase significantly with increasing Fe3 + #.

It is worth mentioning that the change in unit cell volume could not be checked in the present work (e.g. by X-ray powder diffraction), because micro-analyses by EPMA data and Raman spectroscopy were acquired from single grains in a solid rock sample. Therefore, the question of whether the change in Raman-active modes due to the change in unit cell volume only, or other factors (e.g. changes in the high-spin / low-spin state of Fe3 +) could be the main contributors to the large changes in Raman-band positions, is not conclusively resolved.

The excess in the band number in the Raman spectrum of spinels was considered to be caused by lowering of the local crystal structure symmetry or was related to cation disorder (Chopelas and Hofmeister 1991; Cynn et al. 1992; Wang et al. 2002b; Van Minh and Yang 2004). It is generally accepted that the presence of vacancies, interstitial cations, nonstoichiometry and defects may result in additional modes not predicted by FGA. The local distortions around the B3 + cations may cause a reduced MBO6 octahedron symmetry from D3d to C3v and a crystal structure change from O h to T d, which increases the total number of Raman- (and IR-) active modes from five to seven (Grimes and Collett 1971). No apparent crystal symmetry degradation or structural modification was noticed, except for a regular shift to higher Raman-shift values with increasing Fe3 + #. Due to the lack of structure refinements, especially for ferrian chromite, a conclusive explanation of the appearance of extra modes in the investigated minerals due to lowering in the symmetry cannot be given. However, no apparent lowering in the spinel crystal symmetry was detected due to chemical substitution (Wang et al. 2004) or before and after annealing at high temperature (Van Minh and Yang 2004).

The appearance of the modes at 650–670 and 569–583 cm− 1 (Fig. 2 and Table 2) in magnesiochromite and at 333 to 350 cm− 1 (Fig. 2 and Table 2) in ferrian chromite can be directly related to the order–disorder effect of the A2 + and B3 + atoms over the T and M sites. The first-principles calculation by Lazzeri and Thilbaudeau (2006) proposed that the additional modes in spinel are related to an order–disorder transition and not to the presence of chemical impurities or to a combination of harmonic modes.

The B3+O6 group is a regular octahedron only for an ideal O positional parameter geometry (u = 0.25). Published structural data yield u = ~ 0.262 for magnesiochromite (e.g. O’Neill and Dollase 1994; Lenaz and Princivalle 2005) and u = ~ 0.256 for ferrian chromite (O’Neill et al. 1992). Furthermore, u is negatively correlated with the degree of order (Redfern et al. 1999). A distortion to a non-cubic B3+O6 group permits additional Raman bands by lifting of degeneracies or by releasing selection rules of certain modes inactive to active. The former observation may also explain the presence of two extra modes in the magnesiochromite (u > 0.262) versus one additional mode in the ferrian chromite (u > 0.256).

The observation of DeAngelis et al. (1971) and Keramidas et al. (1975) that the completely ordered spinels (viz. normal spinels) exhibit a larger number of Raman and IR bands than the apparent disordered material (namely inverse spinels), explains the increase in band number, in general and the appearance of two additional bands in magnesiochromite (almost ordered state) in comparison with only one extra mode in the ferrian chromite (nearly disordered). It is clear also that the intensities of the extra mode in the ferrian chromite (Fig. 2) decrease with the increase of the Fe3 +# (i.e. toward the disordered direction).

Raman bands – spinel chemistry relations

The relation between the ν 1(A 1g ) Raman-band position and the chemical composition of natural and synthetic spinels was previously studied by different authors. Malézieux et al. (1983) and Wang et al. (2004) concluded that the position of the ν 1(A 1g ) mode in natural and synthetic spinels is the most useful for discriminating B3 + substitutions in the ulvöspinel-chromite and chromite-spinel solid-solutions. Moreover, the E g band position can be used to discriminate between chromates (~ 450 cm− 1) and ferrites (~ 300 cm− 1) (D’lppolito et al. 2015).

The positive correlations of the band positions in magnesiochromite and ferrian chromite with Fe3 +# are shown in Fig. 3. Except for the F 2g (trans) mode in magnesiochromites (not shown in Fig. 3) all modes show very high correlation coefficients between their positions and Fe3 +# (Fig. 3). Based on these correlations, it is obvious that not only the position of the ν 1(A 1g ) mode is useful for discriminating trivalent substitutions in spinels (according to Malézieux et al. 1983; Malézieux 1985; Wang et al. 2004), but also the other bands as well. It is probably not possible to determine whether the investigated natural spinels are chromate or ferrite spinels using the weak E g mode as proposed by D’Ippolito et al. (2015). This is due to the fact that the investigated spinels do not show a clear E g mode in the position suggested by D’Ippolito et al. (2015). However, the modes at ~ 650 and at ~ 550 cm− 1 can be considered characteristic features for identifying at least chromate spinels.

Fig. 3
figure 3

Plots of Fe3 +# against Raman-band positions of magnesiochromite and ferrian chromite, visualizing positive correlations (correlation coefficients R 2 are quoted). Dotted and dashed lines are visual guides

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Furthermore, the correlations can be employed to determine the band positions and / or the Fe3 +#. To simplify the diagrams of determining the band positions and / or the Fe3 +#, it is recommended to use the linear equations of the first-order polynomial fit obtained in Fig. 3. Therefore, for the band positions and / or the Fe3 +# the equations are as follows:

$${\nu _1}{\left( {{A_{1g}}} \right)_{magnesiochromite}}\left( {{\text{c}}{{\text{m}}^{{\text{-1}}}}} \right)=685.08+339.46*{\text{F}}{{\text{e}}^{{\text{3+}}}}\#$$
(1)
$${\nu _3}{\left( {{F_{2g}}} \right)_{magnesiochromite}}\left( {{\text{c}}{{\text{m}}^{{\text{-1}}}}} \right)=592.67+303.85*{\text{F}}{{\text{e}}^{{\text{3+}}}}\#$$
(2)
$${\nu _4}{\left( {{F_{2g}}} \right)_{magnesiochromite}}\left( {{\text{c}}{{\text{m}}^{{\text{-1}}}}} \right)=541.63+260.24*{\text{F}}{{\text{e}}^{{\text{3+}}}}\#$$
(3)
$${\nu _2}{\left( {{E_g}} \right)_{magnesiochromite}}\left( {{\text{c}}{{\text{m}}^{{\text{-1}}}}} \right)=471.06+383.21*{\text{F}}{{\text{e}}^{{\text{3+}}}}\#$$
(4)
$$Mode\,at\,{650_{magnesiochromite}}\left( {{\text{c}}{{\text{m}}^{{\text{-1}}}}} \right)=645.75+327.39*{\text{F}}{{\text{e}}^{{\text{3+}}}}\#$$
(5)
$$Mode\,at\,{569_{magnesiochromite}}\left( {{\text{c}}{{\text{m}}^{{\text{-1}}}}} \right)=565.50+218.44*{\text{F}}{{\text{e}}^{{\text{3+}}}}\#$$
(6)
$${\nu _1}{\left( {{A_{1g}}} \right)_{ferrian}}_{{\,chromite}}\left( {{\text{c}}{{\text{m}}^{{\text{-1}}}}} \right)=630.99+99.34*{\text{F}}{{\text{e}}^{{\text{3+}}}}\#$$
(7)
$${\nu _3}{\left( {{F_{2g}}} \right)_{ferrian}}_{{\,chromite}}\left( {{\text{c}}{{\text{m}}^{{\text{-1}}}}} \right)=598.15+43.14*{\text{F}}{{\text{e}}^{{\text{3+}}}}\#$$
(8)
$${\nu _4}{\left( {{F_{2g}}} \right)_{ferrian}}_{{\,chromite}}\left( {{\text{c}}{{\text{m}}^{{\text{-1}}}}} \right)=435.03+98.82*{\text{F}}{{\text{e}}^{{\text{3+}}}}\#$$
(9)
$${\nu _2}{\left( {{E_g}} \right)_{ferrian\,\;chromite}}\left( {{\text{c}}{{\text{m}}^{{\text{-1}}}}} \right)=407.06+82.45*{\text{F}}{{\text{e}}^{{\text{3+}}}}\#$$
(10)
$${F_{2g}}{\left( {trans} \right)_{ferrian}}_{{\,chromite}}\left( {{\text{c}}{{\text{m}}^{{\text{-1}}}}} \right)=144.17+84.03*{\text{F}}{{\text{e}}^{{\text{3+}}}}\#$$
(11)
$$Mode\,at\,{333_{ferrian}}{\,_{chromite}}\left( {{\text{c}}{{\text{m}}^{{\text{-1}}}}} \right)=310.92+56.74*{\text{F}}{{\text{e}}^{{\text{3+}}}}\#$$
(12)

Finally, a rather poor correlation was found between the observed band positions and Mg# indicating the A2 + substitutions in T sites of these samples (Fig. 4). This observation confirms the predominant effect of the B3 + substitutions in the M site on the Raman spectra. Lenaz and Lughi (2017) noticed also a poor relation between Mg# and the A 1g in natural Cr-spinels whereas Wang et al. (2004) observed no relation between the A 1g band position and Fe2 +/(Fe2 + + Mg) in tetrahedral sites.

Fig. 4
figure 4

Plot of Mg# against Raman-band positions of magnesiochromite and ferrian chromite

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Conclusions

Raman spectroscopic investigations on magnesiochromite and ferrian chromite solid solutions yield Raman fingerprint spectra that can be utilized to gain information about their chemistry. From the above discussion and observations, it is suggested that (1) Raman spectra of magnesiochromite and ferrian chromite are dominated by vibrations of MBO6 groups rather than by TAO4 units; (2) all modes in the magnesiochromite and ferrian chromite spectra are mainly affected by the trivalent substitutions in M sites and are useful for estimating Fe3 + #; (3) the substitutions among divalent atoms (A2 +) in the T sites affect the band positions only weakly and (4) the order–disorder effect of the A2 + and B3 + atoms over the T and M sites causes the appearance of extra modes in the investigated minerals. The obtained results are without doubt interesting for gemology, mineralogy, geology and material sciences and a starting point for further investigations.