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<article xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" dtd-version="3.0" xml:lang="en" article-type="research article">
  <front>
    <journal-meta>
      <journal-id journal-id-type="publisher-id">MSCE</journal-id>
      <journal-title-group>
        <journal-title>Journal of Materials Science and Chemical Engineering</journal-title>
      </journal-title-group>
      <issn pub-type="epub">2327-6045</issn>
      <publisher>
        <publisher-name>Scientific Research Publishing</publisher-name>
      </publisher>
    </journal-meta>
    <article-meta>
      <article-id pub-id-type="doi">10.4236/msce.2019.78002</article-id>
      <article-id pub-id-type="publisher-id">MSCE-94247</article-id>
      <article-categories>
        <subj-group subj-group-type="heading">
          <subject>Articles</subject>
        </subj-group>
        <subj-group subj-group-type="Discipline-v2">
          <subject>Chemistry&amp;Materials Science</subject>
        </subj-group>
      </article-categories>
      <title-group>
        <article-title>
Experimental Study of the Phase Equilibria in the R-Al-Si Ternary Systems (R: Rare Earth Element) the Ho-Al-Si Isothermal Section at 500?C
</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author" xlink:type="simple">
          <name name-style="western">
            <surname>Anna</surname>
            <given-names>Maria Cardinale</given-names>
          </name>
          <xref ref-type="aff" rid="aff1">
            <sup>1</sup>
          </xref>
        </contrib>
        <contrib contrib-type="author" xlink:type="simple">
          <name name-style="western">
            <surname>Nadia</surname>
            <given-names>Parodi</given-names>
          </name>
          <xref ref-type="aff" rid="aff1">
            <sup>1</sup>
          </xref>
        </contrib>
      </contrib-group>
      <aff id="aff1">
        <addr-line>Dipartimento di Chimica e Chimica Industriale, Università di Genova, Genova, Italy</addr-line>
      </aff>
      <pub-date pub-type="epub">
        <day>05</day>
        <month>08</month>
        <year>2019</year>
      </pub-date>
      <volume>07</volume>
      <issue>08</issue>
      <fpage>9</fpage>
      <lpage>17</lpage>
      <history>
        <date date-type="received">
          <day>24,</day>
          <month>May</month>
          <year>2019</year>
        </date>
        <date date-type="rev-recd">
          <day>9,</day>
          <month>August</month>
          <year>2019</year>
        </date>
        <date date-type="accepted">
          <day>12,</day>
          <month>August</month>
          <year>2019</year>
        </date>
      </history>
      <permissions>
        <copyright-statement>&#169; Copyright  2014 by authors and Scientific Research Publishing Inc. </copyright-statement>
        <copyright-year>2014</copyright-year>
        <license>
          <license-p>This work is licensed under the Creative Commons Attribution International License (CC BY). http://creativecommons.org/licenses/by/4.0/</license-p>
        </license>
      </permissions>
      <abstract>
        <p>



          The effect of holmium addition to the Al-Si system has been experimentally studied, as the isothermal section at 500?C. The constitution of the alloys has been determined by means of scanning electron microscopy (SEM), electron microprobe analysis (EDXS) and X-ray powder diffraction. The knowledge of the phase relationships in the R-Al-Si ternary systems (R: rare earths element) is essential to deeply understand the technological properties of the Al-Si based alloys, that are useful in different industrial fields. In the system investigated have been identify nineteen ternary fields and twelve two phase fields. Three ternary compounds have been found in this ternary section: τ
          <sub>2</sub>-Ho
          <sub>2</sub>Al
          <sub>3</sub>Si
          <sub>2</sub> (mS14-Y
          <sub>2</sub>Al
          <sub>3</sub>Si
          <sub>2</sub>), τ
          <sub>4</sub>-Ho
          <sub>2</sub>AlSi
          <sub>2</sub> (oI10-W2CoB
          <sub>2</sub>) and τ
          <sub>5</sub>-Ho
          <sub>6</sub>Al
          <sub>3</sub>Si (tI80-Tb
          <sub>6</sub>Al
          <sub>3</sub>Si). The results obtained can be useful compared with the other known R-Al-Si systems also for predictive purposes.


        </p>
      </abstract>
      <kwd-group>
        <kwd>Al-Si Alloys</kwd>
        <kwd> Rare Earth</kwd>
        <kwd> Thermal Analysis</kwd>
      </kwd-group>
    </article-meta>
  </front>
  <body>
    <sec id="s1">
      <title>1. Introduction</title>
      <p>
        The Al-Si alloys, both in the as cast and after thermal treatment conditions, have been recognized as interesting materials for the industries (e.g. automotive, heat exchanger, etc.). The addition of a rare earth element, at a very low concentration, can modify the property of the alloys, improving some useful characters as low density and thermal expansion coefficients, good casting performance and weld ability, high wear resistance and temperature strength, good corrosion resistance [<xref ref-type="bibr" rid="scirp.94247-ref1">1</xref>] [<xref ref-type="bibr" rid="scirp.94247-ref2">2</xref>] [<xref ref-type="bibr" rid="scirp.94247-ref3">3</xref>] [<xref ref-type="bibr" rid="scirp.94247-ref4">4</xref>]. All of the above leads to an increasing interest in the study of R-Al-Si based alloys (R being a trivalent rare earth element). The knowledge of the phase equilibria and the transformations that take place during the solidification pathway of foundry aluminum based alloys are crucial, especially in planning and develop new materials. The industrially relevant R-Al-Si alloys have usually a concentration lying near the binary Al-Si eutectic composition and mischmetal (alloy of rare earth metals, whose typical composition includes approximately 50% Ce, 25% La and smaller small amounts of Nd and Pr) is often added.
      </p>
      <p>
        Moreover, owing to the definition of pseudo-lanthanide [<xref ref-type="bibr" rid="scirp.94247-ref5">5</xref>] it is possible to predict the behavior of an intermetallic phase not prepared yet, when experimental data are available for the adjacent members of this series. Taking into account the aforementioned considerations, investigations of a number of R-Al-Si systems have been carried out by our research group.
      </p>
    </sec>
    <sec id="s2">
      <title>2. Literature Data</title>
      <sec id="s2_1">
        <title>2.1. Boundary Binary Systems</title>
        <p>
          As far as the binary systems are concerned, the Al-Si phase diagram is a simple eutectic, with the eutectic reaction at 12.2 at % Si and 577˚C and with no intermetallic compounds found in this system [<xref ref-type="bibr" rid="scirp.94247-ref6">6</xref>]. Phase relationships in the Ho-Al system were assessed by [<xref ref-type="bibr" rid="scirp.94247-ref7">7</xref>]. There are five intermetallic compounds: Ho<sub>2</sub>Al (oP12-Co<sub>2</sub>Si type), Ho<sub>3</sub>Al<sub>2</sub> (tP20-Al<sub>2</sub>Zr<sub>3</sub> type), HoAl (oP16-ErAltype), HoAl<sub>2</sub> (cF24-MgCu<sub>2</sub> type) and HoAl<sub>3</sub> (hR60-Al<sub>3</sub>Ho). The Ho-Si system, was recently assessed by [<xref ref-type="bibr" rid="scirp.94247-ref8">8</xref>]; at 500˚C temperature there are six intermetallic compounds in it as well: Ho<sub>5</sub>Si<sub>3</sub> (hP16-Mn<sub>5</sub>Si<sub>3</sub> type), Ho<sub>5</sub>Si<sub>4</sub> (oP36-Sm<sub>5</sub>Ge<sub>4</sub>type), HoSi (oP8-FeB type), Ho<sub>4</sub>Si<sub>5</sub>, HoSi<sub>2−b</sub> (hP3-AlB<sub>2</sub> type, ~38 at % Ho) and HoSi<sub>2−a</sub> (oI12-GdSi<sub>2</sub> type, ~35 at % Ho). The Ho<sub>4</sub>Si<sub>5</sub> compound was investigated [<xref ref-type="bibr" rid="scirp.94247-ref9">9</xref>] by means of single crystal X-ray diffraction and its structure was assumed to be Ho<sub>3</sub>Si<sub>4</sub>oS24-Ho<sub>2</sub>Si<sub>2.67</sub> type.
        </p>
      </sec>
      <sec id="s2_2">
        <title>2.2. R-Al-Si Ternary Systems</title>
        <p>
          To our best effort literature data on R-Al-Si systems isothermal sections (in the whole range of concentrations) and liquid us projections mainly deal with the following: La-Al-Si (0 - 33 at % La) [<xref ref-type="bibr" rid="scirp.94247-ref10">10</xref>], Ce-Al-Si [<xref ref-type="bibr" rid="scirp.94247-ref11">11</xref>], Pr-Al-Si [<xref ref-type="bibr" rid="scirp.94247-ref12">12</xref>] [<xref ref-type="bibr" rid="scirp.94247-ref13">13</xref>], Nd-Al-Si [<xref ref-type="bibr" rid="scirp.94247-ref13">13</xref>], Sm-Al-Si ([<xref ref-type="bibr" rid="scirp.94247-ref13">13</xref>] and refs therein [<xref ref-type="bibr" rid="scirp.94247-ref14">14</xref>]), Eu-Al-Si [<xref ref-type="bibr" rid="scirp.94247-ref15">15</xref>], Gd-Al-Si, Al-Si-Tb and Al-Si-Dy ([<xref ref-type="bibr" rid="scirp.94247-ref13">13</xref>] and refs therein), Ho-Al-Si (0 - 33 at % Ho) [<xref ref-type="bibr" rid="scirp.94247-ref16">16</xref>], Er-Al-Si [<xref ref-type="bibr" rid="scirp.94247-ref17">17</xref>] and Y-Al-Si (0 - 33 at % Y) [<xref ref-type="bibr" rid="scirp.94247-ref18">18</xref>]. In the Ho-Al-Si ternary system, in literature [<xref ref-type="bibr" rid="scirp.94247-ref19">19</xref>], are reported the following compounds: HoAl<sub>2</sub>Si<sub>2</sub> hP5-CaAl<sub>2</sub>O<sub>2</sub> (τ<sub>1</sub>), Ho<sub>2</sub>Al<sub>3</sub>Si<sub>2</sub> mS14-Y<sub>2</sub>Al<sub>3</sub>Si<sub>2</sub> (τ<sub>2</sub>), HoAlSi oS12-YAlGe (τ<sub>3</sub>), Ho<sub>2</sub>Al<sub>1+x</sub>Si<sub>2−x</sub> oI10-W<sub>2</sub>CoB<sub>2</sub> (τ<sub>4</sub>) and Ho<sub>6</sub>Al<sub>3</sub>Si tI80-Tb<sub>6</sub>Al<sub>3</sub>Si (τ<sub>5</sub>).
        </p>
      </sec>
    </sec>
    <sec id="s3">
      <title>3. Experimental Techniques</title>
      <p>A set of eighteen Ho-Al-Si alloys have been prepared starting from pure elements (aluminum, silicon and holmium at 99.999, 99.99 and 99.9 mass % purity respectively all supplied by Newmet Koch, Waltham Abbey, England). The starting metals, prepared in little pieces, have been weighed in a proper amount and then arc melted on a water cooled copper plate under vacuum, the samples were re-weighed after melting to check for any mass losses that were always less than 0.5 mass %. The samples have been annealed (in an alumina crucibles sealed in quartz tube under vacuum) at 500˚C for 720 hours and then quenched in water.</p>
      <p>To characterize the samples after annealing the techniques used have been scanning electron microscopy (SEM), electron probe microanalysis based on energy dispersive X-ray spectroscopy (EDXS) and X-ray diffraction analysis (XRPD). As the metallographic analysis, the samples incorporated in a conductive resin support were prepared according to the standard method by SiC paper and diamond paste polishing. After preparation the samples have been analyzed applying an acceleration voltage of 20 kV for 50 s, and a cobalt standard was used for calibration. For the quantitative analysis the software packaging Inca Energy (Oxford Instruments, Analytical Ltd., Bucks, UK) was employed to process X-ray spectra.</p>
      <p>
        To determine the crystal structures, and calculate lattice parameters of the different phases, the samples were prepared crushing them into powder in an agate mortar; then XRPD analysis was performed by the vertical diffractometer X’Pert MPD (Philips, Almelo, and The Netherlands). The indexing of the obtained diffraction data was achieved by comparison with literature or calculated data (the program Powder Cell [<xref ref-type="bibr" rid="scirp.94247-ref20">20</xref>]), the lattice parameters of the phases were calculated using the program LATCON [<xref ref-type="bibr" rid="scirp.94247-ref21">21</xref>].
      </p>
    </sec>
    <sec id="s4">
      <title>4. Results and Discussion</title>
      <p>
        <xref ref-type="table" rid="table1">Table 1</xref> reports data obtained from the eighteen samples synthesized and characterized by using SEM/EDXS and X-ray powder diffraction, while <xref ref-type="fig" rid="fig1">Figure 1</xref> reports the Ho-Al-Si isothermal section at 500˚C. It was drawn basing on the experimental data in <xref ref-type="table" rid="table1">Table 1</xref> and contains the samples composition, the field described by means of dotted lines are hypothesized on the basis of the experimental data and the knowledge of the different R-Al-Si systems. In <xref ref-type="fig" rid="fig2">Figure 2</xref> are shown the micrographic appearance of some selected samples after annealing and quenching, while <xref ref-type="fig" rid="fig3">Figure 3</xref> reports the PXRD pattern of a three phase sample.
      </p>
      <sec id="s4_1">
        <title>4.1. Ternary Isothermal Section</title>
        <p>
          In the present work the system is characterized by nineteen three-phase fields and twelve two-phase fields. According with the previous study of the Ho-Al-Si system [<xref ref-type="bibr" rid="scirp.94247-ref16">16</xref>], the HoAl<sub>2</sub>Si<sub>2</sub> (τ<sub>1</sub>) compound was not found in the isothermal section at 500˚C, this is an unusual behavior when compared with all the other known R-Al-Si systems all showing the tie triangle (Al), (Si) and τ<sub>1</sub>. Furthermore, in the Er-Al-Si isothermal section at 600˚C [<xref ref-type="bibr" rid="scirp.94247-ref17">17</xref>] the ErAl<sub>2</sub>Si<sub>2</sub> phase was not
        </p>
        <table-wrap id="table1" >
          <label>
            <xref ref-type="table" rid="table1">Table 1</xref>
          </label>
          <caption>
            <title> SEM-EDX and XRPD data on the Ho-Al-Si samples annealed at 500˚C and quenched</title>
          </caption>
          <table>
            <tbody>
              <thead>
                <tr>
                  <th align="center" valign="middle"  rowspan="2"  >N.</th>
                  <th align="center" valign="middle"  rowspan="2"  >Nominal composition Ho, Al, Si/at %</th>
                  <th align="center" valign="middle"  rowspan="2"  >Phases crystal structure</th>
                  <th align="center" valign="middle"  rowspan="2"  >EDXS results Ho, Al, Si/at %</th>
                  <th align="center" valign="middle"  colspan="4"  >Lattice parameters/nm</th>
                </tr>
              </thead>
              <tr>
                <td align="center" valign="middle" >a</td>
                <td align="center" valign="middle" >b</td>
                <td align="center" valign="middle" >c</td>
                <td align="center" valign="middle" >β/˚</td>
              </tr>
              <tr>
                <td align="center" valign="middle"  rowspan="3"  >1</td>
                <td align="center" valign="middle"  rowspan="3"  >5.0, 38.0, 57.0</td>
                <td align="center" valign="middle" >
                  Si cF8-C<sub>diam</sub>
                </td>
                <td align="center" valign="middle" >0.0, 0.0, 100.0</td>
                <td align="center" valign="middle" >0.5428 (1)</td>
                <td align="center" valign="middle" ></td>
                <td align="center" valign="middle" ></td>
                <td align="center" valign="middle" ></td>
              </tr>
              <tr>
                <td align="center" valign="middle" >Al cF4-Cu</td>
                <td align="center" valign="middle" >0.0, 100.0, 0.0</td>
                <td align="center" valign="middle" >0.4045 (1)</td>
                <td align="center" valign="middle" ></td>
                <td align="center" valign="middle" ></td>
                <td align="center" valign="middle" ></td>
              </tr>
              <tr>
                <td align="center" valign="middle" >
                  τ<sub>2</sub>mS14-Y<sub>2</sub>Al<sub>3</sub>Si<sub>2</sub>
                </td>
                <td align="center" valign="middle" >29.0, 45.0, 26.0</td>
                <td align="center" valign="middle" >1.0083 (2)</td>
                <td align="center" valign="middle" >0.4013 (1)</td>
                <td align="center" valign="middle" >0.6560 (8)</td>
                <td align="center" valign="middle" >100.82</td>
              </tr>
              <tr>
                <td align="center" valign="middle"  rowspan="3"  >2</td>
                <td align="center" valign="middle"  rowspan="3"  >16.5, 75.5, 8.0</td>
                <td align="center" valign="middle" >Al cF4-Cu</td>
                <td align="center" valign="middle" >0.0, 100.0, 0.0</td>
                <td align="center" valign="middle" >0.4047 (1)</td>
                <td align="center" valign="middle" ></td>
                <td align="center" valign="middle" ></td>
                <td align="center" valign="middle" ></td>
              </tr>
              <tr>
                <td align="center" valign="middle" >
                  τ<sub>2</sub>mS14-Y<sub>2</sub>Al<sub>3</sub>Si<sub>2</sub>
                </td>
                <td align="center" valign="middle" >30.0, 45.5, 24.5</td>
                <td align="center" valign="middle" >1.0091 (9)</td>
                <td align="center" valign="middle" >0.4015 (5)</td>
                <td align="center" valign="middle" >0.6572 (9)</td>
                <td align="center" valign="middle" >100.78</td>
              </tr>
              <tr>
                <td align="center" valign="middle" >
                  HoAl<sub>3−x</sub>Si<sub>x</sub>hR60-HoAl<sub>3</sub>
                </td>
                <td align="center" valign="middle" >26.0, 67.0, 7.0</td>
                <td align="center" valign="middle" >0.6100 (1)</td>
                <td align="center" valign="middle" >0.6100 (1)</td>
                <td align="center" valign="middle" >3.4961 (9)</td>
                <td align="center" valign="middle" ></td>
              </tr>
              <tr>
                <td align="center" valign="middle"  rowspan="3"  >3</td>
                <td align="center" valign="middle"  rowspan="3"  >18.5, 14.0, 67.5</td>
                <td align="center" valign="middle" >
                  Si cF8-C<sub>diam</sub>
                </td>
                <td align="center" valign="middle" >0.0, 0.0, 100.0</td>
                <td align="center" valign="middle" >0.5426 (3)</td>
                <td align="center" valign="middle" ></td>
                <td align="center" valign="middle" ></td>
                <td align="center" valign="middle" ></td>
              </tr>
              <tr>
                <td align="center" valign="middle" >
                  τ<sub>2</sub>mS14-Y<sub>2</sub>Al<sub>3</sub>Si<sub>2</sub>
                </td>
                <td align="center" valign="middle" >29.5, 44.0, 26.5</td>
                <td align="center" valign="middle" >1.0093 (5)</td>
                <td align="center" valign="middle" >0.4012 (1)</td>
                <td align="center" valign="middle" >0.6563 (1)</td>
                <td align="center" valign="middle" >100.82</td>
              </tr>
              <tr>
                <td align="center" valign="middle" >
                  HoSi<sub>2−a</sub>oI12-GdSi<sub>2</sub>
                </td>
                <td align="center" valign="middle" >36.0, 0.0, 64.0</td>
                <td align="center" valign="middle" >0.3915 (2)</td>
                <td align="center" valign="middle" >0.4015 (1)</td>
                <td align="center" valign="middle" >1.3371 (9)</td>
                <td align="center" valign="middle" ></td>
              </tr>
              <tr>
                <td align="center" valign="middle"  rowspan="2"  >4</td>
                <td align="center" valign="middle"  rowspan="2"  >25.0, 34.0, 41.0</td>
                <td align="center" valign="middle" >
                  Si cF8-C<sub>diam</sub>
                </td>
                <td align="center" valign="middle" >0.0, 0.0, 100.0</td>
                <td align="center" valign="middle" >0.5424 (4)</td>
                <td align="center" valign="middle" ></td>
                <td align="center" valign="middle" ></td>
                <td align="center" valign="middle" ></td>
              </tr>
              <tr>
                <td align="center" valign="middle" >
                  τ<sub>2</sub>mS14-Y<sub>2</sub>Al<sub>3</sub>Si<sub>2</sub>
                </td>
                <td align="center" valign="middle" >31.0, 43.0, 26.0</td>
                <td align="center" valign="middle" >1.0090 (7)</td>
                <td align="center" valign="middle" >0.4011 (3)</td>
                <td align="center" valign="middle" >0.6561 (5)</td>
                <td align="center" valign="middle" >100.94</td>
              </tr>
              <tr>
                <td align="center" valign="middle"  rowspan="2"  >5</td>
                <td align="center" valign="middle"  rowspan="2"  >40.5, 51.0, 8.5</td>
                <td align="center" valign="middle" >
                  Ho Al<sub>(2−x)</sub>Si<sub>x</sub>cF24-MgCu<sub>2</sub>
                </td>
                <td align="center" valign="middle" >33.0, 64.0, 3.0</td>
                <td align="center" valign="middle" >0.7825 (2)</td>
                <td align="center" valign="middle" ></td>
                <td align="center" valign="middle" ></td>
                <td align="center" valign="middle" ></td>
              </tr>
              <tr>
                <td align="center" valign="middle" >
                  HoAl<sub>1−x</sub>Si<sub>x</sub>oP16-AlEr
                </td>
                <td align="center" valign="middle" >48.0, 40.0, 12.0</td>
                <td align="center" valign="middle" >0.5900 (2)</td>
                <td align="center" valign="middle" >1.1401 (9)</td>
                <td align="center" valign="middle" >0.5578 (3)</td>
                <td align="center" valign="middle" ></td>
              </tr>
              <tr>
                <td align="center" valign="middle"  rowspan="2"  >6</td>
                <td align="center" valign="middle"  rowspan="2"  >54.0, 24.0, 22.0</td>
                <td align="center" valign="middle" >
                  Ho<sub>5</sub>Si<sub>3</sub>hP16-Mn<sub>5</sub>Si<sub>3</sub>
                </td>
                <td align="center" valign="middle" >66.5, 0.0, 33.5</td>
                <td align="center" valign="middle" >0.8371 (9)</td>
                <td align="center" valign="middle" >0.8371 (9)</td>
                <td align="center" valign="middle" >0.6276 (9)</td>
                <td align="center" valign="middle" ></td>
              </tr>
              <tr>
                <td align="center" valign="middle" >
                  HoAl<sub>1−x</sub>Si<sub>x</sub>oP16-AlEr
                </td>
                <td align="center" valign="middle" >52.0, 33.0, 15.0</td>
                <td align="center" valign="middle" >0.5739 (4)</td>
                <td align="center" valign="middle" >1.1250 (5)</td>
                <td align="center" valign="middle" >0.5691 (8)</td>
                <td align="center" valign="middle" ></td>
              </tr>
              <tr>
                <td align="center" valign="middle"  rowspan="3"  >7</td>
                <td align="center" valign="middle"  rowspan="3"  >39.0, 37.0, 24.0</td>
                <td align="center" valign="middle" >
                  Ho<sub>5</sub>Si<sub>4</sub>oP36-Ge<sub>4</sub>Sm<sub>5</sub>
                </td>
                <td align="center" valign="middle" >56.0, 0.0, 44.0</td>
                <td align="center" valign="middle" >0.7335 (4)</td>
                <td align="center" valign="middle" >1.4406 (5)</td>
                <td align="center" valign="middle" >0.7614 (2)</td>
                <td align="center" valign="middle" ></td>
              </tr>
              <tr>
                <td align="center" valign="middle" >
                  HoAl<sub>2−x</sub>Si<sub>x</sub>cF24-MgCu<sub>2</sub>
                </td>
                <td align="center" valign="middle" >33.0, 64.5, 2.5</td>
                <td align="center" valign="middle" >0.7800 (3)</td>
                <td align="center" valign="middle" ></td>
                <td align="center" valign="middle" ></td>
                <td align="center" valign="middle" ></td>
              </tr>
              <tr>
                <td align="center" valign="middle" >
                  τ<sub>4</sub>oI10 W<sub>2</sub>CoB<sub>2</sub>
                </td>
                <td align="center" valign="middle" >43.0, 25.0, 32.0</td>
                <td align="center" valign="middle" >0.4005 (1)</td>
                <td align="center" valign="middle" >0.5903 (3)</td>
                <td align="center" valign="middle" >0.8528 (1)</td>
                <td align="center" valign="middle" ></td>
              </tr>
              <tr>
                <td align="center" valign="middle"  rowspan="3"  >8</td>
                <td align="center" valign="middle"  rowspan="3"  >32.0, 55.0, 13.0</td>
                <td align="center" valign="middle" >
                  τ<sub>4</sub>oI10 W<sub>2</sub>CoB<sub>2</sub>
                </td>
                <td align="center" valign="middle" >42.5, 26.0, 31.5</td>
                <td align="center" valign="middle" >0.4143 (6)</td>
                <td align="center" valign="middle" >0.5712 (4)</td>
                <td align="center" valign="middle" >0.8519 (4)</td>
                <td align="center" valign="middle" ></td>
              </tr>
              <tr>
                <td align="center" valign="middle" >
                  HoAl<sub>2−x</sub>Si<sub>x</sub>cF24-MgCu<sub>2</sub>
                </td>
                <td align="center" valign="middle" >34.0, 63.0, 3.0</td>
                <td align="center" valign="middle" >0.7796 (3)</td>
                <td align="center" valign="middle" ></td>
                <td align="center" valign="middle" ></td>
                <td align="center" valign="middle" ></td>
              </tr>
              <tr>
                <td align="center" valign="middle" >
                  HoAl<sub>3−x</sub>Si<sub>x</sub> hR60-HoAl<sub>3</sub>
                </td>
                <td align="center" valign="middle" >26.5, 68.5, 5.0</td>
                <td align="center" valign="middle" >0.6011 (6)</td>
                <td align="center" valign="middle" >0.6011 (6)</td>
                <td align="center" valign="middle" >3.5550 (5)</td>
                <td align="center" valign="middle" ></td>
              </tr>
              <tr>
                <td align="center" valign="middle"  rowspan="2"  >9</td>
                <td align="center" valign="middle"  rowspan="2"  >57.0, 3.0, 40.0</td>
                <td align="center" valign="middle" >
                  Ho<sub>5</sub>Si<sub>3</sub>hP16-Mn<sub>5</sub>Si<sub>3</sub>
                </td>
                <td align="center" valign="middle" >67.5, 0.0, 32.5</td>
                <td align="center" valign="middle" >0.8341 (2)</td>
                <td align="center" valign="middle" >0.8341 (2)</td>
                <td align="center" valign="middle" >0.6215 (5)</td>
                <td align="center" valign="middle" ></td>
              </tr>
              <tr>
                <td align="center" valign="middle" >
                  Ho<sub>5</sub>Al<sub>x</sub>Si<sub>(4−x)</sub>oP36-Ge<sub>4</sub>Sm<sub>5</sub>
                </td>
                <td align="center" valign="middle" >55.0, 4.0, 41.0</td>
                <td align="center" valign="middle" >0.7315 (6)</td>
                <td align="center" valign="middle" >1.4429 (6)</td>
                <td align="center" valign="middle" >0.7610 (2)</td>
                <td align="center" valign="middle" ></td>
              </tr>
              <tr>
                <td align="center" valign="middle"  rowspan="3"  >10</td>
                <td align="center" valign="middle"  rowspan="3"  >57.5, 12.5, 30.0</td>
                <td align="center" valign="middle" >
                  Ho<sub>5</sub>Si<sub>3</sub>hP16-Mn<sub>5</sub>Si<sub>3</sub>
                </td>
                <td align="center" valign="middle" >65.0, 0.0, 35.0</td>
                <td align="center" valign="middle" >0.8329 (3)</td>
                <td align="center" valign="middle" >0.8329 (3)</td>
                <td align="center" valign="middle" >0.6217 (5)</td>
                <td align="center" valign="middle" ></td>
              </tr>
              <tr>
                <td align="center" valign="middle" >
                  Ho<sub>5</sub>Si<sub>(4−x)</sub>Al<sub>x</sub> oP36-Ge<sub>4</sub>Sm<sub>5</sub>
                </td>
                <td align="center" valign="middle" >53.5, 6.0, 40.5</td>
                <td align="center" valign="middle" >0.7321 (5)</td>
                <td align="center" valign="middle" >1.4439 (1)</td>
                <td align="center" valign="middle" >0.7616 (9)</td>
                <td align="center" valign="middle" ></td>
              </tr>
              <tr>
                <td align="center" valign="middle" >
                  HoAl<sub>1−x</sub>Si<sub>x</sub> oP16-AlEr
                </td>
                <td align="center" valign="middle" >45.0, 41.0, 14.0</td>
                <td align="center" valign="middle" >0.5752 (4)</td>
                <td align="center" valign="middle" >1.1167 (2)</td>
                <td align="center" valign="middle" >0.5579 (6)</td>
                <td align="center" valign="middle" ></td>
              </tr>
              <tr>
                <td align="center" valign="middle"  rowspan="3"  >11</td>
                <td align="center" valign="middle"  rowspan="3"  >56.0, 36.0, 8.0</td>
                <td align="center" valign="middle" >
                  Ho<sub>5</sub>Al<sub>x</sub>Si<sub>3−x</sub>hP16-Mn<sub>5</sub>Si<sub>3</sub>
                </td>
                <td align="center" valign="middle" >65.5, 11.5, 23.0</td>
                <td align="center" valign="middle" >0.8354 (2)</td>
                <td align="center" valign="middle" >0.8354 (2)</td>
                <td align="center" valign="middle" >0.6262 (5)</td>
                <td align="center" valign="middle" ></td>
              </tr>
              <tr>
                <td align="center" valign="middle" >HoAloP16-AlEr</td>
                <td align="center" valign="middle" >50.0, 50.0, 0.0</td>
                <td align="center" valign="middle" >0.5803 (9)</td>
                <td align="center" valign="middle" >1.1288 (8)</td>
                <td align="center" valign="middle" >0.5584 (6)</td>
                <td align="center" valign="middle" ></td>
              </tr>
              <tr>
                <td align="center" valign="middle" >
                  τ<sub>5</sub>tI80-Tb<sub>6</sub>Al<sub>3</sub>Si
                </td>
                <td align="center" valign="middle" >55.0, 35.0, 10.0</td>
                <td align="center" valign="middle" >1.1392 (3)</td>
                <td align="center" valign="middle" >1.1392 (3)</td>
                <td align="center" valign="middle" >1.4981 (2)</td>
                <td align="center" valign="middle" ></td>
              </tr>
              <tr>
                <td align="center" valign="middle"  rowspan="2"  >12</td>
                <td align="center" valign="middle"  rowspan="2"  >76.0, 6.0, 18.0</td>
                <td align="center" valign="middle" >
                  Ho<sub>5</sub>Al<sub>x</sub>Si<sub>3−x</sub>hP16-Mn<sub>5</sub>Si<sub>3</sub>
                </td>
                <td align="center" valign="middle" >67.5, 8.0, 26.5</td>
                <td align="center" valign="middle" >0.8355 (3)</td>
                <td align="center" valign="middle" >0.8355 (3)</td>
                <td align="center" valign="middle" >0.6266 (5)</td>
                <td align="center" valign="middle" ></td>
              </tr>
              <tr>
                <td align="center" valign="middle" >(Ho) hP2-Mg</td>
                <td align="center" valign="middle" >100.0, 0.0, 0.0</td>
                <td align="center" valign="middle" >0.3618 (5)</td>
                <td align="center" valign="middle" >0.3618 (5)</td>
                <td align="center" valign="middle" >0.5650 (3)</td>
                <td align="center" valign="middle" ></td>
              </tr>
              <tr>
                <td align="center" valign="middle"  rowspan="2"  >13</td>
                <td align="center" valign="middle"  rowspan="2"  >75.5, 15.0, 9.5</td>
                <td align="center" valign="middle" >(Ho) hP2-Mg</td>
                <td align="center" valign="middle" >100.0, 0.0, 0.0</td>
                <td align="center" valign="middle" >0.3614 (4)</td>
                <td align="center" valign="middle" >0.3614 (4)</td>
                <td align="center" valign="middle" >0.5644 (7)</td>
                <td align="center" valign="middle" ></td>
              </tr>
              <tr>
                <td align="center" valign="middle" >
                  Ho<sub>2</sub>Al<sub>(1−x)</sub>Si<sub>x</sub>oP12-Co<sub>2</sub>Si
                </td>
                <td align="center" valign="middle" >66.5, 19.0, 14.5</td>
                <td align="center" valign="middle" >0.6537 (2)</td>
                <td align="center" valign="middle" >0.5052 (1)</td>
                <td align="center" valign="middle" >0.9330 (2)</td>
                <td align="center" valign="middle" ></td>
              </tr>
              <tr>
                <td align="center" valign="middle"  rowspan="3"  >14</td>
                <td align="center" valign="middle"  rowspan="3"  >46.5, 39.0, 14.5</td>
                <td align="center" valign="middle" >
                  HoAl<sub>1−x</sub>Si<sub>x</sub>oP16-AlEr
                </td>
                <td align="center" valign="middle" >52.5, 15.0, 32.5</td>
                <td align="center" valign="middle" >0.5801 (5)</td>
                <td align="center" valign="middle" >1.1342 (2)</td>
                <td align="center" valign="middle" >0.5641 (4)</td>
                <td align="center" valign="middle" ></td>
              </tr>
              <tr>
                <td align="center" valign="middle" >
                  Ho<sub>5</sub>Al<sub>x</sub>Si<sub>(4−x)</sub>oP36-Ge<sub>4</sub>Sm<sub>5</sub>
                </td>
                <td align="center" valign="middle" >55.0, 36.5, 8.5</td>
                <td align="center" valign="middle" >0.7336 (9)</td>
                <td align="center" valign="middle" >1.4419 (8)</td>
                <td align="center" valign="middle" >0.7597 (8)</td>
                <td align="center" valign="middle" ></td>
              </tr>
              <tr>
                <td align="center" valign="middle" >
                  HoAl<sub>(2−x)</sub>Si<sub>x</sub>cF24-MgCu<sub>2</sub>
                </td>
                <td align="center" valign="middle" >36.5, 60.5, 3.0</td>
                <td align="center" valign="middle" >0.7815 (1)</td>
                <td align="center" valign="middle" ></td>
                <td align="center" valign="middle" ></td>
                <td align="center" valign="middle" ></td>
              </tr>
              <tr>
                <td align="center" valign="middle" >15</td>
                <td align="center" valign="middle" >54.5, 8.5, 37.5</td>
                <td align="center" valign="middle" >
                  Ho<sub>5</sub>Al<sub>x</sub>Si<sub>(4−x)</sub>oP36-Ge<sub>4</sub>Sm<sub>5</sub>
                </td>
                <td align="center" valign="middle" >55.0, 4.0, 41.0</td>
                <td align="center" valign="middle" >0.7310 (9)</td>
                <td align="center" valign="middle" >1.4450 (9)</td>
                <td align="center" valign="middle" >0.7643 (7)</td>
                <td align="center" valign="middle" ></td>
              </tr>
              <tr>
                <td align="center" valign="middle"  rowspan="3"  >16</td>
                <td align="center" valign="middle"  rowspan="3"  >48.5, 8.5, 45.5</td>
                <td align="center" valign="middle" >
                  Ho<sub>5</sub>Si<sub>4</sub>oP36-Ge<sub>4</sub>Sm<sub>5</sub>
                </td>
                <td align="center" valign="middle" >55.0, 0.0, 45.0</td>
                <td align="center" valign="middle" >0.7338 (7)</td>
                <td align="center" valign="middle" >1.4403 (9)</td>
                <td align="center" valign="middle" >0.7611 (9)</td>
                <td align="center" valign="middle" ></td>
              </tr>
              <tr>
                <td align="center" valign="middle" >
                  τ<sub>4</sub>oI10-W<sub>2</sub>CoB<sub>2</sub>
                </td>
                <td align="center" valign="middle" >42.5, 19.0, 38.5</td>
                <td align="center" valign="middle" >0.4022 (4)</td>
                <td align="center" valign="middle" >0.5739 (3)</td>
                <td align="center" valign="middle" >0.8583 (6)</td>
                <td align="center" valign="middle" ></td>
              </tr>
              <tr>
                <td align="center" valign="middle" >
                  HoSi<sub>2−b</sub>hP3-AlB<sub>2</sub>
                </td>
                <td align="center" valign="middle" >38.0, 6.0, 56.0</td>
                <td align="center" valign="middle" >0.3804 (1)</td>
                <td align="center" valign="middle" >0.3804 (1)</td>
                <td align="center" valign="middle" >0.4098 (2)</td>
                <td align="center" valign="middle" ></td>
              </tr>
              <tr>
                <td align="center" valign="middle"  rowspan="3"  >17</td>
                <td align="center" valign="middle"  rowspan="3"  >37.0, 23.0, 40.0</td>
                <td align="center" valign="middle" >
                  τ<sub>4</sub>.oI10-W<sub>2</sub>CoB<sub>2</sub>
                </td>
                <td align="center" valign="middle" >41.0, 18.0, 41.0</td>
                <td align="center" valign="middle" >0.4017 (2)</td>
                <td align="center" valign="middle" >0.5740 (2)</td>
                <td align="center" valign="middle" >0.8577 (2)</td>
                <td align="center" valign="middle" ></td>
              </tr>
              <tr>
                <td align="center" valign="middle" >
                  τ<sub>2</sub>mS14-Y<sub>2</sub>Al<sub>3</sub>Si<sub>2</sub>
                </td>
                <td align="center" valign="middle" >29.0, 44.0, 27.0</td>
                <td align="center" valign="middle" >1.0112 (8)</td>
                <td align="center" valign="middle" >0.4019 (3)</td>
                <td align="center" valign="middle" >0.6564 (7)</td>
                <td align="center" valign="middle" >100.98</td>
              </tr>
              <tr>
                <td align="center" valign="middle" >
                  HoSi<sub>2−a</sub>oI12-GdSi<sub>2</sub>
                </td>
                <td align="center" valign="middle" >36.0, 0.0, 64.0</td>
                <td align="center" valign="middle" >0.3929 (4)</td>
                <td align="center" valign="middle" >0.4019 (2)</td>
                <td align="center" valign="middle" >1.3348 (8)</td>
                <td align="center" valign="middle" ></td>
              </tr>
              <tr>
                <td align="center" valign="middle"  rowspan="3"  >18</td>
                <td align="center" valign="middle"  rowspan="3"  >4.0, 60.5, 35.5</td>
                <td align="center" valign="middle" >
                  Si cF8-C<sub>diam</sub>
                </td>
                <td align="center" valign="middle" >0.0, 0.0, 100.0</td>
                <td align="center" valign="middle" >0.5427 (2)</td>
                <td align="center" valign="middle" ></td>
                <td align="center" valign="middle" ></td>
                <td align="center" valign="middle" ></td>
              </tr>
              <tr>
                <td align="center" valign="middle" >Al cF4-Cu</td>
                <td align="center" valign="middle" >0.0, 100.0, 0.0</td>
                <td align="center" valign="middle" >0.4046 (1)</td>
                <td align="center" valign="middle" ></td>
                <td align="center" valign="middle" ></td>
                <td align="center" valign="middle" ></td>
              </tr>
              <tr>
                <td align="center" valign="middle" >
                  τ<sub>2</sub>mS14-Y<sub>2</sub>Al<sub>3</sub>Si<sub>2</sub>
                </td>
                <td align="center" valign="middle" >29.5, 44.0, 26.5</td>
                <td align="center" valign="middle" >1.0083 (5)</td>
                <td align="center" valign="middle" >0.4013 (2)</td>
                <td align="center" valign="middle" >0.6560 (4)</td>
                <td align="center" valign="middle" >100.81</td>
              </tr>
            </tbody>
          </table>
        </table-wrap>
        <p>
          found and the tie triangle in the Al and Si rich part of the system shows the same vertices as the Ho-Al-Si system. The micrographs of four representative samples are reported in <xref ref-type="fig" rid="fig2">Figure 2</xref>. <xref ref-type="fig" rid="fig2">Figure 2</xref>(a)) shows the appearance of the sample n.8 that describes the triangle constituted by the two phases HoAl<sub>(</sub><sub>2−x)</sub>Si<sub>x</sub> and HoAl<sub>(3−x)</sub>Si<sub>x</sub> (respectively grey and black and both at their maximum silicon solubility), plus light Ho<sub>2</sub>Al<sub>x</sub>Si<sub>(2−x)</sub> (τ<sub>4</sub>) at its maximum aluminum solubility value. In <xref ref-type="fig" rid="fig2">Figure 2</xref>(b), the sample n.5, pertaining to the two HoAl<sub>(</sub><sub>2−x)</sub>Si<sub>x</sub> and HoAl<sub>(1−x)</sub>Si<sub>x</sub> phase field, shows dark primary HoAl<sub>(</sub><sub>2−x)</sub>Si<sub>x</sub> crystals and the binary eutectic between the primary phase and HoAl<sub>(1−x)</sub>Si<sub>x</sub> compound, the medium eutectic composition is Ho 42 at % and Al 46 at % very close to the composition of the sample as confirmed by the micrographic feature. Ongoing throughout the system to the Ho richest part, in <xref ref-type="fig" rid="fig2">Figure 2</xref>(c) the sample n.14 is a three phase sample with gray primary HoAl<sub>(1−x)</sub>Si<sub>x</sub> compound (at its maximum silicon solubility) surrounded by a small quantity of light Ho<sub>5</sub>Al<sub>x</sub>Si<sub>(4−x)</sub> of peritectic formation, plus black HoAl<sub>(2−x)</sub>Si<sub>x</sub> phase. The sample n.16, in <xref ref-type="fig" rid="fig2">Figure 2</xref>(d) belongs to the Ho<sub>2</sub>Al<sub>x</sub>Si<sub>(</sub><sub>2−x)</sub> (τ<sub>4</sub>), Ho<sub>5</sub>Si<sub>4</sub> and HoSi<sub>2−b</sub>tietriangle; the PXRD pattern of sample n.16 is reported in <xref ref-type="fig" rid="fig3">Figure 3</xref>, the main reflections of the three phases identify are highlighted.
        </p>
      </sec>
      <sec id="s4_2">
        <title>4.2. Ternary Compounds</title>
        <p>
          Five ternary intermetallic compounds, are reported in literature: τ<sub>1</sub>-HoAl<sub>2</sub>Si<sub>2</sub> (hP5-CaAl<sub>2</sub>Si<sub>2</sub>), τ<sub>2</sub>-Ho<sub>2</sub>Al<sub>3</sub>Si<sub>2</sub> (mS14-Y<sub>2</sub>Al<sub>3</sub>Si<sub>2</sub>), τ<sub>3</sub>-HoAlSi (oS12-YAlGe), τ<sub>4</sub>-Ho<sub>2</sub>AlSi<sub>2</sub> (oI10-W2CoB<sub>2</sub>) and τ<sub>5</sub>-Ho<sub>6</sub>Al<sub>3</sub>Si (tI80-Tb<sub>6</sub>Al<sub>3</sub>Si). In this work only three compounds were identified at 500˚C; the τ<sub>3</sub> structure seems not to form in the system at 500˚C and the τ<sub>1</sub> phase was not found in the system as discussed in the previous section. The τ<sub>2</sub> compound shows a homogeneity range with constant Ho content, dissolving up to 45 at % Al (stoichiometric composition is located at 42.8 at % Al). As the τ<sub>4</sub> compound has been proved the substitution with Al for Si in a range from 20.0 at % Al (stoichiometric composition) to 25 at % Al.
        </p>
      </sec>
      <sec id="s4_3">
        <title>4.3. Binary Compounds</title>
        <p>
          As expected different boundary binary compounds entry the ternary system, the homogeneity ranges minor of 2 at % are not taking into account. For each compound involved the solubility limit of the third element has been assumed as the medium value of the different experimental measurements in the different samples investigated. From the Ho-Al system, the HoAl<sub>3</sub>, HoAl<sub>2</sub> and HoAl compounds dissolve respectively 7 at %, 3 at % and 15 at % silicon. Ongoing from the Si to the Ho richest part of the binary Ho-Si phase diagram some compounds dissolve aluminium in the following percentage: HoSi<sub>2−b</sub> 4 at %, Ho<sub>5</sub>Si<sub>4</sub> 5 at % and Ho<sub>5</sub>Si<sub>3</sub> 10 at %.
        </p>
      </sec>
    </sec>
    <sec id="s5">
      <title>5. Conclusions</title>
      <p>The Ho-Al-Si-isothermal section at 500˚C has been studied in the whole composition range, as the phase relationships the main conclusions are the following:</p>
      <p>• The studied system consists of nineteen three-phase fields and twelve two-phase fields.</p>
      <p>
        • Of the five known ternary compounds only τ<sub>2</sub>-Ho<sub>2</sub>Al<sub>3</sub>Si<sub>2</sub> (mS14-Y<sub>2</sub>Al<sub>3</sub>Si<sub>2</sub>), τ<sub>4</sub>-Ho<sub>2</sub>AlSi<sub>2</sub> (oI10-W2CoB<sub>2</sub>) and τ<sub>5</sub>-Ho<sub>6</sub>Al<sub>3</sub>Si (tI80-Tb<sub>6</sub>Al<sub>3</sub>Si) have been found in the system at 500˚C, according with [<xref ref-type="bibr" rid="scirp.94247-ref16">16</xref>]. The τ<sub>2</sub> and τ<sub>4</sub> phases dissolve aluminum up to 45 at % and 25 at % respectively.
      </p>
      <p>• Different binary compounds dissolve the third element extending into the ternary system.</p>
      <p>
        • By comparing the different known ternary isothermal sections, some points can be highlighted. All the sections are characterized by the presence of intermediate phases with R content up to 60 at % rare earth. The number of phases decreases on going from the light (Pr, Nd, Sm) to the heavy rare earths (Gd, Tb, Dy, Er). Only the RAl<sub>2</sub>Si<sub>2</sub> compounds form along the whole lanthanides series as point compounds; nevertheless in the previously studied Ho-Al-Si [<xref ref-type="bibr" rid="scirp.94247-ref16">16</xref>] and Er-Al-Si [<xref ref-type="bibr" rid="scirp.94247-ref17">17</xref>] isothermal sections this compound has not been founded. From La to Dyat low R content the three-phase equilibrium: (Al)/(Si)/RAl<sub>2</sub>Si<sub>2</sub> occurs. Many R-Si and R-Al compounds extend in the ternary system forming solid solutions at a constant R-content.
      </p>
    </sec>
    <sec id="s6">
      <title>Conflicts of Interest</title>
      <p>The authors declare no conflicts of interest regarding the publication of this paper.</p>
    </sec>
    <sec id="s7">
      <title>Cite this paper</title>
      <p>Cardinale, A.M. and Parodi, N. (2019) Experimental Study of the Phase Equilibria in the R-Al-Si Ternary Systems (R: Rare Earth Element) the Ho-Al-Si Isothermal Section at 500˚C. Journal of Materials Science and Chemical Engineering, 7, 9-17. https://doi.org/10.4236/msce.2019.78002</p>
    </sec>
  </body>
  <back>
    <ref-list>
      <title>References</title>
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