Custom Taxes with posts

<?php
$taxonomyName = 'types';
$parent_terms = get_terms($taxonomyName, array('parent' => 0, 'hide_empty' => true));

foreach($parent_terms  as $parent_term ) {
  // display top level term name
  echo '<div class="archive_box"><header><h3>'. $parent_term->name . '</h3></header>';
$child_terms = get_terms($taxonomyName, array('parent' => $parent_term->term_id, 'hide_empty' => true));
  foreach($child_terms as $child_term ) {


    // display name of all childs of the parent term
    echo '<div class="tax_section"><h3 class="tax_name">'. $child_term->name . '</h3>';
	echo '<ul class="archive_content">';

	//Loop goes here
	// max 3 posts from each child term, post type 'archives'

	$childposts = new WP_Query(

	    'post_type' => 'archives',
	    'showposts' => 3,
	    'tax_query' => array(
	        array(
	            'taxonomy' => 'types',
	            'field'    => 'term_id',
	            'terms'    => $child_term->term_id
	        ),
	    ),
	);

	foreach($childposts as $cp):
	  echo '<li><a href="'.get_permalink($cp->ID).'">'.$cp->post_title.' <i class="fa fa-arrow-circle-o-right" aria-hidden="true"></i></a></li>';
	endforeach;


	//end loop
	echo'</ul><a href="'. $child_term->slug .'" class="button">More '. $child_term->name .'</a></div>';
  }
  //end archivebox
  echo '</div>';
} ?>